Department of Chemistry, University of Saskatchewan, Saskatoon, SK, S7H 0H1, Canada.
Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran.
Soft Matter. 2023 Feb 15;19(7):1373-1383. doi: 10.1039/d2sm01636b.
Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a statistical mechanics for granular materials that has focused on establishing an equivalent to the microcanonical ensemble and a temperature-like thermodynamic variable. Here, we expand on these ideas by introducing a granular potential into the Edwards ensemble, as an analogue to the chemical potential, and explore its properties using a simple model of a granular system. A simple kinetic Monte Carlo simulation of the model shows the effect of mass transport leading to equilibrium and how this is connected to the redistribution of volume in the system. An exact analytical treatment of the model shows that the compactivity and the ratio of the granular potential to the compactivity determine the equilibrium between two open systems that are able to exchange volume and particles, and that mass moves from high to low values of this ratio. Analysis of the granular potential shows that adding a particle to the system increases the entropy at high compactivity, but decreases the entropy at low compactivity. Finally, we demonstrate the use of a small system thermodynamics method for the measurement of granular potential differences.
颗粒物质，如沙子或谷物，表现出许多与分子系统中观察到的相似的结构和动力学特性，尽管温度对其性质没有影响。这导致了开发一种用于颗粒物质的统计力学的努力，该力学集中于建立类似于微正则系综和温度样热力学变量的等效物。在这里，我们通过在爱德华兹系综中引入颗粒势能来扩展这些想法，作为化学势的类似物，并使用颗粒系统的简单模型来探索其性质。对模型的简单动力学蒙特卡罗模拟显示了质量传输导致平衡的影响，以及这如何与系统中体积的再分配相关联。对模型的精确分析处理表明，压缩性和颗粒势能与压缩性的比值决定了能够交换体积和颗粒的两个开放系统之间的平衡，并且质量从这个比值的高值向低值移动。对颗粒势能的分析表明，向系统中添加一个颗粒会在高压缩性下增加熵，但在低压缩性下会降低熵。最后，我们展示了使用小系统热力学方法测量颗粒势能差的方法。
