Effects of Adsorption of Electroactive Species in Robert €3. Wopschall and Irving Shah Chemistry Department, University of Wisconsin, Madison, Wis. The theory of stationary electrode polarography for single scan and cyclic triangular wave experiments has been extended to describe electrochemical systems where either the reactant, the product, or both the reactant and product are adsorbed at the electrodesolution interface (Langmuir isotherm). A numerical method was applied to solve the integral equations obtained from the boundary value problems, and extensive data were calculated which made it possible to characterize quantitatively the adsorption parameters of the system. Correlation of theoretical and experimental parameters made it possible to develop diagnostic criteria sa that unknown systems could be characterized by studying the variation of peak shape and peak current as a function of scan rate and bulk concentration
,
I
I
C
SINCETHE FIRST electroanalytical study of adsorption by Brdicka ( I , 2) using conventional polarography, similar concepts have been applied to other methods, such as chronopotentiometry (3, 4), electrolysis with constant potential (5, 6)) ac polarography (7), and stationary electrode polarography (chronoamperometry with linear potential scan) (8,9). These have provided versatile tools for the study of adsorption, and although theoretical and experimental studies have been carried out for several of these newer methods, only qualitative studies [with the exception of a method for determining the amount of adsorbed reactant (IO)] have been conducted using stationary electrode polarography. In the presence of weakly adsorbed material, stationary electrode polarograms may exhibit enhancement of the peak currents (IO, I I ) because of electron transfer involving the adsorbed material at nearly the same potential as the “normal” electron transfer (Figure 1 , curves A and B). On the other hand, if the product or reactant is strongly adsorbed, a separate adsorption peak may occur prior to or after the normal peak (9) (Figure 1, curves C and D)in analogy to the polarographic prewave ( I , 2). One of the first studies of strongly adsorbed materials using stationary electrode polarography (single scan) was carried out by Mirri and Favero (8) on the prepeak which is observed with methylene blue. More recently Kemula, Kublik, and Axt (9) carried out qualitative studies on methylene blue under conditions where both ad(1) R. Brdicka, Collection Czech. Chem. Commun., 12, 522 (1947). (2) I. M. Kolthoff and J. J. Lingane. “Polarography,” 2nd ed., Interscience, New York, 1952, Vol. I, p. 256. (3) W. Lorenz, Z . Elektrochem., 59, 730 (1955). (4) W. H. Reinmuth, ANAL.CHEM., 33, 322 (1961). (5) F. C. Anson, Ibid., 38, 54 (1966). (6) J. H. Christie, G. Lauer, and R. A. Osteryoung, J . Electround. Chenz., 7,60 (1964). (7) B. Breyer and H. H. Bauer, “Alternating Current Polarography
and Tensammetry,” Interscience, New York, 1963, p. 69.
(8) A. M. Mirri and P. Favero, Ric. Sci., 28, 2307 (1958). (9) W. Kemula. Z. Kublik, and A. Axt, Roczniki Chem., 35, 1009
I
I
D
I
0.1
0.0 -0.1
0.1
I
0.0 -0.1
Figure 1. Theoretical stationary electrode polarograrns for cases involving adsorption A, reactant adsorbed weakly ; E , product adsorbed weakly ; C, reactant adsorbed strongly; D,product adsorbed strongly.
Dashed lines indicate behavior for the uncomplicated Nernstian charge transfer
sorption and diffusion waves were observed for both cathodic and anodic scans. Hartley and Wilson (12) in a recent study of flavin mononucleotide observed similar adsorption prepeaks on mercury electrodes. These qualitative studies all indicated that additional theoretical work would be necessary to provide a quantitative basis for understanding the effect of the adsorption of electroactive materials in stationary electrode polarography. To proceed with the study, it was necessary to describe the adsorption with an isotherm, and while there are several which could have been employed (13), a Langmuir isotherm was used because it embodies the general characteristics of more accurate isotherms (i.e,, limits adsorption to a fixed amount of material per unit area and reduces to Henry’s law at low concentrations) but is sufficiently simple to be handled conveniently. The mechanism which was considered assumed a reversible charge transfer with both product and reactant adsorbed, and in equilibrium with the dissolved species:
(1961).
(10) R. A. Osteryoung, 6. Lauer, and F. C. Anson, J . Electrochem. SOC.,110,926 (1963). (11) C. A. Streuli and W. D. Cooke, ANAL,CHEM., 26,963 (1954).
15 14
e
ANALYTICAL CHEMISTRY
(12) A. M. Hartley and G. S . Wilson, Ibid., 38,681 (1966). (13) R. Parsons, Proc. Roy. SOC.(London),A261,79 (1961).
OeOh
*
(1)
OadS
+ ne- a R
0
Rsoh
(11) (111)
Rads
The rates of the adsorption-desorption processes were assumed to be sufficiently fast. While this is undoubtedly an important limitation of some adsorption studies (14, IS), especially when the potential scan rate is high, it probably can be neglected for properly selected ranges of the experimental parameters. The boundary value problem was written in terms of the initial charge transfer being a reduction, occurring on a cathodic scan. However, the results are also applicable to cases in which an initial oxidation occurs on an anodic scan, by changing the appropriate signs. BOUNDARY VALUE PROBLEM
For a reversible reduction with adsorption of both reactant 0 and product R (Equations I-III), the boundary value problem for stationary electrode polarography at a plane electrode x is: bCo/bt
=
Do(b2Co/bxz)
(1)
bCR/bt
=
DR(b2CR/bX2)
(2)
0, x 2 0 :
t
CO = C O W ,
T O = TO*, r R =
t
t
2 0, x
> 0, x
= 0:
--f
C R = CR*
rR*
(=a)
(=o)
: CO * cO*, CR * 0
=
r R =
- E")]
+
- D R ( ~ C R / ~ X )b r R / a t
To = ro'Co/(Ko
+ Co)
rRSCR/(KRf CR)
(3)
(5) (6)
(7)
fR(t) = D R @ ~ R / ~ X )
The total current is given by
(8) i = nFA&
(9)
where t is the time, x is the distance from the electrode-solution interface, Co and CR are the solution concentrations of 0 and R, Co* and CR* are the initial bulk concentrations, and Do and DR are the diffusion coefficients. E is the potential of the electrode and E" is the formal reduction potential for Reaction 11. To and rR are the surface concentrations (in moles per unit area), Pos and r R s are the saturation values at maximum surface coverage, and To* and r R * are the initial surface concentrations. The terms KOand KR which appear in the Langmuir adsorption isotherms (Equations 8 and 9) for species 0 and R, are related to the free energies of adsorption, AG, by -In K = AG/RT
Here, v is the rate of potential scan, Et is the initial potential, and Ex is the potential when the scan is reversed. As in previous cases (16),the form of Equation 11 precludes direct application of Laplace transform techniques to this boundary value problem. Instead, the solution involves conversion of Equations 1-5 into the corresponding integral equations relating the fluxes to the concentrations. This transformation is carried out by taking the Laplace transform of the partial differential equations, solving for the transform of the surface concentrations in terms of the transforms of the surface fluxes, and then applying the convolution theorem to obtain:
(4)
Co/cR = exp[(nF/RT) ( E
D ~ ( ~ c ~-/ bro/at ~ x )
For stationary electrode polarography (including the cyclic experiment), the potential is a triangular function of time with the direction of scan reversed when t = A:
(10)
While the free energies of adsorption are normally dependent on solvent, electrode surface, temperature, the presence of other adsorbable materials, electrode potential, and possibly many other variables, all of these except electrode potential are held sufficiently constant in stationary electrode polarography so that to a good approximation KO and KR can be considered dependent only on potential. The problem is essentially the same as the case without adsorption (16)except the relation between the fluxes of 0 and R (Equation 7) includes terms related to the rate of change of the surface concentrations of adsorbed materials.
- bJ?o/bt) = -nFA(fR
- br&t)
where A is the area of the electrode. Combining Equations 6 and 11, c~/cR =
es(t)
where 8 = exp[(nF/Rr> ( E a - E")]
S(t) =
i
exP(--O, exp(at
- 2aX),
o
