The Kinetics of Sorption-Desorption Phenomena: Local and Non-Local Kinetic Equations.

The kinetics of adsorption phenomena are investigated in terms of local and non-local kinetic equations of the Langmuir type. The sample is assumed in the shape of a slab, limited by two homogeneous planar-parallel surfaces, in such a manner that the problem can be considered one-dimensional. The local kinetic equations in time are analyzed when both saturation and non-saturation regimes are considered. These effects result from an extra dependence of the adsorption coefficient on the density of adsorbed particles, which implies the consideration of nonlinear balance equations. Non-local kinetic equations, arising from the existence of a time delay characterizing a type of reaction occurring between a bulk particle and the surface, are analyzed and show the existence of adsorption effects accompanied by temporal oscillations.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

On the equivalence between specific adsorption and kinetic equation descriptions of the admittance response in electrolytic cells.

The response of an electrolytic cell, in the shape of a slab, is analyzed in the framework of the Poisson-Nernst-Planck model in the limit of full dissociation. Two different types of boundary conditions on the electrodes are compared. One type describes the exchange of charges between the volume and the external circuit, in the form originally proposed by Chang and Jaffé and later extended to include specific adsorption, where the surface current density is proportional to the variation of the surface bulk density of ions with respect to the value of equilibrium. The other one describes the surface adsorption, in the limit of Langmuir. We show that in the simple case where the ions dissolved in the insulating liquid are identical in all the aspects, except for the sign of the charge, the two models are equivalent only if the phenomenological parameter entering the boundary condition of the Chang-Jaffé model, κ, is frequency dependent, and related to the adsorption coefficient, k(a), in the form κ = iωτ/(1 + iωτ)k(a), where τ is the desorption time and ω the circular frequency of the applied voltage, as proposed long ago by Macdonald.

Electric impedance of a sample of dielectric liquid containing two groups of ions limited by ohmic electrodes: a study with pure water.

We present a generalization of the Poisson-Nernst-Planck model for a dielectric liquid containing two groups of ions limited by Ohmic electrodes. The theoretical results are used to interpret experimental results of impedance spectroscopy of pure water limited by electrodes of different metallic materials. The agreement between theoretical predictions of the presented model and experimental data obtained with pure water is rather good for all types of electrodes.

Cholesteric-nematic transition induced by a magnetic field in the strong-anchoring model.

We investigate the cholesteric-nematic transition induced by an external bulk field in a sample of finite thickness ℓ. The analysis is performed by considering a tilted magnetic field with respect to the easy direction imposed by rigid boundary conditions inducing planar orientation. In the case of parallel orientation between the magnetic field and of the easy direction, in the limit of ℓ→∞ we reobtain the results of de Gennes where the effective pitch of the cholesteric is a continuous function of the magnetic field diverging at the critical field related to the cholesteric-nematic transition. For finite ℓ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time to avoid divergences in the elastic energy, in a similar manner as solids expel defects in the presence of strong deformation. In the case of oblique orientation between the magnetic field and the easy direction, only the completely untwisted state depends on the tilt angle. Therefore, only the cholesteric-nematic transition depends on the tilt angle while all the other magnetic transition values are unchanged.

Relaxation of the nematic deformation when the distorting field is removed.

We investigate the relaxation of the nematic deformation when the distorting field is switched off. We show that the usual analysis based on the diffusionlike equation does not allow a complete description of the phenomenon because it does not permit one to satisfy the initial boundary condition, at t=0 , on the first time derivative of the nematic tilt angle. An alternative approach to the problem, taking into account the inertial properties of the nematic molecules, allows one to satisfy the initial boundary conditions on the first-order time derivative of the tilt angle. In this framework the dynamical evolution of the nematic deformation, in the initial time, depends on the inertial properties of the nematic molecules. However, the typical relaxation time is so short that, for all practical effects, the first time derivative of the tilt angle is discontinuous at t=0 . A more realistic description involves the switching time of the distorting field. In this framework, the initial boundary condition of the first-order derivative is automatically satisfied. Our analysis shows that the description based on the diffusion equation works well when the switching time is very small with respect to the diffusion time.

Continuum description of the interfacial layer of nematic liquid crystals in contact with solid surfaces.

We investigate when it is possible to introduce surface physical parameters characterizing the nematic/substrate interface. The analysis is performed by solving the problem assuming that the presence of the surface introduces a spatial variation, mainly localized close to the limiting surfaces, of the bulk properties of the nematic (delocalized model). The results of the calculation are compared to the prediction of a model in which the presence of the surface is taken into account by means of new physical parameters, localized to the surface (localized model). We show that if the viscous dissipative effects or the surface alignment effects are considered, the two models predict the same relaxation times and the same threshold for the Freedericksz transition is obtained. From these results we deduce that the localized models are equivalent to the delocalized ones. A continuum description of the interfacial layer of nematic liquid crystals in contact with solid surface in terms of surface properties is then correct, which makes the solution of this kind of problems simpler. Also a softening of the elastic constants near the surfaces can be represented by a localized surface energy term.

Nonmonotonic behavior of the nematic tilt angle in a temperature-induced surface transition.

We report on a nonmonotonic temperature behavior of the pretilt in cells containing polymers as alignment layers. The latter are very promising since they enable control of the anchoring of the liquid crystal. We show that such a behavior cannot be interpreted by the standard Landau or mean-field theory. We propose a generalization of the mean-field model, including the temperature dependence of the anchoring due to the polymer layer that enables a description of the nonlinear behavior. The agreement between the predictions of the model and the experimental data is good.

Role of the adsorption phenomenon on the ionic equilibrium distribution and on the transient effects in electrolytic cells.

We analyze the influence of the adsorption of ions at the interfaces on the transient phenomena occurring in an electrolytic cell submitted to a steplike external voltage. In the limit of small amplitude of the applied voltage, where the equation of the problem can be linearized, we obtain an analytical solution for the bulk and surface densities of ions and for the electrical potential. We also obtain, in this limit, the relaxation time for the transient phenomena.

Statistical theory of the compensating effect when anchoring with two orthogonal photoaligned polymers.

In this paper we extend a statistical microscopic analysis to the anchoring properties of polymer films obtained by two concomitant or subsequent polymerization processes along two different directions. We can thus explain the recently observed compensating effect of two orthogonal polymerization processes. An expression for the anchoring energy has been evaluated from the extra Helmholtz free energy within an interface layer where the interactions shift from polymer-nematic interactions to nematic-nematic interactions, as in bulk. The result includes the angular dependence on the two photoaligning directions. A procedure of getting controlled anchoring strength in situ is suggested.