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mnpl/3659/5548/2023/Quantum capacitance governs electrolyte conductivity in carbon nanotubes
Received 17, March 2023
Revised 26, May 2023
Accepted 29, July 2023
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Quantum capacitance governs electrolyte conductivity in carbon nanotubes
Th´eo Hennequin and Manoel Manghi∗
Laboratoire de Physique Th´eorique, Universit´e Paul Sabatier–Toulouse III, CNRS, France
Adrien Noury, Fran¸cois Henn, Vincent Jourdain, and John Palmeri†
Laboratoire Charles Coulomb, Universit´e de Montpellier, CNRS, France
Micro & Nano Physics J.
DOI- https://www.doi.wikipt.org/10/1490/55874mnpl
Acknolowdgement
NA
Keyword Highlighted
Quantum capacitance, carbon nanotubes, nano
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Abstract
In recent experiments, unprecedentedly large values for the conductivity of electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing to flow slip and a high pore surface charge density whose origin is still unknown. By accounting for the coupling between the quantum CNT and the classical electrolyte-filled pore capacitances, we study the case where a gate voltage is applied to the CNT. The computed surface charge and conductivity dependence on reservoir salt concentration and gate voltage are intimately connected to the CNT electronic density of states. This approach provides key insight into why metallic CNTs have larger conductivities than semiconducting ones.
Introduction
Although much experimental, theoretical, and molecular modeling effort has been devoted over the past years to understanding water and ion (electrolyte) transport through carbon nanotubes (CNTs) [1–3], the origin of the electric charge localized on the surface of industrially important CNT based nanofluidic systems still remains unclear (see Ref. [4] and references therein). It has already been proposed that this surface charge could arise from functional groups at the CNT entrances [5, 6] and/or the specific adsorption of ions, such as OH− [7]. Although the above cited studies lead to the conclusion that this surface charge plays a key role in governing ion transport in CNTs, it is difficult to regulate it directly and one is left to making inferences, for example by studying the variation of ionic conductance G with the pH or salt concentration, cs, of the external bulk reservoirs bounding the CNT. Intriguing results have been obtained, including a power law behavior, G ∝ c α s , with 1/2 ≤ α ≤ 1, which could be interpreted as the manifestation of an underlying surface charge regulation mechanism [8–10]. Through a simplified feasibility study we propose in this work that by biasing a CNT incorporated in a nanofluidic system via an applied gate voltage, Vg, and taking into account explicitly the quantum capacitance (QC) of the quasi-1D CNT structure as well as the nonlinear capacitance of the confined electrolyte ion the pore, it should be possible to quantify the CNT surface charge density σQ and establish a link between the intrinsic CNT electronic properties and ion transport through the same structure, such as the electrolyte conductance through the CNT. A major conclusion it that these intrinsic electronic properties will depend significantly, under certain conditions, on whether the CNT is metallic (M) or semiconducting (SC).
Conclusion
As an concluding example, we consider the experimental results obtained by Liu et al. [30], who measured, for cs = 1 mol/L, conductances of 61.0 nS for M SWCNTs and 5.6 nS for SC ones with 0.8 ≤ d ≤ 2 nm and 5 ≤ L ≤ 10 nm. Using the DOS given in Fig. 1(a) with d = 1.5 nm and L = 8 nm, we can account for these two conductance values by taking Vg ≃ 0.35 V, a value that we interpret as an environmentally induced shift in the zero of the gate tension. More systematic experiments are clearly needed to ascertain to what extent the charge density and therefore the electrolyte conductivity through SWCNTs can be controlled by an applied gate voltage. Presumably, a more complete model for conductivity would be needed to account for the full complexity of real CNTs, including the influence of pH (via charge regulation), residual geometrical capacitances, and dielectric interactions.
Reference
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