Division of Molecular and Materials Simulation, State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China.
J Chem Phys. 2012 Mar 28;136(12):124704. doi: 10.1063/1.3698197.
To study nucleation phenomena in an open system, a constrained lattice density functional theory (LDFT) method has been developed before to identify the unstable directions of grand potential functional and to stabilize nuclei by imposing a suitable constraint. In this work, we answer several questions about the method on a fundamental level, and give a firmer basis for the constrained LDFT method. First, we demonstrate that the nucleus structure and free energy barrier from a volume constraint method are equivalent to those from a surface constraint method. Then, we show that for the critical nucleus, the constrained LDFT method in fact produces a bias-free solution for both the nucleus structure and nucleation barrier. Finally, we give a physical interpretation of the Lagrange multiplier in the constraint method, which provides the generalized force to stabilize a nucleus in an open system. The Lagrange multiplier is found to consist of two parts: part I of the constraint produces an effective pressure, and part II imposes a constraint to counteract the supersaturation.
为了研究开放体系中的成核现象，我们之前开发了一种受限格子密度泛函理论（LDFT）方法，通过施加适当的约束来确定自由能泛函的不稳定方向，并稳定核。在这项工作中，我们从根本上回答了关于该方法的几个问题，并为受限 LDFT 方法提供了更坚实的基础。首先，我们证明了体积约束方法和表面约束方法得到的核结构和自由能势垒是等效的。然后，我们表明对于临界核，受限 LDFT 方法实际上为核结构和成核势垒都提供了无偏差的解。最后，我们给出了约束方法中拉格朗日乘子的物理解释，它为开放体系中稳定核提供了广义力。发现拉格朗日乘子由两部分组成：约束的第一部分产生有效压力，第二部分施加约束以抵消过饱和度。
