Langer J S, Mukhopadhyay Swagatam
Department of Physics, University of California, Santa Barbara, California 93106-9530, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 1):061505. doi: 10.1103/PhysRevE.77.061505. Epub 2008 Jun 6.
We propose a model of a heterogeneous glass-forming liquid and compute the low-temperature behavior of a tagged molecule moving within it. This model exhibits stretched-exponential decay of the wave-number-dependent, self-intermediate scattering function in the limit of long times. At temperatures close to the glass transition, where the heterogeneities are much larger in extent than the molecular spacing, the time dependence of the scattering function crosses over from stretched-exponential decay with an index b=1/2 at large wave numbers to normal, diffusive behavior with b=1 at small wave numbers. There is a clear separation between early-stage, cage-breaking beta relaxation and late-stage alpha relaxation. The spatial representation of the scattering function exhibits an anomalously broad exponential (non-Gaussian) tail for sufficiently large values of the molecular displacement at all finite times.
我们提出了一种非均匀玻璃形成液体的模型，并计算了在其中移动的标记分子的低温行为。该模型在长时间极限下，表现出波数依赖的自中间散射函数的拉伸指数衰减。在接近玻璃化转变温度时，非均匀性的范围比分子间距大得多，散射函数的时间依赖性从大波数下指数b = 1/2的拉伸指数衰减转变为小波数下b = 1的正常扩散行为。早期的笼破裂β弛豫和晚期的α弛豫之间有明显的区分。在所有有限时间内，对于足够大的分子位移值，散射函数的空间表示呈现出异常宽的指数（非高斯）尾部。
