Swelling of polymers in porous media

Abstract

The swelling of polymers in random matrices is studied using computer simulations and percolation theory. The model system consists of freely jointed hard sphere chains in a matrix of hard spheres fixed in space. The average size of the polymer is a nonmonotonic function of the matrix volume fraction, φm. For low values of φm the polymer size decreases as φm is increased but beyond a certain value of φm the polymer size increases as φm is increased. The qualitative behavior is similar for three different types of matrices. In order to study the relationship between the polymer swelling and pore percolation, we use the Voronoi tessellation and a percolation theory to map the matrix onto an irregular lattice, with bonds being considered connected if a particle can pass directly between the two vertices they connect. The simulations confirm the scaling relation RG ∼ (p- pc) δ0 N, where RG is the radius of gyration, N is the polymer degree of polymerization, p is the number of connected bonds, and pc is the value of p at the percolation threshold, with universal exponents δ0 (≈-0.126±0.005) and v (≈0.6±0.01). The values of the exponents are consistent with predictions of scaling theory. © 2009 American Institute of Physics.