He Journal of Chemical Physics 122, 074511 2005

Topics: Thermodynamics, Temperature, Viscosity Pages: 32 (8292 words) Published: June 20, 2013
THE JOURNAL OF CHEMICAL PHYSICS 122, 074511 2005

Pressure dependence of viscosity
Jürn W. P. Schmelzer
Institut für Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany and Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos, UFSCar, 13565-905 São Carlos, Sao Paulo, Brazil

Edgar D. Zanotto
Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos, UFSCar, 13565-905 São Carlos, Sao Paulo, Brazil

Vladimir M. Fokin
Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos, UFSCar, 13565-905 São Carlos, Sao Paulo, Brazil and S. I. Vavilov State Optical Institute, Uliza Babushkina 36-1, 193171 St. Petersburg, Russia

Received 3 August 2004; accepted 1 December 2004; published online 11 February 2005 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 ° 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 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. © 2005 American Institute of Physics. DOI: 10.1063/1.1851510 I. INTRODUCTION

While the temperature dependence of viscosity at isobaric conditions is well established the viscosity increases with decreasing temperature , current discussion on the dependence of viscosity on external pressure at isothermal conditions shows a spectrum of controversial statements. For example, in Refs. 1–5 it is concluded that the viscosity must increase, as a rule, with increasing pressure and this expectation has been confirmed in a variety of experimental studies.1–5 In contrast, the opposite was experimentally found for some glass-forming silicate liquids, such as basalt, dacite, jadeite, and albite6–13 and mentioned as a principal possibility taking as an example the behavior of water also in Ref. 2. In these cases, a decrease of the viscosity of about one...
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