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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:46:01 +0000X-Ray Diffraction Studies of Stable and Supercooled Liquid Gallium
https://resolver.caltech.edu/CaltechETD:etd-09272002-162252
Authors: {'items': [{'id': 'Rodriguez-Sergio-Enrique', 'name': {'family': 'Rodriguez', 'given': 'Sergio Enrique'}, 'show_email': 'NO'}]}
Year: 1964
DOI: 10.7907/ZDWW-TW72
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
X-ray diffraction studies of stable and supercooled liquid gallium (m.p. 29.8[degrees]C.) between 0 and 50[degrees]C. show no important dependence of internal structure on temperature. Atomic radial distribution functions were determined for 0, 10, 20, 29.5, 30, 40, and 50[degrees] from diffraction data to S=11[...]. Diffraction data was obtained in reflection geometry with Ag K-alpha radiation, scintillation counter, and pulse-height analyzer. The sample was contained in a sealed plastic cell with transparent walls. A supporting assembly provided temperature control within 0.1[degrees]C. and a transparent plastic X-ray window which permitted visual inspection of the sample surface. Arguments are presented in favor of normalizing scattered intensities to independent scattered intensity at high S values. The method of inversion is based on a single, piecewise polynomial approximation to the scattering function i(S) for each temperature.https://thesis.library.caltech.edu/id/eprint/3802X-Ray Diffraction Studies of Dense Fluids
https://resolver.caltech.edu/CaltechETD:etd-09182002-140103
Authors: {'items': [{'id': 'Honeywell-Wallace-Irving', 'name': {'family': 'Honeywell', 'given': 'Wallace Irving'}, 'show_email': 'NO'}]}
Year: 1964
DOI: 10.7907/E2BS-WS38
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Radial distribution functions supply useful information for the investigation of the structure of liquids. An x-ray cryostat and supporting equipment have been developed for determination of these functions experimentally. The apparatus has been tested on confined fluids at pressures up to 2000 psia and temperatures to 77 [degrees] K. Although a cylindrical beryllium sample cell is currently used in a geometry of the Debye-Scherrer type, the equipment is adaptable to parafocusing methods and to a wide variety of cell configurations. Except for self-absorption in the sample and cell, absorption of the incident and scattered x rays is less than 1%.
The cryostat and supporting equipment maintain automatic temperature control to ?0.006[degrees] C. The sample temperature is measured to ?0.05[degrees] C with a miniature platinum resistance element placed directly in the sample fluid; temperature homogeniety of the irradiated sample is better than 0.003[degrees] C.
The sample pressure is transmitted through a steel diaphragm to an oil system where it is measured to 1:10,000 on a pressure balance of the dead weight variety. A pressure transducer incorporating the diaphragm is used to balance the sample and oil pressures. The transducer has a sensitivity of 3.27 volts per differential psi.
The analysis of x-ray diffraction data from highly absorbing samples is extended to include losses of incoherent scattering in the sample and cell and in the detection system. Methods for treating incident or scattered beams with nonuniform intensities are also presented. The scattering geometry represents an optimum choice for highly absorbing samples in cylindrical cells. The sample position is determined experimentally to within 0. 001 in.
X-ray diffraction measurements made with molybdenum radiation are presented for liquid argon at -130.00[degrees]C for the densities 0.9098, 0.9818, and 1.0052 gm/[cubic centimeter]. Scintillation detection was employed; monochromatization was effected with [beta] filtering and pulse height selection. Radial distribution functions are derived from the intensity curves for data to S=9[Angstroms][superscript -1)]. The coordination numbers and shell distances show good agreement with previous work at a nearby state, but suggest the possibility of systematic error in the older data.https://thesis.library.caltech.edu/id/eprint/3616An x-ray diffraction study of the structure of fluid argon
https://resolver.caltech.edu/CaltechETD:etd-10012002-162731
Authors: {'items': [{'email': 'pgmikolaj@robyndrive.com', 'id': 'Mikolaj-P-G', 'name': {'family': 'Mikolaj', 'given': 'Paul George'}, 'show_email': 'NO'}]}
Year: 1965
DOI: 10.7907/BYAA-0S21
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Atomic radial distribution functions of fluid argon have been determined from experimental x-ray diffraction measurements at 13 different thermodynamic states. These states, forming a temperature-density grid in the critical region, include isotherms of -130[degrees]C, -125[degrees]C, -120[degrees]C, -110[degrees]C and isochores (in gm/cc) of 0.982, 0.910, 0.780, 0.536 (the critical density), and 0.280 (argon vapor).
Mo radiation, monochromated by a Zr filter and PHS set for 50% [...] transmission, was used in a Debye-Scherrer type geometry and was detected with a NaI scintillation counter. A narrow incident beam was used to partially irradiate the argon sample which was confined in a cylindrical cell constructed from sintered beryllium powder. A calibration experiment, performed with a vitreous SiO2 sample, established the validity of the experimental method and the data processing techniques.
The structural features in the x-ray diffraction patterns were found to depend predominantly on the bulk density of the argon sample and were relatively insensitive to the sample temperature. Except for the low density states, the intensity patterns showed three clearly defined peaks at [...], [...], and [...] The height of the main intensity peak was linear with the bulk sample density and the main peak broadened slightly with increasing temperature.
The radial atomic density functions, [...], had three maxima for the high density states and only a single well defined maximum for the vapor state. Their radial positions were relatively constant and were located at [...], and [...]. The height of these maxima was approximately linear with the bulk sample density and was independent of the sample temperature. The first coordination number showed a simple dependence on the argon density, varying from 6.0 atoms at the highest density to 2.1 atoms at the vapor state. Values of the radial electronic density functions are also reported.
The first maximum in the atomic radial distribution function, g(r), was found to be independent of both the temperature and the bulk sample density. The average height of this maximum was 1.97 and its average radial position was [...]. No abrupt changes or discontinuities were observed in g(r) as the critical state was approached. A subsidiary maximum, appearing at [...], reported in the previous x-ray studies of argon is shown to be spurious. Tables are presented of the estimated g(r) values and also of the smooth x-ray intensity patterns.
https://thesis.library.caltech.edu/id/eprint/3857Thermodynamic study of coupled chemical reactions
https://resolver.caltech.edu/CaltechETD:etd-01122004-145535
Authors: {'items': [{'id': 'Nebeker-E-B', 'name': {'family': 'Nebeker', 'given': 'Eugene Byrd'}, 'show_email': 'NO'}]}
Year: 1965
DOI: 10.7907/HTEW-XR80
To investigate the principles of Non-Equilibrium Thermodynamics, an experimental and theoretical study of a chemical reacting system is made. Nitric oxide, iodine, chlorine, iodine monochloride, and nitrosyl chloride in the gas phase are the macroscopic chemical species which comprise this system.
The system displays a coupling behavior which is uncommon to chemical reacting systems. However, this behavior may be useful in explaining some biological phenomena. The observed coupling effect results in a phenomenological coefficient matrix which is not diagonal.
None of the macroscopic derivations of the Onsager reciprocity relations which are examined appear to be generally applicable. However, a limited derivation is proposed which not only identifies the phenomenological coefficients in the linear rate laws for chemical reacting systems but also indicates the validity of the Onsager relations. Linear transformations of the fluxes and forces which diagonalize or destroy the symmetry of the phenomenological coefficient matrix are not applicable to a chemical reacting system.
Photometric methods are used to experimentally determine the reaction velocities and chemical affinities of this system. The phenomenon of coupling is definitely exhibited by this system, as shown by the existence of the coupling coefficients, L[subscript 12] and L[subscript 21], and by the presence of a negative AV product. The applicability of linear phenomenological rate laws and also rate laws which include quadratic terms are investigated. The linear rate laws are better approximations as the system approaches equilibrium and may be useful at appreciable distances from equilibrium in certain cases. A conclusive test of the Onsager reciprocity relations could not be made.https://thesis.library.caltech.edu/id/eprint/135Studies of liquid mercury and liquid mercury-gallium systems by x-ray diffraction
https://resolver.caltech.edu/CaltechETD:etd-09102002-145935
Authors: {'items': [{'email': 'dreutectic@msn.com', 'id': 'Caputi-R-W', 'name': {'family': 'Caputi', 'given': 'Roger William'}, 'show_email': 'YES'}]}
Year: 1965
DOI: 10.7907/HZ5D-3G89
<p>The purpose of this study was to determine the radial distribution of pure mercury and mercury-gallium mixtures by xray diffraction. Work was also done to resolve the problem of whether microdroplets of the solute metal existed in the solvent metal of the mercury-gallium system or whether the mercury-gallium mixtures were true solutions.</p>
<p>The experimental system used a reflection geometry from a horizontal free surface of the liquid metals. A silver x-ray tube was used in conjunction with a scintillation detector and pulse height analyzer. Data points were taken over an S range of approximately 1.6Å<sup>-1</sup> to 17Å<sup>-1</sup>.</p>
<p>Three samples were run at 0°, 30° and 50° C. The compositions of the three samples were pure mercury, 0.9658 mole froction of mercury, and 0.0197 mole fraction of mercury.</p>
<p>The peak positions of the final radial distribution functions for all samples showed no significant change over the temperature range used. The average positions of the first and second peaks of the mercury curves were 3.01Å and 5.80Å respectively. The coordination numbers for mercury as determined by the symmetrical curve method were 7.5, 7.3, and 7.0 atoms for the 0°, 30° and 50° C runs respectively.</p>
<p>The final results indicated that both samples of mercury-gallium were true solutions.</p>https://thesis.library.caltech.edu/id/eprint/3426A Thermodynamic Study of Multiple Reaction Systems At and Near Equilibrium
https://resolver.caltech.edu/CaltechETD:etd-10012002-101446
Authors: {'items': [{'id': 'Lu-Chien-Shih', 'name': {'family': 'Lu', 'given': 'Chien-Shih'}, 'show_email': 'NO'}]}
Year: 1967
DOI: 10.7907/pjnw-bc68
The near-equilibrium dynamic behavior of a homogeneous batch chemical reactor in which only one reaction occurs has been studied. The system has been analyzed thermodynamically and kinetically near equilibrium. The equations obtained have been linearized and then solved by means of Laplace transform techniques. The derivation for isobaric case has been presented in detail. The solutions for other cases, which include isothermal, isochoric, and adiabatic, have also been given. One numerical application indicates that the linearized equations can be useful even for protracted time intervals providing the forcing function is sufficiently small.
A general expression for the displacement of extent of reactions and mole fractions for multiple reaction systems near equilibrium has been derived. The displacement of extent of reactions for a two-reaction system which obeys ideal solution laws under isobaric condition has also been given. A numerical example has been worked out. The result agrees with the one obtained by brute force approach.
The condition for a multiple reaction system to obey LeChatelier's theorem is derived. It is shown that for the system to obey the theorem the matrix composed of Onsager phenomenological coefficients must be positive definite.
Expressions for the initial distribution of reactants required to maximize a desired product or to suppress an undesired product of a system of chemical reactions proceeding toward equilibrium have been derived. The system consists of R independent reactions and behaves as an ideal solution. It is assumed that the initial feed contains only the reactants and no inerts are present. Three different cases have been considered. They are isothermal-isobaric, isothermal-isochoric and adiabatic-isobaric. The expressions are implicit and complex so that no direct conclusion can be deduced. However, a numerical example (methane-steam system) shows that the effect of initial feed on the distribution of the final product is significant and deserves attention.https://thesis.library.caltech.edu/id/eprint/3846The Refractive Index and the Lorentz-Lorenz Function of Fluid Argon
https://resolver.caltech.edu/CaltechETD:etd-10042002-145820
Authors: {'items': [{'id': 'Teague-Richard-King', 'name': {'family': 'Teague', 'given': 'Richard King'}, 'show_email': 'NO'}]}
Year: 1968
DOI: 10.7907/ZM82-EZ50
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The refractive index, for [gamma][subscript Na]=5893 [angstroms], of dense fluid argon was measured by the determination of the angle of minimum deviation. The study covered states from 133 to 173[degrees]K for pressures 20 to 100 atm. The density data of J. Levelt were used to calculate values of the Lorentz-Lorenz function for these states.
A prism cell with 1/4" diameter sapphire windows in a cryostat was used to contain the sample. The cell temperature was measured to ?0.015[degrees]K and controlled to ?0.001[degrees]K. The pressure was measured with a gage calibrated against a dead weight tester to ?0.06%.
In a detailed study of the critical region the Lorentz-Lorenz function was used to find the difference between coexisting gas-liquid densities, and the critical coefficient resulting from this work is [Beta]=0.361. The critical temperature was varied to find the best fit of the experimental data to a linear equation for the critical coefficient; the value, T[subscript C]=150.704[degrees]K, is significantly different from the accepted value, 150.86[degrees]K. Values of n[subscript C]=1.0859 and P[subscript C]=48.18 atm. were also determined. The measurements on the coexistence curve outside the critical region yielded an average gas value of (L-L)[subscript G]=4.152 cc/mole. The average liquid value is 4.213 cc/mole. There are no indications of an anomalous value at the critical point. The values of L-L on the eight isotherms between 133 and 173[degrees]K show a sharp peak near the critical point, 2.1% maximum, but this is within the experimental uncertainty.https://thesis.library.caltech.edu/id/eprint/3900An X-ray Diffraction Study of the Structure of Argon in the Dense Liquid Region
https://resolver.caltech.edu/CaltechTHESIS:06022017-150552931
Authors: {'items': [{'id': 'Smelser-Stephen-Chester', 'name': {'family': 'Smelser', 'given': 'Stephen Chester'}}]}
Year: 1969
DOI: 10.7907/YYW1-T338
X-ray diffraction measurements were made on argon at six
states in the general liquid region below the critical pressure at
densities between 0.910 to 1.261 gm/cc and at temperatures between
108 to 143 °K. The intensity patterns exhibited three distinct
maxima at s values of 1.91 ± .02, 3.68 ± .06 and 5.43 ± .16 Å <sup>-1</sup>.
The intensity patterns were Fourier transformed to the net radial
distribution function and the direct correlation function. The
functions, 4πr<sup>2</sup>ρh(r), showed 3 maxima at low densities and 4 at the
high densities at values of r of 3.85 ± 0.05, 7.29 ± .10, 10.75 ± .45
and 14.1 ± .5 Å. A subsidiary maximum between the first and second
main peaks was observed to increase in prominence and disappear
systematically as the density increased. It was not noticeably
evident at either the lowest or highest density. The first zero of
the direct correlation function was at an r value of 3.34 ± .03 Å,
whereas the first maximum was at 3.78 ± .06 Å. Unlike previous
determinations of C(r) in this laboratory, the direct correlation
function exhibited secondary features on the shoulder of the main peak.
At the highest density the direct correlation function goes negative
near 6 Å. The intermolecular potential function was calculated from
the data using the Percus-Yevick equation. At the lowest density the
potential predicted in this way closely resembled the Lennard-Jones
12-6 potential for argon. However, the well-depths of these predicted
potentials diminished rapidly with increasing density and decreasing
temperature from 118.0 °K at ρ = .910 to 68.6 °K at ρ = 1.261 gm/cc.
Comparisons of the direct correlation function and the radial
distribution function with analytic predictions based on the Lennard-Jones
potential and the P-Y equation indicated internal consistency
at the lower densities. A comparison of the experimental radial
distribution function at the highest density, with one calculated
by molecular dynamics, indicated substantial agreement.
https://thesis.library.caltech.edu/id/eprint/10256Theoretical 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/3958I. Combinatorial Theory of Nonlinear Graphs, Applied to the Virial Equation of State. II. Chemical Thermodynamics of Open Systems
https://resolver.caltech.edu/CaltechETD:etd-08312006-091634
Authors: {'items': [{'id': 'Larsen-Alvin-Henry', 'name': {'family': 'Larsen', 'given': 'Alvin Henry'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/SCDN-4B19
<p>PART I:</p>
<p>By extension of the concept of a linear graph, as a topological configuration of vertexes with lines (2-bonds) connecting certain pairs of them, a nonlinear graph is defined to include also associations of certain triplets of the vertexes, or 3-bonds, representable by topological "areas" of triangles; quadruplets, or 4-bonds, by "volumes" of tetrahedra; etc. The configurational part of the partition function, including nonadditivity effects or three-body and higher interactions in the potential energy of a configuration of molecules, may be expanded as a sum of integrals over products of cluster functions, corresponding to a sum of nonlinear graphs. Certain special types of graphs, called trees and stars, figure prominently in the combinatorial analysis. The nth virial coefficient corresponds to the sum of all stars on n vertexes. Since topologically equivalent graphs correspond to integrals which yield the same result upon integration, the nth virial coefficient corresponds also to the sum of all topologically distinct stars on n vertexes, each multiplied by the appropriate combinatorial coefficient.</p>
<p>Development of the combinatorial theory for nonlinear graphs, trees, and stars proceeds similarly to that forlinear graphs. An explicit formula for counting nonlinear graphs on distinguishable vertexes is obtained, and generating functions relate the numbers of graphs to the numbers of corresponding nonlinear trees and stars. A novel term, the cycle function, is defined; the triplet cycle function, for 3-bonds, is derived; and cycle functions are used in generalizing Polya's theorem to apply to nonlinear graphs with more than one type of bond present. A theorem is thus obtained which solves the problem of counting nonlinear graphs on indistinguishable vertexes, and a relationship between generating functions permits the number of corresponding trees to be calculated. All of these techniques are extended to apply to multicomponent systems and to rooted graphs and trees. Then the problem of counting stars on indistinguishable or multicomponent vertexes is solved by a systematic procedure. The numbers of such stars are also closely approximated by a simple formula. Including 2- and 3-bonds only, the number of distinct stars on n = 3 indistinguishable vertexes is 5; for n = 4, there are 72 topologically distinct stars; and for n = 5, 10,346.</p>
<p>Because of the rapidly increasing number and complexity of the calculations, a practical limit for actual calculations involving any nonadditivity effects for a pure substance is the fourth virial coefficient. For multicomponent systems, the numbers of topologically distinct stars are always greater than for systems of a single component; hence even more compelling reasons would then be necessary to justify calculation of the fourth virial coefficient including three-body nonadditivity effects.</p>
<p>PART II:</p>
<p>General thermodynamic expressions for partial derivatives of extent of reaction with respect to external composition perturbations by a single species, for multicomponent, multiple-reaction systems constrained to paths of chemical equilibrium under various conditions, are obtained as the solution of a set of simultaneous, linear algebraic equations. The corresponding heat and temperature effects follow immediately. Derivatives of the extent of reaction are evaluated for ideal solutions. For multicomponent composition perturbations, the derivatives result from a linear combination of those for perturbations by a single species, each weighted by the net mole fraction of the given species in the streams crossing the boundary. Possible applications of the thermodynamic expressions include behavior of open systems under externally introduced composition perturbations, error analysis, and optimization of yield.</p>https://thesis.library.caltech.edu/id/eprint/3295A Theory for the Hugoniot of Condensed Media
https://resolver.caltech.edu/CaltechTHESIS:04172018-113351900
Authors: {'items': [{'id': 'Salzman-Paul-Klenett', 'name': {'family': 'Salzman', 'given': 'Paul Klenett'}}]}
Year: 1971
DOI: 10.7907/7nnp-4m89
<p>A shock model is developed that leads to an analytical expression
for the Hugoniot of condensed media. In the analysis the final
state is selected to coincide with the end of the shock transition so
that the total energy change across the shock front is evaluated from
changes in configurational energy only using an n-6 pair potential
(shown to be valid for all n > 0) and a given lattice structure.
Thermal energy changes are ignored because the dwell time of the molecules
in the shock transition region is less than the thermal relaxation
time. The total energy change is equated to the Hugoniot energy
change in the Rankine-Hugoniot conservation relations. This together
with the assumption of linear compression across the shock transition
gives the desired expression for the Hugoniot.</p>
<p>In the "weak form" (WF) solution the Hugoniot depends on molecular
(atomic) weight M and initial density ρ<sub>o</sub> as well as the
collision diameter σ, depth of the potential well ε and repulsive
exponent n of the pair potential. Extrapolation of this solution,
under certain conditions, yields an expression for the sound velocity
U<sub>o</sub> dependent on M, ε and n. In the "strong form" (SF) solution
the Hugoniot depends only on U<sub>o</sub> and n.</p>
<p>The shock data for 13 liquids and 23 metals are compiled and a
selection process used to eliminate poor data and data affected by
phase transitions. Using σ from the literature and ε from a melting
point correlation, the WF solution Hugoniot is applied to the
liquids and the "best" values of n determined using numerical fitting
techniques. Excellent fits are obtained with values of n from
6.2 to 11.7. A common value of 9.2 is found to fit the shock data for
argon at four different initial states. Failure of the theory is
noted only for (di-)ethyl ether and water. The results are generally
concluded to support the validity of the shock model. Values of n
for argon, mercury and nitrogen compare favorably with values reported
in the literature. The WF solution does not yield accurate values of
U<sub>o</sub>.</p>
<p>The SF solution is expanded in Taylor series to eliminate
singularities and applied to the shock data for 10 fcc and 13 bcc
metals and the "best" values of n determined. For the fcc metals
excellent fits are found for values of n from 4.0 to 6.3. Based on
the "pseudo-atom" concept, it is concluded that metals have "softer"
potentials than liquids. The results for the fcc metals are concluded
to generally support the validity of the shock model. For the bcc
metals excellent fits are found for n = 0.1 to 4.6 and it is concluded
that bcc metals are "softer" than fcc metals. Since σ is "not
defined" for all n < 3 it is speculated that the Hugoniot might not
be "well defined" in these cases. The theory is found to be not
applicable to Cs and Ba. The values of n found for Cu, Al and Pb
agree well with values in the literature. The n for metals are found
to roughly correlate with the Grüneisen coefficient γ.</p>
<p>The major assumption of the theory, that the transition region
is "sufficiently thin," is analyzed and found to be reasonable. The
mean number of molecular layers in the transition region is ~ 7 and
the mean residence time ~ 2 x 10<sup>-12</sup>sec. In addition the n-6 potential
is judged to be adequate for the present study.</p>
<p>The SF solution Hugoniot is shown to be compatible with the
classical linear U-µ relation (U = A + Bu) when x-1 « 1. Values of
the slope B from experimental data are found to agree closely with
the derived relation B ≃ (n + 5)/6 for the corresponding metals.
Recommendations for further studies with liquids, fcc and bcc metals
are made, including an evaluation of an explicit expression generally relating
the pair potential to the shock data.</p>
<p>In several subsidiary studies a new method of computing
temperatures along the Hugoniot is found, two statistical approaches to
the definition of "nearest neighbor distance" and its use as a measure
of liquid structure are developed and the effect of phase transitions
on the shock model is determined.</p>
https://thesis.library.caltech.edu/id/eprint/108101. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction
https://resolver.caltech.edu/CaltechTHESIS:04112016-103207668
Authors: {'items': [{'id': 'Gutschick-Vincent-P', 'name': {'family': 'Gutschick', 'given': 'Vincent P.'}}]}
Year: 1972
DOI: 10.7907/B8K2-V070
<p><u>Part 1.</u> Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a <u>lower</u> critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.</p>
<p><u>Part 2.</u> Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H<sub>2</sub>, He, Li, Be, LiH, and N<sub>2</sub> by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities. </p>
<p><u>Part 3.</u> Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H<sub>2</sub>-H<sub>2</sub> collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.</p>
https://thesis.library.caltech.edu/id/eprint/9669The structure of liquid argon as determined by x-ray diffraction
https://resolver.caltech.edu/CaltechTHESIS:04292016-140637476
Authors: {'items': [{'id': 'Kirstein-Bruce-Edward', 'name': {'family': 'Kirstein', 'given': 'Bruce Edward'}}]}
Year: 1972
DOI: 10.7907/88K0-V473
<p>X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.</p>
<p>The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.</p>
<p>Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.</p>
<p>The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.</p>
<p>The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.</p>
https://thesis.library.caltech.edu/id/eprint/9691Study of Equilibrium Critical Phenomena in Fluid Argon
https://resolver.caltech.edu/CaltechTHESIS:11212017-114310188
Authors: {'items': [{'id': 'Wu-Shyue-Yuan', 'name': {'family': 'Wu', 'given': 'Shyue Yuan'}}]}
Year: 1972
DOI: 10.7907/Z20H-HM70
<p>The refractive index of fluid argon was measured by using
the method of angle of minimum deviation for λ<sub>Na</sub> = 5893Å. The
measurements were carried out along the coexistence curve and along
fourteen single phase isotherms from 150.7° to 163°K at pressures from
40 to 90 atmospheres.</p>
<p>The Lorentz-Lorenz relation was used to relate the refractive
index data to the densities and subsequently to find the isothermal
compressibilities along the singla phase isotherms. Following the law
of rectilinear diameter and the simple power laws for critical
exponents, the values of the critical temperature and exponents for
argon were found to be T<sub>c</sub> = 150.725° ± 0.010°K, β = 0.3574 ± 0.0027,
and γ = 1.170 ± 0.013. Also values of n<sub>c</sub> = 1.08611 and
P<sub>c</sub> = 47.983 atm were determined. These values agree well with
others reported for argon. Comparison of the values of β and γ
with those predicted by the classical theory and the three-dimensional
lattice gas model suggests that the latter gives a better description
of the critical behavior of fluid argon.</p>
<p>Analysis of the reduced chemical potential differences, computed
from the refractive index data along the singla phase isotherms,
has been made by using the scaled equation of state first proposed by
Widom. Reasonable values T<sub>c</sub> and γ were obtained when the
value of β determined above was used.</p>https://thesis.library.caltech.edu/id/eprint/10567The X-ray scattering behavior of molecular fluids
https://resolver.caltech.edu/CaltechTHESIS:06062016-090735912
Authors: {'items': [{'id': 'Morrison-Paul-Frederick', 'name': {'family': 'Morrison', 'given': 'Paul Frederick'}}]}
Year: 1972
DOI: 10.7907/R17M-GP28
<p>The Steele-Pecora equation describing the x-ray scattering behavior of molecular fluids has been investigated. Several molecular scattering factor coefficients, molecular distribution functions for chlorine according to the Percus-Yevick theory,and intensity functions for chlorine have been evaluated using orthonormal expansion methods. </p>
<p>Molecular scattering factors for H<sub>2</sub>, N<sub>2</sub>, LiH, and HF have been obtained as spherical harmonic expansions. The coefficients of the expansions and corresponding gas scattering intensities have been evaluated using both the molecular orbital and isolated atom approaches, and significant differences have been found to exist between the two methods. Chlorine scattering factor coefficients were calculated for the isolated atom approximation only. Expressions for the two-centered Gaussian scattering integral coefficients were derived, and the harmonic expansion technique was shown to be a practical method of calculation. </p>
<p>The Percus-Yevick equation was solved for chlorine by an extension of the Hankel transform method of Chen and Steele. Chlorine was represented by an appropriate two-centered Lennard -Jones potential, the σ-and ɛ parameters having been determined from second virial data. Higher order expansions of f(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>), C(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>), and H(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>) were used here than in previous work as well as a more complete representation of the product of two harmonic series. Pair correlation functions were obtained over the density range ρ* = 0.1 to 1.2 for T* = 0.75, 1.00, and 1.30. It was concluded that the first two expansion coefficients of f(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>), C(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>), and H(<u>R</u><sub>1</sub><u>R</u><sub>2</sub>) were sufficient to obtain accurate pair correlation functions over this range of states. For certain states, use of the more complete product expression reduced the error in g<sub>000</sub> by several percent. Evidence for a chlorine critical point was obtained in the vicinity of (ρ*,T*) = (0.65, 0.70). </p>
<p>A version of the Steele-Pecora equation suitable for use with diatomic molecules was derived. Substitution of the chlorine scattering factor coefficients and Percus-Yevick distribution functions into this equation led to the determination of total scattered intensity functions expressed as sums of gas scattering, spherical, and angular intensity contributions. The angular contributions were shown to be experimentally significant in the regions of the first and second peaks at high densities (ρ*1.2). Temperature was shown to have only a slight effect on total intensity. g<sub>000</sub>, g<sub>200</sub>, and g<sub>220</sub> were found to be the principal contributors to the intensity. </p>
https://thesis.library.caltech.edu/id/eprint/9848The Viscosity of Fluids in the Critical Region
https://resolver.caltech.edu/CaltechTHESIS:09062016-112046701
Authors: {'items': [{'id': 'Strumpf-Hal-Jeffry', 'name': {'family': 'Strumpf', 'given': 'Hal Jeffry'}, 'show_email': 'NO'}]}
Year: 1972
DOI: 10.7907/1FYM-6N97
<p>The viscosity of xenon has been measured along ten isochores and the viscosity of ethane has been measured along five isochores in the region of the gas-liquid critical point. The viscometer was a specially cut quartz cylinder, which was excited into a torsionally oscillating mode upon application of an alternating voltage. The
cylinder, oscillating in this manner, generated a viscous wave when immersed in a fluid. The viscous wave caused an impedance loading on the quartz which changed its resonant resistance and frequency. This change in resonant properties can be related to the viscosity-density product of the fluid. </p>
<p>The resonant properties of the quartz crystal were measured by connecting the crystal to the unknown arm of a Wheatstone bridge circuit, modified so as to measure parallel resistance and capacitance. The crystal was driven by a very stable frequency generator, and the circuit was tuned using an oscilloscope as a null detector. </p>
<p>The crystal was enclosed in a high pressure stainless steel cell and placed in a water thermostat which controlled temperature to ± 0.001°C. The temperature was measured with a calibrated platinum resistance thermometer. The density was determined by a gravimetric technique. </p>
<p>The viscosities exhibit an "anomalous" increase as the critical temperature is approached along an isochore of close to critical density. The anomaly is consistent with a logarithmic divergence of the form: </p>
<p>∆ƞ = A log ɛ + ʙ</p>
<p>where ∆ƞ is the anomalous viscosity, ɛ is the reduced temperature difference from critical, and A and ʙ are constants. The possibility of an exponential divergence or a cusp-type finite limit for viscosity is not precluded, however. </p>
<p>The critical temperatures and densities have been determined by visual observations. For xenon, T<sub>c</sub> = 16.627 ± 0.005°C, ρ<sub>c</sub> = 1.11 ± 0.01 g/cm<sup>3</sup> ; for ethane, T<sub>c</sub> = 32.218 ± 0.005°C, ρ<sub>c</sub> = 0.2055 ± 0.002 g/cm<sup>3</sup>. The temperatures are stated with respect to the 1968 International Practical Temperature Scale. </p>
https://thesis.library.caltech.edu/id/eprint/9913A 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/11178A Theoretical Investigation of the Effect of Intermolecular Correlations upon Properties of Simple Liquids from X-Ray Diffraction
https://resolver.caltech.edu/CaltechTHESIS:08272018-085905047
Authors: {'items': [{'id': 'Piliavin-Michael-Aron', 'name': {'family': 'Piliavin', 'given': 'Michael Aron'}, 'show_email': 'NO'}]}
Year: 1973
<p>This work reports a theoretical study on the effect of including intermolecular correlations in x-ray scattering data from simple liquids.</p>
<p>An instantaneous configuration-dependent scattering factor is defined for a molecule in a liquid. Using statistical mechanics and physical principles, an expression is derived that corrects the usual scattering equations, for both coherent and incoherent radiation.</p>
<p>Computations, using the new result, were done on liquid helium and argon. Comparison of correlated scattering factors and isolated molecule scattering factors show significant deviations, especially for larger angles of scattering. Incorporating correlation effects into scattering data for these liquids, the resultant radial distribution function peak is depressed an average of 1% and the potential energy is lowered by 5%. Treatment of data in this manner leads to better agreement with theoretical predictions.</p>
https://thesis.library.caltech.edu/id/eprint/11162I. 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 Study of Critical Phenomena in Krypton
https://resolver.caltech.edu/CaltechTHESIS:09192018-095409363
Authors: {'items': [{'id': 'Gülari-Esin-Cetegen', 'name': {'family': 'Gülari', 'given': 'Esin Cetegen'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/NNTS-KJ75
<p>A detailed experimental study of equilibrium critical phenomena in krypton was made. Using the method of angle of minimum deviation the refractive index was measured along the coexistence curve, along 16 isotherms above and along 11 isotherms below the critical temperature. The range of the temperature measurements in terms of t the reduced temperature difference from T<sub>c</sub> was -6.8 x 10<sup>-2</sup> ≦ t ≦ -5.7 x 10<sup>-5</sup> and 3.8 x 10<sup>-5</sup> ≦ t ≦ 4.8 10<sup>-2</sup>. The measurements were planned so that the region very near the critical point was covered in most detail. The refractive index was related to the density through the Lorentz-Lorenz relation.</p>
<p>After proper weight assignment, the data were analyzed in terms of the asymptotic power laws. The following values of the critical parameters, exponents and coefficients were determined: T<sub>c</sub> = 209.286 ± 0.010°K, P<sub>c</sub> = 54.213 ± 0.003 atm., LL<sub>c</sub> = 0.070588 ± 0.000006, β = 0.3571 ± 0.0008, B = 1.840 ± 0.001 γ = 1.182 ± 0.008, Γ = 0.0835 ± 0.0011; γ<sub>G</sub><sup>’</sup> =1.15 ± 0.01, Γ<sub>G</sub><sup>’</sup> = 0.021 ± 0.001, γ<sub>L</sub><sup>’</sup> = 1.13 ± 0.01, Γ<sub>L</sub><sup>’</sup> = 0.025 ± 0.001; δ = 4.25 ± 0.25. The law of the rectilinear diameter was obeyed with its slope = 0.0918 ± 0.0004.</p>
<p>The reduced chemical potential differences and the reduced density differences were calculated. The chemical potential was observed to show antisymmetry for
-2 x 10<sup>-3</sup> ≦ t < 4.8 x 10<sup>-2</sup> and -0.3 < ΔLL < 0.3. The data in this range were analyzed using Widom's equation of state and the closed-form<sup>(29)</sup> of h(x). The proposed equation was found to fit the experimental data very well.</p>
<p>The predictions of the linear model<sup>(32)</sup> were also checked and were observed to be consistent with the experimental results.</p>
https://thesis.library.caltech.edu/id/eprint/11191Determination 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. Quasi-Elastic Light Scattering from Liquids and Liquid Mixtures: a Study of Mass and Thermal Diffusivities. II. Observation of Translational and Intramolecular Diffusion of Circular Duplex DNA by Quasi-Elastic Light Scattering
https://resolver.caltech.edu/CaltechTHESIS:12062017-094448880
Authors: {'items': [{'id': 'Brown-Ronald-Jerome', 'name': {'family': 'Brown', 'given': 'Ronald Jerome'}}]}
Year: 1975
DOI: 10.7907/VKF3-8056
<p>Part I</p>
<p>A quasi-elastic light scattering spectrometer has been constructed and used to measure the binary mutual diffusion coefficient D<sub>AB</sub> as a function of concentration in eight binary mixtures and the thermal diffusivity x in nine pure liquids and two binary mixtures. The resulting values are in close agreement with the available bulk
values and are accurate to within 3% for mass diffusivities and 5% for thermal diffusivities. Because neither type of measurement is dependent on the imposition of a macroscopic gradient, many of the
problems associated with conventional bulk measurements are
eliminated.</p>
<p>Determinations require less than 2 hours for thermal diffusivities and 30 minutes for mass diffusivities, in contrast to the more time consuming classical approaches.</p>
<p>On the basis of these experimental results, light scattering spectroscopy is established as an effective tool in the determination of
liquid mass and thermal diffusivities. The technique should have wide industrial application.</p>
<p>Part II</p>
<p>Quasi-elastic light scattering experiments on solutions of
ɸX174 RF DNA and PM2 I DNA reveal spectral contributions from
translational and intramolecular motion. A tentative interpretation of the data in terms of Rouse-Zimm theory indicates lowest order relaxation
times qualitatively consistent with theoretical predictions. Further experiments on linear and form II DNA should provide information about the changes in molecular flexibility and translational diffusivity associated with an alteration in conformation.</p>https://thesis.library.caltech.edu/id/eprint/10589I. Dynamics of flowing polymer solutions. II. The measurement of velocity gradients by homodyne light scattering spectroscopy
https://resolver.caltech.edu/CaltechETD:etd-12112006-152815
Authors: {'items': [{'id': 'Fuller-G-G', 'name': {'family': 'Fuller', 'given': 'Gerald Gendall'}, 'show_email': 'NO'}]}
Year: 1980
DOI: 10.7907/5PPN-JZ62
<p>This thesis is presented in two parts. In the first part the results of flow birefringence experiments and modelling efforts on both concentrated and dilute polymer solutions are discussed. The second part presents theoretical developments and complementary experiments which demonstrate the utility of the technique of homodyne light scattering spectroscopy to the measurement of velocity gradients in laminar flow fields.</p>
<p>The flow birefringence experiments were performed using a four roll mill which was designed in order to allow the simulation of a wide range of two dimensional flows ranging from purely extensional flows to purely rotational flows. Flow visualization and homodyne light scattering spectroscopy experiments were used to characterize the flow fields.</p>
<p>Using this device the flow birefringence of concentrated polyethylene/water and polystyrene/tricresyl phosphate solutions was measured. Birefringence measurements of the Polyox solutions over a wide range of flow types indicated that the birefringence could be well correlated against the eigenvalue of the velocity gradient tensor, in agreement with model calculations. Transient experiments were performed in which the birefringence was measured as purely extensional flows were started from rest. Both polymer/solvent systems showed a pronounced overshoot in the birefringence. Turbidity measurements were also performed on the polyox solutions and a 30% increase in the turbidity was measured which persisted for many hours after the cessation of flow (whereas the birefringence decayed to zero in a fraction of a second). This increased turbidity and its persistence with time suggests the occurence of flow induced crystallization of the polymer.</p>
<p>These experiments involving concentrated polymer systems were compared to model calculations using the Yamamoto network theory. Several choices of the polymer entanglements creation and destruction functions were analyzed and it is demonstrated that analytical results can be obtained using these choices. A variety of nonlinear phenomena can be predicted including the correlation of the of purely extensional flows. The predicted response of the stress tensor is also presented and discussed.</p>
<p>Flow birefringence experiments were also carried out in the dilute concentration range. Measurements were taken on three molecular weight samples (2-8x10^6 MW, MW/MN=1.14-1.3) in a viscous polychlorinated biphenyl solvent in the range of 50-100 ppm subjected to a wide range of two dimensional flows. The birefringence was again found to be well correlated against the eigenvalue of the velocity gradient tensor. The normalized birefringence, corrected for concentration, ([delta]n/nc), was observed to approach a saturation value at high velocity gradients in purely extensional flow. This saturation value was independent of both the molecular weight and the concentration c, in agreement with theory. In addition, the magnitude of the saturation value is consistent with nearly fully extended chains and suggests extensions in the range of 20-50 times the rest state size. The experiments were complemented by simple dumbbell model calculations which incorporated the nonlinear spring, internal viscosity and variable hydrodynamic friction. The model was found to simulate the experimental data very well if the effects of molecular weight distribution and finite transit times in the flow were taken into account.</p>
<p>The results of a detailed investigation of the dumbbell model used to analyze the dilute solution experiments is also included. The effects of the nonlinear spring, variable friction factor and internal viscosity to the response of the dumbbell to steady state and transient two dimensional flows are exposed. A perturbation solution for the dumbbell with a small amount of internal viscosity is presented and it is demonstrated that this problem can be solved analytically.</p>
<p>The technique of homodyne light scattering spectroscopy applied to suspensions in laminar flow is investigated. It is demonstrated both theoretically and experimentally that use of this method allows direct measurement of velocity gradients without the need for differentiating velocity data which is the normal method used. This technique was used to characterize the spatial distribution of velocity gradients existing in the four roll mill simulating purely extensional flow.</p>https://thesis.library.caltech.edu/id/eprint/4943I. 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