Langer J S
Department of Physics, University of California, Santa Barbara, California 93106-9530, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012122. doi: 10.1103/PhysRevE.88.012122. Epub 2013 Jul 17.
Numerical simulations by Tanaka and co-workers indicate that glass-forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.
田中及其同事进行的数值模拟表明，二维和三维中适度多分散的硬核粒子的玻璃形成系统表现出发散的关联长度。这些关联由类伊辛临界指数描述，并与发散的、符合沃格尔-富尔彻-塔曼关系的结构弛豫时间相关。对热化硬盘的相关模拟表明，不同多分散性下压力与填充率的曲线呈现出一系列转变点，从单分散情况下的液-六方相转变开始，随着多分散性增加，转变为类似玻璃态的、类伊辛临界点。我提议通过假设玻璃形成流体包含双重简并的、局部有序的粒子团簇来解释这些观察结果，这类似于为解释其他玻璃态现象而引入的双态系统。本文首先对热化硬核粒子的热力学进行简要的统计推导。然后讨论如何在该框架内，用少量统计相关的内部状态变量来描述一个双态、类伊辛模型。所得理论与模拟数据精确吻合。我还为观察到的类伊辛关联长度与沃格尔-富尔彻-塔曼公式之间的关系提出了一种理论依据。
