Molecular Thermodynamics
and Phase Equilibria for Fluid Mixtures
In classical and "modern" chemical engineering, as
well as in biotechnology, processing toward a desired product
is often conducted in a fluid phase containing several components.
For rational process and product design, it is therefore essential
to know the thermodynamic properties of fluid mixtures. While
these properties are required for a variety of processing steps,
they are particularly important for separation operations such
as distillation, extraction, adsorption and crystallization. Through
experimental and theoretical studies, this research contributes
to our understanding of fluid-phase thermodynamic properties for
a diverse set of mixtures that are encountered in the chemical
and related industries. Particular attention is given to polymer
solutions and gels (with applications to membranes and to drug-delivery
systems); to mixtures of paraffins in the vapor-liquid critical
region (with application to natural-gas processing); and to macroions
in aqueous electrolyte solutions (with applications to biotechnology
and to the technology of colloids). In this research, we obtain
new experimental data, obtain insight on molecular behavior through
Monte Carlo simulation calculations, and develop theories for
correlation of limited experimental data toward estimating reliable
properties when no experimental data are available.
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Thermodynamic Properties
of Hyperbranched Polymers in Common Solvents
Vapor-pressure and osmometric measurements are obtained for solutions
of hyperbranched polymers (comb polymers, star polymers and dendrimers)
in nonpolar organic solvents and for highly branched water-soluble
polymers in water or alcohol. Vapor-pressure measurements are
made by contacting a weighesd quantity of polymer (in a pan at
the end of a calibrated quartz spring) with a solvent vapor at
a known pressure. The displacement of the quartz spring gives
the weight fraction of solvent dissolved in the polymer.
Osmotic pressures are measured with a membrane osmometer to determine
polymer molecular weight and osmotic second virial coefficients.
These, in turn, give the potential of mean force for two polymer
molecules dissolved in a solvent. We are interested in how the
potential of mean force varies with polymer structure.
Molecular-simulation (Monte Carlo) calculations have been performed
for the potential of mean force of branched polymers as a function
of polymer structure and forces of attraction between non-bonded
polymer segments.
Monte Carlo studies have also been performed to test the addivity
assumption for potentials of mean force. The potential energy
of three interacting polymer molecules is calculated by Monte
Carlo and compared with the sum of the three two-body potentials.
Deviations from the addivity assumption are not large but nevertheless
significant for some positions of the three polymers.
Monte Carlo calculations have also been made for the potential
of mean force of a polymer molecule and a solid wall. Polymer
structure has a large effect on that potential. The purpose of
these calculations is to provide fundamental information for interpreting
experimental data concerning polymer adsorption on a solid surface.
Co-Workers: Undergraduate students, visiting scholars and Dr.
Dusan Bratko.
Recently we have used our osmometer to determine molecular weights
of inorganic molecular clusters made by Professor Alivisatos and
co-workers at LBNL.
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Solubilities of Heavy Organic Solutes in Polymer
Films
For application in design of water-pollution abatement processes
and in drug-delivery systems, experimental and correlational studies
are in progress to determine the distribution coefficient of a
heavy organic solute between water and a polymer film. These experiments
are not simple because the distribution coefficients are often
very small and, more important, corrections must be made for failure
to reach equilibrium and for possible surface adsorption. (Phase
contact for several weeks is often insufficient to reach equilibrium.)
The distribution coefficient is determined by gravimetric measurements
and by spectroscopic analysis of the aqueous phase as a function
of time. Polymers and solutes are characterized in part by literature
data and in part by measurements using a differential scanning
calorimeter. Independent measurements are also made to determine
the solubility of the (usually solid) solute in water and to determine
the solubility of water in the polymer. From these measurements,
coupled with Flory-Huggins polymer-solution theory, we calculate
the solubility of the dry solute in the polymer. In this calculation,
attention must be given to possible polymer glassiness.
Co-workers: Graduate students, undergraduate students and Visiting
Professor Maria Olaya from the University of Alicante, Spain.
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Molecular Thermodynamics of Gel-Solvent Systems
This research concerns gels that are three-dimensional networks
of linear polymers. Such gels are of much technical interest in
medicine (e.g., inlays in the eye following removal of cataracts),
optometry (contact lenses), pharmacy (drug-delivery systems) and
in the synthesis of a variety of "smart" materials.
In this research we measure the vapor pressure (hence the thermodynamic
activity) of a solvent dissolved in a gel of known composition.
In recent studies, we measured the activities of three alcohols
(methanol, I-propanol and t-butanol) in linear and cross-linked
poly (4-vinyl pyridine) from 55 to 70oC. Similar studies
were also made with a blockcopolymer of poly (4-vinyl pyridine)
with polystyrene. For data interpretation and correlation we use
a modified (and much improved) form of the Flory-Rehner theory.
Co-workers: Graduate and undergraduate students.
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Phase Equilibria for Natural-Gas Mixtures Including
the Critical Region
Upon incorporation of contributions from long-wavelength density
fluctuations by a renormalization-group theory, a crossover equation
of state is developed for describing thermodynamic properties
of chain fluids. Outside the critical region, the crossover equation
of state reduces to the classical equation; inside the critical
region, it gives nonclassical universal critical exponents. The
crossover equation of state correctly represents phase equilibria
and pVT properties of chain fluids in both regions. Good agreement
is obtained upon comparisons with computer simulations for square-well
chain fluids. As obtained from experimental vapor-pressure and
density data, the square-well segment-segment parameters for n-alkanes
from ethane to eicosane are linear functions of molecular weight.
Calculated thermodynamic properties agree well with experiment
for n-alkanes from methane to hexatriacontane.
The engineering-oriented theory developed here has been extended
to mixtures and reduced to practice for binary mixtures; good
agreement with experimental data is obtained. However, computational
difficulties arise when we try to reduce the theory to practice
for ternary (and higher) mixtures. Current efforts are in progress
toward overcoming these difficulties.
Co-workers: Postdoctoral fellows.
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Protein-Protein Interactions in Aqueous Electrolyte
Solutions
For applications in biotechnological separations, we are studying
how protein molecules interact with each other in an aqueous medium
contain a common salt. Toward that end, we use Osmometry, Dynamic
Light Scattering, Static Light Scattering, Fluorescence Polarization
Analysis and Chromatography.
Osmometry and Static Light Scattering give us molecular weights
and osmotic second virial coefficients for proteins in aqueous
saline solution. Dynamic Light Scattering gives us diffusion coefficients
and (through the Stokes-Einstein equation) diameters of protein
molecules. From these data we obtain a potential of mean force
for proteins as a function of ionic strength, nature of the salt
(kosmotropic or chaotropic) and pH. From the potential of mean
force we can calculate the phase diagram for a protein in a given
salt solution; this calculation uses statistical thermodynamics
based on van der Waals theories for the fluids and for the solid.
For all cases of interest we obtain metastable liquid-liquid equilibria,
in addition to stable liquid-solid equilibria. We compare our
calculated phase diagram with cloud-point measurements where a
homogeneous solution of protein and salt is slowly cooled until
a precipitate (cloud point) begins to form.
Experimental data have been obtained for lysozyme and ovalbumin
in a variety of salt solutions at variable pH, and for a peptide
that is believed to be involved in forming an amyloid fibril as
observed in Alzheimer's disease.
We are currently studying interactions of partially denatured
proteins. Fluorescence Polarization Analysis and Chromatography
are experimental techniques for measuring protein-protein binding
constants at conditions (ionic strength, salt type, pH) where
such binding is appreciable. We are particularly interested in
studying the early stages of fibril formation as found, for example,
in Alzheimer's and other neurological diseases.
Co-workers: Graduate students, undergraduate students, visiting
scholars, postdoctoral fellows, Professor Harvey Blanch and Dr.
Dusan Bratko.
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The Potential of Mean Force Between Macroions
(Colloids or Globular Proteins) in Electrolyte Solution
A new technique for Monte Carlo sampling of the hard-sphere collision
force has been applied to study the interaction between a pair
of spherical macroions in primitive-model electrolyte solutions
with valences 1:2, 2:1, and 2:2. Macroions of the same charge
can attract each other in the presence of divalent counterions,
in analogy with earlier observations for planar and cylindrical
geometries. The attraction is most significant at intermediate
counterion concentrations. In contrast to the entropic depletion
force between neutral particles, attraction between macroions
is of energetic origin. The entropic contribution to the potential
of mean force is generally repulsive at conditions corresponding
to aqueous colloids with or without salt. For systems with divalent
counterions, the potentials of mean force predicted by mean-field
approximations like the Derjaguin-Landau-Verwey-Overbeek (DLVO)
theory or the Sogami-Ise (SI) theory are qualitatively different
from those observed in the simulations. However, for systems with
monovalent counterions, predictions of DLVO theory are in fair
agreement with simulation results.
Monte Carlos studies have also been made to test the additivity
assumption for potentials of mean force. Calculations were made
for interactions in assemblies of three macroions; these three-body
calculations were compared with the sum of results for two-body
calculations. Deviations from additivity depend on macroion positions
with a maximum deviation near 10 per cent. Subsequent phase-equilibrium
calculations indicate that the effect of three-body forces is
small.
Current studies concern the potential of mean force between two
macroions with different charge. In an effort toward better understanding
of forces between globular proteins, future efforts will consider
the effect of macroion charge distribution on the potential of
mean force.
Co-workers: Postdoctoral Fellows, Professor Harvey Blanch, Dr.
Dusan Bratko.
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