论文标题
Smoluchowski合奏：聚合的统计力学
The Smoluchowski Ensemble: Statistical Mechanics of Aggregation
论文作者
论文摘要
我们提出了对不可逆二进制聚集的严格热力学处理。我们将Smoluchowski集成构建为一组离散的有限分布，该集合在固定数字合并事件时从所有单体的相同初始状态产生，并在此集合上定义了概率度量，以使平均场近似值中的平均分布受Smoluchowski方程的控制。在缩放限制中，该合奏产生了一组完全类似于熟悉统计热力学的关系。热力学处理的中心元素是选择功能，这是可行分布的功能，该功能将分布的概率与聚合模型的特定细节联系起来。我们获得了常规内核的缩放表达式，并为常数，总和和产品内核的特殊情况提供了封闭形式的结果。我们研究了最可能的分布的稳定性，为溶胶 - 凝胶转变提供了标准，并通过简单的热力学参数获得了凝胶后区域的分布。
We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions generated from the same initial state of all monomers upon fixed number merging events and define a probability measure on this ensemble such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships completely analogous to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the specific details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.
