聚合物在分形基底上的吸附：数值研究
Polymer adsorption on a fractal substrate: numerical study
摘要：
本文研究了柔性高分子在具有临界吸引中心浓度p_c的二维规则无序晶格形成的逾渗团簇上的吸附。逾渗团的分形维数d_s^{p_c}=91/49。接枝到这样的分形基板的聚合物链的构象性质的研究通过修剪丰富的Rosenbluth方法（PERM）。我们发现估计的表面交叉指数控制的缩放的吸附能在附近的转变点，S_s^{p_c}=0.425 \pm 0.009，和吸附转变温度，T_A^{p_c}=2.64 \pm 0.02。正如预期的那样，当基底的分形维数小于普通欧几里得表面的分形维数时，吸附减少。分析了在吸附状态下获得高分子链的典型空间构象的普遍尺寸和形状特征。
英文摘要：
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a fractal dimension d_s^{p_c}=91/49. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method (PERM). We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of the transition point, ϕ_s^{p_c}=0.425\pm0.009, and for the adsorption transition temperature, T_A^{p_c}=2.64\pm0.02. As expected, the adsorption is diminished when the fractal dimension of the substrate is smaller than that of a plain Euclidean surface. The universal size and shape characteristics of a typical spatial conformation which attains a polymer chain in the adsorbed state are analyzed as well.
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