Gebremichael Yeshitila, Vogel Michael, Bergroth Magnus N J, Starr Francis W, Glotzer Sharon C
Departments of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
J Phys Chem B. 2005 Aug 11;109(31):15068-79. doi: 10.1021/jp0512412.
We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.
我们对单组分玻璃形成液体进行了分子动力学模拟，并使用固有结构形式来检验亚当 - 吉布斯（AG）理论的预测，并探索这些预测与空间非均匀动力学之间的可能联系。我们计算了平衡液体平均势能的温度依赖性，结果表明在低温T下它遵循罗森菲尔德 - 塔拉佐纳T(3/5)定律，而平均固有结构能量在低温下与温度成反比，这与势能极小值的高斯分布一致。我们通过平均盆地振动频率研究了构型空间中局部极小值周围盆地的形状，结果表明冷却时盆地会略微变宽。我们评估了构型熵S(conf)，它是系统采样的势能极小值多重性的一种度量，并检验了S(conf)与整体动力学之间AG关系的有效性。我们通过分析相对于特征整体弛豫时间在短和中等时间尺度上可移动的粒子的运动来量化动态非均匀运动。这些可移动粒子在一维“弦”中移动，并且这些弦形成具有明确平均簇尺寸的簇。AG方法预测分子协同重排区域（CRR）的最小尺寸与S(conf)成反比，并且最近（《物理评论快报》2003年，90卷，085506期）已经表明可移动粒子簇与亚当和吉布斯所设想的CRR一致。我们检验了可移动粒子弦而非簇可能描述亚当 - 吉布斯方法的CRR的可能性。我们发现这些弦也与S(conf)遵循几乎反比关系。我们进一步表明，弦和簇最大时的时间的对数，出现在中间散射函数的后期β弛豫区域，与1/TS(conf)遵循线性关系，这与AG关于构型熵与液体经历向新构型转变特征时间之间关系的预测一致。由于弦是簇的基本元素，我们提出弦是导致构型转变的CRR最小尺寸的更合适度量。簇尺寸也与S(conf)成反比这一事实可能是因为簇由弦组成。
