Semi-empirical equation on temperature dependence of heat capacity for polymers and simple liquids

Abstract

The semi-empirical equation for heat capacity at constant volume C v is proposed from the standpoint of the homogeneous function approach and applied to polymers (polystyrene and poly(methyl methacrylate) over the temperature range 0.1–4.0 K, polyethylene over 1–400 K and poly(metrafluoroethylene) over 1–360 K) and simple liquids (argon, methane, n-heptane, carbon tetrachloride and benzene) from the triple point to the gas-liquid critical point T c, using data published by many authors. The equation derived in this work is C v=c 1( Y d 0 T ) exp(−c 0 −1I d 0 where I d 0 is defined by I d 0 = ∫ Y 0 Y Y d 0 (1+Y)dY ,Y= (T c−T) T and c 1, c 0, Y 0 ≈ 0 and d 0 are constants. For simple liquids, C v is expressed by C v=c 1( Y d 0 T ) exp{ −c 0 −1Y d 0+1 (d 0+1) } under the condition Y ⪡1.0, and the value of d 0 estimated from the experimental data is −0.10, which suggests that C v ∝( T c − T) −0.10 near T c. The equation for C v for polymers is expressed by C v=c 1 ∗T a 0 and the value of a 0 obtained in this work is ≈3.0 over 1–4 K, while a 0 ≈ 1.0 over 30–400 K and 0.1–0.4 K. It is found in this work that the heat capacity function C v = AT + BT 3 observed in amorphous polymers below 4 K can be predicted by the semi-empirical equation for C v. Deviations of C v from the Debye model in the extremely low temperature region are discussed, based on the experimental and theoretical work of many authors.