Theory of the Viscosity of Liquids as a Function of Temperature and Pressure

Abstract

An equation for the viscosity of a liquid in terms of the energy of vaporization and the molal volume is developed from the reaction rate theory of viscosity due to Eyring. The degree of freedom corresponding to flow is assumed to be a translational one, and the energy of activation for the elementary flow process is assumed to be some fraction, 1/n, of the energy of vaporization. On applying this equation to a large number of normal liquids it is found that molecules possessing spherical symmetry have n = 3, while nonspherical molecules have n greater than 3, usually about 4. It is shown that the ratio $${\mathrm{\Delta E}}_{\mathrm{vap}}{\mathrm{/\Delta E}}_{\mathrm{vis}}\mathrm{,\hspace{0.17em}\hspace{0.17em}}\mathrm{where}{\mathrm{\hspace{0.17em}\hspace{0.17em}\Delta E}}_{\mathrm{vis}}\mathrm{=R(d}\ln \text{η)/(d(1/T)),}$$ can be taken as an index of the size and shape of the molecule, or more precisely, of the unit of flow in the liquid. The activation energy for flow in liquid metals is a very small fraction of the energy of vaporization, ranging from 1/10 to 1/25, leading to the conclusion that the metal ions flow without their valence electrons. Viscosity data confirm the S₈ ring structure for sulfur below 160° and lead to the conclusion that above 250° sulfur probably consists of long chains containing as a rough average about 36 sulfur atoms. In the long chain hydrocarbons the activated configuration for flow is probably a curled up molecule. The structure activation energy of flow in associated liquids due to the hydrogen bond structure is discussed, and viscosity data are used to compute the degree of coordination in liquid water. At high pressures the energy of vaporization in the equation must be replaced by V(pinternal+pexternal). This yields an equation for computing either the internal pressure of a liquid or the viscosity under pressure, if either is known. Using Bridgman's viscosity data, values of the internal pressures of some liquids are calculated from this equation which agree with internal pressures calculated from compressibility data.