Second- and third-order dielectric constant ε2 and ε3 of three copolymers of vinylidene fluoride and trifluoroethylene were measured over a temperature range from 20 °C to higher than the ferroelectric-to-paraelectric phase transition temperature Tc . The thermodynamical theory predicts that ε2 is negative below Tc  and vanishes at Tc , whereas, for the second-order transition, ε3 is positive below Tc but turns to negative at Tc and, for the first-order transition, ε3 does not change its sign below and above Tc . According to this criterion, it is concluded that the transition is of the second order for a copolymer with vinylidene fluoride fraction of 52 mole %, but of the first order for 65 and 73 mole % copolymers. This conclusion can explain the difference in slope of ε2 versus remanent polarization among the copolymers.

Phase separation temperatures of the ternary system polystyrene (PS) (Mw = 1.67 × 104)/poly(α‐methyl styrene) (PαMS) (Mw = 9.0 × 104)/cyclopentane with a blend ratio PS/PαMS = 55/45 have been determined over the polymer concentration range 0.02 ≤ ψPS + PαMS ≤ 0.52, where ψ PS + PαMS is the segment fraction of polymer in ternary system. Phase separation temperatures for the upper critical separation in the ternary system decrease with increasing ψ PS + PαMS over the range 0.1 ≤ ψ PS + PαMS ≤ 0.52. The vapor—liquid equilibrium in this system with a blend ratio PS/PαMS=50/50 has been determined over the concentration range 0.925 ≤ ψPS + PαMS < 0.995 and the temperature range 60–100°C by the piezoelectric vapor sorption method. The polymer—polymer interaction parameters χ′12 determined are positive except at 100°C and increase with increasing ψ PS + PαMS. Values of χ′12 extrapolated to zero solvent concentration are positive (0.0–1.3) over the temperature range measured. Phase separation behavior is discussed in terms of phase separation temperature in a ternary system and the polymer–polymer interaction parameter.

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A thermodynamic model of nanocomposites is developed taking into account local and collective interactions of the solid nanoparticles with polymer as well as the structure of interfacial layer. The local interactions was characterized by the change of the chemical potential of macromolecules on the solid surface (ΔG ) according to Gibbs-Thomson equation. The collective interactions were calculated using the free energy change upon the addition of a second component to the system (ΔG d ). The equations are derived to calculate change in the thermodynamic parameters of the system as a function of the interfacial energy, solid particle size and supermolecular structure of polymer. Calculated values are in agreement with the experimental data on the dependencies of physicomechanical and electrophysical characteristics of polymer composites on the specific area and surface properties of solid particles. I. IntroductionThe first attempt of a composite system modeling in order to account for the properties of the existing polymeric composites and synthesize novel materials with predetermined performance was made by Barg [1]. The model took into consideration formation of adsorbed layer on the solid particle surface in polymer solutions and polymers composites. This concept was further developed by Yu.S. Lipatov [2] regarding the change of polymer composite properties due to structural transformations of the polymer on the solid surface. The study of the effect of the polymer nature and adhesion to various fibers upon the mechanical properties of polymers filled with glass and carbon fillers (mechanics of reinforced plastics) did not involve the role of the interphase layer. The modern models of composites include the simulation of three components: solid, polymer and interphase layer (IPL). However these data do not provide any quantitative correlations to account for the composite mechanical performance, thermo-and electro conductivity, chemical stability and other properties. Polymer composites, especially nano-composites, are often featured with near-equilibrium states. Thermodynamic models are applicable to simulate such systems and evaluate mechanical and electro-physical properties. Moreover, in this case the addition of even small amounts of finedispersed solid particles can provide the transition of the whole polymeric component into the IPL with the composite strength and other characteristics also approaching those for the IPL.

ABSTRACT:A second order dielectric constant which represents nonlinear properties of material depends remarkably on the remanent polarization of the material. This paper describes the polarization dependence of second order dielectric constants in ferroelectric copolymers of vinylidene fluoride and trifluoroethylene. The remanent polarization of samples is controlled by means of an electrically or thermally stimulating procedure, both of which depolarize partially the fully polarized sample. The second order dielectric constants of the two sorts of samples made by these two methods show different types of dependence on the remanent polarization. This is interpreted by the phenomenological theory which predicts the thermodynamical order of a ferroelectric phase transition. KEY WORDSFerroelectric Polymer / 2nd Order Dielectric Constant / Remanent Polarization / Ferroelectric Phase Transition/ Phenomenological Theory/ Some fluoro-polymers exhibit ferroelectricity which is defined by the existence of spontaneous polarization and its reversal by application of an electric field. 1 -3 These ferroelectric polymers lose the ferroelectric property at the ferroelectric phase transition temperature (Curie transition temperature). 4 • 5 Recently, many studies of ferroelectric polymers have been focused on the phase transition in copolymers ofvinylidene fluoride (VDF) and trifluoroethylene (TrFE). Their trans1t10n behavior changes with composition; the Curie transition occurs in the copolymers including more than 50mol% VDF and the phase trans1t10n temperature is increased with increasing mole ratio of the VDF. 4 Furthermore, copolymers with more than 60mol% VDF exhibit a thermal hysteresis, defined as the difference between the transition temperature in the heating process and that in the cooling one. Thermal hysteresis increases with increasing VDF fraction in the copolymer up to about 80 mo)%. Copolymers with more than 80mol% VDF do not exhibit explicitly the phase transitions because they are covered by melting transitions. From these results, it is presumed that the Curie transition of these copolymers with the VDF fraction above 60 mol % is of the first order thermodynamically.The authors reported the nonlinear dielectric property of the copolymer of VDF and Tr FE. 6 -8 The nonlinear dielectric response includes information about polarization reversal occurring by an electric field stimulus above the coercive electric field Ec. Furthermore, nonlinear dielectric constants related to nonlinearity in fluctuations of dipoles can be obtained from nonlinear response to an applied electric field below Ec.Then-th order dielectric constant a. is defined as a coefficient of E" when an electric 327