CaltechAUTHORS: Combined
https://feeds.library.caltech.edu/people/Sader-J-E/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 14 Oct 2024 13:35:46 -0700Frequency Modulation Atomic Force Microscopy Reveals Individual Intermediates Associated with each Unfolded I27 Titin Domain
https://authors.library.caltech.edu/records/zbe42-rdk03
Year: 2006
DOI: 10.1529/biophysj.105.066571
PMCID: PMC1367068
<p>In this study, we apply a dynamic atomic force microscopy (AFM) technique, frequency modulation (FM) detection, to the mechanical unfolding of single titin I27 domains and make comparisons with measurements made using the AFM contact or static mode method. Static mode measurements revealed the well-known force transition occurring at 100–120 pN in the first unfolding peak, which was less clear, or more often absent, in the subsequent unfolding peaks. In contrast, some FM-AFM curves clearly resolved a force transition associated with each of the unfolding peaks irrespective of the number of observed unfolded domains. As expected for FM-AFM, the frequency shift response of the main unfolding peaks and their intermediates could only be detected when the oscillation amplitudes used were smaller than the interaction lengths being measured. It was also shown that the forces measured for the dynamical interaction of the FM-AFM technique were significantly lower than those measured using the static mode. This study highlights the potential for using dynamic AFM for investigating biological interactions, including protein unfolding and the detection of novel unfolding intermediates.</p>https://authors.library.caltech.edu/records/zbe42-rdk03Microstructure-Hardened Silver Nanowires
https://authors.library.caltech.edu/records/9zb2t-49061
Year: 2006
DOI: 10.1021/nl052427f
<p>To exploit the novel size-dependent mechanical properties of nanowires, it is necessary for one to develop strategies to control the strength and toughness of these materials. Here, we report on the mechanical properties of silver nanowires with a unique fivefold twin structure using a lateral force atomic force microscopy (AFM) method in which wires are held in a double-clamped beam configuration. Force-displacement curves exhibit super elastic behavior followed by unexpected brittle failure without significant plastic deformation. Thermal annealing resulted in a gradual transition to weaker, more ductile materials associated with the elimination of the twinned boundary structure. These results point to the critical roles of microstructure and confinement in engineering the mechanical properties of nanoscale materials.</p>https://authors.library.caltech.edu/records/9zb2t-49061A Generalized Description of the Elastic Properties of Nanowires
https://authors.library.caltech.edu/records/vdvb1-75e04
Year: 2006
DOI: 10.1021/nl060028u
<p>We report a model of nanowire (NW) mechanics that describes force vs displacement curves over the entire elastic range for diverse wire systems. Due to the clamped-wire measurement configuration, the force response in the linear elastic regime can be linear or nonlinear, depending on the system and the wire displacement. For Au NWs the response is essentially linear since yielding occurs prior to the onset of the inherent nonlinearity, while for Si NWs the force response is highly nonlinear, followed by brittle fracture. Since the method describes the entire range of elastic deformation, it unequivocally identifies the yield points in both of these materials.</p>https://authors.library.caltech.edu/records/vdvb1-75e04Erratum: Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope
https://authors.library.caltech.edu/records/6ah36-gxd83
Year: 2006
DOI: 10.1063/1.2213187
<p>Theoretical models for the frequency response of a cantilever beam immersed in a viscous fluid commonly assume that the fluid is unbounded. Experimental measurements show, however, that proximity to a surface can significantly affect the frequency response of a cantilever beam. In this article, we rigorously calculate the effect of a nearby surface on the frequency response of a cantilever beam immersed in a viscous fluid, and present a general theoretical model. Due to its practical relevance to applications of the atomic force microscope and microelectromechanical systems, detailed results are presented for cantilever beams with rectangular geometries executing flexural and torsional oscillations. It is found that dissipative loading in the fluid is primarily responsible for the observed variation in the frequency response, whereas inertial loading exerts a relatively weak influence.</p>https://authors.library.caltech.edu/records/6ah36-gxd83Coupling of conservative and dissipative forces in frequency-modulation atomic force microscopy
https://authors.library.caltech.edu/records/tn4a5-wsw22
Year: 2006
DOI: 10.1103/physrevb.74.195424
<p>Frequency modulation atomic force microscopy (FM-AFM) utilizes the principle of self-excitation to ensure the cantilever probe vibrates at its resonant frequency, regardless of the tip-sample interaction. Practically, this is achieved by fixing the phase difference between tip deflection and driving force at precisely 90°. This, in turn, decouples the frequency shift and excitation amplitude signals, enabling quantitative interpretation in terms of conservative and dissipative tip-sample interaction forces. In this article, we theoretically investigate the effect of phase detuning in the self-excitation mechanism on the coupling between conservative and dissipative forces in FM-AFM. We find that this coupling depends only on the relative difference in the drive and resonant frequencies far from the surface, and is thus very weakly dependent on the actual phase error particularly for high quality factors. This establishes that FM-AFM is highly robust with respect to phase detuning, and enables quantitative interpretation of the measured frequency shift and excitation amplitude, even while operating away from the resonant frequency with the use of appropriate replacements in the existing formalism. We also examine the calibration of phase shifts in FM-AFM measurements and demonstrate that the commonly used approach of minimizing the excitation amplitude can lead to significant phase detuning, particularly in liquid environments.</p>https://authors.library.caltech.edu/records/tn4a5-wsw22Time-resolved spectroscopy of silver nanocubes: Observation and assignment of coherently excited vibrational modes
https://authors.library.caltech.edu/records/z4yzp-nh478
Year: 2007
DOI: 10.1063/1.2672907
The response of single crystal, cubic silver particles to ultrafast laser-induced heating has been examined experimentally and theoretically. The transient absorption traces display clear modulations due to coherently excited vibrational modes. Nanocube samples with edge lengths smaller than 50nm show a single modulation, whereas samples larger than 50nm show two vibrational modes. The results are compared to finite element calculations, where the cubes are modeled as having cubic crystal symmetry with the principal axes parallel to the sides of the particle. The action of the laser pulse is treated in two ways, first, as creating a uniform initial strain. In this case the predominant mode excited is the breathing mode. The period of this mode is in reasonable agreement with the vibrational periods measured for the smaller cubes and with the higher frequency modulation observed for the larger cubes. A nonuniform initial strain is also considered, which could arise from nonuniform heating for particles larger than the optical skin depth of the metal. In this case the predominant mode excited is a nontotally symmetric mode. The calculated periods from this analysis are in reasonable agreement with the lower frequency modulations observed for the larger samples. The results from this study show that, to within the accuracy of these measurements, the elastic constants of cubic silver nanoparticles are the same as bulk silver.https://authors.library.caltech.edu/records/z4yzp-nh478Vibrational Response of Au−Ag Nanoboxes and Nanocages to Ultrafast Laser-Induced Heating
https://authors.library.caltech.edu/records/s4j3p-mrc69
Year: 2007
DOI: 10.1021/nl0702766
<p>Time-resolved spectroscopy has been used to investigate the vibrational properties of hollow cubic nanoparticles: Au−Ag nanoboxes and nanocages. In these experiments, laser-induced heating was used to coherently excite the breathing vibrational modes of the particle. The vibrational periods scale with the edge length of the particle and the nanocages and nanoboxes showing equivalent responses despite a large difference in their morphology. The measured vibrational periods are compared to finite element calculations, where the particles are modeled as a hollow cube, with the principle crystal axes parallel to the sides of the cube. Very good agreement is obtained between the calculations and the experimental data, with the experimental frequencies being slightly lower than the calculated values (by ∼7%). These results demonstrate the importance of accurately modeling the particles in order to interpret experimental data.</p>https://authors.library.caltech.edu/records/s4j3p-mrc69Velocity gradient singularity and structure of the velocity profile in the Knudsen layer according to the Boltzmann equation
https://authors.library.caltech.edu/records/rw2th-tg883
Year: 2007
DOI: 10.1103/physreve.76.026315
<p>Rarefied gas flow modeling presents significant challenges in the characterization of nanoscale devices and their applications. An important feature of such flows is the Knudsen layer, which is known to exhibit non-Newtonian viscosity behavior. Significantly, recent research has suggested that the effective viscosity at the surface is about half the standard dynamic viscosity. We examine these claims using numerical solutions of the linearized Boltzmann equation and direct simulation Monte Carlo calculations and discover that (i) the flow exhibits a striking power-law dependence on distance from the solid surface and (ii) the velocity gradient is singular at this surface. This finding contradicts these recent claims and has direct implications for gas flow modeling and the design of nanoscale devices.</p>https://authors.library.caltech.edu/records/rw2th-tg883Effect of Surface Stress on the Stiffness of Cantilever Plates
https://authors.library.caltech.edu/records/db0j6-e1r09
Year: 2007
DOI: 10.1103/physrevlett.99.206102
<p>Measurements over the past 30 years have indicated that surface stress can significantly affect the stiffness of microcantilever plates. Several one-dimensional models based on beam theory have been proposed to explain this phenomenon, but are found to be in violation of Newton's third law, in spite of their good agreement with measurements. In this Letter, we review this work and rigorously examine the effect of surface stress on the stiffness of cantilever plates using a full three-dimensional model. This study establishes the relationship between surface stress and cantilever stiffness, and in so doing elucidates its scaling behavior with cantilever dimensions. The use of short nanoscale cantilevers thus presents the most promising avenue for future investigations.</p>https://authors.library.caltech.edu/records/db0j6-e1r09Flexural Resonant Frequencies of Thin Rectangular Cantilever Plates
https://authors.library.caltech.edu/records/2ftma-47w36
Year: 2008
DOI: 10.1115/1.2745377
Knowledge of the flexural vibration frequencies of thin rectangular cantilever plates forms the basis for numerous applications in sensing and instrumentation. Despite the seemingly simple nature of the problem, an accurate formula for the fundamental resonant frequency that is valid for all aspect ratios and Poisson's ratios is notably lacking in the literature. In this article, we present such a result using a variational and singular perturbation formulation. This yields a simple analytical formula that exhibits a maximum error of 2%.https://authors.library.caltech.edu/records/2ftma-47w36Measurement of the Optical Properties and Shape of Nanoparticles in Solution Using Couette Flow
https://authors.library.caltech.edu/records/trq7a-y1s18
Year: 2008
DOI: 10.1021/nn700304b
<p>Knowledge of the optical properties and shape of nanoparticles is central to many technological applications including the fabrication of advanced materials and the characterization and formation of ordered films for optoelectronic devices. Measurement of such properties typically involves the independent use of advanced instrumentation such as electron and near field optical microscopy. We propose a simple experimental technique for extracting the optical and geometric properties of dilute suspensions of nanoparticles <i>in situ</i>. A theoretical formalism is developed to determine both the dichroic ratio and aspect ratio from a single measurement of the change in extinction of an incident light beam. The validity of this method is demonstrated for hematite nanorods, for which good agreement with independent measurements is found.</p>https://authors.library.caltech.edu/records/trq7a-y1s18Influence of atomic force microscope cantilever tilt and induced torque on force measurements
https://authors.library.caltech.edu/records/a56s7-x1w63
Year: 2008
DOI: 10.1063/1.2885734
Quantitative force measurements performed using the atomic force microscope (AFM) inherently rely on calibration of the AFM cantilever spring constant to convert the measured deflection into a force. Here, we examine the effect of cantilever tilt and induced torque on the effective normal spring constant resulting from variable placement of the tip probe, as is frequently encountered in practice. Explicit general formulas are presented that account for these combined effects for both sharp tips and spherical probes. In contrast to previous studies, we find that induced tip torque can act to either enhance or reduce the effective normal spring constant of the cantilever. The implications of this study to practical force measurements are discussed.https://authors.library.caltech.edu/records/a56s7-x1w63Artifact-free dynamic atomic force microscopy reveals monotonic dissipation for a simple confined liquid
https://authors.library.caltech.edu/records/bxtrn-kt246
Year: 2008
DOI: 10.1063/1.2950324
We present definitive interaction measurements of a simple confined liquid (octamethylcyclotetrasiloxane) using artifact-free frequency modulation atomic force microscopy. We use existing theory to decouple the conservative and dissipative components of the interaction, for a known phase offset from resonance (90° phase shift), that has been deliberately introduced into the experiment. Further we show the qualitative influence on the conservative and dissipative components of the interaction of a phase error deliberately introduced into the measurement, highlighting that artifacts, such as oscillatory dissipation, can be readily observed when the phase error is not compensated for in the force analysis.https://authors.library.caltech.edu/records/bxtrn-kt246Velocity profile in the Knudsen layer according to the Boltzmann equation
https://authors.library.caltech.edu/records/dm9cw-k1797
Year: 2008
DOI: 10.1098/rspa.2008.0071
Flow of a dilute gas near a solid surface exhibits non-continuum effects that are manifested in the Knudsen layer. The non-Newtonian nature of the flow in this region has been the subject of a number of recent studies suggesting that the so-called 'effective viscosity' at a solid surface is half that of the standard dynamic viscosity. Using the Boltzmann equation with a diffusely reflecting surface and hard sphere molecules, Lilley & Sader discovered that the flow exhibits a striking power-law dependence on distance from the solid surface where the velocity gradient is singular. Importantly, these findings (i) contradict these recent claims and (ii) are not predicted by existing high-order hydrodynamic flow models. Here, we examine the applicability of these findings to surfaces with arbitrary thermal accommodation and molecules that are more realistic than hard spheres. This study demonstrates that the velocity gradient singularity and power-law dependence arise naturally from the Boltzmann equation, regardless of the degree of thermal accommodation. These results are expected to be of particular value in the development of hydrodynamic models beyond the Boltzmann equation and in the design and characterization of nanoscale flows.https://authors.library.caltech.edu/records/dm9cw-k1797Mechanical Properties of ZnO Nanowires
https://authors.library.caltech.edu/records/he1q8-ze691
Year: 2008
DOI: 10.1103/physrevlett.101.175502
<p>Semiconductor nanowires are unique as functional building blocks in nanoscale electrical and electromechanical devices. Here, we report on the mechanical properties of ZnO nanowires that range in diameter from 18 to 304 nm. We demonstrate that in contrast to recent reports, Young's modulus is essentially independent of diameter and close to the bulk value, whereas the ultimate strength increases for small diameter wires, and exhibits values up to 40 times that of bulk. The mechanical behavior of ZnO nanowires is well described by a mechanical model of bending and tensile stretching.</p>https://authors.library.caltech.edu/records/he1q8-ze691Erratum: Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order
https://authors.library.caltech.edu/records/eb8xm-48310
Year: 2008
DOI: 10.1063/1.3009958
The frequency response of a cantilever beam is well known to depend strongly on the fluid in which it is immersed. In this article, we present a theoretical model for the frequency response of a rectangular cantilever beam immersed in a viscous fluid that enables the flexural and torsional modes of arbitrary order to be calculated. This extends the previous models of Sader and Green [J. Appl. Phys. 84, 64 (1998); 92, 6262 (2002)], which were formulated primarily for the fundamental mode and the next few harmonics, to the general case of arbitrary mode order by accounting for the three-dimensional nature of the flow field around the cantilever beam. Due to its importance in atomic force microscope applications, results for the thermal noise spectrum are presented and the influence of mode order on the frequency response investigated.https://authors.library.caltech.edu/records/eb8xm-48310Compressible viscous flows generated by oscillating flexible cylinders
https://authors.library.caltech.edu/records/97sx9-vf404
Year: 2009
DOI: 10.1063/1.3058201
The fluid dynamics of oscillating elastic beams underpin the operation of many modern technological devices ranging from micromechanical sensors to the atomic force microscope. While viscous effects are widely acknowledged to have a strong influence on these dynamics, fluid compressibility is commonly neglected. Here, we theoretically study the three-dimensional flow fields that are generated by the motion of flexible cylinders immersed in viscous compressible fluids and discuss the implications of compressibility in practice. We consider cylinders of circular cross section and flat blades of zero thickness that are executing flexural and torsional oscillations of arbitrary wave number. Exact analytical solutions are derived for these flow fields and their resulting hydrodynamic loads.https://authors.library.caltech.edu/records/97sx9-vf404Electrodynamic ratchet motor
https://authors.library.caltech.edu/records/e6kh4-kh130
Year: 2009
DOI: 10.1103/physreve.79.030105
<p>Brownian ratchets produce directed motion through rectification of thermal fluctuations and have been used for separation processes and colloidal transport. We propose a flashing ratchet motor that enables the transduction of electrical energy into rotary micromechanical work. This is achieved through torque generation provided by boundary shaping of equipotential surfaces. The present device contrasts to previous implementations that focus on translational motion. Stochastic simulations elucidate the performance characteristics of this device as a function of its geometry. Miniaturization to nanoscale dimensions yields rotational speeds in excess of 1 kHz, which is comparable to biomolecular motors of similar size.</p>https://authors.library.caltech.edu/records/e6kh4-kh130Nonmonotonic Energy Dissipation in Microfluidic Resonators
https://authors.library.caltech.edu/records/8g2qs-w4s66
Year: 2009
DOI: 10.1103/physrevlett.102.228103
<p>Nanomechanical resonators enable a range of precision measurements in air or vacuum, but strong viscous damping makes applications in liquid challenging. Recent experiments have shown that fluid damping is greatly reduced in fluidic embedded-channel microcantilevers. Here we report the discovery of nonmonotonic energy dissipation due to the fluid in such devices, which leads to the intriguing prospect of enhancing the quality factor upon miniaturization. These observations elucidate the physical mechanisms of energy dissipation in embedded-channel resonators and thus provide the basis for numerous applications in nanoscience and biology.</p>https://authors.library.caltech.edu/records/8g2qs-w4s66Blunted-Cone Heat Shields of Atmospheric Entry Vehicles
https://authors.library.caltech.edu/records/g5y6n-4a990
Year: 2009
DOI: 10.2514/1.43358
<p>Atmospheric entry of a spacecraft generates extreme temperatures (>5000 K) due to its high speed and the resulting aerodynamic heating. Such extreme conditions require special design considerations to ensure safe passage of the craft through the atmosphere. One commonly employed technique is to use a heat shield. This device protects the craft from the high temperatures generated and also provides the necessary aerodynamic braking and stability for controlled entry through the atmosphere.</p>https://authors.library.caltech.edu/records/g5y6n-4a990Mechanical properties of individual electrospun polymer-nanotube composite nanofibers
https://authors.library.caltech.edu/records/qxynn-5jc34
Year: 2009
DOI: 10.1016/j.carbon.2009.04.022
<p>Singlewalled carbon nanotube/polyvinylalcohol composite nanofibers were electro-spun onto a silicon surface pre-patterned with trenches. These nanofibers were prepared with different loadings of SWCNTs and had radii between 20 and 40 nm. Individual fiber sections were pinned across the trenches and laterally loaded by an AFM tip to yield mechanical response curves. A simple model was exploited to extract the tensile mechanical properties from the lateral force–displacement data. Depending on the fiber composition, the tensile modulus was found to be between 3 and 85 GPa. In addition we have prepared fibers with tensile strength of up to 2.6 GPa. Such optimised fibers break at strains of ∼4% and exhibit toughness of up to 27 MJ/m³.</p>https://authors.library.caltech.edu/records/qxynn-5jc34Damping of acoustic vibrations in gold nanoparticles
https://authors.library.caltech.edu/records/n8yhb-28s76
Year: 2009
DOI: 10.1038/nnano.2009.192
<p>Studies of acoustic vibrations in nanometre-scale particles can provide fundamental insights into the mechanical properties of materials because it is possible to precisely characterize and control the crystallinity and geometry of such nanostructures<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR1">1</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR2">2</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR3">3</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR4">4</a>. Metal nanoparticles are of particular interest because they allow the use of ultrafast laser pulses to generate and probe high-frequency acoustic vibrations, which have the potential to be used in a variety of sensing applications. So far, the decay of these vibrations has been dominated by dephasing due to variations in nanoparticle size<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR5">5</a>. Such inhomogeneities can be eliminated by performing measurements on single nanoparticles deposited on a substrate<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR6">6</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR7">7</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR8">8</a>,<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR9">9</a>, but unknown interactions between the nanoparticles and the substrate make it difficult to interpret the results of such experiments. Here, we show that the effects of inhomogeneous damping can be reduced by using bipyramidal gold nanoparticles with highly uniform sizes<a href="https://www.nature.com/articles/nnano.2009.192#ref-CR10">10</a>. The inferred homogeneous damping is due to the combination of damping intrinsic to the nanoparticles and the surrounding solvent; the latter is quantitatively described by a parameter-free model.</p>https://authors.library.caltech.edu/records/n8yhb-28s76Evolution of Colloidal Nanocrystals: Theory and Modeling of their Nucleation and Growth
https://authors.library.caltech.edu/records/4p2n7-sqa21
Year: 2009
DOI: 10.1021/jp9027673
<p>Through the use of a population balance equation (PBE), the nucleation and growth of nanocrystals evolving under various initial reaction conditions are simulated. Simulations of nanocrystal (NC) growth in both the diffusion and reaction limits are presented, and it is concluded that NC growth proceeds under strongly reaction-limited kinetics. The particle size distributions obtained in the asymptotic diffusion and reaction limits were found to be slightly narrower than the stationary distributions predicted by LSW and Wagner theories, respectively. There is strong experimental evidence indicating that the early stages of NC synthesis involve simultaneous nucleation, growth and coarsening. The simulations performed here are able to replicate these conditions, providing insight into the factors that govern these early time processes, as well as the consequences they have at longer reaction times.</p>https://authors.library.caltech.edu/records/4p2n7-sqa21Frequency response of cantilever beams immersed in compressible fluids with applications to the atomic force microscope
https://authors.library.caltech.edu/records/y2bcs-8p525
Year: 2009
DOI: 10.1063/1.3254191
The dynamics of microcantilever beams can be strongly affected by immersion in fluid. While the importance of viscosity for devices of microscale dimensions is well established, the significance of fluid compressibility has not been investigated in detail. Here, we present a rigorous theoretical model for the frequency response of a rectangular cantilever beam that is executing normal and torsional oscillations, and is immersed in a compressible fluid. Both the viscous case and the inviscid limit are considered, and the model is valid for arbitrary mode number. We find that compressibility becomes increasingly important as the mode number rises. This is particularly relevant for gases, where compressibility is found to be important for high mode numbers of practical interest.https://authors.library.caltech.edu/records/y2bcs-8p525Effect of surface stress on the stiffness of cantilever plates: Influence of cantilever geometry
https://authors.library.caltech.edu/records/bx0wy-43c62
Year: 2009
DOI: 10.1063/1.3262347
Numerous measurements have indicated that surface stress can significantly modify the stiffness of cantilever sensors. In contrast, theoretical calculations using classical beam theory predict that stiffness is independent of surface stress. Using a three-dimensional analysis, we recently showed that surface stress does indeed have an effect within the framework of linear elasticity. However, only cantilevers of rectangular geometry were explored. Here, we vary cantilever geometry and find that it plays a critical role, with V-shaped cantilevers displaying greatly enhanced sensitivity in comparison to rectangular cantilevers. Tuning cantilever geometry therefore provides a sensitive route to controlling the effects of surface stress.https://authors.library.caltech.edu/records/bx0wy-43c62Photoacoustic detection of gases using microcantilevers
https://authors.library.caltech.edu/records/ndz6q-6ra40
Year: 2009
DOI: 10.1063/1.3271157
<p>We describe a new technique for measuring the infrared absorption spectra of gases using atomic force microscope microcantilevers. This photoacoustic system is demonstrated for a dilute acetylene/helium mixture by recording the acetylene ν₁+ν₃ infrared overtone transitions using a wavelength modulated tunable diode laser as the infrared light source. The technique presents significant advantages over existing methods in terms of size, simplicity, speed and insensitivity to ambient vibrations. The maximum achievable signal-to-noise for resonant and non-resonant photoacoustic excitation of the microcantilever is examined and is found to be limited by the microcantilever's Brownian noise.</p>https://authors.library.caltech.edu/records/ndz6q-6ra40Lattice Boltzmann method for oscillatory Stokes flow with applications to micro- and nanodevices
https://authors.library.caltech.edu/records/wgk4j-8vp87
Year: 2010
DOI: 10.1103/physreve.81.036706
<p>A lattice Boltzmann (LB) method based on the linearized Boltzmann Bhatnagar-Gross-Krook equation for numerical simulation of oscillatory (unsteady) Stokes flow is proposed. Unlike the conventional (nonlinear) LB method that utilizes the time domain exclusively, the proposed method is formulated in the frequency domain to allow for direct access to the complex-valued stress, force, and velocity field—these parameters are of direct interest in characterizing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). The proposed method circumvents the requirement for time-dependent boundary velocities, as is needed in the conventional LB method, and convergence of the two methods is compared. Validity of the proposed method is assessed using three classical (unsteady) flows: (1) <i>one-dimensional</i> oscillatory Couette flow between two plates; (2) <i>two-dimensional</i> flow generated by an oscillating circular cylinder; (3) <i>three-dimensional</i> flow generated by an oscillating sphere. The observed excellent numerical performance in all three cases demonstrates that this linear lattice Boltzmann method can be used to study the dynamics of micro- and nanoscale devices of any dimensionality. This is particularly relevant to MEMS and NEMS, where the resonance properties of individual nanomechanical components immersed in fluid can underpin overall device performance.</p>https://authors.library.caltech.edu/records/wgk4j-8vp87Spectral properties of microcantilevers in viscous fluid
https://authors.library.caltech.edu/records/m98jx-96v12
Year: 2010
DOI: 10.1103/physreve.81.046306
<p>We explore analytically, numerically, and experimentally the spectral properties of the flexural vibrations of micron scale cantilevers in a viscous fluid that are driven externally or by Brownian motion. Although the physical origins of driven and thermal cantilever dynamics are quite different, we show that in each case the dynamics can be calculated deterministically using an impulse or step force, respectively. The stochastic dynamics of the cantilever are related to the removal of a step force by the fluctuation-dissipation theorem to yield the autocorrelation and noise spectral density of equilibrium fluctuations. The dynamics of a cantilever driven externally is related to an impulse in force by transfer function theory. Using this approach, we explore the differences between the driven and thermal spectra of microcantilevers. We find that higher order cantilever modes and the spatial distribution of the applied load for the external drive can be critical to the relationship between the thermal and driven spectra.</p>https://authors.library.caltech.edu/records/m98jx-96v12Water bells formed on the underside of a horizontal plate. Part 2. Theory
https://authors.library.caltech.edu/records/scm2h-r6541
Year: 2010
DOI: 10.1017/s0022112009993363
In a companion paper (Part 1, Jameson et al. J. Fluid Mech. vol. 649, 2010, 19–43), the discovery of a new type of water bell was reported. When a vertical liquid jet impacts on the underside of a large horizontal plate, the resulting thin film spreads radially along the plate to an unspecified abrupt departure point, from whence it falls away from the plate of its own accord. The departure radius of the fluid from the plate is seen to depend strongly on the volumetric flow rate. The falling liquid may then coalesce to form a water bell. Here we present a theoretical analysis and explanation of this phenomenon. A force balance determining the maximum radial extension of the thin film flow along the plate is considered as a mechanism for fluid departure from the plate, for which an analytical model is developed. This model gives good predictions of the measured radius of departure. When a water bell has been formed, and the flow rate is altered, many interesting shapes are produced that depend on the shapes at previous flow rates. We discuss the origin of this hysteresis, and also present a leading order theory for the bell shape under a regime of changing flow rate. The models are compared with experimental results spanning two orders of magnitude in viscosity.https://authors.library.caltech.edu/records/scm2h-r6541Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation
https://authors.library.caltech.edu/records/rjpc6-2sj62
Year: 2010
DOI: 10.1017/s0022112009993351
In this study we report discovery of a new type of water bell. This is formed by impinging a vertical liquid jet on to the underside of a large horizontal flat plate. After impact, the liquid spreads radially along the plate before falling at an abrupt unspecified radius. This falling liquid may then coalesce to form a curtain which encloses a volume of air. When the flow rate of the impinging jet is altered from the value at initial formation, a pronounced hysteretic effect in the water bell shape can be observed. We present detailed observations of these new phenomena, including the size and nature of the flow underneath the plate and the shape of the liquid curtain. These observations are interpreted theoretically in a companion paper (Part 2, Button et al. vol. 649, 2010, pp. 45–68).https://authors.library.caltech.edu/records/rjpc6-2sj62Lubrication forces in air and accommodation coefficient measured by a thermal damping method using an atomic force microscope
https://authors.library.caltech.edu/records/gt2gm-wjz65
Year: 2010
DOI: 10.1103/physreve.81.056305
<p>By analysis of the thermally driven oscillation of an atomic force microscope (AFM) cantilever, we have measured both the damping and static forces acting on a sphere near a flat plate immersed in gas. By varying the proximity of the sphere to the plate, we can continuously vary the Knudsen number (Kn) at constant pressure, thereby accessing the slip flow, transition, and molecular regimes at a single pressure. We use measurements in the slip-flow regime to determine the combined slip length (on both sphere and plate) and the tangential momentum accommodation coefficient, σ. For ambient air at 1 atm between two methylated glass solids, the inverse damping is linear with separation and the combined slip length on both surfaces is 250 nm±100 nm, which corresponds to σ = 0.77 ± 0.24. At small separations (Kn>0.4) the measured inverse damping is no longer linear with separation, and is observed to exhibit reasonable agreement with the Vinogradova formula.</p>https://authors.library.caltech.edu/records/gt2gm-wjz65Energy dissipation in microfluidic beam resonators
https://authors.library.caltech.edu/records/xyxfe-91v20
Year: 2010
DOI: 10.1017/s0022112009993521
The fluid–structure interaction of resonating microcantilevers immersed in fluid has been widely studied and is a cornerstone in nanomechanical sensor development. In many applications, fluid damping imposes severe limitations by strongly degrading the signal-to-noise ratio of measurements. Recently, Burget al. (Nature, vol. 446, 2007, pp. 1066–1069) proposed an alternative type of microcantilever device whereby a microfluidic channel was embedded inside the cantilever with vacuum outside. Remarkably, it was observed that energy dissipation in these systems was almost identical when air or liquid was passed through the channel and was 4 orders of magnitude lower than that in conventional microcantilever systems. Here, we study the fluid dynamics of these devices and present a rigorous theoretical model corroborated by experimental measurements to explain these observations. In so doing, we elucidate the dominant physical mechanisms giving rise to the unique features of these devices. Significantly, it is found that energy dissipation is not a monotonic function of fluid viscosity, but exhibits oscillatory behaviour, as fluid viscosity is increased/decreased. In the regime of low viscosity, inertia dominates the fluid motion inside the cantilever, resulting in thin viscous boundary layers – this leads to an increase in energy dissipation with increasing viscosity. In the high-viscosity regime, the boundary layers on all surfaces merge, leading to a decrease in dissipation with increasing viscosity. Effects of fluid compressibility also become significant in this latter regime and lead to rich flow behaviour. A direct consequence of these findings is that miniaturization does not necessarily result in degradation in the quality factor, which may indeed be enhanced. This highly desirable feature is unprecedented in current nanomechanical devices and permits direct miniaturization to enhance sensitivity to environmental changes, such as mass variations, in liquid.https://authors.library.caltech.edu/records/xyxfe-91v20Accurate formula for conversion of tunneling current in dynamic atomic force spectroscopy
https://authors.library.caltech.edu/records/w3paz-kt657
Year: 2010
DOI: 10.1063/1.3464165
Recent developments in frequency modulation atomic force microscopy enable simultaneous measurement of frequency shift and time-averaged tunneling current. Determination of the interaction force is facilitated using an analytical formula, valid for arbitrary oscillation amplitudes [Sader and Jarvis, Appl. Phys. Lett. 84, 1801 (2004)]. Here we present the complementary formula for evaluation of the instantaneous tunneling current from the time-averaged tunneling current. This simple and accurate formula is valid for any oscillation amplitude and current law. The resulting theoretical framework allows for simultaneous measurement of the instantaneous tunneling current and interaction force in dynamic atomic force microscopy.https://authors.library.caltech.edu/records/w3paz-kt657Erratum:Oscillation of cylinders of rectangular cross section immersed in fluid
https://authors.library.caltech.edu/records/2hak1-jtf71
Year: 2010
DOI: 10.1063/1.3487694
The ability to calculate flows generated by oscillating cylinders immersed in fluid is a cornerstone in micro- and nanodevice development. In this article, we present a detailed theoretical analysis of the hydrodynamic load experienced by an oscillating rigid cylinder, of arbitrary rectangular cross section, that is immersed in an unbounded viscous fluid. We also consider the formal limit of inviscid flow for which exact analytical and asymptotic solutions are derived. Due to its practical importance in application to the atomic force microscope and nanoelectromechanical systems, we conduct a detailed assessment of the dependence of this load on the cylinder thickness-to-width ratio. We also assess the validity and accuracy of the widely used infinitely-thin blade approximation. For thin rectangular cylinders of finite thickness, this approximation is found to be excellent for out-of-plane motion, whereas for in-plane oscillations it can exhibit significant error. A database of accurate numerical results for the hydrodynamic load as a function of the thickness-to-width ratio and normalized frequency is also presented, which is expected to be of value in practical application and numerical benchmarking.https://authors.library.caltech.edu/records/2hak1-jtf71On the maximum drag reduction due to added polymers in Poiseuille flow
https://authors.library.caltech.edu/records/0mqej-bs517
Year: 2010
DOI: 10.1017/s0022112010003083
The addition of elastic polymers to turbulent liquids is known to produce significant drag reduction. In this study, we prove that the drag in pipe and channel flows of an unforced laminar fluid constitutes a lower bound for the drag of a fluid containing dilute elastic polymers. Further, the addition of elastic polymers to laminar fluids invariably increases drag. This proof does not rely on the adoption of a particular constitutive equation for the polymer force, and would also be applicable to other similar methods of drag reduction, which are also achieved by the addition of certain particles to a flow. Examples of such methods include the addition of surfactants to a flowing liquid and the presence of sand particles in sandstorms and water droplets in cyclones.https://authors.library.caltech.edu/records/0mqej-bs517Energy dissipation in microfluidic beam resonators: Dependence on mode number
https://authors.library.caltech.edu/records/7vkad-79950
Year: 2010
DOI: 10.1063/1.3514100
Energy dissipation experienced by vibrating microcantilever beams immersed in fluid is strongly dependent on the mode of vibration, with quality factors typically increasing with mode number. Recently, we examined energy dissipation in a new class of cantilever device that embeds a microfluidic channel in its interior—the fundamental mode of vibration only was considered. Due to its importance in practice, we examine the effect of mode number on energy dissipation in these microfluidic beam resonators. Interestingly, and in contrast to other cantilever devices, we find that the quality factor typically decreases with increasing mode number. We explore the underlying physical mechanisms leading to this counterintuitive behavior, and provide a detailed comparison to experimental measurements for which good agreement is found.https://authors.library.caltech.edu/records/7vkad-79950Accuracy of the lattice Boltzmann method for low-speed noncontinuum flows
https://authors.library.caltech.edu/records/krpcb-cfn68
Year: 2011
DOI: 10.1103/physreve.83.045701
<p>Simulation of noncontinuum gas flows presents tremendous challenges, especially for nanoscale devices that usually exhibit low speeds and isothermal conditions. Such simulations are often achieved through use of the Boltzmann Bhatnagar-Gross-Krook equation, which forms the foundation for the lattice Boltzmann (LB) method. Accuracy of the LB method in noncontinuum flows is widely assumed to depend on the order of quadrature used. Here, we study noncontinuum Couette flow and discover that interaction of the lattice with the solid boundaries is the dominant mechanism controlling accuracy—quadrature order plays a comparatively minor role. This suggests the applicability of low-order quadrature in LB simulation of wall bounded isothermal noncontinuum flows, and leads to a framework and rationale for accurate implementation of LB models in noncontinuum flows.</p>https://authors.library.caltech.edu/records/krpcb-cfn68Energy dissipation in microfluidic beam resonators: Effect of Poisson's ratio
https://authors.library.caltech.edu/records/q02bq-7nx34
Year: 2011
DOI: 10.1103/physreve.84.026304
<p>Dissipation of mechanical energy underlies the sensitivity of many nanomechanical devices, with environmental effects often having a significant effect. One case of practical relevance is the interaction of elastic beam resonators with fluid, which is known to dramatically increase energy dissipation. Recently, we investigated energy dissipation in a different class of elastic beam resonator that embeds a microfluidic channel in its interior. In this paper, we examine the effect of the beam material Poisson ratio on these devices and discover that it can strongly affect energy dissipation—this is in direct contrast to conventional cantilever beams immersed in fluid. Increasing the Poisson ratio in these microfluidic devices is found to decrease energy dissipation, with the incompressible material limit providing minimum energy dissipation. Our paper establishes that, in this limit, placement of the fluid channel away from the beam neutral axis has negligible effect on energy dissipation in many cases of practical interest. The physical implications of these findings are discussed, and a detailed comparison with available experimental results is provided.</p>https://authors.library.caltech.edu/records/q02bq-7nx34Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope
https://authors.library.caltech.edu/records/8w7ea-8ra13
Year: 2011
DOI: 10.1063/1.3632122
The thermal noise spectrum of nanomechanical devices is commonly used to characterize their mechanical properties and energy dissipation. This spectrum is measured from finite time series of Brownian motion of the device, which is windowed and Fourier transformed. Here, we present a theoretical and experimental investigation of the effect of such finite sampling on the measured device quality factor. We prove that if no spectral window is used, the thermal noise spectrum retains its original Lorentzian distribution but with a reduced quality factor, indicating an apparent enhancement in energy dissipation. A simple analytical formula is derived connecting the true and measured quality factors – this enables extraction of the true device quality factor from measured data. Common windows used to reduce spectral leakage are found to distort the (true) Lorentzian shape, potentially making fitting problematic. These findings are expected to be of particular importance for devices with high quality factors, where spectral resolution can be limited in practice. Comparison and validation using measurements on atomic force microscope cantilevers are presented.https://authors.library.caltech.edu/records/8w7ea-8ra13Mechanical Damping of Longitudinal Acoustic Oscillations of Metal Nanoparticles in Solution
https://authors.library.caltech.edu/records/5259x-59698
Year: 2011
DOI: 10.1021/jp207971t
<p>We present measurements and theoretical analysis of the damping of high-frequency acoustic vibrations of metal nanoparticles immersed in solution. Building on our previous work [Pelton, M.; Sader, J. E.; Burgin, J.; Liu, M.; Guyot-Sionnest, P.; Gosztola, D. <i>Nat. Nanotechnol. </i><strong>2009</strong>, <i>4</i>, 492–495], we study several bipyramidal gold nanoparticle samples in a series of solvent environments in order to examine the origin of the measured damping. We use a fluid-structure interaction model to explain the damping due to the fluid surrounding the nanoparticles, extending the model to encompass the case of an arbitrary slender body. Good agreement with the theoretical model is found for a range of pure solvents and solvent mixtures, demonstrating that classical continuum theories for fluid mechanics are able to quantify high-frequency phenomena at the nanoscale. The remaining damping rate, which can be attributed to processes intrinsic to the nanoparticles, is consistent across all the measured samples. This demonstrates that the measured intrinsic damping is indeed a characteristic property of these bipyramidal metal nanoparticles, rather than being sample dependent.</p>https://authors.library.caltech.edu/records/5259x-59698Induced flow due to blowing and suction flow control: an analysis of transpiration
https://authors.library.caltech.edu/records/e0q5d-82d74
Year: 2012
DOI: 10.1017/jfm.2011.441
<p>It has previously been demonstrated that the drag experienced by a Poiseuille flow in a channel can be reduced by subjecting the flow to a dynamic regime of blowing and suction at the walls of the channel (also known as 'transpiration'). Furthermore, it has been found to be possible to induce a 'bulk flow', or steady motion through the channel, via transpiration alone. In this work, we derive explicit asymptotic expressions for the induced bulk flow via a perturbation analysis. From this we gain insight into the physical mechanisms at work within the flow. The boundary conditions used are of travelling sine waves at either wall, which may differ in amplitude and phase. Here it is demonstrated that the induced bulk flow results from the effect of convection. We find that the most effective arrangement for inducing a bulk flow is that in which the boundary conditions at either wall are equal in magnitude and opposite in sign. We also show that, for the bulk flow induced to be non-negligible, the wavelength of the boundary condition should be comparable to, or greater than, the height of the channel. Moreover, we derive the optimal frequency of oscillation, for maximising the induced bulk flow, under such boundary conditions. The asymptotic behaviour of the bulk flow is detailed within the conclusion. It is found, under certain caveats, that if the amplitude of the boundary condition is too great, the bulk flow induced will become dependent only upon the speed at which the boundary condition travels along the walls of the channel. We propose the conjecture that for all similar flows, if the magnitude of the transpiration is sufficiently great, the bulk flow will depend only upon the speed of the boundary condition.</p>https://authors.library.caltech.edu/records/e0q5d-82d74Effect of surface stress on the stiffness of thin elastic plates and beams
https://authors.library.caltech.edu/records/hs73j-acr83
Year: 2012
DOI: 10.1103/physrevb.85.085440
<p>Nanomechanical doubly-clamped beams and cantilever plates are often used to sense a host of environmental effects, including biomolecular interations, mass measurements, and responses to chemical stimuli. Understanding the effects of surface stress on the stiffness of such nanoscale devices is essential for rigorous analysis of experimental data. Recently, we explored the effects of surface stress on cantilever plates and presented a theoretical framework valid for thin plate structures. Here, we generalize this framework and apply it to cantilever plates and doubly-clamped beams, exploring in detail the relative physical mechanisms causing a stiffness change in each case. Specifically, Poisson's ratio is found to exert a dramatically different effect in cantilevers than in doubly-clamped beams, and here we explain why. The relative change in effective spring constant is also examined, and its connection to the relative frequency shift is discussed. Interestingly, this differs from what is naively expected from elementary mechanics. Finally, a discussion of the practical implications of our theoretical findings is presented, which includes an assessment of available experimental results and potential future measurements on nanoscale devices.</p>https://authors.library.caltech.edu/records/hs73j-acr83High accuracy numerical solutions of the Boltzmann Bhatnagar-Gross-Krook equation for steady and oscillatory Couette flows
https://authors.library.caltech.edu/records/24zar-z5515
Year: 2012
DOI: 10.1063/1.3692276
Modeling gas flows generated by micro- and nano-devices often requires the use of kinetic theory. To facilitate implementation, various approximate formulations have been proposed based on the Bhatnagar-Gross-Krook (BGK) kinetic model, including most recently, the lattice Boltzmann (LB) method. While there exists a comprehensive numerical data set for the hard sphere linearized Boltzmann equation for steady Couette flow, no such set of data is available for the Boltzmann-BGK equation. The purpose of this article is to present a high accuracy data set for the linearized Boltzmann-BGK equation over the full range of Knudsen numbers and normalized oscillation frequencies – this encompasses both steady and unsteady Couette flows. This data set is expected to be of particular value in the benchmarking and validation of computational methods such as the LB method and other approaches based on the Boltzmann-BGK equation.https://authors.library.caltech.edu/records/24zar-z5515Effect of multiplicative noise on least-squares parameter estimation with applications to the atomic force microscope
https://authors.library.caltech.edu/records/kpt4c-e2z24
Year: 2012
DOI: 10.1063/1.4709496
Measurement of the power spectral density of (stochastic) Brownian fluctuations of micro- and nano-devices is used frequently to gain insight into their mechanistic properties. Noise is always present in these measurements and can directly influence any parameter estimation obtained through a least-squares analysis. Importantly, measurements of the spectral density of stationary random signals, such as Brownian motion, inherently contain multiplicative noise. In this article, we theoretically analyze the impact of multiplicative noise on fit parameters extracted using a least-squares analysis. A general analysis is presented that is valid for any fit function with any number of fit parameters. This yields closed-form expressions for the expected value and variance in the fit parameters and provides a rigorous theoretical framework for a priori determination of the effect of measurement uncertainty. The theory is demonstrated and validated through Monte Carlo simulation of synthetic data and by comparison to power spectral density measurements of the Brownian fluctuations of an atomic force microscope cantilever – analytical formulas for the uncertainty in the fitted resonant frequency and quality factor are presented. The results of this study demonstrate that precise measurements of fit parameters in the presence of noise are inherently problematic – individual measurements of the power spectral density are capable of yielding fit parameters that are many standard deviations away from the mean, with finite probability. This is of direct relevance to a host of applications in measurement science, including those connected with the atomic force microscope.https://authors.library.caltech.edu/records/kpt4c-e2z24Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams
https://resolver.caltech.edu/CaltechAUTHORS:20120711-110835143
Year: 2012
DOI: 10.1103/PhysRevLett.108.236101
PMCID: PMC3839317
The effect of surface stress on the stiffness of cantilever beams remains an outstanding problem in the physical sciences. While numerous experimental studies report significant stiffness change due to surface stress, theoretical predictions are unable to rigorously and quantitatively reconcile these observations. In
this Letter, we present the first controlled measurements of stress-induced change in cantilever stiffness with commensurate theoretical quantification. Simultaneous measurements are also performed on equivalent clamped-clamped beams. All experimental results are quantitatively and accurately predicted using elasticity theory. We also present conclusive experimental evidence for invalidity of the longstanding and unphysical axial force model, which has been widely applied to interpret measurements using cantilever beams. Our findings will be of value in the development of micro- and nanoscale resonant mechanical sensors.https://resolver.caltech.edu/CaltechAUTHORS:20120711-110835143Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams
https://authors.library.caltech.edu/records/3scem-cwm41
Year: 2012
DOI: 10.1103/physrevlett.108.236101
<p>The effect of surface stress on the stiffness of cantilever beams remains an outstanding problem in the physical sciences. While numerous experimental studies report significant stiffness change due to surface stress, theoretical predictions are unable to rigorously and quantitatively reconcile these observations. In this Letter, we present the first controlled measurements of stress-induced change in cantilever stiffness with commensurate theoretical quantification. Simultaneous measurements are also performed on equivalent clamped-clamped beams. All experimental results are quantitatively and accurately predicted using elasticity theory. We also present conclusive experimental evidence for invalidity of the long-standing and unphysical axial force model, which has been widely applied to interpret measurements using cantilever beams. Our findings will be of value in the development of micro- and nanoscale resonant mechanical sensors.</p>https://authors.library.caltech.edu/records/3scem-cwm41Existence of Micrometer-Scale Water Droplets at Solvent/Air Interfaces
https://authors.library.caltech.edu/records/j7cvr-cn316
Year: 2012
DOI: 10.1021/la302420s
<p>Standard surface energy balances using literature values for pure liquids predict that water droplets are unstable at the liquid/air interfaces of many common organic solvents. While the behavior of macroscopic drops in the presence of solvents has been studied, the study of droplets in the micrometer size regime and the possible role of line tension are notably absent. In this article, we experimentally investigate the existence and stability of such micrometer-scale droplets formed at air/solvent interfaces and the possible roles played by partial solubility of organic liquids in water and solvent migration in the lowering of the key air/water surface tension. Three solvents are studied: toluene, butyl acetate, and chloroform, using a technique to optically monitor both condensation and manual deposition of water microdroplets onto air/solvent surfaces. This demonstrates both the existence of stable water droplets and allows measurement of the contact angles at the solvent/water/air interface. Contact angles are shown to be independent of droplet size (diameters: 2–30 μm), ruling out a line tension stabilization mechanism for droplets of radii greater than 1 μm. The interfacial tensions of the deposited water droplets are independently measured using an equivalent macroscopic experiment, which yield results consistent with the partial miscibility of toluene and butyl acetate in water. A discrepancy is observed for chloroform, for which possible mechanisms are discussed.</p>https://authors.library.caltech.edu/records/j7cvr-cn316Spring constant calibration of atomic force microscope cantilevers of arbitrary shape
https://resolver.caltech.edu/CaltechAUTHORS:20130118-102544117
Year: 2012
DOI: 10.1063/1.4757398
The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)]10.1063/1.1150021 for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro- and nanomechanical systems in general.https://resolver.caltech.edu/CaltechAUTHORS:20130118-102544117Spring constant calibration of atomic force microscope cantilevers of arbitrary shape
https://authors.library.caltech.edu/records/a1mbp-anb98
Year: 2012
DOI: 10.1063/1.4757398
The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)]10.1063/1.1150021 for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro- and nanomechanical systems in general.https://authors.library.caltech.edu/records/a1mbp-anb98Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows
https://resolver.caltech.edu/CaltechAUTHORS:20121030-101034564
Year: 2012
DOI: 10.1017/jfm.2012.302
Kinetic theory provides a rigorous foundation for calculating the dynamics of gas flow at arbitrary degrees of rarefaction, with solutions of the Boltzmann equation requiring numerical methods in many cases of practical interest. Importantly, the near-continuum regime can be examined analytically using asymptotic techniques. These asymptotic analyses often assume steady flow, for which analytical slip models have been derived. Recently, developments in nanoscale fabrication have stimulated research into the study of oscillatory non-equilibrium flows, drawing into question the applicability of the steady flow assumption. In this article, we present a formal asymptotic analysis of the unsteady linearized Boltzmann–BGK equation, generalizing existing theory to the oscillatory (time-varying) case. We consider the near-continuum limit where the mean free path and oscillation frequency are small. The complete set of hydrodynamic equations and associated boundary conditions are derived for arbitrary Stokes number and to second order in the Knudsen number. The first-order steady boundary conditions for the velocity and temperature are found to be unaffected by oscillatory flow. In contrast, the second-order boundary conditions are modified relative to the steady case, except for the velocity component tangential to the solid wall. Application of this general asymptotic theory is explored for the oscillatory thermal creep problem, for which unsteady effects manifest themselves at leading order.https://resolver.caltech.edu/CaltechAUTHORS:20121030-101034564Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows
https://authors.library.caltech.edu/records/x7rqy-1yn62
Year: 2012
DOI: 10.1017/jfm.2012.302
AbstractKinetic theory provides a rigorous foundation for calculating the dynamics of gas flow at arbitrary degrees of rarefaction, with solutions of the Boltzmann equation requiring numerical methods in many cases of practical interest. Importantly, the near-continuum regime can be examined analytically using asymptotic techniques. These asymptotic analyses often assume steady flow, for which analytical slip models have been derived. Recently, developments in nanoscale fabrication have stimulated research into the study of oscillatory non-equilibrium flows, drawing into question the applicability of the steady flow assumption. In this article, we present a formal asymptotic analysis of the unsteady linearized Boltzmann–BGK equation, generalizing existing theory to the oscillatory (time-varying) case. We consider the near-continuum limit where the mean free path and oscillation frequency are small. The complete set of hydrodynamic equations and associated boundary conditions are derived for arbitrary Stokes number and to second order in the Knudsen number. The first-order steady boundary conditions for the velocity and temperature are found to be unaffected by oscillatory flow. In contrast, the second-order boundary conditions are modified relative to the steady case, except for the velocity component tangential to the solid wall. Application of this general asymptotic theory is explored for the oscillatory thermal creep problem, for which unsteady effects manifest themselves at leading order.https://authors.library.caltech.edu/records/x7rqy-1yn62Nonlinearity in nanomechanical cantilevers
https://authors.library.caltech.edu/records/fsm16-gw054
Year: 2013
DOI: 10.1103/physrevb.87.024304
<p>Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.</p>https://authors.library.caltech.edu/records/fsm16-gw054Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads
https://authors.library.caltech.edu/records/ty45m-r8843
Year: 2013
DOI: 10.1063/1.4772745
Buckling of elastic structures can occur for loads well within the proportionality limit of their constituent materials. Given the ubiquity of beams and plates in engineering design and application, their buckling behavior has been widely studied. However, buckling of a cantilever plate is yet to be investigated, despite the widespread use of cantilevers in modern technological developments. Here, we address this issue and theoretically study the buckling behavior of a cantilever plate that is uniformly loaded in its plane. Applications of this fundamental problem include loading due to uniform temperature and surface stress changes. This is achieved using a scaling analysis and full three-dimensional numerical solution, leading to explicit formulas for the buckling loads. Unusually, we observe buckling for both tensile and compressive loads, the physical mechanisms for which are explored. We also examine the practical implications of these findings to modern developments in ultra sensitive micro- and nano-cantilever sensors, such as those composed of silicon nitride and graphene.https://authors.library.caltech.edu/records/ty45m-r8843Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads
https://resolver.caltech.edu/CaltechAUTHORS:20130226-095102405
Year: 2013
DOI: 10.1063/1.4772745
Buckling of elastic structures can occur for loads well within the proportionality limit of their constituent materials. Given the ubiquity of beams and plates in engineering design and application, their buckling behavior has been widely studied. However, buckling of a cantilever plate is yet to be investigated, despite the widespread use of cantilevers in modern technological developments. Here, we address this issue and theoretically study the buckling behavior of a cantilever plate that is uniformly loaded in its plane. Applications of this fundamental problem include loading due to uniform temperature and surface stress changes. This is achieved using a scaling analysis and full three-dimensional numerical solution, leading to explicit formulas for the buckling loads. Unusually, we observe buckling for both tensile and compressive loads, the physical mechanisms for which are explored. We also examine the practical implications of these findings to modern developments in ultra sensitive micro- and nano-cantilever sensors, such as those composed of silicon nitride and graphene.https://resolver.caltech.edu/CaltechAUTHORS:20130226-095102405Nonlinearity in nanomechanical cantilevers
https://resolver.caltech.edu/CaltechAUTHORS:20130221-084718989
Year: 2013
DOI: 10.1103/PhysRevB.87.024304
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.https://resolver.caltech.edu/CaltechAUTHORS:20130221-084718989Nonlinear Mode-Coupling in Nanomechanical Systems
https://resolver.caltech.edu/CaltechAUTHORS:20130520-112316098
Year: 2013
DOI: 10.1021/nl400070e
PMCID: PMC3839314
Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement.https://resolver.caltech.edu/CaltechAUTHORS:20130520-112316098Nanomechanical Torsional Resonators for Frequency-Shift Infrared Thermal Sensing
https://resolver.caltech.edu/CaltechAUTHORS:20130521-115710439
Year: 2013
DOI: 10.1021/nl304687p
We investigate use of nanomechanical torsional resonators for frequency-shift-based infrared (IR) thermal sensing. Nanoscale torsion rods, ~1 μm long and 50–100 nm in diameter, provide both extraordinary thermal isolation and excellent angular displacement and torque sensitivities, of order ~10^(–7) rad·Hz^(–1/2) and 10^(–22) (N·m) Hz^(–1/2), respectively. Furthermore, these nanorods act as linear torsional springs, yielding a maximum angular displacement of 3.6° and a dynamic range of over 100 dB; this exceeds the performance of flexural modes by as much as 5 orders of magnitude. These attributes lead to superior noise performance for torsional-mode sensing. We demonstrate the operational principles of torsional-mode IR detection, attaining an uncooled noise equivalent temperature difference (NETD) of 390 mK. By modeling the fundamental noise processes, we project that further reduction of device size can significantly improve thermal responsivity; a room-temperature NETD below 10 mK appears feasible.https://resolver.caltech.edu/CaltechAUTHORS:20130521-115710439Nonlinear Mode-Coupling in Nanomechanical Systems
https://authors.library.caltech.edu/records/37p69-2v105
Year: 2013
DOI: 10.1021/nl400070e
<p>Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement.</p>https://authors.library.caltech.edu/records/37p69-2v105Nanomechanical Torsional Resonators for Frequency-Shift Infrared Thermal Sensing
https://authors.library.caltech.edu/records/qjtnf-yps85
Year: 2013
DOI: 10.1021/nl304687p
<p>We investigate use of nanomechanical torsional resonators for frequency-shift-based infrared (IR) thermal sensing. Nanoscale torsion rods, ∼1 μm long and 50–100 nm in diameter, provide both extraordinary thermal isolation and excellent angular displacement and torque sensitivities, of order ∼10⁻⁷ rad·Hz^(–1/2) and ∼10⁻²² (N·m) Hz^(–1/2), respectively. Furthermore, these nanorods act as linear torsional springs, yielding a maximum angular displacement of 3.6° and a dynamic range of over 100 dB; this exceeds the performance of flexural modes by as much as 5 orders of magnitude. These attributes lead to superior noise performance for torsional-mode sensing. We demonstrate the operational principles of torsional-mode IR detection, attaining an uncooled noise equivalent temperature difference (NETD) of 390 mK. By modeling the fundamental noise processes, we project that further reduction of device size can significantly improve thermal responsivity; a room-temperature NETD below 10 mK appears feasible.</p><p> </p>https://authors.library.caltech.edu/records/qjtnf-yps85Vibration of Nanoparticles in Viscous Fluids
https://authors.library.caltech.edu/records/ec7bn-pf390
Year: 2013
DOI: 10.1021/jp401141b
<p>The dynamics of mechanical structures can be strongly affected by the fluid in which they are immersed. Ultrafast laser spectroscopy has recently provided fundamental insight into this fluid-structure interaction for nanoparticles immersed in a range of viscous fluids. In this article, we present results of a rigorous finite-element analysis and commensurate scaling theory that enable interpretation and analysis of these experiments, for the extensional vibrational modes of axisymmetric nanoparticles immersed in viscous fluids. Right circular, conical, and bipyramidal axisymmetric cylinder geometries are considered. We also develop an approximate analytical model that accounts for finite viscous penetration depth, which displays excellent agreement with finite-element results for particles of large aspect ratio. The finite-element results agree well with available measurements for particles in low-viscosity fluids such as water, but significant discrepancies exist at higher viscosities. Possible mechanisms for these differences are discussed.</p>https://authors.library.caltech.edu/records/ec7bn-pf390Vibration of Nanoparticles in Viscous Fluids
https://resolver.caltech.edu/CaltechAUTHORS:20130607-093933691
Year: 2013
DOI: 10.1021/jp401141b
The dynamics of mechanical structures can be strongly affected by the fluid in which they are immersed. Ultrafast laser spectroscopy has recently provided fundamental insight into this fluid-structure interaction for nanoparticles immersed in a range of viscous fluids. In this article, we present results of a rigorous finite-element analysis and commensurate scaling theory that enable interpretation and analysis of these experiments, for the extensional vibrational modes of axisymmetric nanoparticles immersed in viscous fluids. Right circular, conical, and bipyramidal axisymmetric cylinder geometries are considered. We also develop an approximate analytical model that accounts for finite viscous penetration depth, which displays excellent agreement with finite-element results for particles of large aspect ratio. The finite-element results agree well with available measurements for particles in low-viscosity fluids such as water, but significant discrepancies exist at higher viscosities. Possible mechanisms for these differences are discussed.https://resolver.caltech.edu/CaltechAUTHORS:20130607-093933691Self-Assembled Nanoparticle Drumhead Resonators
https://resolver.caltech.edu/CaltechAUTHORS:20130719-100148854
Year: 2013
DOI: 10.1021/nl401230z
The self-assembly of nanoscale structures from
functional nanoparticles has provided a powerful path to
developing devices with emergent properties from the bottomup.
Here we demonstrate that freestanding sheets selfassembled
from various nanoparticles form versatile nanomechanical
resonators in the megahertz frequency range.
Using spatially resolved laser-interferometry to measure
thermal vibrational spectra and image vibration modes, we
show that their dynamic behavior is in excellent agreement
with linear elastic response for prestressed drumheads of
negligible bending stiffness. Fabricated in a simple one-step
drying-mediated process, these resonators are highly robust and their inorganic−organic hybrid nature offers an extremely low
mass, low stiffness, and the potential to couple the intrinsic functionality of the nanoparticle building blocks to nanomechanical
motion.https://resolver.caltech.edu/CaltechAUTHORS:20130719-100148854Self-Assembled Nanoparticle Drumhead Resonators
https://authors.library.caltech.edu/records/2kv8j-7xg60
Year: 2013
DOI: 10.1021/nl401230z
<p>The self-assembly of nanoscale structures from functional nanoparticles has provided a powerful path to developing devices with emergent properties from the bottom-up. Here we demonstrate that freestanding sheets self-assembled from various nanoparticles form versatile nanomechanical resonators in the megahertz frequency range. Using spatially resolved laser-interferometry to measure thermal vibrational spectra and image vibration modes, we show that their dynamic behavior is in excellent agreement with linear elastic response for prestressed drumheads of negligible bending stiffness. Fabricated in a simple one-step drying-mediated process, these resonators are highly robust and their inorganic–organic hybrid nature offers an extremely low mass, low stiffness, and the potential to couple the intrinsic functionality of the nanoparticle building blocks to nanomechanical motion.</p>https://authors.library.caltech.edu/records/2kv8j-7xg60Damping of Acoustic Vibrations of Immobilized Single Gold Nanorods in Different Environments
https://resolver.caltech.edu/CaltechAUTHORS:20130813-095404253
Year: 2013
DOI: 10.1021/nl400876w
We present measurements of the acoustic vibrations of single gold nanorods deposited on a glass substrate immersed in air and water by ultrafast pump–probe spectroscopy. The nanorods display two vibration modes, the breathing mode and the extensional mode. The damping time of the two modes is influenced by the environment, and a reduction of the quality factor is observed when the particles are immersed in water. The reduced quality factor of the breathing mode is in good agreement with a model that takes into account viscous damping and radiation of sound waves into the medium. The extension mode, however, is heavily damped when the particles are immersed in water, which is attributed to hydrodynamic lubrication forces between the nanoparticle and the glass substrate. Our results identify a new mode of damping in supported nanoparticles and indicate that the immersion medium can have different effects on different modes of vibration.https://resolver.caltech.edu/CaltechAUTHORS:20130813-095404253Damping of Acoustic Vibrations of Immobilized Single Gold Nanorods in Different Environments
https://authors.library.caltech.edu/records/7xr5t-b8q80
Year: 2013
DOI: 10.1021/nl400876w
<p>We present measurements of the acoustic vibrations of single gold nanorods deposited on a glass substrate immersed in air and water by ultrafast pump–probe spectroscopy. The nanorods display two vibration modes, the breathing mode and the extensional mode. The damping time of the two modes is influenced by the environment, and a reduction of the quality factor is observed when the particles are immersed in water. The reduced quality factor of the breathing mode is in good agreement with a model that takes into account viscous damping and radiation of sound waves into the medium. The extension mode, however, is heavily damped when the particles are immersed in water, which is attributed to hydrodynamic lubrication forces between the nanoparticle and the glass substrate. Our results identify a new mode of damping in supported nanoparticles and indicate that the immersion medium can have different effects on different modes of vibration.</p>https://authors.library.caltech.edu/records/7xr5t-b8q80High frequency oscillatory flows in a slightly rarefied gas according to the Boltzmann–BGK equation
https://resolver.caltech.edu/CaltechAUTHORS:20131108-150149059
Year: 2013
DOI: 10.1017/jfm.2013.281
The Boltzmann equation provides a rigorous theoretical framework to study dilute gas flows at arbitrary degrees of rarefaction. Asymptotic methods have been applied to steady flows, enabling the development of analytical formulae. For unsteady (oscillatory) flows, two important limits have been studied: (i) at low oscillation frequency and small mean free path, slip models have been derived; and (ii) at high oscillation frequency and large mean free path, the leading-order dynamics are free-molecular. In this article, the complementary case of small mean free path and high oscillation frequency is examined in detail. All walls are solid and of arbitrary smooth shape. We perform a matched asymptotic expansion of the unsteady linearized Boltzmann–BGK equation in the small parameter ν/ω, where ν is the collision frequency of gas particles and ω is the characteristic oscillation frequency of the flow. Critically, an algebraic expression is derived for the perturbed mass distribution function throughout the bulk of the gas away from any walls, at all orders in the frequency ratio ν/ω. This is supplemented by a boundary layer correction defined by a set of first-order differential equations. This system is solved explicitly and in complete generality. We thus provide analytical expressions up to first order in the frequency ratio, for the density, temperature, mean velocity and stress tensor of the gas, in terms of the temperature and mean velocity of the wall, and the applied body force. In stark contrast to other asymptotic regimes, these explicit formulae eliminate the need to solve a differential equation for a body of arbitrary geometry. To illustrate the utility of these results, we study the oscillatory thermal creep problem for which we find a tangential boundary layer flow arises at first order in the frequency ratio.https://resolver.caltech.edu/CaltechAUTHORS:20131108-150149059High frequency oscillatory flows in a slightly rarefied gas according to the Boltzmann–BGK equation
https://authors.library.caltech.edu/records/b560e-chw08
Year: 2013
DOI: 10.1017/jfm.2013.281
<p>The Boltzmann equation provides a rigorous theoretical framework to study dilute gas flows at arbitrary degrees of rarefaction. Asymptotic methods have been applied to steady flows, enabling the development of analytical formulae. For unsteady (oscillatory) flows, two important limits have been studied: (i) at low oscillation frequency and small mean free path, slip models have been derived; and (ii) at high oscillation frequency and large mean free path, the leading-order dynamics are free-molecular. In this article, the complementary case of small mean free path and high oscillation frequency is examined in detail. All walls are solid and of arbitrary smooth shape. We perform a matched asymptotic expansion of the unsteady linearized Boltzmann–BGK equation in the small parameter <i>ν/ω</i>, where <i>ν</i> is the collision frequency of gas particles and <i>ω</i> is the characteristic oscillation frequency of the flow. Critically, an algebraic expression is derived for the perturbed mass distribution function throughout the bulk of the gas away from any walls, at all orders in the frequency ratio <i>ν/ω</i>. This is supplemented by a boundary layer correction defined by a set of first-order differential equations. This system is solved explicitly and in complete generality. We thus provide analytical expressions up to first order in the frequency ratio, for the density, temperature, mean velocity and stress tensor of the gas, in terms of the temperature and mean velocity of the wall, and the applied body force. In stark contrast to other asymptotic regimes, these explicit formulae eliminate the need to solve a differential equation for a body of arbitrary geometry. To illustrate the utility of these results, we study the oscillatory thermal creep problem for which we find a tangential boundary layer flow arises at first order in the frequency ratio.</p>https://authors.library.caltech.edu/records/b560e-chw08The dominant role of the solvent–water interface in water droplet templating of polymers
https://authors.library.caltech.edu/records/dwzxc-cqm63
Year: 2013
DOI: 10.1039/c3sm51452h
<p>We investigate the formation of microstructured polymer networks known as Breath Figure templated structures created by the presence of water vapour over evaporating polymer solutions. We use a highly controlled experimental approach to examine this dynamic and non-equilibrium process to uniquely compare pure solvent systems with polymer solutions and demonstrate using a combination of optical microscopy, focused ion-beam milling and SEM analysis that the porous polymer microstructure is completely controlled by the interfacial forces that exist between the water droplet and the solvent until a final drying dilation of the imprints. Water droplet contact angles are the same in the presence or absence of polymer and are independent of size for droplets above 5 μm. The polymer acts a spectator that serves to trap water droplets present at the air interface, and to transfer their shape into the polymer film. For the smallest pores, however, there are unexpected variations in the contact angle with pore size that are consistent with a possible contribution from line tension at these smaller dimensions.</p>https://authors.library.caltech.edu/records/dwzxc-cqm63Viscoelastic Flows in Simple Liquids Generated by Vibrating Nanostructures
https://authors.library.caltech.edu/records/1j7fz-pfr54
Year: 2013
DOI: 10.1103/physrevlett.111.244502
<p>Newtonian fluid mechanics, in which the shear stress is proportional to the strain rate, is synonymous with the flow of simple liquids such as water. We report the measurement and theoretical verification of non-Newtonian, viscoelastic flow phenomena produced by the high-frequency (20 GHz) vibration of gold nanoparticles immersed in water-glycerol mixtures. The observed viscoelasticity is not due to molecular confinement, but is a bulk continuum effect arising from the short time scale of vibration. This represents the first direct mechanical measurement of the intrinsic viscoelastic properties of simple bulk liquids, and opens a new paradigm for understanding extremely high frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.</p>https://authors.library.caltech.edu/records/1j7fz-pfr54Viscoelastic Flows in Simple Liquids Generated by Vibrating Nanostructures
https://resolver.caltech.edu/CaltechAUTHORS:20140117-084526325
Year: 2013
DOI: 10.1103/PhysRevLett.111.244502
Newtonian fluid mechanics, in which the shear stress is proportional to the strain rate, is synonymous with the flow of simple liquids such as water. We report the measurement and theoretical verification of non-Newtonian, viscoelastic flow phenomena produced by the high-frequency (20 GHz) vibration of gold nanoparticles immersed in water-glycerol mixtures. The observed viscoelasticity is not due to molecular confinement, but is a bulk continuum effect arising from the short time scale of vibration. This represents the first direct mechanical measurement of the intrinsic viscoelastic properties of simple bulk liquids, and opens a new paradigm for understanding extremely high frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.https://resolver.caltech.edu/CaltechAUTHORS:20140117-084526325Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators
https://resolver.caltech.edu/CaltechAUTHORS:20140403-162009111
Year: 2014
DOI: 10.1103/PhysRevLett.112.015501
Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P_0 is α times that of a scaled-up microscale resonator at a reduced pressure α P_0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.https://resolver.caltech.edu/CaltechAUTHORS:20140403-162009111Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators
https://authors.library.caltech.edu/records/hsjsh-c9317
Year: 2014
DOI: 10.1103/physrevlett.112.015501
<p>Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure <i>P</i>₀ is α times that of a scaled-up microscale resonator at a reduced pressure <i>α P</i>₀, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.</p>https://authors.library.caltech.edu/records/hsjsh-c9317Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope
https://authors.library.caltech.edu/records/qsbmq-8ws24
Year: 2014
DOI: 10.1063/1.4864086
Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noise spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.https://authors.library.caltech.edu/records/qsbmq-8ws24Probing Silver Deposition on Single Gold Nanorods by Their Acoustic Vibrations
https://authors.library.caltech.edu/records/aqthc-d2p68
Year: 2014
DOI: 10.1021/nl404304h
<p>Acoustic vibrations of single gold nanorods coated with silver were investigated. We used single-particle pump–probe spectroscopy to monitor the silver deposition through the particle vibrations. Two vibration modes, the breathing mode and extensional mode, are observed, and the vibrational frequencies are measured as functions of the amount of silver deposited on single gold nanorods. The breathing mode frequency was found to decrease with silver deposition, while the extensional mode frequency was almost constant for silver shells up to 6 nm. The frequency changes agree with a model based on continuum mechanics and on the assumption of a uniform silver coating. The quality factors for the breathing mode and the extensional mode are hardly affected by silver deposition, indicating that the introduced interface between gold and silver contributes negligibly to the damping of the particle vibrations. Finally, we demonstrated that an atomic layer of silver can be detected using the particle acoustic vibrations.</p>https://authors.library.caltech.edu/records/aqthc-d2p68Poisson's ratio of individual metal nanowires
https://authors.library.caltech.edu/records/g9b2y-9v245
Year: 2014
DOI: 10.1038/ncomms5336
PMCID: PMC4102115
<p>The measurement of Poisson's ratio of nanomaterials is extremely challenging. Here we report a lateral atomic force microscope experimental method to electromechanically measure the Poisson's ratio and gauge factor of individual nanowires. Under elastic loading conditions we monitor the four-point resistance of individual metallic nanowires as a function of strain and different levels of electrical stress. We determine the gauge factor of individual wires and directly measure the Poisson's ratio using a model that is independently validated for macroscopic wires. For macroscopic wires and nickel nanowires we find Poisson's ratios that closely correspond to bulk values, whereas for silver nanowires significant deviations from the bulk silver value are observed. Moreover, repeated measurements on individual silver nanowires at different levels of mechanical and electrical stress yield a small spread in Poisson ratio, with a range of mean values for different wires, all of which are distinct from the bulk value.</p>https://authors.library.caltech.edu/records/g9b2y-9v245Publisher's Note: Lattice Boltzmann method for linear oscillatory noncontinuum flows
https://authors.library.caltech.edu/records/ws0t5-3w219
Year: 2014
DOI: 10.1103/PhysRevE.90.039901
<p>Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.</p>https://authors.library.caltech.edu/records/ws0t5-3w219Note: Calibration of atomic force microscope cantilevers using only their resonant frequency and quality factor
https://authors.library.caltech.edu/records/bjv9d-tsw57
Year: 2014
DOI: 10.1063/1.4901227
A simplified method for calibrating atomic force microscope cantilevers was recently proposed by Sader et al. [Rev. Sci. Instrum. 83, 103705 (2012); Sec. III D] that relies solely on the resonant frequency and quality factor of the cantilever in fluid (typically air). This method eliminates the need to measure the hydrodynamic function of the cantilever, which can be time consuming given the wide range of cantilevers now available. Using laser Doppler vibrometry, we rigorously assess the accuracy of this method for a series of commercially available cantilevers and explore its performance under non-ideal conditions. This shows that the simplified method is highly accurate and can be easily implemented to perform fast, robust, and non-invasive spring constant calibration.https://authors.library.caltech.edu/records/bjv9d-tsw57Effect of cantilever geometry on the optical lever sensitivities and thermal noise method of the atomic force microscope
https://authors.library.caltech.edu/records/gxmqe-ycv78
Year: 2014
DOI: 10.1063/1.4900864
Calibration of the optical lever sensitivities of atomic force microscope (AFM) cantilevers is especially important for determining the force in AFM measurements. These sensitivities depend critically on the cantilever mode used and are known to differ for static and dynamic measurements. Here, we calculate the ratio of the dynamic and static sensitivities for several common AFM cantilevers, whose shapes vary considerably, and experimentally verify these results. The dynamic-to-static optical lever sensitivity ratio is found to range from 1.09 to 1.41 for the cantilevers studied – in stark contrast to the constant value of 1.09 used widely in current calibration studies. This analysis shows that accuracy of the thermal noise method for the static spring constant is strongly dependent on cantilever geometry – neglect of these dynamic-to-static factors can induce errors exceeding 100%. We also discuss a simple experimental approach to non-invasively and simultaneously determine the dynamic and static spring constants and optical lever sensitivities of cantilevers of arbitrary shape, which is applicable to all AFM platforms that have the thermal noise method for spring constant calibration.https://authors.library.caltech.edu/records/gxmqe-ycv78Frequency-domain Monte Carlo method for linear oscillatory gas flows
https://authors.library.caltech.edu/records/ghnyw-k2b36
Year: 2015
DOI: 10.1016/j.jcp.2014.12.036
<p>Gas flows generated by resonating <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/nanoscale">nanoscale</a> devices inherently occur in the non-continuum, low <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/mach-number">Mach number</a> regime. Numerical simulations of such flows using the standard direct simulation Monte Carlo (DSMC) method are hindered by high statistical noise, which has motivated the development of several alternate Monte Carlo methods for low Mach number flows. Here, we present a frequency-domain low Mach number <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/monte-carlo-method">Monte Carlo method</a> based on the Boltzmann–BGK equation, for the simulation of oscillatory gas flows. This circumvents the need for temporal simulations, as is currently required, and provides direct access to both amplitude and phase information using a pseudo-steady algorithm. The proposed method is validated for oscillatory <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/couette-flow">Couette flow</a> and the flow generated by an oscillating sphere. Good agreement is found with an existing time-domain method and accurate numerical solutions of the Boltzmann–BGK equation. Analysis of these simulations using a rigorous statistical approach shows that the frequency-domain method provides a significant improvement in computational speed.</p>https://authors.library.caltech.edu/records/ghnyw-k2b36Constitutive models for linear compressible viscoelastic flows of simple liquids at nanometer length scales
https://authors.library.caltech.edu/records/damrt-8zr68
Year: 2015
DOI: 10.1063/1.4919620
Simple bulk liquids such as water are commonly assumed to be Newtonian. While this assumption holds widely, the fluid-structure interaction of mechanical devices at nanometer scales can probe the intrinsic molecular relaxation processes in a surrounding liquid. This was recently demonstrated through measurement of the high frequency (20 GHz) linear mechanical vibrations of bipyramidal nanoparticles in simple liquids [Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. In this article, we review and critically assess the available constitutive equations for compressible viscoelastic flows in their linear limits—such models are required for analysis of the above-mentioned measurements. We show that previous models, with the exception of a very recent proposal, do not reproduce the required response at high frequency. We explain the physical origin of this recent model and show that it recovers all required features of a linear viscoelastic flow. This constitutive equation thus provides a rigorous foundation for the analysis of vibrating nanostructures in simple liquids. The utility of this model is demonstrated by solving the fluid-structure interaction of two common problems: (1) a sphere executing radial oscillations in liquid, which depends strongly on the liquid compressibility and (2) the extensional mode vibration of bipyramidal nanoparticles in liquid, where the effects of liquid compressibility are negligible. This highlights the importance of shear and compressional relaxation processes, as a function of flow geometry, and the impact of the shear and bulk viscosities on nanometer scale flows.https://authors.library.caltech.edu/records/damrt-8zr68Note: Improved calibration of atomic force microscope cantilevers using multiple reference cantilevers
https://authors.library.caltech.edu/records/2e7jm-6h561
Year: 2015
DOI: 10.1063/1.4921192
Overall precision of the simplified calibration method in J. E. Sader et al., Rev. Sci. Instrum. 83, 103705 (2012), Sec. III D, is dominated by the spring constant of the reference cantilever. The question arises: How does one take measurements from multiple reference cantilevers, and combine these results, to improve uncertainty of the reference cantilever's spring constant and hence the overall precision of the method? This question is addressed in this note. Its answer enables manufacturers to specify of a single set of data for the spring constant, resonant frequency, and quality factor, from measurements on multiple reference cantilevers. With this data set, users can trivially calibrate cantilevers of the same type.https://authors.library.caltech.edu/records/2e7jm-6h561Tuning the acoustic frequency of a gold nanodisk through its adhesion layer
https://authors.library.caltech.edu/records/aa6cx-hpn66
Year: 2015
DOI: 10.1038/ncomms8022
<p>To fabricate robust metallic nanostructures with top-down patterning methods such as electron-beam lithography, an initial nanometer-scale layer of a second metal is deposited to promote adhesion of the metal of interest. However, how this nanoscale layer affects the mechanical properties of the nanostructure and how adhesion layer thickness controls the binding strength to the substrate are still open questions. Here we use ultrafast laser pulses to impulsively launch acoustic phonons in single gold nanodisks with variable titanium layer thicknesses, and observe an increase in phonon frequencies as a thicker adhesion layer facilitates stronger binding to the glass substrate. In addition to an all-optical interrogation of nanoscale mechanical properties, our results show that the adhesion layer can be used to controllably modify the acoustic phonon modes of a gold nanodisk. This direct coupling between optically excited plasmon modes and phonon modes can be exploited for a variety of emerging optomechanical applications.</p>https://authors.library.caltech.edu/records/aa6cx-hpn66Compressible Viscoelastic Liquid Effects Generated by the Breathing Modes of Isolated Metal Nanowires
https://authors.library.caltech.edu/records/3t14g-t2m68
Year: 2015
DOI: 10.1021/acs.nanolett.5b00853
<p>Transient absorption microscopy is used to examine the breathing modes of single gold nanowires in highly viscous liquids. By performing measurements on the same wire in air and liquid, the damping contribution from the liquid can be separated from the intrinsic damping of the nanowire. The results show that viscous liquids strongly reduce the vibrational lifetimes but not to the extent predicted by standard models for nanomaterial–liquid interactions. To explain these results a general theory for compressible viscoelastic fluid–structure interactions is developed. The theory results are in good agreement with experiment, which confirms that compressible non-Newtonian flow phenomena are important for vibrating nanostructures. This is the first theoretical study and experimental measurement of the compressible viscoelastic properties of simple liquids.</p>https://authors.library.caltech.edu/records/3t14g-t2m68Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer
https://authors.library.caltech.edu/records/mdr3w-ray15
Year: 2015
DOI: 10.1103/physreve.92.013307
<p>Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.</p>https://authors.library.caltech.edu/records/mdr3w-ray15Frequency-domain deviational Monte Carlo method for linear oscillatory gas flows
https://authors.library.caltech.edu/records/cgv6z-m1x28
Year: 2015
DOI: 10.1063/1.4932108
Oscillatory non-continuum low Mach number gas flows are often generated by nanomechanical devices in ambient conditions. These flows can be simulated using a range of particle based Monte Carlo techniques, which in their original form operate exclusively in the time-domain. Recently, a frequency-domain weight-based Monte Carlo method was proposed [D. R. Ladiges and J. E. Sader, "Frequency-domain Monte Carlo method for linear oscillatory gas flows," J. Comput. Phys. 284, 351–366 (2015)] that exhibits superior statistical convergence when simulating oscillatory flows. This previous method used the Bhatnagar-Gross-Krook (BGK) kinetic model and contains a "virtual-time" variable to maintain the inherent time-marching nature of existing Monte Carlo algorithms. Here, we propose an alternative frequency-domain deviational Monte Carlo method that facilitates the use of a wider range of molecular models and more efficient collision/relaxation operators. We demonstrate this method with oscillatory Couette flow and the flow generated by an oscillating sphere, utilizing both the BGK kinetic model and hard sphere particles. We also discuss how oscillatory motion of arbitrary time-dependence can be simulated using computationally efficient parallelization. As in the weight-based method, this deviational frequency-domain Monte Carlo method is shown to offer improved computational speed compared to the equivalent time-domain technique.https://authors.library.caltech.edu/records/cgv6z-m1x28Viscoelasticity of glycerol at ultra-high frequencies investigated via molecular dynamics simulations
https://authors.library.caltech.edu/records/03kzw-98583
Year: 2016
DOI: 10.1063/1.4940146
<p>We present a calculation of the shear and longitudinal moduli of glycerol in the gigahertz frequency regime and temperature range between 273 K and 323 K using classical molecular dynamics simulations. The full frequency spectra of shear and longitudinal moduli of glycerol between 0.5 GHz and 100 GHz at room temperature are computed, which was not previously available from experiments or simulations. We also demonstrate that the temperature dependence of the real parts of the shear and longitudinal moduli agrees well with available experimental counterparts obtained via time-domain Brillouin scattering. This work provides new insights into the response of molecular liquids to ultra-high frequency excitation and opens a new pathway for studying simple liquids at high frequencies and strain rates.</p>https://authors.library.caltech.edu/records/03kzw-98583Hollow Microtube Resonators via Silicon Self-Assembly toward Subattogram Mass Sensing Applications
https://authors.library.caltech.edu/records/bvt1a-5af46
Year: 2016
DOI: 10.1021/acs.nanolett.5b03703
<p>Fluidic resonators with integrated microchannels (hollow resonators) are attractive for mass, density, and volume measurements of single micro/nanoparticles and cells, yet their widespread use is limited by the complexity of their fabrication. Here we report a simple and cost-effective approach for fabricating hollow microtube resonators. A prestructured silicon wafer is annealed at high temperature under a controlled atmosphere to form self-assembled buried cavities. The interiors of these cavities are oxidized to produce thin oxide tubes, following which the surrounding silicon material is selectively etched away to suspend the oxide tubes. This simple three-step process easily produces hollow microtube resonators. We report another innovation in the capping glass wafer where we integrate fluidic access channels and getter materials along with residual gas suction channels. Combined together, only five photolithographic steps and one bonding step are required to fabricate vacuum-packaged hollow microtube resonators that exhibit quality factors as high as ∼13 000. We take one step further to explore additionally attractive features including the ability to tune the device responsivity, changing the resonator material, and scaling down the resonator size. The resonator wall thickness of ∼120 nm and the channel hydraulic diameter of ∼60 nm are demonstrated solely by conventional microfabrication approaches. The unique characteristics of this new fabrication process facilitate the widespread use of hollow microtube resonators, their translation between diverse research fields, and the production of commercially viable devices.</p>https://authors.library.caltech.edu/records/bvt1a-5af46Taming Self-Organization Dynamics to Dramatically Control Porous Architectures
https://authors.library.caltech.edu/records/keptc-rd917
Year: 2016
DOI: 10.1021/acsnano.5b06082
<p>We demonstrate templating of functional materials with unexpected and intricate micro- and nanostructures by controlling the condensation, packing, and evaporation of water droplets on a polymer solution. Spontaneous evaporation of a polymer solution induces cooling of the liquid surface and water microdroplet condensation from the ambient vapor. These droplets pack together and act as a template to imprint an entangled polymer film. This breath figure (BF) phenomenon is an example of self-organization that involves the long-range ordering of droplets. Equilibrium-based analysis provides many insights into contact angles and drop stability of individual drops, but the BF phenomenon remains poorly understood thus far, preventing translation to real applications. Here we investigate the dynamics of this phenomenon to separate out the competing influences and then introduce a modulation scheme to ultimately manipulate the water vapor–liquid equilibrium independently from the solvent evaporation. This approach to BF control provides insights into the mechanism, a rationale for microstructure design, and evidence for the benefits of dynamical control of self-organization systems. We finally present dramatically different porous architectures from this approach reminiscent of microscale Petri dishes, conical flasks, and test tubes.</p>https://authors.library.caltech.edu/records/keptc-rd917Large-amplitude flapping of an inverted flag in a uniform steady flow – a vortex-induced vibration
https://resolver.caltech.edu/CaltechAUTHORS:20160422-150517531
Year: 2016
DOI: 10.1017/jfm.2016.139
The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped end, have been studied widely and provide insight into the stability of flags and biological phenomena. Recent measurements by Kim et al. (J. Fluid Mech., vol. 736, 2013, R1) show that reversing the sheet's orientation, with the flow impinging on its free edge, dramatically alters its dynamics. In contrast to the conventional flag, which exhibits (small-amplitude) flutter above a critical flow speed, the inverted flag displays large-amplitude flapping over a finite band of flow speeds. The physical mechanisms giving rise to this flapping phenomenon are currently unknown. In this article, we use a combination of mathematical theory, scaling analysis and measurement to establish that this large-amplitude flapping motion is a vortex-induced vibration. Onset of flapping is shown mathematically to be due to divergence instability, verifying previous speculation based on a two-point measurement. Reducing the sheet's aspect ratio (height/length) increases the critical flow speed for divergence and ultimately eliminates flapping. The flapping motion is associated with a separated flow – detailed measurements and scaling analysis show that it exhibits the required features of a vortex-induced vibration. Flapping is found to be periodic predominantly, with a transition to chaos as flow speed increases. Cessation of flapping occurs at higher speeds – increased damping reduces the flow speed range where flapping is observed, as required. These findings have implications for leaf motion and other biological processes, such as the dynamics of hair follicles, because they also can present an inverted-flag configuration.https://resolver.caltech.edu/CaltechAUTHORS:20160422-150517531Photoinduced Electron Transfer in the Strong Coupling Regime: Waveguide–Plasmon Polaritons
https://authors.library.caltech.edu/records/dea0w-kx768
Year: 2016
DOI: 10.1021/acs.nanolett.6b00310
<p>Reversible exchange of photons between a material and an optical cavity can lead to the formation of hybrid light–matter states where material properties such as the work function [Hutchison et al. Adv. Mater. 2013, <i>25</i>, 2481−2485], chemical reactivity [Hutchison et al. Angew. Chem., Int. Ed. 2012, <i>51</i>, 1592−1596], ultrafast energy relaxation [Salomon et al. Angew. Chem., Int. Ed. 2009, <i>48</i>, 8748−8751; Gomez et al. J. Phys. Chem. B 2013, <i>117</i>, 4340–4346], and electrical conductivity [Orgiu et al. Nat. Mater. 2015, <i>14</i>, 1123−1129] of matter differ significantly to those of the same material in the absence of strong interactions with the electromagnetic fields. Here we show that strong light–matter coupling between confined photons on a semiconductor waveguide and localized plasmon resonances on metal nanowires modifies the efficiency of the photoinduced charge-transfer rate of plasmonic derived (hot) electrons into accepting states in the semiconductor material. Ultrafast spectroscopy measurements reveal a strong correlation between the amplitude of the transient signals, attributed to electrons residing in the semiconductor and the hybridization of waveguide and plasmon excitations.</p>https://authors.library.caltech.edu/records/dea0w-kx768Sphere oscillating in a rarefied gas
https://authors.library.caltech.edu/records/q9x5d-26240
Year: 2016
DOI: 10.1017/jfm.2016.143
Flow generated by an oscillating sphere in a quiescent fluid is a classical problem in fluid mechanics whose solution is used ubiquitously. Miniaturisation of mechanical devices to small scales and their operation at high frequencies in fluid, which is common in modern nanomechanical systems, can preclude the use of the unsteady Stokes equation for continuum flow. Here, we explore the combined effects of gas rarefaction and unsteady motion of a sphere, within the framework of the unsteady linearised Boltzmann–BGK (Bhatnagar–Gross–Krook) equation. This equation is solved using the method of characteristics, and the resulting solution is valid for any oscillation frequency and arbitrary degrees of gas rarefaction. The resulting force provides the non-continuum counterpart to the (continuum) unsteady Stokes drag on a sphere. In contrast to the Stokes solution, where the flow is isothermal, non-continuum effects lead to a temperature jump at the sphere surface and non-isothermal flow. Unsteady effects and heat transport are found to mix strongly, leading to marked differences relative to the steady case. The solution to this canonical flow problem is expected to be of significant practical value in many applications, including the optical trapping of nanoparticles and the design and application of nanoelectromechanical systems. It also provides a benchmark for computational and approximate methods of solution for the Boltzmann equation.https://authors.library.caltech.edu/records/q9x5d-26240Flow generated by oscillatory uniform heating of a rarefied gas in a channel
https://authors.library.caltech.edu/records/7br3c-yhg34
Year: 2016
DOI: 10.1017/jfm.2016.398
Kinetic theory provides a rigorous foundation to explore the unsteady (oscillatory) flow of a dilute gas, which is often generated by nanomechanical devices. Recently, formal asymptotic analyses of unsteady (oscillatory) flows at small Knudsen numbers have been derived from the linearised Boltzmann–Bhatnagar–Gross–Krook (Boltzmann–BGK) equation, in both the low- and high-frequency limits (Nassios & Sader, J. Fluid Mech., vol. 708, 2012, pp. 197–249 and vol. 729, 2013, pp. 1–46; Takata & Hattori, J. Stat. Phys., vol. 147, 2012, pp. 1182–1215). These asymptotic theories predict that unsteadiness can couple strongly with heat transport to dramatically modify the overall gas flow. Here, we study the gas flow generated between two parallel plane walls whose temperatures vary sinusoidally in time. Predictions of the asymptotic theories are compared to direct numerical solutions, which are valid for all Knudsen numbers and normalised frequencies. Excellent agreement is observed, providing the first numerical validation of the asymptotic theories. The asymptotic analyses also provide critical insight into the physical mechanisms underlying these flow phenomena, establishing that mass conservation (not momentum or energy) drives the flows – this explains the identical results obtained using different previous theoretical treatments of these linear thermal flows. This study highlights the unique gas flows that can be generated under oscillatory non-isothermal conditions and the importance of both numerical and asymptotic analyses in explaining the underlying mechanisms.https://authors.library.caltech.edu/records/7br3c-yhg34A virtual instrument to standardise the calibration of atomic force microscope cantilevers
https://authors.library.caltech.edu/records/q0a0x-9xw97
Year: 2016
DOI: 10.1063/1.4962866
Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This calibration is performed without reference to a global standard, hindering the robust comparison of force measurements reported by different laboratories. Here, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others—standardising AFM force measurements—and simultaneously enabling non-invasive calibration of AFM cantilevers of any geometry. This global calibration initiative requires no additional instrumentation or data processing on the part of the user. It utilises a single website where users upload currently available data. A proof-of-principle demonstration of this initiative is presented using measured data from five independent laboratories across three countries, which also allows for an assessment of current calibration.https://authors.library.caltech.edu/records/q0a0x-9xw97Resonant frequencies of cantilevered sheets under various clamping configurations immersed in fluid
https://authors.library.caltech.edu/records/pc59b-pyb23
Year: 2016
DOI: 10.1063/1.4964428
Immersion of an elastic cantilevered sheet in a fluid can strongly affect its dynamic response. While significant effort has been expended in studying slender cantilevered sheets, the behavior of wide sheets has received far less attention. Here we study the clamping configuration's effect on the vibrational dynamics of wide cantilever sheets of macroscopic size, which naturally generate inviscid flows. Three practically relevant clamping configurations are investigated: clamping into (i) a thin and rigid horizontal plate, (ii) a rigid vertical wall, and (iii) a rigid line. These are found to produce different resonant frequencies, as expected from the nonlocal flows generated by these cantilevers. The resulting formulas are joined to an existing expression for slender cantilevers, leading to a universal formula valid for all aspect ratios (cantilever length/width) and mode numbers; accuracy is verified using finite element analysis. This study is expected to be of practical value in a host of engineering applications, such as those that utilize fluid-structure interactions for energy harvesting and aerodynamic design.https://authors.library.caltech.edu/records/pc59b-pyb23Stability of slender inverted flags and rods in uniform steady flow
https://resolver.caltech.edu/CaltechAUTHORS:20170105-165851728
Year: 2016
DOI: 10.1017/jfm.2016.691
Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an 'inverted flag'. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.https://resolver.caltech.edu/CaltechAUTHORS:20170105-165851728Position and mode dependent optical detection back-action in cantilever beam resonators
https://authors.library.caltech.edu/records/3qrk0-y8j91
Year: 2017
DOI: 10.1088/1361-6439/aa591e
<p>Optical detection back-action in cantilever resonant or static detection presents a challenge when striving for state-of-the-art performance. The origin and possible routes for minimizing optical back-action have received little attention in literature. Here, we investigate the position and mode dependent optical back-action on cantilever beam resonators. A high power heating laser (100 <i>µ</i>W) is scanned across a silicon nitride cantilever while its effect on the first three resonance modes is detected via a low-power readout laser (1 <i>µ</i>W) positioned at the cantilever tip. We find that the measured effect of back-action is not only dependent on position but also the shape of the resonance mode. Relevant silicon nitride material parameters are extracted by fitting finite element (FE) simulations to the temperature-dependent frequency response of the first three modes. In a second round of simulations, using the extracted parameters, we successfully fit the FEM results with the measured mode and position dependent back-action. From the simulations, we can conclude that the observed frequency tuning is due to temperature induced changes in stress. Effects of changes in material properties and dimensions are negligible. Finally, different routes for minimizing the effect of this optical detection back-action are described, allowing further improvements of cantilever-based sensing in general.</p>https://authors.library.caltech.edu/records/3qrk0-y8j91Optomechanics of Single Aluminum Nanodisks
https://authors.library.caltech.edu/records/ddz1h-rd622
Year: 2017
DOI: 10.1021/acs.nanolett.7b00333
<p>Aluminum nanostructures support tunable surface plasmon resonances and have become an alternative to gold nanoparticles. Whereas gold is the most-studied plasmonic material, aluminum has the advantage of high earth abundance and hence low cost. In addition to understanding the size and shape tunability of the plasmon resonance, the fundamental relaxation processes in aluminum nanostructures after photoexcitation must be understood to take full advantage of applications such as photocatalysis and photodetection. In this work, we investigate the relaxation following ultrafast pulsed excitation and the launching of acoustic vibrations in individual aluminum nanodisks, using single-particle transient extinction spectroscopy. We find that the transient extinction signal can be assigned to a thermal relaxation of the photoexcited electrons and phonons. The ultrafast heating-induced launching of in-plane acoustic vibrations reveals moderate binding to the glass substrate and is affected by the native aluminum oxide layer. Finally, we compare the behavior of aluminum nanodisks to that of similarly prepared and sized gold nanodisks.</p>https://authors.library.caltech.edu/records/ddz1h-rd622Material characterisation of nanowires with intrinsic stress
https://authors.library.caltech.edu/records/ry15a-m5a58
Year: 2017
DOI: 10.1088/1361-6528/aa7c31
<p>When fabricating nanowires (NWs) in a doubly-clamped beam configuration it is possible for a residual axial stress to be generated. Here, we show that material characterisation of metal and semiconductor NWs subjected to residual axial stress can be problematic. Benchmark measurements of the Young's modulus of NWs are performed by sectioning a doubly-clamped NW into two cantilevered wires, eliminating residual axial stress. Use of models for doubly-clamped beams that incorporate the effects of residual stress are found to lead to ambiguity in the extracted Young's modulus as a function of displacement fit range, even for NWs with no residual stress. This is due to coupling of bending and axial stress effects at small displacements, and the limited displacement range of force curves prior to fracture or plastic deformation. This study highlights the importance of fabricating metal and semiconductor NWs that exhibit little or no residual axial stress for materials characterisation.</p>https://authors.library.caltech.edu/records/ry15a-m5a58Modelling apical columnar epithelium mechanics from circumferential contractile fibres
https://authors.library.caltech.edu/records/tfgrx-5xc78
Year: 2017
DOI: 10.1007/s10237-017-0905-7
<p>Simple columnar epithelia are formed by individual epithelial cells connecting together to form single cell high sheets. They are a main component of many important body tissues and are heavily involved in both normal and cancerous cell activities. Prior experimental observations have identified a series of contractile fibres around the circumference of a cross section located in the upper (apical) region of each cell. While other potential mechanisms have been identified in both the experimental and theoretical literature, these circumferential fibres are considered to be the most likely mechanism controlling movement of this cross section. Here, we investigated the impact of circumferential contractile fibres on movement of the cross section by creating an alternate model where movement is driven from circumferential contractile fibres, without any other potential mechanisms. In this model, we utilised a circumferential contractile fibre representation based on investigations into the movement of contractile fibres as an individual system, treated circumferential fibres as a series of units, and matched our model simulation to experimental geometries. By testing against laser ablation datasets sourced from existing literature, we found that circumferential fibres can reproduce the majority of cross-sectional movements. We also investigated model predictions related to various aspects of cross-sectional movement, providing insights into epithelium mechanics and demonstrating the usefulness of our modelling approach.</p>https://authors.library.caltech.edu/records/tfgrx-5xc78Vibrational coupling in plasmonic molecules
https://authors.library.caltech.edu/records/abr9n-0cy86
Year: 2017
DOI: 10.1073/pnas.1712418114
PMCID: PMC5676925
<p>Plasmon hybridization theory, inspired by molecular orbital theory, has been extremely successful in describing the near-field coupling in clusters of plasmonic nanoparticles, also known as plasmonic molecules. However, the vibrational modes of plasmonic molecules have been virtually unexplored. By designing precisely configured plasmonic molecules of varying complexity and probing them at the individual plasmonic molecule level, intramolecular coupling of acoustic modes, mediated by the underlying substrate, is observed. The strength of this coupling can be manipulated through the configuration of the plasmonic molecules. Surprisingly, classical continuum elastic theory fails to account for the experimental trends, which are well described by a simple coupled oscillator picture that assumes the vibrational coupling is mediated by coherent phonons with low energies. These findings provide a route to the systematic optical control of the gigahertz response of metallic nanostructures, opening the door to new optomechanical device strategies.</p>https://authors.library.caltech.edu/records/abr9n-0cy86Mass spectrometry using nanomechanical systems: beyond the point-mass approximation
https://resolver.caltech.edu/CaltechAUTHORS:20180129-091128726
Year: 2018
DOI: 10.1021/acs.nanolett.7b04301
The mass measurement of single molecules, in real time, is performed routinely using resonant nanomechanical devices. This approach models the molecules as point particles. A recent development now allows the spatial extent (and, indeed, image) of the adsorbate to be characterized using multimode measurements (Hanay, M. S., Nature Nanotechnol., 10, 2015, pp 339−344). This "inertial imaging" capability is achieved through virtual re-engineering of the resonator's vibrating modes, by linear superposition of their measured frequency shifts. Here, we present a complementary and simplified methodology for the analysis of these inertial imaging measurements that exhibits similar performance while streamlining implementation. This development, together with the software that we provide, enables the broad implementation of inertial imaging that opens the door to a range of novel characterization studies of nanoscale adsorbates.https://resolver.caltech.edu/CaltechAUTHORS:20180129-091128726Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows
https://authors.library.caltech.edu/records/qccrz-9d896
Year: 2018
DOI: 10.1103/physrevfluids.3.053401
<p>Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, <a href="http://dx.doi.org/10.1007/BF01007482">J. Stat. Phys. <strong>1</strong>, 297 (1969)</a>] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as <i>Mathematica</i> or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.</p>https://authors.library.caltech.edu/records/qccrz-9d896Wrinkling of Transversely Loaded Spinning Membranes
https://resolver.caltech.edu/CaltechAUTHORS:20180214-081512136
Year: 2018
DOI: 10.1016/j.ijsolstr.2018.01.031
Spinning membrane structures provide a mass-efficient solution for large space apertures. This paper presents a detailed study of the wrinkling of spinning circular membranes loaded by transverse, uniform loads. Experimental measurements of the angular velocities at which different membranes become wrinkled, and of the wrinkling mode transitions that occur upon spin down of the membrane, are presented. A theoretical formulation of the problem is presented, from which pairs of critical angular velocities and critical transverse loads are determined. A general stability chart is presented, which identifies the stability limits in terms of only two dimensionless parameters, for any membrane. The transition between bending dominated behavior and in-plane dominated behavior is identified, and it is shown that in the bending-dominated case the critical non-dimensional transverse load is independent from the non-dimensional angular velocity.https://resolver.caltech.edu/CaltechAUTHORS:20180214-081512136Polycrystallinity of Lithographically Fabricated Plasmonic Nanostructures Dominates Their Acoustic Vibrational Damping
https://authors.library.caltech.edu/records/1p4eg-ckv75
Year: 2018
DOI: 10.1021/acs.nanolett.8b00559
<p>The study of acoustic vibrations in nanoparticles provides unique and unparalleled insight into their mechanical properties. Electron-beam lithography of nanostructures allows precise manipulation of their acoustic vibration frequencies through control of nanoscale morphology. However, the dissipation of acoustic vibrations in this important class of nanostructures has not yet been examined. Here we report, using single-particle ultrafast transient extinction spectroscopy, the intrinsic damping dynamics in lithographically fabricated plasmonic nanostructures. We find that in stark contrast to chemically synthesized, monocrystalline nanoparticles, acoustic energy dissipation in lithographically fabricated nanostructures is solely dominated by intrinsic damping. A quality factor of <i>Q</i> = 11.3 ± 2.5 is observed for all 147 nanostructures, regardless of size, geometry, frequency, surface adhesion, and mode. This result indicates that the complex Young's modulus of this material is independent of frequency with its imaginary component being approximately 11 times smaller than its real part. Substrate-mediated acoustic vibration damping is strongly suppressed, despite strong binding between the glass substrate and Au nanostructures. We anticipate that these results, characterizing the optomechanical properties of lithographically fabricated metal nanostructures, will help inform their design for applications such as photoacoustic imaging agents, high-frequency resonators, and ultrafast optical switches.</p>https://authors.library.caltech.edu/records/1p4eg-ckv75When Can the Elastic Properties of Simple Liquids Be Probed Using High-Frequency Nanoparticle Vibrations?
https://authors.library.caltech.edu/records/bqm0p-mxj10
Year: 2018
DOI: 10.1021/acs.jpcc.7b09951
<p>Recent measurements on the gigahertz vibration of nanoparticles immersed in simple liquids, such as glycerol, show that the liquid's viscoelastic properties can significantly affect the nanoparticle's mechanical response. Here, we theoretically explore the high-frequency (elastic) limit of this phenomenon where the characteristic time scale for molecular relaxation in the liquid far exceeds the nanoparticle's vibration period. Paradoxically, we find that the effects of liquid elasticity (and viscosity) may not be visible in the nanoparticle's dynamic response in this high-frequency elastic limit—the response being identical to that of a macroscopic resonator in an inviscid fluid. A comprehensive mechanistic study reveals that the conditions for this unusual behavior are strongly dependent on the nanoparticle's vibration mode and the liquid's properties. A judicious choice of vibration mode is essential for interrogating the viscoelastic properties of simple liquids. Our findings explain recent measurements on nanowires and nanorods immersed in highly viscous liquids.</p>https://authors.library.caltech.edu/records/bqm0p-mxj10On the measurement of relaxation times of acoustic vibrations in metal nanowires
https://authors.library.caltech.edu/records/4nt0k-r9m50
Year: 2018
DOI: 10.1039/c8cp03230k
<p>The mechanical resonances of metal nanostructures are strongly affected by their environment. In this paper the way the breathing modes of single metal nanowires are damped by liquids with different viscosities was studied by ultrafast pump–probe microscopy experiments. Both nanowires supported on a glass substrate and nanowires suspended over trenches were investigated. The measured quality factors for liquid damping for the suspended nanowires are in good agreement with continuum mechanics calculations for an inviscid fluid that assume continuity in stress and displacement at the nanowire–liquid interface. This shows that liquid damping is controlled by radiation of sound waves into the medium. For the nanowires on the glass surface the quality factors for liquid damping are approximately 60% higher than those for the suspended nanowires. This is attributed to a shadowing effect. The nanowires in our measurements have pentagonal cross-sections. This produces two different breathing modes and also means that one of the faces for the supported nanowires is blocked by the substrate, which reduces the amount of damping from the liquid. Comparing the supported and suspended nanowires also allows us to estimate the effect of the substrate on the acoustic mode damping. We find that the substrate has a weak effect, which is attributed to poor mechanical contact between the nanowires and the substrate.</p>https://authors.library.caltech.edu/records/4nt0k-r9m50Solvent-Engineered Stress in Nanoscale Materials
https://authors.library.caltech.edu/records/t5phz-cwe03
Year: 2018
DOI: 10.1021/acsami.8b17201
<p>Nanoscale materials are frequently coated with surface stabilization layers during growth that prevent flocculation in solution and facilitate processing technologies such as ink-jet device printing. Here, we show that few-nanometer-thick stabilization layers typically used swell in the presence of certain solvents and impart significant stresses to the nanomaterial that remains even after the solvent has evaporated. Solvent swelling of the surface layer dramatically enhances nanomaterial–substrate adhesion via the collapse of the stabilization layer during solvent evaporation, preventing stress relaxation. We demonstrate the stress modulation of Ag, Au, and Si nanowires functionalised with surface polymers and surfactant layers and detect strain levels between 0.1 and 0.6% using atomic force microscopy mechanical measurement and Raman spectroscopy. Dry-transferred nanowires exhibit poor adhesion and show no evidence of incorporated stress but become stressed immediately following solvent exposure. Strain engineering is demonstrated by coating nanowires with few-nanometer-thick solvent-responsive polymer layers.</p>https://authors.library.caltech.edu/records/t5phz-cwe03Global modes and nonlinear analysis of inverted-flag flapping
https://authors.library.caltech.edu/records/nq2j6-93t97
Year: 2018
DOI: 10.1017/jfm.2018.728
<p>An inverted flag has its trailing edge clamped and exhibits dynamics distinct from that of a conventional flag, whose leading edge is restrained. We perform nonlinear simulations and a global stability analysis of the inverted-flag system for a range of Reynolds numbers, flag masses and stiffnesses. Our global stability analysis is based on a linearisation of the fully coupled fluid–structure system of equations. The calculated equilibria are steady-state solutions of the fully coupled nonlinear equations. By implementing this approach, we (i) explore the mechanisms that initiate flapping, (ii) study the role of vorticity generation and vortex-induced vibration (VIV) in large-amplitude flapping and (iii) characterise the chaotic flapping regime. For point (i), we identify a deformed-equilibrium state and show through a global stability analysis that the onset of small-deflection flapping – where the oscillation amplitude is significantly smaller than in large-amplitude flapping – is due to a supercritical Hopf bifurcation. For large-amplitude flapping, point (ii), we confirm the arguments of Sader et al. (J. Fluid Mech., vol. 793, 2016a) that classical VIV exists when the flag is sufficiently light with respect to the fluid. We also show that for heavier flags, large-amplitude flapping persists (even for Reynolds numbers <50 ) and is not classical VIV. Finally, with respect to point (iii), chaotic flapping has been observed experimentally for Reynolds numbers of O(10⁴) , and here we show that chaos also persists at a moderate Reynolds number of 200. We characterise this chaotic regime and calculate its strange attractor, whose structure is controlled by the above-mentioned deformed equilibria and is similar to a Lorenz attractor.</p>https://authors.library.caltech.edu/records/nq2j6-93t97Global modes and nonlinear analysis of inverted-flag flapping
https://resolver.caltech.edu/CaltechAUTHORS:20180122-091425148
Year: 2018
DOI: 10.1017/jfm.2018.728
An inverted flag has its trailing edge clamped and exhibits dynamics distinct from that of a conventional flag, whose leading edge is restrained. We perform nonlinear simulations and a global stability analysis of the inverted-flag system for a range of Reynolds numbers, flag masses and stiffnesses. Our global stability analysis is based on a linearisation of the fully coupled fluid–structure system of equations. The calculated equilibria are steady-state solutions of the fully coupled nonlinear equations. By implementing this approach, we (i) explore the mechanisms that initiate flapping, (ii) study the role of vorticity generation and vortex-induced vibration (VIV) in large-amplitude flapping and (iii) characterise the chaotic flapping regime. For point (i), we identify a deformed-equilibrium state and show through a global stability analysis that the onset of small-deflection flapping – where the oscillation amplitude is significantly smaller than in large-amplitude flapping – is due to a supercritical Hopf bifurcation. For large-amplitude flapping, point (ii), we confirm the arguments of Sader et al. (J. Fluid Mech., vol. 793, 2016a) that classical VIV exists when the flag is sufficiently light with respect to the fluid. We also show that for heavier flags, large-amplitude flapping persists (even for Reynolds numbers < 50) and is not classical VIV. Finally, with respect to point (iii), chaotic flapping has been observed experimentally for Reynolds numbers of O(10^4) , and here we show that chaos also persists at a moderate Reynolds number of 200. We characterise this chaotic regime and calculate its strange attractor, whose structure is controlled by the above-mentioned deformed equilibria and is similar to a Lorenz attractor.https://resolver.caltech.edu/CaltechAUTHORS:20180122-091425148Publisher Correction: Interatomic force laws that evade dynamic measurement
https://authors.library.caltech.edu/records/hvc1a-v9b02
Year: 2019
DOI: 10.1038/s41565-019-0364-7
<p>Measurement of the force between two atoms is performed routinely with the atomic force microscope. The shape of this interatomic force law is now found to directly regulate this capability: rapidly varying interatomic force laws, which are common in nature, can corrupt their own measurement.</p>https://authors.library.caltech.edu/records/hvc1a-v9b02Large-Area Nanofabrication of Partially Embedded Nanostructures for Enhanced Plasmonic Hot-Carrier Extraction
https://authors.library.caltech.edu/records/r6nmg-jym17
Year: 2019
DOI: 10.1021/acsanm.8b01988
<p>When plasmonic nanoparticles are coupled with semiconductors, highly energetic hot carriers can be extracted from the metal–semiconductor interface for various applications in light energy conversion. However, the current quantum yields for hot-electron extraction are generally low. An approach for increasing the extraction efficiency consists of maximizing the contact area between the surface of the metal nanostructure and the electron-accepting material. In this work, we developed an innovative, simple, and scalable fabrication technique that partially embeds colloidal plasmonic nanostructures within a semiconductor TiO₂ layer without utilizing any complex top-down nanofabrication method. The successful embedding is confirmed by scanning electron microscopy and atomic force microscopy imaging. Using visible-pump, near-IR probe transient absorption spectroscopy, we also provide evidence that the increase in the surface contact area between the nanostructures and the electron-accepting material leads to an increase in the amount of hot-electron injection into the TiO₂ layer.</p>https://authors.library.caltech.edu/records/r6nmg-jym17Strong vibrational coupling in room temperature plasmonic resonators
https://authors.library.caltech.edu/records/m9mv9-cbt13
Year: 2019
DOI: 10.1038/s41467-019-09594-z
PMCID: PMC6449381
<p>Strong vibrational coupling has been realized in a variety of mechanical systems. However, there have been no experimental observations of strong coupling of the acoustic modes of plasmonic nanostructures, due to rapid energy dissipation in these systems. Here we realized strong vibrational coupling in ultra-high frequency plasmonic nanoresonators by increasing the vibrational quality factors by an order of magnitude. We achieved the highest frequency quality factor products of <i>f</i> × <i>Q</i> = 1.0 × 10¹³ Hz for the fundamental mechanical modes, which exceeds the value of 0.6 × 10¹³ Hz required for ground state cooling. Avoided crossing was observed between vibrational modes of two plasmonic nanoresonators with a coupling rate of <i>g</i> = 7.5 ± 1.2 GHz, an order of magnitude larger than the dissipation rates. The intermodal strong coupling was consistent with theoretical calculations using a coupled oscillator model. Our results enabled a platform for future observation and control of the quantum behavior of phonon modes in metallic nanoparticles.</p>https://authors.library.caltech.edu/records/m9mv9-cbt13Shear-induced buckling of a thin elastic disk undergoing spin-up
https://resolver.caltech.edu/CaltechAUTHORS:20190208-125359102
Year: 2019
DOI: 10.1016/j.ijsolstr.2019.01.038
The stability of a spinning thin elastic disk has been widely studied due to its central importance in engineering. While the plastic deformation and failure of an annular disk mounted on a rigid and accelerating circular shaft are well understood, shear-induced elastic buckling of the disk due to this 'spin-up' is yet to be reported. Here, we calculate this buckling behavior within the framework of the Föppl–von Kármán equations and give numerical results as a function of the disk's aspect ratio (inner-to-outer radius) and Poisson's ratio. This shows that shear-induced elastic buckling can dominate plastic failure in many cases of practical interest. When combined with existing theory for plastic failure, the results of the present study provide foundation results for a multitude of applications including the characterization of accelerating compact disks and deployment of space sails by centrifugal forces.https://resolver.caltech.edu/CaltechAUTHORS:20190208-125359102Mass measurement of graphene using quartz crystal microbalances
https://authors.library.caltech.edu/records/g06rg-1z769
Year: 2019
DOI: 10.1063/1.5111086
Current wafer-scale fabrication methods for graphene-based electronics and sensors involve the transfer of single-layer graphene by a support polymer. This often leaves some polymer residue on the graphene, which can strongly impact its electronic, thermal, and mechanical resonance properties. To assess the cleanliness of graphene fabrication methods, it is thus of considerable interest to quantify the amount of contamination on top of the graphene. Here, we present a methodology for the direct measurement of the mass of the graphene sheet using quartz crystal microbalances (QCMs). By monitoring the QCM resonance frequency during removal of graphene in an oxygen plasma, the total mass of the graphene and contamination is determined with sub-graphene-monolayer accuracy. Since the etch-rate of the contamination is higher than that of graphene, quantitative measurements of the mass of contaminants below, on top, and between graphene layers are obtained. We find that polymer-based dry transfer methods can increase the mass of a graphene sheet by a factor of 10. The presented mass measurement method is conceptually straightforward to interpret and can be used for standardized testing of graphene transfer procedures in order to improve the quality of graphene devices in future applications.https://authors.library.caltech.edu/records/g06rg-1z769What is the oscillation amplitude of a vibrating cantilever?
https://authors.library.caltech.edu/records/49kf5-89a76
Year: 2019
DOI: 10.1063/1.5115768
Resonant amplification of vibrational amplitude underpins the application of nanomechanical sensors. For cantilever sensors, this amplification is widely reported to be equal to the sensor's quality factor, which strongly underestimates its true value. Here, we present a simple analytical formula for this amplification factor, valid for three-dimensional resonators of arbitrary shape, that will find utility in practice.https://authors.library.caltech.edu/records/49kf5-89a76Large-scale parallelization of nanomechanical mass spectrometry with weakly-coupled resonators
https://authors.library.caltech.edu/records/fb0ha-j1218
Year: 2019
DOI: 10.1038/s41467-019-11647-2
PMCID: PMC6733932
<p>Nanomechanical mass spectrometry is a recent technological breakthrough that enables the real-time analysis of single molecules. In contraposition to its extreme mass sensitivity is a limited capture cross-section that can hinder measurements in a practical setting. Here we show that weak-coupling between devices in resonator arrays can be used in nanomechanical mass spectrometry to parallelize the measurement. This coupling gives rise to asymmetric amplitude peaks in the vibrational response of a single nanomechanical resonator of the array, which coincide with the natural frequencies of all other resonators in the same array. A rigorous theoretical model is derived that explains the physical mechanisms and describes the practical features of this parallelization. We demonstrate the significance of this parallelization through inertial imaging of analytes adsorbed to all resonators of an array, with the possibility of simultaneously detecting resonators placed at distances a hundred times larger than their own physical size.</p>https://authors.library.caltech.edu/records/fb0ha-j1218Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow
https://resolver.caltech.edu/CaltechAUTHORS:20181210-110613444
Year: 2019
DOI: 10.1017/jfm.2019.474
The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the 'inverted flag' configuration – a cantilevered elastic sheet aligned with the flow impinging on its free edge – has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag's morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial 'petiole' (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag's dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces, for which an analytical theory is also derived, in addition to increasing the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.https://resolver.caltech.edu/CaltechAUTHORS:20181210-110613444Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow
https://authors.library.caltech.edu/records/24vvw-k1f65
Year: 2019
DOI: 10.1017/jfm.2019.474
The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the 'inverted flag' configuration – a cantilevered elastic sheet aligned with the flow impinging on its free edge – has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag's morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial 'petiole' (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag's dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces, for which an analytical theory is also derived, in addition to increasing the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.https://authors.library.caltech.edu/records/24vvw-k1f65Viscoelasticity of liquid water investigated using molecular dynamics simulations
https://authors.library.caltech.edu/records/pwscq-vhc73
Year: 2019
DOI: 10.1103/physrevfluids.4.123302
<p>Real liquids exhibit a viscoelastic response when excited mechanically to deform at sufficiently high frequency. We use classical nonequilibrium molecular dynamics simulations to calculate the linear viscoelastic response of extended simple point charge (SPC/E) water under both shear and elongation, for frequencies between 50 GHz and 10 THz and temperatures spanning the liquid phase of water at atmospheric pressure. These simulations are validated using equilibrium simulations that make use of Green-Kubo relations. Data up to and including 2 THz is fit to a single relaxation time linear Maxwell model, to facilitate comparison with reported experiments. We find that the resulting elastic moduli agree well with measurement, but this is not the case for the viscous moduli. This data also obeys a generalized Cauchy relation, implying that the elastic response of SPC/E water is dominated by central forces. This opens a pathway toward development of a simplified, molecular elastic water model for viscoelastic flows at high frequency. Furthermore, both elastic and loss moduli obey the time temperature superposition principle for frequencies up to 2 THz; an anomaly is observed above 2 THz, pointing to different physics. This behavior remains to be observed experimentally.</p>https://authors.library.caltech.edu/records/pwscq-vhc73Acoustic flows in a slightly rarefied gas
https://authors.library.caltech.edu/records/q0r69-phf18
Year: 2020
DOI: 10.1103/physrevfluids.5.043401
<p>The Boltzmann equation provides a rigorous description of gas flows at all degrees of gas rarefaction. Asymptotic analyses of this equation yield valuable insight into the physical mechanisms underlying gas flows. In this article, we report an asymptotic analysis of the Boltzmann-BGK equation for a slightly rarefied gas when the acoustic wavelength is comparable to the macroscopic characteristic length scale of the flow. This is performed using a three-way matched asymptotic expansion, which accounts for the Knudsen layer, the viscous layer, and the outer Hilbert region—these are separated by asymptotically disparate length scales. Transport equations and boundary conditions for these regions are derived. The utility of this theory is demonstrated by application to three problems: (1) flow generated by uniformly heating two plates, (2) oscillatory thermal creep induced between two plates, and (3) the flow generated by an oscillating sphere. Comparisons to numerical simulations of the Boltzmann-BGK equation and previous asymptotic theories (for long wavelength) are performed. The present theory is distinct from previous asymptotic analyses that implicitly assume long or short acoustic wavelength. This theory is expected to find application in the design and characterization of nanoelectromechanical devices, which often generate acoustic oscillatory flows of a rarefied nature.</p>https://authors.library.caltech.edu/records/q0r69-phf18Acoustic Vibrations of Al Nanocrystals: Size, Shape, and Crystallinity Revealed by Single-Particle Transient Extinction Spectroscopy
https://authors.library.caltech.edu/records/x2w2n-3x696
Year: 2020
DOI: 10.1021/acs.jpca.0c01190
<p>Acoustic vibrations in plasmonic nanoparticles, monitored by an all-optical means, have attracted significant increasing interest because they provide unique insight into the mechanical properties of these metallic nanostructures. Al nanostructures are a recently emerging alternative to noble metal nanoparticles, because their broad wavelength tunability and high natural abundance make them ideal for many potential applications. Here, we investigate the acoustic vibrations of individual Al nanocrystals using a combination of electron microscopy and single-particle transient extinction spectroscopy, made possible with a low-pulse energy, high sensitivity, and probe-wavelength-tunable, single-particle transient extinction microscope. For chemically synthesized, faceted Al nanocrystals, the observed vibration frequency scales with the inverse particle diameter. In contrast, triangularly shaped Al nanocrystals support two distinct frequencies, corresponding to their in- and out-of-plane breathing modes. Unlike ensemble measurements, which measure average properties, measuring the damping time of the acoustic vibrations for individual particles enables us to investigate variations of the quality factor on the particle-to-particle level. Surprisingly, we find a large variation in quality factors even for nanocrystals of similar size and shape. This observed heterogeneity appears to result from substantially varying degrees of nanoparticle crystallinity even for chemically synthesized nanocrystals.</p>https://authors.library.caltech.edu/records/x2w2n-3x696Sound dissipation from plate-type resonators excited in non-conventional transversal modes in liquids
https://authors.library.caltech.edu/records/fxz11-vsv13
Year: 2020
DOI: 10.1088/1361-6439/ab8bc9
<p>Vibrational modes of higher order in micromachined resonators exhibit low damping in liquid environments, which facilitates accurate sensing even in highly viscous liquids. A steady increment in mode order, however, results in sound dissipation effects at a critical mode number n<i>(crit), which drastically increases damping in the system. Basic understanding in the emerging of sound dissipation in micromachined resonators is therefore of utmost importance, when an application of higher mode orders is targeted. For that reason, we experimentally investigated in this paper the appearance of sound dissipation in higher order non-conventional vibrational modes in MEMS plate resonators in liquids. The results are compared to those of an analytical model and of finite element method analyses. Micromechanical piezoelectric resonators were fabricated and characterized in sample fluids with a dynamic viscosity μ</i>(fluid) ranging from 1 to 5 mPa s and density values ρ(fluid) ranging from 0.774 up to 0.835 kg l⁻¹. Quality factors up to 333 are obtained for the eighth mode order in model solution with a dynamic viscosity of 1 mPa s. By monitoring the resonance and damping characteristics as a function of mode order, sound dissipation effects occur, observed by the detection of increased damping, starting at mode number n = 8, which is in good agreement to the predictions of an analytical model and to finite element method simulations. At the critical mode number n crit, a reduction in quality factor up to 50% is measured. The results show a direct correlation of n crit and the density of the fluid, which agrees to theory. The lowest value of 8 for n(crit) is obtained in a sample liquid with the lowest density value of 0.774 kg l⁻¹, followed by n_(crit) = 9 in a sample liquid with ρ_(fluid) = 0.782 kg l−1 and n(crit) = 10 in a sample liquid with ρ_(fluid) = 0.835 kg l⁻¹. These findings are of particular interest for sensing applications in low dense liquids, as sound dissipation effects emerge even at lower mode numbers.</p>https://authors.library.caltech.edu/records/fxz11-vsv13The automation of robust interatomic-force measurements
https://authors.library.caltech.edu/records/q1sw2-g2250
Year: 2020
DOI: 10.1063/5.0018599
Interatomic-force measurements are regularly performed using frequency-modulation atomic force microscopy. This requires conversion of the observed shift in the resonant frequency of a force-sensing cantilever to the actual force experienced by its tip. Recently, Sader et al. [Nat. Nanotechnol. 13, 1088 (2018)] showed that this force conversion can be unreliable and proposed the inflection point test to identify valid and robust force data. Efficient and user-friendly algorithms are required for its routine practical implementation, which currently do not exist. Here, we (1) advance the theoretical framework of the inflection point test, (2) develop the required efficient algorithms for its complete automation, and (3) demonstrate the utility of this automation by studying two experimental datasets, in ultrahigh vacuum and liquid. The principal outcome of this report is the development of user-friendly software that integrates this automation with a standard force conversion methodology. This software provides the enabling technology for practitioners to now seamlessly perform robust nanoscale and interatomic-force measurements.https://authors.library.caltech.edu/records/q1sw2-g2250On the starting vortex generated by a translating and rotating flat plate
https://authors.library.caltech.edu/records/def7e-1r693
Year: 2021
DOI: 10.1017/jfm.2020.762
<p>We consider the trailing-edge vortex produced in an inviscid fluid by the start-up motion of a two-dimensional flat plate. A general starting motion is studied that includes the initial angle-of-attack of the plate (which may be zero), individual time power laws for plate translational and rotational speeds and the pivot position for plate rotation. A vortex-sheet representation for a start-up separated flow at the trailing edge is developed whose time-wise evolution is described by a Birkhoff–Rott equation coupled to an appropriate Kutta condition. This description includes convection by the outer flow, rotation and vortex-image self-induction. It admits a power-law similarity solution for the (small-time) primitive vortex, leading to an equation set where each term carries its own time-wise power-law factor. A set of four general plate motions is defined. Dominant-balance analysis of this set leads to discovery of three distinct start-up vortex-structure types that form the basis for all vortex motion. The properties of each type are developed in detail for some special cases. Numerical and analytical solutions are described and transition between solution types is discussed. Singular and degenerate vortex behaviour is discovered which may be due to the absence of fluid viscosity. An interesting case is start-up motion with zero initial angle of attack coupled to power-law plate rotation for which time-series examples are given that can be compared to high Reynolds number viscous flows.</p>https://authors.library.caltech.edu/records/def7e-1r693Acoustic Vibrations and Energy Dissipation Mechanisms for Lithographically Fabricated Plasmonic Nanostructures Revealed by Single-Particle Transient Extinction Spectroscopy
https://authors.library.caltech.edu/records/bphcy-m7w61
Year: 2021
DOI: 10.1021/acs.jpcc.0c09782
<p>Acoustic vibrations in plasmonic nanostructures provide deep insight into mechanical properties at the nanoscale for potential applications including optomechanical devices. Lithographic fabrication of plasmonic nanostructures allows precise control over shape and size as well as position. Here, we present a summary of our recent ultrafast studies of lithographically fabricated Au and Al nanostructures using single-particle transient extinction spectroscopy to measure the size- and shape-dependent acoustic frequencies and homogeneous damping times. Electron-beam lithography coupling with single-particle measurements necessitate the presence of a substrate, which we found to cause a blue shift in the acoustic vibration frequencies. This frequency shift enables the determination of the binding strength between Au nanostructures and the substrate. The substrate furthermore facilitates vibrational coupling between adjacent Au nanostructures. Electron-beam lithography also makes it possible to explore other plasmonic metals such as Al, which as the Earth's most abundant metal creates a sustainable pathway toward applications. We compared the ultrafast relaxation dynamics and acoustic properties of Al nanodisks to similar Au nanostructures. For both Au and Al nanostructures, we found an acoustic vibration quality factor which we ascribed to internal defects in the polycrystalline nanostructures that dominate the energy dissipation pathway. These findings provide significant insight into the optomechanical properties of nanostructures fabricated by electron-beam lithography.</p>https://authors.library.caltech.edu/records/bphcy-m7w61Dynamics of an inverted cantilever plate at moderate angle of attack
https://authors.library.caltech.edu/records/fca3f-yfd90
Year: 2021
DOI: 10.1017/jfm.2020.922
<p>The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle ((α ≤ 30°) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The dynamics are shown to differ significantly from the zero-angle-of-attack case, commonly called the inverted-flag configuration. Four distinct dynamical regimes arise at non-zero angles: a small oscillation around a small-deflection equilibrium (deformed regime), a small-amplitude flapping motion, a large-amplitude flapping motion and a small oscillation around a large-deflection equilibrium (deflected regime). The small- and large-amplitude flapping motions are shown to be produced by different physical mechanisms. The small-amplitude flapping motion appears gradually as the flow speed is increased and is consistent with a limit-cycle oscillation caused by the quasi-steady fluid forcing. The large-amplitude flapping motion is observed to appear at a constant critical flow speed that is independent of angle of attack. Its characteristics match those of the large-amplitude vortex-induced vibration present at zero angle of attack. The flow speed at which the plate enters the deflected regime decreases linearly as the angle of attack is increased, causing the flapping motion to disappear for angles of attack greater than α ≈ 28°. Finally, the effect of aspect ratio on the plate dynamics is considered, with a plate of reduced aspect ratio being shown to lack a sharp distinction between flapping regimes for α > 8°.</p>https://authors.library.caltech.edu/records/fca3f-yfd90Viscoelasticity Enhances Nanometer-Scale Slip in Gigahertz-Frequency Liquid Flows
https://authors.library.caltech.edu/records/a51p6-9w474
Year: 2021
DOI: 10.1021/acs.jpclett.1c00600
<p>The interaction between flowing liquids and solid surfaces underpins many physical phenomena and technologies, such as the ability of an airfoil to generate lift and the mixing of liquids for industrial applications. These phenomena are often described using the Navier–Stokes equations and the no-slip boundary condition: the assumption that the liquid immediately adjacent to a solid surface does not move relative to the surface. Herein, we observe violation of the no-slip condition with strong enhancement of slip due to intrinsic viscoelasticity of the bulk liquid. This is achieved by measuring the 20 GHz acoustic vibrations of gold nanoparticles in glycerol/water mixtures, for which the underlying physics is explored using rigorous, theoretical models. The reported enhancement of slip revises current understanding of ultrafast liquid flows, with implications for technologies ranging from membrane filtration to nanofluidic devices and biomolecular sensing.</p>https://authors.library.caltech.edu/records/a51p6-9w474The impulsive swirl of a gas
https://authors.library.caltech.edu/records/k0gzp-07a70
Year: 2021
DOI: 10.1017/jfm.2020.1078
<p>The motion of a sphere in a viscous gas has been studied since the time of Sir George Gabriel Stokes who explored linear, steady and unsteady flows. While the unsteady Stokes equation is often used to calculate these flows, this continuum treatment cannot capture some key physical phenomena. This includes propulsion of a sphere by temperature gradients on its surface, without convection. Taguchi <i>et al.</i> (<i>J. Fluid Mech.</i>, 2021) now calculate the flow generated by the impulsive rotation of a sphere in a gas, a problem first proposed by Stokes, using the linearised Boltzmann-BGK (Bhatnagar, Gross, Krook) equation. This statistical mechanical approach naturally captures continuum through to collisionless flows; the latter occurs even when the gas mean free path is small. The heat flow generated by the sphere is also determined – a non-continuum effect – showing its direction reverses as the flow evolves. The predicted phenomena are yet to be observed in experiment.</p>https://authors.library.caltech.edu/records/k0gzp-07a70Measurement of Navier Slip on Individual Nanoparticles in Liquid
https://authors.library.caltech.edu/records/82yhx-qt426
Year: 2021
DOI: 10.1021/acs.nanolett.1c00603
<p>The Navier slip condition describes the motion of a liquid relative to a neighboring solid surface, with its characteristic Navier slip length being a constitutive property of the solid–liquid interface. Measurement of this slip length is complicated by its small magnitude, expected to be in the nanometer range based on molecular simulations. Here, we report an experimental technique that interrogates the Navier slip length on individual nanoparticles immersed in liquid with subnanometer precision. Proof-of-principle experiments on individual, citrate-stabilized, gold nanoparticles in water give a constant slip length of 2.7 ± 0.6 nm (95% C.I.), independent of particle size. Achieving this feature of size independence is central to any measurement of this constitutive property, which is facilitated through the use of individual particles of varying radii. This demonstration motivates studies that can now validate the wealth of existing molecular simulation data on slip.</p>https://authors.library.caltech.edu/records/82yhx-qt426Inertial and viscous flywheel sensing of nanoparticles
https://authors.library.caltech.edu/records/j5cjq-58676
Year: 2021
DOI: 10.1038/s41467-021-25266-3
PMCID: PMC8385060
<p>Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a 'viscous flywheel'. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.</p>https://authors.library.caltech.edu/records/j5cjq-58676Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit
https://authors.library.caltech.edu/records/hn64b-vvr54
Year: 2021
DOI: 10.1021/acs.nanolett.1c02237
PMCID: PMC8461654
<p>The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.</p>https://authors.library.caltech.edu/records/hn64b-vvr54Autonomous propulsion of nanorods trapped in an acoustic field
https://authors.library.caltech.edu/records/zeptx-skw51
Year: 2022
DOI: 10.1017/jfm.2021.1138
<p>In Collis, Chakraborty & Sader (<a href="https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/autonomous-propulsion-of-nanorods-trapped-in-an-acoustic-field-corrigendum/DBCD533A365349FB85B405586C24BADD#ref1">Reference Collis, Chakraborty and Sader2017</a>), the effect of Lagrangian motion of the particle on its propulsion velocity, Uₚᵣₒₚ was ignored and is now included. Qualitative features of the propulsion remain unchanged, while some quantitative changes arise. All symbols are as defined in Collis <i>et al.</i> (<a href="https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/autonomous-propulsion-of-nanorods-trapped-in-an-acoustic-field-corrigendum/DBCD533A365349FB85B405586C24BADD#ref1">Reference Collis, Chakraborty and Sader2017</a>), unless otherwise specified.</p>https://authors.library.caltech.edu/records/zeptx-skw51A layer of yield-stress material on a flat plate that moves suddenly
https://authors.library.caltech.edu/records/7ekva-wvf86
Year: 2022
DOI: 10.1017/jfm.2022.384
The flow of an unbounded Newtonian fluid above a flat solid plate, set into motion suddenly with uniform velocity, is a canonical problem investigated by Stokes (On the effect of the internal friction of fluids on the motion of pendulums, Trans. Camb. Phil. Soc., vol. 9, 1851) and Rayleigh (Lond. Edinb. Dubl. Philos. Mag. J. Sci., vol. 21, issue 126, 1911, pp. 697–711). We tackle the same problem but with the fluid replaced by a yield-stress material of finite height with a free surface; the latter ensures both yielded (fluid-like) and rigid behaviour. The interface between the yielded and rigid regions – the so-called 'yield surface' – always emerges from the plate at a rate faster than that for momentum diffusion. The rigid region, adjacent to the free surface, is accelerated by the constant yield stress acting at this yield surface. As the velocity of this region increases following start-up, its acceleration climaxes and subsequently diminishes. In this latter period, the thickness of the rigid region increases owing to relaxation of the velocity gradients and the stress. The yield surface eventually collides with the plate in finite time, after which the entire material moves in concert with the plate as a rigid body. Analytical and numerical results are presented that can form the basis for practical applications. This includes the development of a 'rheological microscope' to directly detect and measure the yield stress. The analysis focuses on exploring the flow physics of a Bingham material. This is shown to be similar to that of a general Herschel–Bulkley material with shear-thinning or shear-thickening rheology.https://authors.library.caltech.edu/records/7ekva-wvf86Optical measurement of the picosecond fluid mechanics in simple liquids generated by vibrating nanoparticles: a review
https://authors.library.caltech.edu/records/h1x7x-z9847
Year: 2022
DOI: 10.1088/1361-6633/ac8e82
<p>Standard continuum assumptions commonly used to describe the fluid mechanics of simple liquids have the potential to break down when considering flows at the nanometer scale. Two common assumptions for simple molecular liquids are that (1) they exhibit a Newtonian response, where the viscosity uniquely specifies the linear relationship between the stress and strain rate, and (2) the liquid moves in tandem with the solid at any solid–liquid interface, known as the no-slip condition. However, even simple molecular liquids can exhibit a non-Newtonian, viscoelastic response at the picosecond time scales that are characteristic of the motion of many nanoscale objects; this viscoelasticity arises because these time scales can be comparable to those of molecular relaxation in the liquid. In addition, even liquids that wet solid surfaces can exhibit nanometer-scale slip at those surfaces. It has recently become possible to interrogate the viscoelastic response of simple liquids and associated nanoscale slip using optical measurements of the mechanical vibrations of metal nanoparticles. Plasmon resonances in metal nanoparticles provide strong optical signals that can be accessed by several spectroscopies, most notably ultrafast transient-absorption spectroscopy. These spectroscopies have been used to measure the frequency and damping rate of acoustic oscillations in the nanoparticles, providing quantitative information about mechanical coupling and exchange of mechanical energy between the solid particle and its surrounding liquid. This information, in turn, has been used to elucidate the rheology of viscoelastic simple liquids at the nanoscale in terms of their constitutive relations, taking into account separate viscoelastic responses for both shear and compressible flows. The nanoparticle vibrations have also been used to provide quantitative measurements of slip lengths on the single-nanometer scale. Viscoelasticity has been shown to amplify nanoscale slip, illustrating the interplay between different aspects of the unconventional fluid dynamics of simple liquids at nanometer length scales and picosecond time scales.</p>https://authors.library.caltech.edu/records/h1x7x-z9847The dynamics of a rigid inverted flag
https://authors.library.caltech.edu/records/4djgk-6eb59
Year: 2022
DOI: 10.1017/jfm.2022.718
An 'inverted flag' – a flexible plate clamped at its trailing edge – undergoes large-amplitude flow-induced flapping when immersed in a uniform and steady flow. Here, we report direct numerical simulations of a related single degree-of-freedom mechanical system: a rigid plate attached at its trailing edge to a torsional spring. This system is termed a 'rigid inverted flag' and exhibits the dynamical states reported for the (flexible) inverted flag, with additional behaviour. This finding shows that the flapping dynamics of inverted flags is not reliant on their continuous flexibility, i.e. many degrees of freedom. The rigid inverted flag exhibits additional, novel states including a heteroclinic-type orbit that results in small-amplitude flapping, and a number of chaotic large-amplitude flapping regimes. We show that the various routes to chaos are driven by a series of periodic states, including at least two which are subharmonic. The instability and competition between these periodic states lead to chaos via type-I intermittency, mode competition and mode locking. The rigid inverted flag allows these periodic states and their subsequent interaction to be explained simply: they arise from an interaction between a preferred vortex shedding frequency and a single natural frequency of the structure. The dynamics of rigid inverted flags is yet to be studied experimentally, and this numerical study provides impetus for such future work.https://authors.library.caltech.edu/records/4djgk-6eb59Frequency response of cantilevered plates of small aspect ratio immersed in viscous fluids
https://authors.library.caltech.edu/records/rjb12-22591
Year: 2023
DOI: 10.1063/5.0120736
Comprehensive theoretical models for the dynamic response of slender cantilevered beams immersed in fluid have been widely reported, while the distinct behavior of wide cantilevered plates has received comparatively little attention. In this article, we develop an exact analytical theory for the resonant response of rectangular cantilevered plates of zero length-to-width aspect ratio that are immersed in unbounded viscous fluids. Unlike the opposite slender limit of large aspect ratio, the hydrodynamic load experienced by zero-aspect-ratio cantilevered plates is inherently non-local, which can strongly affect the individual mode shapes of the plate. In addition, finite-element-method simulations are reported for two- and three-dimensional cases of zero and finite aspect ratio, respectively. Accuracy of the present theory and that of Atkinson and Manrique de Lara [J. Sound Vib. 300, 352 (2007)] for small viscosity and zero aspect ratio is assessed using the former simulations. The latter simulations are used to clarify the regime of validity of the present theory as a function of aspect ratio, along with that of existing theory for slender (large aspect ratio) beams. The results of this study are expected to be of practical importance to micro- and nano-electromechanical system design and their applications.https://authors.library.caltech.edu/records/rjb12-22591Strong Substrate Binding Modulates the Acoustic Quality Factors in Gold Nanodisks
https://authors.library.caltech.edu/records/8hbe8-mc450
Year: 2023
DOI: 10.1021/acs.jpcc.2c09099
<p>Lithographically prepared plasmonic nanoparticles are ideal mechanical probes, as their vibrational behavior can be precisely tuned through particle size and shape. But these particles exhibit strong intrinsic and extrinsic damping that results in small vibrational quality (<i>Q</i>) factors. Here, we perform single-particle transient transmission microscopy to investigate the effect of substrate-particle binding strength on the vibrational <i>Q</i>-factor of lithographically prepared gold nanodisks on glass. Weak and strong binding is realized through titanium adhesion layers of variable thickness. We find that strong binding leads to the generation of several new acoustic modes with varying <i>Q</i>-factors that depend on the particle aspect ratio and substrate material. Our work proposes an approach to tune enhanced acoustic <i>Q</i>-factors of lithographically prepared nanoparticles and offers a comprehensive description of their damping mechanism.</p>https://authors.library.caltech.edu/records/8hbe8-mc450The motion of a layer of yield-stress material on an oscillating plate
https://authors.library.caltech.edu/records/r63sc-9mf96
Year: 2023
DOI: 10.1017/jfm.2023.167
<p>The motion of a finite layer of Bingham material on a solid plate that executes in-plane oscillations was reported previously by Balmforth et al. (J. Non-Newtonian Fluid Mech., vol. 158, issue 1–3, 2009, pp. 46–53). There, it was suggested that multiple yielded regions may arise within the material; this contrasts to start-up flow of the same material for which only one yielded region is generated. Here, we explore quantitatively the fluid physics of this oscillatory flow problem through analytical approximations and further numerical computation. Four new key topological properties concerning the generation and termination of the yielded regions are reported. It is shown that the existence of multiple yielded regions is equivalent to the layer never becoming entirely rigid during the periodic motion. For small inertia, the flow is approximately time-reversible with only a single yielded region generated at the plate. For large inertia, shear stress in the material decays rapidly as a function of distance from the plate. A thin zone of yielded material detaches periodically from the plate, and subsequently terminates within the layer. At high oscillation frequency, there can be any number <i>N</i> of distinct rigid regions, satisfying <i>N </i>= [1- π⁻¹ log <i>B</i>] where <i>B</i> is the Bingham number. It is also shown that for <i>B </i>> 0.5370 , there are at most one yielded region and one rigid region throughout the motion. These theoretical results can be used as a basis for oscillatory rheometry, allowing for measurement of the yield stress using existing apparatus.</p>https://authors.library.caltech.edu/records/r63sc-9mf96Effect of intramodal and intermodal nonlinearities on the flexural resonant frequencies of cantilevered beams
https://authors.library.caltech.edu/records/6p68a-z7325
Year: 2023
DOI: 10.1103/physrevb.108.224303
<p>Sensing applications that utilize nanomechanical resonators require careful control of nonlinear effects in their eigenmodes to ensure robust measurement. While the effect of intra- and intermodal nonlinearities on the resonant frequencies of doubly clamped elastic beams have been widely studied using theory and experiment, commensurate studies on cantilevered beams are limited in comparison. Here, we present such a detailed study that includes an explicit and simple formula for the flexural resonant frequencies of slender cantilevered beams that accounts for intra- and intermodal nonlinearities. Using this general theory, numerical results for the modal nonlinear coefficients are tabulated for the first 20 flexural eigenmodes of cantilevered beams possessing uniform cross sections. The accuracy of this theory, and the effect of cantilever aspect ratio (length/width) on these nonlinear coefficients, is explored using high-accuracy laser Doppler vibrometry experiments. We anticipate that these results will find utility in single- and multimode applications, where the effect of finite oscillation amplitude on the cantilever resonant frequencies can significantly impact measurement design and interpretation.</p>https://authors.library.caltech.edu/records/6p68a-z7325Nanomechanical mass measurements through feature-based time series clustering
https://authors.library.caltech.edu/records/87g5c-arh34
Year: 2024
DOI: 10.1063/5.0176303
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<p>Recent years have seen explosive growth in miniaturized sensors that can continuously monitor a wide variety of processes, with applications in healthcare, manufacturing, and environmental sensing. The time series generated by these sensors often involves abrupt jumps in the detected signal. One such application uses nanoelectromechanical systems (NEMS) for mass spectrometry, where analyte adsorption produces a quick but finite-time jump in the resonance frequencies of the sensor eigenmodes. This finite-time response can lead to ambiguity in the detection of adsorption events, particularly in high event-rate mass adsorption. Here, we develop a computational algorithm that robustly eliminates this often-encountered ambiguity. A moving-window statistical test together with a feature-based clustering algorithm is proposed to automate the identification of single-event jumps. We validate the method using numerical simulations and demonstrate its application in practice using time-series data that are experimentally generated by molecules adsorbing onto NEMS sensors at a high event rate. This computational algorithm enables new applications, including high-throughput, single-molecule proteomics.</p>
</div>https://authors.library.caltech.edu/records/87g5c-arh34Variational solution to the lattice Boltzmann method for Couette flow
https://authors.library.caltech.edu/records/h10fb-aw068
Year: 2024
DOI: 10.1103/physreve.109.055305
<p>Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations (PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.</p>https://authors.library.caltech.edu/records/h10fb-aw068Role of Tensile Stress in DNA Nanoresonators for Epigenetic Studies
https://authors.library.caltech.edu/records/ncc44-1kk07
Year: 2024
DOI: 10.1021/acsanm.4c01730
<p>The evaluation of epigenetic features such as DNA methylation is becoming increasingly important in many biochemical processes like gene expression and transcription as well as in several diseases like schizophrenia or diabetes. Here, we report that self-assembled nanomechanical resonators entirely composed of DNA molecules can be used to explore gross changes in DNA methylation levels (0–25–50%), while careful control of tensile stress is needed to reduce the variability of resonance frequency for rigorous quantification. The effect of the tensile stress retained by the suspended DNA nanoresonators on the application of the technique is extensively explored using a combination of laser Doppler vibrometry and atomic force spectroscopy. DNA nanoresonators are real-time, label-free sensors and could avoid chemical functionalization and sample amplification. Therefore, they may represent in the future a key complementary routine tool for global DNA methylation analysis needed to evaluate the consequences of environmental stresses on the human genome.</p>https://authors.library.caltech.edu/records/ncc44-1kk07