Free-energy model of ferroelectric transition in P(VDF-TrFE) copolymer

We develop a physics-based analytical model for the ferroelectric-to-paraelectric phase transition in poly(vinylidene difluoride-co-trifluoroethylene) [P(VDF-TrFE)] copolymers. The low-temperature ferroelectric phase is an orthorhombic crystal analogous to the poly(vinylidene difluoride) β-phase, while the high-temperature paraelectric phase is a conformationally disordered (condis) crystal. The model for a single crystal consists of two coupled components. The first is an Ising-type model that calculates crystal polarization as a function of temperature and electric field by treating a polymer chain as a sequence of coupled dipoles in a molecular field, self-consistently induced by other chains. The key model parameter, the energy of a gauche dihedral, is a strong function of the transverse lattice parameter (the interchain spacing). The second component determines the optimal lattice parameter by minimizing the crystal free energy, which balances interchain potential energy against chain conformational entropy. All single-crystal parameters are calibrated against molecular dynamics simulations of a quasi-infinite P(VDF-TrFE) crystal. To model real semicrystalline polymers, the single-crystal model is extended by introducing a Gaussian distribution of phase transition temperatures T_{c} across crystallites. The distribution parameters are calibrated against literature experimental data for the remanent polarization of P(VDF-TrFE). This extended model calculates hysteresis loops and predicts their strong temperature dependence. At T