Mean-field-theory for polymers in mixed solvents. Thermodynamic and structural properties

Abstract

SUMMARY: Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymersolvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein-Zernike series expansion.

Contraction and Reswelling of a Polymer Chain Near the Critical Point of a Binary Liquid Mixture

“…At temperatures sufficiently close to T c , however, when the correlation length greatly exceeds the radius of gyration (R g ), the polymer coil will be completely immersed in the better solvent, causing the chain to reexpand. Their scaling arguments were later confirmed by various theoretical calculations and simulations [8][9][10][11][12][13].…”

Dynamic relaxations of polymers in mixed solvents

“…Instead, it is much more convenient to turn to collective coordinates or particle density variables. One is related to the polymer concentration fluctuations Using the standard procedure [19] , we find the following result for the Edwards Hamiltonian…”

“…Only, if Áv T 0, the criticality condition applies to all the terms of the structure matrix as indicated in Eq. (11), (18) and (19). This is the situation of interest here.…”

“…The critical parameter decreases upon addition of a small amount of polymer indicating compatibility enhancement. This result was already reported in reference [19] . ii) The more concentrated regime where 0 Â N S 1av gives 1 H c 1 c À Áv 2 a2v.…”

“…The partial structure factors at q 0 are obtained by a straightforward calculation using Eq. (11) to (19). Likewise, the kinetic coefficient v is simplified noting that the function f x in Eq.…”