I. Lelidis

Significance of small voltage in impedance spectroscopy measurements on electrolytic cells

We investigate, theoretically, for what amplitude of the applied voltage to an electrolytic cell the concept of impedance is meaningful. The analysis is performed by means of a continuum model, by assuming the electrodes perfectly blocking. We show that, in the low-frequency range, the electrolytic cell behaves as a linear system only if the amplitude of the measurement voltage is small with respect to the thermal voltage VT=kBT∕q, where kBT is the thermal energy, and q is the modulus of the electrical charge of the ions, assumed identical except for the sign of the charge. On the contrary, for large frequency, we prove that the amplitude of the applied signal has to be small with respect to a critical voltage that is frequency dependent. The same kind of analysis is presented for the case in which the diffusion coefficients of the positive ions is different from that for negative ions, and for the case where surface adsorption takes place.

Elastic continuum theory: Towards understanding of the twist-bend nematic phases

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

The effect of graphene on liquid-crystalline blue phases

The stabilization of liquid-crystalline blue phases is recently attracting considerable interest because of the envisioned applications in fast optical displays and tunable photonic crystals. We report on the effect of surface-functionalized graphene nanosheets on the blue phase range of a chiral liquid crystal. Calorimetric and optical measurements, reproducible on heating and cooling, demonstrate that the resulting soft nanocomposite exhibits an increased blue phase temperature stability range for a minute concentration of dispersed graphene. The impact is stronger on the ordered, cubic structured blue phase I. These findings suggest that anisotropic nanoparticles may be of great usefulness for stabilizing blue phases.

Poisson-Nernst-Planck model with Chang-Jaffe, diffusion, and ohmic boundary conditions

Using the linear Poisson-Nernst-Planck impedance-response continuum model, we investigate the possible equivalences of three different types of boundary conditions previously proposed to model the electrode behavior of an electrolytic cell in the shape of a slab. We show analytically that the boundary conditions proposed long ago by Chang-Jaffe are fully equivalent to the ohmic boundary conditions only if the positive and negative ions have the same mobility, or when only ions of a single polarity are mobile. In the case where the ions have different and non-zero mobilities, we fit exact impedance spectra created for ohmic boundary conditions by using the Chang-Jaffe Poisson-Nernst-Planck response model, one that is dominated by diffusion effects. These fits yield conditions for essentially exact or approximate numerical correspondence for the complex impedance between the two models even in the unequal mobility case. Finally, diffusion type boundary conditions are shown to be fully equivalent to the ohmic one. Some limiting cases of the model parameters are investigated.

Complex dielectric constant of a nematic liquid crystal containing two types of ions: limit of validity of the superposition principle.

We investigate the influence of two groups of ions on the complex dielectric constant of a nematic liquid crystal limited by perfectly blocking electrodes. The analysis is performed by solving the equations of continuity for the two groups of cations and anions, and the equation of Poisson relating the actual electric field to the net density of charge. We consider a typical experiment of impedance spectroscopy, and evaluate the equivalent resistance and reactance of the cell, in the series representation, versus the frequency of the applied voltage to the cell. We show that the presence of two groups of ions gives rise to two plateaux in the spectrum of the resistance, similar to those related to the ambipolar and free diffusion in the case where there is only one type of ions, but for which the cations and anions have different diffusion coefficients. The correspondence between the usual ambipolar and free diffusion coefficients and those related to the presence of two groups of ions is discussed. The spectra of the real and imaginary parts of the complex dielectric constant are obtained, and their dependence on the bulk densities of the two types of ions is investigated. The nonvalidity of the superposition principle is discussed.

A continuum description for cholesteric and nematic twist-bend phases based on symmetry considerations

ABSTRACT The recently discovered twist-bend nematic phase, Ntb, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, n, on a conical helix with a tilt angle θ and helical pitch P. The stability of the Ntb phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of the helical axis, t. In the present article, we investigate the influence of an external bulk field (magnetic or electric) on the Ntb phase. Using symmetry arguments we derive the expression for the flexoelectric polarisation in twist-bend nematic phases. We show that, besides the standard contribution related to the spatial variation of the nematic director, two new contributions connected with the existence of the helical axis appear. In the ground state, where the nematic deformation is a pure heliconical deformation, the new contribution vanishes identically, and the total flexoelectric polarisation is perpendicular to the nematic director. Furthermore, as an example, we study the role of an external magnetic field applied parallel to the helical axis for a material with positive magnetic susceptibility anisotropy. We show that the field modifies the range of values of the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the Ntb phase. GRAPHICAL ABSTRACT

Comparison of two generation-recombination terms in the Poisson-Nernst-Planck model

Two phenomenological forms proposed to take into account the generation-recombination phenomenon of ions are investigated. The first form models the phenomenon as a chemical reaction, containing two coefficients describing the dissociation of neutral particles in ions, and the recombination of ions to give neutral particles. The second form is based on the assumption that in thermodynamical equilibrium, a well-defined density of ions is stable. Any deviation from the equilibrium density gives rise to a source term proportional to the deviation, whose phenomenological coefficient plays the role of a life time. The analysis is performed by evaluating the electrical response of an electrolytic cell to an external stimulus for both forms. For simplicity we assume that the electrodes are blocking, that there is only a group of negative and positive ions, and that the negative ions are immobile. For the second form, two cases are considered: (i) the generation-recombination phenomenon is due to an intrinsic mechanism, and (ii) the production of ions is triggered by an external source of energy, as in a solar cell. We show that the predictions of the two models are different at the impedance as well as at the admittance level. In particular, the first model predicts the existence of two plateaux for the real part of the impedance, whereas the second one predicts just one. It follows that impedance spectroscopy measurements could give information on the model valid for the generation-recombination of ions.

Nematic phases with spontaneous splay–bend deformation: standard elastic description

ABSTRACT Recently, possible deformed states in nematic liquid crystals have been discussed assuming that Frank’s bend elastic constant is negative. The presence of a stable deformed state has been justified by introducing in the elastic energy density a term proportional to the second derivative square of the deformation parameter. This term, widely used in field theory, has been introduced in the elastic theory of liquid crystals mainly to investigate the effect of the splay–bend term in the nematic deformation in confined samples. Nevertheless, in the analysis of bulk properties this term is questionable. An alternative justification of possible spontaneous distortions in nematic liquid crystals is proposed. Our description of the elastic properties is based on an elastic energy density expanded to the fourth order in the deformation parameter. In this framework, we show that a stable nematic state characterised by a uniform deformation, related to a position-independent elastic energy density, is possible. Graphical Abstract

Electrical response of a medium containing dissociable impurities

The effect of the generation-recombination phenomenon on the electrical impedance of an electrolytic cell is investigated. We show that this phenomenon could be responsible for the appearance of a plateau in the real part of the impedance of the cell. The possibility to observe the plateau, arising from the generation-recombination phenomenon, is discussed in relation to the values of the association-dissociation coefficients. The analysis is done by assuming that the generation-recombination phenomenon can be described as a chemical reaction of first order, that the sample is in the shape of a slab, and that the electrodes of the cell are perfectly blocking. To simplify the analysis, the case where only one type of ions can move is considered. The extension of the results to the more general case, in which both types of ions are mobile, is also discussed.

Twist-grain boundary phase induced by Au nanoparticles in a chiral liquid crystal host

ABSTRACT We report on the stabilisation of the liquid-crystalline, twist-grain boundary A (TGBA) phase in mixtures of a chiral liquid crystal and surface-functionalised spherical Au nanoparticles (NPs) of 10 nm diameter. The results, obtained by calorimetric, optical, small-angle X-ray and plasmon resonance measurements, demonstrate that a TGBA phase, which is metastable for the pure liquid crystal host, can be effectively stabilised for a 3 K range in the presence of NPs. Moreover, the role of NPs size on the TGBA stabilisation is briefly discussed. Graphical Abstract