Theory of membrane capacitive deionization including the effect of the electrode pore space

Membrane capacitive deionization (MCDI) is a technology for water desalination based on applying an electrical field between two oppositely placed porous electrodes. Ions are removed from the water flowing through a channel in between the electrodes and are stored inside the electrodes. Ion-exchange membranes are placed in front of the electrodes allowing for counterion transfer from the channel into the electrode, while retaining the coions inside the electrode structure. We set up an extended theory for MCDI which includes in the description for the porous electrodes not only the electrostatic double layers (EDLs) formed inside the porous (carbon) particles, but also incorporates the role of the transport pathways in the electrode, i.e., the interparticle pore space. Because in MCDI the coions are inhibited from leaving the electrode region, the interparticle porosity becomes available as a reservoir to store salt, thereby increasing the total salt storage capacity of the porous electrode. A second advantage of MCDI is that during ion desorption (ion release) the voltage can be reversed. In that case the interparticle porosity can be depleted of counterions, thereby increasing the salt uptake capacity and rate in the next cycle. In this work, we compare both experimentally and theoretically adsorption/desorption cycles of MCDI for desorption at zero voltage as well as for reversed voltage, and compare with results for CDI. To describe the EDL-structure a novel modified Donnan model is proposed valid for small pores relative to the Debye length

The sediment of mixtures of charged colloids: segregation and inhomogeneous electric fields

We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydisperse mixtures of colloidal particles with different buoyant masses and/or charges. We focus on the low-salt regime, where the entropy of the screening ions drives spontaneous charge separation and the formation of an inhomogeneous macroscopic electric field. The resulting electric force lifts the colloids against gravity, yielding highly nonbarometric and even nonmonotonic colloidal density profiles. The most profound effect is the phenomenon of segregation into layers of colloids with equal mass-per-charge, including the possibility that heavy colloidal species float onto lighter ones

Non-Gaussian curvature distribution of actin-propelled biomimetric colloid trajectories

We analyze the motion of colloids propelled by a comet-like tail of polymerizing actin filaments. The curvature of the particle trajectories deviates strongly from a Gaussian distribution, implying that the underlying microscopic processes are fluctuating in a non-independent manner. Trajectories for beads of different size all showed the same non-Gaussian behavior, while the mean curvature decreased weakly with size. A stochastic simulation that includes nucleation, force-dependent dissociation, growth, and capping of filaments, shows that the non-Gaussian curvature distribution can be explained by a positive feedback mechanism in which attached chains under higher tension are more likely to sna

Review on the science and technology of water desalination by capacitive deionization

Porous carbon electrodes have significant potential for energy-efficient water desalination using a promising technology called Capacitive Deionization (CDI). In CDI, salt ions are removed from brackish water upon applying an electrical voltage difference between two porous electrodes, in which the ions will be temporarily immobilized. These electrodes are made of porous carbons optimized for salt storage capacity and ion and electron transport. We review the science and technology of CDI and describe the range of possible electrode materials and the various approaches to the testing of materials and devices. We summarize the range of options for CDI-designs and possible operational modes, and describe the various theoretical–conceptual approaches to understand the phenomenon of CDI

Sedimentation of binary mixtures of like- and oppositely charged colloids: the primitive model or effective pair potentials?

We study sedimentation equilibrium of low-salt suspensions of binary mixtures of charged colloids, both by Monte Carlo simulations of an effective colloids-only system and by Poisson-Boltzmann theory of a colloid-ion mixture. We show that the theoretically predicted lifting and layering effect, which involves the entropy of the screening ions and a spontaneous macroscopic electric field [J. Zwanikken and R. van Roij, Europhys. Lett. {\bf 71}, 480 (2005)], can also be understood on the basis of an effective colloid-only system with pairwise screened-Coulomb interactions. We consider, by theory and by simulation, both repelling like-charged colloids and attracting oppositely charged colloids, and we find a re-entrant lifting and layering phenomenon when the charge ratio of the colloids varies from large positive through zero to large negative values

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) In the "super-capacitor regime" of small voltages and/or early times where the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore. (ii) In the "desalination regime" of large voltages and long times, the porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration

Diffuse charge and Faradaic reactions in porous electrodes

Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage