The respective data are seldom available, and for temperatures above the glass transition temperature data are not available, in principle. 10 By this reason, it is of interest to express the pressure dependence of the viscosity by more accessible thermodynamic coefficients, which refer exclusively to the liquid in the actual state considered, avoiding in this way, in addition, some inconsistency inherent in approaches like those followed in Refs. 10 and 15 see also Sec. VI .
Alternative theoretical approaches connect the decrease of viscosity with structural changes of the respective systems under pressure coordination changes, Is-O bond weakening, changes of degree of popularization, changes of CNN distribution, formation of fivefold and scaffold coordinated Is species, etc. , which are not described appropriately by free volume concepts. 9-11,14,17-21 For these complex systems, a decrease of the viscosity with pressure is observed as a rule, at least, for sufficiently high Gap pressures.
In this way, one has to check, first, whether a decrease of viscosity with increasing pressure s, indeed, in contradiction with free volume theories without favoring any particular viscosity theory and, second, how to incorporate such additional structural effects generally into the theory independently of the particular mechanism of structural change considered. By above mentioned reasons, and in order to arrive at some solution to the referred controversy on the effects of pressure on viscosity, it is highly interesting to revisit this problem in order to develop a comprehensive picture of this phenomenon.
The realization of this task is the aim of the present contribution. The paper is organized as follows. In Sec. II, we derive an equation determining the pressure dependence of viscosity of multiplication liquids of constant composition in stable or metastases equilibrium states for the case that free volume variations determine the behavior. This relation connects the kind of response of viscosity on pressure increase or decrease of viscosity with increasing pressure with the sign of the thermal expansion coefficient of the liquid.
It describes, at least, in a qualitatively correct way the pressure dependence of the viscosity of most liquids at moderate pressures. One exception, the pressure dependence of viscosity of water at moderate erasures, is analyzed in detail in Sec. Ill. In order to cover also this and similar cases, the basic equation is generalized in order to account for additional structural changes of the system with respect to pressure variations and their effect on viscosity. As a first step, this equation is extended in Sec.
IV in order to describe the pressure dependence of the viscosity for systems in “frozen-in” thermodynamic nonequivalence states undercooked liquids below the glass transition temperature, I. E. , glasses . In Sec. V, this approach is further generalized giving the possibility to account for the effect of pressure pressure. As it turns out such mechanisms determine basically the pressure dependence of the viscosity of a variety of glassblowing liquids, in particular, at high pressures CB. , also Ref. 22 . A summary of the basic conclusions and discussion of the results sec.