发表机构
University of North Alabama; University at Buffalo, The State University of New York（北阿拉巴马大学; 纽约州立大学布法罗分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过分子动力学模拟，系统研究了稠密二元硬球混合物的动力学性质，揭示了扩散和粘度的超阿伦尼乌斯行为及动态异质性，为玻璃态动力学提供了基准数据。
AI 中文摘要
我们对二元硬球流体在宽堆积分数范围（$\phi \approx 0.357-0.582$）内的动力学性质进行了广泛的分子动力学（MD）研究。利用爱因斯坦-赫尔芬德方法的高效实现，计算了自扩散系数 $D$ 和剪切粘度 $\eta$。$D$ 中的有限尺寸效应按 $1/N^\alpha$ 缩放，其中 $\alpha$ 随 $\phi$ 的增加从约 $1/3$ 增至 $3/4$，而 $\eta$ 中的有限尺寸效应除 $\phi \gtrsim 0.554$ 外可忽略不计，在该区域它们按 $1/N$ 缩放。随后将数据外推到热力学极限以获得 $D_{\infty}$ 和 $\eta_{\infty}$。两个系数在稠密状态下均表现出对 $\phi$ 的超阿伦尼乌斯依赖性，并伴随斯托克斯-爱因斯坦关系的失效。尽管 $D_{\infty}(\phi)$ 和 $\eta_{\infty}(\phi)$ 数据均能很好地用指数形式描述，但我们证明这些拟合不能提供临界堆积分数 $\phi_0$ 的可靠估计，因为需要超出可及平衡范围进行大量外推。我们发现通常假设的 $\eta$ 与结构弛豫时间 $\tau_\alpha$ 之间的正比关系在此系统中不成立。对于 $\phi\gtrsim 0.570$，范霍夫自相关函数 $G_s(r, \tau)$ 在中间时间 $\tau$ 表现出空间指数衰减，标志着动态异质性。特征衰减长度按 $\lambda \sim \tau^\nu$ 缩放，其中 $\nu \approx 1/3$，与传统的平方根缩放形成对比。我们还通过四点动态磁化率 $\chi_4(\tau)$ 及其峰值时间 $\tau_4$ 研究了时间异质性。这些发现为玻璃态动力学的计算研究提供了严格的基准MD数据，并为稠密无序系统中理论模型的测试建立了参考。
英文摘要
We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, $ϕ\approx 0.357-0.582$. The self-diffusivity, $D$, and shear viscosity, $η$, are computed using an efficient implementation of the Einstein--Helfand method. The finite-size effects in $D$ scale as $1/N^α$, with $α$ increasing from approximately $1/3$ to $3/4$ with increasing $ϕ$, whereas those in $η$ are negligible except for $ϕ\gtrsim 0.554$, where they scale as $1/N$. The data are then extrapolated to the thermodynamic limit to obtain $D_{\infty}$ and $η_{\infty}$. Both coefficients show a super-Arrhenius dependence on $ϕ$ for dense states, accompanied by a breakdown of the Stokes--Einstein relation. Although both $D_{\infty}(ϕ)$ and $η_{\infty}(ϕ)$ data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, $ϕ_0$, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between $η$ and the structural relaxation time, $τ_α$ , to not hold for this system. For $ϕ\gtrsim 0.570$, the van Hove self-correlation function $G_s(r, τ)$ exhibits a spatial exponential decay at intermediate times, $τ$, signaling dynamic heterogeneity. The characteristic decay length scales as $λ\sim τ^ν$, with $ν\approx 1/3$, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, $χ_4(τ)$, and its peak time, $τ_4$. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.
