Julio Pellicer

The physical description of elementary surface phenomena: Thermodynamics versus mechanics

A unified treatment of elementary surface phenomena based on the formalism of thermodynamics is presented and compared to more familiar treatments based on the formalism of Newtonian mechanics. Emphasis is put on the surface free energy concept rather than on surface tension, not only because the former is more fundamental, but also because the latter may mislead if pushed too far. The examples discussed (Young–Laplace and Young–Dupre equations, and capillary rise) can be easily described with the help of the Helmholtz function, and clearly show some of the advantages of the thermodynamic approach. In particular, several misleading results appearing in elementary treatments can be avoided by using this approach. It is concluded that: (i) thermodynamics and physical chemistry courses should favor the formalism of thermodynamics rather than mechanics when dealing with surface phenomena; and (ii) when the mechanical approach is still preferred, some weak points in the standard derivations (e.g., the existenc...

On the demonstration of the Young-Laplace equation in introductory physics courses

The Young-Laplace equation is usually introduced using mechanical rather than thermodynamic arguments when teaching surface phenomena at an elementary level. We discuss here three mechanical methods to deduce this equation, with the intention of avoiding certain misunderstandings that are found in these derivations, thus providing the correct demonstrations of the equation.

Membrane potential of bipolar membranes

Abstract The membrane potential of a bipolar membrane composed of a cation-exchange layer in series with an anion-exchange layer is analyzed theoretically and experimentally. The theoretical approach is based on an extension of the Nernst-Planck equations of monopolar charged membranes to the case of the two ion-exchange layers in series and the diffusion boundary layers adjacent to the bipolar membrane. The experimental results concern the transient behavior, stirring effects and concentration dependence of the membrane potential, and can be explained by means of the above theoretical approach. It is shown that membrane potential measurements can contribute significantly to a better electrochemical characterization of bipolar membranes.

Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space

We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann–Gibbs standard thermostatistics while, in the latter, Tsallis thermostatistics is straightforwardly obtained as the most appropriate formalism. We first focus on the microcanonical ensemble stressing the importance of the limit t→∞ on the form of the microcanonical measure. Interestingly, this approach leads to interpret the entropic index q as the box-counting dimension of the (microcanonical) phase space when fractality is considered.

Current-voltage curves for ion-exchange membranes. Contributions to the total potential drop

Abstract The effect of concentration polarization on the current-voltage (I-V) curves for ion-exchange membranes has been studied theoretically. Firstly, some of the hypotheses found in the literature concerning this field are reviewed. Secondly, we calculate numerically the different contributions to the total potential drop and assess the role of the local electroneutrality condition and the electroosmotic flow and coion flux on the I-V curves. Under the Nernst-Planck/Poisson/Donnan formalism and the conditions assumed, plateau regions in the I-V curves are obtained, thus showing that other “side effects” (water splitting, particular hydrodynamic conditions in the depleted layer, etc.) are responsible for the S-shaped I-V curves reported for most ion-exchange membranes. The analysis carried out can be regarded as an extension of the previous study by Spiegler (Desalination, 9 (1971) 367).

pH and supporting electrolyte concentration effects on the passive transport of cationic and anionic drugs through fixed charge membranes

The effects of pH and supporting electrolyte concentration on the passive transport of an ionized (cationic or anionic) drug through a thick fixed charge membrane have been theoretically studied. This system constitutes a simplified model for the pH controlled ion transport and drug delivery through membranes of biological and pharmaceutical interest. Calculations were carried out for different values of the membrane fixed charge, supporting electrolyte and drug concentrations covering a broad range of the conditions usually found in experiments. The theoretical approach employed is based on the Nernst‐Planck flux equations, and all of the species present in the system (the neutral and ionized forms of the drug, the two supporting electrolyte ions and the hydrogen and hydroxide ions) have been taken into account without any additional assumption. It has been shown that the Goldman constant field assumption together with the total co-ion exclusion assumption provide good approximated solutions for high membrane fixed charge concentrations. The model predictions show that the internal pH within the membrane, the total drug flux and the membrane potential are very sensitive to the external pH values. Comparison of our results with available experimental data confirms the potential utility of the calculations for the analysis and design of experiments involving the pH dependent passive transport of ionized drugs through a fixed charge membrane, especially in the cases of thick biomembranes, biochemical sensors and pH-controlled drug delivery systems. # 1999 Elsevier Science B.V. All rights reserved.

The charge separation process in non-homogeneous electrolyte solutions

Abstract The charge separation process occurring in two different solutions of the same electrolyte brought into contact is studied using Poissons equation and the (simplified) equations of transport. The process is characterized on the basis of the change in observable physical magnitudes. The relevance of the “diffusional” and “electric” relaxations is analysed. The results obtained can be applied to problems of ionic transport across membranes and liquid junctions, and contribute to the study of the transport of charged matter during the time interval in which the “charge” plays a significant role. Although, unfortunately the time domain involved in the electric relaxation seems to be inaccessible to precise experimental measurement, the physical model provides a detailed description of the way charge separation takes place. The latter is consistent with experimental observations at “large times”. An equation for the current density has been obtained from the ionic transport equations and Poissons equation. By using the former, it has been shown that the classical treatment by Planck (commonly used for describing the diffusion potential in ionic transport through membranes) implies neglecting the whole charge separation process (assuming τ e = 0, where τ e is the electric relaxation time). The inconsistencies involved in this have been shown. Finally, the significance of the two terms “conduction” and “displacement” current) in the equation for the total current density is discussed. Both terms play an important role in ionic transport processes through totally or partially blocked interfaces.

Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations

Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.

On the experimental values of the water surface tension used in some textbooks

A thermodynamic study of one component liquid–vapor planar interfaces and the temperature dependence of some relevant thermodynamic quantities is presented. A critical review of data for the surface tension of water found in some textbooks is given. More accurate measurements show a qualitative change in the temperature dependence of the surface tension, from the almost linear dependence of the old data to nonlinear behavior and the occurrence of an inflection point in the more accurate, more recent data.

A finite-difference method for numerical solution of the steady-state Nernst-Planck equations with non-zero convection and electric current density

Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the ternary system NaClHClH2O.