Patchy粒子聚集的统计力学研究

Statistical Properties on the Aggregation of Patchy Particles

应用统计力学原理对AaBb型Patchy粒子的聚集过程进行研究,考察了典型平均物理量在聚集过程中的变化情况.首先基于配分函数导出体系的平衡自由能及描述Patchy粒子之间联接作用的质量作用定律,进而获得团簇的数量分布函数.进一步给出Patchy团簇的数均和重均聚合度以及物理凝胶化条件,探讨了凝胶化区域与Patchy粒子数之间的依赖关系.同时给出Patchy团簇生长的微分动力学方程,并进行了相应的Monte Carlo模拟.本文旨在揭示Patchy粒子的内在和外在因素对体系聚集态结构的影响,为实现对Patchy粒子体系的有效调控提供理论依据.

The aggregation of patchy particle with distinct patchy was investigated by the statistical mechanical method, in which the change in some average physical quantities with degree of association was of the particular interest. Specifically, the equilibrium free energy and laws of mass action describing the two types of associations were derived by the constructed partition function, and then the size distribution of patchy clusters was obtained. Based on these results, the number- and weight-average degrees of association, the gelation condition as well as the dependence of pre-gel and post-gel regimes on the patchy number were discussed. Furthermore, the kinetic differential equation for description of the growth of patchy clusters was proposed and used to perform the Monte Carlo simulation. The consistence between simulation and analytical results demonstrate the validity of the kinetic differential equation. An aim is attempted to correlate thermodynamic and dynamic conditions with the degrees of association, and thereby provide possible clue for regulating the aggregated and phase structures of patchy particles.