Calibration of an Au-coated Quartz Crystal
This Application Note is the second in a series relating to the eQCM 10M™ and assumes that you have read and understand the material covered in the Application Note, Basics of a Quartz Crystal Microbalance.
The purpose of this Application Note is to show the reader a simple experiment where we reduce Cu2+ onto an Au electrode and then oxidize Cu back off. We will then use the result to calculate a calibration factor for the crystal. Conversely, we will show you how to calculate the molar mass of the species deposited using a calibration factor.
Each crystal has a theoretical calibration factor, however, under typical experimental conditions, these calibration factors will vary slightly. We will use Cu2+ to calculate a calibration factor which could then be used in subsequent experiments on the same crystal.
Cu2+ is reduced in a two electron reaction as shown below:
CuSO4(aq) + 2 e- Cu(s) + SO42-(aq)
Our goal is to reduce Cu2+ onto an Au electrode, then use the frequency decrease and the charge passed to calculate a calibration factor.
A solution of CuSO4 (5-10 mM) in 1 M H2SO4 was prepared and placed into the PTFE cell containing a 10 MHz Au-coated quartz crystal. No air/solution interface was present in the cell. The crystal’s electroactive area was 0.209 cm2 and the area of overlap was 0.205 cm2.
Next, the eQCM 10M was interfaced to the cell using the supplied cell cable. A Series G 300 was connected to the working face of the crystal using a stacking
banana plug to stacking pin cable. Cell setup was completed with a Pt counter electrode and an Ag/AgCl reference electrode.
Upon starting Resonator™, the nominal frequency of the crystal, 10 MHz, was entered in Center Freq along with a Freq. Width of 50 kHz and a Freq. Step of 0.2 Hz. Pressing Single Scan resulted in the spectrum shown in Figure 1. Next, the green cursors that appeared on the spectrum were moved closer to the resonant frequencies and Start was pressed to trigger continuous data acquisition.
Next, the potentiostat was set up by selecting Cyclic Voltammetry from the Technique drop-down box and pressing Setup. 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
Cycles (#): 5
I/E Range Mode: Fixed
Max Current (mA): 30
Sampling Mode: Fast
Once the potentiostat was set up, OK was clicked which closed the setup window, followed by Run. A screenshot of the potentiostat panel in Resonator during acquisition is shown in Figure 2. Note that the top plot shows both resonant frequencies for the entire time that the QCM has been acquiring data while the bottom plot shows current/voltage data. It is also possible to show current and voltage versus time by selecting Time in the Display Graph drop-down box.
The first plot in Echem Analyst is a plot of current and frequency change versus voltage as shown in Figure 3 and the second plot is frequency change versus charge as shown in Figure 4.
The Curve Selector can be used to plot data a variety of ways and also allows you 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 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 376 kHz/C.
The calibration factor for the crystal is then calculated according to the equation
where F is the Faraday Constant, EA is the electroactive area, MMCu is the molar mass of Cu, and n is the number of electrons. The 106 is used to convert from grams to micrograms. Cf is calculated to be 232 Hz cm2/µg. This is approximately 3% different than the theoretical value of 226 Hz cm2/µg.
If you already know your calibration factor accurately you can determine the molar mass of the mobile species (deposited in this instance) during your experiment using the following procedure.
Use the Curve Selector to plot change in mass (deltaM) versus charge as shown in Figure 6.
Echem Analyst uses the calibration factor entered into Resonator along with the electroactive area to calculate the mass. The slope of the line, after performing a second linear fit, for the deposition is -347.6 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 67.1 g/mol.
The purpose of this application note was to show how a calibration factor can be calculated for any given crystal. This application note also showed how to calculate the molar mass of a mobile species if the calibration factor of the crystal is known.
The eQCM 10M is shipped with the Gamry Resonator Software, Gamry Echem Analyst Software, a Quick Start Guide, a Hardware Operator’s Manual (CD), a Software Operator’s Manual (CD), one EQCM cell, one AC Power Adapter, one USB interface cable, one
The eQCM 10M is protected by a two-year factory service warranty.
The eQCM 10M must be interfaced to a computer with a Gamry Potentiostat (models include the Reference 3000™, Reference