Effects of reactant and product adsorption in normal pulse polarography

J. Electroanal. Chem., 257 (1977) 257--266 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

257

E F F E C T S OF R E A C T A N T AND PRODUCT ADSORPTION IN N O RMA L PULSE P O L A R O G R A P H Y

J.B. FLANAGAN, K. TAKAHASHI and F.C. ANSON Arthur A. Noyes Laboratory *, California Institute of Technology, Pasadena, Calif. 91125 (U.S.A.)

(Received 8th November 1976; in revised form 28th February 1977)

ABSTRACT Digital simulation is used to characterize the effects of the adsorption of reactants and products on the wave shapes and limiting currents of normal pulse polarograms. Pre- and post-waves induced by adsorption of reactants obeying non-linear isotherms are discussed. Analytical implications of the non-canonical relations between limiting currents and reactant concentrations are stressed.

INTRODUCTION We have recently becom e interested in the ways in which the adsorption of reactants or products modifies current-potential responses in pulse polarography. A discussion of the effects of adsorption in differential pulse polarography has been presented [1,2] and the present w ork extends the analysis t o normal pulse polarography. Perturbations in t he shapes o f normal pulse polarograms were first r e p o r t e d by Barker and Bolzan [ 3] who correctly interpreted the occurrence of peaked " m a x i m a " as arising f r o m reactant adsorption [3a]. An additional result of reactant adsorption is a depression of the limiting current below the value t hat would be obtained in t he absence of adsorption. Barker and Bolzan [ 3] also m e n t i o n e d this effect but discussed it only cursorily. In fact, this feature turns ou t to be a general consequence of reactant adsorption. It results whenever the adsorption is strong enough to lead t o a "Barker-Bolzan p e a k " in the normal pulse polarograms and is of obvious importance in analytical applications of the technique. The depletion o f adsorbing reactants near the electrode surface which is the origin o f the depression in the limiting current, and the pre- and post-waves which result f r o m non-linear adsorption isotherms are examined in this report, b o t h experimentally and by means o f digital simulation. T he normal pulse polarograms were obtained with the modified [2] pulse polarograph (Princeton Applied Research Model 174) by procedures essentially the same as those described in the previous r e p o r t on differential pulse polarography [2].

* Contribution no. 5460.

258 RESULTS AND DISCUSSION

Digital simulation The digital simulation program employed was a straightforward extension of that described previously for differential pulse polarography [2]. The electrode reaction was assumed to be nernstian and reversible at all coverages with both reactant and product soluble in either the solution or the mercury electrode. Initial and boundary conditions were identical to those given previously [ 1,21 except for the constant initial potential and increasing pulse amplitude characteristic of normal pulse polarography [3]. A listing of the simulation program is available upon request.

Experimental observations Figure 1 compares the normal pulse polarograms for Cd(II) in nitrate and iodide supporting electrolytes. The iodide-induced adsorption of Cd(II) produces both a current peak of the type described by Barker and Bolzan [3] and a depression of the limiting current on the plateau of the wave. The adsorption-induced peaking of the current originates from the same phenomenon that produces enhancement of peak currents in differential pulse polarography [ 1 ] : for nernstian reactions the rate of reduction of adsorbed reactant at potentials in the vicinity of the standard potential is limited by the rate at which the reaction product can diffuse away from the electrode surface. As a result, the additional current corresponding to reduction of the adsorbed reactant continues to be a significant component of the total current when it is sampled by the pulse polaro-

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Fig. 1. Normal pulse polarograms for 20 pM Cd(II). Supporting electrolyte: (1) 1 M KNO3; (2,3) 0.9 i KNO3---0.1 M KI. Current sampling time: (1,2) 48.5 ms (current averaged between 39.7 and 57.3 ms); (3) 22.7 ms (current averaged between 19.9 and 25.5 ms). Drop time: 2 s Mercury flow rate: 1.04 m g s - 1 . Initial potential: --450 mV vs. SCE.

259

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Fig. 2. Reverse scan normal pulse polarograms for 20 pM Cd(II). Initial potential: - - 8 0 0 m V vs. SCE. Supporting electrolyte: (1) 1 M KNO3; (2) 0.9 M KNO3--0.1 M KI. Current sampling time: 48.5 ms. Other conditions as in Fig. 1.

graph. For this reason the prominence of the current peak is enhanced by decreases in the current-sampling time (Fig. 1, curve 3). Depletion of the Cd(II) concentration in the solution at the surface of the dropping electrode because of its adsorption is responsible for the depression in the limiting current of the pulse polarogram recorded in the iodide electrolyte (Fig. 1). At potentials on the limiting currrent plateau all of the adsorbed reactant is reduced instantaneously u p o n application of the potential step so that when the current is sampled it contains contributions only from the diffusing reactant whose concentration has been depleted by the prior adsorption and reduction of a portion of the reactant initially present at the electrode surface. If the normal pulse polarograms for Cd(II) in iodide electrolytes are recorded in the anodic direction from initial potentials on the reduction current plateau, no current maximum nor limiting current depression result (Fig. 2). In this case the electrode reaction involves the conversion of an unadsorbed reactant (Cd(Hg)) to an adsorbed product b u t the pulse polarogram contains no clue of the presence of product adsorption. The limiting current is somewhat larger in the electrolyte containing iodide because the diffusion coefficients of Cd(II)-iodide complexes are larger. (Even though a net anodic limiting current is measured its magnitude should be determined by the diffusion coefficient of Cd(II) in the solution phase, not in the mercury electrode, according to eqn. 4 in ref. 4.) The iodide-induced adsorption of Cd(II) obeys a (non-linear) Frumkin isotherm [1]. Before comparing the observed experimental behavior with that calculated b y digital simulation for this more complex case, the calculated behavior of adsorbates which obey linear isotherms will be exposed.

260

Simulated polarograms with a linear adsorption isotherm Figure 3 contains a set of normal pulse polarograms simulated for the case that the adsorption of reactant and product obey a linear (Henry's law) isotherm. The initial potential lies outside the range of faradaic activity and the potential is scanned into the region where the faradaic reaction proceeds ("forward scan", e.g., a cathodic scan with a solution of a reducible reactant). Figure 4 contains a similar set of simulated polarograms for which a faradaic reaction is proceeding at the initial potential which is chosen to lie on the limiting current plateau. The potential is scanned in the direction of decreasing faradaic activity ("reverse scan", e.g., an anodic scan with a solution of a reducible reactant). Curve 1 in both Figures corresponds to no adsorption of either reactant or product. Curve 2 in Fig. 3 corresponds to a strongly adsorbed reactant being converted to a non-adsorbed product. Note the large current maximum and the severely depressed limiting current. Curve 2 in Fig. 4 is the result of a reverse scan with the same system. The shape of this polarogram is identical to that of curve 1 because all of the dissolved reactant which diffuses to the electrode before the application of each potential step is immediately converted to unadsorbed product just as is true when the initial reactant is not absorbed. Note, however, that the position of the wave on the potential axis is shifted because of the adsorption. The magnitude of this shift is determined by the magnitude of the linear adsorption coefficient but it is not influenced by the bulk concentration of the reactant.

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Fig. 3. Simulated polarograms for adsorbed reactants and p r o d u c t s obeying linear adsorption isotherms. Potential scanned in the forward direction. A d s o r p t i o n c o e f f i c i e n t s / c m for react a n t and products, respectively: (1) 0,0 (i.e., no adsorption); (2) 0.05, O; (3) O, 0.05; (4) 0.05, 0.05; (5) 0.05, 0.001. Simulation parameters: reactant c o n c e n t r a t i o n : 100 gM; initial potential: +150 m V vs. E O, the standard potential o f the r e a c t a n t / p r o d u c t couple; n = 2 electrons; diffusion coefficient: 10 - 5 c m 2 s- 1 (for b o t h reactant and p r o d u c t ) ; d r o p time: 5 s; current sampling time: 50 ms; DME m e r c u r y flow rate: 1 mg s-1.

261

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The polarograms labeled 3 in Figs. 3 and 4 are just the converse of those labeled 2 and, mutatis mutandis, their properties can be understood on the basis of the discussion in the preceding paragraph. Note that normal pulse polarograms corresponding to an electrode process which converts an unadsorbed reactant into an adsorbed product are distinguished from the polarograms corresponding to no adsorption of the reactant or the product only by a difference in half-wave potential for the two cases. In the absence of an independent determination of the standard potential of the system involved there is no way to deduce the presence of product adsorption from the normal pulse polarogram. This contrasts with the behavior obtained with differential pulse polarography where enhanced peak currents result from the adsorption of the product as well as the reactant [1,2]. However, for reversible electrode reactions, the presence of adsorption can easily be verified in normal pulse polarography by recording the polarogram in the opposite scan direction, thus interchanging the effective reactant and product. If b o t h the reactant and product are adsorbed with equal adsorption coefficients (curve 4 in Figs. 3 and 4) there is no current maximum nor shift in halfwave potential but the limiting current is depressed identically in both the forward and the reverse scan directions. Finally, the polarograms labeled 5 in Figs. 3 and 4 correspond to adsorption of both product and reactant but with much stronger adsorption of the latter. During the forward scan (Fig. 3} a current maximum appears b u t its magnitude is considerably smaller than is true in the absence of product adsorption (compare curves 2 and 5 in Fig. 3) despite the fact the the same reactant adsorption coefficient is involved. Reactant depletion resulting from the adsorption produces

262

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Fig. 5. Simulated polarograms for adsorption of reactant but not product. Potential scanned in the forward direction. Adsorption coefficient/cm: (1) 0; (2) 0.001; (3) 0.002; (4) 0.005; (5) 0.01. Other simulation parameters as in Fig. 3.

a depressed limiting current with a magnitude that is independent of t he strength of p r o d u c t adsorption (compare curves 2, 4, and 5). The polarogram obtained during the reverse scan (Fig. 4, curve 5) shows no current max im um when the reactant adsorption coefficient exceeds t h a t of the p r o d u c t but th e limiting current is nevertheless depressed by adsorptive depletion. Figure 5 shows how the shape of the polarogram changes as the adsorption coefficient of the reactant is increased in the absence of p r o d u c t adsorption. These polarograms resemble those given by Barker and Bolzan (Fig. 6 of ref. 3) except that adsorptive depletion of the reactant was not included in their approxi. mate calculations. It is evident f r o m the curves in Fig. 5 that the current maximu m is absent when the adsorption coefficient is 10 -3 cm or less although significant depression of the limiting current persists. With non-linear isotherms similar behavior results at bulk reactant concentrations where the adsorption approaches the saturation value. In b o t h cases the behavior can be dangerous analytically if reactant concent r a t i on are being determined from limiting current magnitudes. It should be n o t e d that in the simulation e m p l o y e d here the adsorption coefficient was assumed to be i n d e p e n d e n t of potential (Barker and Bolzan [3] used the same approximation). However, it is n o t difficult to estimate the qualitative effects t hat would be i nt r oduc e d by a potential d e p e n d e n c e of the adsorption coefficient. If a reactant is adsorbed at the initial potential but not at potentials on the plateau of the wave depression of the limiting current arising

263

from the depletion of reactant from solution will be the same whether or not the adsorption coefficient is potential dependent. The initially adsorbed reactant will react essentially instantaneously when the electrode potential is stepped to the diffusion limiting region whether or not it remains adsorbed. In cases where the reaction product is not adsorbed the effect of desorption of the reactant at potentials on the rising portion of the wave because of a decrease in its adsorption coefficient will generally be to produce a maximum in the current-potential curve resulting from the enhancement of the reactant concentration at the electrode surface. The converse case in which there is no adsorption of the reactant at the initial potential but increasing adsorption at potentials where the wave appears would be expected to exhibit shifted waves with altered shapes but the limiting current would not be affected since it remains a function only of the adsorption coefficient of the reactant at the initial potential.

Simulated polarograms with non-linear adsorption isotherms When the reactant adsorption is governed by a linear isotherm the current maxima, limiting currents and half-wave potentials are not influenced by changes in the bulk concentrations of reactant. However, non-linear adsorption isotherms cause all three of these polarographic features to exhibit concentration dependences. With non-linear isotherms and sufficiently large adsorption coefficients preand post-waves may appear in normal pulse polarograms. These waves originate for the same reasons that have been discussed in the cases of differential pulse polarography [2], d.c. polarography [5], linear potential scan voltammetry [6], and chronocoulometry [7]. Figures 6 and 7 shows a set of simulated polaro-

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Fig. 6. S i m u l a t e d p o l a r o g r a m s f o r a n a d s o r b e d r e a c t a n t o b e y i n g a L a n g m u i r i s o t h e r m . B u l k r e a c t a n t concentrations/pM: ( 1 ) 1; ( 2 ) 5 0 ; ( 3 ) 2 0 0 ; ( 4 ) 1 0 0 0 . A d s o r p t i o n c o e f f i c i e n t : 0 . 5 c m ; a d s o r p t i o n a t s a t u r a t i o n o f t h e s u r f a c e : 3 X 10 - 1 ° t o o l c m - 2 . O t h e r s i m u l a t i o n p a r a m e t e r s as in Fig. 3.

264

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Fig. 7. Simulated polarograms for an adsorbed product obeying a Langmuir isotherm. Bulk reactant concentrations//IM: (1) 1; (2) 50; (3) 300; (4) 400; (5) 500; (6) 1000. Other simulation parameters as in Fig. 6.

grams for adsorbing reactants and products, respectively, which obey Langmuir adsorption isotherms. With reactant adsorption (Fig. 6) the post-wave appears in the form of a current m a x i m u m (curves 1, 2, 3). At low concentrations this post-wave so dominates the response that no vestige remains of the unperturbed main wave (curve 4). At higher concentrations where the electrode surface is saturated the post-wave becomes insignificant with respect to the main wave. Only over a rather narrow range of concentrations does a clear double wave appear (curve 3). On the other hand, with product adsorption (Fig. 7) flat-topped pre-waves are obtained with shapes reminiscent of their counterparts in d.c. polarography. However, the concentration range within which the double waves develop is also quite restricted, spanning little more than one order of magnitude. The prominence of the waves is also a sensitive function of the adsorption coefficients of the product. As the coefficient is decreased the pre-waves eventually become imperceptible because their separation from the main wave decreases correspondingly. The pre- and post-waves are most clearly separated from the main wave when the adsorption isotherms rise to saturation coverage over a relatively narrow range of bulk concentrations as with the Langmuir isotherm or, especially, the Frumkin isotherm with an attractive interaction parameter [8]. Cd(II) in iodide electrolytes obeys a Frumkin isotherm with a repulsive interaction parameter and a smaller adsorption coefficient than was used in the simulations in Fig. 6 [2]. The net result is that a clear current m a x i m u m is observed in normal pulse polarograms for Cd(II) in iodide (Fig. 1), but no clearly separated post-wave (such as curve 3 in Fig. 6) is obtained at any concentration of Cd(II). Figure 8 compares the concentration dependences of the experimentally measured values of the (normalized) maximum and limiting currents for Cd(II)

265 I

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Fig. 8. C o n c e n t r a t i o n d e p e n d e n c e s o f t h e p e a k c u r r e n t s a n d limiting c u r r e n t s for C d ( I I ) in 0.9 M KNO3--0.1 M KI. T h e o r d i n a t e is t h e c u r r e n t d e n s i t y divided b y b u l k c o n c e n t r a t i o n o f Cd(II). E x p e r i m e n t a l p o i n t s are p l o t t e d , t h e n u m b e r e d solid lines are s i m u l a t e d . (1, o) M a x i m u m c u r r e n t , d r o p t i m e = 5 s; (2, e ) m a x i m u m c u r r e n t , d r o p t i m e = 1 s; (3, A) limiting c u r r e n t , d r o p t i m e = 5 s; (4, A) l i m i t i n g c u r r e n t , d r o p t i m e = 1 s. M e r c u r y flow r a t e : 1.06 mg s--l; c u r r e n t s a m p l i n g t i m e : 48.5 m s ; d i f f u s i o n coefficients: Cd(Hg) = 1.5 x 10 - 5 c m 2 s--l; Cd(II) = 10 - 5 c m 2 s - 1 ; F r u m k i n a d s o r p t i o n i s o t h e r m p a r a m e t e r s [ 2 ] used in t h e s i m u l a t i o n : a d s o r p t i o n c o e f f i c i e n t = 0.04 c m ; m a x i m u m a d s o r p t i o n : 2.2 x 10 - 1 0 m o l cm--2; repulsive i n t e r a c t i o n p a r a m e t e r : 3.6.

in iodide electrolytes with those obtained from a digital simulation based on the Frumkin adsorption isotherm parameters that were determined previously by an independent technique [2]. The good agreement between the experimental results, plotted as points, and the simulation which involved no adjustable parameters (the continuous lines) justified the conclusion that the factors responsible for the current perturbations have been properly identified and satisfactory accounted for in the simulation. For example, note that with the shorter drop times in Fig. 8 the current maximum is essentially absent at a concentration of 200 pM b u t the normalized limiting current is still ca. 15% below the high concentration (no-adsorption) limit. Just such behavior was shown in Fig. 5 (curve 2) in the case of a linear isotherm. CONCLUSIONS

Both the simulated and experimental results we have presented make it clear that reactant adsorption can lead to normal pulse polarographic waves with anomalous features such as current maxima, double waves and depressed limiting currents. Although the shapes of the current maxima can resemble those of ordinary polarographic maxima [ 3] their origin is clearly different depending, as it does, on the coupling of adsorption, mass transfer and nernstian electrode kinetics rather than changes in interfacial tension and streaming at the surface of liquid mercury electrodes. Adsorption-induced current maxima may also appear in pulse polarograms obtained at solid electrodes with reversibly adsorbing, nernstian reactants.

266 The depression in normal pulse polarographic limiting currents which reactant adsorption induces can have serious analytical consequences because the linear relationship between the limiting current and bulk reactant concentration is lost. When both the reactant and the product of an electrode reaction are adsorbed the situation becomes particularly troublesome if the normal pulse polarograms are being used for analytical purposes because severe depression of the limiting currents may result while the wave shapes give no hint that the adsorption is occurring (e.g., curves 4 in Figs. 3 and 4). Whenever a current m a x i m u m is detected in a normal pulse polarogram obtained with a dropping mercury electrode the ensuing limiting current will be depressed but the electroanalyst has received a clear warning sign. When no maximum is observed other tests which may reveal the presence of adsorption include limiting currents which are very different on forward and reverse scans or anomalous dependences of the limiting currents on drop time or current sampling time. ACKNOWLEDGMENTS This work was supported by the National Science Foundation and the U.S. Army Research Office (Triangle Park). A generous grant from Gould, Inc. in support of this work is also gratefully acknowledged. REFERENCES 1 F.C. A n s o n , J.B. F l a n a g a n , K. T a k a h a s h i a n d A. Y a m a d a , J. E l e c t r o a n a l . C h e m , , 6 7 ( 1 9 7 6 ) 2 5 3 , 2 J.B. F l a n a g a n , K. T a k a h a s h i a n d F.C. A n s o n , J. E l e c t r o a n a l . C h e m . , 81 ( 1 9 7 7 ) 2 6 1 . 3 G.C. B a r k e r a n d J . A . B o l z a n , Z. Anal. C h e m . , 2 1 6 ( 1 9 6 6 ) 2 1 5 . 3 a T h e p o s s i b i l i t y t h a t a d s o r p t i o n c o u l d i n d u c e p e a k e d c u r r e n t - p o t e n t i a l r e s p o n s e s in p u l s e d v o l t a m m e t r i c e x p e r i m e n t s w a s also s u g g e s t e d b y O k a : N i p p o n K a g a k u Zasshi, 8 2 ( 1 9 6 1 ) 1 3 5 6 ; C h e m . A h s t r . , 58 ( 1 9 6 3 ) 1 8 9 2 . 4 K.B. O l d h a m a n d E.P. P a r r y , Anal. C h e m . , 4 2 ( 1 9 7 0 ) 2 2 9 . 5 R. B r i d i c k a , Z. E l e c t r o c h e m . , 4 8 ( 1 9 4 2 ) 2 7 8 , 6 8 6 . 6 R . H . W o p s c h a l l a n d I. S h a i n , A n a l . C h e m . , 39 ( 1 9 6 7 ) 1 5 1 4 . 7 W.H. R e i n m u t h a n d K. B a l a s u b r a m i a n , J. E l e c t r o a n a l . C h e m . , 3 8 ( 1 9 7 2 ) 79. 8 A.N. F r u m k i n a n d B.B. D a m a s k i n in J . O ' M . B o c k r i s a n d B.E. C o n w a y (Eds), M o d e r n A s p e c t s o f E l e c t r o c h e m i s t r y , Vol. 3, B u t t e r w o r t h , L o n d o n , 1 9 6 4 , Ch. 3.