Semiempirical equation of state and the Grüneisen parameter for polymers and rare gas solids

Abstract

The temperature dependence of the specific volume for polyethylene (PE) and poly(cyclopentyl methacrylate) (PC5MA) over 100–300 K for PE and 10–140 K for PC5MA, and for the rare gas solids argon (Ar), krypton (Kr) and xenon (Xe) over 4–83 K for Ar, 4–115 K for Kr and 5–150 K for Xe has been studied. Also, the pressure dependence of the specific volume for PE and poly(methyl methacrylate) (PMMA) over the pressure range up to 30 kbar for PE and 2 kbar for PMMA and for rare gas solids up to 30 kbar at low temperatures (4–150 K) has been studied. The temperature and pressure dependences have been examined using an equation derived by the homogeneous function method. The relationship for the temperature dependence used in this work is given by 1 n T = A 1Z n1 T⩾1 and that for the pressure dependence by V 0 V = B 1(T)(P+P L(T)) m1 where A 1, n 1 and m 1 are constants, B 1(T) and P L( T) are functions of temperature, V 0 is the volume at atmospheric pressure and Z is defined by Z = V − V(0) V where V(0) is V at 0 K. Values of n 1 for polymers and rare gas solids are in the range of 0.099–0.17 with n ̄ 1 = 0.13 , while m 1 values are in the range of 0.14–0.25 with m ̄ 1 = 0.17 for the rare gas solids and 0.07–0.14 with m ̄ 1 = 0.099 for polymers. The Grüneisen parameter γ G defined by Slater is calculated from the equation of state in this work; γ G = 4.89 for polymers and 2.78 for rare gas solids. The difference in γ G for the rare gas solids and polymers is explained by taking into account the volume dependence of the heat capacity.