Diffusion and Chemical Potential in Polymer Solutions (original) (raw)

Diffusion in polymeric systems–A review on free volume theory

Progress in Organic Coatings, 2017

This review paper deals the history and development of various theories to predict the diffusion in polymeric systems. The basis and application of various theories with the prediction capabilities are discussed. The most commonly used theory is Vrentas and Duda free volume theory with excellent agreement with experimental data report so far. This theory predicts the data very accurately in rubbery region. However, few modifications have come up in this theory to predict the diffusion above the glass transition with a little success. Relation between Fujita −Kishimoto theory [15] and Vrentas and Duda Theory [11,12] is

Diffusion in polymer-polymer mixtures

Journal of Polymer Science Part B: Polymer Physics, 1987

Two equations have recently been proposed to relate the mutual diffusion coefficient of a binary polymer-polymer mixture to the two tracer (self) diffusion

Diffusion coefficient in polymer solutions

Journal of Applied Polymer Science, 1979

Molecular diffusivity of a solute in a solvent may be determined by measuring the extent of dispersion of solute in solvent flowing in a straight circular tube under the conditions of laminar flow. This simple and rapid method for determination of molecular diffusivity in aquous polymer solutions is discussed. Experimental results show a substantial reduction in the solute diffusivity with increase in polymer concentration.

Rate type equations for the diffusion in polymers: Thermodynamic constraints

AIChE Journal, 1993

ABSTRACT Conditions imposed by the second law of thermodynamics on viscoelastic rate type constitutive equations for the diffusive mass flux are considered. The analysis of three different rate type models proposed in the literature points out that presently physically unrealistic predictions are possible in desorption processes. The thermodynamic analysis of such models, based on the entropy inequality and on the stability requirement of the equilibrium states, leads to precise relationships among relaxation times, diffusion coefficients, and entropy equations of state. In particular, the analysis shows that relaxation times and diffusion coefficients cannot be simply constant numbers. When the thermodynamic constraints imposed on the constitutive equations are introduced, the models do not show physically unrealistic behaviors any more; Fickian diffusion close to the pure penetrant or pure polymer regions is also recovered. Finally, it is shown that the stability requirement for the equilibrium states may introduce very rigid requirements for the model feasibility, well beyond what appears explicitly from the kinetic equations alone.

Thermodynamics of polymer solutions as functions of pressure and temperature

Journal of Colloid and Interface Science, 1972

The construction of a light scattering photometer for use at different temperatures and pressures up to 1000 atm permits measurement of the chemical potential and the second osmotic virial coefficient for high polymer solutions. From this one can determine entropy, enthalpy, and volume changes of solvent on dilution. Measurement of the scattered intensity at several wavelengths (the scattering angle being held constant) gives the dimensions of the dissolved molecules. The above-mentioned quantities are determined for polystyrene and polyisobutylene in different solvents as functions of pressure, temperature and molecular weight. The total number of experiments shows the following results: 1. The enthalpies of dilution are shifted in the same direction with increasing pressure. All endothermal systems become more endothermal with increasing pressure and all exothermal ones become less exothermal. Both for endothermal and exothermal pseudoideal systems the appropriate ~ temperatures (A2 = 0) increase with growing pressure. 2. Calculation of volume changes of solvent on dilution (by measuring the pressure dependence of light scattering) shows that these volume changes are positive for endothermal systems and negative for athermal and exothermal ones. A theoretical treatment is made on the basis of the excluded volume theory and the principle of corresponding states.

On the Pace–Datyner theory of diffusion of small molecules through polymers

Journal of Polymer Science Part B: Polymer Physics, 1989

The Pace-Datyner theory for diffusion of penetrant molecules in polymers has been analyzed. I t has been found that the correct solution of the problem they pose is possible only at 0 K, since then the separation of two chains at x = m is equal to the minimum of the DiBenedetto potential for their interaction. Otherwise the energy of symmetrical separation is infinite. By using the linearization method to solve the differential equation, Pace and Datyner neglected the problem of unnatural boundary conditions at x = 00 for temperatures above 0 K. The exact numerical solutions of differential equations at temperature 0 K were therefore compared with the results of the Pace-Datyner linear approximation. For temperatures different from 0 K the solution of the problem is possible only when the proper cutoff is imposed. The analytical expression for the coefficients in the DiBenedetto potential has been found, and the potential can be written as

Dependence of the solvent diffusion coefficient on concentration in polymer solutions

Macromolecules, 1993

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Diffusion phenomena in ternary systems polymer-nonsolvent-solvent

Journal of Solution Chemistry, 1993

Diffusion in a boundary between a polymer + solvent solution and nonsolvent was treated by accounting for the presence of the four diffusion coefficients that describe the isothermal transport process in a three component system. Diffusion equations were integrated assuming a concentration dependence of diffusion coefficients that account for the thermodynamic conditions on the cross diffusion terms of Eq. (1). The presence of non-zero cross terms promotes an incongruent diffusion of polymer whose concentration increases at the boundary between the polymer + solvent solution and the non-solvent. Although our model describes diffusion in the range of homogeneous solution, this incongruent polymer diffusion is a process similar to that promoted by the solvent evaporation from the polymer + soIvent film that some authors suggested as an intermediate step before the film immersion into the coagulation bath to obtain good asymmetric membranes. KEY WORDS: Diffusion; polymer solutions.

Statistical Thermodynamics of Polymer Solutions

Macromolecules, 1978

The lattice fluid theory of solutions is used to calculate heats and volumes of mixing, lower critical solution temperatures, and the enthalpic and entropic components of the chemical potential. Results of these calculations are compared with literature data on several polyisobutylene solutions. In most instances the agreement with experiment is favorable and comparable to that obtained with the Flory equation of state theory. Several insights into polymer solution behavior are obtained and include: (1) differences in equation of state properties of the pure components make an unfavorable entropic contribution to the chemical potential that becomes large and dominant as the gas-liquid critical temperature of the solvent is approached; (2) limited miscibility of nonpolar polymer solutions at low and high temperatures is a manifestation of a polymer solution's small combinatorial entropy; and (3) negative heats of mixing in nonpolar polymer solutions are caused by the solvent's tendency to contract when polymer is added. Suggestions on how the theory can be improved are made Freeman and Rowlinson' in 1960 observed that several hydrocarbon polymers dissolved in hydrocarbon solvents phase separated at high temperatures. These nonpolar polymer solutions exhibited what are known as lower critical solution temperatures (LCST), a critical point phenomenon that is relatively rare among low molecular weight solutions. Soon after the discovery of the universality of LCST behavior in polymer solutions, Flory and c o -~o r k e r s~-~ developed a new theory of solutions which incorporated the "equation of state" properties of the pure components. This new theory of solutions, hereafter referred to as the Flory theory, demonstrated that mixture thermodynamic properties depend on the thermodynamic properties of the pure components and that LCST behavior is related to the dissimilarity of the equation of state of properties of polymer and solvent. P a t t e r~o d -~ has also shown that LCST behavior is associated with differences in polymer/solvent properties by using the general corresponding states theory of Prigogine and collaborators.1° Classical polymer solution theory, i.e., Flory-Huggins theory," which ignores the equation of state properties of the pure components, completely fails to describe the LCST behavior.