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The most basic assumption of the classical nucleation theory (CNT) is to treat nucleus/liquid surface energy, r, as a macroscopic property having a value equal to that of a planar interface, r I . Therefore, when the CNT is used to analyze experimental data, the size dependence of surface energy is often neglected. To date, there has been no reliable method to measure the surface energy of the nucleus/liquid interface except by ®tting nucleation rate data to the theory. In this case, one obtains the surface energy of critical size nuclei as a function of temperature. However, the ®tted r(T) dependence arises from two di erent factors: the temperature dependence of r for a planar interface and its size dependence. This paper focuses on the temperature dependence of the macroscopic value of surface energy, decoupling it from the size dependent part. TolmanÕs equation was used to eliminate the size dependence of surface energy from published nucleation data for two stoichiometric silicate glasses (Li 2 O á 2SiO 2 and Na 2 O á 2CaO á 3SiO 2 ). It is shown that the Tolman parameter may be chosen so that surface tension decreases with temperature; dr I adT`0. The value of dr I adT obtained in this way is close to theoretical predictions. Ó

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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.

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