Santos Andrés
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):040102. doi: 10.1103/PhysRevE.86.040102. Epub 2012 Oct 5.
In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities {ρ(i)} only through the four scaled-particle-theory variables {ξ(α)}, i.e., Φ({ρ(i)})→Φ({ξ(α)}). By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form Φ({ξ(α)})=-ξ(0)ln(1-ξ(3))+Ψ(y)ξ(1)ξ(2)/(1-ξ(3)), where y≡ξ(2)(2)/12πξ(1)(1-ξ(3)) is a scaled variable and Ψ(y) is an arbitrary dimensionless scaling function which can be determined from the free-energy density of the one-component system. Extension to the inhomogeneous case is achieved by standard replacements of the variables {ξ(α)} by the fundamental-measure (scalar, vector, and tensor) weighted densities {n(α)(r)}. Comparison with computer simulations shows the superiority of this bulk free energy over the White Bear one.
在基本度量理论中，硬球流体混合物的体过量自由能密度仅通过四个标度粒子理论变量{ξ(α)}依赖于粒子数密度{ρ(i)}，即Φ({ρ(i)})→Φ({ξ(α)})。通过施加一致性条件，在此证明这种依赖关系必然具有以下形式：Φ({ξ(α)})=-ξ(0)ln(1 - ξ(3)) + Ψ(y)ξ(1)ξ(2)/(1 - ξ(3))，其中y≡ξ(2)(2)/12πξ(1)(1 - ξ(3))是一个标度变量，Ψ(y)是一个任意的无量纲标度函数，可由单组分系统的自由能密度确定。通过将变量{ξ(α)}用基本度量（标量、矢量和张量）加权密度{n(α)(r)}进行标准替换，可实现向非均匀情况的扩展。与计算机模拟的比较表明，这种体自由能优于白熊自由能。
