Field-theoretical approach to critical microphase behavior of symmetric crosslinked polymer blends

Abstract

Critical properties of symmetric crosslinked binary polymer mixtures is studied using the renormalization-group. It is assumed that chains have a low-molecular-weight, in order to have a wide critical regime where a nonclassical behavior is observed. Use is made of a scalar field model of φ4 type, where the order parameter φ is the local fluctuations in the composition. The parameters of the problem are the temperature t∝χ0−χ, the rigidity constant of the gel C, and the coupling constant u. χ is the Flory interaction parameter, χ0=2/N its critical value if the system is uncrosslinked, and N the degree of polymerization. We first show that the set of demixing critical points is a continuous line, in the two-dimensional half-space of parameters −∞<t<+∞ and 0≤C<+∞, defined by the equation, −t≂C1/φ, where φ is a crossover exponent of values φ≂2.501±0.005 and φ=15/4 (exact) at three and two dimensions, respectively. We establish scaling laws, with respect to the relevant parameters which are the wave vector q, t, and C, for any correlation function, in particular, for the structure factor which is simply the two-point correlation function. We formulate these scaling laws in terms of assertions, which show an analogy with those relative to systems governed by finite size scaling; their typical size L corresponds to the critical fluctuations size ξ*≂C−ν/φ of the crosslinked systems. Some preliminary results found previously are recovered.