Prediction of discontinuous change of volume, entropy, and heat capacity at melting transition in crystalline polymers based on the Landau theory

The discontinuous changes of volume ΔVm, entropy ΔSm and heat capacity at constant pressure ΔCP, m at the melting point have been predicted by the Landau theory of phase transition where the Gibbs free energy Φ in order state is expressed by Φ = Φ0 + Aη2 − Cη4 + Eη6, where η is an order parameter. In this work, A is given by a function that A = k0(T − T0)m(P0 − P)n, where k0, m, n, T0, and P0 are constants. The order parameter ηmin for the minimum of Φmin is related to the volume of solid Vs and is expressed by:CA*2ηmin4−38CA*3ηmin6=1−ΔVΔVmwhere ΔV = Vs − Vm, s, ΔVm = Vm, l − Vm, s and A* is the value of A at the melting point. The volume of Vs changes from Vm, s to Vm, l, where ΔVm, s and ΔVm, l are volumes of solid and liquid phases at the melting point, respectively. The discontinuous change of thermal pressure coefficient γv = (∂P/∂T)V, thermal expansion (∂V/∂T)P and compressibility −(∂V/∂P)T at the melting point has been calculated. A typical function of Φ for a polymer has been demonstrated as a function of η and C at the melting transition.