*2.4. EQCM Measurements*

The working principle of the electrochemical quartz crystal microbalance (EQCM) [27] is based on an inverse piezoelectric effect with a quartz crystal working at its resonance frequency. The changes in the mass of the deposited conductive polymer can be determined during reversible redox cycles (ions and solvent exchanged) by the frequency change. The cut AT crystal, with a 15 mm diameter (oscillation area 0.28 cm2), was coated on both sides with a thin layer (20 nm) of chromium to improve the stability of the following platinum layer that was in the range of 60 nm and was coated via vacuum deposition. The platinum-coated quartz was clamped between two O-rings with one side facing the solution and the other side facing air. An Amel potentiostat (Amel model 533, Milano, Italy) was used to control a three-electrode cell with the platinum-coated quartz as the working electrode, an Ag/AgCl wire reference electrode, and a platinum mesh as a counter electrode. Measurement and data collection was performed with in-house software with a Hameg HM 2122 frequency counter (HAMEG Instruments GmbH, Mainhausen, Germany) connected to an IEEE-488 interface bus (Hewlett-Packard, Palto Alto, CA, USA). The potentiostatic polymerizations (1.0 V, 1.2 V, and 1.5 V) took place in a monomer solution under an argon atmosphere (0.1 M EDOT, 0.1 M TBAPF6 in propylene carbonate), until the resonance frequency decreased by 5 kHz, which corresponds to a mass addition of 14 μg (i.e., a film thickness in range of 400–500 nm). After polymerization, the polymeric layer was discharged at 0.0 V in the monomer solution. Cyclic voltammetry of the PEDOT-deposited quartz at different polymerization potentials (scan rate 10 mV s<sup>−</sup>1) was performed in an electrolyte solution (0.1 M TBAPF6 in PC) and the changes in frequency (mass) during reversible redox cycles with a potential range of ±1.0 V were recorded. The correlation of frequency change (Δ*f*) to mass change (Δ*m*) in an electrochemical process, with a good linear approximation with a constant *CQMW* value (gravimetrical proportionality constant), is given in by the Sauerbrey equation (Equation (1)) [28].

$$
\Delta m = \mathbb{C}\_{\mathbb{Q}M\mathbb{W}} \cdot \Delta f \tag{1}
$$

The relationship between the changes of mass on the electroactive surface (Δ*mel*, g) to changes of charge (Δ*Q*, C) is shown in Equation (2) as the modified faradaic law.

$$
\Delta Q = n \cdot z \cdot F = z \cdot F \cdot \frac{\Delta m^{el}}{M\_R} \tag{2}
$$

where *F* is the Faraday constant (96,492 C mol<sup>−</sup>1), n is the mole number, z is the number for electrons, and *MR* (g mol<sup>−</sup>1) is the molar mass change in the reaction. It needs to be considered that the active surface (A) between the conductive polymer (PEDOT) *Ael* and the AT quartz crystal (*Aosc* with mass change Δ*m*osc) can be different. As such, Equation (3) denotes the densities of those surfaces (ρ = Δ*mel*/*Ael* = Δ*mosc*/*Aosc*), leading to linear dependence between the change of frequency Δ*f* to the change of charge Δ*Q*:

$$
\Delta f = \frac{M}{z \cdot F \cdot \mathbb{C}\_{QMW}} \cdot \frac{A\_{\text{osc}}}{A\_{el}} \cdot \Delta Q = \frac{M}{z} \cdot \mathbb{C}\_{EQMW} \cdot \Delta Q \tag{3}
$$

The electrogravimetric proportionality constant *CEQMW* [29] is a product from the gravimetric proportionality constant CQMW, the Faraday constant, and the quotient of surfaces *Aosc*/*Ael*. The equation relates to univalent anions/cations, and, as such, the value for "*z*" is 1. The term CEQCM is influenced by the experimental setup and must be calibrated (i.e., measured) using metal deposition for a known thickness of Cr and Pt, as well as the area of the electrically oscillated surface (*Ael* = 30.8 mm2, *Aosc* = 27.38 mm2), the density of the quartz (ρ<sup>Q</sup> = 2.65 106 g m<sup>−</sup>3), the speed of the shear wave (vQ = 3340 m s<sup>−</sup>1), and

the resonance frequency (fQ = 5 MHz), which, in our case, led to a value for *CEQMW* of −1.98 mol Hz g<sup>−</sup>1mC<sup>−</sup><sup>1</sup> and −4.85 ng Hz−<sup>1</sup> for the gravimetric proportionality constant *CQMW*. The change of frequency Δ*f* against charge Δ*Q* led to a specific curve where several positions of the slope could be determined, where division by *CEQMW* yields the molecular weight of the charge compensating species *MCCS* (Equation (4)).

$$\frac{\Delta f}{\Delta Q} = \frac{slope}{\mathcal{C}\_{EQMW}} = M\_{\text{CCS}}\tag{4}$$
