Abstract: The ability of polyelectrolytes to condense into a liquidlike, polyelectrolyte-rich phase out of a dilute supernatant phase through complex coacervation has led to fascinating phenomena, such as membraneless organelles and self-assembled capsules for drug delivery. Recent experiments have demonstrated that heating above a lower critical solution temperature (LCST) can drive complex coacervation. Here, we show that a coarse-grained model of electrostatic correlations is sufficient to model an LCST when accounting for the empirical decrease in the dielectric constant of the solvent upon heating. The predictions of the model agree qualitatively with experimental measurements of the compositions of the coexisting coacervate and supernatant phases. The model also achieves modest quantitative agreement with experiments, despite incorporating no other experimental parameters besides the dielectric constant and a fitted length scale. This agreement underscores the important role that can be played by electrostatic correlations in driving complex coacervation above an LCST.

Publication: Macromolecules Vol.: 54 No.: 24 ISSN: 0024-9297

ID: CaltechAUTHORS:20211221-866875000

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Abstract: Using molecular dynamics simulation, we study shear banding of entangled polymer melts under a steady shear. The steady shear stress vs shear rate curve exhibits a plateau spanning nearly two decades of shear rates in which shear banding is observed, and the steady shear stress remains unchanged after switching the shear rates halfway in the range of shear rates within the plateau region. In addition, we find strong correlation in the location of the shear bands between different shear rates starting from the same microstate configurations at equilibrium, which suggests the importance of the inherent structural heterogeneity in the entangled polymer network for shear banding. Furthermore, for the steady shear bands persisting to the longest simulated time of 9.0τ_(d0) (disengagement time), the shear rate in the slow band and the relative proportion of the bands do not change very much with the increase of imposed shear rate, but the shear rate in the fast band increases approximately in proportion to the imposed shear rates, in contradiction to the lever rule.

Publication: ACS Macro Letters Vol.: 10 No.: 12 ISSN: 2161-1653

ID: CaltechAUTHORS:20211201-231210047

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Abstract: We study the coil-to-globule (C–G) transition of a test polymer of chain length N1 in a polymeric solvent of chain length N using the self-consistent field theory. For short-chain solvents, the C–G transition point is given by (χN)_(tr)–1/2 ∼ (pN)^(3/4)N₁^(–1/2), consistent with an extended Lifshitz theory, where p = b²/v_m^(2/3) is the stiffness parameter. However, for long-chain solvents, the C–G transition becomes strongly first order, with the transition point given by (χN)_(tr)–1/2 ∼ pNN₁^(–2/3). A scaling analysis suggests that the transition point for any chain length combination is a universal function of the scaling variable x ≡ (pN)^(3/2)/N₁, which has the clear interpretation as the ratio between the pervaded volume of the solvent chain and the physical volume of the test chain and that a crossover between the two transition scenarios occurs at x ∼ 1. Furthermore, when properly nondimensionalized, the density profile in the globule state and the center density and the interfacial thickness of the globule at the transition also exhibit universal behavior. For both the short-chain and long-chain solvent cases, the C–G transition corresponds to the point when the interfacial thickness of the globule becomes comparable to the core size.

Publication: Macromolecules Vol.: 54 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20211201-231208714

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Abstract: We develop a simple inhomogeneous mean-field theory to study the interfacial structure and tension of polyelectrolyte complex coacervates in equilibrium with a supernatant solution. Our theory treats the electrostatic correlation by combining the Debye–Hückel theory with the first-order thermodynamic perturbation theory within the local density approximation, and incorporates the conformation entropy contribution for both polyions using Lifshitz’s ground-state dominance approximation. Using this theory, we systematically examine the interfacial properties of both symmetric and concentration-asymmetric coacervates. The interfacial tension γ is generally rather low, on the order of 1 mN/m or less. For asymmetric coacervates, an intricate electric double layer forms in the interfacial region, which can even contain several oscillations under certain conditions. The interfacial tension generally decreases with increasing the stoichiometric asymmetry, the added-salt concentration, and the initial polymer concentration of the mixture. We further find that the interfacial tension can be quantitatively related to the degree of phase separation S, where S is the Euclidean distance in composition between the two coexisting phases. In particular, we find that γ as a function of S for different concentration asymmetries collapses approximately to two master curves, which merge together and follow γ ∼ S³ for small S.

Publication: Macromolecules Vol.: 54 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20211201-231209762

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Abstract: We investigate the effects of pore size and ion adsorption on the room-temperature ionic liquid capacitor with nanoporous electrodes, with a focus on optimizing the capacitance and energy storage. Using a recently developed modified BSK model accounting for both ion correlations and nonelectrostatic interactions, we find that ion crowding proximate to the electrode surface induced by the spontaneous charge separation due to strong ion correlations is responsible for the anomalous increase in the capacitance with decreasing pore sizes observed in experiments. Reducing the strength of ion correlations increases the capacitance and suppresses the anomalous size dependence. For a given pore size, the capacitance peak diverges when the ion correlation strength α reaches a critical value, α_(sc,L). The capacitance peak shifts to smaller pore size as α decreases because of rapid decrease of α_(sc,L) with decreasing pore size. Asymmetric preferential ion adsorption is shown to lead to significantly enhanced energy storage close to the transition point for any pore sizes. For a given correlation strength, the energy storage is optimal at a pore size where α = α_(sc,L).

Publication: ACS Nano Vol.: 15 No.: 7 ISSN: 1936-0851

ID: CaltechAUTHORS:20210709-222308605

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Abstract: The available blue energy (or salinity gradient energy) in a capacitive double-layer expansion (CDLE) process is directly determined by the interplay between adsorption and release of ions from the electrodes at different salt concentrations. In this work, we explore the effect of asymmetric preferential ion adsorption at nanoporous anode and cathode surfaces as a means to enhance the available blue energy. We find that preferential adsorption can not only enhance the available energy output but also shift the supplied potential difference in the CDLE process toward the “spontaneous voltage”. We determine the maximum available energy for the CDLE process as a function of the pore size and the degree of asymmetric adsorption. In the mixing of river water and saltwater, we find that preferential adsorption can give as much as 10% more available energy compared to indifferent electrode surfaces.

Publication: ACS Sustainable Chemistry & Engineering Vol.: 9 No.: 28 ISSN: 2168-0485

ID: CaltechAUTHORS:20210728-155607490

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Abstract: Electrostatic interactions near surfaces and interfaces are ubiquitous in many fields of science. Continuum electrostatics predicts that ions will be attracted to conducting electrodes but repelled by surfaces with lower dielectric constant than the solvent. However, several recent studies found that certain “chaotropic” ions have similar adsorption behavior at air/water and graphene/water interfaces. Here we systematically study the effect of polarization of the surface, the solvent, and solutes on the adsorption of ions onto the electrode surfaces using molecular dynamics simulation. An efficient method is developed to treat an electrolyte system between two parallel conducting surfaces by exploiting the mirror-expanded symmetry of the exact image-charge solution. With neutral surfaces, the image interactions induced by the solvent dipoles and ions largely cancel each other, resulting in no significant net differences in the ion adsorption profile regardless of the surface polarity. Under an external electric field, the adsorption of ions is strongly affected by the surface polarization, such that the charge separation across the electrolyte and the capacitance of the cell is greatly enhanced with a conducting surface over a low-dielectric-constant surface. While the extent of ion adsorption is highly dependent on the electrolyte model (the polarizability of solvent and solutes, as well as the van der Waals radii), we find the effect of surface polarization on ion adsorption is consistent throughout different electrolyte models.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 118 No.: 19 ISSN: 0027-8424

ID: CaltechAUTHORS:20210506-081218514

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Abstract: Polymer-mediated interaction between two solid surfaces is directly connected to the properties of the adsorbed polymer layers. Nonelectrostatic interactions with a surface can significantly impact the adsorption of polyelectrolytes to charged surfaces. We use a classical density functional theory to study the effect of various polyelectrolyte solution properties on the adsorption and interaction between two like-charged surfaces. Our results show that nonelectrostatic interactions not only enhance polyelectrolyte adsorption but can also result in qualitatively different salt effects with respect to the adsorbed amount. In particular, we observe decreasing, increasing, and a previously unreported nonmonotonic behavior in the adsorbed amount of polymer with added salt under the conditions studied, although the nonmonotonic regime only occurs for a narrow range in the parameter space. With sufficient nonelectrostatic adsorption, the adsorbed polymer layers produce a long-range repulsive barrier that is strong enough to overcome dispersive interactions that cause surfaces to attract. Concurrently, a short-range bridging attraction is observed when the two polyelectrolyte layers span both the surfaces. Both the repulsive barrier and bridging attraction depend on the charge density of the polymer backbone and the bulk salt concentration but not on the chain length in the semidilute regime studied.

Publication: Langmuir Vol.: 37 No.: 18 ISSN: 0743-7463

ID: CaltechAUTHORS:20210429-132053968

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Abstract: Liquid mixtures are ubiquitous. Miscibility and dielectric constant are fundamental properties that govern the applications of liquid mixtures. However, despite their importance, miscibility is usually predicted qualitatively based on the vaguely defined polarity of the liquids, and the dielectric constant of the mixture is modeled by introducing mixing rules. Here, we develop a first-principles theory for polar liquid mixtures using a statistical field approach, without resorting to mixing rules. With this theory, we obtain simple expressions for the mixture’s dielectric constant and free energy of mixing. The dielectric constant predicted by this theory agrees well with measured data for simple binary mixtures. On the basis of the derived free energy of mixing, we can construct a miscibility map in the parameter space of the dielectric constant and molar volume for each liquid. The predicted miscibility shows remarkable agreement with known data, thus providing a quantitative basis for the empirical “like-dissolves-like” rule.

Publication: Science Advances Vol.: 7 No.: 7 ISSN: 2375-2548

ID: CaltechAUTHORS:20210216-121335555

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Abstract: Using a dynamic density functional theory, we study the charging dynamics, the final equilibrium structure, and the energy storage in an electrical double layer capacitor with nanoscale cathode–anode separation in a slit geometry. We derive a simple expression for the surface charge density that naturally separates the effects of the charge polarization due to the ions from those due to the polarization of the dielectric medium and allows a more intuitive understanding of how the ion distribution within the cell affects the surface charge density. We find that charge neutrality in the half-cell does not hold during the dynamic charging process for any cathode–anode separation, and also does not hold at the final equilibrium state for small separations. Therefore, the charge accumulation in the half-cell in general does not equal the surface charge density. The relationships between the surface charge density and the charge accumulation within the half-cell are systematically investigated by tuning the electrolyte concentration, cathode–anode separation, and applied voltage. For high electrolyte concentrations, we observe charge inversion at which the charge accumulation exceeds the surface charge at special values of the separation. In addition, we find that the energy density has a maximum at intermediate electrolyte concentrations for a high applied voltage.

Publication: Journal of Physical Chemistry B Vol.: 125 No.: 2 ISSN: 1520-6106

ID: CaltechAUTHORS:20210112-091401503

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Abstract: Salt-induced liquid–liquid phase separation in liquid mixtures is a common phenomenon in nature and in various applications, such as in separation and extraction of chemicals. Here, we present results of a systematic investigation of the phase behaviors in water–acetonitrile–salt mixtures using a combination of experiment and theory. We obtain complete ternary phase diagrams for nine representative salts in water–acetonitrile mixtures by cloud point and component analysis. We construct a thermodynamic free energy model by accounting for the nonideal mixing of the liquids, ion hydration, electrostatic interactions, and Born energy. Our theory yields phase diagrams in good agreement with the experimental data. By comparing the contributions due to the electrostatic interaction, Born energy, and hydration, we find that hydration is the main driving force for the liquid–liquid separation and is a major contributor to the specific ion effects. Our theory highlights the important role of entropy in the hydration driving force. We discuss the implications of our findings in the context of salting-out assisted liquid–liquid extraction and make suggestions for selecting salt ions to optimize the separation performance.

Publication: Journal of the American Chemical Society Vol.: 143 No.: 2 ISSN: 0002-7863

ID: CaltechAUTHORS:20210114-164619058

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Abstract: Using the first-order perturbation theory, we compute the osmotic second and third virial coefficients, the mean-square end-to-end distance ⟨R_e²⟩, and the mean-square radius of gyration ⟨R_g²⟩ of a polymer near the Θ point. Our model is based on the discrete Gaussian chain model and includes a square-gradient term accounting for the finite-range interaction (characterized by κ), in addition to the usual monomer second and third virial coefficients (characterized by v and w, respectively). The use of the discrete model avoids the divergence problems encountered in previous studies using the continuous model. Our study identifies four special temperatures in the Θ regime: the temperature Θ_N where the osmotic second virial coefficient vanishes, the critical temperature Θ_N^(cr) for phase separation, and two compensation temperatures Θ_N^((e)) and Θ_N^((g)) at which ⟨R_e²⟩ and ⟨R_g²⟩ reach their respective ideal values. In the infinite chain-length limit N → ∞, all of these four temperatures approach Θ∞, the Θ temperature for the infinitely long chain. These temperatures differ from each other by terms of order N^(–1/2). In general, these temperatures follow the order Θ_N > Θ_N^(cr) and Θ_N > Θ_N^((e)) > Θ_N^((g)). Furthermore, Θ_N > Θ∞, in agreement with the result obtained by Khokhlov some time ago. On the other hand, depending on the ratio w/κb, Θ∞ can be higher than Θ_N^((e)) (for w/κb < 9.45), lower than Θ_N^((g)) (for w/κb > 11.63), or in between Θ_N^((e)) and Θ_N^((g)) (for 9.45 < w/κb < 11.63). Θ_N^(cr) can be either higher or lower than Θ∞ depending on whether w/b⁶ is larger or smaller than 0.574. From the order of these temperatures, we conclude that the chain is mostly expanded relative to the ideal chain at its Θ_N. However, at Θ∞, the chain can be either expanded or contracted, depending on the relative position of Θ∞ with respect to Θ_N^((e)) and Θ_N^((g)) and depending on whether the chain dimension is measured by ⟨R_e²⟩ or ⟨R_g²⟩.

Publication: Macromolecules Vol.: 53 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20201116-151452336

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Abstract: Solid-state polymer electrolytes and high-concentration liquid electrolytes, such as water-in-salt electrolytes and ionic liquids, are emerging materials to replace the flammable organic electrolytes widely used in industrial lithium-ion batteries. Extensive efforts have been made to understand the ion transport mechanisms and optimize the ion transport properties. This perspective reviews the current understanding of the ion transport and polymer dynamics in liquid and polymer electrolytes, comparing the similarities and differences in the two types of electrolytes. Combining recent experimental and theoretical findings, we attempt to connect and explain ion transport mechanisms in different types of small-molecule and polymer electrolytes from a theoretical perspective, linking the macroscopic transport coefficients to the microscopic, molecular properties such as the solvation environment of the ions, salt concentration, solvent/polymer molecular weight, ion pairing, and correlated ion motion. We emphasize universal features in the ion transport and polymer dynamics by highlighting the relevant time and length scales. Several outstanding questions and anticipated developments for electrolyte design are discussed, including the negative transference number, control of ion transport through precision synthesis, and development of predictive multiscale modeling approaches.

Publication: Journal of Chemical Physics Vol.: 153 No.: 10 ISSN: 0021-9606

ID: CaltechAUTHORS:20200911-133136426

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Abstract: Room-temperature ionic liquids (RTILs) are synthetic electrolytes with electrochemical stability superior to that of conventional aqueous-based electrolytes, allowing a significantly enlarged electrochemical window for application as capacitors. In this study, we propose a variant of an existing RTIL model for solvent-free RTILs, accounting for both ion–ion correlations and nonelectrostatic interactions. Using this model, we explore the phenomenon of spontaneous surface charge separation in RTIL capacitors and find that this transition is a common feature for realistic choices of the model parameters in most RTILs. In addition, we investigate the effects of asymmetric preferential ion adsorption on this charge separation transition and find that proximity of the transition in this case can result in greatly enhanced energy storage. Our work suggests that differential chemical treatment of electrodes can be a simple and useful means for optimizing energy storage in RTIL capacitors.

Publication: Journal of Physical Chemistry Letters Vol.: 11 No.: 5 ISSN: 1948-7185

ID: CaltechAUTHORS:20200211-074528495

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Abstract: The unique pressure exerted by active particles—the “swim” pressure—has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density—an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an “equivalent pressure” (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.

Publication: Physical Review E Vol.: 101 No.: 1 ISSN: 2470-0045

ID: CaltechAUTHORS:20200116-094602547

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Abstract: We use a numerical implementation of polymer classical density functional theory with an incompressibility condition to study the system consisting of nonadsorbing polyelectrolytes confined by two planar surfaces and quantify the effective interaction between the two planar surfaces as a function of the polyelectrolyte and salt concentrations. Our results indicate that for the uncharged surfaces (and weakly charged surfaces), the effective interaction primarily consists of a short-range attraction due to the depletion followed by repulsion due to the electric double layer overlapping and electrostatic correlations. For salt-free and low salt concentration systems, the magnitude of the repulsion barrier is determined by the overlap between the electric double layers, while at relatively high salt concentrations, the magnitude of the repulsion barrier is determined by the electrostatic correlations. Due to the competition between the electric double layer and the electrostatic correlations, the magnitude of the repulsion barrier varies nonmonotonically. In contrast, a mean-field Poisson-Boltzmann treatment of the electrostatics predicts a monotonically decreasing repulsion barrier with increasing salt concentration. At moderate salt concentrations, our theory predicts oscillatory interaction profiles. A comparison with the mean-field Poisson-Boltzmann treatment of electrostatics suggests that the oscillations are due primarily to electrostatic correlations.

Publication: Journal of Chemical Physics Vol.: 151 No.: 21 ISSN: 0021-9606

ID: CaltechAUTHORS:20191202-105354237

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Abstract: It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_α is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_α, of the overall system is related to the relaxation time of the LD particles, τ_(LD), as τ_α = τ₀exp(Ωτ_(LD)/k_BT).

Publication: Physical Review E Vol.: 100 No.: 5 ISSN: 2470-0045

ID: CaltechAUTHORS:20191115-074621027

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Abstract: Systems consisting of a polyelectrolyte solution in contact with a cross-linked polyelectrolyte network are ubiquitous (e.g., biofilms, drug-delivering hydrogels, and mammalian extracellular matrices), yet the underlying physics governing these interactions is not well understood. Here, we find that carboxymethyl cellulose, a polyelectrolyte commonly found in processed foods and associated with inflammation and obesity, compresses the colonic mucus hydrogel (a key regulator of host–microbe interactions and a protective barrier) in mice. The extent of this polyelectrolyte-induced compression is enhanced by the degree of polymer negative charge. Through animal experiments and numerical calculations, we find that this phenomenon can be described by a Donnan mechanism. Further, the observed behavior can be quantitatively described by a simple, one-parameter model. This work suggests that polymer charge should be considered when developing food products because of its potential role in modulating the protective properties of colonic mucus.

Publication: Biomacromolecules Vol.: 20 No.: 7 ISSN: 1525-7797

ID: CaltechAUTHORS:20190619-091518942

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Abstract: Using molecular dynamics simulation, we investigate the evolution of chain conformation, stress relaxation, and fracture for a polymer melt between two walls after step shear. We find that the characteristic overlap time for the reduced relaxation moduli and the time that the stretched primitive chain retracts to its equilibrium length are both much longer than the Rouse time. Importantly, we observe significant fracture-like flow after shear cessation. While there is considerable randomness in the location of the fracture plane and the magnitude of displacement from sample to sample, our analysis suggests that the randomness is not due to thermal noise, but may reflect inherent structural and dynamic heterogeneity in the entangled polymer network.

Publication: Macromolecules Vol.: 52 No.: 11 ISSN: 0024-9297

ID: CaltechAUTHORS:20190523-094613725

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Abstract: In this work, we utilize bifurcation diagrams to study the role of mathematical artifacts in deteriorating the physical behavior in statistical mechanically based equations of state of pure fluids. We study the impact of common empirical approximations usually employed to overcome some of the mathematical and physical challenges such as the parametrization of mean field models or pair correlations functions at contact. The proposed diagrams elucidate how the reduced molar volume bifurcates with the variation of temperature at constant pressure. We generate bifurcation diagrams for the modified van der Waals equation of state (EOS) of Poole et al, SAFT-VR Mie, Soft-SAFT, CK-SAFT, and the original SAFT EOSs for spherical and nonspherical molecules. We find that the bifurcation diagram can serve as a useful schematic tool to reveal the unphysical PVT behavior, demonstrate the existence of physical and spurious two-phase separation regions, and illustrate how the number of molar volume roots vary with temperatures. Our method shows that the presence of unphysical branches can cause spurious two-phase separation regions and create erroneous behavior in the stability limit of vapor–liquid equilibrium. We demonstrate that the existence of customary and spurious phase envelopes is accompanied by S-shaped behavior in the volume-temperature bifurcation diagrams. The study reveals that none of the SAFT models is free from producing unphysical behavior. While the SAFT-VR Mie EOS exhibits solid–liquid-like behavior for nonspherical molecules, the CK-SAFT EOS shows liquid–liquid demixing behavior for spherical and nonspherical compounds. For the soft-SAFT EOS, three different two-phase separation regions are observed in addition to the common vapor–liquid phase separation region.

Publication: Industrial & Engineering Chemistry Research Vol.: 58 No.: 3 ISSN: 0888-5885

ID: CaltechAUTHORS:20190114-073829851

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Abstract: External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces—forces that are generated by driven components within a system—in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material.

Publication: ACS Nano Vol.: 13 No.: 1 ISSN: 1936-0851

ID: CaltechAUTHORS:20190102-092234094

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Abstract: Networks assembled by reversible association of telechelic polymers constitute a common class of soft materials. Various mechanisms of chain migration in associative networks have been proposed; yet there remains little quantitative experimental data to discriminate among them. Proposed mechanisms for chain migration include multichain aggregate diffusion as well as single-chain mechanisms such as “walking” and “hopping”, wherein diffusion is achieved by either partial (“walking”) or complete (“hopping”) disengagement of the associated chain segments. Here, we provide evidence that hopping can dominate the effective diffusion of chains in associative networks due to a strong entropic penalty for bridge formation imposed by local network structure; chains become conformationally restricted upon association with two or more spatially separated binding sites. This restriction decreases the effective binding strength of chains with multiple associative domains, thereby increasing the probability that a chain will hop. For telechelic chains this manifests as binding asymmetry, wherein the first association is effectively stronger than the second. We derive a simple thermodynamic model that predicts the fraction of chains that are free to hop as a function of tunable molecular and network properties. A large set of self-diffusivity measurements on a series of model associative polymers finds good agreement with this model.

Publication: Journal of the American Chemical Society Vol.: 140 No.: 43 ISSN: 0002-7863

ID: CaltechAUTHORS:20181001-131358075

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Abstract: Using a simple liquid-state theory, we study the phase behaviors of concentration-asymmetric mixtures of polycation and polyanion solutions. We construct a three-dimensional (3D) phase diagram in terms of the concentrations of the three independent charged components: polycation, polyanion, and small cation (p_(P^+) − p_(P^−) − p_+), for a given Bjerrum length. This phase diagram yields rich and complex phase-separation scenarios. To illustrate, we sequentially examine the following three systems that are directly relevant to experiments: a symmetric mixture, an asymmetric mixture with one type of small ions, and an asymmetric mixture with both types of small ions. We re-express the information in the 3D phase diagram using three experimentally more easily controllable parameters—the asymmetry factor r, the initial extra-salt concentration p_(s,0), and the initial polyelectrolyte (PE) concentration p_(P,0) of both solutions prior to mixing. We construct three reduced phase diagrams in the p_(P,0) − r, r − p_(s,0), and p_(s,0) − p_(P,0) planes, respectively, and examine the evolution of the volume fraction of the coexisting phases, concentration of the PE and small-ion species in each phase, and the Galvani potential Ψ_G, as functions of these experimental controlling parameters. We rationalize our findings in terms of the key thermodynamic factors, namely, the translational entropy of the small ions, the electrostatic correlation energy, and the requirement for charge neutrality.

Publication: Journal of Chemical Physics Vol.: 149 No.: 16 ISSN: 0021-9606

ID: CaltechAUTHORS:20180706-133157000

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Abstract: Using a variational field-theoretic approach, we derive a theory for polar fluids. The theory naturally accounts for the reaction field without resorting to the cavity construct and leads to a simple formula for the dielectric constant in terms of the molecular dipole moment and density. We apply our formula to calculate the dielectric constants of nonpolarizable liquid models for more than a hundred small molecules without using any adjustable parameters. Our formula predicts dielectric constants of these nonpolarizable liquid models more accurately than the Onsager theory and previous field-theoretic dielectric theories, as demonstrated by the closer agreement to the simulation results. The general theory also yields the free energy, which can describe the response of polar fluids under applied electric fields.

Publication: Journal of Chemical Physics Vol.: 149 No.: 12 ISSN: 0021-9606

ID: CaltechAUTHORS:20180926-103709613

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Abstract: We perform a general thermodynamic analysis for the salt partitioning behavior in the coexisting phases for symmetric mixtures of polycation and polyanion solutions. We find that salt partitioning is determined by the competition between two factors involving the ratio of the polyelectrolyte concentration in the coacervate phase to that in the supernatant phase and the difference in the exchange excess chemical potential Δμ_(ex) -- the excess chemical potential difference between PE segments and small ions -- between the coexisting phases. The enrichment of salt ions in the coacervate phase predicted by the Voorn−Overbeek theory is shown to arise from its neglect of chain connectivity in the excess free energy which results in Δμ_(ex) = 0 under all conditions. We argue that chain connectivity in general leads to a finite value of Δμex, which decreases with increasing PE concentration. Explicit calculations using theories that include the chain connectivity correlations -- a simple liquid-state theory and a renormalized Gaussian fluctuation theory -- show nonmonotonic behavior of the salt-partitioning coefficient (the ratio of salt ion concentration in the coacervate phase to that in the supernatant phase): it is larger than 1 at very low salt concentrations, reaches a minimum at some intermediate salt concentration, and approaches 1 at the critical point. This behavior is consistent with recent computer simulation and experimental results.

Publication: Macromolecules Vol.: 51 No.: 15 ISSN: 0024-9297

ID: CaltechAUTHORS:20180718-144046071

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Abstract: An improved density functional theory (DFT) for an inhomogeneous charged system (including electrolyte and/or polyelectrolyte) is proposed based on fundamental measure theory, thermodynamic perturbation theory and mean-spherical approximation. Our DFT combines the existing treatment of hard-sphere contributions using fundamental measure theory (FMT) with a new treatment of the electrostatic correlations for the non-bonded ions and chain connectivity that are approximated by employing a first-order Taylor expansion, with the reference fluid density determined using the technique from Gillespie et al. [D. Gillespie et al., J. Phys.: Condens. Matter, 2002, 14, 12129]. We show that the first-order Taylor expansion for the non-bonded electrostatic correlations yields numerically comparable results to the more involved second-order expansion. Furthermore, we find that the existing treatment of the chain connectivity correlation predicts a spurious layer-by-layer phase at moderately large Bjerrum lengths, which is avoided in our new treatment. These simplifications and improvements should significantly facilitate the implementation and reduce the computational cost.

Publication: Soft Matter Vol.: 14 No.: 28 ISSN: 1744-683X

ID: CaltechAUTHORS:20180628-112107625

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Abstract: We investigate how ion–polymer complexation suppresses molecular motion in conventional polymer electrolytes using molecular dynamics (MD) simulations of lithium hexafluorophosphate in poly(ethylene oxide) and a modified Rouse model. The employed model utilizes an inhomogeneous friction distribution to describe ion–polymer interactions and provides an effective way to examine how ion–polymer interactions affect polymer motion. By characterizing the subdiffusive Li^+ transport and polymer relaxation times at several salt concentrations, we observe that increases in local friction due to ion-polymer complexation are significantly smaller than previously assumed. We find that a Rouse-based model that only considers local increases in friction cannot simultaneously capture the magnitude of increased polymer relaxation times and the apparent power-law exponent for Li^+ subdiffusion observed in MD simulations. This incompatibility is reconciled by augmenting the modified Rouse model with a term that increases the global friction with the square of the salt concentration; this significantly improves the agreement between the model and MD, indicating the importance of ion–ion interactions and distributions on ion/polymer mobility.

Publication: ACS Macro Letters Vol.: 7 No.: 6 ISSN: 2161-1653

ID: CaltechAUTHORS:20180606-124846827

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Abstract: Using a recently developed renormalized Gaussian fluctuation (RGF) field theory that self-consistently accounts for the concentration-dependent coupling between chain structure and electrostatic correlations, we study the phase behavior of polyelectrolyte solutions, with a focus on the effects of added salts and chain structure. For solutions of a single polyelectrolyte species plus salt, the RGF theory predicts the existence of a loop in the phase boundary at Bjerrum lengths (inverse temperature) below (above) the critical value of the salt-free system. This loop behavior can occur at electrostatic interaction strengths lb/b at which the loop no longer exists for the TPT-1 theory, and at fixed lb/b the loop can persist for infinitely long chains, in contrast to theories using a fixed-Gaussian structure (fg-RPA). For systems of oppositely charged (but otherwise symmetric) chains, we again find that the fg-RPA greatly overpredicts the driving force for phase separation, especially at higher charge fractions (but still below the critical Manning charge density). In general, stiff chains have a narrower two-phase region than intrinsically flexible chains, although intrinsically flexible chains can still experience a local stiffening which persists in semidilute solution; for higher charge fractions the local stiffening of flexible chains is crucial for reproducing qualitatively correct thermodynamics and phase diagrams. For fully charged flexible chains, we find that phase diagrams are quite similar to those for semiflexible rods and that it is possible to capture the coacervate phase diagrams of the full self-consistent calculations using a constant, renormalized chain stiffness.

Publication: Macromolecules Vol.: 51 No.: 5 ISSN: 0024-9297

ID: CaltechAUTHORS:20180221-073146606

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Abstract: Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)] proposed a local lattice Monte Carlo algorithm for simulating charged systems based on Gauss’s law, which scales with the particle number N as O(N). This method includes two degrees of freedom: the configuration of the mobile charged particles and the electric field. In this work, we consider two important issues in the implementation of the method, the acceptance rate of configurational change (particle move) and the ergodicity in the phase space sampled by the electric field. We propose a simple method to improve the acceptance rate of particle moves based on the superposition principle for electric field. Furthermore, we introduce an additional updating step for the field, named “open-circuit update,” to ensure that the system is fully ergodic under periodic boundary conditions. We apply this improved local Monte Carlo simulation to an electrolyte solution confined between two low dielectric plates. The results show excellent agreement with previous theoretical work.

Publication: Journal of Chemical Physics Vol.: 148 No.: 11 ISSN: 0021-9606

ID: CaltechAUTHORS:20180327-084056793

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Abstract: The study of the conformation properties of macromolecules is at the heart of polymer science. Essentially all physical properties of polymers are manifestations of the underlying polymer conformations or otherwise significantly impacted by the conformation properties. In this Perspective, we review some of the key concepts that we have learned over nearly eight decades of the subject and outline some open questions. The topics include both familiar subjects in polymer physics textbooks and more recent results or not-so-familiar subjects, such as non-Gaussian chain behavior in polymer melts and topological effects in ring polymers. The emphasis is on understanding the key concepts, with both physical reasoning and mathematical analysis, and on the interconnection between the different results and concepts.

Publication: Macromolecules Vol.: 50 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20171120-102752509

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Abstract: We study associating polymer gels under steady shear using Brownian dynamics simulation to explore the interplay between the network structure, dynamics, and rheology. For a wide range of flow rates, we observe the formation of shear bands with a pronounced difference in shear rate, concentration, and structure. A striking increase in the polymer pressure in the gradient direction with shear, along with the inherently large compressibility of the gels, is shown to be a crucial factor in destabilizing homogeneous flow through shear-gradient concentration coupling. We find that shear has only a modest influence on the degree of association, but induces marked spatial heterogeneity in the network connectivity. We attribute the increase in the polymer pressure (and polymer mobility) to this structural reorganization.

Publication: Physical Review Letters Vol.: 119 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:20170913-100922884

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Abstract: We carry out simultaneous mechanical and IR-thermal-imaging based temperature measurements of SBR melts during uniaxial extension in order to delineate the nature of the observed mechanical responses. Using the first law of thermodynamics, we evaluate the enthalpy change h_1 associated with the temperature rise in the extending melt, estimate the heat loss to the surrounding, and conclude that there is an appreciable non-thermal enthalpic buildup h_2 = (w – h_1 − q) during either adiabatic or isothermal extension. The monotonic increase of h_2 with the stretching ratio λ until the onset of inhomogeneous extension or melt rupture reveals that fast melt extension is largely elastic even after yielding in presence of partial chain disentanglement. At high rates, the lock-up of chain entanglement produces such a high level of h_2 that is rarely seen in extension of crosslinked rubbers. When melt extension is carried out under isothermal condition, we show that the time-temperature superposition principle (TTS) fails to predict the transient response of a SBR melt at a fixed effective rate involving three temperatures. The failure of the TTS suggests that the terminal chain dynamics show different temperature dependence from the local segmental dynamics that control the transient stress responses.

Publication: Polymer Vol.: 124ISSN: 0032-3861

ID: CaltechAUTHORS:20170907-083345533

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Abstract: We present a novel method for obtaining salt polarizabilities in aqueous solutions based on our recent theory for the refractive index of salt solutions, which predicts a linear relationship between the refractive index and the salt concentration at low concentrations, with a slope determined by the intrinsic values of the salt polarizability and the density of the solution. Here we apply this theory to determine the polarizabilities of 32 strong electrolyte salts in aqueous solutions from refractive index and density measurements. Setting Li^+ as the standard ion, we then determine the polarizabilities of seven cations (Na^+, K^+, Rb^+, Cs^+, Ca^(2+), Ba^(2+), and Sr^(2+)) and seven anions (F^–, Cl^–, Br^–, I^–, ClO_4^–, NO_3^–, and SO_4^(2–)), which can be used as important reference data. We investigate the effect of temperature on salt polarizabilities, which decreases slightly with increasing temperature. The ion polarizability is found to be proportional to the cube of bare ionic radius (r_(bare)^3) for univalent ions, but the relationship does not hold for multivalent ions. Contrary to findings of Krishnamurti, we find no significant linear relationship between ion polarizability and the square of the atomic number (N^2) for smaller ions.

Publication: Journal of Physical Chemistry B Vol.: 121 No.: 26 ISSN: 1520-6106

ID: CaltechAUTHORS:20170612-155734285

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Abstract: The development of solid polymer electrolytes for lithium battery applications is a challenge of profound technological significance. We have established a collaboration with the aim of understanding and designing improved polymer electrolytes that combines theoretical modeling, polymer synthesis, and experimental characterization. By studying diverse polymer chemistries, we have discovered that ion-solvation-site connectivity is an important feature of polymer electrolytes that is necessary for high lithium-ion conductance. We are employing this insight into search for improved polymer electrolytes, with promising early-stage results.

Publication: Accounts of Chemical Research Vol.: 50 No.: 3 ISSN: 0001-4842

ID: CaltechAUTHORS:20170322-074051393

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Abstract: Coiled-coil domains can direct the assembly of protein block copolymers into physically crosslinked, viscoelastic hydrogels. Here we describe the use of fluorescence recovery after photobleaching (FRAP) to probe chain mobility in reversible hydrogels assembled from engineered proteins bearing terminal coiled-coil domains. We show that chain mobility can be related to the underlying dynamics of the coiled-coil domains by application of a 3-state “hopping” model of chain migration. We further show that genetic programming allows the effective mobility of network chains to be varied 500-fold through modest changes in protein sequence. Destabilization of the coiled-coil domains by site-directed mutagenesis increases the effective diffusivity of probe chains. Conversely, probe mobility is reduced by expanding the hydrophobic surface area of the coiled-coil domains through introduction of the bulky leucine surrogate homoisoleucine. Predictions from the 3-state model imply asymmetric sequential binding of the terminal domains. Brownian Dynamics simulations suggest that binding asymmetry is a general feature of reversible gels, arising from a loss in entropy as chains transition to a conformationally restricted bridged state.

Publication: Journal of the American Chemical Society Vol.: 139 No.: 10 ISSN: 0002-7863

ID: CaltechAUTHORS:20170224-091637468

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Abstract: We address the effects of chain connectivity on electrostatic fluctuations in polyelectrolyte solutions using a field-theoretic, renormalizedGaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang, Phys. Rev. E 81, 021501 (2010)], the RGF provides a unified theory for electrostatic fluctuations, accounting for both dielectric and charge correlation effects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energy depends intimately on the chain conformation, and our theory naturally provides a self-consistent determination of the response of intramolecular chain structure to polyelectrolyte and salt concentrations. The effects of the chain-conformation on the self-energy and thermodynamics are especially pronounced for flexible polyelectrolytes at low polymer and salt concentrations, where application of the wrong chain structure can lead to a drastic misestimation of the electrostatic correlations. By capturing the expected scaling behavior of chain size from dilute to semi-dilute regimes, our theory provides improved estimates of the self energy at low polymer concentrations and correctly predicts the eventual N-independence of the critical temperature and concentration of salt-free solutions of flexible polyelectrolytes. We show that the self energy can be interpreted in terms of an infinite-dilution energy μ^(el)_(m,0) and a finite concentration correlation correction μ^(corr) which tends to cancel out the former with increasing concentration.

Publication: Journal of Chemical Physics Vol.: 146 No.: 8 ISSN: 0021-9606

ID: CaltechAUTHORS:20170224-103032443

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Abstract: In this work, the physical region exhibiting the common three volume roots is located a priori for the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) equation of state without the need to determine the other non-physical volume roots. The loci of all multiple volume roots are first determined and investigated for the PC-SAFT equation of state over a broad range of temperatures and pressures using bifurcation diagrams. The study then illustrates how the number of multiple volume roots varies with temperature and pressure. The influence of each SAFT term is studied for several kinds of fluids ranging from spherical molecules to polymers. The technique presented in this study provides a simple method to identify artificial two-phase separation regions. Our study demonstrates that the problem of multiple volume roots found in non-cubic equations of state can be easily managed once the variation of volume loci with temperature and pressure are analyzed and understood using bifurcation diagrams.

Publication: Fluid Phase Equilibria Vol.: 434ISSN: 0378-3812

ID: CaltechAUTHORS:20170301-153738586

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Abstract: We study the phase behavior of polyelectrolyte (PE) solutions with salt using a simple liquid-state (LS) theory. This LS theory accounts for hard-core excluded volume repulsion by the Boublik–Mansoori–Carnahan–Starling–Leland equation of state, electrostatic correlation by the mean-spherical approximation, and chain connectivity by the first-order thermodynamic perturbation theory. We predict a closed-loop binodal curve in the PE concentration-salt concentration phase diagram when the Bjerrum length is smaller than the critical Bjerrum length in salt-free PE solution. The phase-separated region shrinks with decreasing Bjerrum length, and disappears below a critical Bjerrum length. These results are qualitatively consistent with experiments, but cannot be captured by the Voorn–Overbeek theory. On the basis of the closed-loop binodal curve and the lever rule, we predict three scenarios of salting-out and salting-in phenomena with addition of monovalent salt into an initially salt-free PE solution. The Galvani potential—the electric potential difference between the coexisting phases—is found to depend nonmonotonically on the overall salt concentration in some PE concentration range, which is related to the partition of the co-ions in the coexisting phases. Free energy analysis suggests that phase separation is driven by a gain in the electrostatic energy, at the expense of a large translational entropy penalty, due to significant counterion accumulation in the PE-rich phase.

Publication: Macromolecules Vol.: 49 No.: 24 ISSN: 0024-9297

ID: CaltechAUTHORS:20161213-100941959

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Abstract: Using statistical-field techniques, we develop a molecular-based dipolar self-consistent-field theory (DSCFT) for charge solvation in liquid mixtures under equilibrium and nonequilibrium conditions, and apply it to compute the solvent reorganization energy of electron-transfer reactions. In addition to the nonequilibrium orientational polarization, the reorganization energy in liquid mixtures is also determined by the out-of-equilibrium solvent composition around the reacting species due to preferential solvation. Using molecular parameters that are readily available, the DSCFT naturally accounts for the dielectric saturation effect and the spatially varying solvent composition in the vicinity of the reacting species. We identify three general categories of binary solvent mixtures, classified by the relative optical and static dielectric permittivities of the solvent components. Each category of mixture is shown to produce a characteristic local solvent composition profile in the vicinity of the reacting species, which gives rise to the distinctive composition dependence of the reorganization energy that cannot be predicted using the dielectric permittivities of the homogeneous solvent mixtures.

Publication: Journal of Physical Chemistry B Vol.: 120 No.: 26 ISSN: 1520-6106

ID: CaltechAUTHORS:20160524-080318394

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Abstract: The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer (θ_L) is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U(r) between two ring polymers as well as the second virial coefficient A_2 of ring polymers at θ_L, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A_2 of ring polymers at θ_L: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.

Publication: Science China Chemistry Vol.: 59 No.: 5 ISSN: 1674-7291

ID: CaltechAUTHORS:20160602-150436719

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Abstract: Screening is one of the most important concepts in the study of charged systems. Near a dielectricinterface, the ion distribution in a salt solution can be highly nonuniform. Here, we develop a theory that self-consistently treats the inhomogeneous screening effects. At higher concentrations when the bulk Debye screening length is comparable to the Bjerrum length, the double layerstructure and interfacial properties are significantly affected by the inhomogeneous screening. In particular, the depletion zone is considerably wider than that predicted by the bulk screening approximation or the WKB approximation. The characteristic length of the depletion layer in this regime scales with the Bjerrum length, resulting in a linear increase of the negative adsorption of ions with concentration, in agreement with experiments. For asymmetric salts, inhomogeneous screening leads to enhanced charge separation and surface potential.

Publication: Journal of Chemical Physics Vol.: 144 No.: 13 ISSN: 0021-9606

ID: CaltechAUTHORS:20150812-091441877

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Abstract: Taking PEO/PS polymer blends doped with lithium salt as example, we study the effects of cross-linking of the EO segments by the Li^+ ions on the phase behavior. Combining the Flory–Huggins theory with a statistical model accounting for the combinatorics in forming the cross-links and accounting for the charge neutrality due to the presence of anions, we find an entropic driving force that favors phase separation when the number of EO segments coordinating an Li^+ ion exceeds 2. As a result of the asymmetric interaction between the ions and the two polymers, the phase diagram in the polymer composition becomes asymmetric upon addition of the lithium salts. In addition, we examine the effects of preferential solvation energy of the ions which has been shown previously to lead to an increase in the effective χ parameter between the two polymers. We find that the magnitudes of these two driving forces are comparable, but their effects are nonadditive.

Publication: Macromolecules Vol.: 49 No.: 1 ISSN: 0024-9297

ID: CaltechAUTHORS:20160211-082427816

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Abstract: Using field-theoretic techniques, we develop a molecularly based dipolar self-consistent-field theory (DSCFT) for charge solvation in pure solvents under equilibrium and nonequilibrium conditions and apply it to the reorganization energy of electron transferreactions. The DSCFT uses a set of molecular parameters, such as the solvent molecule’s permanent dipole moment and polarizability, thus avoiding approximations that are inherent in treating the solvent as a linear dielectric medium. A simple, analytical expression for the free energy is obtained in terms of the equilibrium and nonequilibrium electrostatic potential profiles and electric susceptibilities, which are obtained by solving a set of self-consistent equations. With no adjustable parameters, the DSCFT predicts activation energies and reorganization energies in good agreement with previous experiments and calculations for the electron transfer between metallic ions. Because the DSCFT is able to describe the properties of the solvent in the immediate vicinity of the charges, it is unnecessary to distinguish between the inner-sphere and outer-sphere solvent molecules in the calculation of the reorganization energy as in previous work. Furthermore, examining the nonequilibrium free energy surfaces of electron transfer, we find that the nonequilibrium free energy is well approximated by a double parabola for self-exchange reactions, but the curvature of the nonequilibrium free energy surface depends on the charges of the electron-transferring species, contrary to the prediction by the linear dielectrictheory.

Publication: Journal of Chemical Physics Vol.: 143 No.: 22 ISSN: 0021-9606

ID: CaltechAUTHORS:20151221-130932462

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Abstract: Using off-lattice Monte Carlo simulation, we investigate the effects of topological constraints on the free energy and metric properties of an unknotted ring polymer without exclude volume interactions confined in a slit with width d, as well as the effect of confinement on the probability of forming an unknot in a freely jointed ring. Because of the topological constraints, the polymer size of an unknotted ring is shown to behave differently from that of a freely jointed ring: the in-plane radius of gyration R_(g∥) increases with increasing confinement. However, the free energy of an unknotted ring follows the same scaling law as a freely jointed ring for strong confinement. This abnormal phenomenon is explained on the basis of the fact that the length of subchains inside the confinement blobs is smaller than the topological blob size, i.e., the characteristic length below which topological constraints become unimportant. As in the bulk, the probability of forming an unknot decreases exponentially with the chain length, but the decay length decreases with decreasing confinement length. We propose an efficient method for calculating the probability of forming unknot from a freely jointed ring in confinement.

Publication: Macromolecules Vol.: 48 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20160105-135117569

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Abstract: We introduce a coarse-grained approach for characterizing the long-timescale dynamics of ion diffusion in general polymer electrolytes using input from short molecular dynamics trajectories. The approach includes aspects of the dynamic bond percolation model [ J. Chem. Phys. 1983, 79, 3133−3142] by treating ion diffusion in terms of hopping transitions on a fluctuating lattice. We extend this well-known approach by using short (i.e., 10 ns) molecular dynamics (MD) trajectories to predict the distribution of ion solvation sites that comprise the lattice and to predict the rate of hopping among the lattice sites. This yields a chemically specific dynamic bond percolation (CS-DBP) model that enables the description of long-timescale ion diffusion in polymer electrolytes at a computational cost that makes feasible the screening of candidate materials. We employ the new model to characterize lithium-ion diffusion properties in six polyethers that differ by oxygen content and backbone stiffness: poly(trimethylene oxide), poly(ethylene oxide-alt-trimethylene oxide), poly(ethylene oxide), poly(propylene oxide), poly(ethylene oxide-alt-methylene oxide), and poly(methylene oxide). Good agreement is observed between the predictions of the CS-DBP model and long-timescale atomistic MD simulations, thus providing validation of the model. Among the most striking results from this analysis is the unexpectedly good lithium-ion diffusivity of poly(trimethylene oxide-alt-ethylene oxide) by comparison to poly(ethylene oxide), which is widely used. Additionally, the model straightforwardly reveals a range of polymer features that lead to low lithium-ion diffusivity, including the competing effects of the density of solvation sites and polymer stiffness. These results illustrate the potential of the CS-DBP model to screen polymer electrolytes on the basis of ion diffusivity and to identify important design criteria.

Publication: Macromolecules Vol.: 48 No.: 19 ISSN: 0024-9297

ID: CaltechAUTHORS:20150929-202516731

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Abstract: We propose a density-functional theory (DFT) to describe inhomogeneous mixtures of AB random copolymer and carbon dioxide (CO_2). The statistical sequence of monomer in the polymer chain backbone is modeled by a transition matrix in a Markov-step growth process. The parameters of the theory are determined by fitting the bulk experimental data. We apply the DFT to the interfacial properties of binary mixtures of CO_2 with poly(methyl methacrylate co ethyl methacrylate) (P(MMA-co-EMA)), poly(methyl methacrylate co ethyl acrylate) (P(MMA-co-EA) and poly(styrene co ethyl acrylate) (P(S-co-EA)). The dependence of CO_2 solubility and interfacial tension on the copolymer composition and pressure is examined. We find that higher fractions of EA or EMA result in higher solubility of CO_2 at a given pressure, but also results in higher interfacial tension at a fixed CO_2 content in the polymer-rich phase. Using the classical nucleation theory as a rough estimate, we examine the effect of the copolymer composition on the free energy barrier of bubble nucleation in random copolymer–CO_2 mixtures.

Publication: Macromolecules Vol.: 48 No.: 16 ISSN: 0024-9297

ID: CaltechAUTHORS:20150918-144002667

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Abstract: We propose a simple theoretical formula for describing the refractive indices in binary liquid mixtures containing salt ions. Our theory is based on the Clausius–Mossotti equation; it gives the refractive index of the mixture in terms of the refractive indices of the pure liquids and the polarizability of the ionic species, by properly accounting for the volume change upon mixing. The theoretical predictions are tested by extensive experimental measurements of the refractive indices for water–acetonitrile-salt systems for several liquid compositions, different salt species, and a range of salt concentrations. Excellent agreement is obtained in all cases, especially at low salt concentrations, with no fitting parameters. A simplified expression of the refractive index for low salt concentration is also given, which can be the theoretical basis for determination of salt concentration using refractive index measurements.

Publication: Journal of Physical Chemistry B Vol.: 119 No.: 33 ISSN: 1520-6106

ID: CaltechAUTHORS:20150911-091014738

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Abstract: Understanding the mechanisms of lithium-ion transport in polymers is crucial for the design of polymer electrolytes. We combine modular synthesis, electrochemical characterization, and molecular simulation to investigate lithium-ion transport in a new family of polyester-based polymers and in poly(ethylene oxide) (PEO). Theoretical predictions of glass-transition temperatures and ionic conductivities in the polymers agree well with experimental measurements. Interestingly, both the experiments and simulations indicate that the ionic conductivity of PEO, relative to the polyesters, is far higher than would be expected from its relative glass-transition temperature. The simulations reveal that diffusion of the lithium cations in the polyesters proceeds via a different mechanism than in PEO, and analysis of the distribution of available cation solvation sites in the various polymers provides a novel and intuitive way to explain the experimentally observed ionic conductivities. This work provides a platform for the evaluation and prediction of ionic conductivities in polymer electrolyte materials.

Publication: ACS Central Science Vol.: 1 No.: 4 ISSN: 2374-7943

ID: CaltechAUTHORS:20150724-073254175

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Abstract: Numerical solution of a coupled set of Smoluchowski convection-diffusion equations of associating polymers modelled as finitely extensible dumbbells enables computation of time-dependent end-to-end distributions for bridged, dangling, and looped chains in three dimensions as a function of associating end-group kinetics. Non-monotonic flow curves which can lead to flow instabilities during shear flow result at low equilibrium constant and high association rate from two complementary phenomena: a decrease in the fraction of elastically active chains with increasing shear rate and non-monotonic extension in the population of elastically active chains. Chain tumbling leads to reformation of bridges, resulting in an increased fraction of bridged chains at high Deborah number and significant reduction in the average bridge chain extension. In the start-up of steady shear, force-activated chain dissociation and chain tumbling cause both stress overshoot and stress ringing behaviour prior to reaching steady state stress values. During stress relaxation following steady shear, chain kinetics and extension mediate both the number of relaxations and the length of time required for system relaxation. While at low association rate relaxation is limited by the relaxation of dangling chains and the rate of dangling chain formation, at high association rate coupling of dangling and bridged chains leads to simultaneous relaxation of all chains due to a dynamic equilibrium between dangling and bridged states.

Publication: Soft Matter Vol.: 11 No.: 11 ISSN: 1744-683X

ID: CaltechAUTHORS:20150410-103544942

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Abstract: It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid description for charged surfaces in the so-called weak coupling limit. Here, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, there is no limiting condition for which the PB theory is valid.

Publication: Journal of Chemical Physics Vol.: 142 No.: 10 ISSN: 0021-9606

ID: CaltechAUTHORS:20150316-074943499

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Abstract: We propose an efficient simulation algorithm based on the dissipative particle dynamics (DPD) method for studying electrohydrodynamic phenomena in electrolyte fluids. The fluid flow is mimicked with DPD particles while the evolution of the concentration of the ionic species is described using Brownian pseudo particles. The method is designed especially for systems with high salt concentrations, as explicit treatment of the salt ions becomes computationally expensive. For illustration, we apply the method to electro-osmotic flow over patterned, superhydrophobic surfaces. The results are in good agreement with recent theoretical predictions.

Publication: Journal of Chemical Physics Vol.: 142 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:20150219-082241993

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Abstract: We provide a perspective on the thermodynamics of salt-doped block copolymer electrolytes consisting of ion-conducting and inert blocks, taking poly(ethylene oxide)-b-polystyrene and lithium salts as an example. We focus on the origin for enhanced immiscibility between the constituent blocks upon addition of lithium salts and discuss issues from selected experiments and from our recent self-consistent field study.

Publication: ACS Macro Letters Vol.: 3 No.: 8 ISSN: 2161-1653

ID: CaltechAUTHORS:20140918-092228450

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Abstract: We study the solvation of a single nanoparticle in poly(methyl methacrylate)–CO_2 mixture at coexistence by using statistical classical density-functional theory. In the temperature range where there is triple-phase coexistence, the lowest solvation free energy occurs at the triple point pressure. Beyond the end point temperature of the triple line, and for particle radii less than a critical value, there is an optimal pressure in the solvation free energy, as a result of the competition between the creation of nanoparticle–fluid interface and the formation of cavity volume. The optimal pressure decreases with increasing nanoparticle radius or the strength of nanoparticle attraction with the fluid components. The critical radius can be estimated from the pressure dependence of the interfacial tension between the fluid and the particle in the limit of infinitely large particle size (i.e., planar wall).

Publication: Journal of Physical Chemistry B Vol.: 118 No.: 28 ISSN: 1520-6106

ID: CaltechAUTHORS:20140821-090639372

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Abstract: Using the language of the Flory χ parameter, we develop a theory that unifies the treatment of the single-chain structure and the solution thermodynamics of polymers in poor solvents. The structure of a globule and its melting thermodynamics is examined using the self-consistent filed theory. Our results show that the chain conformation involves three states prior to the globule-to-coil transition: the fully collapsed globule, the swollen globule, and the molten globule, which are distinguished by the core density and the interfacial thickness. By examining the chain-length dependence of the melting of the swollen globule, we find universal scaling behavior in the chain properties near the Θ point. The information on density profile and free energy of the globule is used in the dilute solution thermodynamics to study the phase equilibrium of polymer solution. Our results show different scaling behavior of the solubility of polymers in the dilute solution compared to the F–H theory, both in the χ dependence and in the chain-length dependence. From the perspectives of single chain structure and solution thermodynamics, our results verify the consistency of the Θ point defined by different criteria in the limit of infinite chain length: the disappearance of the effective two-body interaction, the abrupt change in chain size, and the critical point in the phase diagram of the polymer solution. Our results show χ_Θ = 0.5 (for the case of equal monomer and solvent volume), which coincides with the value predicted from the F–H theory.

Publication: Macromolecules Vol.: 47 No.: 12 ISSN: 0024-9297

ID: CaltechAUTHORS:20140731-113937619

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Abstract: Mixtures of block copolymers and lithium salts are promising candidates for lithium battery electrolytes. Structural changes that occur during the order-to-disorder transition (ODT) in a diblock copolymer/salt mixture were characterized by small-angle X-ray scattering (SAXS). In salt-free block copolymers, the ODT is sharp, and the domain size of the ordered phase decreases with increasing temperature. In contrast, the ODT of the diblock copolymer/salt mixture examined here occurs gradually over an 11 °C temperature window, and the domain size of the ordered phase is a nonmonotonic function of temperature. We present an approach to estimate the fraction of the ordered phase in the 11 °C window where ordered and disordered phases coexist. The domain spacing of the ordered phase increases with increasing temperature in the coexistence window. Both findings are consistent with the selective partitioning of salt into the ordered domains, as predicted by Nakamura et al. ( ACS Macro Lett. 2013, 2, 478−481).

Publication: Macromolecules Vol.: 47 No.: 8 ISSN: 0024-9297

ID: CaltechAUTHORS:20140602-135911591

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Abstract: By treating both the short-range (solvation) and long-range (image force) electrostatic forces as well as charge polarization induced by these forces in a consistent manner, we obtain a simple theory for the self-energy of an ion that is continuous across the interface. Along with nonelectrostatic contributions, our theory enables a unified description of ions on both sides of the interface. Using intrinsic parameters of the ions, we predict the specific ion effect on the interfacial affinity of halogen anions at the water-air interface, and the strong adsorption of hydrophobic ions at the water-oil interface, in agreement with experiments and atomistic simulations.

Publication: Physical Review Letters Vol.: 112 No.: 13 ISSN: 0031-9007

ID: CaltechAUTHORS:20140530-110321209

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Abstract: Nucleation is a ubiquitous phenomenon in many physical, chemical, and biological processes. In this review, we describe recent progress on the theoretical study of nucleation in polymeric fluids and soft matter, including binary mixtures (polymer blends, polymers in poor solvents, compressible polymer–small molecule mixtures), block copolymer melts, and lipid membranes. We discuss the methodological development for studying nucleation as well as novel insights and new physics obtained in the study of the nucleation behavior in these systems.

Publication: Annual Review of Physical Chemistry Vol.: 65ISSN: 0066-426X

ID: CaltechAUTHORS:20140403-133743029

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Abstract: The study of the electrical double layer lies at the heart of soft matter physics and biophysics. Here, we address the effects of the image charges on the double layer structure and forces. For electrolyte solutions between two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. In comparison to a 1:1 electrolyte solution, both the attractive and the repulsive parts of the interaction are stronger for the 2:1 electrolyte solution. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like-charge attraction and charge inversion. These results are in stark contrast with predictions from the Poisson-Boltzmann theory.

Publication: Journal of Chemical Physics Vol.: 139 No.: 12 ISSN: 0021-9606

ID: CaltechAUTHORS:20131101-074353722

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Abstract: We present a general theory for the intrinsic viscosity of flexible polymers of arbitrary architecture. The theory is based on a partially permeable sphere model for which we introduce two phenomenological functions, the drag function ξ and the drainage function κ, that are determined by the density profile of the polymer. At the mean-field level, these functions capture the long-range, multibody, accumulative hydrodynamic interactions, that are responsible for the frictional dissipation in and around a polymer. The density profiles for a diversity of chain architectures are obtained by Monte Carlo simulation. Predictions from our theory are in good agreement with experimental data on all the polymer structures examined, ranging from linear, ring, and stars to hyperbranched and dendrimers. The concepts and methods we introduce in this work should be useful for studying other dilute solution frictional properties, such as the self-diffusivity, and provide a convenient framework for understanding the relationship between the molecular architecture and their dilute solution properties.

Publication: Macromolecules Vol.: 46 No.: 14 ISSN: 0024-9297

ID: CaltechAUTHORS:20130906-092122971

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Abstract: We study the microphase separation of block copolymer electrolytes containing lithium salts. Taking poly(ethylene oxide)-b-polystyrene (PEO-b-PS) as an example, we show that in the presence of lithium salts the disordered-to-lamellar phase transition becomes first-order even at the level of mean-field theory, with a moderate range of temperature in which both the disordered and lamellar phases coexist, and different salt concentration in the coexisting phases. The coexistence arises from the different partitioning of the salt ions between the disordered phase and the lamellar phase, driven primarily by the solvation energy of anions. A striking consequence of the coexistence is that heating a lamellar phase into the coexistence region leads to increased order in the remaining lamellar phase.

Publication: ACS Macro Letters Vol.: 2 No.: 6 ISSN: 2161-1653

ID: CaltechAUTHORS:20130916-150307749

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Abstract: We illustrate the effects of dielectric inhomogeneity on the statistical properties of polyelectrolytes in solution, by a lattice Monte Carlo simulation that combines the bond fluctuation model with a local algorithm for computing the electrostatic interactions. Our model accounts for the difference in the dielectric properties between the polymer backbone and the solvent. Taking the coil–globule transition of a single polyelectrolyte chain in solvent as an example, we show that the chain conformation and the degree of counterion condensation are substantially affected by the dielectric contrast.

Publication: Soft Matter Vol.: 9 No.: 24 ISSN: 1744-683X

ID: CaltechAUTHORS:20130712-081405274

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Abstract: We combine a newly developed density-functional theory with the string method to calculate the minimum free energy path of bubble nucleation in compressible polymer–CO_2 mixtures. Nucleation is initiated by saturating the polymer liquid with high pressure CO_2 and subsequently reducing the pressure to ambient condition. Below a critical temperature, we find that there is a discontinuous drop in the nucleation barrier with increased initial CO_2 pressure, as a result of an underlying metastable transition from a CO_2-rich-vapor phase to a CO_2-rich-liquid phase. This phenomenon is different from previously proposed nucleation mechanisms involving metastable transitions.

Publication: Journal of Physical Chemistry Letters Vol.: 4 No.: 10 ISSN: 1948-7185

ID: CaltechAUTHORS:20130815-134341407

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Abstract: We combine density-functional theory with the string method to calculate the minimum free energy path of bubble nucleation in two polymer–CO_2 mixture systems, poly(methyl methacrylate) (PMMA)–CO_2 and polystyrene (PS)–CO_2. Nucleation is initiated by saturating the polymer liquid with high pressure CO_2 and subsequently reducing the pressure to ambient condition. Below a critical temperature (Tc), we find that there is a discontinuous drop in the nucleation barrier as a function of increased initial CO_2 pressure (P0), as a result of an underlying metastable transition from a CO_2-rich-vapor phase to a CO_2-rich-liquid phase. The nucleation barrier is generally higher for PS–CO_2 than for PMMA–CO_2 under the same temperature and pressure conditions, and both higher temperature and higher initial pressure are required to lower the nucleation barrier for PS–CO2 to experimentally relevant ranges. Classical nucleation theory completely fails to capture the structural features of the bubble nucleus and severely underestimates the nucleation barrier.

Publication: Soft Matter Vol.: 9 No.: 40 ISSN: 1744-683X

ID: CaltechAUTHORS:20131025-104557519

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Abstract: Using field-theoretic techniques, we study the solvation of salt ions in liquid mixtures, accounting for the permanent and induced dipole moments, as well as the molecular volume of the species. With no adjustable parameters, we predict solvation energies in both single-component liquids and binary liquid mixtures that are in excellent agreement with experimental data. Our study shows that the solvation energy of an ion is largely determined by the local response of the permanent and induced dipoles, as well as the local solvent composition in the case of mixtures, and does not simply correlate with the bulk dielectric constant. In particular, we show that, in a binary mixture, it is possible for the component with the lower bulk dielectric constant but larger molecular polarizability to be enriched near the ion.

Publication: Physical Review Letters Vol.: 109 No.: 25 ISSN: 0031-9007

ID: CaltechAUTHORS:20130204-114214911

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Abstract: Within self-consistent field theory, we develop an “on-the-fly” string method to compute the minimum free energy path for several activated processes involving a charged, solvophobic nanoparticle and a lipid membrane. Under tensions well below the mechanical stability limit of the membrane, and in the regime where the event can occur on experimentally relevant time scales, our study suggests that there can be at least three competing pathways for crossing the membrane: (1) particle-assisted membrane rupture, (2) particle insertion into a metastable pore followed by translocation and membrane resealing, and (3) particle insertion into a metastable pore followed by membrane rupture. In the context of polymer-based gene delivery systems, we discuss the implications of these results for the endosomal escape mechanism.

Publication: Soft Matter Vol.: 8 No.: 48 ISSN: 1744-683X

ID: CaltechAUTHORS:20121220-114824437

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Abstract: We study the anomalous concentration effects in mixtures of side-chain liquid crystalline polymers (SCLCPs) and low-molecular-weight liquid crystals (LMWLCs) by modifying the theory of Brochard, Jouffroy, and Levinson (BJL) to include the effects of the polymer backbone. Our new theory considers both the interaction of the polymer backbone with the global nematic field, as well as the local steric constraints due to the grafting of the side groups onto the polymer backbone. In addition, we consider the enhancement in the coupling between the pedant mesogens and the LMWLC molecules as the SCLCP concentration increases. The resulting phase diagram and nematic order parameters are in qualitative agreement with experimental observations, but drastically different from the predictions by the BJL theory.

Publication: Macromolecules Vol.: 45 No.: 15 ISSN: 0024-9297

ID: CaltechAUTHORS:20120925-105542854

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Abstract: We study the phase equilibrium and nucleation behavior of polymers in poor solvent by accounting for the large, localized fluctuations in the form of single-chain globules and multichain clusters. The density profile and free energy of the single-chain globule and multichain clusters are obtained by self-consistent-field theory. This information is then used in the dilute solution thermodynamics to investigate the equilibrium cluster size distribution, solubility limit, and nucleation in the supersaturated state. Our results show that the solubility of the polymer in the dilute side of the solution is enhanced by several orders of magnitude relative to the prediction of the Flory–Huggins (F–H) theory, which scales with the chain length to the 2/3 power rather than a linear power as predicted from the F–H theory. Our results also suggest a higher critical value of χ, consistent with computer simulation and experiment results. In the supersaturated state, we work out an effective spinodal where the nucleation barrier to phase separation via growth of the clusters becomes comparable to the thermal energy k_(B)T. For a given supersaturation, we find that the nucleation barrier is quadratic in the chain length, suggesting a much slower precipitation rate for longer polymer chains.

Publication: Macromolecules Vol.: 45 No.: 15 ISSN: 0024-9297

ID: CaltechAUTHORS:20120926-114840182

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Abstract: We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO_2 and poly(methyl methacrylate) CO_2 systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.

Publication: Journal of Chemical Physics Vol.: 137 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20121115-103218482

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Abstract: We develop a self-consistent field theory for salt-doped diblock copolymers, such as polyethylene oxide (PEO)–polystyrene with added lithium salts. We account for the inhomogeneous distribution of Li+ ions bound to the ion-dissolving block, the preferential solvation energy of anions in the different block domains, the translational entropy of anions, the ion-pair equilibrium between polymer-bound Li+ and anion, and changes in the χ parameter due to the bound ions. We show that the preferential solvation energy of anions provides a large driving force for microphase separation. Our theory is able to explain many features observed in experiments, particularly the systematic dependence in the effective χ-parameter on the radius of the anions, the observed linear dependence in the effective χ on salt concentration, and increase in the domain spacing of the lamellar phase due to the addition of lithium salts. We also examine the relationship between two definitions of the effective χ parameter, one based on the domain spacing of the ordered phase and the other based on the structure factor in the disordered phase. We argue that the latter is a more fundamental measure of the effective interaction between the two blocks. We show that the ion distribution and the electrostatic potential profile depend strongly on the dielectric contrast between the two blocks and on the ability of the Li+ to redistribute along the backbone of the ion-dissolving block.

Publication: Soft Matter Vol.: 8 No.: 36 ISSN: 1744-6848

ID: CaltechAUTHORS:20121001-151047732

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Abstract: We propose a new density-functional theory (DFT) describing inhomogeneous polymer–carbon dioxide (CO2) mixtures. The theory is constructed by combining the bulk Peng–Robinson equation of state (PR-EOS) with the statistical associating fluid theory (SAFT) and the fundamental measure theory (FMT). The weight density functions from FMT are used to extend the bulk excess Helmholtz free energy of PR-EOS to the inhomogeneous case, while the SAFT is used to describe correlations due to polymer chain connectivity and short-range forces due to weakly polar or association interactions. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene–CO_2 and poly(methyl methacrylate)–CO_2 systems. The calculated interfacial tension values are in good agreement with experimental data at low to intermediate pressures. The inclusion of association energy for CO_2 is shown to have a significant effect. We also point out the limitation of the PR-EOS for describing polymer–CO_2 mixtures at high pressures (P > 35 MPa).

Publication: Industrial & Engineering Chemistry Research Vol.: 51 No.: 9 ISSN: 0888-5885

ID: CaltechAUTHORS:20120403-134847921

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Abstract: We present a simple theory for the intrinsic viscosity of polymers of arbitrary architectures, based on a partially permeable sphere model. The model introduces two phenomenological functions, the drainage function κ(r) and the drag function ξ(r), which are determined by the density profile, as a mean-field description of the multi-body, long-range and accumulated effects of the hydrodynamic interactions. By combining Debye's theory for free draining polymer chains with Einstein's theory for hard spheres, we arrive at a simple expression for the intrinsic viscosity. Results from our theory show broad agreement in all the key features of the intrinsic viscosity with existing experimental results for polymers ranging from linear chain to branched polymers to dendrimers.

Publication: Europhysics Letters Vol.: 97 No.: 6 ISSN: 0295-5075

ID: CaltechAUTHORS:20120502-145603835

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Abstract: We develop a theory for the thermodynamics of ion-containing polymer blends and diblock copolymers, taking polyethylene oxide (PEO), polystyrene and lithium salts as an example. We account for the tight binding of Li^+ ions to the PEO, the preferential solvation energy of anions in the PEO domain, the translational entropy of anions, and the ion-pair equilibrium between EO-complexed Li^+ and anion. Our theory is able to predict many features observed in experiments, particularly the systematic dependence in the effective χ parameter on the size of the anions. Furthermore, comparison with the observed linear dependence in the effective χ on salt concentration yields an upper limit for the binding constant of the ion pair.

Publication: Physical Review Letters Vol.: 107 No.: 19 ISSN: 0031-9007

ID: CaltechAUTHORS:20111223-110114533

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Abstract: We establish an appropriate thermodynamic framework for determining the optimal genome length in electrostatically driven viral encapsidation. Importantly, our analysis includes the electrostatic potential due to the Donnan equilibrium, which arises from the semipermeable nature of the viral capsid, i.e., permeable to small mobile ions but impermeable to charged macromolecules. Because most macromolecules in the cellular milieu are negatively charged, the Donnan potential provides an additional driving force for genome encapsidation. In contrast to previous theoretical studies, we find that the optimal genome length is the result of combined effects from the electrostatic interactions of all charged species, the excluded volume and, to a very significant degree, the Donnan potential. In particular, the Donnan potential is essential for obtaining negatively overcharged viruses. The prevalence of overcharged viruses in nature may suggest an evolutionary preference for viruses to increase the amount of genome packaged by utilizing the Donnan potential (through increases in the capsid radius), rather than high charges on the capsid, so that structural stability of the capsid is maintained.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 108 No.: 41 ISSN: 0027-8424

ID: CaltechAUTHORS:20111109-073727841

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Abstract: We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.

Publication: Journal of Chemical Physics Vol.: 135 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:20110804-092317279

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Abstract: The dynamics of a collapsing polymer under a temperature quench in dilute solution is investigated by dissipative particles dynamics. Hydrodynamic interactions and many-body interaction are preserved naturally by incorporating explicit solvent particles in this approach. Our simulation suggests a four-stage collapse pathway: localized clusters formation, cluster coarsening in situ, coarsening involving global backbone conformation change into a crumpled globule, and compaction of the globule. For all the quench depths and chain lengths used in our study, collapse proceeds without the chain getting trapped in a metastable “sausage” configuration, as reported in some earlier studies. We obtain the time scales for each of the first three stages, as well as its scaling with the quench depths ξ and chain lengths N. The total collapse time scales as τ_c ~ ξ^(−0.46 ± 0.04)N^(0.98 ± 0.09), with the quench depth and degree of polymerization.

Publication: Journal of Chemical Physics Vol.: 134 No.: 24 ISSN: 0021-9606

ID: CaltechAUTHORS:20110718-093610060

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Abstract: We combine dynamic self-consistent field theory with the string method to calculate the minimum energy path to membrane pore formation and rupture. In the regime where nucleation can occur on experimentally relevant time scales, the structure of the critical nucleus is between a solvophilic stalk and a locally thinned membrane. Classical nucleation theory fails to capture these molecular details and significantly overestimates the free energy barrier. Our results suggest that thermally nucleated rupture may be an important factor for the low rupture strains observed in lipid membranes.

Publication: Physical Review Letters Vol.: 106 No.: 16 ISSN: 0031-9007

ID: CaltechAUTHORS:20110525-082556253

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Abstract: We employ self-consistent field theory to study the thermodynamics of membrane-particle interactions in the context of gene delivery systems, with the aim to guide the design of dendrimers that can overcome the endosomal escape barrier by inserting into membranes and creating pores. We consider the interaction between a model polyamidoamine dendrimer and a membrane under controlled tension as a function of the separation between the dendrimer and the membrane. In all the cases we have studied, the lowest free energy state corresponds to the membrane partially wrapping the dendrimer. However, with moderate tension, we find that a G5 (or larger) generation dendrimer, through thermal fluctuation, can induce the formation of metastable pores. These metastable pores are subsequently shown to significantly lower the critical tension necessary for membrane rupture, thus possibly enhancing the release of the trapped genetic material from the endosome.

Publication: Biophysical Journal Vol.: 100 No.: 5 ISSN: 0006-3495

ID: CaltechAUTHORS:20110322-135958575

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Abstract: We study the thermodynamics and chain conformation of side-chain liquid crystal polymers (SCLCPs) in the bulk using the self-consistent-field approach and a new model to account for the coupling between the orientation of the side-chain liquid-crystal (LC) groups and that of the backbone segments. The new model accounts for both a global coupling between the polymer backbone and the nematic field and a local coupling between the polymer backbone and its attached LC group. Here, the terms global and local refer to the chemical (backbone) distance between the groups. A phenomenological parameter is introduced to represent the coupling strength and nature of the attachment, i.e., end-on vs side-on. The nematic field is shown to control the chain conformation through both the global and the local coupling effects. For the side-on SCLCPs, these two coupling effects act cooperatively so that the chain conformation is always prolate. For the end-on SCLCPs, these two effects act competitively. The chain conformation can be either oblate or prolate in this case, and depends on the relative strengths of these two couplings. On the other hand, the chain conformation also affects the nematic field, primarily through the global coupling. The prolate conformation enhances the nematic field and increases the phase transition temperature, whereas the oblate conformation frustrates the nematic field and decreases the transition temperature. The nematic order parameter is found to be determined mainly by the reduced temperature, and is not sensitive to the coupling effects. Furthermore, we show that the grafting density of the LC side groups has a significant effect on the chain conformation due to the orientational competition between the LC attached and unattached segments. For the end-on SCLCPs with lower graft density, the conformation of the chain backbone can be oblate at higher temperatures and prolate at lower temperatures, in agreement with the re-entrant nematic phase observed in experiments.

Publication: Macromolecules Vol.: 43 No.: 23 ISSN: 0024-9297

ID: CaltechAUTHORS:20110105-134943048

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Abstract: We report on the thermal properties, phase behavior, and thermodynamics of a series of polystyrene-block-poly(ethylene oxide) copolymers (SEO) mixed with the ionic species Li[N(SO_(2)CF_3)_2] (LiTFSI), imidazolium TFSI (ImTFSI), and an equimolar mixture of LiTFSI and ImTFSI (Mix). Differential scanning calorimetric scans reveal similar thermal behavior of SEO/LiTFSI and SEO/ImTFSI at the same salt concentrations. Phase behavior and thermodynamics were determined using a combination of small-angle X-ray scattering and birefringence. The thermodynamics of our mixtures can be mapped on to the theory of neat block copolymer phase behavior provided the Flory−Huggins interaction parameter, χ, between the blocks is replaced by an effective χ (χ_(eff)) that increases linearly with salt concentration. The phase behavior and the value of m, the slope of the χ_(eff) versus salt concentration data, were similar for SEO/LiTFSI, SEO/ImTFSI, and SEO/Mix blends. The theory developed by Wang [ J. Phys. Chem. B. 2008, 41, 16205] provides a basis for understanding the fundamental underpinnings of the measured value of m. We compare our experimental results with the predictions of this theory with no adjustable parameters.

Publication: Macromolecules Vol.: 43 No.: 19 ISSN: 0024-9297

ID: CaltechAUTHORS:20101028-094727435

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Abstract: We perform lattice Monte Carlo simulation using the bond-fluctuation model to examine the conformation and dynamic properties of a single small flexible ring polymer in the matrix of linear chains as functions of the degree of polymerization of the linear chains. The average conformation properties as gauged by the mean-square radius of gyration and asphericity parameter are insensitive to the chain length for all the chain lengths examined (30, 100, 300, and 1000). However, in the longer chain (300 and 1000) samples, there is an increased spread in the distribution of the value of these quantities, suggesting structural heterogeneity. The center-of-mass diffusion of the ring shows a rapid decrease with increasing chain length followed by a more gradual change for the two longer chain systems. In these longer chain systems, a wide spread in the value of the apparent self-diffusion coefficient is also observed, as well as qualitatively different square displacement trajectories among the different samples, suggesting heterogeneity in the dynamics. A primitive path analysis reveals that in these long chain systems, the ring can exist in topologically distinct states with respect to threading by the linear chains. Threading by the linear chain can dramatically slow down and in some cases stall the diffusive motion of the ring. We argue that the life times for these topological conformers can be longer than the disentanglement time of the linear chain matrix, so that the ring exhibits nonergodic behavior on time scales less or comparable to the life time of these conformers. Our results suggest a picture of the ring diffusion as one where the diffusion path consists of distinctive segments, each corresponding to a different conformer, with slow interconversion between the different conformers.

Publication: Journal of Chemical Physics Vol.: 133 No.: 6 ISSN: 0021-9606

ID: CaltechAUTHORS:20100908-152606750

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Abstract: The intrinsic viscosity of dendrimers in solution shows several anomalous behaviors that have hitherto not been explained within the existing theoretical frameworks of either Zimm or Rouse. Here we propose a simple two-zone model based on the radial segmental density profile of the dendrimers and combine a non-draining core with a free-draining outer region description, to arrive at a simple formula that captures most of the main features in the intrinsic viscosity data obtained in experiments.

Publication: Soft Matter Vol.: 6 No.: 12 ISSN: 1744-6848

ID: CaltechAUTHORS:20100630-143040341

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Abstract: We study micelles formed by the coil−comb block copolymer, A-b-(A-g-B), in a B-selective solvent, S. The equilibrium distribution of micelles is obtained according to the thermodynamics of noninteracting micellar solutions, with the free energy of a single isolated micelle calculated using the self-consistent-field theory. Depending on the lengths of the various blocks and the balance of interactions, two types of micelles of different sizes and structures can be observed. This is a manifestation of the competition between two micellar assemblies of the coil−comb block copolymer at different length scales.

Publication: Macromolecules Vol.: 43 No.: 4 ISSN: 0024-9297

ID: CaltechAUTHORS:20100302-131414201

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Abstract: We address the issue of the self energy of the mobile ions in electrolyte solutions within a general Gaussian renormalized fluctuation theory using a field-theoretic approach. We introduce the Born radii of the ions in the form of a charge distribution allowing for different Born radii between the cations and anions. The model thus automatically yields a theory free of divergences and accounts for the solvation of the ions at the level of continuous dielectric media. In an inhomogeneous dielectric medium, the self energy is in general position dependent and differences in the self energy between cations and anions can give rise to local charge separation in a macroscopically neutral system. Treating the Born radius a as a smallness parameter, we show that the self energy can be split into an O(a^(−1)) nonuniversal contribution and an O(a^0) universal contribution that depends only on the ion concentration, valency, and the spatially varying dielectric constant. For a weakly inhomogeneous dielectric medium, the nonuniversal part of the self energy is shown to have the form of the Born energy with the local dielectric constant. This self energy is incorporated into the Poisson-Boltzmann equation as a simple means of including this local fluctuation effect in a mean-field theory. We illustrate the phenomenon of charge separation by considering cations and anions of difference sizes and valencies in a periodic dielectric medium.

Publication: Physical Review E Vol.: 81 No.: 2 ISSN: 1539-3755

ID: CaltechAUTHORS:20100324-111453101

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Abstract: Hepatitis B virus (HBV) is a contagious human pathogen causing liver diseases such as cirrhosis and hepatocellular carcinoma. An essential step during HBV replication is packaging of a pregenomic (pg) RNA within the capsid of core antigens (HBcAgs) that each contains a flexible C-terminal tail rich in arginine residues. Mutagenesis experiments suggest that pgRNA encapsidation hinges on its strong electrostatic interaction with oppositely charged C-terminal tails of the HBcAgs, and that the net charge of the capsid and C-terminal tails determines the genome size and nucleocapsid stability. Here, we elucidate the biophysical basis for electrostatic regulation of pgRNA packaging in HBV by using a coarse-grained molecular model that explicitly accounts for all nonspecific interactions among key components within the nucleocapsid. We find that for mutants with variant C-terminal length, an optimal genome size minimizes an appropriately defined thermodynamic free energy. The thermodynamic driving force of RNA packaging arises from a combination of electrostatic interactions and molecular excluded volume effects. The theoretical predictions of the RNA length and nucleocapsid internal structure are in good agreement with available experiments for the wild-type HBV and mutants with truncated HBcAg C-termini.

Publication: Biophysical Journal Vol.: 96 No.: 8 ISSN: 0006-3495

ID: CaltechAUTHORS:20090903-143638577

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Abstract: We study the interplay between microphase assembly and macrophase separation in A/B/AB ternary polymer blends by examining the free energy of localized fluctuation structures (micelles or droplets), with emphasis on the thermodynamic relationship between swollen micelles (microemulsion) and the macrophase-separated state, using self-consistent field theory and an extended capillary model. Upon introducing homopolymer B into a micelle-forming binary polymer blend A/AB, micelles can be swollen by B. A small amount of component B (below the A-rich binodal of macrophase coexistence) will not affect the stability of the swollen micelles. A large excess of homopolymer, B, will induce a microemulsion failure and lead to a macrophase separation. Between the binodal and the microemulsion failure concentration, macrophase separation in A/B/AB occurs by a two-step nucleation mechanism via a metastable microemulsion droplet of finite size. Our results illustrate a recently proposed argument that the two-step nucleation via a metastable intermediate is a general phenomenon in systems involving short-range attraction and long-range repulsion.

Publication: Journal of Chemical Physics Vol.: 130 No.: 15 ISSN: 0021-9606

ID: CaltechAUTHORS:20090803-100239123

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Abstract: We develop a mechanochemical model for the dynamics of cellulase, a two-domain enzyme connected by a peptide linker, as it extracts and hydrolyzes a cellulose polymer from a crystalline substrate. We consider two random walkers, representing the catalytic domain (CD) and the carbohydrate binding module (CBM), whose rates for stepping are biased by the coupling through the linker and the energy required to lift the cellulose polymer from the crystalline surface. Our results show that the linker length and stiffness play a critical role in the cooperative action of the CD and CBM domains and that, for a given linker length, the steady-state hydrolysis shows a maximum at some intermediate linker stiffness. The maximum hydrolysis rate corresponds to a transition of the linker from a compressed to an extended conformation, where the system exhibits maximum fluctuation, as measured by the variance of the separation distance between the two domains and the dispersion around the mean hydrolysis speed. In the range of experimentally known values of the parameters of our model, improving the intrinsic hydrolytic activity of the CD leads to a proportional increase in the overall hydrolysis rate.

Publication: Journal of Physical Chemistry B Vol.: 113 No.: 14 ISSN: 1520-6106

ID: CaltechAUTHORS:20090629-095421715

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Abstract: We study the effects of adding salt ions on the miscibility of a binary blend of polymers having different dielectric constants. The competition between the preference of the ions to be solvated by the component of the higher dielectric constant and the entropic tendency for the ions to be distributed uniformly results in nontrivial effects on the miscibility. We first study the thermodynamics of the polymer blend−ion mixture using a simple Born model in a uniform dielectric medium of the average composition of the polymer blend. We then study the effect of local enrichment of the higher dielectric constant polymer near the ion. We find that when the dielectric constants of the polymers are both low, adding salt decreases the miscibility, while when the dielectric constants of the polymers are both high, the addition of salt enhances the miscibility. When the blend consists of a high dielectric constant polymer and a low dielectric constant polymer, miscibility is decreased if the low dielectric constant component is the majority and is increased if the high dielectric constant component is the majority. The effect becomes significant at ion concentrations corresponding to an order of one ion per polymer chain. The quantitative change in the effective χ parameter depends on the functional form of the composition dependence of the dielectric constant of the mixture. We also illustrate the difference between fixed ion concentration and fixed chemical potential of the ions.

Publication: Journal of Physical Chemistry B Vol.: 112 No.: 50 ISSN: 1520-6106

ID: CaltechAUTHORS:WANjpcb08

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Abstract: When cooled or compressed sufficiently rapidly, a liquid vitrifies into a glassy amorphous state. Vitrification in a dense liquid is associated with jamming of the particles. For hard spheres, the density and degree of order in the final structure depend on the compression rate: simple intuition suggests, and previous computer simulation demonstrates, that slower compression results in states that are both denser and more ordered. In this work, we use the Lubachevsky-Stillinger algorithm to generate a sequence of structurally arrested hard-sphere states by varying the compression rate. We find that while the degree of order, as measured by both bond-orientation and translation order parameters, increases monotonically with decreasing compression rate, the density of the arrested state first increases, then decreases, then increases again, as the compression rate decreases, showing a minimum at an intermediate compression rate. Examination of the distribution of the local order parameters and the distribution of the root-mean-square fluctuation of the particle positions, as well as direct visual inspection of the arrested structures, reveal that they are structurally heterogeneous, consisting of disordered, amorphous regions and locally ordered crystal-like domains. In particular, the low-density arrested states correspond with many interconnected small crystal clusters that form a polycrystalline network interspersed in an amorphous background, suggesting that jamming by the domains may be an important mechanism for these states.

Publication: Europhysics Letters Vol.: 84 No.: 2 ISSN: 0295-5075

ID: CaltechAUTHORS:LIZepl08

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Abstract: Recent experimental and theoretical studies of biomimetic membrane adhesions [Bruinsma et al., Phys. Rev. E 61, 4253 (2000); Boulbitch et al., Biophys. J. 81, 2743 (2001)] suggested that adhesion mediated by receptor interactions is due to the interplay between membrane undulations and a double-well adhesion potential, and should be a first-order transition. We study the nucleation of membrane adhesion by finding the minimum-energy path on the free energy surface constructed from the bending free energy of the membrane and the double-well adhesion potential. We find a nucleation free energy barrier around 20kBT for adhesion of flexible membranes, which corresponds to fast nucleation kinetics with a time scale of the order of seconds. For cell membranes with a larger bending rigidity due to the actin network, the nucleation barrier is higher and may require active processes such as the reorganization of the cortex network to overcome this barrier. Our scaling analysis suggests that the geometry of the membrane shapes of the adhesion contact is controlled by the adhesion length that is determined by the membrane rigidity, the barrier height, and the length scale of the double-well potential, while the energetics of adhesion is determined by the depths of the adhesion potential. These results are verified by numerical calculations.

Publication: Physical Review E Vol.: 77 No.: 2 ISSN: 1539-3755

ID: CaltechAUTHORS:ZHApre08

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Abstract: In this paper, we analyze the thermodynamics of interactions between surfaces mediated by polymer-tethered ligand-receptor binding. From statistical thermodynamics calculations, we obtain an effective two-dimensional binding constant reflecting contributions from the microscopic binding affinity as well as from the conformation entropy of the polymer tethers. The total interaction is a result of the interplay between attractive binding and repulsion due to confinement of the polymer chains. We illustrate the differences between three scenarios when the binding molecules are (1) immobile, (2) mobile with a fixed density, and (3) mobile with a fixed chemical potential (connected to a reservoir), which correspond to different biological or experimental situations. The key features of interactions, including the range of adhesion (onset of binding) and the equilibrium separation, can be obtained from scaling analysis and are verified by numerical solutions. In addition, we also extend our method of treating the quenched case with immobile ligands and receptors developed in a previous paper [Martin, J. I.; Zhang, C.-Z.; Wang, Z.-G. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2621−2637] as a density expansion in terms of both ligand and receptor densities. Finally, we examine several cases having ligand-receptor pairs with different tether lengths and binding affinities, and/or nonbinding linear polymers as steric repellers. Such systems can exhibit complex interactions such as a double-well potential, or a bound state with an adjustable barrier (due to the repellers), which have both biological and bioengineering relevance.

Publication: Langmuir Vol.: 23 No.: 26 ISSN: 0743-7463

ID: CaltechAUTHORS:20170725-072342785

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Abstract: The authors examine the possibility of a two-step nucleation to the bulk condensation transition that proceeds via a metastable liquid cluster intermediate having some preferred size. The metastable intermediate is stabilized by electrostatic repulsion, which becomes screened by small mobile ions at sufficiently large cluster sizes, thus allowing the eventual condensation to a bulk phase. Our calculation employs a capillary model for the cluster and the electrostatic interactions are treated using the Poisson-Boltzmann approach. Condensation via this metastable intermediate may be a very general phenomenon which applies not only to solutions of charged particles (e.g., proteins, colloidal particles, and polyelectrolytes) but to any system involving short-range attraction and long-range repulsion undergoing macrophase separation in which a metastable microphase separation is also possible.

Publication: Journal of Chemical Physics Vol.: 127 No.: 8 ISSN: 0021-9606

ID: CaltechAUTHORS:HUTjcp07

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Abstract: We present a thermodynamic analysis of protein adsorption to a mixed lipid monolayer containing a binding component and a nonbinding component at constant surface pressure. We derive the general equations for the adsorption isotherm and for the area expansion of the monolayer. In the limits of either low or high surface coverage, simplified forms of these equations are obtained. We construct simple thermodynamic models to examine the crossover from low to high surface coverage.

Publication: Industrial & Engineering Chemistry Research Vol.: 45 No.: 16 ISSN: 0888-5885

ID: CaltechAUTHORS:20170421-092507037

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Abstract: A simple field-theoretic simulation method based on a compressible random-phase approximation (RPA) theory has been suggested to understand the self-assembly behavior and its pressure responses of compressible block copolymer systems. Finite compressibility is incorporated in the free energy functional for the dissipative dynamics through effective RPA interactions that account for the excluded volume and the attractive nonbonded interactions. It was shown that basic equation-of-state parameters completely characterizing given block components readily yield stable and metastable morphologies without any presumed symmetry over a wide range of temperature−pressure−composition space for copolymer melts in unconfined or confined geometry. It was demonstrated that the simulation tool is capable of predicting in a unified way block copolymer phase behavior, not only exhibiting nanoscale ordering either upon cooling or reversely upon heating, but also revealing barotropicity and baroplasticity.

Publication: Macromolecules Vol.: 39 No.: 13 ISSN: 0024-9297

ID: CaltechAUTHORS:20170724-095313046

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Abstract: In this work we introduce a simple lattice model with T-shaped molecules in two dimensions that exhibits a rich range of morphological behaviors. Depending on the volume fraction and quench path, this system can adopt uniform liquid, solution, and phase-separated states, as well as inhomogeneous glass or gel-like states, as revealed by dynamic mean-field simulations. An important characteristic of this system is the existence of a large number of degenerate low-energy states with small barriers that leads to a broad, kinetically explored landscape. The mean-field stability and phase diagram of this model is constructed and provides a useful guide for understanding the complex behaviors of the system. One striking feature is that there is a cascade of instabilities that converge to mark the onset of what we identify as the glass transition. Both dynamic mean-field and Monte Carlo simulations reveal glass-like relaxation dynamics. Our results lead to a picture of gelation as a continuation of the glass transition into the two-phase region, or equivalently, as an incomplete phase separation arrested by the onset of the glass transition.

Publication: Journal of Physical Chemistry B Vol.: 110 No.: 12 ISSN: 1520-6106

ID: CaltechAUTHORS:20170606-105748587

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Abstract: We study the microstructural glass transition in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter—the inverse of the scaled degree of polymerization [overline N]—which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite chain length, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of microphase-separating system. We also study the order-disorder transition (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous studies of the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. In melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), but for asymmetric copolymers, it is possible for the glass transition to precede the ordering transition.

Publication: Physical Review E Vol.: 73 No.: 3 ISSN: 1539-3755

ID: CaltechAUTHORS:ZHApre06

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Abstract: We find exact expressions for the end-to-end distance vector distribution function with fixed end orientations for the wormlike chain model. This function in Fourier-Laplace space adopts the form of infinite continued fractions, which emerges upon exploiting the hierarchical structure of the moment-based expansion. Our results are used to calculate the root-mean-square end displacement in a given direction for a chain with both end orientations fixed. We find that the crossover from rigid to flexible chains is marked by the root-mean-square end displacement slowly losing its angular dependence as the coupling between chain conformation and end orientation wanes. However, the coupling remains strong even for relatively flexible chains, suggesting that the end orientation strongly influences chain conformation for chains that are several persistence lengths long. We then show the behavior of the distribution function by a density plot of the probability as a function of the end-to-end distance vector for a wormlike chain in two dimensions with one end pointed in a fixed direction and the other end free (in its orientation). As we progress from high to low rigidity, the distribution function shifts from being peaked at a location near the full contour length of the chain in the forward direction, corresponding to a straight configuration, to being peaked near zero end separation, as in the Gaussian limit. The function exhibits double peaks in the crossover between these limiting behaviors.

Publication: Physical Review E Vol.: 72 No.: 4 ISSN: 1539-3755

ID: CaltechAUTHORS:SPApre05

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Abstract: A theoretical examination of kinetic mechanisms for forming knots and links in nucleic acid structures suggests that molecules involving base pairs between loops are likely to become topologically trapped in persistent frustrated states through the mechanism of ‘helix-driven wrapping’. Augmentation of the state space to include both secondary structure and topology in describing the free energy landscape illustrates the potential for topological effects to influence the kinetics and function of nucleic acid strands. An experimental study of metastable complementary ‘kissing hairpins’ demonstrates that the topological constraint of zero linking number between the loops effectively prevents conversion to the minimum free energy helical state. Introduction of short catalyst strands that break the topological constraint causes rapid conversion to full duplex.

Publication: Nucleic Acids Research Vol.: 33 No.: 13 ISSN: 0305-1048

ID: CaltechAUTHORS:BOInar05

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Abstract: Taking a nucleation perspective, we study the nature of the disordered micelles in highly asymmetric, sphere-forming diblock copolymer melts using the self-consistent-field theory. The micelles are shown to correspond to strong, activated, localized composition fluctuations in the disordered state due to finite molecular weights. By taking into account the translational entropy of the micelles, we obtain the concentration and the free energy of the disordered micelles. The critical micelle temperature (in terms of the familiar combination χN), operationally defined to correspond to the onset of sufficient number of micelles in the system, is identified by invoking a criterion involving the concentration of micelles. The disordered micelles are part of the disordered phase, and the only phase transition between the disordered state and the ordered phase is the order−disorder transition (ODT). However, there exists a sharply defined temperature (higher than the critical micelle temperature), which we term the micelle dissociation temperature, beyond which micelles with finite lifetimes become impossible. The range of χN for the disordered micelles to be observable shrinks as N-1/2 with increasing degrees of polymerization N of the copolymers. In the infinite molecular weight limit, the window vanishes and the mean-field phase diagram calculated by Matsen and Bates is recovered. The disordered micelles, as a part of the disordered phase, contribute to the increased scattering intensity and the low-q shift of the structure factor in diblock copolymer melts near the ODT.

Publication: Macromolecules Vol.: 38 No.: 5 ISSN: 0024-9297

ID: CaltechAUTHORS:20170724-072208958

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Abstract: We develop a method for calculating the exact free energy of tree clusters formed from associating telechelic molecules. The method uses the concept of rooted trees from the graph theory to enumerate all topologically distinct trees having a maximum degree of branching; it recursively separates the trees into different classes based on their connectivity, thus enabling the exact summation of the trees weighted by their respective Boltzmann factors. We apply our method to studying the pregel properties in pure telechelic solutions and in mixed telechelic and single-associating-end polymer solutions. We highlight the effect of energetic tendency for branching in the former and the effect of competitive association in the latter.

Publication: Langmuir Vol.: 20 No.: 18 ISSN: 0743-7463

ID: CaltechAUTHORS:20170427-110128717

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Abstract: We provide exact results for the Laplace-transformed partition function of a wormlike chain subject to a tensile force and in a nematic field, in both two and three dimensions. The results are in the form of infinite continued fractions, which are obtained by exploiting the hierarchical structure of a moment-based expansion of the partition function. The case of an imaginary force corresponds to the end-to-end distance distribution in Laplace−Fourier space. We illustrate the utility of these exact results by examining the structure factor of a wormlike chain, the deformation free energy of a chain in a nematic field, and the self-consistent-field solution for the isotropic−nematic transition of wormlike chains.

Publication: Macromolecules Vol.: 37 No.: 15 ISSN: 0024-9297

ID: CaltechAUTHORS:20170426-132616212

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Abstract: We study nucleation in binary polymer blends in the presence of mesoscopic spherical particles using self-consistent field theory, considering both heterogeneous and homogeneous nucleation mechanisms. Heterogeneous nucleation is found to be highly sensitive to surface selectivity and particle size, with rather subtle dependence on the particle size. Particles that preferentially adsorb the nucleating species generally favor heterogeneous nucleation. For sufficiently strong adsorption, barrierless nucleation is possible. By comparing the free energy barrier for homogeneous and heterogeneous nucleation, we construct a kinetic phase diagram.

Publication: Journal of Chemical Physics Vol.: 121 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:WANJjcp04

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Abstract: Protein function can be tuned using laboratory evolution, in which one rapidly searches through a library of proteins for the properties of interest. In site-directed recombination, n crossovers are chosen in an alignment of p parents to define a set of p(n + 1) peptide fragments. These fragments are then assembled combinatorially to create a library of p^(n+1) proteins. We have developed a computational algorithm to enrich these libraries in folded proteins while maintaining an appropriate level of diversity for evolution. For a given set of parents, our algorithm selects crossovers that minimize the average energy of the library, subject to constraints on the length of each fragment. This problem is equivalent to finding the shortest path between nodes in a network, for which the global minimum can be found efficiently. Our algorithm has a running time of O(N^3p^2 + N^2n) for a protein of length N. Adjusting the constraints on fragment length generates a set of optimized libraries with varying degrees of diversity. By comparing these optima for different sets of parents, we rapidly determine which parents yield the lowest energy libraries.

Publication: Protein Engineering, Design and Selection Vol.: 17 No.: 7 ISSN: 1741-0126

ID: CaltechAUTHORS:20111012-101511149

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Abstract: We study the thermodynamics and single-chain statistics of wormlike polymer solutions with Maier–Saupe-type interactions using self-consistent-field (SCF) theory. The SCF equations are derived using a systematic field-theoretical approach which yields the SCF equations as the lowest order approximation, but permits fluctuation corrections to be incorporated. We solve the SCF equations using the spheroidal functions, which provides a nonperturbative description of the thermodynamics and single-chain statistics in the nematic state for arbitrary degrees of nematic order. Several types of phase diagrams are predicted, with an emphasis on the limit of metastability (spinodal) associated with each phase. The shape and location of these spinodals suggest interesting scenarios for the phase transition kinetics. A large but finite persistence length is shown to significantly decrease the isotropic–nematic transition temperature relative to that for rigid rods. In the nematic state, the mean-square end-to-end distance in the parallel and perpendicular directions are governed by two separate correlation lengths. An exact relationship between these correlation lengths and the eigenvalues of the spheroidal functions is provided, which reproduces the analytical expressions predicted from earlier studies in the limit of large nematic strength. The dominant contribution to the single-chain thermodynamics is shown to arise from small amplitude undulations in the directions perpendicular to the nematic direction; the presence of hairpins, though crucial for determining the dimensions of the polymer, has insignificant consequences on the single-chain thermodynamics.

Publication: Journal of Chemical Physics Vol.: 119 No.: 24 ISSN: 0021-9606

ID: CaltechAUTHORS:SPAjcp03

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Abstract: In this paper, we develop a model for the dynamics of water near a protein surface and compare with experimental results obtained with femtosecond resolution. The model consists of a layer of bound and free water molecules at the surface of the protein in dynamic equilibrium with each other, coupled to bulk water away from the protein surface. A previous model (Pal et al. J. Phys. Chem. B 2002, 106, 12376) considered the exchange in the layer without the coupling to the bulk. We find that water dynamics at the protein surface are described by two time scales, a fast, bulklike time scale, and a slower one more than 1 order of magnitude longer. The slow time scale, as in the previous model, is shown to be inversely proportional to the bound-to-free water conversion rate, k_2, but with a significant dependence on the free-to-bound conversion rate k_1, the diffusion of the free water molecules, and the thickness of the layer. This effect, identified as the feedback mechanism, is found to depend on the degree of orientation of the bound water molecules at the surface. The weight of the contribution of the slow component to the overall relaxation dynamics is shown to be inversely proportional to the slow decay time. For a heterogeneous surface with spatially varying k_2, the water dynamics in a probe region covering several sites is described by the cumulated effects from these water molecules, with the slow dynamics given by a sum of exponentials, with contributions inversely proportional to their respective decay times. To a very good degree, we find that this exponential behavior can be fitted to a single exponential; however, the apparent time scale does not represent that of any particular site. These conclusions are in good agreement with experimental results and provide important insight to the observed dynamical behavior.

Publication: Journal of Physical Chemistry B Vol.: 107 No.: 47 ISSN: 1520-6106

ID: CaltechAUTHORS:20160817-132622138

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Abstract: We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length lp, and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/lp. For R/lp>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/lp<4, a damped oscillatory behavior is predicted.

Publication: Physical Review Letters Vol.: 91 No.: 16 ISSN: 0031-9007

ID: CaltechAUTHORS:SPAprl03

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Abstract: The computational algorithm SCHEMA was developed to estimate the disruption caused when amino acid residues that interact in the three-dimensional structure of a protein are inherited from different parents upon recombination. To evaluate how well SCHEMA predicts disruption, we have shuffled the distantly-related beta-lactamases PSE-4 and TEM-1 at 13 sites to create a library of 2^(14) (16,384) chimeras and examined which ones retain lactamase function. Sequencing the genes from ampicillin-selected clones revealed that the percentage of functional clones decreased exponentially with increasing calculated disruption (E = the number of residue-residue contacts that are broken upon recombination). We also found that chimeras with low E have a higher probability of maintaining lactamase function than chimeras with the same effective level of mutation but chosen at random from the library. Thus, the simple distance metric used by SCHEMA to identify interactions and compute E allows one to predict which chimera sequences are most likely to retain their function. This approach can be used to evaluate crossover sites for recombination and to create highly mosaic, folded chimeras.

Publication: Protein Science Vol.: 12 No.: 8 ISSN: 0961-8368

ID: CaltechAUTHORS:20110913-173426256

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Abstract: The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the mean-field Landau–Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free energy is anisotropic and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar–cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30–400 cylinders across with aspect ratios of 4–10 and nucleation barriers of (30–40)kBT are typically found. The general trend is to larger critical droplets, higher aspect ratios, and smaller nucleation barriers as the mean-field critical point is approached.

Publication: Journal of Chemical Physics Vol.: 118 No.: 22 ISSN: 0021-9606

ID: CaltechAUTHORS:WICjcp03

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Abstract: The effects of adding AB diblock copolymers to A/B binary blends on the structure and thermodynamics of critical nuclei are studied using the self-consistent field theory. At a fixed ratio of the amount of the two homopolymers, depending on the degree of polymerization and composition of the diblocks, their addition to the blends can either increase or decrease the nucleation free energy barrier relative to the pure A/B blends. The qualitative trend can be deduced from the shift in the coexistence boundary and the spinodal. The distribution of diblock copolymers in critical nuclei depends on the composition of the diblocks and the quench depth. Near the coexistence, symmetric diblocks exhibit surfactant behavior, being highly concentrated on the interface of the critical nuclei. Near the spinodal, they act more like co-solvent with a relatively uniform distribution.

Publication: Journal of Chemical Physics Vol.: 118 No.: 19 ISSN: 0021-9606

ID: CaltechAUTHORS:WANjcp03

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Abstract: A theory for concentration fluctuations in binary polymer blends is developed using field-theoretic techniques. The theory provides a simple, unified framework for addressing a number of important issues. First, consideration of the fluctuation and correlation effects on different length scales leads to a clarification of three different chi parameters and their interrelationship. By incorporating interaction (modeled by the bare χb) and packing effects up to the polymer size, an effective chie emerges as the natural parameter for characterizing the molecular compatibility of the two polymer species. The measured quantity in small-angle neutron scattering (SANS) experiments is an apparent chia that includes long wavelength critical and spinodal fluctuations, and is related to χe through a self-consistent equation. χa exhibits the typical upward parabolic composition dependence observed in experiments and computer simulations. Second, a unified Ginzburg criterion involving both the composition and temperature (or temperaturelike variable) is derived that is applicable to both the critical and the off-critical spinodal regimes. The common characterization of the Ginzburg criterion in terms of a range of temperature (or temperaturelike variable) alone is generally inadequate. The molecular weight scaling proposed by de Gennes and Binder in the respective critical and off-critical spinodal regimes are recovered as special cases in the limit of large molecular weights. For typical molecular weights used in experiments the Ginzburg region is larger than commonly believed. Finally, the nature of the thermodynamic spinodal is examined. It is shown that a true off-critical thermodynamic spinodal does not exist in spatial dimensions less than 4. In its place, a pseudo-spinodal can be defined where the susceptibility reaches a finite maximum. The pseudo-spinodal precedes the mean-field spinodal but approaches the latter in the limit of infinite molecular weights. The pseudo-spinodal correlates strongly with the free energy barrier for nucleation becoming order kT. Thus it provides a kinetic limit for the physically accessible metastable state, beyond which phase separation may exhibit features characteristic of spinodal decomposition. The calculated location of the pseudo-spinodal for two samples used in a recent experiment of Balsara and co-workers agrees with the onset of spinodal-decomposition-like nucleation observed in the experiment.

Publication: Journal of Chemical Physics Vol.: 117 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:WANjcp02

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Abstract: Borrowing concepts from the schema theory of genetic algorithms, we have developed a computational algorithm to identify the fragments of proteins, or schemas, that can be recombined without disturbing the integrity of the three-dimensional structure. When recombination leaves these schemas undisturbed, the hybrid proteins are more likely to be folded and functional. Crossovers found by screening libraries of several randomly shuffled proteins for functional hybrids strongly correlate with those predicted by this approach. Experimental results from the construction of hybrids of two beta-lactamases that share 40% amino acid identity demonstrate a threshold in the amount of schema disruption that the hybrid protein can tolerate. To the extent that introns function to promote recombination within proteins, natural selection would serve to bias their locations to schema boundaries.

Publication: Nature Structural Biology Vol.: 9 No.: 7 ISSN: 1072-8368

ID: CaltechAUTHORS:20110927-143229047

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Abstract: We study the structure and thermodynamics of the critical nuclei in metastable binary polymer blends using the self-consistent field method. At the mean-field level, our results are valid throughout the entire metastable region and provide a smooth crossover from the classical capillary-theory predictions near the coexistence curve to the density functional predictions of Cahn and Hilliard (properly transcribed into expressions involving the parameters of the binary polymer blends) near the spinodal. An estimate of the free energy barrier provides a quantitative criterion (the Ginzburg criterion) for the validity of the (mean-field) self-consistent approach. The region where mean-field theory is valid and where there can be a measurable nucleation rate is shown to be poorly described by the existing limiting theories; our predictions are therefore most relevant in this region. We discuss our results in connection with recent experimental observations by Balsara and co-workers.

Publication: Journal of Chemical Physics Vol.: 116 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:WOOjcp02

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Abstract: The deterministic proliferation of the orientation of hexagonally packed cylinders (HEX) from the twinned body-centered cubic (BCC) phase is investigated by synchrotron small-angle X-ray scattering (SAXS) and rheo-optical methods for di- and triblock copolymers of styrene and isoprene (SI and SIS). Repeated heating and cooling cycles starting from an initially aligned HEX produce a proliferation of cylinder orientations from successively twinned BCC states. The evolution of the orientation distribution of HEX cylinders produces a decrease in the birefringence and increase in the modulus with each successive generation. The cylinder axes of the degenerate HEX states coincide with the 〈111〉 directions of the twinned BCC due to the epitaxial growth of cylinders from the twinned BCC. The distribution of the cylinder axes of the degenerate HEX states among the 〈111〉 directions of the twinned BCC is found to be affected by memory of the prior HEX state, which decays with annealing time in the BCC state.

Publication: Macromolecules Vol.: 35 No.: 3 ISSN: 0024-9297

ID: CaltechAUTHORS:20170720-075310985

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Abstract: The dynamics of an elastic polymer filament undergoing contour length expansion is studied using computer simulation. The expansion occurs by development of transverse buckling waves that grow through a coarsening process. The growing buckles locally organize into a helical structure with a characteristic persistence length. The helical domain boundaries are eliminated from the relaxing structure by unwinding through the ends of the rod. The growth of the helical domains results in self-propulsive motion of the expanding rod, as one large helix spanning the entire chain relaxes during the late stages of the dynamics. Stability analyses and scaling arguments are provided to explain the simulation results.

Publication: Physical Review E Vol.: 64 No.: 6 ISSN: 1063-651X

ID: CaltechAUTHORS:SPApre01

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Abstract: The linear viscoelasticity of semiflexible polymers is studied through Brownian Dynamics simulations covering a broad range of chain stiffness and time scales. Our results agree with existing theoretical predictions in the flexible and stiff limits; however, we find that over a wide intermediate-time window spanning several decades, the stress relaxation is described by a single power law t^(-alpha), with the exponent alpha apparently varying continuously from 1/2 for flexible chains, to 5/4 for stiff ones. Our study identifies the limits of validity of the t^(-3/4) power law at short times predicted by recent theories. An additional regime is identified, the "ultrastiff" chains, where this behavior disappears. In the absence of Brownian motion, the purely mechanical stress relaxation produces a t^(-3/4) power law for both short and intermediate times.

Publication: Physical Review E Vol.: 64 No.: 5 ISSN: 1063-651X

ID: CaltechAUTHORS:DIMpre01

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Abstract: We clarify some of the subtle issues surrounding the observational cluster method, a simulation technique for studying nucleation. The validity of the method is reaffirmed here. The condition of the compact cluster limit is quantified and its implications are elucidated in terms of the correct enumeration of configuration space.

Publication: Journal of Chemical Physics Vol.: 115 No.: 15 ISSN: 0021-9606

ID: CaltechAUTHORS:KUSjcp01

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Abstract: We introduce a computational method to optimize the in vitro evolution of proteins. Simulating evolution with a simple model that statistically describes the fitness landscape, we find that beneficial mutations tend to occur at amino acid positions that are tolerant to substitutions, in the limit of small libraries and low mutation rates. We transform this observation into a design strategy by applying mean-field theory to a structure-based computational model to calculate each residue's structural tolerance. Thermostabilizing and activity-increasing mutations accumulated during the experimental directed evolution of subtilisin E and T4 lysozyme are strongly directed to sites identified by using this computational approach. This method can be used to predict positions where mutations are likely to lead to improvement of specific protein properties.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 98 No.: 7 ISSN: 0027-8424

ID: CaltechAUTHORS:VOIpnas01

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Abstract: Directed evolution has proven to be a successful strategy for the modification of enzyme properties. To date, the preferred experimental procedure has been to apply mutations or crossovers randomly throughout the gene. With the emergence of powerful computational methods, it has become possible to develop focused combinatorial searches, guided by computer algorithms. Here, we describe several computational methods that have emerged to aid the optimization of mutant libraries, the targeting of specific residues for mutagenesis, and the design of recombination experiments.

Publication: Journal of Cellular Biochemistry Vol.: 84 No.: S37 ISSN: 0730-2312

ID: CaltechAUTHORS:20110927-154155139

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Abstract: We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastable structures. Application of this method to ABC star and linear triblock copolymers using an approximate free energy reveals new morphologies not yet observed in experiment.

Publication: Physical Review Letters Vol.: 85 No.: 16 ISSN: 0031-9007

ID: CaltechAUTHORS:BOHprl00

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Abstract: We report a novel transient instability upon temperature quench in weakly ordered block copolymer microphases possessing a soft direction or directions, such as the lamellar and hexagonal cylinder (HEX) phases. We show that reequilibration of the order parameter is accompanied by transient long wavelength undulation of the layers or cylinders—with an initial wavelength that depends on the depth of the temperature quench—that eventually disappears as the structure reaches its equilibrium at the new temperature. Such undulation leads to a transient transverse broadening of the scattering peaks near the Bragg positions. We argue that this instability might be responsible for the experimentally observed unusual ordering dynamics of the HEX phase of a diblock copolymer after quenching from the disordered state.

Publication: Journal of Chemical Physics Vol.: 111 No.: 23 ISSN: 0021-9606

ID: CaltechAUTHORS:QISjcp99

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Abstract: An expression is derived that relates the average population of a particular type of cluster in a metastable vapor phase of volume Vtot to the probability, estimated by simulation, of finding this cluster in a system of volume V taken inside Vtot, where V<

ID: CaltechAUTHORS:KUSjcp99

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Abstract: We have developed a classical mechanical model for the H2SO4/H2O binary system. Monte Carlo simulation was performed in a mixed ensemble, in which the number of sulfuric acid molecules is fixed while that of water molecules is allowed to fluctuate. Simulation in this ensemble is computationally efficient compared to conventional canonical simulation, both in sampling very different configurations of clusters relevant in nucleation and in evaluating the free energy of cluster formation. The simulation yields molecular level information, such as the shape of the clusters and the dissociation behavior of the acid molecule in the cluster. Our results indicate that the clusters are highly nonspherical as a result of the anisotropic intermolecular interactions and that a cluster with a given number of acid molecules has several very different conformations, which are close in free energy and hence equally relevant in nucleation. The dissociation behavior of H2SO4 in a cluster differs markedly from that in bulk solution and depends sensitively on the assumed value of the free energy f(hb) of the dissociation reaction H2SO4+H2O-HSO4-. H3O+. In a small cluster, no dissociation is observed. As the cluster size becomes larger, the probability of having an HSO4-. H3O+ ion pair increases. However, in clusters relevant in nucleation, the resulting ion pairs remain in contact; about 240 water molecules are required to observe behavior that resembles that in bulk solution. If a larger value of f(hb) is assumed to reflect its uncertainty, the probability of dissociation becomes negligible. A reversible work surface obtained for a condition typical of vapor to liquid nucleation suggests that the rate-limiting step of new particle formation is a binary collision of two hydrated sulfuric acid molecules. The ion pairs formed by dissociation play a key role in stabilizing the resulting cluster. The reversible work surface is sensitive to the assumed value of f(hb), thus pointing to the need for an accurate estimate of the quantity either by ab initio calculations or experiments.

Publication: Journal of Chemical Physics Vol.: 108 No.: 16 ISSN: 0021-9606

ID: CaltechAUTHORS:KUSjcp98b

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Abstract: A new approach to cluster simulation is developed in the context of nucleation theory. This approach is free of any arbitrariness involved in the definition of a cluster. Instead, it preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution in a single simulation, thereby completely bypassing the computationally expensive free energy evaluation that is necessary in a conventional approach. The validity of the method is demonstrated for a single component system using a model potential for water under several values of supersaturation.

Publication: Journal of Chemical Physics Vol.: 108 No.: 9 ISSN: 0021-9606

ID: CaltechAUTHORS:KUSjcp98a

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Abstract: Microstructures of block copolymers in the strong segregation limit are characterized by well-defined interfaces separating the different block materials into domains on a nanometer scale. In this paper, we address the effects of architectural and conformational asymmetry of the blocks on the interfacial curvature characteristics and on the degree of long-range order in the cylindrical morphologies. Experimental (TEM and SAXS) curvature data from polyisoprene−polystyrene (I2S) simple graft block copolymers and from polyisoprene−poly(tert-butyl methacrylate) (PtBMA) linear, conformationally asymmetric diblock copolymers are presented and compared to data from polyisoprene−polystyrene linear diblock copolymers. The experimental data are elucidated by a simple curvature free energy model which accounts for core-space-filling without explicitly specifying the shape of the microdomain. This model allows the prediction of preferred interfacial curvature characteristics as a function of molecular architecture. Good agreement is obtained between the theoretically calculated mean and Gaussian curvatures and the experimentally measured values. A key finding is that the degree of frustration, as measured by the difference between the free energy of the preferred curvature of a given block copolymer and that of the nearest accessible space-filling structure (such as the cylindrical structure), is correlated with the degree of long-range order.

Publication: Macromolecules Vol.: 30 No.: 22 ISSN: 0024-9297

ID: CaltechAUTHORS:20180313-141816020

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Abstract: We study the interaction forces between two plates in a semi-dilute solution of polymers each having one weakly adsorbing end-group. We show that this system exhibits both repulsive and attractive interactions of comparable magnitude and well-separated length scales: when the plate separation is within a range of order the end-to-end distance of the end-adsorbed polymer, repulsion arises with a magnitude of ϵ Φ/Na³ where ϵ is the end-adsorption energy, N is the degree of polymerization, a is the Kuhn length and Φ the volume fraction of the polymer. This repulsion is due to desorption of the end-adsorbed chains. At plate separations of order the correlation length of the solution, a depletion attraction sets in with a magnitude that scales with the bulk osmotic pressure.

Publication: Journal de Physique II Vol.: 7 No.: 8 ISSN: 1155-4312

ID: CaltechAUTHORS:20200320-144002936

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Abstract: The nature, stability, and mechanism of formation of the block copolymer perforated lamellar structure are elucidated. This structure is shown to develop from the anisotropic fluctuations of the lamellar phase when it reaches its spinodal. It is proposed that there can be two different perforated lamellar structures, one based on a hexagonal close packed (hcp) lattice and one based on a body-centered cubic (bcc) lattice, with nearly degenerate free energy. In the framework of a Leibler-type free energy functional, it is shown that the perforated lamellar structure is only pseudostable (corresponding to a saddle point in the free energy surface) in the weak-segregation limit but can become metastable in the intermediate-segregation regime. Calculation of the fluctuation spectrum of metastable perforated lamellar structures enables us to explain in a simple and consistent manner several puzzling structural data from small-angle neutron scattering studies.

Publication: Macromolecules Vol.: 30 No.: 15 ISSN: 0024-9297

ID: CaltechAUTHORS:20180719-153004411

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Abstract: We study the kinetics of order-disorder and order-order transitions in weakly segregated diblock copolymers using a time-dependent Ginzburg-Landau (TDGL) approach. In particular, we investigate the microstructural change as well as the order-parameter evolution after a sudden temperature jump from one phase to another. Direct numerical simulation of the TDGL equations shows that depending on the extent of the temperature jump, these transitions often occur in several stages and can involve nontrivial intermediate states. For example, we find that transition from the lamellar phase to the hexagonal cylinder phase goes through a perforated lamellar state within a certain temperature range. The numerical results are elucidated by a multimode analysis under the single-wave-number approximation. The analysis reveals that the geometric characteristics of the free energy surface, particularly saddle points and ridgelike features, are responsible for the nontrivial intermediate states on the kinetic pathways. On the basis of this analysis, a generalized kinetic ``phase diagram'' is constructed, which is able to account for all the different scenarios observed in the numerical simulation. Our results are discussed in connection with available experimental observations. In particular, we suggest the possibility that the perforated-modulated lamellar structures obtained by Bates and co-workers [I. W. Hamley, K. A. Koppi, J. H. Rosedale, F. S. Bates, K. Almdal, and K. Mortensen, Macromolecules 26, 5959 (1993); S. Förster, A. K. Khandpur, J. Zhao, F. S. Bates, I. W. Hamley, A. J. Ryan, and W. Bras, Macromolecules 27, 6922 (1994)] may be kinetic, intermediate states rather than new equilibrium phases.

Publication: Physical Review E Vol.: 55 No.: 2 ISSN: 1063-651X

ID: CaltechAUTHORS:QUIpre97

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Abstract: This paper discusses the modification of several spreading properties of a liquid on a solid surface by the addition of end-adsorbing polymers. End-adsorption of the polymers at the liquid−solid interface decreases the interfacial free energy. If this decrease is sufficient to overcome the negative spreading power of an otherwise nonspreading liquid, the liquid will spread on the surface. Using a self-consistent field method, we construct a phase diagram for spreading of a liquid drop of fixed volume as a function of the concentration of end-adsorbing polymers and the energy of end-adsorption to the surface. The equilibrium thickness of a spread film is also calculated and is shown to be closely related to the thickness of a self-assembled polymer brush in an unbounded fluid but relatively insensitive to the bare spreading power of the liquid or the Hamaker constant, which determine the equilibrium thickness of a film of a simple liquid. When a solid surface of a given area is covered by a film thicker than the predicted equilibrium thickness of a spread film, an instability due to the depletion attraction causes the excess liquid to form drops on top of the spread film of the equilibrium thickness.

Publication: Langmuir Vol.: 12 No.: 20 ISSN: 0743-7463

ID: CaltechAUTHORS:20180719-162404743

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Abstract: Studies carried out using engineered proteins have demonstrated that protein adsorption to functional surfaces involves multiple interactions between specific groups on the protein and complementary binding sites distributed on the surface. A consequence of multipoint interactions is that protein binding affinity should depend strongly on the distribution of surface binding sites. In this investigation we present a thermodynamic framework for multipoint protein binding to a random arrangement of surface binding sites that also includes lateral interactions among adsorbed protein molecules. This framework results in reversible adsorption behavior analogous to that predicted by the Temkin model and chromatographic behavior analogous to that predicted by the “stoichiometric displacement” model (SDM). Using this framework we can now interpret the semiempirical parameters obtained using these models for protein binding in chromatographic systems in terms of thermodynamic parameters for protein−surface interactions. We show a correlation between Temkin model parameters for a series of cytochrome c variants in immobilized metal affinity chromatography (IMAC) that is consistent with protein adsorption to a nonuniform arrangement of surface binding sites. Lateral interactions among adsorbed protein molecules are shown to be insignificant for this system.

Publication: Journal of Physical Chemistry Vol.: 100 No.: 12 ISSN: 0022-3654

ID: CaltechAUTHORS:20180720-141711681

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Abstract: The kinetics of hexagonal to disordered and hexagonal to body-centered-cubic phase transitions in weakly segregated, microstructured systems (e.g., diblock copolymers) is studied using a time-dependent Ginzburg-Landau (TDGL) approach. Both computer simulation of the TDGL equation and analysis of a simplified two-mode model reveal nontrivial pathways during the transition.

Publication: Physical Review Letters Vol.: 76 No.: 10 ISSN: 0031-9007

ID: CaltechAUTHORS:QISprl96

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Abstract: Density functional theory is applied to ion-induced nucleation of polarizable multipolar molecules. The asymmetric nature of the ion-molecule interaction is shown to cause the sign preference in ion-induced nucleation. When the ion-molecule interaction is weak, the observed sign preference is consistent with that of the bare ion-molecule interaction potential and decreases with increasing supersaturation. However, as the ion-molecule interaction becomes stronger, the sign preference in the reversible work exhibits some nontrivial behavior. For molecular parameters applicable for CS2 and CH4, the predicted values of the reversible work of nucleation depend on the sign of the ion charge, yielding a difference in the nucleation rate by factors of 10 to 10^(2) and 10 to 10^(5), respectively.

Publication: Journal of Chemical Physics Vol.: 103 No.: 20 ISSN: 0021-9606

ID: CaltechAUTHORS:KUSjcp95b

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Abstract: This work discusses the results of a self-consistent-field calculation of conformational and thermodynamic properties of polymers end-grafted to a surface in athermal solvents. Three primary issues are addressed. First, we address the question raised recently by Carignano and Szleifer as to whether the second virial treatment of previous numerical and analytical self-consistent-field theories provides an adequate description of polymer brushes. We show that, for grafted chains that are sufficiently long, there exists a broad range of grafting densities where the lateral pressure and the brush thickness both scale as predicted by the second virial treatment. For shorter chains (of 100 monomers or less), no distinct scaling regime is observed. A related effect due to finite chain lengths is the interpenetration of brushes upon compression and its importance to compression forces. We find that, even for quite large chains (of up to 1000 monomers), there is significant interbrush penetration at high compression. However, the force profiles are relatively insensitive to penetration at such high compressions. Instead, finite chain lengths affect the interaction forces most prominently at the onset of the interactions. Next, we address the crossover from wet brushes to dry brushes as the molecular weight of the solvent increases. This crossover is driven purely by entropic effects and is interpreted on the basis of the conformation of the polymeric solvent molecules in the vicinity of the brush. It is found that the state of the brush is determined by two crossover scaling variables, the ratio of the degree of polymerization of the free and grafted chains, N_f/N_g and N_fσ^2, where σ is the grafting density. Finally, we investigate brush configurations and interactions in mixed solvents. It is observed that, for polymer brushes in a solution of mixed free polymers and monomers, there are three distinct regimes in the interactions between two brushes. Upon the onset of the interaction, the brushes attract one another as the solvent is transferred from an unfavorable proximity to the brush to the infinite reservoir. Then, there is a very rapidly increasing repulsive force as the brushes begin to overlap and the remainder of the free polymer is removed from the system. Once all of the polymeric component has been squeezed out of the brushes, the compression becomes indistinguishable from the compression of brushes in a monomeric solvent.

Publication: Journal of Physical Chemistry Vol.: 99 No.: 9 ISSN: 0022-3654

ID: CaltechAUTHORS:20180525-133235076

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Abstract: Density functional theory is applied to ion-induced nucleation of dipolar molecules. The predicted reversible work shows a sign preference, resulting in a difference in the nucleation rate by a factor of 10–10^2, for realistic values of model parameters. The sign effect is found to decrease systematically as the supersaturation is increased. The asymmetry of a molecule is shown to be directly responsible for the sign preference in ion-induced nucleation.

Publication: Journal of Chemical Physics Vol.: 102 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:KUSjcp95a

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Abstract: We reveal a deep theoretical relationship between equilibrium statistical physics of smectic-A liquid crystals and nonequilibrium statistical physics of the Kardar-Parisi-Zhang dynamical model [M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986)] for interfaces growing in the presence of a flux of incoming particles. This relationship provides an exact approach to study Landau-Peierls phenomena and anomalous elasticity of two-dimensional smectic-A liquid crystals. Also, it yields prediction of an unusual elastic critical point in three-dimensional smectic-A liquid crystals with broken inversion symmetry (head-to-tail packing of layers). We discuss the elasticity and fluctuations of these unusual smectic-A phases.

Publication: Physical Review E Vol.: 49 No.: 4 ISSN: 1063-651X

ID: CaltechAUTHORS:GOLpre94

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Abstract: We study the quasistatic behavior of the lamellar phase of diblock copolymers under uniaxial compression and tension along the normal direction of the layers, in both the weak segregation limit (WSL) and the strong segregation limit (SSL). In the SSL, we derive a (nonlinear) continuum free energy description of the system in terms of local displacement of the lamellar layers, and use this free energy to study the mechanical behaviors. While compression induces the usual Hookian elastic response (for strains or stresses that are not too large), tension leads to square-lattice wave undulations in the transverse directions when the strain exceeds a critical value. In the WSL close to the order–disorder transition temperature, compression can ``melt'' the lamellar phase to the isotropic phase; such a melting can take the form of three types of instabilities, a quasithermodynamic instability, a spinodal at controlled strain, and a mechanical instability at controlled stress. It is shown that the third instability always precedes the second one under controlled-stress conditions. For a weakly first-order transition, the quasithermodynamic instability precedes the mechanical instability; but for a (hypothetical) second-order transition, the mechanical instability appears first as the stress is increased. In the case of tension, a transverse square-lattice wave deformation again develops at a critical strain. This deformation can be followed by a subsequent melting of types similar to the compressional case, upon further increase of the stress or strain. In both the SSL and WSL, the modulus undergoes an abrupt decrease when layer undulation develops, to a value 7/15 of that before the onset of undulation. Because the critical strain for the onset of undulation is usually very small, the modulus for tension will appear different from the modulus for compression, the former being 7/15 of the latter. As a result of this decrease in the modulus, melting of the lamellar phase in the WSL will occur at larger strains under tension than under compression.

Publication: Journal of Chemical Physics Vol.: 100 No.: 3 ISSN: 0021-9606

ID: CaltechAUTHORS:WANjcp94

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Abstract: We present a theoretical study of spatially modulated phases in self-assembled monolayers of mixed surfactants. We propose two models which are appropriate, respectively, for monolayers at a fluid–fluid interface and monolayers on a solid substrate. We show that in both cases, the molecular shape asymmetry, coupled with the local composition variation, can lead to spontaneous formation of periodic structures. In the case of liquid-supported monolayers, the molecular shape asymmetry is manifested as a spontaneous curvature of each component of the film, which induces periodic variations both in the composition of the amphiphiles and in the height profile of the interface (ripples). In the case of solid-supported monolayers, the shape asymmetry is reflected in the spontaneous splay of the orientation of the amphiphiles, and the spatial modulation involves the composition as well as the orientation of the amphiphilic molecules. We analyze these models in some detail near the critical region, where we highlight the roles played by various length scales in determining the critical wavelength. We show that gravity has some very subtle and nontrivial effects for a liquid-supported, tension-free monolayer. We also present some preliminary results for the low temperature cases.

Publication: Journal of Chemical Physics Vol.: 99 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:WANjcp93

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Abstract: Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry. The order parameter that characterizes this symmetry breaking is coupled to variations in the direction of molecular tilt. As a result, chiral symmetry breaking leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt. A Landau theory for this pattern formation gives a general phase diagram, which includes a uniform nonchiral phase, a striped pattern, a square lattice, and a uniform chiral phase.

Publication: Physical Review Letters Vol.: 70 No.: 8 ISSN: 0031-9007

ID: CaltechAUTHORS:SELprl93

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Abstract: We show how the n → 0 vector spin model is especially naturally suited for treating the solution properties of flexible, cylindrical micelles. In particular, an isomorphism is established between coupling constants in the spin Hamiltonian and surfactant energies in the micellar situation. The appropriately generalized n → 0 vector spin model is then solved in mean field approximation and shown to describe the phenomenon of mi cellar growth at low concentrations and crossover through the semidilute regime. Osmotic pressure and average aggregation number are calculated as a function of concentration, and our basic approach is compared and contrasted with those for "ordinary" and "living" polymer solutions.

Publication: Journal of Physical Chemistry Vol.: 97 No.: 6 ISSN: 0022-3654

ID: CaltechAUTHORS:20180313-105825017

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Abstract: We present a quantitative study of the bicontinuous cubic phases in the didodecyl alkyl-β-D-glucopyranosyl-rac-glycerol (rac-di-12:0 β-GlcDAG) lipid-water system. A temperature-composition phase diagram determined using X-ray diffraction shows Ia3d and Pn3/Pn3m cubic phase regions in addition to inverted hexagonal (H^(II)) and several lamellar phase regions. The diffraction data was used to determine the lattice repeat vector, d, and, using suitable models, the lipid monolayer thickness, d_L, for all temperatures and compositions in the diagram. The models chosen for the cubic phases were based on lipid bilayers straddling infinitely periodic minimal surfaces (IPMS) as described previously in the literature [1]. Using the structural data derived from the phase diagram, the lyotropic phase transition between the two cubics was modeled by a simple curvature free energy theory. A new result of this theory was an estimate for the Gaussian curvature bending modulus of the lipid monolayer. The model was found to quantitatively describe the phase transition, particularly for phase behavior at low hydration. Our model suggests some universal features should be present in any system that shows non-lamellar phases and we discuss those features with respect to the phase diagrams available in the literature.

Publication: Journal de Physique II Vol.: 2 No.: 11 ISSN: 1155-4312

ID: CaltechAUTHORS:20200320-123553945

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Abstract: We relate anharmonic equilibrium thermal fluctuations of smectics A to fluctuations of the Kardar-Parisi-Zhang (KPZ) dynamical model for a growing interface. The KPZ model in 1+1 dimensions is one to one related to a 2D smectic elastic model whose scaling behavior is then obtained exactly. The KPZ model in 2+1 dimensions maps into an elastic critical point of 3D smectics A with broken inversion symmetry (head-to-tail packing of layers). We discuss the elasticity and fluctuations of these novel smectic-A phases.

Publication: Physical Review Letters Vol.: 69 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:GOLprl92

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Abstract: The curvature expansion of the free energy for diblock copolymers aggregated into bilayers is studied for strongly incompatible diblocks. It is shown that sufficient asymmetry in the di block composition leads to an instability of the flat bilayer with respect to spherical or saddle-splay deformations: when the bilayer consists of two (diblock copolymer) monolayers each having a strong tendency to curve convexly toward the solvent, i.e., when the outer block is much larger than the inner block, spherical vesicles become favored by the curvature elastic free energy over flat bilayers. In the opposite case, saddle-splay deformations are favored.

Publication: Macromolecules Vol.: 25 No.: 14 ISSN: 0024-9297

ID: CaltechAUTHORS:20180313-152006067

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