Fluctuation effects on the coexistence curve for binary polymer-solvent systems

2014 The phase equilibrium in polymer-solvent systems has been described in terms of the Landau-Ginzburg-Wilson model. The scaling law for the coexistence curve which has been derived in the present article is in good agreement with the experimental data. The prediction of the present theory that the scaling region narrows with increasing degree of polymerization, is consistent with the experimental data. J. Physique 48 (1987) 2037-2039 DTCEMBRE 1987, Classification Physics Abstracts 05.20 64.70 61.40K Recent experimental studies [1-4] showed that the Flory-Huggins theory fails in describing the coexistence curves for binary polymer-solvent systems. Sanchez [1] found the following scaling law for the coexistence curve where N is the degree of polymerization of polymer chains, (D is the polymer volume fraction along the coexistence curve, Wc is the critical polymer volume fraction. T = (T2013Tc)/Tc, where T is the temperature and Tc is the critical temperature. The critical exponent {3 has been measured to be 0.327. In contrast to (1), the mean field Flory-Huggins theory predicts the following equation for the coexistence curve The experimental value of (3 for polymer segregation is the same as that for the segregation in binary liquids or for the Ising model. On that account one can expect that the critical exponent {3 = 0.327 in (1) has to be attributed to the fluctuations of the order parameter. It is well-known that the fluctuation effects in the vicinity of the critical point are described by using the LandauGinzburg-Wilson (LGW) model. In combination with the renormalization group method the latter is the basis of the modern theory of critical phenomena. One may assume that the N exponent of (1) is also affected by the fluctuations of the order parameter. Recently, Muthukumar [5] made an attempt to attribute the N exponent of (1) to the three-body interactions between the polymer segments. In the present article we propose the theory of segregation taking into account the fluctuations of the order parameter. The main idea of our approach consists in the following. Starting with the Flory-Huggins theory we reformulate the latter in the vicinity of the critical point in terms of the Landau theory of phase transitions. After that, in usual manner, we go from the Landau theory to the Landau-Ginzburg-Wilson model. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198700480120203700