[论文解读] Large temperature-up-jump simulations of a binary Lennard-Jones system

Aude Amari, Lorenzo Costigliola+1 more|arXiv (Cornell University)|Jan 25, 2026

Material Dynamics and Properties被引用 0

一句话总结

论文使用模拟量化 Tool-Narayanaswamy 物质时间 aging 描述在对二元 Kob–Andersen 型 Lennard-Jones 液体的大温度跃升下的适用性，以评估时间相关函数是否在物质时间差上坍塌。

ABSTRACT

This paper presents simulations of the physical aging of a binary Kob-Andersen-type Lennard-Jones liquid following large temperature up-jumps from equilibrated states of high relaxation time. The purpose is to investigate how well the Tool-Narayanaswamy (TN) material-time concept works for this rather extreme case of aging. First the triangular relation of the potential energy is studied. This is found to be well obeyed, making it possible to define a potential-energy-based material time $ξ$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37, monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility $χ_4$, and the non-Gaussian parameter $α_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference $ξ_2-ξ_1$. This is found to work better for the $0.43 o 0.48$ temperature jump than for the $0.37 o 0.48$ jump, however. Our findings thus confirm the general understanding that the TN aging formalism works best for systems that are never very far from equilibrium. This raises two questions for future work: Is the collapse significantly improved if each aging quantity is allowed its own material time? Can better collapse be obtained if the material-time is generalized to be locally defined (in order to reflect dynamic heterogeneity)?

研究动机与目标

• 评估是否可以用来自势能的单一物质时间线性化在大温度跃升后的 aging。
• 评估势能自相关在 aging 过程中 CK 三角关系的成立情况。
• 测试多种时间自相关函数（五种可观测量）在物质时间差上坍塌。
• 比较小跃升与大跃升至最终温度时的 aging 行为，并评估 TN aging 描述的极限。

提出的方法

• 使用二元 Lennard-Jones 混合物（80% A，20% B），采用移位力截断并用 GPU 优化代码 RUMD 进行模拟。
• 通过势能自相关定义物质时间 xi(t)，使得 Cuu(t1,t2)=phi_eq(xi(t2)-xi(t1))。
• 通过在温度跃升后遍历数百万个时间三元组，验证 CK 三角关系 C13=F_A(C12,C23) 的成立性。
• 在 aging 过程中监测五个量：Cuu、Fs、<Delta r^2>、chi4 和 alpha2，在从 T=0.43 和 T=0.37 跃升至 T=0.48 的情景下。
• 当以 xi2−xi1 而非 t2−t1 作图时，评估这些观测量的坍塌情况。
• 比较小跃升与大跃升的结果。

Figure 1 : Physical aging. (a) Schematic drawing of a temperature up jump starting and ending in thermal equilibrium (with time on the x-axis). Even though not all quantities relax in identical manner, the standard TN aging formalism operates with a single “global” clock controlling all relaxations

实验结果

研究问题

• RQ1 来自势能的单一 TN 物质时间是否充分描述了对 Kob–Andersen 型 LJ 液体在大温度跃升后的 aging？
• RQ2 在跃升后的 aging 过程中，势能自相关的 CK 三角关系保持程度如何？
• RQ3 多种动力学观测量是否能坍塌到物质时间差的通用函数，坍塌是否依赖跃升大小？
• RQ4 在跃升较大时，是否需要本地化或多物质时间来描述 aging？

主要发现

• 势能自相关遵循良好的三角关系，从而可基于势能得到物质时间。
• 在使用共同的物质时间时，小跃升（0.43→0.48）的 aging 观测量坍塌更好，而大跃升（0.37→0.48）的坍塌较差。
• 对于较小跃升，Cuu 与 Fs 显示强烈坍塌；MSD、chi4 与 alpha2 显示较弱但部分坍塌。
• 对于较大跃升，五个观测量都未能展示出单一物质时间的令人信服坍塌，表明单时钟 TN aging 有局限性。
• 物质时间在长期接近最终温度的平衡时趋于与实时时间成正比；短时段存在偏离。
• 作者建议要么每个观测量有其自身的物质时间，要么在存在动力学异质性时需要局部物质时间。

Figure 2 : Parametric representation of the triangular relation, Eq. ( 2 ). (a) Illustration of the sampling of time triplets used to calculate correlation “triangles”. The values on the time axis illustrate the logarithmic increase in time intervals within a single simulation block. (b) Illustratio