## 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, φ_{m}. For low values of φ_{m} the polymer size decreases as φ_{m} is increased but beyond a certain value of φ_{m} the polymer size increases as φ_{m} 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.

Original language | English |
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Article number | 124908 |

Journal | Journal of Chemical Physics |

Volume | 130 |

Issue number | 12 |

DOIs | |

State | Published - 2009 |