Depolarization field effect on the ferroelectric behavior of polymers

The effect of the depolarization field in crystallites on the ferroelectric behavior of polymers is discussed on the assumption that the crystallite is a prolate ellipsoid with its major axis directed along the electric field. The theory relates the polarization P and the electric field E in the crystallite to the overall values P and E for the polymer. The determination of the P -E hysteresis of a crystallite from the P-E hysteresis is given with examples for poly(vinylidene fluoride) (PVDF) and vinylidene fluoride (VDF)–trifluoroethylene (TrFE) copolymer. The ratio R = J/(P_s ? P), with J the switching current density and P_s the saturation polarization of polymer, is proved to be free from the depolarization field effect and the plot of logR against logarithmic time is shown to have merit for characterization of switching behavior. Examples of the curves are given for PVDF and VDF-TrFE copolymers. The temporal change of local electric field in the unreversed domains in the crystallite in the course of polarization reversal is predicted by the theory and this change is proved to be a significant mechanism of switching acceleration.     

Analysis of the effect of electrical conductance of ferroelectric polymers on D-E hysteresis curves measured by the sawyer–tower method

The D-E (electric displacement vs. field) hysteresis curve of a ferroelectric polymer is conventionally measured by the Sawyer–Tower method. The effect of the electrical conductance of the polymer on the measured hysteresis curve is theoretically analyzed and a new method is proposed for elimination of the error arising from the conductance. Examples of original and corrected hysteresis curves of vinylidene fluoride–trifluoroethylene copolymer are presented.     

Effect of annealing on the ferroelectric behavior of nylon - 11 and nylon - 7

We have discovered recently that melt-quenched and cold-drawn Nylon - 11 films exhibit very clear ferroelectric hysteresis behavior. In the present study, a remanent polarization as high as 86 mC/m² has been found in Nylon - 7 samples; this is significantly higher than that usually observed in poly (vinylidene fluoride) films. The effect of annealing on the electric displacement versus electric field characteristics of both Nylon - 11 and Nylon - 7 films have been studied and show an increased coercive field (62 to 115 MV/m for Nylon - 11 and 79 to 97 MV/m for Nylon - 7) and a decreased remanent polarization (51 to 17.3 mC/m² for Nylon - 11 and 86 to 70.5 mC/m² for Nylon - 7) with increasing annealing temperature from 25 to 145°C.     

Evaluation of piezoelectric poly(vinylidene fluoride) polymers for use in space environments. I. Temperature limitations

Smart materials, such as thin‐film piezoelectric polymers, are interesting for potential applications on Gossamer spacecraft. This investigation aims to predict the performance and long‐term stability of the piezoelectric properties of poly(vinylidene fluoride) (PVDF) and its copolymers under conditions simulating the low‐Earth‐orbit environment. To examine the effects of temperature on the piezoelectric properties of PVDF, poly(vinylidenefluoride‐co‐trifluoroethylene), and poly(vinylidenefluoride‐co‐hexafluoropropylene), the d₃₃ piezoelectric coefficients were measured up to 160 °C, and the electric displacement/electric field (D–E) hysteresis loops were measured from ?80 to +110 °C. The room‐temperature d₃₃ coefficient of PVDF homopolymer films, annealed at 50, 80, and 125 °C, dropped rapidly within a few days of thermal exposure and then remained unchanged. In contrast, the TrFE copolymer exhibited greater thermal stability than the homopolymer, with d₃₃ remaining almost unchanged up to 125 °C. The HFP copolymer exhibited poor retention of d₃₃ at temperatures above 80 °C. In situ D–E loop measurements from ?80 to +110 °C showed that the remanent polarization of the TrFE copolymer was more stable than that of the PVDF homopolymer. D–E hysteresis loop and d₃₃ results were also compared with the deflection of the PVDF homopolymer and TrFE copolymer bimorphs tested over a wide temperature range. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1310‐1320, 2005     

Dielectric relaxations in poly(vinylidene fluoride)

Molecular motions in poly(vinylidene fluoride) were studied by the dielectric technique. Three distinct absorption peaks (α_c, α_a, and β) were observed in the frequency range from 0.1 cps to 300 kcps and in the temperature range from ?66 to 100°C. The molecular mechanisms for these absorptions and their temperature dependence are discussed, and results are compared with x-ray diffraction and the NMR measurements. It is concluded that the α_c absorption located at 97°C (1 kcps) is related to molecular motion in the crystalline region. The α_a absorption located at ?27°C (1 kcps) can be interpreted as due to the micro-Brownian motion of the amorphous main chains. The β absorption located at ?47°C (1 kcps) is attributed to local oscillation of the frozen main chains.     

Persistent polarization in poly(vinylidene fluoride). III. Depolarization and pyroelectricity of poly(vinylidene fluoride) thermoelectrets

Persistent polarization in poly(vinylidene fluoride) thermoelectrets prepared under high electric field has been studied by measurements of depolarization and pyroelectricity. Various polarizations are examined in detail; the polarizations related to a characteristic molecular motion near 60°C and the polarizing temperature are not responsible for the major piezoelectric effect in β-form electrets. The piezoelectricity is attributed to a polarization appearing near the melting temperature. The persistent polarization corresponding to d₃₁ of 2 × 10^?11 coul/N is about 5 × 10^?6 coul/cm². The pyroelectricity of β-form electrets is linearly correlated with the piezoelectricity.     

Crystal forms and ferroelectric properties of poly(vinylidene fluoride)/polyamide 11 blends prepared by high‐shear processing

Nanostructured poly(vinylidene fluoride) (PVDF)/polyamide 11 (PA11) blends have been melt‐processed using a high‐shear extruder. Uniaxially oriented blended films were fabricated by hot rolling to prepare ferroelectic films. The effects of rolling temperature and draw ratio on the crystal forms of both PVDF and PA 11 were investigated by means of Fourier transform infrared spectra (FTIR) and wide‐angle X‐ray diffraction (WAXD). It was shown that hot rolling in the range of 25–110 °C results in the crystal form transformation from the nonpolar α‐form into the polar β‐form for PVDF. The content and orientation function of β‐crystallites are strongly dependent upon the rolling temperature and the draw ratio. The highest content of well‐oriented β‐crystallites was achieved with a draw ratio of 4.0 upon rolling at 80 °C. At the same time, the content of the α‐form of PA11 in the blend was also found to decrease by hot rolling. The ferroelectric properties (D‐E hysteresis) of the oriented blended films were measured. The remanent polarization of the PVDF/PA11 = 90/10 blend is as high as 91 mC/m², which is about 1.2 times higher than that of pure PVDF. The D‐E hysteresis curves and the temperature dependence of the piezoelectric stress coefficients of the high‐shear‐processed sample suggested that the formation of nano‐dispersed structures resulted in the improvement of the remanent polarization and thermal characteristics at a temperature higher than 80 °C. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2707–2714, 2007     

Nuclear magnetic resonance and x-ray determination of the structure of poly(vinylidene fluoride)

In this study, wide-line NMR and x-ray diffraction have been used in conjunction to study the crystal structure of poly(vinylidene fluoride). Drawn poly(vinylidene fluoride) film was found to contain two crystal phases, the relative amounts of each depending on the draw temperature. Drawing at 50°C. yields a single phase, designated as phase I, while drawing at temperatures between 120 and 160°C. yields a mixture of phase I and a second phase (phase II). The fraction of phase II increases with increasing draw temperature, but this phase was never obtained without some phase I. A tentative orthorhombic unit cell is proposed for phase II. The structure of phase I has been determined from x-ray data. The unit cell is orthorhombic, space group Cm2m, having lattice constants a = 8.47, b = 4.90, and c (chain axis) = 2.56 A. There are two polymer chains in this unit cell. The conformation of the polymer chains is planar zigzag. The details of this structure have been confirmed by experimentally determining at ?196°C. the change in the NMR second moment with the angle between the magnetic field and the draw direction of phase I (drawn at 50°C.), and by comparing these results with a theoretical calculation of the second moments, based on the atomic positions obtained from the proposed structure.     

Enhanced electrical properties of highly oriented poly(vinylidene fluoride) films prepared by solid‐state coextrusion

Oriented poly(vinylidene fluoride) (PVDF) films with β‐form crystals have been commonly prepared by cold drawing of a melt‐quenched film consisting of α‐form crystals. In this study, we have successfully produced highly oriented PVDF thin films (20 µm thick) with β‐crystals and a high crystallinity (55–76%), by solid‐state coextrusion of a gel film to eight times the original length at an established optimum extrusion temperature of 160°C, some 10°C below the melting temperature. The resultant drawn films had a highly oriented (orientation function f_c = 0.993) fibrous structure, showing high mechanical properties of an extensional elastic modulus of 8.3 GPa and tensile strength of 0.84 GPa, along the draw direction. Such highly oriented and crystalline films exhibited excellent ferroelectric and piezoelectric properties. The square hysteresis loop was significantly sharper than that of a conventional sample. The sharp switching transient yielded the remnant polarization P_r of 90 mC/m², and the electromechanical coupling factor k_t was 0.24 at room temperature. These values are about 1.5 times greater than those of a conventional β‐PVDF film. Thus, solid‐state coextrusion near the melting point was found to be a useful technique for the preparation of highly oriented and highly crystalline β‐PVDF films with superior mechanical and electrical properties. The morphology of the extrudate relevant to such properties is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2549–2556, 1999     

Development of oriented structure and properties on drawing of poly(vinylidene fluoride) by solid‐state coextrusion

Gel films of poly(vinylidene fluoride) (PVDF) consisting of α‐form crystals were drawn uniaxially by solid‐state coextrusion to extrusion draw ratios (EDR) up to 9 at an optimum extrusion temperature of 160 °C, about 10°C below the melting temperature (T_m). The development of an oriented structure and mechanical and electrical properties on coextrusion drawing were studied as a function of EDR. Wide‐angle X‐ray diffraction patterns showed that the α crystals in the original gel films were progressively transformed into oriented β‐form crystals with increasing EDR. At the highest EDR of 9 achieved, the drawn product consisted of a highly oriented fibrous morphology with only β crystals even for the draw near the T_m. The dynamic Young's modulus along the draw direction also increased with EDR up to 10.5 GPa at the maximum EDR of 9. The electrical properties of ferroelectricity and piezoelectricity were also markedly enhanced on solid‐state coextrusion. The D–E square hysteresis loop became significantly sharper with EDR, and a remanent polarization P_r of 100 mC/m² and electromechanical coupling factor along the thickness direction k_t of 0.27 were achieved at the maximum EDR of 9. The crystallinity value of 73–80% for the EDR 9 film, estimated from these electrical properties, compares well with that calculated by the ratio of the crystallite size along the chain axis to the meridional small‐angle X‐ray scattering (SAXS) long period, showing the average thickness of the lamellae within the drawn β film. These results, as well as the appearance of a strong SAXS maximum, suggest that the oriented structure and properties of the β‐PVDF are better explained in terms of a crystal/amorphous series arrangement along the draw axis. Further, the mechanical and electrical properties obtained in this work are the highest among those ever reported for a β‐PVDF, and the latter approaches those observed for the vinylidene fluoride and trifluoroethylene copolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1371–1380, 2001     

Measuring the stress relaxation behaviour of engineering thermoplastic composites

An apparatus for measuring the stress relaxation behaviour of chopped fibre reinforced engineering thermoplastics have been assembled. The equipment, fitted with ancillary computer hardware and appropriate software, has been designed for determining the stress relaxation behaviour of a 0·32-cm ($\text{1}\text{8}\text{-}\text{in}\text{.}$) thick beam of plastic material, 21·6 cm long and and 1·9 cm wide ($\text{8}\text{1}\text{2}\text{in. long and}\text{3}\text{4}\text{in. wide}$), that is deflected in a cantilever mode. The decrease in stress occurring in the specimen after its end has been deflected to a 2·54 cm (1 in) strain at one end (representing about 0·6% strain in outer convex skin) is measured through a load cell. The signal from the load cell is conditioned, processed and fed into a computer for the data collection phase of the experiment. Data, taken in equal units of log time, are later retrieved in a calculated form and are simultaneously processed to fit a stress relaxation equation set forth by McLoughlin for glassy polymers. Plots of log E_r (E_r = relaxation modulus) vs. log t (t = time) may then be used to display stress relaxation data. The use of this apparatus has been demonstrated on Nylon 6/6, polyphenylene sulphide, and polyamide-imide resins. Unreinforced, glass fibre reinforced and carbon fibre reinforced grades of these materials were tested at 30°C, 40°C and 50°C. Smooth, low stress decay and stress relaxation behaviour was observed for the polyphenylene sulphide and polyamide-imide resins. With Nylon 6/6, the data at 30°C and 40°C were somewhat well behaved with more stress relaxation curvature occurring. The data at 50°C did not follow this trend; the Nylon 6/6 stress relaxed at a linear log E_r vs. log t trend that was slower than the stress relaxation rate at 30°C and 40°C. This behaviour is attributed to the fact that at 50°C the Nylon 6/6 material is approaching its glass transition temperature (about 60°C).     

Electromechanical Responses of a Crosslinked Polydimethylsiloxane

A high molecular weight polydimethylsiloxane, PDMS, gel was prepared and investigated as an electroactive polymer actuator. Electromechanical properties of the PDMS gels were measured under an oscillatory shear mode at the temperature of 27 °C to determine the effects of crosslink ratio and electric field strength. The storage modulus, G′, of PDMS gel increases linearly with crosslink density but nonlinearly with electric field. The increase in the storage modulus with crosslink density is due to the increase in the number of junction points and strands. With increasing electric field strength, the storage modulus increases as the electric field induces dipole moments generating the electrostatic forces within the matrices. The gel with the crosslink ratio of 0.01 possesses the highest G′ sensitivity of 41% at 2 kV/mm. The temporal response of PDMS gels upon repeated applications of electric field strength of 2 kV/mm was investigated. For the crosslink PDMS (N_c/N_m = 0.01) system, at the electric field of 2 kV/mm, G′ immediately increases and rapidly reaches a steady-state value. With electric field off, G′ decreases and nearly recovers its original value. The crosslinked PDMS (N_c/N_m = 0.01) is nearly a reversible system. Finally, we investigated the bending response of the PDMS films, suspended in silicone oil between copper electrodes. From the deformation data, we estimated the dielectrophoresis force, F_D, to be a linear function of electric field strength.     

Cooperative chain relaxation in miscible polymer blends

Orientation relaxation of dissimilar chains in the molten miscible blends, poly(methyl methacrylate)/poly(vinylidene fluoride) and poly(methyl methacrylate)/poly(vinylidene fluoride-co-trifluoroethylene), were investigated by measuring (1) the change of infrared dichroic ratio with time after the uniaxial stretching of film specimens, (2) the shear stress relaxation spectrum, and (3) birefringence relaxation in shear. The dissimilar polymers showed an identical time variation of the normalized Hermans orientation function. The blend showed a relaxation spectrum with a single characteristic relaxation time τ_c, depending on the blend composition. The birefringence relaxed monotonically, remaining positive. These results suggest that the dissimilar polymers do not relax independently but cooperatively. This behavior may be induced by a constraint due to the specific interactions between the dissimilar polymers, e.g., weak hydrogen bonding. For the cooperative chain relaxation, a third power relationship was found; τ_c/τ_e vprop; (M/M_e),³ where τ_e and M_e are the relaxation time and molecular weight of entanglement strand, respectively, and M is the number average molecular weight in the blend.     

Dielectric relaxations and molecular motions in poly(vinylidene fluoride) with crystal form II

Molecular motions in poly(vinylidene fluoride) were studied by dielectric measurements. Of the three relaxation processes, the α_a and the α_c were studied. The α_a relaxation was attributed to the molecular motions in the amorphous regions and the α_c relaxation to molecular motions in the crystalline regions and their surfaces. The relaxation time and the magnitude of the α_a absorption were analyzed on the basis of the Adam-Gibbs theory of the temperature dependence of the size of the cooperatively rearranging region. As a result it was concluded that the molecular structure of crystal form II holds locally, even in the amorphous regions. The relaxation time and the magnitude for the α_c absorption were analysed on the basis of the two-site model. It was concluded that the α_c relaxation is attributable not only to molecular motions in the folds of the lamellar crystals, but also to those in the interior of the crystal; the folded chain is relatively mobile, while the molecular chain in the interior of the crystal executes restricted rotation around the chain axis.     

High field electrostrictive response of polymers

It is well known that electrostrictive strains are proportional to the square of the applied electric field. It therefore appeared reasonable to assume that for some polymeric materials, a large acoustic thickness response, d_T, \[ \left( {d_T = \frac{{dS}}{{dE}}} \right) \] might be obtained by application of high dc bias fields, ～ 20 MV/m, to a film while driving the film with an ac signal to access the high slope region of the electrostrictive strain vs. applied field curve. Previous studies of crystallizing poly(vinylidene fluoride) (PVF₂) from solution under high electric fields have demonstrated that gel-like samples of PVF₂ with high content of the plasticizer tricresyl phosphate (TCP) could be subjected to electric fields as high as ～ 100 MV/m. Using this type of heavily plasticized PVF₂ d_T values ～ 4 Å/V were obtained. Values of 9 Å/V were obtained for a certain class of thermoplastic elastomer (i.e., a polyurethane). These d_T values are considerably greater than those obtained from conventional piezoelectric ceramic materials. In addition, large elastic strains (> 3%) were observed as a function of applied dc field. © 1994 John Wiley & Sons, Inc.     

NEW MATERIALS DERIVED FROM POLY(4-HYDROXYSTYRENE) AS LITHIUM BATTERY CELL COMPONENTS

A new class of polyethers has been prepared by the Mitsunobu coupling of poly(4-vinyl phenol), P4VP, with low molecular weight poly(ethylene glycol)methyl ether. These comb-like polymers, having ca. 20–30% residual phenols, were characterized by IR, DSC, and TGA. Results of thermal analysis on the polymers suggest thermal stability to at least 300°C and a glass transition temperature in the range ?30 to ?40°C. Complexes with LiPF₆ gave conductivities of ca. 1 × 10^?5 S/cm at room temperature. The polymers were blended with plasticized poly(vinylidene fluoride) (PVDF) to prepare porous films and subsequently infiltrated with lithium salts and ethylene and ethyl methyl carbonate. Ionic conductivities of these hybrid films were measured from ?20°C to 40°C. Conductivities as high as 2.4 × 10^?3 S/cm are observed at room temperature. The electrochemical stability of hybrid materials was studied by cyclic voltammetry.     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

Heat capacity of poly(vinylidene fluoride) and polytetrafluoroethylene between 5 and 200°K

Heat capacities of poly(vinylidene fluoride) (PVF₂) and polytetrafluoroethylene (PTFE) have been measured between 5 and 100°K with an accuracy of (1–5)% by adiabatic calorimetry. Calculations based on contributions from known optical lines and the Tarasov continuum model are in good agreement with experimental results down to 30°K for PVF₂ and 10°K for PTFE, and yield characteristic temperatures θ₁ and θ₃ which are consistent with previous values determined from high-temperature (100—350°K) data. At lower temperature the measured heat capacity is significantly higher [(30–100)%] than the model prediction, and can be satisfactorily accounted for by the introduction of localized vibrators at a concentration of about 1% as compared to acoustical oscillators and at a characteristic temperature of about 20°K. Using established data on polyethylene for comparison, the principle of additivity for heat capacities is found to be valid down to at least 20°K, convering the region (<60°K) where interchain vibrations contribute significantly to the heat capacity. Possible reasons for this unexpected behavior are discussed.     

Effects of annealing on the polarization switching of phase I poly(vinylidene fluoride)

To obtain information about microscopic processes involved in the polarization switching in uniaxially oriented poly (vinylidene fluoride) film, a least-squares estimation of nonlinear parameters was developed to yield parameters of an equation which describes the nucleation and domain growth process. Time domain measurements of polarization reversal revealed that switching times decreased as the annealing temperature T_a increased (67.0, 52.4, and 41.3 μs at –20°C under a 200 MV/m pulse field for the as-stretched samples, the samples being annealed at 120 and 160°C, respectively). The analysis showed that the value of the domain growth speed increased as T_a increased. This is consistent with x-ray diffraction data which indicated that the annealing process brought about better chain packing and increased crystallite perfection. The analysis also showed that the nucleation probability significantly increased as T_a increased. This result was interpreted in terms of a morphological transformation, which was indicated by the decrease in elastic modulus with increasing T_a with no corresponding loss of orientation. It is suggested that the annealing process brought about an increase in the number of nucleation sites as a result of a transformation from a fibrous structure to a crystal-amorphous series structure which has increased boundary zone area.     

Raman spectra of magnetic field induced cholesteric → nematic phase transition in doped p-octoxybenzoic acid

Raman spectroscopy is employed to investigate helical twist formation in nematic and smectic C phases of p-n-octoxybenzoic acid (OBA) doped with a small amount of Cholesteric Nonanoate (CN). A cholesteric→ nematic phase transition in OBA/CN is induced by an external magnetic field in the temperature range 135–148°C. The threshold field (H_c) is equal to 8.0 kGauss for 0.33 % by weight CN/OBA, and no hysteresis is observed.