分子晶体无序动力学与无序相变的微观理论
摘要
我们推导了分子晶体dynamical orientational correlators的运动方程。该方法基于模式耦合理论。与液体相比，我们发现主要有四个差异：(i)记忆核包含Umklapp过程；(ii)除了静态的两分子orientational correlators外，还需要作为输入的静态单个分子orientational density，后者是非平凡的；(iii)静态orientational current density correlator贡献了一个各向异性的、与惯性无关的记忆核部分；(iv)如果假设分子固定在刚性晶格上，张量形式的orientational correlators和记忆核将具有消失的l,l'=0分量。求解得到的模式耦合方程用于刚性sc晶格上形状互为倒数的硬椭球体。采用Percus-Yevick理论中的静态orientational correlators，我们发现由于取决于X和p——椭球体的长宽比和密度比例的取向有序前驱物质而产生理想无序相变。对于椭圆盘状（oblate）椭球体的无序形成程度高于椭圆柱状（prolate）椭球体。对于X\lesssim0.7的椭圆盘状椭球体和X\lesssim4的椭圆柱状椭球体，临界非平衡参数在倒数空间中在区心附近表现为较尖锐的峰值，而此处值很小；对于2\lesssim X\lesssim2.5的椭圆柱状椭球体，我们在区边处发现峰值。非对角线非平衡参数取值不局限于正值，显示出类似的行为。对于0.7\lesssim X\lesssim2，未发现无序相变。在无序相中，非平衡参数表现出明显的q依赖性。
引用
@article{arxiv.cond-mat/0411759,
title = {Microscopic theory of glassy dynamics and glass transition for molecular crystals},
author = {Michael Ricker and Rolf Schilling},
journal= {arXiv preprint arXiv:cond-mat/0411759},
year = {2009}
}
备注
17 pages, 12 figures, accepted at Phys. Rev. E. v4 is almost identical to the final paper version. It includes, compared to former versions v2/v3, no new physical content, but only some corrected formulas in the appendices and corrected typos in text. In comparison to version v1, in v2-v4 some new results have been included and text has been changed