Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
J Chem Phys. 2013 Jan 7;138(1):014502. doi: 10.1063/1.4771976.
The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.
威克斯（Weeks）及其同事们所发展的局域分子场理论（LMF）在处理各种非均匀液体的结构和热力学方面已被证明是成功的。通过将 LMF 重新表述为单体质点直接关联函数，我们将该理论重新构建到经典密度泛函理论（DFT）的框架中。我们表明，有效参考势φ（R）（r）的一般 LMF 方程直接源自于对吸引力原子间力的标准平均场 DFT 处理。通过对非均匀硬球参考流体进行精确（基本度量）DFT 处理，我们确定了硬心 Yukawa 液体在平面硬壁上吸附时的 φ（R）（r）。在接近液体-气体共存的方法中，我们发现有效势表现出丰富的结构，其中包括在远离壁面的较大距离处的阻尼振荡，以及在壁面附近产生完整干燥的低密度“气体”层所需的排斥驼峰。我们认为，很难从 LMF 的其他（非 DFT 为基础）实现中获得相同的细节。LMF 强调了将完整系统的原子间对势智能地划分为参考部分和可以用平均场近似处理的剩余部分的重要性。我们研究了一个完全可解的一维模型的不同划分，其中对势具有硬心和线性吸引尾部。均匀流体的结构因子和状态方程的结果表明，在参考系统中包含相当一部分吸引力可以比用平均场近似处理整个吸引力尾部更准确。我们进一步讨论了 LMF 和 DFT 之间的关系。
