Das Dibyendu, Farrell Greg, Kondev Jané, Chakraborty Bulbul
Indian Institue of Technology Bombay, Powai, India 400076.
J Phys Chem B. 2005 Nov 17;109(45):21413-8. doi: 10.1021/jp051636l.
The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.
玻璃化转变的亚当 - 吉布斯观点将弛豫时间与构型熵联系起来，构型熵在所谓的考兹曼温度下连续趋近于零。我们在具有熵消失相变和随机环动力学的二聚体模型背景下研究这种情况。我们提出了一个用于序参量动力学的粗粒化主方程，该方程用于计算时间相关的自相关函数和相关的弛豫时间。通过结合精确结果、标度论证和主方程的数值对角化，我们发现在相变附近存在非指数弛豫和弛豫时间的沃格尔 - 富尔彻发散。由于在二聚体模型中，熵一直保持有限直到相变点，然后不连续地跃变为零，我们证明了与亚当 - 吉布斯情形的明显偏离。二聚体覆盖是典型受挫系统——三角伊辛反铁磁体的“固有结构”。因此，我们的结果从固有结构动力学的角度为过冷液体中的玻璃化转变提供了一种新的情形。
