A molecular Density Functional Theory for associating fluids in 3D geometries - J. Chem. Phys. (2023)

A new free-energy functional is proposed for inhomogeneous associating fluids. The general formulation of Wertheim's thermodynamic perturbation theory is considered as the starting point of the derivation. We apply the hypotheses of the statistical associating fluid theory in the classical density functional theory (DFT) framework to obtain a tractable expression of the free-energy functional for inhomogeneous associating fluids. Specific weighted functions are introduced in our framework to describe association interactions for a fluid under confinement. These weighted functions have a mathematical structure similar to the weighted densities of the fundamental-measure theory (\textit{i.e.}, they can be expressed as convolution products), such that they can be efficiently evaluated with Fourier transforms in a 3D space. The resulting free-energy functional can be employed to determine the microscopic structure of inhomogeneous associating fluids of arbitrary 3D geometry. The new model is first compared with Monte Carlo simulations and previous versions of DFT for a planar hard wall system in order to check its consistency in a 1D case. As an example of application in a 3D configuration, we investigate then the extreme confinement of an associating hard-sphere fluid inside an anisotropic open cavity with a shape that mimics a simplified model of zeolite. Both the density distribution and the corresponding molecular bonding profile are given, revealing complementary information to understand the structure of the associating fluid inside the cavity network. The impact of the degree of association on the preferential positions of the molecules inside the cavity is investigated as well as the competition between association and steric effect on adsorption.本文针对非均匀缔合流体提出了一种新的自由能泛函。推导以韦尔特海姆（Wertheim）热力学微扰理论的通用形式为出发点。我们将统计缔合流体理论（statistical associating fluid theory）的假设引入经典密度泛函理论（DFT）框架中，从而得到适用于非均匀缔合流体的简洁可控的自由能泛函表达式。我们在该框架中引入特定加权函数，用以描述受限流体的缔合相互作用。这些加权函数的数学结构与基本度量理论（fundamental-measure theory）的加权密度类似（即可表示为卷积积），因此可通过三维空间中的傅里叶变换实现高效求值。所得自由能泛函可用于求解任意三维几何构型下非均匀缔合流体的微观结构。首先，我们将该新模型与蒙特卡洛（Monte Carlo）模拟结果以及经典DFT的现有版本进行对比，以验证其在一维平面硬壁体系中的一致性。作为三维构型下的应用示例，我们研究了缔合硬球流体在模拟简化沸石模型的各向异性开放空腔内的极端受限行为。文中给出了密度分布与对应的分子键合轮廓，二者可互补以揭示空腔网络内缔合流体的微观结构。本文同时研究了缔合程度对空腔内分子优先吸附位置的影响，以及缔合作用与空间位阻效应对吸附过程的竞争机制。