Nonequilibrium $1/f$ Noise in Rectifying Nanopores

We report a single rectifying conically shaped nanopore system with ion current fluctuations whose $1/f$ noise characteristics observed at low frequencies are voltage dependent. Switching the voltage polarity allows one to switch between a system that produces equilibrium and nonequilibrium $1/f$ ion current fluctuations. The nonequilibrium fluctuations in the high-conductance state of the device are characterized by exponential dependence of the normalized power spectrum on voltage. The asymmetric $1/f$ noise is found characteristic for rectifying polymer nanopores and absent in pores with Ohmic current-voltage curves.

Figure 1

(a) Current-voltage ($I\mathrm{\text{−}}V$) curves of a single PET conical nanopore with openings of 5 nm and 400 nm (open triangles), and a single polyimide pore with openings of 2 nm and 1000 nm (open squares) recorded in $0.1M$ KCl, $p\mathrm{H}$ 8, $2\mathrm{m}M$ PBS buffer. The pores do not rectify at acidic $p\mathrm{H}$; an example of a recording for the PET pore at $p\mathrm{H}$ 3.5, $0.1M$ KCl, adjusted with $0.1M$ HCl is shown (filled triangles). (b) Examples of ion current signals in time at $p\mathrm{H}$ 8 for the PET pore whose $I\mathrm{\text{−}}V$ curves are shown in (a). (c) Power spectra of the data shown in (b): for $-1000\mathrm{mV}$ (blue), and $+1000\mathrm{mV}$ (red), together with power-law fits; dashed lines indicate the levels of the shot noise for $+1000\mathrm{mV}$ (red) and $-1000\mathrm{mV}$ (blue). (d) Black: $S(f)/⟨I{⟩}^2$ for three pores: two PET pores with the opening diameter of 5 nm (squares with crosses) and 8 nm (filled squares), and 2 nm polyimide pore (stars). Solid lines indicate exponential fits of $S(1\mathrm{Hz})/⟨I{⟩}^2$ for negative voltages. Error bars for the 8 nm PET pore were calculated according to a standard error analysis taking into account standard deviation of ion current and of the values of $S(1\mathrm{Hz})$. The latter was estimated as a standard deviation of values found after dividing each time series into 9 segments. In blue: exponent $\alpha$ of the $1/f^{\alpha }$ scaling of the power spectra for one PET (filled circles) and one polyimide pore (open circles), calculated in the range between 0.1 Hz and 2.0 Hz. The error for α is up to 20%. All power spectra were corrected for the equilibrium noise [6].

Figure 2

Power spectra of ion current through a conical 8 nm PET (a), and 2 nm polyimide (b) nanopore recorded in $0.1M$ KCl and various $p\mathrm{H}$ values, as indicated in the figure.

Figure 3

Numerical calculations for the concentration profiles of potassium and chloride ions along the $z$ axis of a conical nanopore (as shown in the inset). Numerical solutions of the Poisson-Nernst-Planck equations were obtained using COMSOL, Inc. [18]. A conical pore with openings of 5 and 500 nm in diameter, and $0.5e/{\mathrm{nm}}^2$ surface charge density was modeled.

Figure 4

(a) Power spectra of ion current time series recorded for a single PET cylindrical nanopore with a diameter of 100 nm. Recordings were performed in $0.1M$ KCl, $p\mathrm{H}$ 8, $+1000\mathrm{mV}$ (red) and $-1000\mathrm{mV}$ (blue). The power spectra were corrected for the equilibrium noise [6]. The dotted line indicates the shot noise level for both recordings. (b) Magnitude of power spectra at 1 Hz normalized by the squared value of average current for different voltages. High values of the normalized power spectrum at low voltages can most probably be attributed to very low values of the current, which decreased the signal to noise ratio.