DNRF Center "Glass and Time," IMFUFA, Dept. of Sciences, Roskilde University, P. O. Box 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2013 Nov 14;139(18):184506. doi: 10.1063/1.4827090.
We derive exact results for the rate of change of thermodynamic quantities, in particular, the configurational specific heat at constant volume, CV, along configurational adiabats (curves of constant excess entropy Sex). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. The slope of the isomorphs in a double logarithmic representation of the density-temperature phase diagram, γ, can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where γ increases (decreases) with density, the contours of CV have smaller (larger) slope than configurational adiabats. We clarify also the connection between γ and the pair potential. A fluctuation formula for the slope of the CV-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid, and the Girifalco fluid. The sign of dγ∕dρ is thus a third key parameter in characterizing Roskilde liquids, after γ and the virial-potential energy correlation coefficient R. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient, along adiabats and CV-contours, finding it more invariant along adiabats.
我们推导出热力学量变化率的精确结果，特别是等容构型比热 CV 沿着构型绝热线（即过剩熵 Sex 不变的曲线）的变化率。由于沿着这些曲线各种结构和动力学性质具有不变性，因此将其称为所谓的罗西基德液体的同构曲线。在密度-温度相图的双对数表示中，同构曲线的斜率 γ 可以解释为有效逆幂次势指数的三分之一。我们表明，在 γ 随密度增加（减少）的液体中，CV 的轮廓线的斜率小于（大于）构型绝热线的斜率。我们还澄清了 γ 与对势能之间的关系。推导出 CV 轮廓线斜率的涨落公式。理论结果得到了两个系统——伦纳德-琼斯流体和格里菲考尔流体的计算机模拟数据的支持。因此，在表征罗西基德液体方面，除了 γ 和范德瓦尔斯势能相关系数 R 之外，γ 的导数 dγ∕dρ 的符号是第三个关键参数。为了超越同构理论，我们比较了动力学量——自扩散系数——沿着绝热线和 CV 轮廓线的不变性，发现沿着绝热线的不变性更强。
