Scaling for rectification of bipolar nanopores as a function of a modified Dukhin number: the case of 1:1 electrolytes

ABSTRACT

The scaling behaviour for the rectification of bipolar nanopores is studied using the Nernst-Planck equation coupled to the Local Equilibrium Monte Carlo method. The bipolar nanopore's wall carries σ and $-\sigma$ surface charge densities in its two half regions axially. Scaling means that the device function (rectification) depends on the system parameters (pore length, H, pore radius, R, concentration, c, voltage, U, and surface charge density, σ) via a single scaling parameter that is a smooth analytical function of the system parameters. Here, we suggest using a modified Dukhin number, $\mathrm{mDu}=|\sigma |l_{\mathrm{B}}^{\ast }{\lambda }_{\mathrm{D}}HU/(R{U}_0)$, where $l_{\mathrm{B}}^{\ast }=8\pi l_{\mathrm{B}}$, $l_{\mathrm{B}}$ is the Bjerrum length, ${\lambda }_{\mathrm{D}}$ is the Debye length, and $U_0$ is a reference voltage. We show how scaling depends on H, U, and σ and through what mechanisms these parameters influence the pore's behaviour.

KEYWORDS:

• Scaling
• nanopores
• rectification
• Dukhin number
• Nernst-Planck

Acknowledgments

We acknowledge KIF for awarding us access to resource based in Hungary at Szeged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We gratefully acknowledge the financial support of the National Research, Development and Innovation Office – NKFIH K124353.