Electrosorption valency determination by impedance measurements

J. Electroanal. Chem., 97 (1979) 293--295 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

293

Preliminary note ELECTROSORPTION VALENCY DETERMINATION BY IMPEDANCE MEASUREMENTS

R. DURAND Laboratoire d'Energ~tique Electrochimique (L.A. C.N R.S. 265) E N.S E.E.G , 38401 St Martin d'H~res (France) (Received 27th November 1978; in revised form 3rd January 1979)

The object of this note is to point out that the electrosorption valancy nB can be obtained from the diffusion impedance constant WB in the case of electrosorption of a species B, in excess supporting electrolyte. From this determination and from the measurement of the electrosorption capacitance CB the variations of the surface concentration P can be deduced. We give an example of application of this method in the case of the H+/H(Pt) system. EXPRESSION OF THE ELECTROSORPTION IMPEDANCE

Different expressions of this impedance are known [ 1,2] ; starting from a thermodynamic basis we briefly establish one of them, chiefly with the purpose of explaining the symbols and approximations used. In the case of a constant concentration of a non-electrosorbed supporting electrolyte we can use the simplified electrocapillary relation: - d 7 = Q d E + Fdp where Q = thermodynamic electrode charge, E = electrode potential relative to a constant-potential reference electrode, ~ = chemical potential of species B in the solution). Furthermore, the supporting electrolyte concentration being high, we can neglect in F its purely electrostatically adsorbed part F e, and neglect the potential drop in the diffuse layer. Introducing the electrosorption valency [3] nB and the "high frequency" capacity C : nB = ( l / F ) (ag/aE)r = - ( l / F ) (~QI~F)E

C

= (SQ/SE)r

we can write for the equilibrium state: dp = ( ~ p / ~ F ) E d F + n B F d E

(1)

dQ =-nBFdF+C

(2)

dE

For small deviations from the equilibrium state, the current i can be expressed with the aid of eqn. (2) as:

294 i =dQ/dt =-nBFdF/dt+C

dE~dr = i B + i c

and introducing in relation (1) the irreversibility term related to the adsorption rate, we obtain the electrosorption impedance ZB ; for example in the case of semi-infinite linear diffusion, i.e. for a not too small Laplace parameter p (p = j ¢o in a.c.): ~ E = (R B + WB/X/P + 1 / C B P ) iB = ZBiB with: RB = (aE/aiB)~.r

WB = R T / ( n B 2 F 2 c~/D)

CB = n B 2 F 2 ( a r / a g ) E = - n B F (ar/aE)~

(3)

(4)

The electrode impedance can therefore be represented by the classical equivalent circuit shown in Fig. 1.

ic

I

l Coo I

RB

WB

CB

Fig. 1. Equivalent circuit for electrosorption impedance. It can be noticed that an interfacial parameter (nB 2) is included in the diffusional impedance expression [6] : the concentration polarization is A p / n B F (eqn. 1) and the Fick relation gives the Ac and ~p dependence against the diffusion flux, which is equal to the adsorption rate iB/nBF. PROPOSED METHOD The complete determination of the four components C , R B, WB and CB with an 1--2% accuracy is possible if a wide range o f p values is used [4] ; for the chosen concentration c of the species B in the bulk solution, from WB (E) we can deduce nB (E) with the same magnitude of accuracy, if the diffusion coefficientD of the species B is known with a 4% uncertainty (eqn. 3). The variations of F with E can then be directly deduced from the nB (E) and CB (E) values (eqn. 4). Actually, it can be easily demonstrated [4] that such impedance measurements, made with various concentrations c, allow the determination of all the t h e r m o d y n a m i c and kinetic parameters of the studied system; nevertheless the charges will be determined with the same unknown additional constant, except when the p.z.c, is known by another means for one of the concentrations studied (c = 0, for example). EXAMPLE Measurements on the H ÷/H (polycrystalline Pt) system in the Hz to MHz frequency range [4], were made in the case of a 1M Na2SO4 + 0.01M H2SO4 solution among others.

295 C/pF.©m-z Co~ ,C B 30--900

/k*

\'/~

20--

c= 'n B

,o

%

1

°"\ 05

0

i

100

i

200

i

300

E~mVIRHE 400

500

Fig. 2. V a r i a t i o n s o f t h e e l e c t r o s o r p t i o n v a l e n c y riB, o f t h e h i g h f r e q u e n c y c a p a c i t y C = a n d o f t h e e l e c t r o s o r p t i o n c a p a c i t y C B v e r s u s p o t e n t i a l E, f o r a s p h e r i c a l P t e l e c t r o d e in a 1 M Na~SO 4 0 . 0 1 M H~SO 4 s o l u t i o n .

The problems related to the solid electrodes were resolved to a large extent by using spherical electrodes obtained in an H2--O2 flame; we found that, between +25 and +300 mV (RHE), the circuit of Fig. 1 is a very satisfactory model within the experimental accuracy limits: on one hand the electrosorption and the dissociation of HSO4- ions are therefore not involved in a predominant manner, on the other hand the assumption of semi-infinite linear diffusional control seems justified (especially beyond 400 Hz). The nB values obtained (Fig. 2) are very close to those deduced from thermodynamic measurements on platinized platinum [5], but the maximum of nB(E) occurs in our results at a less positive potential: not only are the surface structures different, but also C= and nB are obtained after many successive thermodynamic measurements and calculations. However, in both cases, nB values can differ from the unity, and this cannot be neglected in the determination of F(E) from the CB(E) dependence. We plan to apply this method for studies on well-defined single-crystal surfaces.

REFERENCES 1 2 3 4 5 6

W. Lorenz, Z. Elektrochem., 62 (1958) 192. B.M. Grafov and E.A. Ukshe, A.C. Electrochemmal Circuits. ~lauka, Moscow, 1973 (m Russzan). J.W. Schultze and K.J. Vetter, J. Electroanah Chem., 44 (1973) 63. R. Durand, thesis, Grenoble, 1978; R. Durand, to be pubhshed. B.M. Grafov, E.V. Pekar and O.A. Petty, J. Eleetroanal. Chem., 40 (1972) 179. R. de Levie and L. Posplsfl, J. Electroanal. Chem., 22 (1969) 277.