Scaling Behavior for Ionic Transport and its Fluctuations in Individual Carbon Nanotubes

Abstract

In this Letter, we perform an experimental study of ionic transport and current fluctuations inside individual carbon nanotubes (CNTs). The conductance exhibits a power law behavior at low salinity, with an exponent close to 1/3 versus the salt concentration in this regime. This behavior is rationalized in terms of a salinity dependent surface charge, which is accounted for on the basis of a model for hydroxide adsorption at the (hydrophobic) carbon surface. This is in contrast to boron nitride nanotubes which exhibit a constant surface conductance. Further, we measure the low frequency noise of the ionic current in CNTs and show that the amplitude of the noise scales with the surface charge, with data collapsing on a master curve for the various studied CNTs at a given pH.

Analysis of ionic conductance of carbon nanotubes

“…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.…”

“…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.…”

“…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 theory with a Langmuir isotherm for ionizable surface charge to describe the data of Secchi et al [7,8] for the conductance of CNTs.When we neglect axial gradients in salt concentration, SC theory only requires a (numerical) solution of the PB equation in a cylindrical nanopore, to calculate potential ψ as a function of r coordinate,whereis the Debye length, ε the dielectric constant, ε = ε w ε 0 , V T = RT /F = k B T /e the thermal voltage, and c the salt concentration in the external baths, in mol/m 3 . Unless otherwise noted, all parameters are dimensional (except for ψ and Pe 0 ).…”

“…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 theory with a Langmuir isotherm for ionizable surface charge to describe the data of Secchi et al [7,8] for the conductance of CNTs.…”

“…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] …”