Stillinger Frank H, Debenedetti Pablo G
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
J Phys Chem B. 2005 Apr 14;109(14):6604-9. doi: 10.1021/jp0456584.
By performing an elementary transformation, the conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) has been reformulated to emphasize how initial particle momentum biases final mean displacement. Using collective flow variables, an analogous expression has been derived for 1/eta(T,rho), the inverse of shear viscosity. The Stokes-Einstein relation for liquids declares that D and T/eta should have a fixed ratio as T and rho vary, but experiment reveals substantial violations for deeply supercooled liquids. Upon analyzing the self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins, one possible mechanism for this violation emerges. This stems from the fact that interbasin transitions become increasingly Markovian as T declines, and though self-diffusion is possible in a purely Markovian regime, shear viscosity in the present formulation intrinsically relies on successive correlated transitions.
通过进行一次初等变换，重新推导了依赖于温度和密度的自扩散常数(D(T,\rho))的传统速度自相关函数表达式，以强调初始粒子动量如何影响最终平均位移。利用集体流变量，推导出了剪切粘度倒数(1/\eta(T,\rho))的类似表达式。液体的斯托克斯 - 爱因斯坦关系表明，随着(T)和(\rho)的变化，(D)与(T/\eta)应具有固定比值，但实验表明深度过冷液体存在显著偏差。在根据构型空间固有结构及其盆地之间的动力学转变来分析自扩散和粘性流动过程时，出现了这种偏差的一种可能机制。这源于随着(T)下降，盆地间转变越来越具有马尔可夫性，并且尽管在纯马尔可夫区域中自扩散是可能的，但在当前公式中剪切粘度本质上依赖于连续的相关转变。
