cependent Chronoamperometry. Disproportionation y
8x1 Irreversible
Chemical Reaction
by Lynn Marcoux Department of Chemistry, Texas Tech University, Lubbock, Texas
79409
(Received April 6, 1972)
It has been suggested that anodic substitution reactions proceed via an ECE reaction pathway, i e . , A - e Iz B. I3 $. Z + C,C - e D; however, the possibility exists that the reaction might instead involve dispro-
+
=;
Kdiapio
+
+
k'
B, 2B C A, C Z --+ D. In addition to these portionation leading to the sequence A - e possibilities, the ECC variation of the ECE mechanism which includes provision for the solution equilibrium, KECC
e +
A 3.D B C, must also be considered. A potential-dependentform of double-step chronoamperometry is shown to be diagnostically valuable for distinguishing between these alternative mechanisms.
The ECE reaction sequence which is most commonly notated in the following fashion
A -e
B
EO1
the several alternative mechanisms could be distinguished. The following very specific mechanism
(6)
A - e z B
(1)
k
+z+c C -e Z D
(2)
E",
has been the subject of a great deal of recent comment due to the fact that several related combinations of reactions give rise to similar electrochemical responses. The first of these variant mechanisms was described by Feldberg,lU3 who noted that an oxidation-reduction equilibrium of the type KECC
A R
~
+- D ~-B + C . A
~= exp C [R"T -
EO^ -
EO^)]
k'
(3)
C+Z+D
has recently been suggested as a possible route for anodic substitution reactions.1° In both of these sequences Z is an electroinactive nucleophile and is usually assumed to be present in excess in order to permit the reaction to be treated as pseudo-first order. The disproportionation mechanism assumes the presence of a second electron transfer step
(4)
(5)
(8)
B-e z C Consequently,
Kdispro may
Eo3
(9)
be written
K!!
K d i s p r o = exp -(EO1 - E"3) (10) existed in solution and that its presence must be taken into account when deriving equations for voltammetric This suggestion was based on the observation of responses. This complication was dubbed the ECC and coworkers that this mechanism was the mechanism. and its existence was theoretically described and experimentally confirmed. For both the (1) ,M. D. Hawley and S. W.Feldberg, J . Phys. Chem., 70, 3459 organic oxidations and reductions to which ECE be(1966). (2) R. N. Adams, M. D. Hawley, and S. W. Feldberg, ibid., 71, 851 havior has been ascribed. species C is quite oiten an (1967). aromatic free radiical which is oxidized (reduced) at (3) S. W.Feldberg, ibid., 75, 2377 (1971). potentials much less positive (negative) than species (4) S. W.Feldberg, ibid., 73, 1238 (1969). A. This, in addition to the fact that electron transfer (5) M. Mastragostino, L. Nadjo, and J, M. Saveant, Ekctrochim. reactions of this type are normally quite rapid in soluActa, 13, 721 (1968). (6) M. Mastragostino and J. M. Saveant, ibid., 13, 751 (1968). tion, would lead one to believe that the ECC case should (7) L. Nadjo and J. M.Saveant, ibid., 16, 887 (1971). be more prevalent than the ECE. This refinement has (8) L. Nadjo and J. M . Saveant, J . El~ctroanal.Chem., 33. 417 unfortunately been ignored by several investigators. (1971). Disproportionation pathways also give rise to over(9) C. P. Andrieux and J. M. Saveant, ibid., 33, 453 (1971). all reactions indentical t o ECC or ECE mechanisms, (IO) L. Marcoux, J . Amer. Chem. Soc., 93, 537 (1971). and several of the possibilities have been d e ~ c r i b e d . ~ - ~(11) H. J. Shine and Y .Murata, ibid., 91, 1872 (1969). The goaj of thcse authors was to find means by which (12) Y. Murata and H. J. Shine, J . Org. Chem., 34, 3368 (1969).
The Journal of Physical Chemistry, Val. 76, it'o. 22, 1978
POTENTIAL-DEPEN DENT CHRONOAMPEROMETRY most likely explanation for the disappearance kinetics of some chemically prepared cation radicals. This proposal is contrary to the results of other investigator^.^^*'^ The reason for disagreement as to mechanism stems from the fact that the previously published diagnostic methods are somewhat equivocal. The purpose of this work is to prlesent an electroanalytical approach which permits a less ambiguous assignment of mechartism.
3255
2.0
1
ECE
1.6
1.2 Napp
0.8
Results
tEo-/
The approach chosen is a chronoamperometric method in which the potential is not necessarily stepped 0.4 into the region of diRusion control. This technique has been named potential-dependent chronoamperom0.0 etry, and it has been shown to be a useful approach to -2 -1 0 1 2 3 the E C reaction sequence.lG It was pointed outlGthat log k t this potential program accomplished the same result as other methods but possessed several experimental Figure 1. Single-step potential dependent working curves for advantages. It should also be noted that this type of the ECE reaction; E a refers t o Elo in this and other figures. experiment is easity extended to the chronocoulometrie” and double-step18methods. Variation of the apI plied potential permits the systematic variation of the 2.0 concentration ratios of the reactants within the diffusion layer. This, of course, may affect different reaction mechanisms to different extents, and this is the 1.6 origin of the diagnostic value of this technique. Although the EC case16 was simple enough to allow 1.2 . an analytical solution, this was not the most expedient approach to the present problem; consequently, the Napp R arking curves were generated by digital sim~1ation.l~ 0.8 . To introduce potential dependence into these calculations one assumes Nernstian behavior and the boundary condition a t the electrode surface becomes
. .
when t > 0 and x =: 0 and where E,,, is the applied potential. For a,l1three calculations the follow-up reactions, eq 2 and 8 , vere assumed to be pseudo-first order. In the case of disproportionation, it was assumed that the equilibrium, pq 7, was rapid and that there existed a very small steadystate concentration of species C. The rate law for this situation is
0.4
.
OP
I
I
I
I
I
-2
-1
0
1
1
2
3
log k t
Figure 2. Single-step potential-dependent working curve for the ECC, K = 0 reaction.
(12)
cated than these models. To treat the E C E and ECC sequences by a double-potential step program, it is necessary to assume a relationship between the final applied potential and E O 1 and E’z. For those pur-
To carry out calculations for the ECC mechanism, it is necessary to know the value of the equilibrium constant KECCsince the shape of this curve varies extensively with this parameter.’ For the present case it was assumed that the second electrode reaction, eq 3, took place a t a potential much less positive than that of eq 1. This approaches the K = 0 limiting case of Fe1dberg.I This assumption is consistent with previous findings,20but it must be borne in mind that the actual chemical cases are probably much more compli-
(13) J. J. Silber and H. J. Shine, J. Org. Chem., 36, 2923 (1971). (14) G. Manning, V. D. Parker, and R. N. Adams, J . Amer. Chem. SOC.,91, 4584 (1969). (15) V. D. Parker and L. Eberson, &id., 92, 7488 (1970). (16) L. Marcoux and T. J. P. O’Brien, J. Phys. Chem., 76, 1666 (1972). (17) J. H. Christie, 1.Electroanal. Chem., 13, 79 (1967). (18) W. M. Schwara and I. Shain, J. Phus. Chem., 69, 30 (1965). (19) S. W. Feldberg in “Electroanalytical Chemistry, A Series of Advances,” Vol. 3, A . J. Bard, Ed., Marcel Dokker, New York, N. Y., 1969. (20) R. Dieta and B. E. Larcombe, J. Chem. Soe. B , 1369 (1970).
d @-~ CZ T
JC’KdisproCB’
____I
GA
The Journal of Physical Chemistry, VoL 7 6 , N o . 22, 1972
LYNNMARCOUX
3256
2 .o
1.6
1.2
b
p
0.8
0.4
0.0 -2
-1
2
1
0
3
log kt
Figure 3. Single-step potential-dependent working curve for the disproportionation mechanism. -3
I
-2
0
-1
1
log kY
0.7
Figure 5. Double-step potential-dependent working curve for the ECC reaction. 0.6
0.5
0.7
0.4
0.6
_Lr 'f 05
0.3
OA
0.2
_Ir 'f 0.1
0.3
0.0
az
- 0.1
01
-3
-2
0
-1
*
I
1
2
on -3
-2
-1
0
1
2
log k Y log
kr
Figure 4. Double-step potential-dependent working curve for the ECE reaction.
poses the final potential was assumed to be such that the reaction B + e z A The Journal of Physical Chemistry, Vol. 76, No. 3.2, 197.2
(13)
Figure 6. Double-step potential-dependent working curve for the disproportionation mechanism.
was diffusion eontrolled and that the reaction
D+e7-'fC could not take place.
:POTENTIAL-DEPE:NDENT CHBQNQAMPEROMETRY
IS
1.6
Nwp 1.4
1.2
l.0 -2
-3
2
1
0
-1
log k t
Figure 7. Single-step diffusion-controlled working curves for all three mechanisms. The abscissa has been shifted to facilitate comparison.
3257 These plots are the same format previously u ~ e d . ' ~ ~ ~ " J The working curves for the double-step experiments are shown in the same order in Figures 4, 5, and 6. These data are presented in the same manner as Schwarz and Shain.l8 The curves shown represent the ratio of the current for the reverse step t o that of the forward step as a function of rate constant and reversal time, r. The cases shown are appropriate to experiments in which the currents arc: measured a t a time corresponding to one-tenth of the time of the forward step, i.e., in the notation of Schwarz and. ShainIB ( t - T ) / T = 0.1. For example, for an experiment with a reversal time r = 100 msec, the fornard current would be measured 10 msec after the experiment was initiated and the reversal current at IfQ msec after initiation. For the purposes of comparison the results for the diffusion-controlled single-step method are shown in Figure 7, and Figure 8 shovws the results for the corresponding double-step expermarit also a t ( t - r ) / r = 0.1.
Discussion 0.7
0.6
0.5
0,4
.-!L
0.3
fif
0.2
0.1
01)
- 0.1 I
I
I
I
I
I
-3
-2
-1
0
1
2
log k P
Figure 8. Double-step diffusion-controlled working curves for all three mechanisms. The abscissa has been shifted to frtcilitate comparison.
Figures 1, 2 , and 3 represent the results for the singlestep experiment a t a variety of E,,, values for the ECE, ECC, and disproportionation cases, respectively.
The diagnostic approach is made clear by the accompanying figures. T o differentiate the disproportionation possibility from the ECE and ECC mechanisms, one need only carry out the appropriate experiment a t several different applied potentials. Both the einglestep and double-step methods distinguish between the disproportionation and ECE-EC@ pathways; however, the difference is more pronounced 111 the case of the reversal experiment. It is also clear frxn these figures that it is unlikely that one could distinguish the ECE from the ECC mechanism by this method. These latter two mechanisms are fortunately fairly easily distinguished from one another by the conventional diffusion-controlled chronoamperometrrc techniques shown in Figures 7 and 8. The two results we therefore com\$ere seplimentary. The computed values of Eapp lected arbitrarily, but they encompass the most likely experimental range since current magnitudes 11 o d d be quite small and consequently irreproducible in the = E" - 0.060. region below- Eagp Philosophically this technique is not unlike that of S a ~ e a n t 5 -in~ which the variation of the peak potential of single-sweep stationary electrodr voltammograms is observed as a function of scan rate. 'The predicted shifts vary on the order of 10-28 mV per decade of sweep rate. 'These shifts are reproducibly observable and diagnostically meaningful as Xaveant has convincingly demonstrated; however, it must be noted that the work cited was carried out on mercury electrodes and one could not anticipate data of this quality with solid electrodes. The present results should also be compared with the cyclic voltammetric method which has previously been suggested.15 The cyclic voltammetric method was more specifically directed at the region between the two electron transfers, z.e., The Journal
of
Physical Chemistry, Vol. 7 G , S o . !22? 1972
LYNNMARCOTJX
3258
Ea1t'E < Eo2. This method was presented in a qualitative fashion, and the solution equilibrium between the cation, dication, and parent molecule was ignored. I n actual fact, this method should be effective in the region E O 1 rtr 0.060; however, it suffers from the drawback that the best diagnostic region falls prior to the voltammetric peak on the steeply rising portion of the wave. This, of course, renders difficult the accurate and reproducible measurement of current. The cyclic voltammetric method is quite analogous to the previously proposed step-sweep techniquez1 which was developed for EC reactions. It must be emphasized that the difference between the present method and the others discussed herein is purely operational. The experimental variable in this case is more easily measured and also varies to a greater extent from one mechanism to another. 'The experimerkd restraints to the present method are not severe; nonetheless, one must be certain that the initial electron transfer reaction is rapid. This is normally true for organic molecules in nonaqueous solvents. Because She exact value of the applied potential is an essential quantity in this experiment, high quality potential control is assumed. Uncompensated -I___-
Table I : Chronocoulometric Data
for the Oxidation of Phenothiazine a t Various Applied Potentials -Ea,,, V, US. Ag/Ag+---
r,
aec
0,500~
0.020 0.030 0.040 0.050 0.060 0.070 0.080 0,090 0.100 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0.180 0.200 0.100 0.150 0 "200 0 250 0.300 0 350 0 400 0 450 0.500
6.56 6.64 6.70 6.65 6.55 6.65 6.78 6,65 6~76 6.70 6.55 6.72
I
I
I
Av a
(QT-''~)
6.70 6.75 6.68 6.75 6.64 6.60 6 76 6.65 6.60 0.68 6.55 6,67 6.60 6.60 6.65 8.66 jI 0.06
____
0.320
0.290
0.260
5.53 5.40 5.35 5.48 5.32 5.40 5.40 5.46 5.42 5.50 5.51 5.48 5.48 5.40 5.54 5.54 5.48 5.86 5.64 5.55 5.52 5.55 5.48 5.48 5.85 5.45 5.85 5.475 0.05
4.25 4.31 4.25 4.24 4.28 4.26 4.38 4.24 4.27 4.30 4.34 4.38 4.34 4.35 4.38 4.38 4.35 4.28 4.27 4.26 4.20 4.26 4.20 4.19 4.22 4.23 4.25 4.285 0.05
2.55 2.49 2.44 2.46 2.44 2.45 2.41 2.50 2.53 2.50 2.37 2.37 2.52 2.48 2.42 2.50 2.43 2.38 2.53 2.33 2.37 2.44 2.39 2.42 2.38 2.44 2.35 2.44 i 0.05
Region of diffusion control.
The Journal of Physical Chemistry, Val. 76,X o . 22, 10'73
resistancez2therefore cannot be tolerated, and this is a serious consideration in nonaqueous media, This complication must also be considered when utilizing the sweep method so it is not a unique disadvaniage. To ascertain the limits of certainty within which this technique could be applied the following approach was taken. The experimental limitations were first determined from potential-dependent chronocoulometric measurements of an uncomplicated system, m d then calculations were made to establish the effect of this uncertainty upon the calculated worliing curves. Table I shoms the value of the product @-'Iz obtained at a series of times and at various values of applied potential for a 1.85 mM solution of phenothiazine in acetonitrile which contained 0.148 M tetraethylammonium perchlorate as supporting electrolyte. The reversibility of this system has been previously e ~ t a b l i s h e d . ~ ~ - ~ ~ A PAR Model 170 electrochemistry system was used; t h e P t working electrode was 0.024 emZ,and an Ag/Ag+ (acetonitrile) reference electrode was employed. Based upon the average deviations shown in Table I, data obtained on the wave are no more subject t o scatter than those obtained in the region of diffusion control, A more important criterion might be how accurately these data compare with the known value of E" for this system. From cyclic voltammetry using the relationshipz6E,,, = Ep12 0.0285 one finds that E,,, = 0.28 V for this particular seference electrode. Since the system in question is reversible, the approximation E" Ei is valid. The relationship
+
may be easily obtained and applied to the data in Table I. For the applied potentials of 0.320, 0.290, and 0.260 V one obtains E" values of 0.281, 0.275, and 0.277 V, respectively. Using these data pessimistically and assuming that Eappis uncertain, A 5 mV, disproportionation working curves were obtained for E,,, values of E" - 0.025, E" - 0.030, E" - 0.035. The maximum total uncertainty in the log ktC axis was found to be 0.2 unit. This is the amount of uncertainty that one normally encounters with solid electrodes in the region of diffusion control. lo Since most experimental data are obtained from oscilloscope traces, the source of this uncertainty (21) W. M . Sohwarz and I. Shain, J . Phys. Chem., 70, 848 (1966). (22) E. R. Brown, T. G. McCord, and E). I).DeFord, Anal. Chem., 38, 1117 (1966). (23) J. P. Billon, Bull. Sac. Chim. Fr., 1784 (1961). (24) J. P. Billon, ibid., 1923 (1961). (25) J. P. Billon, G. Cauquis, J. Combrisson. and A . Li, ibid., 2062 (1960). (26) R. S.Nicholson and I. Shain, Anal. Chem., 36, 708 (1964).
WETTINGOF HIGH-AND LOW-ENERGY SOLIDSURFACES
is as likely to arise in the mode of data presentation as it is from electrochemical sources. Based upon these estimates it can be seen that the working curves for the ECE and ECC cases will be as far as experiment is concerned essentially invariant with potential. Furthermore it is clear that a 30-mV variation in potential will probably reflect, disproport8ionationbehavior and that a 6O-mV increment certainly will. A fact inore discomforting than possible experimental difficulties is that the usefulness of these calculations is ulltimately liniited by the validity of the model. In
3259 most cases anodic substitution reactions are probably much more complicated than they are herein portrayed. I n spite of the several complications mentioned above, potential-dependent chronoamperometry appears, thus far, to be the best experimental approach to the question of the role of disproportionation in anodic substitution reactions.
Acknowledgment. This work was partially supported by Research Corporation in the form of a Frederick Gardner Cottrell grant-in-aid.
emperature on Wetting of High- and Low-Energy Solid Surfaces by Elaine G. Shafrin* and W. A. Zisman Laboratory for Chemical Physics, Naval Research Laboratory, Washington, D . C. 80390 (Received May 30, l9'72) Publication costs assisted by the Naval Research Laboratory
Various investigators have extended to high-energy surfaces the concept of the critical surface tension of wetting ( y o )and its method of measurement at constant temperature, developed from earlier contact-angle investigations of low-energy surfaces. Recently, Rhee proposed and applied an alternate approach to obtaining a critical tension ( y e s )for a high-energy surface by increasing the temperature ( T ) to the critical value (Tea) at which a previously nonspreading liquid metal just spreads on a metal or ceramic surface. Using literature data on the effect of increasing T on the wetting of low-energy surfaces by organic liquids, we demonstrate the following: (a) Rhee's yesis equal to y o for the specific temperature Tea; (b) when interpreted and used correctly, the variable-temperature method is applicable to low- as well as high-energy surfaces; and (e) values of y o obtained by the constant- and the variable-temperature methods agree. Literature data have been processed to obtain ya values at various constant temperatures. A graphical summary of results for seven solid organic polymers revealed that a straight-line relation of small negative slope characterized the y o US. T data for these surfaces at least up to 125O, and the overall effect of T on ye for organic solids approximated that on the liquid surface tension of organic liquids. il proper basis now exists for more extended use of the variable-temperature method and for the correct interpretation of the results so obtained in terms of a which is measured at constant T; thus, two separate but complementary methods for determining yo are now available. The concepts of yo and To,and the recognition that y c is a linearly decreasing function of temperature provide a sound foundation for knowledge of wettability.
Irxtroductiion The concept of the critical surface tension of spreading (-yo) as an empirical parameter characterizing the wettability of a solid surface a t a constant temperature was developed by our laboratory originally from research on the equilibrium contact angle (0) of a wide variety of pure organic and inorganic liquids in contact with well-defined lo w-energy solid surfaces including organic polymers1s2and crystal^.^^^ The concept later proved equally applicable to the wettability of highenergy surfaces such as metals, metal oxides, sapphire, and various glasses when these had been modified, either deliberately or inadvertently, by the presence of adsorbed films of organic molecule^^^^-^ or of
I n view of the technological as well as theoretical significance of the wetting of unmodified high-energy surfaces, there has been increasing interest in deter(1) H. W. Fox and W. A. Zisman, J . Colloid Sci., 5 , 514 (1950). (2) W. A. Zisman, Advan. Chem. Ser., No. 43, 1 (1964). (3) H. W. Fox and W. A. Zisman, J. Colloid Sci., 7, 428 (1952) (4) E. G. Shafrin and W. A. Zisman, ibid., 7, 166 (1952). ( 5 ) H.W. Fox, E. F. Hare, and W. A. Zisman, J. Phys. Chem., 59, 1097 (1955). (6) W. A. Zisman, J . Paint Technol., 44, No. 564, 41 (1972). (7) E, G. Shafrin and W. A. Zisman, J. Amer. Ceram. ~ o c . 50, , 478 (1967). (8) M. K. Bernett and W. A. Zisman, J . Colloid Inter,face Sci., 2 9 , 413 (1969). (9) M. K . Bernett and 757. A. Zisman, ibid., 28, 243 (1968). The Journal of Physical Chemistry, Vol. '76, KO.$3, 1971
