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Table IV. Reaction -Rate Working Curve for 1 asebHydrocortisoneconcn, mg/dL Rate, AmA /sC RSD, o c

1.06 3.38 0.81.5 9 4.92 0.22.12 6.78 2.62.65 8.5 3 2.73.18 10.01 0.4Slope = 3.17, intercept = -0.01, r =Analysis using 30-s delay time and 30-sAverage of 4 determinations on a

a Working curve:0.9993.measurement time.single sample.By decreasing the base strength, we were able to slow thereaction so th at th e reaction-rate curve is linear over a longerperiod of time. For the case where a man ual mixing operationmust be performed, it may take 30 s or longer to mix the twosolutions and place the cuvette in the spectrophotom eter. W eshow in Table IV th e results obtained for a 30-9delay timea nd a 30-s measurement time for the series of standardsanalyzed previously. Good precision and a linear workingcurve were still obtained, but at twice the previous analysistime. However, this is still a vast improvement over th e90-min equilibrium procedure.

It should be emphasized th at these results were obtainedon an automated spectrophotometric system which incor-porates several features to ensure high reliability in itsmeasure ments. A beam splitter and reference detector areemployed to correct for light source fluctuations which mayoccur during th e measurement time (IO). Th e stopped-flowmodule provides precisions better th an 0.2% RSD for thealiquoting, m ixing, and transfer of solutions to the 2-cm longobserv ation cell. F inally, control of the spectroph otom eter,

acquisition of d ata , and reduction of these d ata to providequantitative information are all reproducibly performed bya minicom puter and associated interface electronics. It alsoshould be noted th at the sample and standards were run inrapid succession, thus precluding the necessity of therm o-stating th e solutions. If standard and sample information areto be obtained a t significantly different times, precise tem-perature control of the stopped-flow module can be m ain-tained (8) over long periods. The se factors should be con-sidered when comparing results obtained with other in-struments. ACKNOWLEDGMENTThe authors thank McKinley Health C enter, University ofIllinois, and R. D. OKeefe, Champaign, Ill., for the phar-maceutical skin preparations used in this study.

LITERATURE CITEDR. E. Graham, P. A. Wllliams, and C. T. Kenner, J.Pharm. Scl., 59, 11521970).W. Madder and R. Buck, Anal. Chem., 24, 666 1952).C. Chen, J. Wheeler, and H. Tewell, J. Lab. Gin. Med., 42, 463 1956).The National Formulary, XIV, Mack Publishing Company, Easton, Pa.,1975, p 976.The United States Pharmacopeia, XIX, Mack Publlshing Company,Easton, Pa., 1975, p 622.R. E. Graham, E. R. Biehl, C. T. Kenner, G. H. L w e i , and D. L. Midleton,J. Pharm. Scl . , 84, 226 1975).H. V. Malmstadt, E. A. Cordos, and C. J. Delaney, Anal. Chem., 44, 12),26A 1972).D. L. Krottlnger, M. S.McCracken, and H. V. Malmstadt, Am. Lab., 9(3), 1 1977).R. E. Graham, P. A. Wllliams, and C. T. Kenner, J. Pharm. Sc;., 59, 14721970).K. R. OKeefe and H. V. Malmstadt, Anal. Chem., 47, 707 1975).

RECEIVEDor review M ay 6, 1977. Accepted June 13, 1977.Research partially supported by the NI H through G rant HE WPHS GM 21984-02.

Cyclic and Differential Pulse Voltammetric Behavior ofReactants Confined to the Electrode SurfaceA la n P. Br o wn a n d F r e d C. A n s o n A . A. Noyes Lab oratory , Cal i fornia Inst i tute of Technology, Pasaden a, Cali fornia 9 25

Experlmental and theoretical cyclic and dlfferentlal pulsevoltammograms are com pared for react ants Irreversibly at-tached to the surface of g raphlte electrodes. Ouantltatlveagreement betw een experiment and theory can b e Obtainedonly If account Is taken of possible nonldeal behavior Inapplying the Nernst equation to the attac hed reactant s. Thelntentlonal addttlon of extern al unwmpensated resistance whenrecordlng dlfferentl al pulse voltammograms leads to s lgnlflcantIncreases In the sensltlvtty of thls technique for monltorlng smallquantltles of attached reactants. An approximate method Isdesctlbed whlch allows the surface conc entratlons of attachedreactants o be estlmated when the quantltles present are toosmall to yleld dlscernlble cycllc voltammograms.

Electrochemistry with electroactive reactants attached toelectrode surfaces is under active study in a number oflaboratories 1-5). In a recent p ublication 6), e described

the electrochemical behavior of several reactants th at w erebound to the surface of graphite electrodes by strong,spontaneous adsorption. The experimental data indicated tha tdifferential pulse voltammetry could prove to be a moresensitive technique t han cyclic voltammetry for examiningthe electrochemical behavior of such systems. Th e advantag esof the former technique are particularly noteworthy when thequan tity of bound reactant is small.In this paper, more detailed experimental results arepresented and are com pared with theoretical analyses of theexpected cyclic and differential pulse voltammetric behaviorof reacta nts irreversibly attach ed to electrode surfaces. T oaccount for the observed peak heights a nd wave shap es (e.g.,half-peak w idths), it was necessary to include activity coef-ficients which depend on the surface concentrations in th eNerns t equation as written for the surface-bound reactants.One unique v irtue of t he differential pulse voltammetrictechnique is tha t enhanced sensitivity can be obtained by theintentiona l addition of uncomp ensated resistance to the cell

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circuit. In add ition, th e dependence of peak cu rrents on theamount of uncompensated resistance added provides anapproximate method for determining the surface concen-tration of the attached reactant.EXPERIMENTALM ater ials . Electrodes were constructed from both pyrolyticgraphite and vitreous carbon. All of the electrodes used werecylindrical rods which were sealed onto glass tubing by meansof heat-shrinkable polyolefin tubing (A lpha Wire Co., style FI T300). With pyrolytic graphite (Union Carbide Corporation, P m a ,

Ohio), the electrodes were mounted so as to expose either thebasal-plane surfaceor the plane edges to the solution. Th e vitreouscarbon electrodes (Grade GC-A, Tokai, Ltd., Toky o, Japan) andthe exposed-edgepyrolytic graph ite electrodes were polished withan aqueous slurry of 0.5 alumina before use, producing smooth,shiny surfaces. Th e basal-plane pyrolytic graphite electrodes werefreshly cleaved with a razor blade just prior to being used. Th eexposed electrode areas were 0.2 cm2 for the v itreous carbon andbasal-plane pyrolytic graphite and 0.08 cm2 for the exposed-edgepyrolytic graphite.9,lO-Phenanthrenequinoneand benzo[c]cinnoline were re-crystallized twice from benzene and 9,10-anthraquinone-2-monosulfonate was recrystallized from ethanol. 1,4-Naph tha-quinone was sublimed just prior to use. Iron protoporphyrin IXchloride (Aldrich Chemical Company) was used as received. Irontris dibenzy1dithiocarbamate)was prepared according to reference7). Its electrochemical behavior matched that described inreference (8). Supporting electrolyte salts and buffen were reagentgrade materials used without further purification.Apparatus. A conventional w o-compartmentelectrochemicalcell was employed. In perchlorate electrolytes, potentials weremeasured vs. a sodium chloride-sa turatedcalomel electrode whichhas a potential 5 mV more negative than th e conventional SCE.Cyclic and differential pulse voltammograms were recordedwith a Model 174 Polarographic Analyzer (Princeton AppliedResearch, Princeton, N.J.). For some experiments, a modifiedversion of this instrum ent was used in which the pulse width,sampling time, and memory time constant could be varied (9).Method ology. In early experiments it was observed tha t thedifferential pulse voltammetric peak currents obtained withmoderate to high concentrations of attached reactants exhibitedstrong and u nexpected dependences on the rate a t which the dcpotential of the electrode was scanned. This was traced to th erelatively large memory time constant employed in the standardPAR 174 instrument (10, 11). To obtain differential pulsevoltammetric responses that accurately reflected the true in-stantaneous currents for which the equations in this paper werederived, it proved necessary either to restrict the ra te of th e dcpotential scan to values no greater th an 1 mV s- or to utilize amodified version of the PAR 174 (9) in which shorter memorytime constants could be selected. Acceptable values of scan rateor memory time constant were established by d etermining thepoint a t which no significan t changes in the peak curren t resultedfrom further decreases in scan rate or memory time constant.Th e o ther experimen tal settings employed during the recordingof differential pulse polarogram s were: Pulse amplitude: 5 mV;Drop time : 0.5 s (Le. pulse repetition rate: 2 d . he effectivetime at which the current is measured in the unmodified PAR174 is 48.5 ms.Most experiments were conducted in solutions containing0.5-1.0 pM concentration of the adso rbate . At these concen-trations about 30 min were required for the adsorption to reacha stable value. If the equilibra ted electrodes were washed andtransferred to solutions free of ad sorbate, their initial behaviorwas identical to th at ob served in the solution of low adsorbateconcentration. However, with no adsorbate in solution, slowdesorption gradually lowered the surface concentration. To avoidthis desorptive loss, the very dilute solutions of th e adsorbateswere usually employed.Numerical calculations were carried out with a PDP 11/40computer.

RESULTS AND DISCUSSIONCyclic Voltammetry. T he solid curve in Figure 1 s acyclic voltamm ogram recorded for 9,lO-phenanthrenequinone

Flgure 1 Experimental and theoretical cyclic voltammograms for 1.X 10-l' mol cm-2of 9,lO-phenanthrenequinone rreversibly adsorbeon a basal-plane pyrolytic graphite electrode. Potentlal scan rate : 5mV s-'. Supporting electrolyte 1 M HCIO,. (-) experimental volammogram. (----) theoretlcal voltammogram calculated from Equatio2. 0 ) oints calculated from Equations 7 and 8 with a nonldealitparameter, r , of -2.7 X lo8 mol-' cm2irreversibly adsorbed on a basal-plane pyrolytic graphitelectrode. Th e area under the curve corresponds to abo ut 1.X mol cm-' of th e quino ne (Q) n th e electrode surfaceIf the electrode reaction, Equation 1,

(1is assumed to obey th e Nern st equation (written in terms oth e concentrations of Q and HZQ on th e electrode surface)th e expected current-potential behavior in cyclic-voltammetrexperim ents is given by E quatio n 2 12, 13)

Q + 2 e - 2 H,Q

where r T is the total amou nt of Q initially prese nt on t helectrode surface, is the potential scan rate, = exp[(nFR T ) E EO ], and t he other symbols have their customarsignificance. It follows th at th e cathodic and anodic currenpeaks will both appear at E O , he standard potentia l for theQ/H,Q couple, and will have equal magnitudes given byEquation 3.3

The dashed curve in Figure 1 is the cyclic voltammogramcalculated on th e basis of Equ ation 2 using th e value of rTobtained from the area under the experimental voltammogram(corrected for the background curren t). Th e calculated andexperimental voltammograms are quite similar in shap e buthe use of Equation 2 does not produce a good quantitativmatch. Although th e smaller experim ental peak curren tcould be the result of slow electron tran sfer kinetics, th e lackof an y significant separation of th e anodic and cathodic peakpotentials and th e lack of asymmetry in the wave shapes [bothof which are also predicted consequences of slow chargetransfer kinetics 1 4 ) ]do not support such an interpretationAnother possible explanation for th e differences betweenth e calculated and observed curves in Figure 1 is tha t thesurface activities of the a ttached r eactants differ fro m theirsurface concentrations. T o account for such nonideal behaviorsurface activities must be used in place of surface concen-

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Table I. Nonideality Parameters and Peak Potentials for9,10-Anthraquinone-2-monosulfonatet tached toVarious Carbon Electrodes4Peakpoten-Total attach ed tial,eElec- react ant, 10 -9 r, mV vs.t rodeb mol cm -ZC mol- ' cm Zd N a SCE

BPG 1.4 X lo- - 5.86 - 208EPG 1.3 X lo-' ' 4.44 - 209vc 1.1x lo- ' ' -6.05 - 209Supporting electrolyte was 1 M NaC10,-0.01 MHC10,. BPG = basal-plane pyro lytic graphite. EPG =polished exposed-edge pyrolytic graphite.ished vitreous carbon .area und er a cyclic voltamm ogram.ting the cyclic voltammograms to Equation 8. e Averageof the ca thod ic and anodic peak poten tials; peak sep-arations were smaller than 10 mV.

VC = pol-Determined by measuring theEvaluated by fit-

t ra t ions in wri t ing the Nernst equation for the at tachedreactant couple:(4)

where a,y nd r are the surfac e activities, activity coefficients,and concentrations, respectively; the subscripts indicate theoxidized (0) nd reduced (R) forms of the adsorbate. Theexistenc e of nonid eal behavior in reversibly a dsorb ed moleculesis well recognized 15) and i t is not surprising that i t shouldalso occur with irreversib ly adsorb ed species. Reversiblyadsorbing organic species often exhibit activity coefficientswhich are exponentially dependent on their surface con-centrations 15, 16). T he activity coefficients for the twospecies on the electrode surface in the present case weretherefore represented as in Equations 5 and 6:

roo a nd r0R are parameters which describe the perturbinginfluen ce expe rienced by a given molecule of attache d oxidan tdue to the presence of th e other a t tached oxidant and re-du ctan t mo lecules, respectively. rRR nd rR0 are the analogousparam eters for a given reductan t molecule. A very similartreatm ent of th e nonidealities encountered in th e reversibleadso rption of m olecules on electro de surfaces has been utilizedby Laviron 17). s did she, we will neglect the possibilityth at th e interaction parameters depend upon potential .Subst i tut ing Equations 5 a nd 6 in Equation 4 an d desig-nating the fract ion of the m olecules on the surface in theiroxidized form as f , eads to Equation 7:7 )

where ro = roo roR a nd rR = rRR - rRo.Th e use of Equation 7 in place of the N ernst equ ation inderiving the expected cyclic voltammetric behavior givesEquation 8 from which th e current-potential behavior canbe calculated, using Equation 7 to relate the potential andthe parameter f .

As expected, Equation 8 reduces to Equ ation 2 if ro = r R =0 . Im por tant predictions of Equation 8 are tha t the cathodicand anodic peak currents have equal magnitudes given byEquation 9.

and the two peak potentia ls are given by Equation 109)

R T r T r O R )2nFpa= Epc = E O,Rwhere E OR is the formal potential for th e attached couple.Equation 10 predicts tha t the two peak poten tials, whileremaining equal, wil l shift along the potential axis as a functionof the to tal concentration of attac hed reactant u nless ro = rR.We observed constant peak potentials (f 2 mV) for all of thereactants examined even though r T was varied by more thanan order o magnitude. For this reason the two nonidealityparameters, ro and rR, were equated in fitting the experimentalcurrent-potential da ta to Equation 8.Th e current-potential da ta calculated with a value of r =ro = r R = -2.7 X l o 9 molm1 m2 n Equa tion 8 are shown bythe po ints plot ted in Figure 1. The agreement with theexperim ental curve is very good. Com parably good fits alsoresulted with the o ther reactants examined (see Expe rimentalsection) independent of the particular type of electrodeemployed. For example, T able I lists the nonideality pa-rameter evaluated from cyclic voltammog rams for th e stronglyadsorbing 9,10-anthraquinone-2-monosulfonate olecule onthree types of electrode. Note th at while the value of rdepend s on the type of carbon used, the peak potentials areinvariant. This observation add s supp ort to he approximationmade in equating ro a nd rR in Equation 8.Table I1 summ arizes nonideality parameters ev aluated fora variety of reactants that are very strongly adsorbed onbasal-plane pyrolytic graphite electrodes. In every case wehave examined thu s far, the current-potential behavior couldbe accounted for quantitatively only if a no nideality parameterwas introd uced, i.e., n o system yield ed an r value of zero. Thefact th at th e values of r in Table I1 are negative indicates tha tthe processes responsible for the no nideality act to destabilizethe at tached reactants.Although th e origins of nonid eal behavior of reacta nts o nsurfaces have been discussed in a variety of contexts 16-20),

Table 11 Nonideality Parameters for Several Reactants Attached to Basal-PlanePyrolytic Graphite E lectrodes

Attached reactantQuan li yattached,mol cm-* lOS9r,Supporting electrolyte x loLo mol - ' c mZb

1,4-Naphthaquinone 1M HC10, 5.1 1.69,lO-Phenanthrenequinone 1M HClO, 1.9 2.7Iron protoporphyrin IX 0.1 M Na,B,O, adjusted to pH 1 0 1.1 -4 .0Benzo[c]cinnoline 1 M HCl 1 . 2 -3 .19,10-Anthraquinone-2-monosulfonate 1M NaC10,-0.01 M HC10, 1.4 5.9Iron tris(dibenzyldithiocarbamate) 1M HClO, 0.5 3.4

Determined by measuring the area under a cyclic voltamm ogram. Evaluated by fitting the cyclic voltammogram toEquation 8.A N A L Y T I C A L C H E M I S T R Y , VOL. 49, NO. 11 , SEPTEMBER 1 9 7 7 1591

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Flgure 2. Simple equivalent circuit for an irreversibly attached reactant.R, is the total uncompensated resistance in the cell and measuringcircuit, Cdl is the double layer capacitance, and C , is the faradaicpseudo-capacitancenone of the p revious treatmen ts seems directly applicable tothe cases at hand. We wish to complete additional experi-ments involving kinetic measurements and temperaturevariations before sp eculating further on the physical basis forthe observed nonideal behavior of the attached reactants.Differential Pulse Voltammetry. Th e differential pulsevoltammetric response to be expected with attached re actantscan be usefully discussed in term s of th e simple equivalentcircuit given in Figure 2. Th e parallel combination of th eelectrode double layer capacitance, Cdl, and the faradaicpseudocapacitance, Cf, arising from th e attached reactant isin series with the uncompensated cell resistance, R,. T h epotential-dependent, faradaic pseudocapacitance can beexpressed as in Eq uation 11:

r o can be calculated from Equ ation 7 which leads to Equation12 when r = r g = rR:

Differentiation of Equation 1 2 and substitution in Equation11 produ ces th e following expression for Cf:n 2 F Z r , f 1- f )c, =- R T 1 2 r , r f l - f )

If the amplitude of the potential steps employed in re-cording the differential pulse voltammogram is sufficientlysmall to allow the change in surface concentrations of theoxidant and reductant to be ignored, the faradaic pseudo-capacitance can be regarded as cons tant during the life-timeof each pulse. Making this assumption, and neglecting themuch sm aller potential dependence of C, the current flowingin the circuit of Figure 2 following each poten tial pulse canbe shown to obey Equation 14.AE tRUi = - e x p -

where AE is the magnitude of each potential pluse and t isth e time since its application.Equation 14 predicts th at at any fixed t the largest currentswill result when Cf is largest and according to Equations 7 and13 Cf will reach its m aximum value a t the stand ard potential.In fact, although experim ent differential pulse voltammogramsfor irreversibly attached reactan ts exhibit current peaks a tthe stand ard potential, the magnitudes of the peak cu rrentsare typically several orders of magnitude grea ter tha n thosecalculated from Equation 14. Th e source of this discrepancywas traced to the ap proximation th at Cf remains constan t forth e duration of each potential pulse. Even with pulse am-plitudes as small as a few millivolts, the value of Cf canund ergo significant changes during the life-time of e ach pulse,1592 ANALYTICAL CHEMISTRY, VOL. 49,NO. 1 1 SEPTEMBER 1977

E v s SC EFlgure3. Experimental and theoretical differential pulse vottammogramfor 1.9 X lo- mol cm-' of 9,lO-phenanthrenequinone irreversiblyadsorbed on a basal-plane pyrowic graphite electrode. Potential scanrate: 5 mV s- ; memory time constant of the modified PAR 174polarograph: 14.0ms. a )Experimental voltammogram; supportingelectrolyte: 1 M HC1O4 b )Theoretical voltammogram calculated asdescribed in the text using a nonideality parameter, r , of -2.7X lomol-' cm'. (c)Theoretical voltammogram calculated for r = 0especially when th e d c potential is near the stan dard potentialAllowing Cf to vary dur ing the d uratio n of th e pulse leads toEquation 15 which c ann ot be solved analytically.A E - - E de

RU d tCcllf q-=where e is the tru e po tential difference across the parallecom bination of c d l and Cf with th e p otential dependence ofthe lat ter being implicitly expressed in Equatio n 13. Equation15 was solved numerically by means of a stan dard fo urth-o rdeRunga-Kutta method 21) as par t of a complete numericaevaluation of the expected differential pulse voltammetricresponse.Figure 3 shows a comparison of such a theoretical volt-ammogram (curve b ) with the experimental voltammog ram(curve a) for attached 9,lO-phenanthrenequinone. he valuesof r , rT, nd c d l employed in the calculation were evaluatedfrom a cyclic voltammogram recorded jus t prior to th e dif-ferential pulse voltammogram . Th e value of R, used to obtainthe best fit shown in the figure compares favorably withindepen dent measurements of the uncom pensated resistance

Curve c in Figure 3 is the differential pulse voltammogramcalculated by neglecting any non ideality in writing the Nern stequation, Le., setting r = 0. Comparing curves b and c inFigure 3 with their cyclic voltammetric counterparts in Figure1 shows that t he d ifferential pulse response is much moresensitive to the nonideal behavior of th e attache d reactants.Th e fact th at the half-peak widths of the experimental andsimulated voltammograms in Figure 3 do not m atch as welas do the peak currents is probably a reflection of uncertaintiesin accounting for the background currents. Th e circuit inFigure 2 is not a good model for the background currentobserved in the absence of attached reactants. These curre ntsappear to contain appreciable contributions from faradaicprocesses associated with the graphite electrode surface.Accurate correction for this current is not straightforwardbecause of its uncertain origin and because its magnitude isaffected by the attac hm ent of reactants to the surface.

50-100 Q)

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twLLcc

i a.

E v s SCE2b

O .3 @.I 0.3 0.1E v s SCE E vs SCEFigure 4. Experimental cyclic and differential pulse voltammogramsfor 1.2X lo-mol cm- of 9,lO-phenanthrenequinone irreversiblyadsorbed on a basal-plane pyrolytic graphite electrode. Supportingelectrolyte: 1 M HC104. a) yclic voltammogram recorded with potentialscan rate of 50 mV s-. b )Differential pulse voltammogram recordedwith a potential scan rate of 2 mV s-;modified PAR 174 memory timeconstant: 22.3ms; uncompensated resistance -75 a. (c)A s in bexcept that 2 kR of additional uncompensated resis tance was placedin the measuring circuitTh e most imp ortant point to note in comparing the dif-ferential pulse voltammograms in Figure 3, and the cyclicvoltammograms in Figure 1, s that they both yield currentpeaks a t the sam e potential, i .e., the form al potential for th eattached rea ctant couple. This observation coupled with theability of th e num erical calculation to match the peak currentsan d potentials of the differential pulse voltamm ogram s s goodevidence that this technique can be used confidently toidentify q uantities of a ttached rea ctants too small to be foundwith cyclic voltamm etry alone. However, it should be em-phasized that discrepancies between the peak potentialsobtained with th e two techniques can result unless the dif-ferential pulse voltammograms are recorded a t scan rates nogreater than 1mV s-l with the standard PAR 174 instrumen t

or with an instrumen t modified to provide a shorter memorytime constant (9).Th e small over-shoot a t the foot of th e calculated differ-ential pulse voltammograms in Figure 3 arises because th enum erical calculation is approachin g a tru e derivative of thecyclic voltammogram . Indeed, under certain conditions (smallpulse amplitude, scan rate, and un compensated resistance),experimental differentia l pulse voltammograms havingnegative compon ents on one side of th e peak have been re-corded by employing the m odified version of th e PAR 174instrument (9) with a m emory time constant of a few mil-liseconds (22). Th e fact that such behavior is not obtainedunder most exp erimental conditions results primarily fromth e slow effective response time of the unm odified PAR 174instrumen t an d th e larger uncom pensated resistance usuallyencountered.Effect of Uncompensated Resistance. Th e rate of decayof the cu rren t following the applicatio n of each potential pulsedecreases as R , increases. So long as R , is not too large (seebelow), the m agnitude of the curren t sampled near the en dof each pulse is correspondingly greater a nd the more so thelarger the value of Cf. Thus, adding external resistance inseries with t he working electrode can lead to larger differentialpulse voltamm etric peak curren ts and enh anced sensitivityin the detection of small quantities of attached reactants. Forexample, Figure 4 shows a cyclic voltammogram for anelectrode with only 1.2 X mol cm-2 of 9,lO-p henan -threnequino ne on its surface. Th e faradaic peaks are nowalmost dominated by the background currents. By contrast,th e differential pulse voltammogram for the sam e electrode

a.0 5pA /.1 1 I I l I 13.2 -0.1 0.1 0.2 0.3 0.4E v s SCE

b.

Flgure 5. Cyclic and differential pulse voltammograms for an edge-onpyrolytic graphite electrode to which approximately 4.2X lo-molof a ruthenium(I1) pentammine complex is covalently attached 23).Supporting electrolyte: 1 M CF3COOH. a ) Cyclic voltammogram.Potential scan rate: 50 mV s-. b )Differential pulse voltammogram.Potential scan rate: 5 mV s-;memory time constant: 114 ms;uncompensated resistance: -100 a c) s in b )but with 1000 Qof additional uncompensated resistance phced in the measuring circuit(curve b , Figure 4) leaves no dou bt about the presence of th eattached reactant and when 2 k0 of additional uncompensatedresistance is added (curve c), the response is very large andeasy to measure.An even more persuasive example of the enhanced sen-sitivity obtainable by th e intentional addition of ex tra un-compensated resistance to the cell is evident in Figure 5 whichshows the behavior of a ruthenium(I1) pentam mine complexcovalently bonded to an exposed-edge pyrolytic graphiteelectrode (23). Th e faradaic peaks in the cyclic voltammogram(curve a, Figure 5) are almost imperceptible. Th e differentialpulse voltammetric response for th e same electrode (curve b ,Figure 5) shows a small, but clearly evident peak a nd w henan additional 1000 9 of uncom pensated resistance is adde dto th e circuit (curve c , Figure 5), the peak is enhanced sig-nificantly a nd provides excellent evidence for th e presenceof th e attached reactant. Th e implications for the study ofelectrodes to which only very small quantities of reactan ts areattache d seem clear.Differentiating Equ ation 14 with respect to R, leads to thepredict ion tha t th e cu rrent a t any fixed sampling t ime willreach a m aximum a t the value of R , given in Eq uation 16:

The plotted points in Figure 6 show the variation in peakcurrent produ ced by increasing R , with an electrode to w hich9,lO-phenanthrenequinone as attached. Th e predicted peakcurrent maximu m is evident. Th e solid curve in Figure 6represents th e peak currents of voltammograms calculatedfor ea ch value of R, by mean s of the same numerical procedureused to obtain voltammogram b in Figure 3. The goodagreement between the experimental and calculated peakcurrents is apparent.When R, is selected to produce the maximum peak current,th e rat e of chan ge of r o (and IR) is much smaller tha n whenno uncompensated resistance is intentionally added. Th eapproximation involved in regarding Cf as a constantthroughout th e d uration of the potential pu lse is more justifiedunder these conditions an d the evaluation of Cf can then beused to estimate rT . The maximum p redicted peak current,( ,, in plots such as Figure 6 is given by Equ ation 17.

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R, , RF l g u r e 6 Differential pulse voltammetric peak current vs. the totaluncompensated resistance in the measuring circuit for 1.9 X lo- molom-* of 9,lO-phenanthrenequinone rreversibly adsorbed on a bas-al-plane pyrolytic graphiteelectrode. Supporting electrolyte: 1M HC104.Potential scan rate: 5 mV s-I. 0) xperimental points; modified PAR174 memory time constant was 14 ms. -) peak currents of differentialpulse voltammograms evaluated numerically as described in the textWhere hE is the m agnitude of the po tential pulse, Cf)p s thefaradaic pseudocapacitance at the peak po tential, r is the timeafter the p ulse application when the curre nt is measured, ande = 2.718. Since (Cf), corresponds to f = 0.5 in Equation 13,its magnitude is given by

With systems such as 9,10-phenanthrenequinone, hichyield values of Cf)pmuch larger than Cdl, the contributionof the latter to the peak current given by Equation 17 isvirtually negligible. In such instances the peak curre nt mayjustifiably be measure d with respect to t he extrapolation ofth e background cur ren t flowing on either side of the peak inthe voltammogram. (T his cur ren t presumably results fromfaradaic processes associated with the oxidation an d reductionof th e graphite electrode surface.) Making this approxim ationand combining E quations 17 and 18 yields Equation 19

from which r T can be calculated if r is know n. Th e value ofip),,, shown in Figure 6 and the r parameter obtained fromthe cyclic voltammogram r = -2.7 X lo9 mol-' cm2 ) weresubstituted in Eq uation 1 9 with the other known experimentalparameters to obtain a value of I T of 1.9 X mol cm-2.The value obtained from integration of the area under thecyclic voltammogram obtained with the same electrode was1.9 f .2 X mol cm-2. Th us, Equ ation 19 can providea reliable estimate of r T when (Cf)p>> Cdl.Figure 7 shows a differential pulse voltammogram forat tached 9,lO-phenanthrenequinone ecorded with the valueof R , required to produce the maximum peak current . Theplotted points were calculated numerically asdescribed above.Th e excellent agreement shows that th e shapes of differentialpulse voltammograms can be understood quantitatively under1594 ANALYTICAL CHEMISTRY, VOL. 49, NO. 11, SEPTEMBER 1977

t-zWirr

F l g u r e 7 A comparison of experimental and theoretical differentiapulse voltammograms recorded with a value of total uncompensatereslstance (4000 orresponding to themaximum peak current in Flgu6. (-) experimental voltammogram; 0)calculated currents. Experimental parameters as in Flgure 6conditions where backgrou nd curren ts are negligible comp areto the faradaic current resulting from the a ttached reactantEven when the attached reactan t is present in quantities tosmall to yield discernible cyclic voltammo grams from whichthe nonideality parameter, r , would be evaluated, Equation16, 17, and 18 may still prove useful: A t sufficiently lowsurface concentrations, the second term in th e denom inatoof Equation 18will become negligible compared to th e firstconcentration-independent t e rm so th at a know ledge of r inot required.

In cases where the double layer an d faradaic capacitanceare more nearly commensurate, the peak cur ren t measure dwith respect to an extrapolation of the background currenwill not correspond to the cu rrent calculated from E quatio n19 because the faradaic and background c urren ts cannot besepar ated reliably in this way. A simple, approximate procedure for obtaining a rough estimate of t he surface concentra tions in such cases is to evaluate Cf ia Equation 1using the value of R, corresponding t o the maximum peakcurre nt in a plot such as Figure 6 and t he effective value oc d l estimated from th e background curre nt in a cyclic voltammogram. Th e value of r T is the n calculated from Equation14 by assuming th at th e surface concentration is low enoughto allow the nonideality paramete r to be neglected. Foexample, the differential pulse voltammogram shown in Figur4 corresponds to 1.2 0.2 X 1O-I mol cm-2 of 9,lOphenanthrenequinone (determined from the area of a cyclivoltammog ram). Th e value of c d l estimated from t he cyclivoltammogram was 10 pF and the maximum peak currenresulted when R , was 2.5 kO. The se data and Eq uation s 1and 18 (with r set equal to zero) lead to 1.2 X 10-l' mol cm-for I T. Th is good agreement is somewhat fortu itous and icritically depen dent upon having an accurate value for theeffective doub le layer capacitance. On fresh ly cleaved, basal-plane pyrolytic graphite electrodes, c d l can be determinedwith reasonable accuracy. Th e same cannot be said foroughened, edge-on pyrolytic graphite, vitreous carbon, oheavily oxidized graphite electrodes, at least in ou r h ands (23However, even in these cases, the differential pulse volt-ammograms obtained with ad ded uncompensated resistance

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produced readily detectable waves where n o cyclic voltam-metric responses were noted. Th e use of Equ ation 16 inestimating attache d reac tant concentrations for such waves,while exceedingly approx imate, is not likely to produce errorsgreater tha n a factor of five to ten in th e calculated valuesCONCLUSIONS

Th e primary objective of this stud y was to demonstrate theproperties of differential pulse voltammetry as applied toreacta nts attach ed to electrode surfaces in order to allow thishighly sensitive technique to be utilized in exa minations ofsub-monolayer quantities of attached reactants. Th e resultshave shown th at i t is possible to provide a semiqu antitativeaccount of the observed differential pulse and cyclic vol-tam me tric responses by introducing concentration-dependen tactivity coefficients for the attached reactant molecules.Having don e so, the magnitude of differential pulse peakcurrents can be correlated with the quantity of adsorbedreactant and the peak potentials with th e standard po tentialsof th e reactan t couples. Tes ts of the equations and suggestionspresented here are under way with a wider variety of attachedreacta nts in o rder to verify more precisely th e ranges of the irvalidity.

ACKNOWLEDGMENT

of rT.

Helpful suggestions and comments from Carl Koval andJam es Flanaga n are a pleasure to acknowledge.

LITERATURE CITED(1) R. F. Lane and A. T. Hubbard, J . Phys. Chem.,7 7 , 1401, 1444 1973).2) C. M Elliott and R. W. Murray, Anal. Chem., 48, 1247 1976).3) P. R. Moses and R. W. Murray, J . Am . Chem. SOC., 8, 7435 1976).4) D. 0 Davis and R. W. Murray, Anal. Chem., 49, 194 1977).5) T. Kuwana and co-workers, private communlcatlon 1977).(6)A. P. Brow n, C. Kov ai, and F. C. Anson, J . Electroanel. Che m., 72, 3791976).7) A. H. White, E. Kokot, R. Roper , H. Waterman, and R. L. Martin, Aust.J . Chem., 17, 294 1964).8) R. Chant, A. R. Herdrickson, R. L. Martin, and N. M Rohde, Inorg. Chem.,14, 1894 1975).9) R. H. Abei, J. H. Christie, L. L. Jackson , J. G. Osteryoung , and R . A.

Osteryoung, Chem. Instrum., 7, 123 1976).10) PAR 174 Manual, Princeton Applied Researc h Corp., Princeton, N.J.11) J. H. Christie, J. G. Osteryoung, and R A. Osteryoung, Anal . Chem.,45, 210 1973).12) E. Lavlron, Bull. SOC. Chim. F r., 3717 1967).13) H. A. Laitlnen, C. A. Vlncent, and J. J. Bednarski, J . Electrochem. Soc.,115, 1024 1968).14) A. T. Hubbard and F. C. Anson In Electroanalytical Chemistry , Voi. 4,A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1970.15) B. B. Damaskin,0. . Petri, and V. V. Batrakov, Adsorption of OrganicCompounds on Electrodes, Plenum Press, New York, N.Y., 1971.(16) A. N. Frumkin, 2. hys. Chem., 116, 466 1925).17) E. Laviron, J . Electroanal. Chem ., 52, 395 1974).18) B. E. Conway and E. Giieadl, Trans. Fararaday Soc., 58, 2493 1962).19) M. Boudart, J. Am. Chem. Soc., 74, 3556 1952).20) G. Haisey and H. S. Taylor, J . Chem. Pep., 15, 624 1947).21) M. Abrarnowitz and 1. A. Segun, Ed., Handbook of MathematicalFunctions , Dover Pubiicatlons, New York, N .Y., 1964.22) K. Takahashi and F. C. Anson, unpublished results , 1976.23) C. A. Koval and F. C. Anson. to be submitted.RECEIVEDor review May 16, 1977. Accepted Ju n e 22, 1977.This work was supported by a g rant from NSF-RANN .

Ion-Exchange Separation and Determination ofCalcium and MagnesiumM i c h a e l D Argue l lo and James S. F r i t z Ames Labora tory -ERDA and Depar tment of Chemis t r y , Iow a S ta te Un i vers it y , Ames , Iow a 5001

Magnesium 11 and calcium I1) are separated from eachother and from several other metal ions by ion-exchangechrom atography on a sulfonated macroporous resln of 1.8 to2.0 mequ lv/g capacity . The eluent Is 1 M ammonlum chlorldeor 0 03 M ethylenedlammoniumchloride. The sep arated metalions are det ected automatically with a color-forming reagentand are quantitated with t he ald of a callbratlon plot.

The separat ion and determination of calcium and mag-nesium has been a problem of continuing analytical interestbecause of th e many k inds of materials in which significantamo unts of these two elements occur together. Cation-ex-change procedures for separation of calcium an d magnesiumhave included elution with hydrochloric acid 1-3),ammoniumchloride 4 ) , ammonium ace ta te 5), ammonium acetyl-acetonate 6), DTA 7) , ammonium lactate @), and pH-5a-hydroxybutyricacid (9). The se procedures are rather slowand are not readily adaptable to automatic detect ion of th eeluted m etal ions. Ion exchange with forced eluen t flow andautomatic detection of eluted species has been successfullyused for separation of a number of metal ions. Fritz and Story( I O ) used spectrophotometric detection after addition of a

color-forming reagent. Small, Stevens, and Ba um an 11)employed conductance detection afte r removal of elu ent ionson a strip per column. Freed 12) used flame emission fordetection of calcium, strontium , and barium separated on aZipax SCX cation exchanger.A method is now given for rapid se paration of calcium an dmagnesium from each other and from other metal ions. Th eseparation is done on a column containing a sulfonatedmacroporo us resin of low capacity. T he elution curves arerecorded using a unique color-forming system and spectro-photometric detection.

EXPERIMENTALA pp ar atu s. Th e liquid chromatograph has been describedpreviously 13)and is shown schematically in Figure 1. A MiltonRoy minipump (M odel 396) and a C hromatrix CMP-2 meteringpump were used for solvent delivery as well as for delivery ofbuffered color-forming reagent.Columns were constructed from lengths of 4-m m i.d. Pyrextubing onto which Altex 200-28 glass connecto rs had been fused.The use of Viton 0 rings between the polypropylene bushingsand caps of t he glass connectors resulted in columns tha t wereboth leak- tight and chemically inert. All plumbing componen ts(tubing, tube-end fittings, couplings, plugs, tees, valves, sampleloops, etc.) used were either purchased from Laboratory Data

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