粘度の自由容積理論について

概要

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The Doolittle free volume equation η=A exp(B_<v_0/v_&fnaf;>), (1) which was first proposed for the viscosity of n-alkanes, is widely accepted as the viscosity equation for various kinds of liquids and polymeric substances. However, Bueche modified it according to a normal coordinate computation for the thermal motion of a simple array of molecules connected by Hookian spring, and derived the following equation η=A exp{(B_(v_0/v_&fnaf;)^2}. (2) The purpose of the present study is to clarify the theoretical background for the free volume representation of the liquid viscosity from the view-point of the thermal fluctuation theory. The probability that the thermal fluctuations of energy and volume will amount to ΔE and ΔV respectively in a small, but macroscopic system which is a part of a large macroscopic system, is denoted by prob. (ΔE,ΔV). By a simple thermodynamic computation, it is given by [numerical formula]. (3) in which C_υ and C_p are the specific heats at constant volume and constant pressure respectively, α the thermal expansion coefficient, and k_T the isothermal compressibility. Then, the probability that the volume fluctuation is larger than a certain critical value ΔV^* and energy fluctuation is [numerical formula], (4) where γ is the ratio of the specific heat.
社団法人日本材料学会の論文
1965-04-15