37 1
Anal. Chem. 1985, 57, 371-372
Levich behavior. Time-consumingand tedious polishing with submicrometer-sized abrasives is unnecessary. Registry No. Pt, 7440-06-4;Au, 7440-57-5;Sic, 409-21-2;silver, 7440-22-4; iodide, 20461-54-5; alumina, 1344-28-1.
LITERATURE CITED Bard, A. J.; Fauikner, L. R. "Electrochemical Methods"; Wiiey: New York, 1980;Chapter 8. Riddiford, A. C. I n "Advances In Electrochemistry and Electrochemical Engineering"; Deiehay, P., Ed.; Interscience: New York, 1968;Vol. 4. Levich, V. G. "Physicochemical Hydrodynamics", 2nd ed Prentice Hail: Englewood, NJ, 1962;p 64 (as cited in ref 2,p 71). Theodorsen, T.; Regler, A. NaN. Advis. Comm. Aeronaut., Rep. 1844, No. 793, 1. Meklati. M.: Daauenet. M. C . R. Hebd. Seances Acad. Scl. Ser. C 1971, 272, 2057. "Buehler Analyst"; Buehler Ltd.: Lake Bluff, IL, 1983;Section 7. Symanskl, J. S. Ph.D. Thesis, SUNY at Buffalo, Buffalo, NY, 1984. Blegler, T.; Rand, A. J.; Woods, R. J. Nectroanal. Chem. 1971, 2 9 , 269. i i i m m e r , S. B.; Makrldes, A. C. J. Nectrochem. Soc. 1964, 1 1 1 ,
1122. "Metal Digest"; Buehler Ltd.: Lake Bluff, IL, 1981; Vol. 2 0 , no. I. Samuels, L. E. "Metallographic Polishing by Mechanical Methods", 2nd ed.; Eisevier: New York, 1971.
(12) "CRC Handbook", 61st ed.; CRC Press: Boca Raton, FL; 1981. (13) Kolthoff, I.M.; Jordan, J. J. Chem. Soc. 1953, 75, 1571. (14) Johnson, D. C. Ph.D. Thesis, University of Minnesota, Minneapolis, 1973. (15) Swathirajan, S.;Bruckensteln, S. J. Electroanal. Chem. 1983, 143, 167
(16) Washburn, E. W. "International Critical Tables"; McGraw-Hill: New York. 1929.Voi. 111. (17) Washburn, 'E. S. "International Critical Tables"; McGraw-Hill: New York, 1929;Vol. V. Present address: Matec Instrument, Inc., Warwick, R I 02886.
Stanley Bruckenstein* J o h n W.Sharkey J u n e Y.Yip' Chemistry Department State University of New York at Buffalo Buffalo, New York 14214
RECEIVED for review July 9, 1984. Accepted October 5, 1984. This work was supported by the Air Force Office of Scientific Research through AFOSR Grant 83-0004.
Determination of the Reaction Entropy of a Quasi-Reversible Redox Reaction with Cyclic Voltammetry Sir: In several recent papers (1-7) it has been demomtrated that the reaction entropy (AS") is a sensitive probe for structural changes in the inner and outer coordination layer which occur upon reduction or oxidation of transition-metal complexes. Interesting information concerning the charge distribution within the complexes, specific solvent/solute interaction, the influence of the stereochemistryof the solvent dipoles, the rate of the intramolecular electron transfer in mixed-valence complexes, and the extensiveness of the polarized solvent layer could be obtained. The determination of AS" for quasi-reversible electrode processes is possible using potentiometry, provided that both members of the redox couple are available and sufficiently stable in solution ( I ) . Using cyclic voltammetry it has been shown profitable to add an electrode adsorbent to the solution to render the process to a reversible one ( I ) . We will show that, when none of these conditions can be fulfilled, accurate AS" values can be measured with cyclic voltammetry provided that the anodic-cathodic peak-potential separation (AEp)is constant and not larger than about 200 mV.
DETERMINATION OF A S " AS" determinations have been carried out in both aqueous and nonaqueous media using a nonisothermalcell arrangement (I). With the nonisothermal cell it is possible to obtain AS" for a reversible redox reaction from the determination of Ellz as a function of the temperature Ox
+ ne
-
Red
(1)
and
AS" = nFdEl12/dT
(2)
since -FEl,2 -FE" = AGO = AH" - TAS" and assuming dAH"/dT and dAS"/dT are close to zero. It turns out that AS" data of satisfactory accuracy and reproducibility (1-2 entropy units) can be obtained even at solid electrodes. An underlying approximation in applying eq,2 is that El12 E". For a simple reversible electrode reaction (peak po0003-2700/85/0357-0371$01.50/0
tential separation in a cyclic voltammogram AE, N 60 mV at 298 K) this is no problem since in that case Ellz = E" + (RT/nF) In (Dox/Dm)1/2.Because the diffusion coefficients Dox and DRed are normally very close it follows that Ellz E" and thus dEl12/dT dE"/dT. El12can be easily determined from the anodic and cathodic peak potentials in the cyclic voltammogram (CV): Ellz = EP,J/2. Although it is suggested for quasi-reversible electrode reactions that the approximation dEl12/dT dE"/dT is accurate enough for AE, values less than 100,Jn mV ( I ) , there is no detailed evidence for that assumption. Indeed the difference between Ell2 and E" can be considerable (vide infra) for quasi-reversible electrode reactions measured with cyclic voltammetry using finite switching potentials (Eh). Transition-metal complexes show often quasi-reversibleredox processes and this deviation from electrochemical reversibility might be due to inner shell reorganization. It would be interesting to search if such inner shell reorganization has an influence on AS". In the following we will show that it is possible to determine AS" for quasi-reversible redox reactions with reasonable accuracy.
+
RESULTS AND DISCUSSION We tackled the problem by simulating cyclic voltammograms for several values of the electrochemical transfer coefficient a and the peak potential difference (by varying the kinetic parameter \k (=0.1-20)) (8). From each CV we extracted Ellz and compared it with the E" value used in the simulation. The results are assembled in Table I. We see, as expected, a steady increase in IEllz- E"I with increasing AE,. For 01 = 0.5 the nonzero values of the JEllz- EO1 differences indicate the influence of the switching potential, that was kept at a constant value during the simulations. As noted above the crucial parameter in the AS" determination is dE"/dT and not E". So the next step was to generate Table I at several temperatures in the interval 303-253 K. Eo was kept constant in these calculations, corresponding with ASo 0 1984 American Chemical Society
372
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
Table I. E l l z - E o (mV)as a Function of
(Y
and AE, at T = 303 K”(Switching Potential E x at Least 140 mV Positive of E,,J
(Y
0.7 0.6 0.5 0.4
-0.5 -0.5
0.3
0.0
up, mV
60
0.9 1.3 0.5
0.0 0.0
0.0
-0.5 80
3.7 2.8 1.4 0.4 -0.5
0.2 5.8 3.1
100
13.5 9.3 4.1
-0.1
-1.1
-2.7 125
-5.6 150
26.3 16.6 5.7 -4.8 -14.9 200
20.0
13.1
4.8 -2.7 -9.7 175
” Small irregularities are due to the accuracy in Ellzwhich is k0.5 mV in the simulation. Table 11. Error (cal/(mol K))=in A S ” as a Function of a and A E P b oi
0.7
-0.3 L
.
9
0.6 0.5
-0.2
-0.3
0.4
-0.2
-0.2
0.3 aEp,mV a See note positive of
0.2 60 a
-l\
-1.6
-1.7
-1.8
-0.6
-1.0
-0.8
-0.9
-0.2
-0.1
0.0
0 .o
0.2
0.4
0.9
1.3
1.2
1.6
2.2
0.1
80
in Table I.
100
125
150
-1.8
-0‘9 2.4
175
200
140 mV positive of E,,,. ACKNOWLEDGMENT We thank W. F. M. Gootzen for supplying the computer programs and J. J. Steggerda and J. G. M. van der Linden for their interest in this work. This investigation was supported in part by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organisation of Pure Research (ZWO). LITERATURE CITED (1) Yee, E. L.; Cave, R. J.; Guyer, K. L.; Tyma, P. D.; Weaver, M. J. J. Am. Chem. SOC.1079, 701, 1131. (2) Sahami, S.; Weaver, M. J. J. Elecfroanal. Chem. 1981, 722, 155. (3) Schmitz, J. E. J.; Koonen, P. J.; van der Linden, J. G. M.; Steggerda, J. J. Extended Abstracts 164th Meeting of the Electrochemical Society, Part 11, 1984; p 487. (4) Schmitz. J. E. J. Ph.D. Thesis, Nijmegen, 1984. (5) Schmitz, J. E. J.; van der Linden, J. G. M. Inorg. Chem. 1084, 23, 117.
(6) Schkitz, J. E. J.; van der Linden, J. G. M. h o r g . Chem. 1084, 2 3 , 3298. (7) Hupp, J. T.; Weaver, M. J. Inorg. Chem. 1084, 23, 256. (8) Nicholson, R. S. Anal. Chem. 1085, 3 7 , 1351. (9) Whiting, L. F.; Carr, P. W. J. Elecfroanal. Chem. 1977, 87, 1. (10) Gootzen, W. F. M.; Montree, A. H.; Schmitz, J. E. J., manuscript in preparation.
’
Present address: Philips Research Laboratorium, Eindhoven, The Netherlands.
J. E. J. Schmitz*l A. H. Montree Department of Inorganic Chemistry University of Nijmegen Toernooiveld, 6525 ED Nijmegen, The Netherlands RECEIVED for review May 7,1984. Accepted August 27,1984.
