J. Horno

Numerical study of colloidal suspensions of soft spherical particles using the network method. 1. DC electrophoretic mobility

The electrophoretic mobility of a spherical particle coated with a uniformly charged permeable membrane and suspended in a general electrolyte solution is calculated numerically. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as the membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of the ionic species, and electrolyte concentration. The theoretical model used is similar to the one presented by Ohshima (H. Ohshima, J. Colloid Interface Sci. 228 (2000) 190), except for the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle. This inclusion is theoretically proven in the limiting case of a nonconducting suspending medium, in which the equation system can be analytically solved. The results obtained coincide with existing analytical expressions when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high.

Poisson-Boltzmann description of the electrical double layer including ion size effects.

The electrical double layer is examined using a generalized Poisson-Boltzmann equation that takes into account the finite ion size by modeling the aqueous electrolyte solution as a suspension of polarizable insulating spheres in water. We find that this model greatly amplifies the steric effects predicted by the usual modified Poisson-Boltzmann equation, which imposes only a restriction on the ability of ions to approach one another. This amplification should allow for an interpretation of the experimental results using reasonable effective ionic radii (close to their well-known hydrated values).

Numerical study of colloidal suspensions of soft spherical particles using the network method: 2. AC electrokinetic and dielectric properties

The network simulation method is used to solve numerically the equation system that determines the dynamic electrophoretic mobility and the dielectric response of dilute suspensions of soft particles. This system was extensively studied theoretically by Ohshima (H. Ohshima, J. Colloid Interface Sci. 233 (2001) 142-152), who obtained analytical expressions for the static and dynamic electrophoretic mobility. However, the validity of his analytical result is restricted to relatively thick membranes with high drag coefficient and to relatively high electrolyte concentrations. As for the dielectric properties, there are only a few works dealing with particles without a core (ion exchange resins) and, to our knowledge, no numerical studies. Our theoretical model is basically similar to Ohshimas, except that we take into account the mechanical force acting on the surface of the core, which he neglects. The inclusion of this term is crucial when the general problem including arbitrary values of the parameters is analyzed. However, it has little bearing when the membrane is thick and the drag coefficient is high, so that our results for the electrophoretic mobility generally confirm Ohshimas equation when all the required conditions are met.

Digital simulation of electrochemical processes by the network approach

Abstract The network approach has been used to simulate chronoamperometric reaction schemes. In this method the spatial variable in the diffusion kinetic equations is discretized, but the time variable remains continuous. This allows the mathematical model to be described by a network model and its simulation can then be carried out by a suitable electric simulation routine without having to deal explicitly with the differential equations. Thus it is not necessary to consider either numerical or computational aspects. Moreover, this method is not limited by the complexity of the processes occurring in the system and we can solve problems of mathematical complexity by an efficient graphical method and at a moderate cost in computer time. Network models for reversible electron transfer and for the ECE mechanism at a planar electrode have been used to obtain currents and concentrations from numerical simulations by means of the computer program PSPICE. The accuracy of the network model and its digital simulation have also been considered.

Electrokinetic characterization of magnetite nanoparticles functionalized with amino acids

The synthesis of nanoparticles consisting of a magnetite core coated with one or more layers of amino acid (L-arginine, L-lysine, glycine, and L-glutamine) is described in this paper. For all the amino acids it is found that adsorption increases with concentration in solution in the range 0.5-10 mg/mL. The adsorption, however, differs substantially from one amino acid to another, depending on the length of the hydrocarbon chain and the polarity and charge of the side group. Thus, for given concentration and pH, adsorption is found to increase in the order L-arginine < L-lysine < L-glutamine < glycine. This order corresponds roughly to amino acids with decreasing chain length; in addition, the presence of the less polarizable guanidine group in the arginine molecule may explain why this amino acid is slightly less adsorbed than lysine. The pH dependence of the adsorption of each amino acid is reasonably explained considering the surface charge of magnetite and the charge of the amino acid molecules for different pHs, indicating a significant role of electrostatics in adsorption. This is further checked by means of determinations of the electrophoretic mobility of amino acid-coated magnetite as a function of pH: the results indicate a shift of the isoelectric point of the raw magnetite toward more basic pHs, an indication of adsorption of positive species, as confirmed by the tendency of the mobility of amino acid-coated magnetite toward more positive values below neutral pH. The electrophoretic mobility of coated particles was also measured as a function of the concentration of amino acid, and it was found that for low concentrations the four amino acids provoke charge inversion and overcharging of the magnetite surface at pH 6. Finally, the dependence of the electrophoretic mobility on the ionic strength indicated that from an electrophoretic point of view, the functionalized magnetite-amino acid particles do not behave as soft particles, and that the amino acid coating should be very compact.

Excluded volume effect on the electrophoretic mobility of colloidal particles.

In a recent work [J. Colloid Interface Sci. 316 (2007) 196] we studied the influence of the excluded volume effect on spatial distributions of ionic species and electrostatic potential in the neighborhood of a suspended spherical particle. It was shown that the excluded volume effect considerably increases the surface potential (for a given value of the particle charge) as compared to the case when ideal ion behavior is assumed. In the present work we extend our previous equilibrium results to the perturbed/nonequilibrium problem and analyze the effect of ion size constraints on the electrophoretic mobility of a rigid spherical particle immersed in a general electrolyte solution. We find that the electrophoretic mobility always increases with the excluded volume effect, which might broaden the range of experimental data that can be interpreted, including those cases where the measured mobility exceeded the theoretical maximum value predicted by the standard model.

Application of the network method to heat conduction processes with polynomial and potential-exponentially varying thermal properties

Nonlinear transient heat conduction in a finite slab with potential-exponential temperature-dependent specific heat and thermal conductivity is investigated numerically by using the network method. A general network model for this process is proposed, whatever the exponent of the temperature-dependent functions may be, including initial and boundary conditions. With this network model and using the electrical circuit simulation program PSPICE, time-dependent temperature and heat flux profiles at any location can be obtained. This approach allows us to solve this conduction problem by a general, efficient, and relatively simple method. To show the accuracy of the network method, a comparison is made of the present results and those obtained by other methods for a particular case.

Equilibrium electric double layer of charged spherical colloidal particles: effect of different distances of minimum ion approach to the particle surface.

A study of the equilibrium double layer surrounding charged spherical particles is presented, considering that ions in the suspending medium have a finite size. It is assumed that each ionic species has a different minimum approach distance to the particle surface, while the distance of minimum approach between ions in the bulk has the same value for all ion species. Numerical calculations made using the network simulation method and including all the features of the considered model are presented, together with rigorous analytical results valid for a flat interface and point ions in the bulk electrolyte solution. It is shown that the double-layer parameters are very sensitive to the difference between the minimum approach distances of co-ions and counterions. For negative particles and greater approach distances for co-ions than for counterions, the potential always increases with this difference and, under appropriate circumstances, attains positive values leading to charge reversal. This phenomenon is favored by a high electrolyte concentration, high counterion valences, and low surface charge (in modulus). An analytical expression relating these parameters to the threshold value of the difference between the minimum approach distances of co-ions and counterions to the particle surface is presented.

Computer simulation of a square scheme with reversible and irreversible charge transfer by the network method

Digital simulation of the square scheme in cyclic voltammetry has been carried out by the network method. A network model for this mechanism, with or without cross-reaction and with reversible or irreversible charge transfer, is proposed. Results obtained using uniform or quasi-uniform grids are compared with those obtained by other methods using exponential grids. It is shown that the network method is accurate and efficient over all kinetic domains of interest, without increases in CPU time, and it is not necessary to consider either numerical- or programming aspects. The influence of the second-order cross-reaction on the cyclic voltammograms has also been examined for reversible and irreversible charge transfers.

Electrokinetics of suspended charged particles taking into account the excluded volume effect

In two recent works [López-García et al., J. Colloid Interface Sci. 316 (2007) 196; López-García et al., J. Colloid Interface Sci. 323 (2008) 146] we presented a simple modification of the standard electrokinetic model that takes into account the finite size of ions in the electrolyte solution. In the first we presented numerical results for the equilibrium properties while, in the second, we calculated the effect of the excluded ion volume on the electrophoretic mobility. In the present work we first extend our previous results incorporating a distance of closest approach of the ions to the particle surface. We then calculate the conductivity increment and present a detailed interpretation of the mobility and conductivity increment results, based on the analysis of the equilibrium and field-induced ion concentrations and of the convective fluid flow in the neighborhood of the particle surface. We show that the inclusion of the ion size effect generally improves the predictions of the standard electrokinetic model: both the electrophoretic mobility and the conductivity increment increase. We also show that, largely due to the above-noted extension of considering a minimum approach distance between the ions and the particle surface, the excluded volume effect is not negligible even for weakly charged particles.