Numerical investigation of current–voltage and the current-noise in nanoporous membranes

In this paper we perform numerical simulations to understand linear current–voltage characteristics inside nanopores. The conductance of nanopores for different potassium chloride, KCl concentrations are studied. Our results match the experiments. We model the current–noise inside nanopores for the first time. The model has steady state current term for potassium K⁺ ion, I_K⁺ = q_K⁺ u/L_nanopore + m_K⁺ a u/V, where q_K⁺ is the potassium ion charge, u is the velocity of the ions, L_nanopore is the length of the nanopore, m_K⁺ is the mass of potassium ions, a is the acceleration of the ions and V is the voltage. The high frequency potassium ion noise current is modelled as I^high_K+ = √(4k_B GTB) where k_B is Boltzmann constant, G is the conductance of nanopores at the salt concentrations, T is the temperature and B is frequency. The low frequency potassium ion noise current is modelled as I^low_K+ = A/f where A is the charge carrier and f is frequency term. The total potassium current with noise is I^total_K+ = q_K⁺ u/L_nanopore + m_K⁺ a u/V + √(4k_B GTB) + A/f. The chloride ion current is simulated in our study. Here the simulation current matches experiments. The power spectral density gives the 1/f noise as seen in experiments. The power spectral density has dependence on applied voltage as seen in experiments.