Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA.
Phys Rev E. 2018 May;97(5-1):052114. doi: 10.1103/PhysRevE.97.052114.
In this paper, the virial series expansion and constant pressure Monte Carlo method are used to study the longitudinal pressure equation of state for hard spheres in narrow cylindrical pores. We invoke dimensional reduction and map the model into an effective one-dimensional fluid model with interacting internal degrees of freedom. The one-dimensional model is extensive. The Euler relation holds, and longitudinal pressure can be probed with the standard virial series expansion method. Virial coefficients B_{2} and B_{3} were obtained analytically, and numerical quadrature was used for B_{4}. A range of narrow pore widths (2R_{p}), R_{p}<(sqrt[3]+2)/4=0.9330... (in units of the hard sphere diameter) was used, corresponding to fluids in the important single-file formations. We have also computed the virial pressure series coefficients B_{2}^{'}, B_{3}^{'}, and B_{4}^{'} to compare a truncated virial pressure series equation of state with accurate constant pressure Monte Carlo data. We find very good agreement for a wide range of pressures for narrow pores. These results contribute toward increasing the rather limited understanding of virial coefficients and the equation of state of hard sphere fluids in narrow cylindrical pores.
在本文中，我们使用维里级数展开和恒压蒙特卡罗方法研究了硬球在窄圆柱形孔中的纵向压力状态方程。我们利用降维方法将模型映射到具有相互作用内部自由度的有效一维流体模型中。该一维模型是扩展性的，欧拉关系成立，并且可以使用标准的维里级数展开方法来探测纵向压力。我们通过解析方法得到了第二维里系数 B_{2}和第三维里系数 B_{3}，并使用数值积分方法计算了第四维里系数 B_{4}。我们使用了一系列窄孔宽度（2R_{p}），R_{p}<(sqrt[3]+2)/4=0.9330...（以硬球直径为单位），对应于重要的单分子链形成的流体。我们还计算了维里压力级数系数 B_{2}^{'}, B_{3}^{'}, 和 B_{4}^{'}，以比较截断的维里压力级数状态方程与准确的恒压蒙特卡罗数据。我们发现，对于窄孔的宽压力范围，两者非常吻合。这些结果有助于增加对硬球流体在窄圆柱形孔中的维里系数和状态方程的理解。
