Pressure dependence of the Flory-Huggins interaction parameter in binary polymer blends investigated by SANS

The pressure dependence of the Flory Huggins interaction parameter of two binary polymer blends was investigated by small angle neutron scattering (SANS). We studied the polymer blends deutero PoIystyrene / Polyvinylmethylether (d PS / PVME) and deutero Polystyrene / Polyphenylmethylsiloxane (d PS / PPMS), exhibiting decomposition at high and at low temperatures, respectiveIy. In both cases the enthalpic contribution of the Flory Huggins parameter is not affected by pressure in the investigated pressure range between 1 and 1200bars, whereas the absolute value of the entropic contribution is generally a decreasing function of pressure. 1 Theoretical Concepts Polymer blends follow the predictions of the mean field theory, except in the vicinity of the critical point, where, ruled by the Landau Ginzburg criterion, a crossover to 3d Ising critical behaviour occurs [I] [5]. In the mean field concept the Gibbs free enthalpy of mixing AGM is given by [6] Here @, VA7 VB, R, and x represent the volume fraction of component A, the molecular volumes of the two components, the gas constant, and the Flory Huggins interaction parameter, respectively. x is a purely segmental quantity 161, which depends on the temperature T, the volume fraction a, and on the external pressure p. In a small angle neutron scattering experiment the reciprocal structure factor, extrapolated to Q = 0 is given by If we combine eqs. (1) and (2) we yield Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993803 18 JOURNAL DE PHYSIQUE IV 1 with , = ( + ) r is the so called generalized Flory Huggins parameter, which is related to x by 1 a2 r = (@(I @)x) 2 aQ2 (4) r depends on the same external parameters as x and can be written as with rh and r,, the respective enthalpy and entropy of mixing. r, is a segmental entropy of mixing correlated to the free volume of the blend [7]. By equation of state arguments Patterson et al. [8] showed that pressure does not affect rh, but diminishes the absolute value of r,, because the free volume gets reduced at increasing pressure. However, recent lattice cluster calculations by Dudowicz et al. [9] have shown a very weak pressure dependence of rh.