Electrochemical Synthesis of Sound: Hearing the Electrochemical Double Layer

Electrochemical double layers (EDLs) govern the operation of batteries, fuel cells, electrochemical sensors, and electrolyzers. However, their invisible nature makes their properties and function difficult to conceptualize, creating an impediment to the broader understanding of double-layer function required for future technologies in energy storage and chemical synthesis. To render the behavior of electrochemical interfaces more intuitive, we made the rearrangement of interfacial components audible by employing the EDL as a variable element in a relaxation oscillator circuit. Connecting the circuit to a speaker generated an audible output corresponding to the change in potential resulting from EDL rearrangement. Variations in the applied voltage, electrolyte concentration and identity, as well as in the electrode material, yielded audible frequency variations that provide an intuitive understanding of EDL behavior. We expect that hearing the trends in behavior will provide a helpful and alternative method for understanding molecular movement at the electrochemical interface.


Detailed Information on Circuit Components
In the following we detail the circuit layout and the employed components.R1: 33 kΩ resistor (low concentration), 100k resistor (1 M runs) R2: 33 kΩ resistor R3: 10 kΩ resistor R4:, 23 Ω resistor Op-amp: OPA551PA (Texas Instruments) All voltages in the main text are plotted centered on 0 V for clarity.Due to a small asymmetry in the power supply, at pin 2 there is a −0.04 V DC offset, and at pin 6 there is a −0.1 V DC offset.The magnitudes of the voltages plotted are corrected for the offset to reflect the true voltage magnitude spanned.We verified that this did not impact the measured frequency.

Relationship Between Capacitance and Frequency
As shown in Equation S1 and S2 the output frequency of a relaxation oscillator circuit is linearly proportional to the inverse of the capacitance, (Equation S1, S2).
In these equations,  is the output frequency of the circuit,  3 is the resistance of the feedback resistor R3,  is the capacitance of the circuit capacitor, and  is the ratio of resistances between R1 and R2 as described in Eq.S2.We have verified this relationship experimentally (Figure S2) using capacitors.If additional elements of the electrochemical interface such as series and charge transfer resistances become relevant in magnitude, numerical simulation is required to devise oscillation frequencies.

Equivalent Circuit of the Electrochemical Cell
As shown below in Figure S3, the equivalent circuit for our two-electrode electrochemical cell is modeled as two Randles circuits in series connected through the series resistance.Utilizing an Ag/AgCl (3 M KCl) reference electrode as the counter electrode enabled us to probe the working electrode interface in isolation as a good reference electrode acts as an ideal resistor over a wide frequency range.We verified this using electrochemical impedance spectroscopy, which showed that the phase angle of the reference electrode is near-zero at all frequencies relevant to our system (Figure S4).

Detailed Explanation of Oscillation Cycle
A relaxation oscillator circuit generates a square wave voltage output with a specific frequency based on the time constant obtained by continuously charging and discharging a capacitor through a feedback resistor.The circuit generates a square wave output because the operational amplifier (triangle symbol in Figure S3) is operating at saturation, meaning it switches between outputting its maximum positive and negative supply voltages.In our circuit, the capacitor is replaced by a two-electrode electrochemical cell (Figure S1), dominated by the electrochemical interface of the working electrode, where the electrochemical double layer recruits and releases charge as the electrostatic potential difference varies with a set amplitude defined by Vref.The induced oscillation of the electrostatic potential causes charges to be recruited to and released from the interface in a cyclic manner, with the frequency of the cycle depending upon the properties of the EDL.In the following, we detail an oscillation cycle for Vapp = 0, with the assumption that the intrinsic difference in electrostatic potential between the electrode and electrolyte is positive 1.We will assume that the depicted cycle begins with Vcell = −Vref (Figure S5a).
Upon reaching this condition, the op-amp flips to a positive output (Figure S5b).
When the op-amp output is positive, the solution potential increases, attracting negative charges away from the working electrode.This leads to an increase in Vcell as the working electrode releases negative charge from the interface (Figure S5c, Figure S6).2. Once the voltage across the electrochemical cell equals the positive reference voltage (Figure S7a), the operational amplifier once again changes the sign of the output voltage, now becoming negative (Figure S7b).When the op-amp output is negative, the solution potential decreases, driving negative charges towards the working electrode.This leads to a decrease in Vcell as the working electrode accumulates negative charge at the interface (Figures S7c, S8).Illustrations not to scale, rearrangement of solvent molecules and positive charges not drawn for simplicity.
3. The charge recruitment and release cycle continuously repeats with the output frequency of the cycle dictated by the time it takes for the interfacial rearrangement of ions and solvent molecules to compensate for the perturbation of interfacial electrostatic potential by the circuit.
4. The same principle applies in the presence of an applied potential.However, in these experiments, we first apply a voltage across the electrochemical cell with a DC power supply to generate a difference in electrostatic potential between the electrode and electrolyte (Vapp).This leads to the rearrangement of electrolyte components and the modification of the electrochemical double layer as illustrated in Figure S9, which changes the time constant of its rearrangement under oscillation and therefore the frequency output of our circuit.The voltage then oscillates between Vapp+Vref and Vapp−Vref as described above (Figure S9).

Impact of Oscillation Amplitude on Frequency Trends
In the concentration study, the peak-to-peak magnitude of the oscillating reference voltage (Vpp,ref) was 864 mV.To verify whether this amplitude impacts the measured frequency trends, we repeated the experiments on a Pt electrode with a 50 mM KClO4 electrolyte using a peak-to-peak Vpp,ref magnitude of 38.4 mV and 312 mV.As shown in Figure S15, the potential-dependent trends in frequency were preserved across all oscillation magnitudes.While the observed frequency trends were largely independent of Vpp,ref, the frequency values increased at lower oscillation magnitudes.This behavior is expected because smaller potential oscillations cause less charge to be recruited and released from the interface.To conduct these experiments probing the effect of Vpp,ref , different combinations of R1, R2, and R3 were used (Table S1).To reduce Vpp,ref, the ratio of R1 to R2 was increased by switching R2 from 33 kΩ to 10 kΩ then adjusting R1 as needed.Additionally, R3 was increased to 75 kΩ for the 38.4 mV case to bring the frequency into the audible range.This change in R3 did not impact the frequency trends but contributes to the discrepancy in frequency value measured between the different conditions.

Figure S1 .
Figure S1.Detailed circuit diagram with op-amp pinout.R1 depicted as set for runs with concentrations <1 M. Runs with a concentration of 1 M had an R1 value of 100k.

Figure S2 .
Figure S2.Linear fit of frequency versus inverse capacitance, as is consistent with expected circuit behavior.

Figure S3 .
Figure S3.Circuit diagram with equivalent circuit for 2-electrode electrochemical cell depicted with 2 simplified Randles circuits in series.Cdl,CE = double layer capacitance for the counter electrode.Rct, CE = charge transfer resistance for the counter electrode.Rs = series resistance.Cdl,WE = double layer capacitance of the working electrode.Rct,WE = charge transfer resistance of the working electrode.

Figure S4 .
Figure S4.Electrochemical impedance spectroscopy of Ag/AgCl (3 M KCl) reference electrodes.This data was recorded using a two-electrode cell where both the working and counter electrodes are 3 M KCl Ag/AgCl electrodes, demonstrating resistive behavior over the frequency range relevant to this study.

Figure S5 .
Figure S5.Visual depiction of charge recruitrelease cycle showing (a) the initial state, (b) the change in sign of the op-amp output, and (c) the resulting release of negative charges from the electrochemical double layer, leading to an increase of Vcell.

Figure S6 .
Figure S6.Depiction of EDL behavior when the working electrode is releasing negative charges under condition of positive op-amp output (Vref positive).Illustrations not to scale, rearrangement of solvent molecules and positive charges not drawn for simplicity.

Figure S7 .
Figure S7.Visual depiction of the charge recruiting phase of the cycle, which starts (a) when Vcell = +Vref causing (b) the change in sign of the op-amp output, and (c) the resulting recruitment of negative charges towards the electrochemical double layer, leading to a decrease of Vcell.

Figure S8 .
Figure S8.Depiction of EDL behavior when the working electrode is recruiting negative charges to the interface under condition of negative op-amp output (Vref negative).Illustrations not to scale, rearrangement of solvent molecules and positive charges not drawn for simplicity.

Figure S9 .
Figure S9.Illustration showing the variation in interfacial potential drop occurring under oscillation in the presence of an applied potential.

Figure S13 .
Figure S13.Close-up view of circuit, pin 1 of op-amp is on the upper left.

Figure S14 .
Figure S14."Electrochemical synthesizer" instrument, using the control voltage output of a keyboard to control Vapp of the cell.

Figure S15 .
Figure S15.Oscillation frequency for a 1.6 mm OD Pt electrode in 50 mM KClO4 with peak-to-peak oscillation amplitudes of 38.4,312, and 864 mV.Frequency trends were preserved across different amplitudes.

Table S1 .
Resistor values for the various Vpp,ref cases