Strain effects on the microphase separation in interpenetrating polymer networks and cross‐linked polymer mixtures

Abstract

SUMMARY:We study the microphase separation in cross-linked polymer mixtures and interpenetrating polymer networks by taking into account the coupling between the fluctuations of the order parameter and the strain tensor. We predict that thermal fluctuations of the order parameter decrease the compression and shear moduli and that compression of the sample decreases the critical temperature of microphase separation. We also compute the scattering function in the case of shear and uniaxial deformations.The microphase separations in polymer systems such as block copolymers cross-linked polymers 6,7) and interpenetrating polymer networks (IPNs) 8-13) are of current interest in the literature. TWO chemically different, incompatible polymers A and B d o not completely segregate because they are kept together by cross-links, but can segregate on some scale r* -2 x /q*. de Gennes6) proposed a description of the microphase separation based on an electrostatic analogy. According to this idea the appearance of a nonzero value of the order parameter @ ( r ) (charge density) is accompanied by a local polarization P ( r ) representing the elastic forces due to the cross-links. The latter is connected with the charge density as follows divP(r) = -@ ( r )The effective Hamiltonian (in units of KT) is given by H = 1 dd r& with where x is the Flory-Huggins interaction parameter, x, is its critical value at which the phase separation occurs, and e = a2/(24p). de Gennes estimated the elasticity constant c as c = 36/(pnR2), with n being the number of monomer units between two consecutive cross-links, and R2 = nu2 being the mean square distance between two consecutive cross-links. p is the average density of the network. Here we consider the most symmetric case, i. e. parameters such as n and a being the same for both polymers