Ricker Michael, Schilling Rolf
Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 1):011508. doi: 10.1103/PhysRevE.72.011508. Epub 2005 Jul 28.
We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes if the total momentum of two orientational modes is outside the first Brillouin zone, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial due to the crystal's anisotropy, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, and (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have vanishing l,l(') = 0 components, due to the absence of translational motion. The resulting mode coupling equations are solved for hard ellipsoids of revolution on a rigid sc lattice. Using the static orientational correlators from Percus-Yevick theory we find an ideal glass transition generated due to precursors of orientational order which depend on X(0) and psi, the aspect ratio and packing fraction of the ellipsoids. The glass formation of oblate ellipsoids is enhanced compared to that for prolate ones. For oblate ellipsoids with X(0) < or = 0.7 and prolate ellipsoids with X(0) < or = 4, the critical diagonal nonergodicity parameters in reciprocal space exhibit more or less sharp maxima at the zone center with very small values elsewhere, while for prolate ellipsoids with 2 < or = X(0) < or = 2.5 we have maxima at the zone edge. The off-diagonal nonergodicity parameters are not restricted to positive values and show similar behavior. For 0.7 < or = X(0) < or = 2, no glass transition is found because of too small static orientational correlators. In the glass phase, the nonergodicity parameters show a much more pronounced q dependence.
我们推导了分子晶体动力学取向关联函数的微观运动方程。我们的方法基于模式耦合理论。与液体相比，我们发现四个主要差异：（i）如果两个取向模式的总动量在第一布里渊区之外，记忆核包含倒格矢过程；（ii）除了静态双分子取向关联函数外，还需要静态单分子取向密度作为输入，由于晶体的各向异性，后者并非平凡的；（iii）静态取向电流密度关联函数确实对记忆核贡献了一个各向异性的、与惯性无关的部分；（iv）如果假设分子固定在刚性晶格上，由于不存在平移运动，张量取向关联函数和记忆核的(l, l') = 0分量为零。针对刚性简单立方晶格上的硬旋转椭球体求解了所得的模式耦合方程。利用珀西 - 耶维克理论的静态取向关联函数，我们发现由于取向序的前驱体产生了理想的玻璃化转变，这些前驱体取决于(X(0))和(\psi)，即椭球体的纵横比和堆积分数。与长椭球体相比，扁椭球体的玻璃形成得到增强。对于(X(0)\leq0.7)的扁椭球体和(X(0)\leq4)的长椭球体，倒易空间中的临界对角非遍历性参数在区中心或多或少呈现出尖锐的最大值，而在其他地方值非常小，而对于(2\leq X(0)\leq2.5)的长椭球体，我们在区边缘有最大值。非对角非遍历性参数不限于正值，并表现出类似的行为。对于(0.7\leq X(0)\leq2)，由于静态取向关联函数太小，未发现玻璃化转变。在玻璃相中，非遍历性参数表现出更明显的(q)依赖性。
