Analysis of electrolyte transport through charged nanopores

Peters, Patrick; Roij, René van; Bazant, Martin Z.; Biesheuvel, P.M.

doi:10.1103/physreve.93.053108

Cited by 145 publications

(189 citation statements)

References 74 publications

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“…Equations (5)- (38) are equivalent to the "uniform potential model" and "fine capillary model" [109] and have a long history in membrane science [103][104][105]. For example, Tedesco et al [110] recently used an electroneutral version of Eq.…”

Section: A Model Problemmentioning

confidence: 99%

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

Yan

Bazant

Biesheuvel³

et al. 2017

Phys. Rev. E

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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 PoissonNernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage 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 is also studied, for early time transients at reactive electrodes and for nonreactive 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.

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Section: A Model Problemmentioning

confidence: 99%

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

Yan

Bazant

Biesheuvel³

et al. 2017

Phys. Rev. E

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“…The ionic conductance of a nanopore, G (in A/V), is the ratio of current over voltage drop, in the absence of axial gradients in concentration or pressure [7]. In SC theory, G is given by [9,11,12,14,15,17,20] where Pe 0 = (εV T )/(μ w μ D ) is the "normalization" Péclet number [21], where μ D = D/V T and D is the ion diffusion coefficient, assumed to be the same for both ions. Furthermore, μ w is the dynamic viscosity of water, ψ w the dimensionless electric potential at the tube surface (wall), F is Faraday's constant, and the length of the nanotube.…”

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confidence: 99%

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confidence: 99%

Analysis of ionic conductance of carbon nanotubes

Biesheuvel¹,

Bazant

2016

Phys. Rev. E

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116

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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 a function of pore size, salt concentration c, and pH. Using realistic values for surface site density and pK, SC theory well describes published experimental 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 ∝ √ c, while for realistic salt concentrations, SC theory does not lead to a simple power law for G(c). DOI: 10.1103/PhysRevE.94.050601 The ionic conductance, G, of carbon nanotubes (CNTs) is of relevance for applications in membrane technology for water desalination, energy harvesting, and energy conversion [1][2][3][4][5][6]. Secchi et al. [7,8] recently reported the first experimental results for G of single carbon nanotubes of different radii and lengths, in a large salt concentration range (1-1000 mM) and at several values of pH. The observed dependence of G on pH, and the absence of a plateau in G at low salinity, were taken as evidence that CNTs acquire a surface charge by reversible adsorption of hydroxyl ions from water. A theoretical analysis led to a 1/3 power-law scaling of G with salt concentration, which is supported by the data.In the present work, to describe the same data of Secchi et al. [7,8], we use the general classical dilute solution theory for long and thin capillary pores, combining the extended Nernst-Planck equation with the Stokes equation for fluid flow and the Poisson-Boltzmann (PB) equation for the structure of the electrical double layer (EDL), evaluated in radial direction. This model was developed by Osterle and co-workers [9,10] and is known as the capillary pore model, or space charge (SC) theory. SC theory is based on ideal Boltzmann statistics of ions as point charges, and assumes validity of the equilibrium PB equation in the radial, r, direction [11][12][13][14][15][16][17]. SC theory also includes an axial salt concentration gradient, but this effect is neglected in the present analysis. Secchi et al. [7,8] use SC theory with several simplifications to arrive at an analytical expression for G versus pore size and salt concentration. For CNTs they introduce the key idea that the surface charge depends on pH (in the external bath) and surface potential, via a model for the reversible adsorption of hydroxyl ions.The structure of this report is as follows. We present the SC theory for the conductance G and show model simplifications when the Donnan approach, or uniform potential model [16][17][18][19] is used, valid for highly overlapped EDLs. We derive a scaling law of G with salt concentration in the low-salinity limit. We assess the assumptions made in the derivation of the analytical solution of Secchi et al. Finally we combine the full SC theor...

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“…The stationary flow and ion transport are described by the Navier-Stokes, Nernst-Plank, and Poisson equations [15,16,21]. We introduce dimensionless variables by taking the characteristic scales of length L (to be specified later), velocity J V , pressure ρJ 2 V , concentration C L , and potential RT /F .…”

Section: Problem Statementmentioning

confidence: 99%

“…Different contributions of diffusion and migration fluxes to ion rejection were observed for cases of constant surface potential / charge density. The SC model was revisited in [16] by using the flux-force formalism with Onsager symmetry properties, which allowed a significant simplification of working formulas.…”

Section: Introductionmentioning

confidence: 99%