arXiv subjects

P. M. Biesheuvel

Publications and source records attributed to P. M. Biesheuvel.

36 records · Page 2Linked to original sources

arXiv2019

Electrostatic cooling in Ion-Exchange Membranes

In ion-exchange membrane processes, ions and water flow under the influence of gradients in hydrostatic pressure, ion chemical potential, and electrical potential (voltage), leading to solvent flow, ionic fluxes and ionic current. At the outer surfaces of the membranes, electrical double layers (EDLs) are formed (Donnan layers). When a current flows through the membrane, we argue that besides Joule heating in the bulk of the membrane and in the electrolyte outside the membrane, there is also electrostatic heating and cooling in the EDLs. In addition, when fluid flows through a charged membrane, at the outsides of the membrane there is pressure-related heating or cooling due to the osmotic and hydrostatic pressure differences across the EDLs.

physics.chem-ph↗

arXiv2018

Performance Metrics for the Objective Assessment of Capacitive Deionization Systems

In the growing field of capacitive deionization (CDI), a number of performance metrics have emerged to describe the desalination process. Unfortunately, the separation conditions under which these metrics are measured are often not specified, resulting in optimal performance at minimal removal. Here we outline a system of performance metrics and reporting conditions that resolves this issue. Our proposed system is based on volumetric energy consumption (Wh/m$^3$) and throughput productivity (L/h/m$^2$) reported for a specific average concentration reduction, water recovery, and feed salinity. To facilitate and rationalize comparisons between devices, materials, and operation modes, we propose a nominal standard testing condition of removing 5 mM from a 20 mM NaCl feed solution at 50% water recovery for CDI research. Using this separation, we compare the desalination performance of a flow-through electrode (fte-CDI) cell and a flow between membrane (fb-MCDI) device, showing how significantly different systems can be compared in terms of generally desirable desalination characteristics. In general, we find that performance analysis must be considered carefully so to not allow for ambiguous separation conditions or the maximization of one metric at the expense of another. Additionally, for context we discuss a number of important underlying performance indicators and cell characteristics that are not performance measures in and of themselves but can be examined to better understand differences in performance.

physics.chem-ph↗

arXiv2018

AC-Driven Electro-Osmotic Flow in Charged Nanopores

In this paper we report the theory describing the electro-osmotic flow in charged nanopores with constant radius and charge density driven by alternating current. We solve the ion and solution transport in unsteady conditions as described by the Navier-Stokes and Nernst-Planck equations considering the electrical potential inside the charged nanopore uniform in the radial direction (Uniform Potential model approximation). We derive the transport equation system in the case in which the pore is connected to two boundary diffusion layers and the cations and anions have different diffusion coefficients. This approach allows the theoretical description of the characteristic frequency dependence of the phase shift between the applied current density and the electro-osmotic flow. Additionally we show how the analysis of the dynamic response of the electro-osmotic coupling factor versus the AC frequency allows us to quantify the apparent ion diffusion coefficient in membranes. Notably, the frequency window where the phase-shift is predicted is well inside the commonly used sampling rate for electro-osmotic flow experiments $f\in\left[10^{-4},10^1\right]$ Hz, hence the proposed method can be useful to determine the apparent diffusion coefficient of ions (such as redox complex for flow batteries) in charged membranes.

physics.chem-ph↗

arXiv2017

Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access --for the first time-- to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models.

physics.chem-ph↗

arXiv2017

Capacitive Deionization -- defining a class of desalination technologies

Over the past decade, capacitive deionization (CDI) has realized a surge in attention in the field of water desalination and can now be considered as an important technology class, along with reverse osmosis and electrodialysis. While many of the recently developed technologies no longer use a mechanism that follows the strict definition of the term "capacitive", these methods nevertheless share many common elements that encourage treating them with similar metrics and analyses. Specifically, they all involve electrically driven removal of ions from a feed stream, storage in an electrode (i.e., ion electrosorption) and release, in charge/discharge cycles. Grouping all these methods in the technology class of CDI makes it possible to treat evolving new technologies in standardized terms and compare them to other technologies in the same class.

physics.app-ph↗

arXiv2017

Theory of ion and water transport in reverse osmosis membranes

We present theory for ion and water transport through reverse osmosis membranes based on a Maxwell-Stefan framework combined with hydrodynamic theory for the reduced motion of particles in thin pores. We include all driving forces and frictions both on the fluid (water), and on the ions, including ion-fluid friction as well as ion-wall friction. By including the acid-base character of the carbonic acid system, the boric acid system, H$_3$O$^+$/OH$^-$, and the membrane charge, we locally determine pH and thus the effective charge of the membrane as well as the dissociation degree of boric acid. We present calculation results for a dead end experiment with fixed feed concentration, where effluent composition is a self-consistent function of fluxes through the membrane. Comparison with experimental results from literature for fluid flow vs. pressure, and for salt and boron rejection, shows that theory agrees well with data. Our model is based on realistic assumptions for the effective sizes of the ions and for the diameter of the RO membrane pore in the polyamide toplayer ($\sim$0.75 nm).

physics.chem-ph↗

arXiv2017

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Transport of water through ion-exchange membranes is of importance both for electrodialysis (ED) and reverse electrodialysis (RED). In this work, we extend our previous theory [J. Membrane Sci., 510, (2016) 370-381] and include water transport in a two-dimensional model for (R)ED. Following a Maxwell-Stefan (MS) approach, ions in the membrane have friction with the water, pore walls, and one another. We show that when ion-ion friction is neglected, the MS-approach is equivalent to the hydrodynamic theory of hindered transport, for instance applied to nanofiltration. After validation against experimental data from literature for ED and RED, the model is used to analyze single-pass seawater ED, and RED with highly concentrated solutions. In the model, fluxes and velocities of water and ions in the membranes are self-consistently calculated as function of the driving forces. We investigate the influence of water and coion leakage under different operational conditions.

physics.chem-ph↗

arXiv2017

A one-dimensional model for water desalination by flow-through electrode capacitive deionization

Capacitive deionization (CDI) is a fast-emerging water desalination technology in which a small cell voltage of ~1 V across porous carbon electrodes removes salt from feedwaters via electrosorption. In flow-through electrode (FTE) CDI cell architecture, feedwater is pumped through macropores or laser perforated channels in porous electrodes, enabling highly compact cells with parallel flow and electric field, as well as rapid salt removal. We here present a one-dimensional model describing water desalination by FTE CDI, and a comparison to data from a custom-built experimental cell. The model employs simple cell boundary conditions derived via scaling arguments. We show good model-to-data fits with reasonable values for fitting parameters such as the Stern layer capacitance, micropore volume, and attraction energy. Thus, we demonstrate that from an engineering modeling perspective, an FTE CDI cell may be described with simpler one-dimensional models, unlike more typical flow-between electrodes architecture where 2D models are required.

cs.CE↗

arXiv2017

Theory of linear sweep voltammetry with diffuse charge: unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck (PNP) equations with generalized Frumkin-Butler-Volmer (FBV) boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated currentvoltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times) and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers (EDL) is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

physics.chem-ph↗

arXiv2016

Induced Charge Capacitive Deionization: The electrokinetic response of a porous particle to an external electric field

We demonstrate the phenomenon of induced-charge capacitive deionization (ICCDI) that occurs around a porous and conducting particle immersed in an electrolyte, under the action of an external electric field. The external electric field induces an electric dipole in the porous particle, leading to its capacitive charging by both cations and anions at opposite poles. This regime is characterized by a long charging time which results in significant changes in salt concentration in the electrically neutral bulk, on the scale of the particle. We qualitatively demonstrate the effect of advection on the spatio-temporal concentration field which, through diffusiophoresis, may introduce corrections to the electrophoretic mobility of such particles.

physics.flu-dyn↗

arXiv2016

Analysis of ionic conductance of carbon nanotubes

We use space-charge (SC) theory (also called the capillary pore model) to describe the ionic conductance, $G$, of charged carbon nanotubes (CNTs). Based on the reversible adsorption of hydroxyl ions to CNT pore walls, we use a Langmuir isotherm for surface ionization and make calculations as function of pore size, salt concentration $c$, and pH. Using realistic values for surface site density and pK, SC theory well describes published experimentally data on the conductance of CNTs. At extremely low salt concentration, when the electric potential becomes uniform across the pore, and surface ionization is low, we derive the scaling $G\sim \sqrt{c}$, while for realistic salt concentrations, SC theory does not lead to a simple power law for $G(c)$.

physics.chem-ph↗

arXiv2016

Theory of fluid slip in charged capillary nanopores

Based on the capillary pore model (space-charge theory) for combined fluid and ion flow through cylindrical nanopores or nanotubes, we derive the continuum equations modified to include wall slip. We focus on the ionic conductance and streaming conductance, cross-coefficients of relevance for electrokinetic energy conversion and electro-osmotic pumping. We combine the theory with a Langmuir-Stern 1-pK charge regulation boundary condition resulting in a non-monotonic dependence of the cross-coefficients on salt concentration.

physics.chem-ph↗

arXiv2015

Activated carbon is an electron-conducting amphoteric ion adsorbent

Electrodes composed of activated carbon (AC) particles can desalinate water by ion electrosorption. To describe ion electrosorption mathematically, accurate models are required for the structure of the electrical double layers (EDLs) that form within electrically charged AC micropores. To account for salt adsorption also in uncharged ACs, an "attraction term" was introduced in modified Donnan models for the EDL structure in ACs. Here it will be shown how instead of using an attraction term, chemical information of the surface structure of the carbon-water interface in ACs can be used to construct an alternative EDL model for ACs. This EDL model assumes that ACs contain both acidic groups, for instance due to carboxylic functionalities, and basic groups, due to the adsorption of protons to the carbon basal planes. As will be shown, this "amphoteric Donnan" model accurately describes various data sets for ion electrosorption in ACs, for solutions of NaCl, of CaCl2, and mixtures thereof, as function of the external salt concentration and of the cell voltage between two AC electrodes in a process called capacitive deionization (CDI). The amphoteric Donnan model can be used to relate the conditions of activation treatment and electrode preparation (which both influence the carboxylic acid content) to the EDL-structure and desalination performance of ACs.

physics.chem-ph↗

arXiv2015

Theory of water desalination by porous electrodes with fixed chemical charge

Water desalination by capacitive deionization (CDI) is performed via electrochemical cells consisting of two porous carbon electrodes. Upon transferring charge from one electrode to the other, ions are removed from the feedwater by electrosorption into electrical double layers (EDLs) within the micropores of the porous carbon. When using electrodes containing fixed chemical charge in the micropores, various counterintuitive observations have been made, such as "inverted CDI" where upon charging, ions are released from the electrode, and the feedwater is only desalinated when the cell is discharging. We set up an EDL model including chemical charge that explains these observations and makes predictions for a working range of enhanced desalination by CDI.

cond-mat.mtrl-sci↗

arXiv2014

Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nm), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by meanfield theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.

physics.chem-ph↗

arXiv2012

Current-induced membrane discharge

Possible mechanisms for over-limiting current (OLC) through aqueous ion-exchange membranes (exceeding diffusion limitation) have been debated for half a century. Flows consistent with electro-osmotic instability (EOI) have recently been observed in microfluidic experiments, but the existing theory neglects chemical effects and remains to be quantitatively tested. Here, we show that charge regulation and water self-ionization can lead to OLC by "current-induced membrane discharge" (CIMD), even in the absence of fluid flow. Salt depletion leads to a large electric field which expels water co-ions, causing the membrane to discharge and lose its selectivity. Since salt co-ions and water ions contribute to OLC, CIMD interferes with electrodialysis (salt counter-ion removal) but could be exploited for current-assisted ion exchange and pH control. CIMD also suppresses the extended space charge that leads to EOI, so it should be reconsidered in both models and experiments on OLC.

physics.chem-ph↗

arXiv2009

Diffuse-Charge Effects on the Transient Response of Electrochemical Cells

We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or "space charge") near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern monolayer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time-scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulae for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and super-limiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the super-limiting current beyond the diffusion-limiting current.

physics.chem-ph↗

arXiv2009

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.

physics.chem-ph↗