Prussian Blue coated quartz crystal microbalance as a detector for

Prussian Blue Coated Electrode as a Sensor for Electroinactive Cations in Aqueous Solutions. Houston Byrd , Blake E. Chapman , and Christopher L. Tall...
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Anal. Chem. 1989, 61, 290-295

290

Prussian Blue Coated Quartz Crystal Microbalance as a Detector for Electroinactive Cations in Aqueous Solution Mark R. Deakin* and Houston Byrd'

Department of Chemistry, Florida State University, Tallahassee, Florida 32306-3006

A fllm of Prusslan Blue (PB) deposlted on a quartz crystal microbalance (QCM) Is used to detect electrolnacthre catlons In solutlon. thls composlte devlce Is the basis of a new analytical technlque. The current and frequency responses of the device are related to the lon-exchange and redox propertles of the electroactlve PB fllm and are generally nonllnear wlth concentratlon. The response of the device Is demonstrated both In static solution and In a flowlng stream of solutlon. Optlmlzatlon of the flow cell Is not complete. However, detectlon llmlts for the Injection of K+ In 0.01 M HNO, are currently 0.1 mM when obtalned from the frequency response of the QCM and less than 0.1 mM when the current response of the PB film Is used.

INTRODUCTION A number of authors have explored the equilibria that affect ion incorporation in redox polymers (1-3), and the broader topic of ion exchange has been reviewed in several classic texts ( 4 5 ) . Recently, the voltammetric response of redox ion-exchange films has been applied to solution analysis, both for pH measurement (2) and the detection of electroinactive anions (6). In this paper we present a method for the detection of electroinactive cations using an electroactive polymer film attached to a quartz crystal microbalance. The method is demonstrated by using flow injection analysis. Within the last few years several research groups have demonstrated the use of the quartz crystal microbalance (QCM) in solution (7-9). They have shown that the QCM functions as a mass-sensitive detector a t the solid/solution interface (10). A few of these authors have used the QCM for analysis in solution (11). Other researchers have applied the QCM to the study of electrochemical phenomena. One interesting application of the QCM to redox chemistry is the use of the QCM to monitor the movement of ions in and out of electroactive polymer films (12,13). The frequency of the QCM reflects the mass of ions and any trapped solvent in a polymer affixed to the QCM surface. During oxidation or reduction of the polymer, ions migrate in or out of the film, often with associated solvent molecules. This changes the total mass of the polymer f i i and alters the frequency of the QCM. Additionally, any changes in the viscoelastic properties of the film will affect the frequency of the QCM. The electroactive polymer film chosen for this series of experiments is Prussian Blue (PB). The electrochemistry of P B has been discussed by many authors and was the subject of a recent comprehensive review (14). PB is an electroactive, mixed-valence iron-cyanide complex that can be affixed to a QCM surface. It forms as a rigid, highly cross-linkedpolymer with a zeolite structure (4). During reduction of the film and subsequent reoxidation to PB, cation transport in and out of the film greatly predominates over anion transport (12, 14, 15). For that reason, the electrochemistry of P B films is

Present address: Department of Chemistry, Samford University, Birmingham, AL 35229. 0003-2700/89/036 1-0290$01.50/0

affected by the type and concentration of cations in solution. Thus, the voltammetric response of PB should be useful for detecting cations in solution. To add specificity to the detection scheme, the mass of the cations in the film could be measured in the film during the voltammetric response. This type of experiment is possible with a PB-coated QCM (PBQCM). Due to the rigid nature of the film, the viscoelastic properties of PB should remain constant during redox cycling. Thus, the frequency of the QCM should reflect the mass of cations and solvent transported in and out of the film. Indeed, cation incorporation into P B has been measured with the QCM (12). However, in this previously published paper, the authors restricted themselves to work in static solutions and did not discuss the analytical applications of the PB-QCM. EXPERIMENTAL SECTION The microbalance employed 2.5-cm-diameter,AT-cut, quartz wafers with fundamentalfrequencies near 5.0 MHz. The electrode pads, consisting of a 2.5-nm Cr film followed by a 150-nmAu fib, were evaporated onto the quartz wafer (Edwards 306A coater). The Cr provided an adhesion layer for the gold and did not influence the experiments described herein. The orientation of the electrode pads and the associated mcillator circuitry have been described previously (9,16). Prussian Blue films were deposited onto the working electrode pad by reductive crystallization at 10 WAcmd2for 1000 s (1.0 X C cm-2) from a solution of 2 mM FeC1, and 2 mM K3Fe(CN)6adjusted to pH 2 with HCl. After deposition of PB, the electrode was cycled in 0.5 M KNO, until a stable frequency response was obtained. This cycling was necessary in achieving a reproducible frequency response (vide infra). The PB films on the electrodes were kept damp during transfer between electrochemical cells. Reagent grade nitrate salts were used without further purification. Salt solutions were prepared with purified water from a Milli-Q ion-exchange system (Millipore). Acid solutions were prepared from reagent grade HNO, (Fisher) and purified water. Electrochemical experimentsin static solutionswere performed in a glass cell with separate reference and auxiliary compartments. The PB-covered QCM was mounted in a side arm of the cell between two O-rings. The static solutions were deoxygenated by bubbling with ultrahigh-purity nitrogen. Experiments in flowing solutions employed a PB-QCM mounted between O-rings with a jet of solution directed at the center of the working electrode pad. A low-pressure injection valve and a sample loop of approximately 200 ILLwere employed. Solution flow was provided by a syringe pump (Isco LC-5000) at a flow rate of 60 mL h-l. The flow cell contained both the auxiliary electrode and the PB-QCM. A gold foil auxiliary was located directly opposite the working electrode at a distance of approximately 0.5 mm. The reference compartment was located downstream from the working-auxiliary pair and contained a sodium saturated calomel electrode (SSCE). No attempt to deoxygenatethe flowing solutions was made. The potentiostat and galvanostat used with the QCM were similar to those described previously (16,17). The frequency of the QCM was monitored with a high-resolutioncounter (Philips PM6654). All current, potential, and frequency data were digitized and stored on a microcomputer for later analysis. RESULTS AND DISCUSSION Redox Ion-Exchange Theory. Prussian Blue (PB) is an electroactive ion exchanger. It can be deposited onto an @31989 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989

281

electrode surface by reductive crystallization with a probable composition of Fei1'(Fe"(cN)& (15). If the redox state of the film is cycled in a solution of some alkali-metal cations, these cations are incorporated into the polymer film. The structural changes resulting from this cycling are a matter of controversy. However, after several redox cycles, a steadystate response is obtained that is characteristic of the following half-reaction:

+

Fe111Fe11(CN)61- e-

-

Fe1'Fe1*(CN)62-

(1)

Cation migration from solution balances the charge developed during the reduction of the polymer. To facilitate the coupling of ion-exchange equilibria with redox equilibria, we have chosen not to include the cation in half-reaction 1. The type and quantity of cations in a film of PB depend on both the applied potential and the concentration of cations in solution. As a consequence, the electrochemistry of the film is governed by both redox and ion-exchange equilibria. Cation exchange between solution and the PB film affects the redox process by adding a potential drop at the solution/film interface. This potential drop is referred to as the Donnan potential and is given by

where ziis the valence of species i, a; and d j are the activities of species i in solution and the film, respectively, II is the swelling pressure, and v; is the partial molar volume of species i. Several authors have pointed out that the formal potential for reduction of PB depends on the concentration of cations in the solution (18). This shift in the formal potential, AEf, can be calculated from the shift in the Donnan potential, AEbn. Since Ebn is defined as the potential in the film relative to solution, AEf = AED,. For the case of a single type of cation in solution, at Ef the concentration of cations in the film is constant. Thus, the values of ai, II, and v; are constant, and AEf is given by the following:

AEf = AED, = ( R T / z i F ) AIn ai

(3)

This relation, for example, leads to an observed shift in Ef of 0.059 V per decade of change in [K+] for the reduction of PB (18).

For the case of two different types of cations in solution, the situation is a bit more complex. A relationship between the activities and concentrations of the two ions in the film and solution is needed. A parameter that is used frequently for this purpose in discussions of ion exchange is the molar selectivity constant, KAB(2,19). For two cations, A and B, carrying charges of ZA and zB, K M is defined as (4)

where Ci and Cj are the molarities of ion A or B in solution and the film, respectively. The variation of KAB with the molarities of A or B reflects changes in the activity coefficients of the ions in solution and in the polymer and changes in the polymer swelling pressure. Electroneutrality in the film requires that zACA

+ zBCB

=S

(5)

where S is the total number of anionic sites in the film. For Prussian Blue, S is a function of the redox state of the film and equals the number of sites of the type FenFem(CN)Bplus twice the number of sites of the type Fe11Fen(CN)62-.Thus, S is a function of both the applied potential and the formal potential of the redox couple.

0.001

0.01

0.1

1.0

IO

100

1000

CA CA,f

cA,

Flgure 1. Concentration of cation A in the film, relative to the solution ccncentration,CA,and referenced to condltbns at the formal potential, Chf and Ck(.Applled potentials, [ = ( E - €,)zf/(RT), were (a) f = -5, (b) f = -1, (c) = 0, (d) f = 1, and (e) f = 5.

The combination of eq 4 and 5 yields expressions for the concentrations of cations A and B in the film:

(7) These expressions can be solved for specific valencies of the two cations. For example, for the case where Z A = ZB = 1

while for zA = 1 and zE = 2, the following applies:

The quantity C B can be obtained from C A with eq 5, or specific expressions for C B can be derived from eq 7. For the case of two cations in solution the formal potential is referenced to the situation when only cation A is in solution. The shift in the formal potential for the film is now approximated by the following relationship:

AEf

AEDon

= ( R T / z ; F ) AIn (C,/C,)

(10)

The use of this equation implies that only the Donnan potential contributes to E6 in other words, that in the absence of AEDon, Ef is invariant with the type of cation in the film. Voltammetricdata for PB films in several electrolytes suggest that this is a fairly good approximation (15). Contributions to AEf from variations in the sue of cations, swelling pressure in the film, and changes in activity coefficients are included in the term K B , so assumptions about their effects are not necessary at this point. The expressions above are used with the Nernst equation for half-reaction 1to calculate the quantity and type of cations in the film for a variety of solution conditions. The case for a single type of ion in solution is considered first. Figure 1 depicts the change in the concentration of ion A in a PB film relative to the concentrationin the f ilm at the formal potential, CA,has the solution concentration of A is varied relative to the concentrationin solution at the formal potential, C u The activity coefficient for A is assumed to be constant. As CA varies, the formal potential of the film shifts, as noted in eq 3. Thus, changes in CAcan lead to oxidation or reduction of the film depending on the potential applied to the film, f =

292

ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989 C

0.0

0.5

I .o

/

0.0

CA

.

.

.

0.5

.

I

I.o

CA+ CB Flgm 2. ConcentraUon of monovalent cations A (solid) and B (dashed) in the fikn, C,,referenced to conditions at the formal potential with only A In solution, Selecttvlty coefficients were (a) KCIB= 10, (b) K, = 1, and (c) K A B = 0.1: applied potentlal of 5 = 0.

cA,,.

(E - Ef)ziF/(R7'). As the redox state of the film changes, the number of anionic sites, S, varies, and the concentration of A in the film changes. Of course, if the film is not under potential control, no redox processes occur, and no change in C A is observed as CA is varied. For the case of two cations in solution, the concentration of A or B in the film depends on several factors: the applied potential, the ratio of A to B in solution, the valencies of the ions, and the selectivity coefficient. Similar to the case for a single cation, the redox state of the film can be shifted as the total concentration of cations is varied, and the concentrations of ions in the film will change accordingly. A more interesting situation occurs when the total ion concentration is held constant and the relative concentrations of cations A and B are varied. Figure 2 depicts the case for two monovalent cations when the film is held at the formal potential (,$ = 0, measured when only A is present in solution). As the concentration of A is lowered relative to the total concentration of ions in solution, cation B enters the film by ion exchange. Depending on the selectivity coefficient, the value of ED, may increase or decrease. As E%,, varies, the film is oxidized or reduced, causing further ion transport between the film and solution. The results are a simple linear relationship between concentration in the film and solution when KAB = 1 (EDon is constant), and a series of nonlinear relationships for other values of KAB (Eh,,varies). If the cations have different valencies, the equilibria are shifted. For example, if Z A = 1 and Z B = 2, the equilibrium concentrations in Figure 3 are predicted. Again, linear behavior is calculated when K B = 1and nonlinear behavior when K B is greater or less than 1. For simplicity, the discussion above includes a few assumptions. KABis treated as a constant as the relative concentration of the cations in solution is varied. For most ion exchangers, KABvaries with the solution composition. Since PB has a rigid, zeolitic structure, this variation is minimized (4). However, KABincludes contributions from changes in activity coefficients of both ions in solution and the film as well as changes in the swelling pressure and partial molar volumes of ions A and B. Since these factors can vary with concentration, the figures above are useful only as a guide in predictingthe equilibria for a real fii. Additionally, PB films often contain variations in their structure (14). Thus, variations in Ef and K B may appear within the film. The treatment above is still valuable in understanding the response of a P B film to changes in electrolyte composition and concentration. Response of the Microbalance. The response of the QCM in solution is governed by the Sauerbrey equation (20) A t = -2Amfo2/[nA(pp)1/2] (11)

Flgure 3. Concentration of monovalent cation A (solid) and divalent cation B (dashed)in the film, e,,referenced to conditbns at the formal potential with only A in solutlon, eA,vSelectivity coefficients were (a) KAE= 10, (b) K A E = 1, and (c) K A B = 0.1; applied potential of 5 = 0.

0 I

0.4

0.2

0.0

,

!

-0.2

E ( V vs SCE)

Figure 4. Response of the PB-QCM in 0.5 M KNO, cycled at 0.01 V s-': (a) current, (b) frequency change. Osclllation was at f , = 5.02 MHz; average of five scans. where Af is the change in oscillation frequency, AmlA is the change in mass of the film per unit area, f o is the oscillation frequency a t the nth harmonic, p is the shear modulus of quartz (2.947 X lo1*g cm-' s - ~ ) ,and p is the density of quartz (2.648 g ~ m - ~During ). the reduction and oxidation of PB films on a QCM, the frequency varies as cations move in and out of the film. The frequency also varies as one cation is replaced by another of differing molecular weight during ion exchange. The value of Am/A is obtained from Af and used with the charge per unit area (obtained from the current density, j ) to calculate a mass to charge ratio for ion transport during a redox process. Response of the PB-QCM to K+.The electrochemical response of PB films is often demonstrated in K+ electrolytes. The potassium ion has a hydrated radius that allows transport in and out of the PB lattice. Figure 4 shows both the current and QCM response after several voltammetric cycles of PBQCM in 0.5 M KNOB. The first few cycles of the film result in a net mass loss in the film as some Fe3+ions are replaced by K+ (12). However, after several cycles a constant response is obtained. The number of available anionic sites per unit area can be estimated from this data or from the amount of charge passed during deposition of the film. During film deposition a total charge of 1.00 X C cm-2 is passed. Assuming initial formation of a Fet11(Fer1(CN)6)3 lattice followed by loss of Fe3+ to give a Fe111Fe11(CN)6lattice, a site density of 1.0 x mol cm-2 is calculated. This value can be compared with a site density calculated from the total

ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989

203

0.3

I

4

,

l

,

I

,

I

,

I

,

1

CK

+

C",

Figure 5. Mass flux during constant current (0)reduction and (0) oxidation of a PB film for various relative concentrations of K+ and NH4+. Current densky was 20 FA cm-'; each point is the average of

0

five scans.

charge passed during reduction of the film, 8.1 X lo4 mol While this data does not prove the postulated change in lattice structure, it does provide a useful correlation between deposition current and the number of ion-exchangesites in the film. Selectivity of PB Films. Several authors have pointed out that redox processes in PB films depend on the type of cation in solution. Certain cations appear to enter the film easily while other are excluded. This exclusion is usually correlated with the hydrated radius of the cation. Ions with hydrated radii much greater than the channel radius for PB, about 0.16 nm (21),should not be able to enter the rather rigid PB lattice. This difference in the ability of ions to enter the P B film is reflected in the molar selectivity constants, Km, for pairs of cations. The selectivity constants are expected to favor the incorporation of K+, Rb+, Cs+, and NH4+ over that of larger solvated ions like Li+, Na+, and Ba2+ (15). Additionally, the response of PB in acid solutions suggests that the incorporation of H30+ into the film is not favored (15). The magnitude of the selectivity constants can be estimated from experimental data for some pairs of cations. PB films are exposed to solutions containing two kinds of cations, and these ions are forced in and out of the film by passing constant reducing and oxidizing currents or by stepping the potential applied to the film. The ion flux is known from the current passed, while the mass flux in or out of the film is calculated from the response of the QCM. The mass flux includes the cations transported between solution and the film as well as any solvent molecules carried with the cations. Comparison of the mass flux at a constant current or the mass to charge ratios for a series of solution compositions yields Km for the cation pair. These experiments also can indicate how K m varies as a function of the relative cation concentrations in solution. Data for the incorporation of K+ and NH4+ is given in Figure 5. A PB f i i is placed in a static solution and exposed to 25-s cathodic and anodic current pulses of 20 FA cm-2. About 5% of the film is reduced and oxidized during this process. The total cation concentration in solution is held at 0.1 M while the relative concentrations of K+ and NH4+are varied. As noted in the figure, increasing the relative concentration of K+ increases the observed frequency change and, thus, the mass flux. This is due to the greater molecular weight of K+. Comparison of the mass flux for a mixture of K+ and NH4+to the mass flux for solutions of only K+ or NH4+ yields an estimate of K m for this cation pair. For an equal mixture of K+and NH4+,the mass flux is approximately the average of the mass fluxes for solutions of the individual ions. This indicates that both cations are entering the film at about the same rate and that the value of K m is approximately 1 for this pair of cations.

V

-12

1

80

40

t

120

.

1

.

160

(SI

F ure 6. Response of the PB-QCM to the flow Injection of 0.005 M K and 0.005 M H+ in a stream of 0.01 M HN03: (a) current, (b)

'a

frequency change. The applied poteMial was (solid) 0.1 V and (dashed) 0.5 V vs SCE.

Experiments performed with other sets of cations were less conclusive than those presented above. Constant current experiments were performed with K+ in association with each of the following cations: Na+, H+, and Ca2+. In every case the incorporation of K+ into the fiim is favored over the other cation. However, due to fluctuations in the frequency data, precise values of Km could not be determined. Response of t h e PB-QCM to Flow Injection. The analytical utility of the PB-QCM is demonstrated by placing the PB-covered microbalance in a flow injection apparatus. With the device in a flowing stream the character and concentration of the solution in contact with the detector can be varied rapidly. When the PB film on the QCM is under potentiostatic control, the PB-QCM will respond to changes in cation type and concentration in two ways, by passing a redox current and by changing frequency. The response to an injection of K+ in a solution of "03 is shown in Figure 6. During the injection, the concentration of cations in solution is constant and the potential is held a t 0.1 V vs SCE, near Effor the film. As K+ replaces H+ in solution, the concentrations of H+ and K+ in the film shift as described in eq 5, 8, and 10 and in the Nernst equation for half-reaction 1. These shifts in CH and CK are manifested as changes in the mass of the film and as a shift in Ef for the film. The frequency of the QCM reflects the mass change while the observed current is due to AEo Since the PB film favors the incorporation of K+over H+ (KHK< I), increasing C K results in a cathodic current and a net mass increase. The mass of the film continues to increase as long as a cathodic current is flowing. As CKreturns to zero, Efreturns to ita initial value as an anodic current and mass decrease are observed at the PB-QCM. If a similar experiment is performed with the electrode held at 0.5 V vs SCE, far from Et, almost no current response is observed, and the frequency change is diminished. This variation in reponse with potential is an important property of the PB-QCM. The sensitivity of the detector is enhanced if the electrode is held near the formal potential of the P B film. In that potential region small shifts in Efinduced by changes in the Donnan potential result in observable changes in the redox state of the polymer. This phenomenon also indicates why the use of an electroactive polymer is important in the detector design. An electroinactive polymer on the QCM can change mass only through ion exchange between the polymer and solution; no change in redox state is possible. Thus, assuming approximately the same density of ion-exchange sites, the response of an electroinactive film will be

ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989

294

Table I. Response of the PB-QCM to the Flow Injection of Various Cations ion

A), PA cm-'

A f , Hz

AQ, fiC cm-'

NH4+

48.9 34.6 74.2 8.0 8.2

8.1 13.4 14.2 7.2 10.2

635 296 671 71 74

Na+

K+ Ca2+ Ba2+

AmlN

g

equiv-*

Q

1.0

21.2 75.3 35.2 84.5 115

smaller than that of an electroactive film poised near its Ef. The PB-QCM also responds to the flow injection of other electroinactive ions. Table I summarizes the response to a series of ions injected a t 0.1 V vs SCE in a flowing stream of 0.01 M "0% The injected solutions had salt concentrations of 0.005 M for the monovalent cations and 0.0025 M for the divalent cations as well as an acid concentration of 0.005 M. It is clear from the table that both the current and frequency changes recorded at the PB-QCM vary with the type of ion injected. It is also evident that the PB-QCM responds to the injection of ions that are thought to be too large to enter the PB lattice. The ions K+ and NH4+have solvated radii small enough to enter the P B lattice. The PB-QCM responds as outlined above, producing both a current flow and a mass flux. The mass to charge ratios observed during the injection are 35 and 21 g equiv-' for K+ and NH4+,respectively. These values are slightly less than the molecular weighb of the ions, suggesting that some water or H30+is released from the film during ion uptake. The other ions in Table I have larger hydrated radii and should not enter the PB lattice easily. However, both the current and mass flux measurements suggest that these ions do enter the film. The mass to charge ratios calculated for Na+ and Ca2+are substantially greater than their molecular weights. This may be due to the stronger hydration of these ions leading to swelling and the trapping of additional water in the film. The response of the PB-QCM to changes in the relative concentration of an ion in solution is demonstrated in Figure 7. This data is obtained when various concentrations of K+ are injected in a flowing stream of 0.01 M HN03 with the PB-QCM held at 0.1 V vs SCE. The total ion concentration in solution is maintained a t 0.01 M to reflect the conditions that might be encountered by a detector in single-column ion chromatography. As the relative concentration of K+ is decreased, the response of the PB-QCM to the injection diminishes. Both the frequency shift in the QCM and the charge passed during the injection tend nonlinearly toward zero. This nonlinear response to concentration is due to the preference of the film for K+ (KHK < l),as discussed above. Error bars of approximately fl Hz are placed on the At data due to fluctuations in the response of the PB-QCM. In general, the current response of the PB-QCM is more stable than the corresponding frequency response. Therefore, error bars are not placed on the charge data. At present, the data from only two electrodes is available, so the data set is too small to estimate errors due to variations between electrodes. The frequency data in Figure 7 indicate that the detection limit for K+ in a solution of pH 2 HN03 is about 1 X lo-* M. This limit is set by noise in the frequency measurement. The QCM is very sensitive to pressure changes in the flow cell. Pressure changes are minimized by using a syringe pump as the solution source. However, the cell design is not optimized. It is possible that turbulence in the flow causes some of the low-frequency noise in the frequency data. This effect would be minimized by replacing the wall-jet cell design with one that provides a more laminar flow over the QCM surface. In contrast, the current and charge data have a much higher signal to noise ratio than the frequency data. Detection limits

Figure 7. Response of the PB-QCM to the flow injection of various concentrations of K+ in "0,: (a)total charge, (b) frequency change. Total cation concentration is constant at 0.01 M.

based on this data would be lower than those reported above. Stability of the PB film on the QCM surface is important in determining the lifetime of the PB-QCM detector. The films prepared as described above are stable in solution for several hours, assuming that no extreme potentials are applied to the PB film. Loss of PB appears to be highest where the jet of solution strikes the PB-QCM surface. This loss could be decreased by redesigning the flow cell. Long-term stability of the f i b , however, will need improvement before this device can be applied routinely. CONCLUSIONS The PB-QCM is useful for the detection of a variety of electroinactive cations in aqueous solution. Both the frequency and current response of the detector will, in most cases, be nonlinear with concentration. The response also will vary with the type of cation being detected. This property may be useful for identification of the cation during detection. In addition, the sensitivity of the PB-QCM is affected by the potential applied to the PB film. Maximum response is obtained when the film is held near the formal potential for the film. Since potential control is difficult in media of low ionic strength, the detection scheme described above is most appropriate in solutions of high ionic strength. However, for work in weakly conducting media, it may be possible to adapt the PB-QCM for constant current detection and eliminate the need for potential control. LITERATURE CITED (1) Dublhofer, K.; Armstrong, R. D. Nectrochim. Acta 1988, 33, 453-460. (2) Naegeii, R.; Redepenning, J.; Anson, F. C. J . Phys. Chem. 1986, 9 0 , 6227-6232. ( 3 ) Espenscheid, M. W.; Martin, C. R. J . Electroanal. Chem. Interfackrl Nectrochem. 1985, 188, 73-84. (4) Helfferich, F. Ion Exchange; McGraw-HIII: New York, 1962. (5) Ion Exchange; Marinski, J. A., Ed.; Marcel Dekker: New York, 1966. (6) Ikariyama, Y.; Heineman, W. R. Anal. Chem. 1986, 58, 1803-1806. (7) . . Kaufman. J. H.: Kanazawa.. K. K.:. Street. G. B. phvs. Rev. Lett. 1984. 53,2461-2464. (8) Bruckenstein, S.; Shay, M. Nectrochlm. Acta 1985, 3 0 , 1295-1300. (9) Melroy, 0.;Kanazawa, K.; Gordon, J. G., 11; Buttry, D. Langmulr 1986, 2. 697-700. (10) Kanazawa, K. K.; Gordon, J. G., 11; Anal. Chim. Acta 1985, 175, 99-105. (11) Thompson. M.; Arthur, C. L.; Dhaliwai, 0. K. Anal. Chem. 1988, 58, 1206-1209. (12) FeMman, 8. J.; Melroy, 0. R. J . Electroanal. Chem. InterfacialElectrochem. 1987, 234, 213-227. (13) Orata, D.; Buttry, D. A. J . Am. Chem. SOC.1987, 109, 3574-3581.

Anal. Chem. 1989, 61, 295-302 (14) Itaya, K.; Uchlde, I.; Neff, V. D. Acc. Chem. Res. 1986, 19, 162-168. (15) Itaya, K.; Ataka, T.; Toshima, S. J . Am. Chem. SOC. 1982, 104, 4767-4772. (16) Deekin, M. R.; Melroy, 0.J . E/ectroanal. Chem. Inferfackl €kcfrochem. 1988, 239, 321-331. (17) Deakln. M. R.; Melroy, 0. R. J . Nechochem. Soc.,in press. (18) Ellis, D.; Eckhoff, M.; Neff, v. D. J . phvs. Chem. ~ 8 1 8, 5 , 1225-1231. (19) Reichenberg, D. In Ion Exchange; Marinski, J. A., Ed.; Marcel Dekker: New York, 1966; Vol. 1, Chapter 7. (20) Sauerbrey, 0. 2. 2.fhys. 1959, 155, 206.

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(21) Itaya, K.; Shoji, N.; UchMa, I. J . Am. Chem. Soc. 1984, 106, 3423-3429.

RECEIVEDfor review September 2,1988. Accepted November 21, 1988. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work. A summer salary award from the Council on Research and Creativity at Florida State University also is acknowledged.

Signal-to-Noise Ratio in Microelectrode-Array-Based Electrochemical Detectors Stephen G . Weber Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

The signal-to-nolse ratlo at an electrode array depends on the electrode area, the perimeter-to-area ratlo of the electroactlve portion of the surface, the mass transfer coefficient of the analyte-eiectrode comblnation, the measurement bandwidth, and the sources and magnttudes of the nolses. Simple models for chronoamperometry with an array In quiescent solution and for hydrodynamlc current at an array In one wail of a rectangular condutt through which analyte-containing solution is following are glven. Noises from seven sources, includlng environmental noises, are considered In a noise model. The signal and noise models are combined to yield a model for slgnal-tmoke ratlo at array-based electrochemical detectors. There exists an optimum array density for a given area that depends on the noise power, noise reslstance, the current density at a sparse array, and the current density at a solid electrode of the same area. Approximations that lead to Simple expresshs for the optimum eiectroacthm area fractlon and noise resistance lead to results that are in good agreement with more complex and less approximate calculations. Electrodes of millimeter dimenslons consisting of about 1% active surface with electroactlve “pieces” of micrometer dimenslons are anticipated to yield detection limits of about 1 fmoi injected Into a typlcai packed-column liquid chromatograph. Thls corresponds to about lo-’’ M anaiyte In the detector and about an order of magnitude improvement over solid electrodes.

INTRODUCTION Electrochemical detectors have proven to be useful owing to their selectivity and low detection limits (Id). Notwithstanding the success the detector has enjoyed, there are still electroactive compounds such as tyrosine containing neuroactive peptides (6)that are present in concentrations below the detection limit of electrochemicaldetectors. It is possible to decrease detection limits considerably by using microbore liquid chromatography (7,8). In this analytical system there are two means by which detection limits can be improved over those found for large column liquid chromatography. The concentration of the mass injected is larger because the peak volume is smaller, and the flow rate and dimensions are smaller so the electrochemical detector efficiency is higher. 0003-2700/89/0361-0295$01.50/0

Caliguri and Mefford realized an improvement of a factor of 20 from the former effect and 2.5 from the latter effect. Note that the major improvement in the mass detection limit of the system is because of the peak volume effect. The efficiency increase only provides a factor of 2.5. We are interested in understanding ways to improve the concentration detection limits of electrochemical detectors (9,lO). From our signal and noise studies we have predicted that there is an optimum area for electrochemical detectors. Wightman (11)has pointed out that the area dependence on sensitivity depends on the electrode shape. We have therefore developed a simple computational approach to the signalto-noise ratio (snr) problem in order to understand how one should, in principle, construct the best detector. Our approach is based on array electrodes (12-36). Both experimental and theoretical work have shown that such electrodes, in which many electrodes are used to collect current, are more efficient than a solid electrode with the same electrode area. This efficiency arises from the diffusive or hydrodynamic transport of electroactive material from regions of the array surface that are insulating to regions that are electroactive. Composite electrodes or random microelectrode arrays such as Kel-Graf (25), which consists of Kel-F and graphite, have shown higher snr in hydrodynamic systems than solid electrodes. Optimum performance seems to be at around 15% carbon (26). Regular microelectrode arrays (24,27,29, 31-35) have been studied as well. The agreement between calculated and predicted current is excellent (34). For low flow rates, arrays are less flow rate sensitive than solid electrodes (27) because at low flow rates the dominant mass transport path is edge diffusion. This work is an attempt to formulate a theory for array electrodes that is at the same time simple and useful. Signal production in chronoamperometry will be discussed in some detail, as will steady-state signal production in flowing streams. The latter is relevant to amperometric detectors, in which the lowering of detection limits is of interest. Thus, after a brief overview of the noise model, snr calculations illustrating several main points are given. It is concluded that an optimum electrochemically active area exists that depends upon the background current, electrode capacitance, the current-tovoltage converter noise power and noise resistance, the importance of environmental contributions to noise, the bandwidth of the measurement, and the perimeter-to-area ratio 0 1989 American Chemical Society