逆向统计力学与新颖材料的非“试错法”理论设计

In this project, there are five main research contents, and they are described briefly below. (i) Designing an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to target many-particle configurations with desirable novel properties. (ii) Further adjusting the optimized potential to be sure that the single-phase region of the target structure is as large as possible, and this is very important for experimental realization and practical applications of the target structures.(iii) To guide experimental realization of the target structures, we will find appropriate soft matter systems and range of relevant state parameters, wherein the “synthesized” effective two-body potential, after superimposed with three-body interaction, can form a good approximation to the optimized and adjusted potential. (iv) To accomplish the goal (ii), we will construct global phase diagram for the optimized potentials, and for this we will propose new solid perturbation theory, which is applicable to calculations of various lattice free energy. (v) To accomplish the goal (iii), we will propose a theoretical scheme, by which the soft matter system interacting through an effective two-body potential superimposed with the three-body interaction has structures and thermodynamic behaviors similar to the same system considering both two- and three-body effective potentials. Methodological significance of the present project includes: (i) the inverse statistical-mechanical methodology innovates upon the traditional materials design method in that it is essentially systematic and deductive rather than on a basis of trial and error; (ii) the inverse statistical-mechanical methodology extends the traditional idea of self-assembly in that the targeted many-particle configuration may possess varying degrees of disorder such as crystalline, quasi-crystalline, or amorphous;(iii) the proposed theoretical scheme serving to superimpose the three-body interaction on the two-body potential enables one to easily investigate the three-body effects on the soft matter system structures and thermodynamic properties in the traditional liquid state theory framework.considering only two-body potential.

项目主要内容有五个方面。1，提出一套逆向统计力学方法学，最优化可自发形成新颖特性材料的成对加和势。2，进一步微调优化势以确保目标结构稳定区域在全局相图中尽可能大，这对目标结构的实验实现与应用很关键。3，通过理论计算选定合适的软物质体系及状态参数，使叠加有三体作用的有效二体相互作用势与优化势尽可能一致，以指导目标结构的实验实现。4，为了实现目标2，绘制出优化势全局相图；为此，提出适用于任何点阵热力学摄动理论。5，为了实现目标3，提出一套方案，使二体与三体势体系等价于叠加有三体作用的二体势体系。项目的方法学意义有三：逆向统计力学革新了传统的材料设计方法，因为其本质上是推导性的而非基于试错法；扩展了传统的自组装概念，因为目标结构可有不同的无序度（晶体、准晶、无定形）；被提出的理论方案通过将三体作用叠加在二体势之上，使得可以在传统的只考虑二体势的液体理论框架中处理三体作用对体系热力学与结构的影响。

长期以来，有关自组装的理论工作主要集中在从具有给定相互作用的基本结构单元出发，预测这些基本结构单元在较大的长度尺度上的功能结构，这属于统计力学的正向问题；这就使得长期以来，关于自组装问题的设计工作都是基于所谓的“试错法”。从给定宏观体系的特定行为，比如多粒子构象信息，推导出相应的粒子之间的相互作用势，这是逆向统计力学所要研究的基本内容。逆向统计力学的一个重要应用就是自组装的理论设计。可以用来发现、并优化可自发形成目标结构（晶体、准晶、或无定形结构）的势函数。从而不仅扩展传统的自组装概念只限于周期性结构的含义，而且超越传统的材料设计中的“试错法”，以达到节省人力、物力、以及更精准的控制、并有助于发现新的自组装结构的宏伟目标。. 逆向统计力学用于自组装研究涉及到多个方面，本项目系统深入地研究了其中的两个方面：（i）通过理论计算选定合适的软物质体系及状态参数，使叠加有三体作用的有效二体相互作用势与优化势尽可能一致，从而为实验上“合成”优化势提供理论指导、大大减小实验成本，也为实现目标结构提供实验体系。为此，我们编制了静电体系的二维、三维经典 DFT 代码、并计算了胶粒表面电荷成点状分布、条形分布、胶粒表面整体中性但正负电荷分离、考虑了溶剂分子颗粒性的两体、三体有效静电相互作用，在此基础上进行理论分析，获得了有效静电相互作用的机理性认识。（ii）绘制出优化势全局相图。为此，研究了CPSE对能自发形成非常规结构的球形对称势函数如diamond势、wurtzit e势、Lennard–Jones–Gauss 势的可靠性。研究了Padé 近似在高阶高温级数展开热力学摄动理论方面的可行性。提出了计算浸润温度的理论方法，可以适用于任意情形浸润温度的计算，并比传统的零接触角方法与预浸润外推方法优越。为优化势全局相图的绘制提供了相边界信息。