In the Laboratory 1340 Journal of Chemical Education • Vol. 84 No. 8 August 2007 • www.JCE.DivCHED.org When the quartz-crystal microbalance (QCM) was first introduced in 1959 (1), it represented a major step forward in our ability to weigh matter. This technique extended the sensitivity by two or three orders of magnitude, into the sub- nanogram range. However, to use the QCM as a mass sen- sor one must be sure that the measured mass is rigidly attached to its surface. When working with liquids it is im- portant that during the process studied there is no change in the roughness of this surface and that the viscosity and den- sity of the surrounding medium remain constant. Only un- der these conditions will the frequency shift, ∆fm, be proportional to the change in mass, ∆m, expressed in units of mass per surface area, ∆ fm = Cm∆m (1) where the constant, Cm, is determined by the properties of the QCM (2). In this article we describe an experiment in which the QCM is used as a mass sensor during the electro- chemical deposition of copper. Experimental Detailed descriptions of the devices used and construc- tion of the cell are given a previous article (2). A schematic presentation of the setup is shown in Figure 1. In the experi- ment, control of the potential between the WE and the RE is imperative to ensure that the only reactions taking place are the deposition or dissolution of copper. The problem is not only one of achieving 100% Faradaic efficiency of this reaction, but also in preventing reactions that could lead to the formation of gas bubbles (H2 or O2) on the QCM sur- face or dissolution of the gold from the QCM. The first could lead to drastic distortion of the response of the QCM and the second could damage it. The necessity of potential con- trol provides an opportunity to introduce the role of elec- trode potential in electrochemical kinetics and, with the help of the table of standard potentials, to discuss with students the limiting potentials that could be chosen. The estimation of limiting values of potentials and of frequencies could be a prelaboratory exercise for the students. When copper is deposited on a bare gold surface it is often found that the initial response of the QCM can reflect not only mass changes, but also some other phenomena con- nected with changes in the state of the surface (3, 4). To avoid these added complications, the first stage of the experiment should consist of depositing a layer of copper on the gold surface of the QCM. The thickness of this layer (about 0.2– 0.5 µm), can be controlled either by the change in frequency, (eq 1) or by the charge passed through the cell. The experi- ment must be planned so that the surface of the QCM al- ways remains covered with a layer of copper not thinner than 0.05 µm. It is important to note that depositing layers thicker than 1–2 µm could lead to departure of the results from those expected according to eq 1 because of significant changes in the roughness of the surface. This can also happen when so- lutions with low copper concentrations are used or when high currents are applied. The use of an aqueous solution of 0.5 M CuSO4 and 0.5 M H2SO4 and current densities less than 20 mA�cm2 enable one to avoid some of these problems. The best way to avoid other problems is to carry out the experi- ment under computer control of the potential and ∆fm. All modern devices have suitable interfaces. In our setup the volt- meter (DV) and frequency controller (XTM�2) were con- nected to a computer. The program used enables one to set limiting values of potential and ∆fm, the attainment of which causes a relay of the XTM�2 to break the circuit (Figure 1). The Quartz-Crystal Microbalance W in an Undergraduate Laboratory Experiment III. Measuring Mass Vladimir Tsionsky School of Chemistry, Tel-Aviv University, Ramat-Aviv 69978, Israel;
[email protected] Figure 1. Scheme of the setup: XTM/2–frequency controller; PS–dc power supply (±(10–15) V) with ungrounded outputs; A–ammeter; DV–digital voltmeter; 1–set of resistors (1–30 kΩ, any type with watt- age more than 0.5 W); 2–Teflon cell; 3–Viton O-rings; QCM–quartz- crystal resonator; RE–reference electrode, Cu-wire inserted in a Teflon tube: CE–counter electrode, Pt-disk; WE and CE connections to elec- trodes of the resonator. The upper electrode serves as a working electrode and must be grounded (Gr). Both electrodes of the QCM (WE and SE) are connected to XTM/2 by screened cables. In the Laboratory www.JCE.DivCHED.org • Vol. 84 No. 8 August 2007 • Journal of Chemical Education 1341 Hazards Sulfuric acid is harmful if inhaled and can cause diges- tive and respiratory tract burns. It is corrosive. Copper sul- fate is harmful by inhalation or ingestion. In our laboratory the stock solution is prepared by a technician. Results and Discussion The data obtained from this experiment for different values of the current, (shown on the graph in milliamperes), are presented in Figure 2A. On the assumption that the elec- trochemical reaction studied has an efficiency of 100%, these data are shown in Figure 2B as the frequency shift, ∆fm, ver- sus mass change per unit surface area, m J A M nF t∆ = (2) where J is the applied current, A is the surface area of the QCM electrode in contact with the electrolyte, n is the num- ber of electrons participating in the reaction CuCu2+ + 2e− (A) M and F are the molar mass and the Faraday number, re- spectively, and t is the time of the experiment. With these values, all the data show a good fit to the same straight line. The slope of this line is used to calculated the experimen- tally obtained sensitivity of the QCM (eq 1): it is found to be Cmexp = (0.078 ± 0.001) (Hz cm2)�ng, about 4% lower than that expected for the 6 MHz QCM used, for which Cmtheor = 0.0812 (Hz cm2)�ng. This small deviation is con- sistent with the fact the chosen reaction is a two-step pro- cess, which takes place with the formation of univalent cop- per ions as a soluble intermediate, Cu +Cu2+ + e− K1 c K1 a K2 c K2 a CuCu+ + e− and (B) where superscripts c and a represent the cathode and anode, respectively. Transport of the univalent copper to the bulk of the solution, without taking part in the following step, de- creases the Faradaic efficiency of reaction. As a result, Cmexp < Cmtheor. Lowering the oxygen concentration in the solutions could reduce this discrepancy. It disappears completely when a one-step reaction is studied (e.g., Ag+ + e− Ag). Rate of Corrosion Copper dissolves in acid solutions in the presence of dis- solved oxygen: CuSO4 + H2OO2 + H2SO4 1 2Cu + (C) The rate of this process is determined by the rate of diffu- sion of dissolved oxygen to the electrode surface and can be obtained by following the frequency shift with time (Figure 3). Two curves shown here follow the corrosion of copper after the anodic (curve 1) and cathodic (curve 2) currents are switched off. The difference in the initial behavior of these curves is immediately noted and results from the above men- tioned peculiarities of the reaction studied. The concentra- tion of univalent copper in the vicinity of the electrode is determined by its rate of diffusion into the bulk of the solu- tion and the relations between the rate constants of the indi- vidual steps K1(2)a(c) of the overall reaction (reaction B). Figure 2. Frequency shift vs time of deposition and dissolution of copper (A), (applied currents, in mA, are shown near correspond- ing lines) and vs calculated (eq 2) changes of mass (B). Figure 3. Time dependence of the frequency shift after interruptions of the anodic, +3.5 mA, (1) and the cathodic, -3.5 mA, currents (2). In the Laboratory 1342 Journal of Chemical Education • Vol. 84 No. 8 August 2007 • www.JCE.DivCHED.org After 150–200 seconds, both curves have the same slope, corresponding to 1.3–1.4 ng�(cm2 s). Obviously, this is the time required for the concentration profile to reach its steady state. These measurements emphasize the advantages of the technique: such slow corrosion cannot be observed in situ and in real time by any technique other than the QCM. To obtain reproducible data, we recommend the use of freshly prepared solutions. This part of the experiment could be im- proved by suitable changes in the construction of the cell that would allow working with a controlled concentration of oxy- gen in solution or in stirred solutions. Electrochemical Kinetics As mentioned above, the experiments on metal deposi- tion or dissolution involve control of the electrode poten- tial. This can serve to introduce students to the basic principles of electrochemical kinetics. Figure 4 shows the volt- age–current dependence obtained during the deposition or dissolution of copper. This dependence can be described by the Butler–Volmer equation, j j0= a cf f − −e eα η α η (3) where j is the current density, j0 the exchange-current den- sity, η the overvoltage and αa and αc are the transfer coeffi- cients of anodic and cathodic reactions, respectively. Their sum equals the number of electrons participating in the re- action: αa + αc = n. For reaction A, n = 2. f = F�(RT ) where F, R, and T are the Faraday number, the gas constant, and the temperature, respectively. At low overvoltages, the cur- rent–potential dependence is linear, j = j0nFη�(RT), and this enables us to calculate j0. For the data presented in Figure 4, j0 = 0.9 mA�cm2. In accordance with eq 3, at high overvolt- ages the current–potential dependence shows remarkable de- viation from the linear dependence. All experimental data presented in Figures 2–4 were ob- tained in a typical student experiment. Conclusion The experiments described give the students an under- standing of the principles of the QCM technique and of the precautions to be taken when the QCM is used as a mass sensor. The experiments on copper deposition and dissolu- tion provide reproducible data that can be obtained in a two- to three-hour laboratory period. In the course of a semester about 20 experiments were made with the same quartz-crys- tal resonator without the need for renewing or disassembling the apparatus. Before the experiments we strongly recom- mend that the students refresh their knowledge of the basic principles of electrochemical reactions. The relevant chapters in textbooks of physical chemistry, (e.g., ref 5), would be ap- propriate. Figure 4. Overvoltage vs current density. Experimental data used for drawing the solid line and for calculating the exchange-current density (j0) are marked as closed circles. In principle, all the experiments could be organized with- out computer control. However, doing this would entail greater precautions to avoid the formation of bubbles on the surface of the QCM and its damage. Acknowledgments Financial support for this work by the Israel Science Foundation (grant 174�05) is gratefully acknowledged. I thank my colleagues S. Cheskis, E. Gileadi, and M. Urbakh and J. Penciner for their support and help. WSupplemental Material The principles of operation of the QCM and a descrip- tion of the equipment with remarks for instructors can be found in the Supplemental Material of our previous publi- cation (2). Instructions for students related to the experiments described in this article are available in this issue of JCE On- line. Literature Cited 1. Sauerbrey, G. Z. Phys. 1959, 155, 206–222. 2. Tsionsky, V. J. Chem. Educ. 2007, 84, 1334–1336. 3. Tsionsky, V.; Gileadi, E. Mater. Sci. Eng. A-Struct. Mater. 2001, 302, 120–127. 4. Tsionsky, V.; Daikhin, L.; Urbakh, M.; Gileadi, E. Looking at the Metal/Solution Interface with the Electrochemical Quartz-Crystal Microbalance: Theory and Experiment. In Electroanalytical Chemistry; Bard, A. J., Rubinstein I., Eds.; Marcel Dekker, Inc.: New York, 2003; Vol. 22, Chapter 1. 5. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford United Kingdom, 1998; pp 877–895.