Schmelzer Jürn W P, Zanotto Edgar D, Fokin Vladimir M
Institut für Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany.
J Chem Phys. 2005 Feb 15;122(7):074511. doi: 10.1063/1.1851510.
We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.
我们重新分析了等温条件下组成恒定的液体的粘度与压力的关系。仅基于关于粘度与“自由体积”之间关系的非常一般的考虑，我们表明，在中等压力值下，通常情况下，只要液体处于稳定或亚稳（过冷）平衡状态，粘度会随着压力的增加而增加。然而，即使粘度的行为受自由体积效应支配，当液体的热膨胀系数为负时，也可能出现与正压力依赖性的偏差。我们推导了一个方程，该方程允许人们定量确定粘度的压力依赖性，在最简单的情况下，仅需要知道恒压下粘度的温度依赖性、热膨胀系数和液体的等温压缩率。例如，水在0 - 4摄氏度范围内以及几种硅酸盐液体，如钠长石、硬玉、英安岩、玄武岩等的负压力依赖性就可以这样解释。其他玻璃形成液体最初（对于中等压力）表现出粘度的正压力依赖性，当受到高（约吉帕）等静压时会变为负压力依赖性。对吉帕压力下的水和已提及的硅酸盐熔体的详细分析表明，除了自由体积效应外，在各种情况下可能还必须考虑其他压力诱导的结构转变。因此，理论分析得到扩展：（i）以描述处于冻结热力学非平衡状态（玻璃，即低于玻璃转变温度Tg的过冷液体）的系统的粘度压力依赖性；（ii）扩展到除自由体积变化外，还经历其他结构参数的压力诱导变化的系统。在这种情况下，原则上即使热膨胀系数为正，粘度也可能随着压力的增加而降低。通过这种方式，本分析提供了一个估计粘度压力依赖性的通用工具，并有望解决当前文献中的争议。
