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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:50:22 +0000Theoretical Investigation of the Effect of Intramolecular Interactions on the Configuration of Polymeric Chains
https://resolver.caltech.edu/CaltechETD:etd-10072002-145049
Authors: {'items': [{'email': 'jgcurro@gmail.com', 'id': 'Curro-John-Gillette', 'name': {'family': 'Curro', 'given': 'John Gillette'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/8KEP-R512
<p>A theoretical investigation of the effect of intramolecular interactions on the configurational statistics of a polymer molecule is presented. This problem has been studied by many authors and is known as the "excluded volume problem" in the literature. A statistical mechanical approach is used. Many of the similarities between the theory of "classical fluids" and the excluded volume problem are exploited.</p>
<p>The configurational statistics of 2 and 3 segment chains are computed exactly for the "hard sphere potential". The integrations were performed by introducing bipolar and tripolar coordinate systems. It was found that the mean square end-to-end distance for these cases was n<sup>1.33</sup> where n is the number of segments. These results are of no practical use in predicting the properties of real polymer chains which are much longer. It is instructive, however, to compare these exact results with approximate theories in the limit of short chain length.</p>
<p>A "cluster expansion" is written for the partition function of a polymer chain with the ends of the chain fixed. This is analogous to the cluster expansion for the partition function of an imperfect gas. The first-order term in this expansion is evaluated for the hard core potential. In the limit of small hard core diameters, the first-order term leads to the wellknown first-order perturbation theory for the mean square end-to-end distance. The exact results of this first-order correction term are used to construct higher-order terms of a specified "isolated topology". If only these terms are used in the cluster expansion, incorrect results are obtained for the mean square end-to-end distance. This indicates that higher-order terms of complicated topology are significant for longer chain length.</p>
<p>Various approximate integral equations for the restricted partition function of a polymer chain are presented. The most promising of these equations is the analog of the well-known Percus-Yevick equation in the theory of liquids. In deriving this equation two topologically distinct types of graphs are defined. These are the "nodal and elementary" graphs. An exact equation relating these types of graphs is presented. The analog of the Percus-Yevick approximation is made which leads to an integro-difference equation. This equation is solved exactly using the hard core potential for the special case of the hard core diameter equal to the polymer segment length. Results of numerical calculations are given for other intermediate values of this diameter ranging from zero to the segment length (the "pearl necklace" model). This leads to values of γ ranging correspondingly from 1.0 to 2.0 where <r<sup>2</sup><sub>1N</sub> ∝ M<sup>γ</sup>> with <r<sup>2</sup><sub>1N</sub> the mean square end-to-end distance and M the molecular weight. The numerical results for <r<sup>2</sup><sub>1N</sub> as a function of chain length are in good agreement with the second-order perturbation theory of Fixman for small hard core diameters.</p>https://thesis.library.caltech.edu/id/eprint/3958The Flow of Human Blood Through Capillary Tubes with Inside Diameters Between 8.7 and 221 Microns
https://resolver.caltech.edu/CaltechTHESIS:10182017-151706373
Authors: {'items': [{'id': 'Barbee-James-Henry', 'name': {'family': 'Barbee', 'given': 'James Henry'}}]}
Year: 1971
DOI: 10.7907/3RKR-TH95
<p>The purpose of this study was to investigate the pressure drop
flow rate behavior of normal human blood flowing through small
capillary tubes. A sensitive pressure transducer was used to measure the
pressure gradient along an experimental tube when various red cell
suspensions passed through glass and plastic capillary tubes.
In particular, the effect of capillary tube diameter on the rheological
properties of blood was observed for capillary tube diameters from
8 to 221 microns.</p>
<p>For tubes of 221 microns and smaller, it was found that the
hematocrit (volume fraction of red cells in a blood sample) of the
blood flowing through a capillary tube is less than the hematocrit
of the blood in the feed reservoir. The tube hematocrit decreases
linearly with the logarithm of the tube diameter at constant feed
reservoir hematocrit and for a given diameter tube, increases linearly
with the feed reservoir hematocrit.</p>
<p>An equation was developed from data taken in an 811-micron ID
tube that allows the shear stress-shear rate relation to be predicted
from the tube diameter, tube hematocrit, and the temperature.</p>
<p>It was found that the rheological properties of blood can be
accurately predicted from the equation developed if the average
hematocrit inside the capillary tube is used as the correct hematocrit
parameter. A surprising result found is that fluid properties
can be predicted for blood flow through a 29-micron ID tube; in such
a tube, the equation of motion may not be valid because the "continuous
fluid" assumption is not valid. Blood flow data were taken at
98.6°F as well as 73.5°F. Blood heated to 111°F and then cooled to
96.6°F was also investigated.</p>
<p>Blood flow through 15- and 9-micron ID capillaries was investigated.
Blood exhibits no yield stress in a 15-micron ID tube
because rouleaux formation cannot restrict the flow as it does in
larger tubes.</p>
<p>An increased yield stress was found in a 9-micron ID tube.
The measured shear stress was only slightly larger (for a given U)
than predicted by the continuum model in both the 15- and 9-micron
ID capillary tubes.</p>https://thesis.library.caltech.edu/id/eprint/10529I. Latent Heat of Vaporization of Propane. II. Partial and Total Heats of Vaporization for the N-Propane/N-Decane Mixture
https://resolver.caltech.edu/CaltechTHESIS:08272018-112734108
Authors: {'items': [{'id': 'Helgeson-Norman-Lewis', 'name': {'family': 'Helgeson', 'given': 'Norman Lewis'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/GPGR-N481
<p>Experimental measurements are reported for total and partial heats-of-vaporization for the n-propane/n-decane system. Results are given for the 100, 130 and 160°F. isotherms and cover the entire composition range. It is shown that the temperature and concentration gradients which develop within the system during the vaporization process may, in some cases, cause a significant (~0.4%) deviation in the calculated results. A method is provided for introducing a correction for this effect. Based on the partial heat-of-vaporization of n-propane, heats-of-mixing for the liquid solution are calculated. The results are in qualitative agreement with predictions from theories for n-alkane liquid mixtures.</p>https://thesis.library.caltech.edu/id/eprint/11163A Laser Light Scattering Study of Transport and Critical Phenomena
https://resolver.caltech.edu/CaltechTHESIS:09072018-113523680
Authors: {'items': [{'id': 'Gülari-Erdogan', 'name': {'family': 'Gülari', 'given': 'Erdogan'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/6YQH-1T42
<p>The intensity and Rayleigh linewidth have been measured as a function of temperature and scattering angle for light scattered by concentration fluctuations near the
critical point of the binary liquid system 2,6-lutidine-water.</p>
<p>From the intensity data it is found that γ = 1.26 ± 0.02 and ν = 0.61 ± 0.07. From the linewidth data the mutual diffusion coefficients were calculated as a function of
temperature. It is found that the diffusion coefficient decreases as the critical point is approached. The behavior of the linewidth as a function of k∈ was compared
with the Kawasaki theory without the nonlocal viscosity and vertex corrections. General agreement with some systematic deviations is observed.</p>
<p>The shear viscosity anomaly in the same system was also studied in detail by measuring the shear viscosities as a function of temperature near the critical point.
Results of analyses indicate that the viscosity is at most weakly divergent, with an exponent ø ≃ ±0.001.</p>
<p>Light scattering techniques have been employed to measure the mutual diffusion coefficient D as a function of concentration in ten binary mixtures and the thermal
diffusivity χ in nine pure liquids and one binary mixture. The diffusion coefficient was also measured at one or two concentrations for four binary mixtures. The values obtained are in excellent agreement with the available literature data determined by more classical methods. Under most circumstances light scattering is found to offer
a fast and accurate way of determining χ and D.</p>
<p>The turbidity τ and the decay rate Γ of the density fluctuations have been measured as a function of temperature on the critical isochore of ethane near the critical
point.</p>
<p>From the turbidity data absolute values of isothermal compressibilities and correlation lengths were calculated. The isothermal compressibility K<sub>T</sub> and the correlation length ∈ are found to behave as:</p>
<p> K<sub>T</sub> = 1.24 ± 0.11 x 10<sup>-3</sup>(ΔT/T<sub>c</sub>)<sup>-1.225 ± 0.02</sup>atm<sup>-1</sup></p>
<p> ∈ = 1.64 ± 0.20 (ΔT/T<sub>c</sub>)<sup>-0.664 ± 0.02</sup> Å.</p>
<p>From the Γ data thermal diffusivities, thermal conductivities and excess thermal conductivities were calculated as a function of temperature. It is found that the thermal
diffusivity does not exhibit a simple power law behavior whereas the excess thermal conductivity does with an exponent of ψ = 0.605 ± 0.02. The singular part of the decay
rate Γ<sup>s</sup>, was compared with the Kawasaki expression with the nonlocal viscosity correction. It is observed that the nonlocal viscosity correction together with the vertex and the correlation function corrections improve the agreement between the theory and the experiment.</p>
<p>The results for the isothermal compressibility, the thermal conductivity and the excess thermal conductivity are in very good agreement with the available literature
data.</p>
https://thesis.library.caltech.edu/id/eprint/11178Determination of the Argon Intermolecular Pair Potential from Distribution Functions Measured by X-ray Diffraction from Fluid Argon
https://resolver.caltech.edu/CaltechTHESIS:07212021-212145639
Authors: {'items': [{'id': 'Karnicky-Joseph-Francis', 'name': {'family': 'Karnicky', 'given': 'Joseph Francis'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/htpg-c668
<p>X-ray diffraction experiments were carried out on fluid argon at a temperature of -100°C and densities of .0824 g/cm<sup>3</sup>, .1331 g/cm<sup>3</sup>, .2087 g/cm<sup>3</sup>, and .3111 g/cm<sup>3</sup>. The measurements of the state at .2087 g/cm<sup>3</sup> were repeated to establish reproducibility. The methods used to obtain the experimental quantities and to subsequently analyze the data included significant improvements over previous investigations.</p>
<p>The data from each experiment at the three higher densities were analyzed to obtain a set of structure factors which were Fourier transformed to obtain sets of direct correlation functions and radial distribution functions. The Percus-Yevick equation was applied to these distribution functions to obtain the effective intermolecular potential from each experiment. These potentials were corrected for three-body effects to give four estimates of the argon pair potential, and a final estimate which is the precision weighted average of the four seperate estimates.</p>
<p>The characteristics of these potentials, with error limits determined by a perturbation analysis of the uncertainties in the experimental quantities, are:</p>
<p>state 1- n = .2087 g/cm<sup>3</sup>, σ = 3.401 ± .038 A°, ∈ = 143.2 ± 10.2 °K, r<sub>min</sub> = 3.89 ± .09 A°.</p>
<p>state 1R- n = .2087 g/cm<sup>3</sup>, σ = 3.402 ± .035 A°, ∈ = 149.9 ± 10.2 °K, r<sub>min</sub> = 3.87 ± .07 A°.</p>
<p>state 2- n = .3111 g/cm<sup>3</sup>, σ = 3.375 ± .0233 A°, ∈ = 146.6 ± 6.8 °K, r<sub>min</sub> = 3.87 ±.05 A°.</p>
<p>state 3- n = .1331 g/cm<sup>3</sup>, σ = 3.379 ± .050 A°, ∈ = 145.1 ± 16.0 °K, r<sub>min</sub> = 3.83 ± .13 A°.</p>
<p>average u(r)- σ = 3.389 ± .015 A°, ∈ = 146.3 ± 4.9 °K r<sub>min</sub> = 3.86 ± .05 A°.</p>
<p>Physical quantities were calculated from the average potential and agreed with the experimental values for the second virial coefficient of argon and the vibrational transition energies of the argon dimer, as well as the theoretical long range dispersion potential.</p>
<p>The range of densities studied was not large enough to allow direct determination of three-body forces. Methods are suggested whereby information about nonadditive forces could be derived from the combination of the results of these experiments with the results of previous x-ray experiments or with third virial coefficient data.</p>https://thesis.library.caltech.edu/id/eprint/14311I. Depolarized Light Scattering Studies of Rotational-Translational Coupling in Liquids Composed of Small Anisotropic Molecules. II. Investigation of the Coupling Between Reorientation and Longitudinal Modes in the Brillouin Spectra of Liquids Composed of Anisotropic Molecules
https://resolver.caltech.edu/CaltechETD:etd-09142006-110153
Authors: {'items': [{'id': "O'Steen-Byron-Lance", 'name': {'family': "O'Steen", 'given': 'Byron Lance'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/wda1-bj76
<p>Part I</p>
<p>In an attempt to better understand the molecular interactions governing the behaviour of the coupling parameter R measured in light scattering experiments, the depolarized (l<sub>VH</sub>) spectra for a series of liquids composed of small aromatic molecules, very similar in size and shape, have been measured. The molecules studied here were generally monosubstituted benzene and pyridine derivatives. All were found to exhibit the doublet structure indicative of dynamic coupling between molecular reorientation and shear modes, or more simply, rotational-translational coupling. The degree of this coupling is measured by a parameter R (0 ≤ R ≤ 1) which is often thought of as the fraction of the shear viscosity attributable to reorientational motion. From the depolarized spectra the coupling parameter R, collective reorientation frequency, and low frequency shear viscosity were determined.</p>
<p>The values of R were found to vary from 0.24 to 0.55 for the liquids studied here. This range is nearly as broad as that observed in all previous studies, which have included such diverse molecules as carbon disulfide, tri-phenyl phosphite, and the highly anisotropic liquid crystal MBBA. This suggests that size and shape considerations, or steric forces, are not the primary factor in determining the degree of rotational-translational coupling as measured by light scattering. If this is indeed the case then other non-steric interactions must be producing the observed variation in R. With this in mind, we have examined possible electrostatic interactions. A simple correlation with dipole moment was not found to exist. Instead it appears that the variation in R can only be understood by consideration of the detailed molecular charge distribution. This is determined to a large extent by resonance interactions with the aromatic ring which are generally reflected in the change of dipole moment from the aliphatic compound (CH<sub>3</sub>-R) to its aromatic analog (C<sub>6</sub>H<sub>5</sub>-R).</p>
<p>Based upon resonance structure arguments and our own experimental results, it is concluded that the anomolously large R values found for pyridine from the l<sub>HH</sub> depolarized spectrum might well be correct and the more orthodox l<sub>VH</sub> measurements in error. If this assertion is indeed correct, then the reliability of rotational-translational coupling measurements by l<sub>VH</sub> depolarized light scattering must be considered questionable for weakly scattering molecules such as pyridine.</p>
<p>Part II</p>
<p>The coupling of reorientational motion to longitudinal modes was investigated by studying the Brillouin spectra of aniline and p-anisaldehyde over a wide range of scattering angles. The primary goal of these studies was to attempt to confirm the microscopic theory of orientational relaxation in the polarized spectrum. Theoretically it has been shown that for symmetric tops the coupling between longitudinal modes and reorientation in the polarized spectrum is identical to that between shear modes and reorientation in the depolarized spectrum. Thus the Brillouin scattering studies performed here also provide an internal check on the consistency of the 2-variable molecular theory for depolarized scattering and the corresponding theory of orientational relaxation in the Brillouin spectrum. Aniline and p-anisaldehyde were chosen for this investigation since their depolarized spectra at the temperature of interest are well described by the simple 2-variable molecular theory coupling shear modes to orientation. The collective reorientation frequency for both liquids could easily be varied in the low gigahertz range by operating at temperatures near the freezing point. Thus the effects of orientational relaxation in the propagation of longitudinal waves (1 - 10 GHz) should be observable in an angular study of the Brillouin spectra. Moderate viscosites and large rotational-translational couplings also made these liquids attractive from an experimental standpoint since these quantities determine the relaxation strength.</p>
<p>Our results for attenuation and velocity of the longitudinal waves demonstrate that there is indeed relaxation in the shear viscosity as predicted by theory. However, shear relaxation in addition to that due to reorientational motion is indicated by the k-dependence of the attenuation results. This stands as an apparent contradiction to the depolarized results which suggest that only orientational relaxation should be important under these conditions. Since the different relaxation effects cannot be unambiguously separated here, a detailed confirmation of orientational relaxation theory could not be obtained.</p>https://thesis.library.caltech.edu/id/eprint/3535