Nonlinear dielectric relaxation spectroscopy of ferroelectric liquid crystals

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

Nonlinear dielectric effects in liquids: a guided tour

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye's initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Electric-field-induced weakly chaotic transients in ferroelectric liquid crystals

Nonlinear dynamics induced in surface stabilized ferroelectric liquid crystals by strong alternating external electric fields is studied both theoretically and experimentally. As has already been shown, molecular reorientations induced by sufficiently strong fields of high-enough frequencies can reveal a long transient behavior that has a weakly chaotic character. The resulting complex dynamics of ferroelectric liquid crystals can be considered not only as a consequence of irregular motions of particular molecules but also as a repercussion of a surface-enforced partial decorrelation of nonlinear molecular motions within smectic layers. To achieve more insight into the nature of this phenomenon and to show that the underlying complex field-induced behavior of smectic liquid crystals is not exceptional, ranges of system parameters for which the chaotic behavior occurs are determined. It is proved that there exists a large enough set of initial phase trajectory points, for which weakly chaotic long-time transitory phenomena occur, and, thereby, it is demonstrated that such a chaotic behavior can be regarded as being typical for strongly field-driven thin liquid crystal systems. Additionally, the influence of low-amplitude random noise on the duration of the transient processes is numerically studied. The strongly nonlinear contribution to the electro-optic response, experimentally determined for liquid crystal samples at frequencies lower than the actual field frequency, is also analyzed for long-time signal sequences. Using a statistical approach to distinguish numerically response signals of samples from noise generated by measuring devices, it is shown that the distribution of sample signals distinctly differs from the device noise. This evidently corroborates the occurrence of the nonlinear low-frequency effect, found earlier for different surface stabilized liquid crystal samples.

Nonlinear dielectric effect in supercritical diethyl ether

Nonlinear dielectric effect (NDE) describes changes of dielectric permittivity induced by a strong electric field in a liquid dielectric. The most classical finding related to this magnitude is the negative sign of NDE in liquid diethyl ether (DEE), recalled by Peter Debye in his Nobel Prize lecture. This article shows that the positive sign of NDE in DEE is also possible, in the supercritical domain. Moreover, NDE on approaching the gas-liquid critical point exhibits a unique critical effect described by the critical exponent ψ ≈ 0.4 close to critical temperature (T(C)) and ψ ≈ 0.6 remote from T(C). This can be linked to the emergence of the mean-field behavior in the immediate vicinity of T(C), contrary to the typical pattern observed for critical phenomena. The multi-frequency mode of NDE measurements made it possible to estimate the evolution of lifetime of critical fluctuations. The new way of data analysis made it possible to describe the critical effect without a knowledge of the non-critical background contribution in prior.

Strongly nonlinear dynamics of ferroelectric liquid crystals

Molecular reorientation processes induced in thin ferroelectric liquid crystal systems by strong alternating external electric fields are studied both by solving numerically the equation of reorientation motion of molecules and by measuring the electro-optic response of thin samples. It is shown that the occurrence of a wide band in nonlinear response spectra above the Goldstone-mode frequency is a consequence of complex partially uncorrelated molecular reorientations enforced within smectic layers by sufficiently high fields of high enough frequencies. Such nonlinear reorientational motions of molecules are argued to have a character of weakly chaotic long-lasting transients, related to almost periodic modulations of the amplitude of rotational oscillations performed by molecules with the field frequency. These modulations have been numerically proved to proceed with lower frequencies than the field frequency and with space-dependent depths of temporal changes. The occurrence of the modulations has experimentally been confirmed by registering distinct contributions to electro-optic response spectra at frequencies less than the running frequency of the applied electric field.

Linear and non-linear dielectric properties of a short-pitch ferroelectric liquid crystal stabilized by a polymer network

Linear and non-linear dielectric measurements were carried out on a ferroelectric liquid crystal stabilized by an anisotropic polymer network. The polymerization process was achieved at room temperature. It was performed from an achiral monomer in the ferroelectric chiral smectic C phase, exhibiting a very short helical pitch and a large polarization. The linear and non-linear dielectric spectroscopy were also completed by textural morphology as well as structural and ferroelectric characterizations. All these measurements were carried out on a pure ferroelectric liquid crystal material and on composite films containing two polymer concentrations. The increase of the polymer network density leads to a decrease of the dielectric strength determined in the linear and non-linear dielectric spectroscopy. The complementarity between the linear and non-linear dielectric measurements and their confrontation with a theoretical model allowed the simultaneous determination of some physical parameters such as macroscopic polarization, rotational viscosity and twist elastic energy. We also discuss the effect of the polymer network density on the obtained physical parameters.

Anomalous temperature behavior of nonlinear dielectric effect in supercooled nitrobenzene

Studies of the nonlinear dielectric effect (NDE), describing changes of the dielectric permittivity induced by a strong electric field, in normal and supercooled liquid nitrobenzene are presented. An unusual increase of the stationary NDE, portrayed by the critical-like relation approximately (T-T+)(-1), was obtained. Nitrobenzene samples solidified at TS approximately T+ +2 K , approximately 10 K below the reported melting temperature Tm approximately 278 K . The anomalous increase of the NDE coincided with a slow relaxation process, detected in time-resolved measurements. The results presented offer a reinterpretation of the classical description by Piekara and Piekara [A. Piekara and B. Piekara, C. R. Hebd. Seances Acad. Sci. 203, 852 (1936)] of a positive sign contribution to the NDE in liquids. It is suggested that the obtained anomaly may be associated with the appearance of local quasinematic structures. This is supported by a speculative link to a general model for liquid-liquid transitions [H. Tanaka, Phys. Rev. E 62, 6968 (2000)] and a phenomenological model originally developed for the self-focusing of laser beams [J. Hanus, Phys. Rev. 178, 420 (1969)]. The case of the isotropic-nematic transition in liquid crystalline materials is also recalled. The NDE results reported here are related neither to the glass transition phenomenon nor to the recently developed concept of a second liquid-liquid transition.

Fractional dynamics and nonlinear harmonic responses in dielectric relaxation of disordered liquids

The problem of the nonlinear dielectric response due to the application of a strong electric field is reconsidered in the context of fractional kinetic equations. To accomplish that, we start from a fractional noninertial Fokker-Planck equation and restrict ourselves to the case of anomalous subdiffusive processes characterized by the critical exponent alpha ranging from 0 to 1, the limit of normal diffusion. In particular, we evaluate the first- and third-order nonlinear harmonic components of the electric polarization in the case of either a pure ac field or a strong dc bias field superimposed on a weak ac field. The stationary regime is therefore calculated from an infinite set of differential recurrence relations by using a perturbation method. The results so obtained are illustrated by three-dimensional dispersion and absorption plots in order to show the influence of alpha. Cole-Cole diagrams are also presented, allowing one to see that the arcs become more and more flattened as alpha-->0, and corresponding to a broadening of the absorption peaks as effectively observed in complex liquids. The theoretical model is supported by comparison with experimental data of the third-order nonlinear dielectric permittivity of a ferroelectric liquid crystal.

Rotational Brownian motion and nonlinear dielectric relaxation of asymmetric top molecules in strong electric fields

A general theoretical treatment of the nonlinear dielectric response of an assembly of asymmetric top molecules in strong electric fields is presented in the context of the noninertial rotational diffusion model. The calculation proceeds by obtaining an infinite hierarchy of recurrence equations for the expectation values of Wigner's D functions describing nonlinear relaxation of the system. This hierarchy may be used for the evaluation of both transient and ac nonlinear responses in strong electric fields. The solution of this hierarchy is obtained for the particular case of rigid rodlike molecules in superimposed ac and strong dc bias electric fields, allowing one to evaluate the corresponding nonlinear response. The results are in agreement with available experimental data on nonlinear dielectric relaxation of dilute solutions of polar rodlike molecules in nonpolar solvents.

Critical behavior of nonlinear permittivity in the smectic-A phase of chiral liquid crystals

We study the nonlinear permittivity of chiral liquid crystals in the smectic-A (Sm-A) phase near the ferroelectric smectic-C* (Sm-C*) phase and the smectic-C(*)(alpha) (Sm-C(*)(alpha)) phase theoretically and experimentally. The third-order nonlinear permittivity epsilon(3) shows the critical behavior with the exponent of four near the Sm-C* phase and its sign depends on the order of the phase transition. In the case of the Sm-A-Sm-C(*)(alpha) phase transition, the sign inversion of epsilon(3), presumably due to the large fluctuation of order parameter, is observed near the transition temperature.