Theoretical Background To order this title, and for more information, click here
By K. Kamide, Faculty of Economics, Nara Sangyo University, Nara 636-8503, Japan T. Dobashi, Faculty of Engineering, Gunma University, Gunma 376-8515, Japan
Description This book is mainly concerned with building a narrow but secure ladder which polymer chemists or engineers can climb from the primary
level to an advanced level without great difficulty (but by no means easily, either). This book describes some fundamentally important
topics, carefully chosen, covering subjects from thermodynamics to molecular weight and its distribution effects. For help in self-education
the book adopts a "Questions and Answers" format. The mathematical derivation of each equation is shown in detail. For further reading,
some original references are also given. Numerous physical properties of polymer solutions are known to be significantly different
from those of low molecular weight solutions. The most probable explanation of this obvious discrepancy is the large molar volume ratio
of solute to solvent together with the large number of consecutive segments that constitute each single molecule of the polymer chains
present as solute. Thorough understanding of the physical chemistry of polymer solutions requires some prior mathematical background
in its students. In the original literature, detailed mathematical derivations of the equations are universally omitted for the sake
of space-saving and simplicity. In textbooks of polymer science only extremely rough schemes of the theories and then the final equations
are shown. As a consequence, the student cannot learn, unaided, the details of the theory in which he or she is interested from the existing
textbooks; however, without a full understanding of the theory, one cannot analyze actual experimental data to obtain more basic and
realistic physical quantities. In particular, if one intends to apply the theories in industry, accurate understanding and ability to
modify the theory are essential.
Audience
For students at universities and researchers, who are studying the physical chemistry of polymer solutions. Also as a reference text
for technologists intending to apply the physical chemistry of polymer solutions to industrial practice and to educators teaching this
or related subjects.
Contents
Preface. Glossary. Fundamentals of thermodynamics. Internal energy, free energy and enthalpy. Partial molar quantities.
Gibbs-Duhem relation. Mixing volume change and mixing entropy. Gibbs condition for two-phase equilibrium. Heat of mixing.
Ideal
and non-athermal solutions. Ideal solution. Molar quantities in mixing. Entropy of mixing for ideal solution. Raoult's
law. Boiling point elevation and freezing point depression (I). Boiling point elevation and freezing point depression (II). Membrane
osmometry. van 't Hoff's equation. Empirical determination of osmotic pressure. Empirical determination of number-average molecular
weight. Non-ideal solution (I). Non-ideal solution (II). Mixing in non-ideal solution. Real solution. Vapor pressure osmometry (I).
Vapor pressure osmometry (II). Vapor pressure osmometry (III). Vapor pressure osmometry (IV). Vapor pressure osmometry (V). Vapor
pressure osmometry (VI). Vapor pressure osmometry (VII). Vapor pressure osmometry (VIII).
Lattice Theory. Lattice
theory for low molecular weight solution. Bragg-Williams approximation. Free energy of mixing for random mixing. Free energy of mixing
for athermal solution. Flory's theory (I): 0th approximation theory for polymer solution. Flory's theory (II): entropy of
polymer solution. Flory's theory (III): entropy of mixing for polymer solution. Flory's theory (IV): partial molar entropy of mixing
of solvent and
polymer. Flory's theory (V): van Laar-Scatchard approximation. Flory's theory (VI): Gibbs free energy of mixing of polymer
solution. Flory's theory (VII): chemical potential of solvent for non-athermal random mixing polymer solution. Flory's theory (VIII):
chemical potential of polymer for non-athermal random mixing polymer solution. Flory's theory (IX): Gibbs-Duhem relation for polymer
solution. Flory's theory (X): assumptions in Flory's 0th approximation theory. Thermodynamic interaction parameter χ.
Concentration dependence of χ. Virial coefficient at θ point. Determination of χ from cloud point curve. Chemical
potential of polymer in multicomponent polymer solution. Huggins' free energy correction parameter g. Gibbs free energy of mixing for
ternary system.
Phase Equilibria. Stability of thermodynamic system (I). Stability of thermodynamic system (II).
Stability of thermodynamic system (III). Stability of thermodynamic system (IV). Criteria for stable equilibrium for binary mixture.
Gibbs free energy surface and phase diagram for binary mixture. Criteria for stable equilibrium for ternary mixture. Gibbs free energy
on composition triangle. Critical condition for ternary mixture. Critical condition for (r+1)-component system. Critical condition
for ideal solution and regular solution. Critical condition for Flory-Huggins solution. Range of critical temperature and critical
composition. Determination of θ and ψ (I): Shultz-Flory plot. Determination of θ and ψ (II): application to experimental
data. Determination of θ and ψ (III). Chemical potential in Flory-Huggins solution. Mean molar Gibbs free energy of regular
solution. Mean volume Gibbs free energy and critical condition for Flory-Huggins solution. Critical condition for homologous polymer
solution. Critical parameters for homologous polymer solutions with concentration-independent χ. Chemical potential for polydisperse
polymer in single solvent (P/S) with concentration-dependent χ. Critical condition for polydisperse polymer in single solvent (P/S)
with concentration-dependent χ. Determination of cloud point curve for polydisperse polymer in single solvent (P/S) with concentration-dependent χ. Effect of molecular weight distribution on critical concentration. Experimental method for determining Flory's θ condition.
Experimental method for determining θ and ψ. Experimental method for determining κ0. Critical condition
in terms of g. Relationship between g, θ and ψ. Slope of spinodal curve. Phase equilibria of polymer blend (P1/P2)
(I): Gibbs free energy of mixing per unit volume for monodisperse polymer / monodisperse polymer. Flory-Huggins free energy for multicomponent
solution. Phase equilibria of polymer blend (P1/P2) (II): Critical parameters for
monodisperse polymer / monodisperse
polymer. Phase equilibria of polymer blend (P1/P2) (III): chemical potential for polydisperse polymer / polydisperse
polymer. Phase equilibria of polymer blend (P1/P2) (IV): critical condition for polydisperse polymer / polydisperse
polymer. Phase equilibria of polymer blend (P1/P2) (V): critical condition for polydisperse polymer / polydisperse
polymer. Phase equilibria of polymer blend (P1/P2) (VI): critical parameters for polydisperse polymer / polydisperse
polymer. Second-order derivatives of Gibbs free energy for ternary mixtures
P2/S1/S0, P2/P1/S0
and P2/P1/P0. Spinodal condition for quasi-ternary system polydisperse polymer /
polydisperse polymer
/ solvent (P2/P1/S0). Neutral equilibrium condition for quasi-ternary system polydisperse
polymer /
polydisperse polymer/ solvent (P2/P1/S0). Chemical potential of mixing for (r+1)-component Flory-Huggins
solution. Critical condition for quasi-ternary system polydisperse polymer in mixed solvent (P3/S2/S1).
Symmetry of critical condition. Fractionation (I): coexistence curve of polymer solution. Fractionation (II). Fractionation (III):
partition coefficient. Fractionation (IV): Weight of polymer partitioned in each phase. Fractionation (V): characteristic specific
value for the degree of polymerization na. Fractionation (VI): fractionation efficiency. Fractionation (VII): molecular
weight distribution of polymers remaining in concentrated phase. Fractionation (VIII): effect of fraction size. Fractionation (IX):
effect of overall concentration on efficiency. Fractionation (X): shape of molecular weight distribution. fractionation (XI): successive
precipitation fractionation and successive solution fractionation.
Colligative Properties and Virial Coefficients of Polymer
Solutions. Osmotic pressure (I): vapor pressure and osmotic pressure of polymer solution. Osmotic pressure (II): virial expansion.
Osmotic pressure (III). Second virial coefficient (I): internal energy and entropy terms. Second virial coefficient (II): van der
Waals equation. Flory temperature for van der Waals equation. Partition function for semi-grand canonical ensemble (I). Partition function
for semi-grand canonical ensemble (II). N-body distribution function. Osmotic pressure (IV): cluster integrals. Osmotic pressure (V):
relationship for second and third virial coefficients with cluster integrals. Second virial coefficient (III): relationship with pair
segment potential. Second virial coefficient (IV). Second virial coefficient (V): polymer segment with rigid sphere potential. Second
virial coefficient (VI): comparison of Flory lattice theory with imperfect gas theory. Second virial coefficient (VII): mean force potential.
Second virial coefficient (VIII): temperature dependence. Second virial coefficient (IX): ideal solution. Second virial coefficient
(X): rigid sphere solution. Second virial coefficient (XI): molecular weight dependence. Two-body cluster integral. Second virial
coefficient (XII): various polymer solutions. Second virial coefficient (XIII): rod-like molecule. Second virial coefficient (XIV):
chain molecule with n sequential rigid rod segments. Relationship between second virial coefficient and excess chemical potential.
Third virial coefficient of rigid sphere solution. Relationship between second and third virial coefficients.
Statistical Mechanics
and Excluded Volume of Polymer Chains. Probability density distribution for Gaussian chain. Distribution function of end-to-end
distance of random chain (I). Distribution function of end-to-end distance of random chain (II). Elastic force of Gaussian chain (I).
Elastic force of Gaussian chain (II). Mean square end-to-end distance of Gaussian chain. End-to-end distance for chain molecule with
internal rotation (I). End-to-end distance for chain molecule with internal rotation (II). End-to-end distance for chain molecule
with internal rotation (III): Oka's equation. Distribution function of end-to-end distance of polymer chain. Bresler-Frenkel's equation.
Mean square radius of gyration. End-to-end distance of partial chain. Distribution function of separation between segments and the
center of gravity. Excluded volume effect (I). Excluded volume effect (II). Excluded volume effect (III). Increase in free energy
by swelling. α5-law. Segment density at the origin. Mean internal energy. Relationship between α and Z (I). α3-law.
Relationship between α and Z (II). Relationship between α and Z (III). Relationship between α and Z (IV). Relationship
between α and Z (V). Relationship between α and Z (VI): Kurata-Stockmayer-Roig's equation. Relationship between α and Z
(VII). Determination of Flory constant K. Determination of Z. αs and ψ comparison between experiment and theory.
Light Scattering. Rayleigh's equation for scattered light intensity. Total scattered light intensity. Turbidity
(I). Rayleigh ratio. Scattering from large particles. Particle scattering factor. Guinier plot. Determination of the shape of particles
from P(θ) (I). Determination of the shape of particles from P(θ) (II). Determination of the shape of particles from P(θ)
(III). Determination of polarizability α. Scattering from small particles. Scattering from polymer solution. Effect of molecular
weight distribution of polymer chains on P(θ). Zimm plot. Particle scattering factor for polymers with Schulz-Zimm molecular weight
distribution (I). Particle scattering factor for polymers with Schulz-Zimm molecular weight distribution (II). Light scattering arising
from concentration fluctuation. Relationship between concentration fluctuation and chemical potential. Light scattering arising from
copolymer (I). Light scattering arising from copolymer (II). Light scattering arising from optically anisotropic particles (I). Light
scattering arising from optically anisotropic particles (II). Fluctuation theory of light scattering. Turbidity (II). Light scattering
arising from polymer solution with molecular weight distribution. Osmotic pressure of polymer solution with molecular weight distribution.
Light scattering arising from the system polymer in mixed solvent (P2/S1/S0).
Hydrodynamic
Properties. Equation of motion for viscoelastic fluids (I). Stress-strain relationship. Lamé constant. Stress equation.
Equation of motion for viscoelastic fluids (II). Equation of continuity. Navier-Stokes equation and Euler's equation. Reynolds number.
Couette flow. Equation of motion and equation of continuity for slow steady flow (I). Equation of motion and equation of continuity
for slow steady flow (II). Equation of motion and equation of continuity for slow steady flow (III). Oseen tensor. Capillary flow.
Frictional heat and viscosity. Estimation of volume fraction dependence of viscosity coefficient. Two-dimensional steady shear flow
of solution of dumbbell-like molecule (I): diffusion equation. Two-dimensional steady shear flow of solution of dumbbell-like molecule
(II): force and its corresponding moment acting on molecule. Two-dimensional steady shear flow of solution of dumbbell-like molecule
(III): probability density. Two-dimensional steady shear flow of solution of dumbbell-like molecule (IV): viscous dissipation. Limiting
viscosity number of solution of dumbbell-like molecule (I): estimated from heat dissipation. Limiting viscosity number of solution of
dumbbell-like molecule (II): from the ratio of shear stress to shear rate. Definition of solution viscosities. Determination of relative
viscosity by viscometer. Huggins' plot and Kraemer's plot (I). Huggins' plot and Kraemer's plot (II). Empirical functional form of
the concentration dependence of viscosity. Einstein's viscosity equation: rigid sphere model. Molecular weight dependence of [η]
(I): unpenetrable sphere formed by chain polymer or linear polymer forming sphere. Angular velocity of molecular chain in steady flow.
Molecular weight dependence of [η] (II): free draining random coil molecules. Molecular weight dependence of [η] (III): Linear
polymer Gaussian chain with hydrodynamic interaction (Kirkwood-Riseman theory). Flory constant K (I). Flory constant K (II). Viscosity
parameter. Upper limit of the exponent in Mark-Houwink-Sakurada equation. Theoretical relations between two parameters in Mark-Houwink-Sakurada
equation (I). Theoretical relations between two parameters in Mark-Houwink-Sakurada equation (II). Flory-Fox-Schaefgen equation. Flory
constant K (III). Evaluation of parameters in Mark-Houwink-Sakurada equation by Kurata-Yamakawa theory. Molecular weight dependence
of sedimentation coefficient (I). Molecular weight dependence of sedimentation coefficient (II). Molecular weight dependence of diffusion
coefficient (I). Molecular weight dependence of diffusion coefficient (II). Two-dimensional steady shear flow of solution of dumbbell-like
molecule (V).
Molecular Weight and Molecular Weight Distribution. Definition of average molecular weight. Schulz
polymolecularity index. Average degree of polymerization (I). Average degree of polymerization (II). Condensation polymerization (I).
Condensation polymerization (II). Condensation polymerization (III). Condensation polymerization (IV). Molecular weight distribution
function (I). Molecular weight distribution function (II). Average degree of polymerization for Schulz-Zimm distribution. Average
degree of polymerization for the most probable distribution. Average degree of polymerization for Wesslau distribution. Average degree
of polymerization for Lansing-Kraemer distribution. Average degree of polymerization for general log-normal distribution. Average degree
of polymerization for Poisson distribution. Molecular weight distribution for equilibrium condensation polymerization. Molecular weight
distribution for radical polymerization. Viscosity-average molecular weight. Effect of molecular weight distribution on Mark-Houwink-Sakurada
equation (I): Schulz-Zimm type. Effect of molecular weight distribution on Mark-Houwink-Sakurada
equation (II): logarithmic-normal type.
Effect of molecular weight distribution on Mark-Houwink-Sakurada equation (III). Effect of molecular weight distribution on Mark-Houwink-Sakurada
equation (IV). Effect of molecular weight distribution on viscosity parameter Φ. Effect of molecular weight distribution on Flory-Fox
equation. Correction parameter q for viscosity parameter Φ. Effect of molecular weight distribution on parameter qw,z.
qw and qw,z for Schulz-Zimm distribution (I). qw and qw,z for Schulz-Zimm distribution
(II). Sedimentation coefficient and diffusion coefficient for polydisperse polymer solution (I). Sedimentation coefficient and diffusion
coefficient for polydisperse polymer solution (II). Radius of gyration for polymer solution with Schulz-Zimm molecular weight distribution
(I). Radius of gyration for polymer solution with Schulz-Zimm molecular weight distribution (II). Chemical potential of mixing for
polydisperse polymer solution.
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