分子动力学模拟中玻璃transition temperature的不确定度及其唯一确定的数值算法
The uncertainty of glass transition temperature in molecular dynamics simulations and numerical algorithm for its unique determination
摘要：
当冷却速率$v$小于特定的材料依赖性阈值时，玻璃化转变温度$T_g$在一定程度上变成几乎与冷却速率无关的“材料参数”。测定$T_g$的常用方法是将液态的粘度$ν$在比冻结条件高不远的温度下外推到液体冻结且粘度几乎不可测量的较低温度。通常认为，当粘度下降$13\leq n\leq17$数量级时，发生玻璃化转变。$T_g$的精度取决于外推质量。我们在这里提出了一个算法的唯一确定$T_g$。这个想法是明确地外推$ν(T)$到低温，而不依赖于特定的模型。它可以使用$ν(T)$ -函数的数值分析延拓从$T_g$以上（其中它是可测量的）到$T\gtrsim T_g$来完成。对于数值解析延拓，我们使用Pade逼近方法。
英文摘要：
When the cooling rate $v$ is smaller than a certain material-dependent threshold, the glass transition temperature $T_g$ becomes to a certain degree the "material parameter" being nearly independent on the cooling rate. The common method to determine $T_g$ is to extrapolate viscosity $ν$ of the liquid state at temperatures not far above the freezing conditions to lower temperatures where liquid freezes and viscosity is hardly measurable. It is generally accepted that the glass transition occurs when viscosity drops by $13\leq n\leq17$ orders of magnitude. The accuracy of $T_g$ depends on the extrapolation quality. We propose here an algorithm for a unique determining of $T_g$. The idea is to unambiguously extrapolate $ν(T)$ to low temperatures without relying upon a specific model. It can be done using the numerical analytical continuation of $ν(T)$-function from above $T_g$ where it is measurable, to $T\gtrsim T_g$. For numerical analytical continuation, we use the Pade approximant method.
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