Wilson D Scott, Lee Lloyd L
School of Chemical, Biological, and Materials Engineering, University of Oklahoma, Norman, Oklahoma 73072, USA.
J Chem Phys. 2005 Jul 22;123(4):044512. doi: 10.1063/1.1961399.
We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.
给定系统温度，我们研究了 Lennard-Jones 型分子二元混合物的气液相行为，其中一种组分为超临界状态。我们将自洽方法应用于 Ornstein-Zernike 积分方程以获得相关函数。一致性检验不仅包括热力学一致性（压力一致性和 Gibbs-Duhem 一致性），还包括逐点一致性，例如关于空穴函数的零间距定理。通过包含可调参数的封闭项中的桥函数来强制实现这些一致性。完整的解不仅需要单体化学势的值，还需要零间距定理中存在的二聚体化学势的值。这些通过直接化学势公式[L. L. Lee, J. Chem. Phys. 97, 8606 (1992)]进行评估，该公式不需要温度或密度积分。为了评估积分方程的准确性，在研究状态的同时进行了分子动力学模拟。积分方程结果与模拟数据比较良好。在相计算中，保持压力一致性和有效的化学势很重要，因为相边界的匹配需要液相和气相的压力和化学势相等。所研究的混合物是甲烷型和戊烷型分子，均由有效的 Lennard-Jones 势表征。对一条等温线的计算表明，与 Sage 和 Lacey 的实验数据相比，积分方程方法给出了有效的答案。为了研究气液相行为，有必要使用一致的理论；任何不一致性，特别是压力方面的不一致，都会破坏相边界计算。
