Instrumentation for simultaneous measurement of double-layer capacitance and solution resistance at a QCM electrode

Sensors and Actunmrs B, 17 (1994) 247-255

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Instrumentation for simultaneous measurement of double-layer capacitance and solution resistance at a QCM electrode David W. Paul, Steven R. Clark and Theodore

L. Beeler

Department of Chemistty and Biochemiwy, UniversiIyof Arkansas, Fayetteville AR 72701 (USA)

(Received August 13, 1992; in revised form June 22, 1993; accepted July 15, 1993)

Abstract Double-layer capacitance and solution resistance are two parameters that can be used to indicate dynamic changes occurring near the surface of an electrode. Here, we report the development of instrumentation tbat simultaneously monitors data from the quartz-crystal microbalance (QCM) sensor and the electrical double-layer without the use of a potentiostat. The development of this instrumentation is reported along with some preliminary data. Early indications are that the capacitance responds to structural changes in the electrical double-layer. Changes in resistance reflect changes in the solution anywhere between the two electrodes. The frequency shifts of the QCM originate in structural changes that occur not only in the electrical double-layer but also farther out into the solution.

Iotroduction The quartz-crystal microbalance (QCM) employs an AT-cut quartz piezoelectric crystal that is used as a sensor in vacuum [l], air [2], or liquid [3]. A number of theories have been proposed to describe how the QCM electrode is coupled to an adjacent liquid [4-71. These models are of electrical networks that allow frequency shifts to be predicted from properties of the quartz and the liquid. Two kinds of experiments, ‘active’ and ‘passive’, are performed with the QCM. In ‘passive’ experiments [8] the impedance characteristics of the crystal and the QCM electrode/solution interface are determined using a network analyzer. In ‘active’ experiments the QCM is active in an electronic oscillator, and the series resonance is the only parameter measured. Several oscillator circuits have previously been used to drive piezoelectric sensors. Oscillators have been constructed using ‘ITL line drivers [9], discrete transistors [IO], or integrated differential video amplifiers [ll]. The performance of several of the more popular oscillator circuits has been reviewed by Barnes [12]. In general, the type of oscillator used has a profound effect on the frequency stability of the QCM oscillator. The overall performance of the piezoelectric sensor depends upon the electronic oscillator, the acoustic properties of the bulk crystal, the QCM electrode/ solution acoustic coupling, and the crystal/circuitry impedance match. Although the ‘passive’ experiment provides a more complete description of the QCM electrode/solution

09254005/94/$07.00 0 1994 Elsevier Sequoia. All rights reserved SSDI 0925-4005(93)00872-V

interface, it cannot separately monitor the changes in solution that occur within the electrical double-layer or within the influence of the oscillating sensor. In addition, network analyzers are orders of magnitude more expensive than simple oscillator circuits, precluding them from routine use. Although the active mode does not provide a complete description of the QCM electrode/solution interface, additional information about electrochemical Faradaic processes at the QCM electrode has been obtained by coupling a potentiostat to a QCM that is actively participating in an electronic oscillator [3]. The measurement of additional interface parameters is very useful in descriiing events that occur on the surface of a sensor. Other than Faradaic processes, double-layer capacitance is a descriptive parameter of the solid/solution interface. Several existing techniques measure doublelayer capacitance: bridge methods [13], charging methods [14], and vector impedance methods [15]. Doublelayer capacitance reflects structural changes that occur near the surface of the sensor [16]. The ability to monitor double-layer restructuring has led to the development of immunosensors in which capacitance changes represent the interaction between an antigen that is bound to the surface and antibodies that are in solution [17]. There have been reports indicating that the frequency of a piezoelectric crystal is a function of the ionic strength of the electrolyte solution [18, 191. In the experiments reported, both sides of the crystal were

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in contact with the liquid so that the impedance of the solution was in parallel to the crystal. The frequency of oscillation shifted according to this combined impedance and, therefore, with the admittance of the bulk solution. The instrumentation reported here is fundamentally different and is arranged so that capacitance changes at the electrode/solution interface are recorded separately from the frequency shifts of the QCM. Here we describe the development of new instrumentation that can measure the frequency of a QCM in resonance with an oscillator circuit, simultaneously with double-layer capacitance and solution resistance. Our experimental results indicate that the piezoelectric sensor changes frequency in response to changes at the QCM electrode/solution interface. In addition, the sensor itself (its surface roughness, the way fluid flows over it, and its mechanical oscillation) affects the doublelayer capacitance and solution resistance.

Experimental

Circuitry Simultaneously measuring the double-layer capacitance and oscillation frequency of the QCM electrode seemed straight forward, and we constructed an apparatus based on the design shown in Fig. 1 using available equipment. The oscillator circuit was one which we had previously developed [20], and had been successfully used in electrochemical quartz-crystal microbalance (EQCM) experiments [21]. The double-layer capacitance at the QCM electrode was measured by an impedance method previously developed by Ivarsson et al. using a commercial lock-in amplifier [22]. This method gave a reliable estimate of the double-layer capacitance and of frequency, but not both simultaneously, because the crystal stopped oscillating when

Fig. 1. Block diagram showing proposed instrumentation to measure double-layer capacitance and piezoelectric crystal frequency simultaneously: f=frequency counter; OSC=oscillator circuit.

the electrochemical cell was placed in the circuit. Oscillation failed for many reasons, and to find out what they were, we had to consider the impedance of all pathways available when the circuits were connected. Figure 2 encapsulates numerous unsuccessful attempts to measure double-layer capacitance and crystal frequency simultaneously. There are two circuit loops in the system: one through the crystal and the electronic oscillator and a second through the QCM electrode, electrolyte solution, counter electrode, and capacitance meter. Shown in the Figure is an electrical equivalent circuit for a mechanically resonating piezoelectric caystal. The series elements R, C,, and L express the QCM’s internal frictional losses, the compliance, and the mass of the crystal, respectively. The capacitor in parallel, C,, is a true electrical capacitance from the two electrodes separated by the quartz dielectric. The extra inductor, L,, prevents the megahertz frequency of the oscillator from entering the electrochemical cell. Likewise, the small capacitance of the crystal should prevent the 2 kHz signal of the capacitance circuitry from entering the oscillator loop. Unfortunately, the length of the leads between the QCM and the lock-in amplifier generated enough parasitic capacitance to upset the oscillation of the crystal [23]. In addition, the oscillator’s electrical excitation signal, which was meant for the QCM, was shorted through the electrolyte solution. Figure 3 shows circuitry that measures double-layer capacitance/solution resistance and crystal frequency simultaneously. The most important aspect of this arrangement is that the two measuring circuits have only one point in common, the QCM electrode, and this point is held at zero volts. We therefore redesigned the oscillator electronics so that the solution side of the crystal was at oscillator common. Details of this circuit will appear shortly [24]. To decouple double-layer measurements from the frequency measurements, the grounds between the two circuits must be isolated. Without isolation, the r.f.

Fig. 2. Illustration of instrumental problems encountered during development: I =pathway through oscillator and crystal; 2=pathway through capacitance meter and solution; other arrows indicate alternative pathways (see text).

249

IEEE

Fig. 3. Block diagram showing successful design for measuring both double-layer capacitance and crystal frequency.

signal from the crystal finds a low-impedance pathway to ground through the electrolyte solution or through the capacitance circuitry. We isolated plug outlet-ground by using separate power supplies or by using batteries to power the oscillator and capacitance circuitry. The frequency output of the oscillator was isolated by an r.f. transformer that separated oscillator common from the capacitance common, which would otherwise be connected via the shared ground between the frequency counter and the voltmeter. If complete circuit isolation is accomplished, no inductor (L,) is needed to prevent crosstalk between the circuits. In order to keep the leads to the crystal as short as possible, we developed an inexpensive dual-phase lockin circuit for measuring both double-layer capacitance and cell resistance [25]. This circuit was constructed on a single printed circuit board and placed back-toback with the oscillator electronics. In this way connections to the crystal were kept to 1 cm. We measured cell impedance under ‘open-circuit’ conditions with no d.c. potential imposed between the electrodes. The capacitance circuitry was conceptually no different from that of Ivarsson et al. [22], but has the added advantages of compact size, low cost, and the ability to obtain the cell resistance. To give orthogonality between in-phase and quadrature components, we adjusted the phase prior to each experiment by substituting resistance and capacitance values that were similar to those of the cell. Data-collection system

A block diagram of the data-collection system is shown in Fig. 4. Frequency data were recorded using an HP 5334A frequency counter (261, and voltages representing the in-phase and quadrature components of the cell were recorded on a Keithley DM 199 scanning multimeter [27].The data collected by these instruments were transferred to an HP Vectra personal computer [26] via IEEE interfaces. A program in Quick Basic [28] was written to pre-program the instruments and collect the data. The data were imported to the spread-

Fig. 4. Data-collection system: flow cell housing crystal; OX = oscillator circuit; freq - frequency output from oscillator circuit; meter=capacitance/resistance meter; cap =vohage output proportional to double-layer capacitance; res =voltage output proportional to solution resistance; P=pressure sensor measuring hydrostatic pressure in cell; counter=HP 5334A frequency counter, volt meter=Keithley DM 199 scanning multimeter; PC=HP Vectra personal computer.

sheet of the graphing program Axum [29] for transgeneration and presentation. Solutions and electrode preparation

A 0.15 M Trixma Base (Sigma Chemical Company) test solution was prepared, degassed, and brought to pH 7.4 by the addition of tritbtoroacetic acid. We used 10 MHz, AT-cut crystals polished to a 1 pm mirror finish or to a 3-S pm rough finish (International Crystal Manufacturing, OMahoma City, OK). These crystals were cleaned in a mixture of NH,OH, 30% Hz02, and double-distilled H,O to remove organic contaminants. The gold surface was considered to be hydrophilic after this procedure and was perfectly wetted by deionized water. The crystal is mounted in a Plexiglass cell similar in design to one by Hancock and Synovec [30], which provides laminar solution flow. The cell allowed only one side of the crystal to be exposed to the solution. An identical crystal, cleaned in exactly the same way, was used as the counter electrode. The test solution was passed over the crystal by a gravity feed system, which maintained a constant hydrostatic pressure over the cell. Results and discussion In electrochemical (EQCM) experiments, one of the crystal’s electrodes serves both as an active component in the oscillator circuit and as the working electrode in the electrochemical cell. In these cases, the electrical potential between the solution and the QCM electrode is established using a potentiostat. Such an arrangement allows the simultaneous measurement of both Faradaic current and mass changes resulting from an applied potential at the QCM electrode. If the equipment for measuring double-layer capacitance is similar to that of Faradaic responses, why could not standard electrochemical equipment be used? Indeed, Lacour et al.

[31] have recently used commercial equipment to measure both frequency and double-layer capacitance from a QCM electrode. However, an additional factor in all these applications is that the electrical potential at the QCM electrode (also the working electrode for the cell) is held at virtual ground by the potentiostat. In the Wenking potentiostat, the working electrode is connected directly to the common or ground of the potentiostat. This arrangement works very well and numerous experiments recording both Faradaic current and frequency measurements from an applied potential have been reported. In the absence of a potentiostat, the electrode in contact with the solution was not held at any imposed potential. In addition, our oscillator circuit placed the QCM’s electrodes at some d.c. level where stray capacitance coupling between the two circuits became a serious problem [12]. The mechanism for this coupling could be through the fringing r.f. fields entering the liquid, causing electrochemical processes or acoustoelectric interactions [32, 331. These processes were not investigated, but the major instrumental problem was solved by designing an oscillator circuit that has one side of the crystal grounded and exposing this same side of the crystal to the solution. If this same crystal face is also connected to the common of the capacitance circuitry, the only point the two circuits have in common is ground, and no d.c. potentials can develop. Figure 5 shows that when all the circuits are connected, the resistance/capacitance circuitry is electronically decoupled from the oscillator electronics. To test the circuitry, an oscillating crystal was placed in contact with the electrolyte solution, and the resistance and capacitance standards were varied. The recorded values of resistance and capacitance were those set by the standards. The frequency and capacitance were monitored as the standard resistance was varied by 1000 0,. Figure 5(a) and (b) shows that the frequency of the crystal drifted because of variations in power supply voltage; however, no abrupt frequency change occurred when capacitance or resistance values were altered. No impedance pathways exist between the oscillator and capacitance circuitry. Thus we believe we have developed a method to measure double-layer capacitance and QCM frequency simultaneously. .Results of our preliminary experiments depicting the effects of surface roughness, fluid flow, and mechanical oscillation of the crystal on double-layer capacitance and solution resistance are shown in Figs. 6 and 7. The trends of the data between the rough and smooth surfaces are similar, but there are ditI%rences that will be pointed out below. Frequency and capacitance increase when the buffer stops flowing over the QCM surface; when the oscillator stops vibrating the resistance increases and the capacitance decreases.

The following argument does not explain all aspects of the data, as many events occur simultaneously at the surface; it represents only a preliminary qualitative interpretation. The emphasis here centers on the type of information that can be obtained from simultaneous collection of QCM and double-layer data. We believe that capacitance reflects changes that occur very near the surface and within the electrical double-layer; solution resistance reflects conductivity changes that occur anywhere between the QCM electrode and the counter electrode, and frequency measurements reflect changes that occur anywhere in the viscoelastic layer of the solution dragged by the sensor. This viscous layer is expected to extend about 200 nm out into the liquid [34] and should include all of the electrical double-layer and a portion of the bulk solution. When the flow is turned off, a small change in capacitance is seen. This would indicate that once established, the electrical double-layer is little affected by solution convection. This is not surprising, as hydrodynamic boundaries separating convective flow from the inner stagnant layer next to the surface are known to be further from the electrode than the limits of the electrical double-layer [35]. Under the no-flow condition, the solution resistance slowly decreases, indicating an increase in the conductivity of the solution. The large frequency change indicates that some structural changes have occurred in the viscoelastic layer of the crystal. The changes in all three parameters can be rationalized by the following argument. The simplest model for motion of the piezoelectric crystal is that of a mass-spring model with the resonance frequency, fo,given by

where k is the stiffness constant for the spring and m is the mass of the attached body. The pressure in the cell was continuously monitored during the course of the experiment (not shown) and increased from 0.1237 to 0.1252 psi when the flow was stopped. Because of the increased pressure, the fluid over the crystal would be expected to compress slightly, yielding a more rigid structure. Apparently, the more rigid structure increases the restoring force on the displaced crystal surface. This increase in spring stiffness causes the frequency to increase. The increase in pressure causes a compression of the outer Hehnholtz layer and increases the charge density of the layer, causing a slight increase in capacitance. The resulting increase in charge density also causes a decrease in solution resistance. Flowing solution also produces ‘noisier’ frequency data, indicating that the QCM is sensitive to the convective movement of solution.

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Tbe response caused by disconnecting the oscillator indicates that the mechanical shear motion of the crystal has a profound effect on the structure of the doublelayer. The change in capacitance is caused by either redistribution of charge after the shear motion ceases or by the shear motion itself, which may increase the polarization of the dielectric in the inner Helmholtx plane [36]. These results contrast with the results of experiments by Lacour et al. [31], which indicated that crystal vibration does not affect the double-layer capacitance of the bare gold surface. The difference in our work is that the potential of the electrode is not under potentiostatic control and the effects of oscillation were measured at a single electrode in one experiment. These authors did, however, report that the motion of the crystal does affect the kinetics of protein adsorption, indicating that transport of material into and out of the double-layer is altered by the vibration of the crystal.

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The shear motion of tbe crystal is known to produce some electrokinetic effects. Hager et al. [37) have defined an electrokinetic term in the equation for frequency shift, which is expressed as the electrokinetic force per unit area between the QCM electrode and the solution. The motion of the QCM drags charge in the electrical double-layer, which in turn produces an electric field. This additional electric field may caused the molecules in the electrical double-layer to polarize further. When the QCM ceases to vibrate, the electrokinetic effect is removed and the capacitance decreases. An alternative argument may be that the motion of the QCM merely traps charge in the microscopic grooves on the gold surface and that this charge escapes when the oscillation stops (see below). What causes the differences in the data between the ‘rough’ (Fig. 6), and the ‘smooth’ (Fig. 7), surfaces? When the oscillator stops, the capacitance decreases

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Fig. 6. Effect of 0.1 M Trizma buffer on hydrophilic rough gold QCM electrodes at a flow rate of 0.24 mknin, for the following conditions: O-190 min, buffer flowing over oscillating crystal; 190-370 min, crystal oscillating in stagnant buffer; 370-800 min, ctystal oscillation disabled in stagnant solution. (a) Frequency (-) and capacitance ( . . . . .) changes. (b) Frequency (-) and resistance (. . . .) changes. The frequency trace is the same in both graphs.

more on the rougb surface than on the smooth surface, but it does decrease on both, indicating that the doublelayer structure of the two surfaces is similar. Resistance fluctuates much more on the smooth surface than on the rough. These changes must be related to changes in solution structure that are within sensing range of the crystal, since the frequency also fluctuates more on tbe smooth surface than on the rough surface. Studies of the effects of surface roughness on the frequency shift of a QCM [38, 391 have shown that an oscillating rough surface traps solution and moves it with the motion of the surface. This would indicate that the motion of the rough surface is a dominant force in determining the structure of the solution next to it. Ions trapped in the rough surface during motion would escape after the motion ceases, leading to the observed drop in capacitance and increase in resistance.

This would explain why the resistance and capacitance changes on the rough surface are larger than those of the smooth one. The idea of interfacial slip of the thickness shear waves could also be used to explain some of the data [7]. We suppose that the motion of the rough surface provides for a well-defined slip-layer boundary. The smooth surface allows the position of the slip-layer boundary to drift to and from the electrode, causing the resistance and tbe frequency to vary more on the smooth surface.

Conclusions The instrumentation presented bere provides a means to measure double-layer capacitance, solution resis-

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Fig. 7. Effect of 0.1 M Trizma buffer on hydrophilic polished gold QCM electrodes at a Bow rate of 0.25 mUmin, for the following conditions: O-180 min, buffer flowing over oscillating crystal; 18&4CKlmin. crystal oscillating in stagnant buffer; 400-800 min, crystal and resistance oscillation disabled in stagnant solution. (a) Frequency (-) and capacitance (. . . . . ) changes. (b) Frequency (-) (. .. ..) changes. The frequency trace is the same in both graphs.

tance, and crystal frequency simultaneously. For successful operation, the oscillator electronics and capacitance circuitry must use separate and isolated grounds. In addition, the two circuits hold the QCM electrode in common, at zero volts. Isolation of frequency output is essential, since oscillator and capacitance common can be shorted via instrument ground. Our intent in developing this instrumentation was to measure double-layer capacitance in the absence of an externally imposed d.c. potential from a potentiostat. An important use of such a system would be, for example, to observe protein adsorption without an externally imposed potential, and thereby reflect more accurately the conditions found in nature, where no such imposed potential exists. Under these conditions, the potential between the QCM electrode and the solution will be

established by the double-layer processes only. This potential is unknown, but it can be measured using an electrometer and a reference electrode [40, 411. We have shown that this instrumentation can be used to probe the structure of the surface layer over a liquidimmersed piezoelectric crystal electrode with both static and flowing liquids. Our findings are expected to be of significant future relevance, leading to possible reinterpretation of past studies of molecular reactions and structural reorganizations sensed at the oscillating surface of AT-cut quartz and other piezo-devices. These structural changes would include: molecular rearrangement caused by hydrophobic/hydrophilic interactions [41], conformational changes that occur during and after protein adsorption [42], and enzyme/substrate [43, 441 or antigen/antibody (45-481 interactions. Operating

254 in the active mode, this instrumentation should prove useful in probing all the above types of surface interactions, and could lead to the development of new generations of inexpensive biosensors. We hope to report on a more theoretical model for our system in the very near future.

Acknowledgements This work was supported by a grant from the Whitaker Foundation; US-Sweden Cooperative Science Program, of the National Science Foundation, INT - 8813562 and NSF EPSCoR Phase III. The authors also wish to thank Ingemar Lundstrom of Linkiiping Institute of Technology for his helpful suggestions.

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Biographies David W. Paul holds a B.S. degree from Southwestern University and a Ph.D. in analytical chemistry from the University of Cincinnati. He is currently an associate professor of analytical chemistry in the Department of Chemistry and Biochemistry, University of Arkansas at Fayetteville.

Steven R. Clark holds both B.A. and Ph.D. degrees from the Department of Chemistry and Biochemistry, University of Arkansas at Fayetteville. He is currently a postdoctoral student in the Interface Biology Group at the Laboratory of Applied Physics, University of Linkoping, LinkGping, Sweden. Theodore L. Beekr obtained a BSEE degree from the University of Arkansas and a MSEE degree from Newark College of Engineering. After holding positions with Bell Telephone Laboratories and General Electric Co., he is now a research associate in the Department of Chemistry (retired), University of Arkansas at Fayetteville.