M. L. Jiménez

Predictions of the maximum energy extracted from salinity exchange inside porous electrodes

Capacitive energy extraction based on double layer expansion (CDLE) is the name of a new method devised for extracting energy from the exchange of fresh and salty water in porous electrodes. It is based on the change of the capacitance of electrical double layers (EDLs) at the electrode/solution interface when the concentration of the bulk electrolyte solution is modified. The use of porous electrodes provides huge amounts of surface area, but given the typically small pore size, the curvature of the interface and EDL overlap should affect the final result. This is the first aspect dealt with in this contribution: we envisage the electrode as a swarm of spherical particles, and from the knowledge of their EDL structure, we evaluate the stored charge, the differential capacitance and the extracted energy per CDLE cycle. In all cases, different pore radii and particle sizes and possible EDL overlap are taken into account. The second aspect is the consideration of finite ion size instead of the usual point-like ion model: given the size of the pores and the relatively high potentials that can be applied to the electrode, excluded volume effects can have a significant role. We find an extremely strong effect: the double layer capacitance is maximum for a certain value of the surface potential. This is a consequence of the limited ionic concentration at the particle-solution interface imposed by the finite size of ions, and leads to the presence of two potential ranges: for low electric potentials the capacitance increases with the ionic strength, while for large potentials we find the opposite trend. The consequences of these facts on the possibility of net energy extraction from porous electrodes, upon changing the solution in contact with them, are evaluated.

Multi-ionic effects on energy production based on double layer expansion by salinity exchange.

It has been recently shown that the free energy change upon salinity mixing in river mouths can be harvested taking advantage of the fact that the capacitance of charged solid/liquid interfaces (electrical double layers, EDLs) depends strongly on the ionic composition of the liquid medium. This has led to a new generation of techniques called Capmix technologies, one of them (CDLE or capacitive energy extraction based on DL expansion) based precisely on such dependence. Despite the solution composition playing a crucial role on the whole process, most of the research carried out so far has mainly focused on pure sodium chloride solutions. However, the effect of other species usually present in river and seawaters should be considered both theoretically and experimentally in order to succeed in optimizing a future device. In this paper, we analyse solutions of a more realistic composition from two points of view. Firstly, we find both experimentally and theoretically that the presence of ions other than sodium and chloride, even at low concentrations, may lead to a lower energy extraction in the process. Secondly, we experimentally consider the possible effects of other materials usually dispersed in natural water (mineral particles, microbes, shells, pollutants) by checking their accumulation in the carbon films used, after being exposed for a long period to natural sea water during CDLE cycles.

Electric permittivity of concentrated suspensions of elongated goethite particles

This paper describes an investigation on the electric permittivity of concentrated suspensions of non-spherical particles, specifically prolate spheroids. It is first discussed how the determination of the frequency (omega) dependence of the electric permittivity (a phenomenon traditionally known as LFDD or low-frequency dielectric dispersion) can provide ample information on the properties of the dispersed material (shape, size, state of aggregation, conductivity) and of its interface with the (typically aqueous) medium. The basic quantities are the strength and frequency dependence of the dipole moment induced by the applied field, and its dimensionless counterpart, the dipole coefficient, C(*)(omega). It is explicitly shown how the (complex) relative permittivity of the suspension, epsilon(r)(*)(omega), can be calculated from it. Two theoretical models on the polarizability of spheroidal colloidal particles will be used as theoretical starting point; one of them (Model I) explicitly considers two relaxations of the permittivity, each associated to one of the particle axes. The other (Model II) is a semi-analytical theory that yields an LFDD practically independent of the axial ratio of the particles. Both models are aimed to be used if the suspensions are dilute (low volume fraction of solids, phi), and here they are generalized to concentrated systems by means of a previously published approximate evaluation of the permittivity of concentrated suspensions. Experiments are performed in the 1 kHz-1 MHz frequency range on suspensions of elongated goethite particles; the effects of ionic strength, pH, and volume fraction are investigated, and the two models are fitted to the data. In reality, taking into account that the particles are non-uniformly charged (a fact that contributes to their instability), two zeta potentials (roughly representing the lateral surface and the tip of the spheroid) are used as parameters. The results indicate that, when experimental conditions are optimal (high ionic strength and low zeta potential), the suspensions do indeed display two relaxations, that we ascribe to the long axis (and to flocs likely present in suspension) and to the short one. The permittivity increases with ionic strength, a result found with other systems, and compatible with a zeta potential that, on the average, decreases with ionic strength, an equally well known result, consequence of electric double layer compression. Another reasonable finding is the increase of estimated average dimensions and the decrease of electrokinetic potentials when the pH is close to the isoelectric point of goethite (around pH 9). The increase in volume fraction, finally, produces an overall increase in the permittivity, and the approximate model used for the evaluation of volume fraction variations can describe properly these effects, with basically constant zeta potentials and dimensions.

Dielectric response of a concentrated colloidal suspension in a salt-free medium.

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.

Giant permittivity and dynamic mobility observed for spherical polyelectrolyte brushes

We present a study of the electrodynamic behavior of concentrated suspensions of spherical polyelectrolyte brushes (SPBs). The dynamic mobility of the SPBs exhibits giant values. Concomitantly, the dielectric spectra of suspensions of these particles display enormous loss peaks in the kHz frequency range. The strong dielectric relaxation is a direct consequence of the inhomogeneity of the counterion distribution inside the polyelectrolyte layer. As can be concluded from the experimentally determined relaxation frequency, the mobility of monovalent counterions is strongly diminished in the brush region. The dynamic behavior of the SPBs at high volume fractions can be explained by the assumption that the polyelectrolyte chains deform when particles approach each other.

Geometrical properties of materials for energy production by salinity exchange

Environmental context Oceans and seas have the potential to play a significant role in providing renewable and clean energy. In particular, salinity difference energy aims to extract the enormous amount of energy that is released when fresh water rivers flow into the oceans. Capmix methods are focused on this challenge by using capacitive carbon electrodes whose optimisation will certainly help in developing salinity difference energy. Abstract One of the most powerful marine renewable resources is salinity difference energy, also termed blue energy. Numerous techniques have been investigated to harvest this energy but, recently, the capmix proposal has increased in importance due to its easy implementation and use of low cost materials, very often activated carbon. Two methods based on this principle are tested in this work, namely CDLE (energy production by double layer expansion in bare electrodes) and SE (the electrodes are made ‘soft’ by polyelectrolyte coating). The characteristics of the carbon materials play a central role in capmix energy production. In this work, we focus on understanding the required pore structure that might be demanded from carbon samples. The balance between micro- and mesopores, the wettability of the material and its electrical resistance are explored by using hierarchical carbons, and their combination with graphene oxide and carbon nanotubes. It is found that the CDLE technique requires a large fraction of mesopores for easy solution exchange, while SE performance improves with a large amount of micropores. The addition of carbon nanotubes to the activated carbon reduces the capmix cycle duration, increasing the extracted power. In the case of electrodes containing graphene the internal resistance decreases, but the hydrophobicity of graphene oxide works against the improvement in energy extraction.

Dynamic electrophoretic mobility and electric permittivity of concentrated suspensions of plate-like gibbsite particles

In this paper we present experimental results on the electrokinetic behavior of planar gibbsite particles in concentrated suspensions. The dc electrophoretic mobility measurements are in this case of little significance, as they are scarcely informative. In the present investigation, we show that the dielectric dispersion and dynamic electrophoresis can in contrast provide such information. The complicating factors are of course the non-spherical shape and the finite particle concentration, as no complete theory of these phenomena exists for such systems. We propose to use first of all a model of dynamic electrophoresis of spheroids in which the effect of volume fraction is considered by means of an approximate theory previously obtained for spheres, based on the evaluation of electrical and hydrodynamic interactions between particles. In addition, the role of volume fraction on the high frequency inertial relaxation is also ascertained and used to obtain a volume fraction-independent radius of the gibbsite spheroids. A similar approach is used for the evaluation of dielectric dispersion data. Both the dynamic mobility and dielectric constant dependencies on frequency were obtained for gibbsite suspensions of different volume fractions in 0.5mMKCl. The theoretical treatments elaborated were applied to these data, and a coherent picture of the geometrical and electrical characteristics of the particles was obtained.