Sung Bong June, Chang Rakwoo, Yethiraj Arun
Department of Chemistry, Sogang University, Seoul 121-742, Republic of Korea.
J Chem Phys. 2009 Mar 28;130(12):124908. doi: 10.1063/1.3100398.
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, phi(m). For low values of phi(m) the polymer size decreases as phi(m) is increased but beyond a certain value of phi(m) the polymer size increases as phi(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 R(G) approximately (p-p(c))(delta(0))N(nu), where R(G) is the radius of gyration, N is the polymer degree of polymerization, p is the number of connected bonds, and p(c) is the value of p at the percolation threshold, with universal exponents delta(0)(approximately = -0.126+/-0.005) and nu(approximately = 0.6+/-0.01). The values of the exponents are consistent with predictions of scaling theory.
利用计算机模拟和渗流理论研究了聚合物在随机基体中的溶胀情况。模型系统由固定在空间中的硬球基体中的自由连接硬球链组成。聚合物的平均尺寸是基体体积分数φ(m)的非单调函数。对于较低的φ(m)值，聚合物尺寸随φ(m)的增加而减小，但超过一定的φ(m)值后，聚合物尺寸随φ(m)的增加而增大。三种不同类型的基体的定性行为相似。为了研究聚合物溶胀与孔隙渗流之间的关系，我们使用Voronoi镶嵌和渗流理论将基体映射到一个不规则晶格上，如果一个粒子可以直接在两个顶点之间通过，则认为连接这两个顶点的键是连通的。模拟结果证实了标度关系R(G)≈(p - p(c))^(δ(0))N^ν，其中R(G)是回转半径，N是聚合物的聚合度，p是连通键的数量，p(c)是渗流阈值处的p值，普适指数δ(0)≈ -0.126±0.005，ν≈ 0.6±0.01。这些指数的值与标度理论的预测一致。
