Inhomogeneous polymer solutions: Theory of the interfacial free energy and the composition profile near the consolute point

Abstract

The Flory–Huggins formulation of the combinatorial entropy, supplemented with residual free energy, is applied locally to obtain the interfacial free energy and the concentration profile of polymer in the interface between two demixed polymer solution phases. Two choices were investigated for the residual free energy: a “regular solution” formulation and an empirical formulation of Koningsveld for polystyrene in cyclohexane. Asymptotic, analytical solutions of the equations near the critical solution point and solutions obtained by numerical calculations are given as a function of temperature for several molecular weights. At temperatures farther below the critical temperature the equations have no solutions. The reason for this is not entirely clear. The local formulation of the free energy used here is an improved version of a previous one, which gave wrong results for asymmetric systems (polymer in a low molecular weight solvent). This newer version is consistent with our theory of critical opalescence and gives a relation between the interface “thickness” and the correlation range of the concentration fluctuations. The calculated correlation ranges were in good accord with those found experimentally by Debye, Chu, and Woerman. That the newer version of our equations for an interface gives no acceptable solutions at lower temperatures could be caused by a “collapse” of a diffuse to a sharp interface as suggested by Nose.

Thermodynamic Modeling of Polymer Solution Interface

“…This shows very close agreement with the experimental relationship of Equation (17). [23] Equation (30) is a theoretically-based power law relationship that incorporates the molecular weight N dependence of the interfacial tension g, is in excellent agreement with the experimentally-based relationship [Equation (17)], and is able to accurately predict interfacial tension from equilibrium data, f a , and f b .…”

Study of the surface tension of polymer solutions: theory and experiments in theta solvent conditions

“…Recently, new theoretical studies [1][2][3][4][5][6][7][8][9][10] on these interfacial properties, in particular for the behaviour of polymer at liquid interfaces or free surfaces (melt or solution) have been developed and have raised new interest for experimental measurements.…”

Phase separation in polymer solutions near the critical point

“…and evaluating the momentum integrals in this expression, S R may be written in terms of the reference configuration integral (12) Thus far the discussion has been perfectly general, and no approximation has been made other than to absorb the effects of the solvent into the potential of mean force H. To proceed further, the reference system H R and the perturbation H' must be specified. Since phase separation in polymer solutions is generally understood from both experiment 4 and theory24 to take place close to the theta point, the statistics of the chains are expected to reflect the existence of excluded volume effects that are qualitatively similar to those in the theta domain.…”