Debye screening length of electrolytic solutions from capacitive force measurements using atomic force microscopy

We present a method to obtain the Debye screening length of a dilute electrolytic solution by measuring the capacitve force using atomic force microscopy (AFM). A small AC bias voltage of frequency $\omega$ was applied between an AFM cantilever and conducting substrate in an electrolytic solution and the resulting capacitive force between them was measured from the cantilever oscillations. The $2\omega$ component of the oscillating force was used to obtain the capacitance gradient between the AFM cantilever tip and substrate as a function of tip-sample distance $z$. An analytic expression relating tip-sample distance $z$ and capacitance gradient between AFM tip and conducting substrate in an electrolytic solution was derived using the solution of the linearized Poisson-Boltzmann equation. We find that the analytic expression fits well with the experimental data for dilute KCl-water solutions. The fit parameters were further used to calculate the Debye screening length of the electrolytic solution.