SEMIEMPIRICAL EQUATION OF STATE FOR POLYMERS AND SIMPLE LIQUIDS .2. TEMPERATURE AND VOLUME DEPENDENCE OF THERMAL PRESSURE COEFFICIENT

The temperature and volume dependence of the thermal pressure coefficient gamma-v have been examined using experimental data on gamma-v for simple liquids argon and water based on the equation of state derived in a previous work. The expression for gamma-v is given by gamma approximately v is given by gamma approximately v V approximately [{(T(c) - T)/T}-delta-0 + C0]X-beta-0 exp(alpha-0-1I0) where gamma approximately v = gamma-v - gamma-v,c, T(c) is the critical temperature and I0 is defined by I0 = integral-v(c)v X-beta-0/V dV where X = (V(c) - V)/V and V(c) is the critical volume. The heat capacity at constant volume C(v) is given by C(v) approximately C(v)(T) - [{(T(c) - T)/T}-delta-0-1/T] x alpha-0 exp(alpha-0-1I0) where C(v)(T) is a function of of temperature. Values of alpha-0,beta-0,delta-0 and C0 are constants. The equation of state for simple liquids is expressed using Y = (T(c) - T)/T by P approximately = (X-beta-0/V)[{T(Y-delta-0 + C0)- integral-0Y Y-delta-0-1/(1 + Y)dY} exp(alpha-0-1I0)-D0 exp(alpha-0-1I0)] where D0 is a constant. The temperature dependence of gamma-v at constant volume for polymers is examined based on the experimental data by Simha and is given by gamma-v approximately T(k)0-1 and KBAR0 is -0.24 for polystyrene and poly(n-butyl methacrylate) and 2.8 for polymethyl methacrylate. The equation of state for a polymer is derived by the same procedure as for a simple liquid and is given by P = C'2(T)(Z-tau-0/V)T exp(alpha-0-1I(z, tau-0) - C'1(T) (Z-lambda-0/V) exp(alpha'-0-1I(z,lambda-0)) where Z = (V - V0)/V,I(z,x0 = integral-0V Z(x0)/V dV, C'i(T) is a function of temperature, tau-0, lambda-0, alpha'-0 are constants and V0 is a constant volume at 0 K. The expression for gamma-v is given by gamma' approximately v(V) approximately Z-tau-1 where tau-1 is a constant. The values of tau-1 determined by the experimental data are -1.89 for polystyrene, -1.64 for polyisobutylene and -2.67 for polydimethyl siloxane. An essential difference between polymers and simple liquids is discussed in terms of the functional form of the equation of state. A characteristic feature of the volume dependence of entropy and internal energy is discussed through the experimental data on gamma-v over a wide range of temperature and pressure.