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We discuss the foundations of a model based on an extension of the Langmuir approximation for the adsorption–desorption phenomena, in which the phenomenological coefficients depend on the bias potential, in addition to their dependence on the adsorption energy. The theoretical analysis focuses on the effect of these effective coefficients on the electrical response of an electrolytic cell to an external electric field, as predicted by the Poisson–Nernst–Planck model. Kinetic balance equations govern the current densities on the electrodes when the adsorption phenomenon occurs in the presence of an electric bias. The influence of the phenomenological parameters entering the model, as well as of the symmetry of the cell on the cyclic voltammetry, is investigated.

It is shown that the frequency dependence of the phenomenological parameters entering Langmuir kinetic equation describing the surface adsorption could be related to a random distribution of relaxation times. A theoretical model based on a generalization of Langmuir isotherm, taking into account a homogeneous distribution of relaxation times is proposed for supercapacitor modeling. Its theoretical predictions agree well with experimental data derived by the analysis of Lissajous figures describing the response of an electrochemical cell excited with a well defined frequency. According to our data, the effective desorption time is a rapidly decreasing function of the frequency of the applied signal, whereas the effective adsorption coefficient is an increasing function of it. The effective relaxation time is independent of the ionic concentration, whereas the effective adsorption coefficient strongly depends on this quantity. A large increase in the adsorption coefficient is reported, for the electrochemical cells with high surface area of the electrodes.

The boundary conditions proposed to discuss the charge exchange taking place in an ionic liquid in contact with non-blocking electrodes are reconsidered in a dynamic situation. Assuming that the variation of the bulk ionic current density depends linearly on the surface value of the ionic current density, the frequency dependence of the phenomenological parameter is determined. The analysis has been performed in the framework where the relaxation times are smaller than a maximum relaxation time τM, and that the response function is independent on the value of the relaxation time. Using simple physical considerations, an expression for the surface conductivity describing the ionic charge exchange at the electrode is obtained. According to our calculations, its frequency dependence is similar to that predicted for the electric conductivity in disordered materials when the mechanism is of the hopping type. From measurements of impedance spectroscopy, by the best fit of the experimental data, the temperature dependence of the hopping time, of the dc surface conductivity, and of the diffusion coefficient are derived. They are in good agreement with the theoretical predictions obtained with the random distribution of surface energy barrier. Keywords: Ionic liquids, Non-blocking electrodes, Electrical impedance spectroscopy, AC hopping surface conductivity

The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of the nematic strain tensor, as in classical elasticity of solids, is also developed. The twist-bend nematic modulated phase is investigated by both approaches and the results are critically compared. The conical angle of the twist-bend phase is calculated as function of the elastic constants. Surface-like effects are considered. Finally, we demonstrate that a splay-bend nematic phase with small oscillations of the nematic director around an axis is prohibited.

The electric responses of electrochemical capacitors produced with electrodes build up of reduced graphene oxide (rGO) deposited on Fluorine-doped tin oxide (FTO) coated glass have been experimentally investigated by cyclic voltammetry measurements. According to our experimental data, the parametric curve of the current in the circuit versus the external voltage is a continuous curve without discontinuity points respect to the inversion points of the external voltage. A few equivalent electric circuits able to reproduce the electric response of the capacitor are discussed. The dependence of the area delimited by the parametric cyclic voltammetry curve on the elements of the circuit is investigated. The possible evaluation of the effective capacitance of the capacitor by the numerical evaluation of the area delimited by the parametric curve is critically discussed and the limit of the procedure is underlined. A model based on the Poisson-Nernst-Planck theory with adsorbing electrodes is developed and used to fit the experimental voltammogram. The agreement between the theoretical model and the experimental data is good, indicating the importance of the adsorption phenomenon in the electric response of electrochemical capacitor to an external electric field.

We propose that a kinetic equation of fractional order may be used to account for the frequency dispersion of the effective parameters in the framework of the Langmuir approximation for the adsorption–desorption phenomena. A frequency dependence of these parameters naturally arises in this formalism, indicating that it may play a similar role of a generalization of the Langmuir isotherm obtained from a homogeneous distribution of relaxation times. The fractional approach formalism opens the possibility to consider different relaxation regimes characterizing the interfacial behaviour of electrolytic cells, and may be a powerful tool to interpret complex impedance spectroscopy data.

To reduce or completely remove the viewing angle dependence of liquid crystal (LC) displays and devices, we have recently introduced a new electrode structure for LC displays. This electrode structure has openings (holes) in the pixel electrode (PixE) for generating fringe electric field with azimuthal degenerated distribution of the field lines around each hole, resembling a fountain. Such a field is promoting azimuthally degenerated switching of the LC molecules and thus generation of images with 360° viewing angle constant contrast when a pair of crossed circular polarisers are used. A theoretical model of the fountain fringe field, generated around a single circular hole and plurality of such holes in the PixE, is presented.

To investigate the conduction properties of ionic liquid crystal electrolytes and to correlate them to their molecular structure, two electrolytes based on imidazolium iodides have been chosen for a comparative study: one ionic liquid crystal (1-dodecyl-3-methylimidazolium iodide) (C12) and one ionic liquid (1-hexyl-3-methylimidazolium iodide) (C6). For the electrical characterization of the samples the electrochemical impedance spectroscopy technique (EIS) has been used in the frequency range 1 MHz ÷ 10 mHz. For both electrolytes three frequency domains have been singled out. At large frequencies a hopping mechanism ensures the relative high conductivity of ionic liquids. A good fit of the conductivity data with respect to temperature with a Vogel-Tamman-Fulcher (VTF) equation has been done. The interesting result is that although C12 has a higher viscosity than C6 and thus a smaller conductivity was expected the observed conductivity is actually larger, this fact being attributed to the smectic A liquid crystal order of C12. At medium frequencies and especially at low frequencies the buildup of double layers by the electrodes is well observed. Assuming that in this region (10 Hz ÷ 10 mHz) the cell is equivalent to an electric circuit formed by the parallel of a resistance, R0, and a capacitance, C0, the simple Debye relaxation model, characterized by one relaxation time, has been modified taking into account the adsorption phenomenon in the Langmuir approximation. A theoretical interpretation of the experimental results based on the double layer model is presented.

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants ...

We present a fast-switching liquid crystal device comprising FFS electrode structure deposited onto one of the device substrates. Initially, the liquid crystal in the device has a homeotropic alignment. The generated periodic electric field by the FFS electrode results in a periodic splay/bend elastic deformation, thus giving rise to flexoelectric polarization along the substrate normal. At low applied voltages, this periodic elastic deformation, is substantially localized in a very thin portion of the liquid crystal layer adjacent to the substrate surface bearing the electrode and it is stabilized by a polymer network. Thus, the flexoelectric polarization becomes permanently present in the device and has non-zero value at field-off state. The polymer network with splay/bend configuration occupies very small part of the liquid crystal layer (~ 0.5μm), which is thinner than the light wavelength and therefore is optically invisible. Simultaneously with the formation of the polymer network, possessing splay/bend configuration, a polymer network with polymeric bundles oriented preferably along the substrates' normal is formed. As we will show, the presence of the polymer network, consisting of surface and bulk parts, reduces substantially the switching times of the liquid crystal device more than one order bringing them to μs range.

We investigate the electric response of an electrolytic cell of water and KCl, limited by gold electrodes, to derive information on the role of the electrodes in the spectra of the real and imaginary parts of the electric impedance of the cell. Our experimental data can be interpreted by means of the Poisson–Nernst–Planck model with Ohmic boundary conditions for the electrodes, where the surface conductivity is consistent with that derived by a random-walk model for the charge exchange on the electrodes. By using a best-fit procedure, the direct current (DC) conductivity and the hopping time are determined. The measurements have been performed in the absence and presence of a DC bias. In the absence of DC bias, the agreement between the theoretical predictions and the experimental data is good over the full explored frequency range. On the contrary, in the presence of the DC bias, the theoretical predictions in the low-frequency range do not describe the experimental results very well and the agreement de...

The electric response of an electrical double layer capacitor is analyzed by means of the impedance spectroscopy technique. From the spectrum of the imaginary part of the electric impedance of the cell, in the low frequency region, it follows that the electrodes are blocking. To interpret the experimental data we assume that the electrodes are adsorbing. The kinetic equation describing the adsorption phenomenon used in our analysis is a generalization of Langmuir isotherm, where the effective adsorption coefficient and desorption time are frequency dependent. Their frequency dependence is deduced considering the adsorption as a linear phenomenon relating the bulk density of particles to the surface density of particles, characterized by a distribution of relaxation times. The agreement between the experimental data and the theoretical predictions is very good within explored frequency range.

The adsorption phenomenon is often described by means of a kinetic equation, in the form proposed by Langmuir. From the statistical point of view, the analysis is done in terms of adsorption sites, in the framework of Boltzmann or Fermi-like statistics. We show that a more simple description can be done in terms of an effective adsorption energy, taking into account its dependence on the density of adsorbed particles. Some elementary lateral interaction potentials are analyzed to illustrate this dependence. We show that the effective adhesion energy may be written as a power law of the surface coverage ratio. Eventually, we propose a generalization of the Frumkin-Fowler-Guggenheim model as a self-consistent non-linear relation determining the actual equilibrium distribution of surface particles.

The influence of the electrode properties on the electric response of nematic liquid crystal cell limited by ITO surfaces is investigated. From electrochemical impedance spectroscopy measurements (EIS) of the real and imaginary parts of the electric impedance of the cell it is evident that in the DC limit the cell behaves as a pure resistance, since its reactance tends to zero linearly with the frequency of the applied voltage. The spectrum of the real part of the impedance shows the presence of two plateaux, one related to the bulk properties of the cell, and the other to the electrode properties. The experimental data can be interpreted in terms of Poisson–Nernst–Planck model, assuming that the presence of the non-blocking electrodes is described by a boundary condition according to which the conduction current across the electrode due to the charge exchange between ions and electrons is due to the surface electric field, as in Ohmic electrodes, and to the variation of the bulk density of ions just in front to the electrodes, as in the Chang–Jaffe model.

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.

The electric response of a capacitive deionisation cell submitted to a periodic external electric field is investigated. The case in which the applied potential has a nonzero average value on one period (polarised cell) is considered. The theoretical analysis of the experimental data, relevant to nearly symmetric electrodes, is done in the framework of the Poisson-Nernst-Planck model. The current densities on the electrodes are described by kinetic equations related to the adsorption phenomenon in the presence of a bias potential. We propose a new form for the Langmuir isotherm in which the effective adsorption coefficients depend on the bias potential according to the Boltzmann statistics. This kinetic equation extends the Butler-Volmer equation for non-blocking electrodes also to the blocking ones. The equation proposed here is such that for dc external voltage the total current across the electrodes vanishes.

Characterization of electrolytic cells is often inferred from measurements of their electrical properties as a function of frequency by applying a sinusoidal voltage. In some cases, a dc bias is intrinsically present in addition to the ac stimulus and its effects are often neglected although they may become relevant in certain situations. As a consequence, the interpretation of the observed results might be misleading. Our aim is to estimate the influence of the bias solving numerically the Poisson-Nernst-Planck model for an electrolytic cell submitted to an ac external voltage superimposed to a bias. According to our analysis, even in the case of a small bias, the estimated Debye frequency and the low-frequency resistance of the cell are significantly influenced by it.

The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metric range, in agreement with experimental results. For a sample of finite thickness, we show that the wave vector of the stable periodic structure depends not only on the elastic parameters but also on the anchoring energy, easy axis direction, and the thickness of the sample., Comment: 11 pages

The response of a cholesteric liquid crystal film to mechanical confinement is theoretically investigated considering planar anchoring conditions on the limiting surfaces and pure twist distortion of the liquid crystal director. We evaluate the total twist angle and normal force acting on the surfaces as a function of the film thickness. Assuming the Rapini-Papoular functional form for the surface anchoring energy, we show that the surface twist angle undergoes discontinuous jumps or continuous transitions as a function of the film thickness and anchoring strength. The transitions take place at well-defined film thicknesses, related to the intrinsic periodicity of the cholesteric liquid crystal, and produce oscillations in the normal force and position of the optical band-gap as the film thickness is varied.

The derivation of Warburg's impedance is revisited and critically analyzed. We show that the original derivation where the electric current is assumed to be due only to the diffusion of ions, as proposed by Warburg, raises some fundamental questions. The roles of the drift current, in the absence of which the equilibrium is never reached in the dc case, and of the displacement current, which is important even in the low frequency region where the Warburg's impedance appears, are discussed. Finally, the utility of models based on equivalent electric circuits, ladder networks, or transmission lines in the analysis of impedance spectroscopy data is investigated.

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 to...

We have developed a mathematical model able to predict the dependence of the current density, j0, in the dc limit, on the thickness of a photoactive semiconductor layer, d, in contact with an electrolyte. The model considers the application of an external bias. The theoretical analysis has been done by means of a diffusive model, where the excess of charges moves by diffusion in the presence of a generation term, due to the incident light, and a recombination term, proportional to the excess of charge carriers. We show that a non-monotonic dependence of j0 vs. d is expected. For small d, the photocurrent density is proportional to d and the proportionality constant is related to both the attenuation of the light in the photoactive semiconductor layer and to the applied potential. In the opposite limit of large d, the current tends to a constant value that is dependent on both the light intensity and the applied bias. Our theoretical predictions are in qualitative agreement with the experimental data reported in literature for BiVO4 films. © 2017 Elsevier B.V.

We propose a model to interpret the concentration dependence of the ζ-potential of a suspension of silica nanoparticles of spherical shape in an electrolytic solution. The model is based on the numerical solution of Poisson-Boltzmann equation, in spherical geometry, taking into account the ionic adsorption from the nanoparticles. The kinetic equation used for the description is a generalization of the Langmuir's isotherm, modified to take into account the saturation of the adsorption phenomenon. A good agreement between the theoretical model and the experimental data is found. The model allows the determination of adsorption/desorption parameters of the nanoparticles.

From the elastic point of view, the twist-bend nematic phase, (NTB), has a ground state characterised by a spontaneous bend with a precession of the director n along the direction of an axis t. The...

We discuss the origin of Warburg's impedance in unsupported electrolytic cells containing only one group of positive and one group of negative ions. Our analysis is based on the Poisson-Nernst-Planck model, where the generation-recombination phenomenon is neglected. We show that to observe Warburg-like impedance the diffusion coefficient of the positive ions has to differ from that of the negative ones, and furthermore the electrodes have to be not blocking. We assume that the non-blocking properties of the electrodes can be described by means of an Ohmic model, where the charge exchange between the cell and the external circuit is described by means of an electrode conductivity. For simplicity we consider a symmetric cell. However, our analysis can be easily generalized to more complicated situations, where the cell is not symmetric and the charge exchange is described by the Chang-Jaffe model, or by a linearized version of the Butler-Volmer equation. Our analysis allows justification of the expression for Warburg's impedance proposed previously by several groups, based on wrong assumptions.

We investigate the role of the displacement current in the analysis of the electric response of an electrolytic cell to an external stimulus. We show that several models proposed to interpret the spectra deduced by means of the impedance spectroscopy technique are questionable. In particular, we demonstrate that even in the frequency range below the Debye frequency the role of the displacement current is fundamental, and its omission leads to incorrect results for the impedance of the cell. In our analysis, the boundary conditions on the bulk current density are of Nernstian and of Ohmic type. The analysis is limited to a fully dissociated electrolyte, and for only one type of mobile ions, as discussed in several papers devoted to the subject. Particular attention is given to the spatial dependence of the current density. We show that Warburg-like behavior is never predicted in the framework of the Poisson-Nernst-Planck model, if the electric impedance of the cell is correctly evaluated. From this conclusion, valid for media with only one type of mobile ions, it follows that if Warburg-like behavior is experimentally observed the theoretical interpretation is still an open problem, and its origin is probably related to the 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.

We evaluate the effect of ions on the electric response of an insulting liquid by means of the total electric polarization induced in a cell by an external field. The limiting surfaces are assumed blocking and identical and the ions pointike nonpolarizable charged particles. The analysis is limited to the case where the selective ionic adsorption is absent, in such a manner that in the absence of external electric field the sample is locally and globally neutral. We obtain formulas for the effective dielectric constant renormalized by the presence of the ions in the absence and presence of adsorption from the surfaces. Our results coincide with those obtained by means of the electric impedance of the cell. From the coincidence of the results relevant to the effective dielectric constant we infer that the ions in an insulating liquid do not have a conductive or dielectric nature. They are just electric charges dissolved in an insulating liquid.

We report on the temperature dependence of the Milli-Q water cell response, limited by surgical steel electrodes, to an external periodic excitation. Using the Electrochemical Impedance Spectroscopy technique (EIS), the spectra of the real and imaginary parts of the electrical impedance of the cell are experimentally obtained. Important deviations from the theoretical predictions of the Poisson–Nernst–Planck model, assuming blocking electrodes, are observed. Our experimental results indicate that the properties of the electrodes play an important role in the low frequency part of the spectra. In the absence of a simple physically based theoretical model, we fit our data utilizing three equivalent electric circuits containing a constant phase element (CPE) charged to describe the properties of the electrodes. From our analysis it follows that a “good” equivalent electric circuit for the analysis of the response of an electrolytic cell to an external periodic voltage is formed by a parallel of a bulk capacitance and resistance of ionic origin. The CPE is then charged to mimic the interface effects. From a mathematical point of view this is equivalent to assume that the phenomenological parameters describing the non-ideal blocking properties of the electrode, in the Chang-Jaffe, Ohmic or Langmuir models, are frequency dependent.

The effective electric charge of a nanoparticle in an ionic magnetic colloidal system (an ionic ferrofluid) is determined by using the impedance spectroscopy technique. The electric response of the samples to a harmonic external electric field excitation is described by means of the Poisson-Nernst-Planck model. The model proposed for the theoretical interpretation of the impedance spectroscopy data considers that the magnetic particles are electrically charged with H+ and have in their vicinity Cl− counterions, resulting in an effective charge Qeff. In the presence of an harmonic, in time, external field (frequency bigger than 104Hz) particles are assumed to be at rest, due to inertial reason. In this framework, the response of the cell is due to the H+ and Cl− present in the solution. From the spectra of the real and imaginary components of the electric impedance of the cell, by means of a best fit procedure to our model, we derive the effective electric charge of the magnetic particles and the bulk dens...

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.

A Poisson–Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities exhibit the bell-like and the camel-like shapes as a function of the applied voltage, when the thickness of the sample or the surface charge is varied. The problem is formulated in such a way that an applied voltage dependent Debyeʼs screening length arises as a fundamental length governing the electrical behavior of the system.

We investigate the pitch transitions induced by an external bulk field in a Cholesteric Liquid Crystal slab of finite thickness ℓ that contains an incomplete number of π-twists. The analysis is performed for a magnetic field that is (i) perpendicular to the helical axis, and (ii) tilted with respect to one of the easy directions imposed by planar and rigid boundary conditions. For finite ℓ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time with increasing field to avoid divergences in the elastic energy. The dependence of the threshold magnetic field inducing the expulsion on the easy axes twist angle δ is investigated for all the cascade of pitch transitions and in particular for the final one, corresponding to the Cholesteric-Nematic transition. In the ℓ → ∞ limit this dependence disappears and we reobtain the results of de Gennes for an infinite sample.

The role of the electrodes on the electrical response of a medium containing ions is investigated. The analysis is performed in the linear limit, where the variation of the bulk density of ions due to the presence of the external field is negligible with respect to the ionic bulk density in thermodynamical equilibrium. The case of fully dissociated impurities is considered. The non-ideal character of the electrodes is described by means of a linear dependence of the density of ionic current on the surface electric field, similar to the law of Ohm valid for metallic conductors. In this framework, it is shown that in the low frequency region, the electrical response of the medium strongly depends on the electrical properties of the interface electrode-medium. On the contrary, in the high frequency region, it is independent of the nature of the electrodes. Approximated formulae in the limit of small and large frequency are reported for the real and imaginary parts of the impedance and of the admittance. The peculiar frequencies of the spectra, related to the maxima and minima of the imaginary parts of the impedance and of the admittance, are determined. The importance of the reported theoretical results on the experimental characterization of liquid media is discussed.

Two empirical, but plausible, previously published independent generalizations of the standard Poisson−Nernst−Planck (PNP) continuum diffusion model for mobile-charge conduction in liquids and solids are discussed, their responses are compared, and their physical appropriateness and usefulness for data fitting are investigated. They both involve anomalous diffusion of PNPA type with power-law frequency-response elements involving fractional exponents. Both models apply to finite-length regions of material between completely blocking electrodes and, for simplicity, deal primarily with positive and negative charge carriers of equal valence numbers and mobilities. The charge carriers may be either ionic or electronic. The first PNPA model, model A, involves the common separation of the expression for ordinary PNP impedance into an interface diffusion part and a high-frequency limiting conductance and capacitance, followed by the replacement of all normal diffusion elements in the former by anomalous ones. It...

The effect of composition on the dielectric properties of hydrogels for biomedical applications is experimentally investigated. The hydrogels, containing hydroxyethylcellulose (HEC), are characterized by means of the impedance spectroscopy technique. The real and imaginary parts of the electrical impedance of the hydrogels are determined for several concentrations of HEC, and of KCl, dissolved in it, for the frequency range of interest for biomedical applications. The results are compared with those corresponding to depurated water. The equivalent conductivity of the hydrogels is evaluated by performing measurements on samples of different thicknesses. With the limit of a small concentration of salt (≤ 6%), the dependence of the electrical conductivity of the hydrogel on the salt concentration is linear.

We propose a simple model to investigate the rheological properties of a nematic cell oriented in a planar manner. The storage and loss modulus are evaluated in the case of strong and weak anchoring conditions. The contribution of the surface viscosity to the rheological parameters is also considered.

We analyze the influence of the surface viscosity on the relaxation of the nematic deformation induced by an external field on a nematic cell, when the distorting field is removed. The analysis is performed by assuming that the anchoring energy describing the anisotropic part of the nematic–substrate surface tension can be approximated by the form proposed by Rapini and Papoular, and that the viscous torque at the surface is characterized by a surface viscosity η s . We consider a simple situation where by means of an external action the surface easy direction is modified, and investigate the evolution of the nematic orientation, from the initial state to the final one. The Green function approach is used to obtain the exact solution for the tilt angle profile. The results show that the surface viscosity modifies the relaxation process which becomes slower for increasing values of η s .

A method for a continuous control of the pretilt angle of the easy axis in the range 0-90° degrees and of the anchoring strength by using nanostructured polymers as alignment layers is described. The nanostructured polymers are blends of two different side-chain polymers each of them promoting planar and homeotropic alignment, respectively. A model to interpret the alignment of a nematic liquid crystal induced by such polymer layers is proposed. We show that in this case the anisotropic part of the surface tension can be approximated by a simple extension of the Rapini-Papoular expression. The predicted trend of the pretilt of the easy axis versus the concentration of the side-chain polymer promoting the planar alignment, for instance, is in good agreement with the experimental data. We also show that the effective anchoring strength of the system depends on the concentration of the side-chain polymer promoting planar alignment, and exhibits a minimum for a well-defined value of this quantity. The results obtained in this work seems to be of importance for liquid crystal displays technology since the control of the pretilt and the anchoring strength strongly affect the performance of liquid crystal displays.

The influence of the ions on the electrochemical impedance of a cell is calculated in the framework of a complete model in which the fractional drift-diffusion problem is analytically solved. The resulting distribution of the electric field inside the sample is determined by solving Poisson's equation. The theoretical model to determine the electrical impedance we are proposing here is based on the fractional derivative of distributed order on the diffusion equation. We argue that this is the more convenient and physically significant approach to account for the enormous variety of the diffusive regimes in a real cell. The frequency dependence of the real and imaginary parts of the impedance are shown to be very similar to the ones experimentally obtained in a large variety of electrolytic samples.

A simple description of the electrode potential based on the selective ionic adsorption is proposed. It is shown that if the adsorption–desorption coefficients entering in the Langmuir kinetic equation for the adsorption at the limiting surfaces are not identical, a difference of potential between the electrode and the bulk of the solution exists. In the case where the thickness of the sample is large with respect to the length of Debye, this difference of potential depends only on the adsorption–desorption coefficients and on the length of Debye of the ionic solution.

We analyze the dielectric properties of the liquid crystal M5 used to investigate the electrohydrodynamics instability in nematic liquid crystals. We show that the spectra of the electrical impedance of doped samples of M5 with several concentrations of salt and of acid can be interpreted by assuming the doped liquid crystal as a dispersion of ions in a dielectric liquid. The analysis has been performed by considering the electrodes as blocking. From the best fit of the experimental data relevant to the real and imaginary parts of the electrical impedance of the cells, we derive the diffusion coefficients for the positive and negative ions and their bulk density. According to our analysis, in the limit of small concentrations of doping substance, the effective dielectric constant of the resulting liquid is, practically, independent of the doping.

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

We evaluate the relaxation times for an electrolytic cell subject to a step-like external voltage, in the case in which the mobility of negative ions is different from that of positive ions. The electrodes of the cell, in the shape of a slab, are supposed to be perfectly blocking. The theoretical analysis is performed by assuming that the applied voltage is so small that the fundamental equations of the problem can be linearized. In this framework, the eigenvalues equations defining all relaxation times of the problem are deduced. In the numerical analysis, we solve the complete set of equations describing the time evolution of the system under the action of the external voltage. Two relaxation processes, connected with the ambipolar and free diffusion phenomena, are sufficient to describe the dynamics of the system, when the diffusion coefficients are of the same order of magnitude.

The adsorption–desorption phenomenon is investigated with the help of a modified kinetic equation at the interface fluid-substrate. This equation incorporates memory effects in the process by means of three different kernels, whose importance is associated to the predominance of chemisorption or physisorption in the adsorption–desorption processes. The time evolution of the density of adsorbed particles is exactly calculated. The results are shown to be relevant for adsorption phenomenon in general and, in particular, for the phenomenon of adsorption with oscillation, for which a comparison with the experimental data from adsorption of organosilane on oxides surfaces reveals a good agreement.