2.2.6. Fast Fourier Transform Impedance Spectroscopy of BLMs

Fast Fourier transform electrochemical impedance spectroscopy (FFT-EIS) is based on measurements in the time domain, applying a multisine perturbation signal of a smallamplitude ~10 mV peak-to-peak covering the desired frequency range of 1.5 Hz–50 kHz. The perturbation and the respective response signals are simultaneously measured and subsequently transferred to the frequency domain using the fast Fourier transformation (FFT). The major advantages of the approach chosen here are the fast acquisition of the impedance spectrum obtained in a couple of seconds and the possibility to easily recognize violation of stationarity [46,47]. Thus, the FFT-EIS method appears to be suitable for studying the impedance properties of dynamic and unstable samples such as lipid bilayers. The perturbation voltage is applied potentiostatically using a two-electrode scheme with two platinum electrodes to supply the current and to measure the voltage across membrane. The contact area of Pt electrodes with the bulk phase in both compartments of Montal– Mueller cell is large enough to guarantee that the contribution of the electrode double electric layer is negligible in the frequency range covered.

The analysis of FFT-EIS data is performed by equivalent circuit modeling. From electrical point of view Montal–Mueller BLM set-up is represented by the capacitance CBLM and resistance RBLM of the planar lipid bilayer, connected in parallel together with the capacitance of the Teflon membrane CTM. The resistance R<sup>s</sup> of the surrounding solution is connected in series as depicted in Figure 1. Considering the 100 µm aperture surface area *S*<sup>m</sup> = 8.10−<sup>5</sup> cm<sup>2</sup> we deduce membrane-specific capacitance *C<sup>m</sup>* = *C*BLM/*S*<sup>m</sup> and resistance *R*<sup>m</sup> = *R*BLM*S*m. The reported values are calculated as the weighted average of 4–7 independent measurements averaged over 10 repetitions each. The capacitance CTM is measured independently as discussed below.

R

<sup>୫</sup> = <sup>୫</sup>

 ୱ **Figure 1.** Equivalent circuit model of Montal–Mueller cell for formation of bilayer lipid membranes (BLMs): *C*BLM—BLM capacitance; *R*BLM —BLM resistance; *C*TM —capacitance of the Teflon membrane; *R*s —resistance of the aqueous solution.

C R<sup>ୱ</sup>

<sup>୫</sup> = <sup>−</sup> = /<sup>୫</sup>

C

C

= 0.51 ±
