Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation

Balme, Sébastien; Picaud, Fabien; Manghi, Manoel; Palmeri, John; Bechelany, Mikhaël; Cabello-Aguilar, Simon; Abou-Chaaya, A.; Miele, Philippe; Balanzat, Emmanuel; Janot, Jean‐Marc

doi:10.1038/srep10135

Cited by 89 publications

(94 citation statements)

References 59 publications

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“…050601-2 which is the counterion-only limit, or "good co-ion exclusion limit" [20]. Equation (9) shows that in this limit the surface charge becomes smaller when salt concentration goes down.…”

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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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Analysis of ionic conductance of carbon nanotubes

Biesheuvel¹,

Bazant

2016

Phys. Rev. E

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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Analysis of ionic conductance of carbon nanotubes

Biesheuvel¹,

Bazant

2016

Phys. Rev. E

116

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“…In Fig. 1b [26]. Thus in order to confirm the presence of charge on the nanopore surface, the rectification factor (G 1V /G -1V ) was also analyzed.…”

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“…For polymeric materials, the ALD process is performed at low temperature (60°C). It permit to reduce the diameter up to 1 nm in PET nanopores [26].…”

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