Calibration of a Gold-Coated Quartz Crystal
Cu2+ is reduced in a two-electron reaction:
CuSO4(aq) + 2 e- Cu(s) + SO42-(aq)
Our goal is to reduce Cu2+ onto a gold electrode, then use the decrease in frequency and the charge passed to calculate a calibration factor.
Upon starting Gamry Instruments Resonator™ software, the nominal frequency of the crystal, 10 MHz, was entered in the Center Freq. field along with a Freq. Width of 50 kHz and a Freq. Step of 0.2 Hz. Clicking the Single Scan button resulted in a spectrum shown in Figure 1. Next, the green cursors that appeared on the spectrum were moved closer to the resonant frequencies and the Start button was clicked to trigger continuous data acquisition.
Figure 1. Resonator screenshot after entering initial parameters and clicking the Single Scan button.
The potentiostat was set up by selecting Cyclic Voltammetry from the Technique drop-down menu and clicking the Setup button. A setup screen for cyclic voltammetry appeared and parameters were entered as shown below:
|Initial E (V):||0.050|
|Scan Limit 1 (V):||–0.250|
|Scan Limit 2 (V):||0.300|
|Final E (V):||0.050|
|Scan Rate (mV/s):||50|
|Step Size (mV):||2|
|I/E Range Mode:||Fixed|
|Max Current (mA):||30|
Figure 2 Screenshot of Resonator during acquisition.
After the acquisition was finished, the data file was then opened in Gamry Instruments’ Echem Analyst™ software.
The first plot in Echem Analyst is a plot of the change in current and frequency versus voltage (Fig. 3), and the second plot is change in frequency versus charge (Fig. 4).
Figure 3. Echem Analyst showing change in current and frequency versus voltage for the five cycles.
Figure 4. Echem Analyst showing change in frequency versus charge for the five cycles.
Use the Curve Selector button to plot data a variety of ways and also to show or hide specific curves. The deposition portion of the curve was selected by clicking on the Select Portion of the Curve using the Mouse tool button A linear fit was then calculated by choosing the Linear Fit option under the Common Tools menu. The Quick View pane at the bottom of the window in Figure 5 gives the slope of the linear fit as 23.94 kHz/C.
Figure 5. Echem Analyst showing the linear fit of change the bottom of the window.
The calibration factor for the crystal is then calculated according to the equation
Figure 6. Echem Analyst showing the linear fit for change in mass versus charge in the Quick View pane at the bottom of the window.
Echem Analyst uses the calibration factor entered into Resonator software, along with the electroactive area, to calculate the mass. The slope of the line, after performing a second linear fit, for the deposition is –361.8 µg/C. The molar mass of the Cu2+ can be calculated using the equation
where F and n are as described previously. In this instance the molar mass was calculated to be 69.8 g/mol.
|Frequency range||1–10 MHz|
|Frequency resolution||0.02 Hz|
|Operating temperature range||0–45°C|
|Relative humidity||maximum 90% non-condensing|
|Storage and shipping temperature||–25 to 75°C|
|Dimensions||175 × 115 × 80 mm|
|AC power adapter||100–264 VAC, 47–63 Hz|
|Quartz-crystal microbalance||12 VDC, 25 W|