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Anal. Chem. 1993, 65, 3137-3142
Electrochemical Studies on Anion Coordination Chemistry. Application of the Molar-Ratio Method to Competitive Cyclic Voltammetry Antonio Bianchi$ Antonio Dombnech,’J Enrique Garcia-Espafia,t and Santiago V. Luis8 Department of Chemistry, University of Florence, Via Maragliano 75-77, 50144-, Florence, Italy, Department of Inorganic Chemistry, University of Valencia, CI Dr. Moliner 50, 46100 Burjassot, Valencia, Spain, and Laboratory of Organic Chemistry, Department of Experimental Sciences, University Jaume I, 12080 Castellbn, Spain
A generalization of the molar-ratio method for elucidating the stoichiometry and conditional constant of complex formation from cyclic voltammetry and chronoamperometry is described for systems not accessible by conventional polarographic procedures. Application to complex formation equilibria between [Fe(CN)614-,[Fe(CN)#-, and different polyammonium receptors is discussed. Extension to nonelectroactive complex formation of ATP and carboxylateions with these receptorsby means of the competitiveinteraction with hexacyanoferrate(I1) ion is presented. INTRODUCTION The study of anion coordination chemistry has been the object of considerable experimental work and discussion during the last two decades.’ Among others, studies dealing with the interactions of polyammonium macrocycles and/or linear polyamines with carboxylate anions, complex anions such as [Fe(CN)61Cand [Co(CN)6IS-,ATP, ADP, polyphosphates, and carboxylates have been reported.2 The two main forcescontrolling the nature of the receptormbstrate adducts formed are electrostatic and hydrogen-bond interactions. Since multiple protonation and complex formation equilibria are involved, computer-assisted analysis of potentiometric data is by far the most accurate technique for studying these kinds of systems. However, other electrochemical techniques, such as cyclic voltammetry and chronoamperometry, are of great help in confirming the extent of the interaction between receptors and electroactive species. In addition, competitive effects between electroactive and nonelectroactive species could be a promising tool in studying the interactions between receptors and nonelectroactive anionsby means of these techniques. Althoughthis procedure was first suggested as early as 1981: as far as we know, until now no studies have been further developed. The purpose of this paper is to present a simple and versatile application of cyclic voltammetry and chronoamperometry t University of Florence.
University of Valencia. University Jaume I. (1) Dietrich, B.; Hoeseini, M. W.; Lehn, J. M.; Sessions, R. B. J. Am. Chem. SOC.1981,109,1282-1283. Kimura, E. Top. Curr. Chem. 1986, 128,113-141. Colquhoun, H. M.; Stoddart, J. F.; Williams, D. J. Angew. Chem. 1986,98,483-503. Hosseini, M. W.; Lehn,J. M.; Maggiora, L.; Mertes, K. B.; Mertas, M. P. J. Am. Chem. SOC.1987,109, 537-544. (2) Bencini, A.; Bianchi,A.;Dapporto,P.;Garcla-~pafia, E.; Micheloni, M.; Paoletti, P.; Paoli, P. J. Chem. Soc., Chem. Commun. 1990, 13821384. Bianchi, A.; Garcla-Eepafia,E.;Giusti, M.; Mangani, 5.;Micheloni, M.; Orioli,P.;Paoletti, P. Znorg. Chem. 1987,26,3902-3907. Bencini, A.; Bianchi, A.; Burguete, M. I.; Garcla-Espafia,E.; Lub, S. V.; Ramlrez, J. A. J. Am. Chem. Soc. 1992,114, 1919-1920. (3) Peter, F.; Groea, M.; Hoeaeini, M. W.; Lehn,J. M.; Sessions, R. B. J. Chem. Soc., Chem. Commun. 1981,1067-1069. t i
0003-2700/93/0385-3 137$04.00/0
to elucidate the stoichiometries and formation constants of electroactive complex species by applying a generalization of the molar-ratio method.4 Although other electrochemical techniques can be used to study these kinds of systems, the simplicity of the treatment proposed here makes this procedure an interesting and versatile way to rapidly analyze the data. However, it must be advertised that the precision of cyclic voltammetry is poor relative to what could be reached with potentiometry. If precision approaching that obtained with potentiometry is to be achieved, methods other than cyclic voltammetry, such as pulse, ac, and square wave, should be used. Two main points are addressed. First, the method is applied to the determination of the stoichiometryof complexes formed in different oxidation states of the redox center. Second, an extension of this method to investigate the formation equilibria of nonelectroactive species is described on the basis of competitive complexation equilibria with electroactive species.
ELECTROCHEMISTRY The polarographic and cyclic voltammetric methods of studying metal complex equilibria are based upon the fact that half-wave and peak potentials of metal ions are shifted, usually to more negative values, by complex formation.6Early polarographicapplications were restricted to single equilibria! and the treatment was later extended to multiple equilibria involving 01187 and multiple ligands.8 Recent works have applied these methods to cyclic voltammetry, including the DeFord-Hume and the Watters-DeWitt methods.0 These procedures refer to the cases in which weak complexation occurs, and only one polarographic wave or voltammetric couple is observed. Consequently, these methods are based on the measurement of the shifts in the half-wave or peak potentials, although some polarographic methods involving current measurements for diffusion-controlledprocesses have been devised.sJ0 The mentioned approaches are used for the determination of the stability constants of metal complex ions in solution, (4) Beltrh, A.; Beltrb, D.; Cervilla, A.; Ramlrez, J. A. Talanta 1989, 30,124-126. (5) Crow, D. R. Polarography of Metal Complexes; Academic Press: London, 1970. Heyrovsky, J.; Kuta, J. Principles of Polarography; Academic Press: New York, 1966. (6) Heyrovaky, J.; Ilkovic, D. Collect. Czech. Chem. Commun. 19S6, 7,198. Kolthoff, I. M.; Lingane, J. J. Polarography; Interscience: New York, 1952. (7) DeFord, D. D.; Hume, D. N. J. Am. Chem. SOC.1961, 73, 53215322. Schaap, W. B.; McMasters, D. L. J. Am. Chem. SOC.1961, 83, 4699-4706. (8) Watters, J. I.; DeWitt, R. J. J. Am. Chem. SOC.1960,82,1333-1339. (9) Killa, H. M. J. Chem. SOC.,Faraday Trans. 1 1986,81,2659-2666. Killa, H. M. Polyhedron 1989,8,2299-2303. (10) Kacena, V.; Matousek, L. Collect. Czech. Chem. Commun. 1963, 18,294-301. Crow, D. R. J.Electroanal. Chem. Interfacial Electrochem. 1968,16,137-144. 0 1993 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 21, NOVEMBER 1, 1993
corresponding to their stepwise formation equilibria. However, the scopeof these procedures is (i)limited by the accuracy required in the potential measurements11 and (ii) restricted to series of mononuclear complexes. In recent papers, general simulation procedures for linear scan or cyclic voltammetric curves have been described for the characterization of complexes with low11 and large excess of ligand12 in pH-dependent complex equilibria.13 However, an extension to more complicated stoichiometries (for instance,binuclear complex species)is problematic and requires, most likely, a reasonable combination of computer-assisted simulation procedures and traditional graphical methods. Although other electrochemical techniques may be used for these purposes14 (semidifferentialvoltammetric data, second harmonic AC voltammetry, etc.), we have chosen a simple analysis of conventional cyclic voltammetric and chronoamperometric data, requiring inexpensive instrumentation, and a relatively simple numerical treatment of the data. The molar-ratio method16 is based on the measurement of any physical quantity which might be assumed to be proportional to the concentration of complex species or to one of the reactants (typically absorbances). If a stable complex is formed which does not show significant dissociation, plots of the measured quantity against the ligand-tometal molar ratio exhibit a sharp break. The molar ratio at the break indicates the stoichiometry of the complex. If a weak complex is formed, the plot is curved near the equivalence point. We consider here the general case in which both the uncomplexed metal and its complexed ions are reversibly reduced (or oxidized) from a higher to a lower valence state. The simplest scheme for this case may be represented as
E , 0.8
0.4
0.2
V
YS
SCE
0.0
Flgurr 1. Effect of increasing amounts of Me2pentaenon the cyclk voltammogram8 of [Fs(CN)#- (c = 2.0 mM) at pH 4.0. Platinum worklng electrode, Y = 0.10 Vls. Ligand-to-[Fe(CN)#- ratio equal to (A) 0.0, (B) 0.30, and (C) 1.20. The cyclic voltammogram B Is identical to that obtained for a solution of [Fe(CN)slC, ligand, and ATP, ail in 2.0 mM concentration.
THEORETICAL EQUATIONS FOR THE MOLAR-RATIO METHOD Let us consider the equilibria of complex formation and ligand protonation described by the following equations (charges omitted for brevity): mM nL qH = M,L,H, (3)
+ +
This scheme is also valid for the coordination of [Fe(CN)al' by polyammonium receptors. As previously reported,'e solutions of [Fe(CN)#- exhibit a well-known reversible or quasireversibleone-electroncyclic voltammetric couple which is significantly modified by the addition of different anion receptors. Increasing the receptor/[Fe(CN)#- ( C ~ C M )ratio leads to a shift of the peaks toward more positive potentials and to a significant decrease of the peak current. It can be observed that for C ~ C M < 0.4, the cyclic voltammograms are rather broad and look like the superposition of two waves (see Figure 1). For molar ratios larger than 0.4, only one couple appears whose electrochemical parameters remain unchanged for C ~ C Mvalues close to 1. If the total concentration of [Fe(CN)#-, CM, is kept constant and the total ligand concentration, CL, is varied until it reaches a sufficient excess, we can consider the complex quantitatively formed in concentration c d m . Therefore, a limiting cyclic voltammogram is obtained, allowing direct estimates of the formal potential and the diffusion coefficient of the complex species.
L+jH=LHj (4) If the system forms just one stable complex at a given pH, well-known molar-ratio curves are obtained by changing the concentration of ligand (or metal) with constant metal ion (or ligand) concentration. Then
In a typical molar-ratio experiment, the molar fraction of complexed metal, CYM, is experimentally determined. Assuming that only one complex exists in solution, CYMis equal to IXI[M,L,H,]/CM and [MI = (1- CYM)CM. Accordingly, the stability constant for the formation of the q-protonatedspecies will be given by
8, =
[MmLnHql
[Ml"'[Ll"[Hlq
~
~
~ zflj[H]j)"[H]+ ~ ~ ~
-
(7)
Then,
~~
(11) Klatt, L. N.; Roueef, R. L. Anal. Chem. 1970,42,1234-1238. (12) Killa, H. M.; Mercer, E. E.; Philp, R. H.Anal. Chem. 1984,56, 241-2406. Gampp, H. Anal. Chem. 1987,59,2466-2460. (13) Spell,J. E.; Philp, R. H. J. Electroanal. Chem. 1980,112, 281293. Killa, H. M.; Philp, R. H. J. Electroanal. Chem. 1984,176,223-228. S a v b t , J. M.; Xu, F.J. Electroanal. Chem. 1986,208, 197-217. (14) Bard, A. J.; Faulkner, L.R. Electrochemical Methoda; Wiley & Sone: New York, 1980. (16) Yoe, J. H.; Jones, A.L.Znd.Eng. Chem. Anal. Ed. 1944,16,11-14. (18) Bencini, A.; Bianchi, A.; Burguete, M. I.; Domhech, A.; GarcfaEapafia, E.; Luk,9. V.; Nifio, M. A.; RamIrez,J. A. J. Chem. SOC.,Perkin Tram. 1991,14461461. Arag6,J.; Bencini, A,; Bianchi, A.; Domhech, A,; Garcia-Espafia,E. J. Chem. SOC., Dalton Tram. 1991,319-324.
If pH is kept constant, substitution of the appropriate m and n values must satisfy the relationship
It should be noted that the value of K M allows an estimate of the stability constant, ,Bq (providing that the degree of protonation of the complex and the protonation constants of the ligand, Pj, are known), by using eq 7.
~
(
l
ANALYTICAL CHEMISTRY, VOL. 85, NO. 21, NOVEMBER 1, 1993
This method can reasonably be extended, in some favorable conditions, to the study of complex formation involving nonelectroactive species by making use of the phenomenon of competitive complexation. Competitive procedures have been described for polarography," and their extension to other electrochemical techniques seems natural. Thus, let us consider the complex formation and the protonation equilibria affecting a given substate X, rX + SL + wH = X&,H,
(10)
X + tH = XH,
(11)
which occurs in a solution containing M ions. Providng that no interaction exists between M and X, and assuming that the only electrochemicalresponse must be attributed to the M-containing species, it can be expected that addition of X to solutionscontaining M and L cause a measurable alteration of its electrochemicalresponse. In fact, as X competes with M in the binding of L, addition of increasing amounts of X must displace the values of the electrochemical parameters toward those corresponding to the free metal ion, M, and, in the limiting case, the cyclic voltammogram of the free metal will be regenerated. For this ternary system, we can write cL = [Ll + x [ L H j l
+ xn[M,LnH,I + xs[X&,H,l (12)
cx = [XI + z [ X H , l + xr[X&,H,l
+~ X C X
(15)
Combining the above equations, we can arrive at the following relationship which enables us to obtain the ax values from the experimental UM: cL - (n/m)aMcM- aM 1/nKM-1ml/n (1- CYM)+"/~ ax = (s/r)cx (16) This requires the coefficients m, n, and the constant KMto be previously known. Then, the stability constant for the formation of the w-protonated species will be
Bx = [X"Hwl
[XI'[Ll' [HI
= Kx'cXl4(l
species exist in solution for the familiar case of a series of complexeswith the same X and L stoichiometrybut different protonation degree. Introducing the total molar fraction of complexed X as ax = Cr[XrL,Hw1/cx,we can write (19) Then eq 14 is still valid, but the value of K. is now related with the BW and Bt constants by means the relationship
EVALUATION OF THE MOLAR FRACTION OF COMPLEXED METAL A SEMIEMPIRICAL APPROACH Sincethe normal potential shift technique is not applicable, a simplified procedure for calculating the molar fraction of complexed [Fe(CN),#- has been used with cyclic voltammetric and chronoamperometric data. This procedure is based on the method of Kacena and Matousek,lo which involves the measurement of a mean diffusion coefficient, D, which verifies, for a multiple complex formation equilibria:
For the case in which a unique complex exists in solution, eq 19 becomes
(13)
Assuming that for a certain pH value a unique M,,,L,H, complex and a unique X&,H, complex exist, by introducing the molar fraction of the latter, ax = r[X,L,H,l/cx, we obtain
cx = [Xl(1+ xB,[Hlt)
8189
+ x/3j[H]j)r(l +
~Bt[Hlt)'[Hl" (17) Therefore,the correct r ands stoichiometriccoefficientsverify
For a molar-ratio experiment, one can easily obtain aM = (D - DM)/ (Dm - DM)
(23) where D Mdenotes the diffusion coefficient of the [Fe(CN)#ion and D m that for the complex species. A direct estimate of these coefficientscan be obtained from chronoamperograms at a potential sufficientlylarge to ensure diffusion-limited current for all species.14J8 Altematively, the diffusion Coefficients can be directly calculated from the chronoamperometric analysis of the diffusive portion of the cyclic voltammograms.19 This is based on the fact that in many linear sweep voltammetry experiments, the current will become purely diffusion-controlledat a potential sufficiently past the peak. Then, the i-E curve effectivelyobeys a simple Cottrell equation,
= constant
i;.
where t* represents the convergencetime, at which the linear sweep voltammetric current becomes equal to the chronoamperometriccurrent, and the other symbolshave their usual significance. Since t = E/u, u being the voltammetric sweep rate, eq 24 can be rewritten as *
nFAcvTivG =
&=dZEzG It is interesting to note that this procedure involves, as previously discussed, an estimate of the (YM values from only cyclic voltammetricand chronoamperometricmeasurements. As before, the value of KXcan be compared with the stability and protonation constants determined from potentiometric data by means of eq 17. The competitive method described here may easily be extended to the most realistic situation, in which several (17) Schwarzenbach,G.; Gut, R.;Anderegg, G. Helu. Chim. Acta 1964, 37,937-957.
(24)
4 - n - n -
(25)
Since E* (or t*) is not known a priori, it is convenient to rearrange this equation to give
-1= n ( E - E * ) (26) i2 n2pA2c2Dv Then, for pure diffusion control, a plot of l/i2 vs E should (18) Nicholson, R. S.; Shah, I. Anal. Chem. 1964,36,706-723. (19) Nicholson, R. S. Anal. Chem. 1966,37,667-671. Polcyn, D.S.; Shain,I.Anal. Chem. 1966,38,370-375. Ginzburg,G. Anal. Chem. 1978, 50,375-376. Bontempelli, G.; Magno, F.;Daniele, S . Anal. Chem. 1986, 57,1503-1504.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 21, NOVEMBER 1, 1993
give a straight line whose slope allows a direct estimate of the diffusion coefficient D for a defined composition of the solution. This procedure can be extended to the elucidation of the stoichiometry and stability constants of the complex species formed between the receptors and the hexacyanoferrate(II1)ion by analyzing the diffusiveregion of the cathodic peak in the cyclic voltammograms. The main difficulty arises in properly determining the base line for current measurements. Under our experimental conditions, with an adequate switching potential, the base line was satisfactorily defined when the CV curves were recorded on astrip-chart re~0rder.l~ Taking into account that the instability of the [Fe(CN)sl” aqueous solutions20 makes nonconclusive long-time experiments (and, in particular, potentiometry), this method may be of special interest for studying complex formation in unstable oxidation states. Thus, providing that the equilibria are rapidly established near the electrode surface and that Fe(II1) stable species are formed a t the time scale of cyclic voltammetric experiments, a second set of K M values can be calculated and correlated with the corresponding stability constants, j3q1n,by using eq 7. These j3 values must correspond with those calculated from the limiting shift in the formal potential, which must verify the relationship6 Eo’(FeU’LH,/FenLH,) = Eo’(Feln/Fe”)
+
59/nl0g((3”,/pq) (27)
EXPERIMENTAL SECTION Cyclicvoltammogams were obtained on a conventional device witha potentiostat(AR loo),a signal generator (Newtronic2OOP), and an le-y recorder (Riken-Denshi F35). A standard threeelectrode cell was used with platinum (A = 0.11 cmz), gold (A = 0.018 cm2),andglassy carbon (A = 0.071 cm2)working electrodes, a saturated calomel reference electrode (SCE), and a platinumwire auxiliary electrode. Potentiostaticchronoamperogramsand cyclic voltammograms were monitored on a y-t recorder (JJ CR55O) by applying a constant potential of +0.45 V. To compensate for eventual differences in the effective area of the electrodes, [Fe(CN)~lCsolutions were used as standards for each of the series of experiments. Then, the ratio D/DMwas tabulated for calculations. All experiments were carried out under argon atmosphere in a cell thermostated at 298.1 & 0.1 K. Prior to the series of runs, the working electrodes were cleaned, polished, and activated.21 The diffusion coefficientsl were determined from the experimental i-t chronoamperometric curves (a) by directly applying from the slope of the Cottrell equation, (i = n F A c f i / d & ) the i vs plot or (b) from the least-squares intercept of W2 vs t 1 / 2 plots. Since a recent report has stated that chronoamperometric data obtained at short times (4s) are often unreliable and seems to imply that such data cannot be used to accurately determine diffusion conventional long-time experiments were used. In all experiments, linear relationships between the observed anodic current and were observed for times up to 3 s after the potential step. For the cyclic voltammetric data, linear relationshipsbetween l/PandE were foundinallcasesfor the+0.40to+0.60Vpotential range, corresponding to the diffusive region of the anodic cyclic voltammetric curve. The D values calculatedfrom the slopes of these representations agreed with those calculated from chronoamperometric data. In molar-ratio experiments, a series of samples containing a constant amount of potassium hexacyanoferrate(I1) and, eventually, competitive product and varying concentrationsof ligand were prepared. All samples were 0.15 M in NaC104, the pH (20)Cotton,F.A.;Wilkineon, G. Aduanced Inorganic Chemistry, 3rd ed.; Interscience: New York, 1973;p 861. (21)Engstrom, R.C.;Straseer, V. A. Anal. Chem. 1984,56,136141. Ravichandran, K.; Baldwin, R. P. Anal. Chem. 1984,56, 1744-1747. (22)Yap, W. T.;Doane, L.M. Anal. Chem. 1982,54,1437-1439.
ie
i’
-f
14
10 0
1
2
CL ~ M
Flgure 2. Dependence of the formal potentlal (A) and anodk peak current (B) on the Q/c+,,ratio for the [Fe(CNklC-[2l]aneN, system at pH 6.5 in the absence (e)and In the presence (0)of 1,3,5-BTC. c+,, = 0.84 mM; 4( = 1.88 mM. wtlnum working electrode, Y = 0.10 VIS.
adjusted to the required value by the addition of the appropriate amounts of HClOl and/or NaOH. Potentiometric measurements were carried out in aqueous solution at 298.1 f 0.1 K in the same medium using equipment already described.8 The program SUPERQUAD,u a widespread program based on a regression nonlinear fit with variable statistical weighting, was used to calculate the stability and protonation constants. The titration curvesfor each systemwere treated as a single set or separatelywithout significant variations of the values of the constants.
APPLICATION TO REAL SYSTEMS In order to compare experimental data with predictions, we have examined several polyazaalkane[Fe(CN)#- systems. Prior potentiometric studies showed that, for each system, several complexes with 1:l receptor:[Fe(CN)61C stoichiometry and different numbers of protons are formed in stepwise manner. The stability constants for these species differ to such an extent from one another that each tends to predominate in well-defined pH ranges. At the same time, cyclic voltammetric data indicated that both the uncomplexed [Fe(CN)#- and its complex species give nearly reversible one-electron couples for all systems in the studied pH range (from 4.0 to 10.0),as indicated by the peak-to-peak separation criterion (typicalvalues of 70 mV a t 0.10 V/s). Gold, platinum, and glassy carbon working electrodes provided similar results, and no adsorption problems were detected under our experimental conditions. Once adequate pH values were selected,cyclic voltammetric and chronoamperometricdata were used to apply the molarratio method. Curves A and B in Figure 2 show the variation of the formal potential and the peak current with C ~ C M ratio for the system [Fe(CN),+-[2lIaneN, ([2llaneN, = 1,4,7,10,13,16,19-heptaazacyclohenicosane,Chart I) a t pH 6.5, revealing significant differences in the cyclic voltammetric parameters. Application of the generalized molar-ratio method gives satisfactory results in all cases. For instance, Figure 3 shows the plots of K M vs a M corresponding to the [Fe(CN)slP-TAEC system (TAEC = N,N,N,N-tetrakis(Z aminoethyl)-1,4,8,1l-tetraazacyclotetradecane, Chart I) at pH 4.50 for different stoichiometries. It is observed that KMvs aM gives a horizontal line only for 1:l substratareceptor stoichiometry, whereas K M monotonically increases or decreases when (YMincreasesfor any other stoichiometry. For (23)Garcla-EspaAa, E.;Micheloni, M.; Paoletti, P.; Bianchi, A. Inorg. Chim. Acta. 1986,102,L9-Lll. Bencini, A; Bianchi, A, Dappom, P.; Garcla-EepaAa, E.; Micheloni, M.; Paoletti, P. Znorg. Chem. 1989,28, 1188-1191. (24)Gane, P.; Sabatini, A.; Vaccn, A. J. Chem. SOC., Dalton Tram. 1985,1196.
ANALYTICAL CHEMISTRY, VOL. 85, NO. 21, NOVEMBER 1, 1993
3141
Table I. Application of the Molar-Ratio Method to the [Fe(CN)#--Me4[ 18IaneNa System at pH 7.0.
KM X 109
I 00
I
04
08
CLICM
DIDM
CYM
0.303 0.465 0.625 0.678 0.752 0.969 1.048 1.157 1.372
0.863(1) 0.795(1) 0.733(2) 0.716(2) 0.687(2) 0.636(2) 0.617(2) 0.592(2) 0.573(2)
0.259(4) 0.385(4) 0.501(5) 0.533(5) 0.587(5) 0.683(6) 0.719(6) 0.766(6) 0.801(6)
1:l
2:2
2:l
33
5.8(7) 5.8(5) 5.9(3) 5.7(3) 6.3(4) 5.5(2) 5.7(2) 6.1(3) 5.2(2)
8(1) 6.6(5) 5.9(3) 5.5(3) 5.8(3) 4.7(2) 4.7(2) 5.0(2) 4.1(1)
2.0(1) 2.2(1) 2.8(1) 3.0(2) 3.6(2) 4.8(2) 5.7(2) 7.6(3) 8.6(4)
lO(1) 7.6(6) 6.5(4) 6.0(3) 6.3(4) 4.9(2) 4.9(2) 5.0(2) 4.2(1)
a Mean diffusion coefficientacalculated from the cathodic diffusive portion of the CV. CM = 1.360 mM,D ~ D =M0.467(2).
am 3. App#cetkn Of the m0lW-M methodto the [Fe(CNhlC-TAEC system at pH 4.5. Plots of KM vs aMfor dlfferent stolchlometrles.
chart I
TAEC
each molar ratio, individual D values were obtained from the slope of the cyclic voltammetric i-2 vs E plots and the i vs t 1 / 2 representation of the chronoamperometric data. In all cases, high linearity was encountered and the regression analysis (made with account of the errors in the two variables26) provides excellent values of the correlation coefficients. The representative value of the diffusion coefficient was calculated as the average of three individual D values obtained from independent cyclic voltammograms. Standard deviations in the D values were always better than 1% and, accordingly, in U M better that 4%, even in the less favorable conditions. From the mean value of KM (2.2(6) X 104, log KM = 4.3(1)), and inserting the log(1 + Cflj[Hlj) value determined from potentiometricdata (21.9(2)),we obtain log86 = 53.3(4) from eq 7, in close accordance with the potentiometric value, log 66 = 52.90(1). Experiments at pH 6.0 confirmed the 1:l stoichiometry. These results are of particular interest, taking into account that some binuclear compounds existing in crystalline state of this receptor with metal ions have been reported.% (25) Lichten, W. Am. Jour. Phys. 1989,57,1112-1115. (26) Murase, I.; Mikuriya, M.;Snoda, H.; Kida, S.J. Chem. SOC.,Chem. Commun. 1984,692-694. Murase, I.; Ueda, I.; Marubayashi, N.; Kida, 5.;Matemtoto, N.; Kudo, M.; Toyohara, M.; Hiate, K.; Mikuriya, M. J. Chem. SOC.,Dalton Tram. 1990, 2763-2769.
Cyclic voltammetric and chronoamperometric data, confirming potentiometric results, indicate that only monomer species exist in solution. Application of the molar-ratio method to the diffusive part of the cyclic voltammograms also gives satisfactory results. For instance, for the [Fe(CN)61C-TAEC system at the same pH, we obtain 10gKM = 2.7(1) and log ben1 = 51.6(5), in close accordance with the value calculated from the shift in the formal potential (95mV) and the potentiometric log @envalue by applying eq 27 (log = 51.3(1)). Table I exemplifies the application of the molar-ratio method for the hexacyanoferrate(III)-Me4[18laneN6 system at pH 7.00, with uncertainties assigned to the different quantities. The anion coordination equilibria between polyammonium receptors and nonelectroactive monohydrogen and dihydrogen carboxylate anions, ATP, and other anions has been studied by using cyclic voltammetry and chronoamperometry on the basis of the competitive effect of the [Fe(CN)#- i0ns.n As expected, addition of competitive anions to a solution containing [Fe(CN)61Cand a receptor causes a displacement of the cyclic voltammetric parameters toward those corresponding to the uncomplexed hexacyanoferrate(I1). This can be seen in the curves of Figure 2, which exhibit the formal potential and peak current variations with the C ~ C M ratio in the presence of a constant amount of X. As plotted in Figure 4, increasing amounts of substrate X lead to molar-ratio curves which increasingly differ from those in the absence of competitive agent. Application of the generalized molar-ratio method for competitive equilibria also leads to satisfactory results. Thus, Figure 5 shows the plots of Kx vs ax for the [Fe(CN)6lC-[2l1aneNrl,3,5-BTC (1,3,5-BTC = benzenetricarboxylic acid) system at pH 6.50. The values of KX remain constant only for 1:l substrate:receptor stoichiometry. From the mean value of KX (1.7(4) X 104, log KX = 4.2(2)), one obtains Cj3JHI" = 12.6(3), in agreement with the potentiometric value (CflJHI" = 12.7(1)).
FINAL CONSIDERATIONS The inherent capabilities of the molar-ratio method have already been discussed.28 The usefulness of the competitive method is limited, obviously, by the dependence of the ax and KX values upon the CYM and K Mvalues; therefore, errors in estimating the latter may affect the confidence level of the results concerning the complexation of the substrate X. In addition, the analysis of the effect of experimental variables on the coordination number and the calculated equilibrium (27) Bencini,A.; Bianchi, A.; Burguete, M. I.; Dapporto, P.; Domhech, A,; Garcia-Espah, E.; Luis, S. V.; Paoli, P.;Ramirez, J. A. J.Chem. SOC., Perkin Trans., in press. (28) Momoki, K.; Sekino, J.; Sato, H.; Yamaguchi, N. Anul. Chem. 1969,41, 128€-1299.
ANALYTICAL CHEMISTRY, VOL. 85, NO. 21, NOVEMBER 1, 1993
3142
Table 11. Generalization of the Molar-Ratio Method for the Hexacyanoferrate(I1)-Merpentaen-ATP system at pH 6.15. K 1V
1.o
c~(mM) DIDM
E
0268 0.560 0.840 0.955 1.272 1.549 1.723 2.005
0.8
0.6
0.4
a
1 0
2
6
4
C LICM
Flgure 4. Plots of the ratio D/& vs the ligar~d-to-[Fe(CN)s]~ molar ratio of the system [Fe(CN)(I]C-[21]aneNrcitric acid at pH 4.75. a = 1.27 mM. (A) q = 0; (B) q = 10.3 mM; (C) q = 38.1 mM. Glassy
(CM
0.987(1) 0.967(1) 0.947(1) 0.933(1) 0.893(2) 0.860(2) 0.833(2) 0.787(2)
aM
0.026(4) 0.066(4) 0.105(4) 0.132(4) 0.210(5) 0.276(5) 0.329(5) 0.421(5)
ax
(1:l)
0.179(8) 6.2(7) 0.351(8) 5.8(7) 0.514(8) 6.8(7) 0.559(9) 8.3(7) 0.674(9) 5.9(7) 0.777(9) 6.9(8) 0.816(9) 6.8(8) 0.862(9) 6.5(7)
(2:2) 6.9(7) 6.7(7) 6.0(6) 5.1(5) 5.6(5) 5.4(5) 5.0(5)
2.145 mM,CAW = 1.167 mM,D d D u = 0.493(1)).
of the stoichiometric coefficients of the hexacyanoferratereceptor complex species. To evaluate the uncertainties associated with the K values, we shall use the conventional theory of error propagation by assuming that only the uncertainty in the aMvalues is relevant for this purpose. Then, differentiating the logarithmic form of eq 9, one arrives at
carbon working electrode.
3:3
12
5
x“
8
4
1:l
0
1:2
00
04
08
Application of the generalized molar-ratio method for the [Fe(CN)#--[21]aneN7-l ,3,5-BTC system at pH 6.5.
Flgure 5.
constants is complicated by the fact that propagation of concentration errors depends on the stoichiometry of complex species. Despite these difficulties, the competitive molar-ratio method can be considered as a plausible procedure to complement potentiometric studies on complex formation equilibria. As significant aspects, one can mention (i) the possibility of distinguishing between mononuclear complexes and polynuclear ones, (ii) the possibility of elucidating complex formation in oxidation states nonaccesible to potentiometry, and (iii) the availability of the method for analyzing mixtures of complexes of the same stoichiometry. To summarize, standard cyclic voltammetric and chronoamperometric experiments can be satisfactorily applied to the study of competitive complexation equilibria between electroactive and nonelectroactive substrates. By a judicious use of potentiometric and voltammetric techniques, fruitful results may be expected from further studies concerning anion coordination chemistry.
ACKNOWLEDGMENT We are indebted to the Spanish DGCYT (PB90-0567) and IVEI for financial support and Italian Minister0 della Universia e della Ricerca Scientifica e Tecnologica.
APPENDIX: ANALYSIS OF ERRORS Application of the generalized molar-ratio method to cyclic voltammetric measurements is focused on the determination
where the symbol A denotes the uncertainty attributed to each quantity. It should be noted that the second term in parentheses is enhanced when the ratio CJCM diverges from n a d m , Le., when strong complexation occurs. This indictaes that the method allows accurate estimates of K M when relatively weak complexes are formed in solution. At this time, the uncertainty in the log Sq values can be derived from eq 7: A(1og 8,) = nA(1og KM) + A log(1 + Cj3j(H)”)+ qA(pH) (A21 For instance, for the hexacyanoferrate(I1)-TAEC system at pH 4.50(2), potentiometric data yield: q = 6, log pq = 52.90(1) log 81 10.41(1); log 82 = 20.04(2); log 08 = 29.39(2); log 8 4 = 38.22(2); log 8 5 = 44.03(3); log j3s = 48.61(2); log j3, = 50.2(3). From which one obtains log(1 + EOj(HY’) = 21.9(2) and qpH = 27.0(1). Combining these values with the log& value, 4.4(1), determined by applying the molar-ratio method to the CV and CA experimental data, one obtains log Bq = 53.3(4), in agreement with the potentiometric value. Similar considerations also apply for the competitive method. In this case, it is interesting to note that, from eq 16,
Accordingly, if KMis relatively larger and a reasonable C ~ C ratio is selected, one obtains uncertainties in ax not exceeding significantly those of a~ (see Table 11). This result is particularly relevant, indicating that, as expected, the most favorable conditions for applying the competitive method hold for a relatively weak X-L complex and a strong M-L complex.
RECEIVED for review February 10, 1993. Accepted July 13, 1993.8
* Abstract published in Adoance ACS Abstract& September 1,1993.
X
