J . Phys. Chem. 1988, 92, 5274-5282
5274
log
,c/y ~
10
5
I
,,, , 10
1
2
, , I l l 1
5
IO2
1
1
l
l
5
2
1
l
l
I
l
1v
rl/T ( C P l O ' K 1
Figure 2. Debye-Stokes-Einstein plot for the orientational relaxation time. dependence of T for DOS, we first plot T versus q / T , using the result obtained in the 20-129.5 "C temperature range, in the form of the modified Debye-Stokes-Einstein equation: T = a$/T TO (2)
+
where q/ is in centipoise. The plot gives a straight line with a correlation coefficient equal to 0.9917, corresponding to a standard The a and T,, values for the linear deviation equal to 4.3 X plot are 1.66 X lo-* s K/cP and 1.09 X s, respectively. We next incorporate the low-temperature (below 20 "C) result by fitting all T data of DOS to
(T - T O )
=A
+ C log ( $ / T )
(3)
using T~ = 1.09 X s obtained above. The best fit of T to eq -7.78. 3 is shown in Figure 2. It gives C = 1.047 and A Considering the excellent linear correlation between T and q/ T , one can conclude that the pair correlation factor g2/J2,given in eq 1, is independent of temperature over the temperature range of -12 to 129.5 "C. Although dynamic pair correlation is known to be mostly negligible so that the parameter J2 is known to be mostly close to 1,' the temperature-independence result for g2 does not suggest the presence of a mesomorphic transition in this system, because, as mentioned above, the presence of a mesomorphic transition will result in a change in the static pair correlation factor g2, resulting in a significant change in T. Furthermore, the factor a in eq 2 (or A in eq 3) is related to the volume of the reorienting unit. The smoothness in the Debye-Stokes-Einstein plot, as shown in Figure 2, indicates no volume change in the -1 2 to 129.5 "C temperature range. Thus, corroborating the finding of polarized scattering2 the depolarized Rayleigh scattering result clearly does not support the mesomorphic transition in the liquid phase in DOS or in the n-alkane system. Acknowledgment. We thank Professor E. W. Fischer for discussion. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial financial support of the research. Partial financial support by NSF (the polymer program, DMR-8606884) is also acknowledged. Registry No. DOS, 122-62-3.
Electrochemical Evaluation of Charge-Transport Rates in Polypyrrole Reginald M. Penner,+Leon S. Van Dyke, and Charles R. Martin* Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: January 14, 1988)
The theoretical and experimental aspects of a new current-pulse method for electrochemical investigations of charge-transport rates in thin redox active films on electrode surfaces are described. This method yields an apparent diffusion coefficient, Dapp,which is a quantitative measure of the rate of the charge-transport process in the film. This method is ideally suited for solving the myriad problems associated with electrochemicalanalyses of electronicallyconductive polymers (e.g., polypyrrole, polyaniline, etc.). When applied to such polymers, the Dappobtained is a quantitative measure of the rate of the insulator-to-conductor switching reaction. We have used this method to obtain values of Dappfor the polymer polypyrrole.
Introduction Electronically conductive polymers are a fascinating new class of materials with unique electronic, electrochemical, and optical pr0perties.I One of the most interesting aspects of these polymers is that they can be reversibly "switched" between electronically insulating and electronically conductive states. Numerous researchers in a variety of different fields of science are currently investigating this insulator/conductor transition.' In addition to being an interesting scientific phenomenon, this switching process plays an integral role in nearly all of the proposed chemical applications of electronically conductive polymer^.^-'^ Assuming that the polymer is insulating in the reduced form and conductive in the oxidized form, the insulator-to-conductor reaction could be expressed as -Py-
+ X-,
-
-Py+-X-p
+ e-
(1)
where -Py- and -Py+- symbolize reduced and oxidized monomer *To whom correspondence should be addressed. Present address: Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91 125.
0022-3654/88/2092-5274$01.50/0
units, respectively, and X- is a charge-compensating anion; Xis initially present in a contacting solution phase but, upon oxidation of the polymer, is incorporated into the polymer phase. (1) Handbook of Conducting Polymers; Skotheim, T. A,, Ed.; Marcel
Dekker: New York, 1986.
(2) Burgemayer, P.; Murray, R. W. J . A m . Chem. SOC.1982,104,6139. ( 3 ) Burgemayer, P.; Murray, R. W. J . Phys. Chem. 1984, 88, 2515. (4) Gamier, F.; Tourillon, G.; Gazard, M.; Dubois, J . C. J . Elecrroanal. Chem. Interfacial Electrochem. 1983, 148, 299. (5) Gazard, M . In Handbook of Conducting Polymers; Skotheim, T. A., Ed.; Marcel Dekker: New York, 1986; Vol. 1 , Chapter 19. (6) Kaufman, J. H.; Chung, T.-C.;Heeger, A. J.; Wudl, F. J . Electrochem. Soc. 1984, 131, 2092. (7) Mermilliod, N.; Tanguy, J.; Petiot, F. J . Electrochem. SOC.1986, 133, 1073. (8) Button, P.; Mastragostino, J.; Panero, S.;Scrosati, G. Electrochim. Acta 1986, 31, 783. (9) White, H. S.; Kittlesen, G. P.; Wrighton, M. S. J . Phys. Chem. 1985, 89, 5133. (10) Kittlesen, G. P.; White, H. S.; Wrighton, M. S. J . Am. Chem. SOC. 1984, 106,7389. (11) Thackeray, J. W.; White, H. S.; Wrighton, M . S. J . Phys. Chem. 1985,89, 5133. (12) Thackeray, J. W.; Wrighton, M. S. J . Phys. Chem. 1986, 90, 6674. ( 1 3 ) Chao, S.; Wrighton, M. S. J . Am. Chem. SOC.1987, 109, 2197.
0 1988 American Chemical Society
Charge-Transport Rates in Polypyrrole Equation 1 shows that the switching reaction involves a chargetransport process, in which oxidized monomer sites and chargecompensating counterions move through the polymer film. While the case is far from closed, the bulk of the currently available evidence suggests that the rate of this charge-transport process is controlled by ionic diffusion in the polymer phase.I4-l8 Because diffusional mass transport plays a roll in many electrochemical experiments, it should be possible to assess the rate of the insulator/conductor switching reaction by using an electrochemical method. For example, large-amplitude electrochemical methods have been used to assess the rates of charge transport in redox-type polymer films on electrode surface^.'^-^^ These experiments yield an apparent diffusion coefficient, Dapp,which is a quantitative measure of the charge-transport rate in the film. 19-24 Because large-amplitude electrochemical methods have proven useful for evaluations of charge-transport rates in redox-type polymers,1F24analogous experiments have recently been conducted on polypyrrole and other electronically conductive polymer^.^^-^^ While this may appear to be a logical extension of the redox polymer work, we maintain that it is difficult, if not impossible, to obtain meaningful Dappdata for conducting polymers using large-amplitude methods. The above statement is explicated in the Theory Section. We have recently developed a small-amplitude current-pulse method which is uniquely suited for solving the myriad problems (see below and ref 30) associated with electrochemical analyses of electronically conductive polymers. This method can be used to obtain reliable D,, values for these polymers. The theoretical and experimental aspects of this new current-pulse method are discussed. In addition, this paper provides what we believe are the first reliable electrochemically generated Dappvalues for the conductive polymer polypyrrole. This current-pulse experiment is performed at a conductive polymer-film-coated electrode and requires (1) values for the capacitance of the double layer at the electrode/film interface and (2) that the relationship between the open-circuit potential (E,) and the extent of oxidation of the polymer (i.e., eq 1) is quantitatively defined. We have used a current-step method to obtain the capacitance data and a coulometric titration procedure to define the relationship between E, and the extent of oxidation of polypyrrole. These data are also reported here. In the most general sense, this current-pulse method was specifically designed to obtain Dappvalues associated with charge (14) Kanazawa, K. K.; Diaz, A. F.; Geiss, R. F.; Gill, W. D.; Kwak, J. F.; Logan, J. A,; Rabolt, J. F.; Street, G. B. J . Chem. SOC.,Chem. Commun. 1979, 854. (15) Bull, R. A,; Fan, F.-R.; Bard, A. J. J . Electrochem. SOC.1982,129, 1009. (16) Kaufman, J. H.; Kanazawa, K. K.; Street, G. B. Phys. Rev. Lett. 1984, 53, 2461. (17) Miller, L. L.; Zinger, B.; Zhou, X.-Q. J . Am. Chem. SOC.1987, 109, 2267. (18) Buttry, D. A. Presented at the 193rd National Meeting of the American Chemical Society, Denver, CO, April 1987. (19) Peerce, P. J.; Bard, A. J. J . Electroanal. Chem. Interfacial Electrochem. 1980, 114, 89. (20) Martin, C. R.; Rubenstein, I.; Bard, A. J. J. Am. Chem. SOC.,1982, 104, 4817. (21) Martin, C. R.; Dollard, K. A. J . Electroanal. Chem. Interfacial Electrochem. 1983, 159, 127. (22) Oyama, N.; Anson, F. C. J . Electrochem. SOC.1980, 127, 247. (23) Shigehara, K.; Oyama, N.; Anson, F. C. J . Am. Chem. SOC.1981, 103, 2552. (24) Oyama, N.; Shimomura, T.; Shigehara, K.; Anson, F. C. J . Electroanal. Chem. Interfacial Electrochim. 1980, 112, 27 1. (25) Genies, E. M.; Bidan, G.; Diaz, A. F. J . Electroanal. Chem. Interfacial Electrochem. 1983, 149, 101. (26) Marque, P.; Roncali, J.; Gamier, F. J . Electroanal. Chem. Interfacial Electrochem. 1987, 218, 107. (27) Nagasubramanian, G.; Di Stefano, S.; Moacanin, J. J. Phys. Chem. 1986, 90, 4447. (28) Chiba, C . ; Ohsaka, T.; Oyama, N. J . Electroanal. Chem. Interfacial Electrochem. 1987, 217, 239. (29) Osaka, T.; Naoi, K.; Ogana, S.; Nakamura, S . J . Electrochem. SOC. 1987, 134, 2096. (30) Feldburg, S. W. J . A m . Chem. SOC.1984, 106, 4671.
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5275 transport in thin redox active films which have been coated onto electrode surfaces. This method should be applicable to nearly any thin-film-modified electrode system. Furthermore, this current-pulse method has a number of advantages over the conventional electrochemical methods for studying charge transport in these s y s t e m ~ . l ~For - ~ ~example, this method can provide transport information which cannot be obtained by the more conventional electrochemical methods. This and other advantages of this current-pulse method are also discussed.
Theory Section Why Large-Amplitude Methods Should Not Be Used To Obtain Dapp)s for Electronically Conductive Polymers. Our objections to large-amplitude methods can be illustrated by considering a chronoamperometric experiment at a conducting polymer-film-coated electrode.31 The first problem which must be addressed concerns the area of the electrode. Analysis of chronoamperometric data via the Cottrell equation requires semiinfinite linear diffusion to a planar electrode of known area.32 If the experiment is initiated in the potential region where the polymer film is conductive, one has, in effect, a large-area porous metal e l e c t r ~ d e . Thus, ~ ~ , ~ two ~ questions arise: first, is diffusion in this porous electrode linear, and second, what is the available electrode area?33 These questions are complicated by the fact that, during the course of the experiment, the film becomes nonconductive; clearly, the available electrode area changes,33but how and when? One might suggest that the above criticism could be circumvented by initiating the potential step in a potential region where the polymer is reduced. In this case, at time = 0, the substrate conductor defines the electrode area. Therefore, initially, the area is known and diffusion is linear. However, at some time during the course of the experiment, the film becomes conductive and the unresolved questions, noted above, return. The second problem concerns the capacitive current ( i c ) . In the potential region where the polymer is an electronic insulator, the film-coated electrode shows capacitive currents which are similar in magnitude to i:s at the corresponding uncoated electrode. As will be discussed in detail below, these currents are associated with charging the double layer at the electrode/reduced-film interface. In contrast, in the potential region where the polymer is conductive, a much larger “capacitive-like” current is observed. This larger i, has been ascribed to charging the double layer associated with the conductive polymer film i t ~ e l f . ” ~ ~ ~ ~ ~ ~ The term “capacitive-like” was used above because, although this current has the qualitative appearance of an i,, it is clear that this current results from oxidation (or reduction) of the polymer just as the “faradaic” portion of the current ( i f ) results from oxidation (or reduction) of the p ~ l y m e r . ~ The ~ , ~ following ~ fundamental question arises: because both the “faradaic” and ”capacitive” currents result from the same chemical process, should the apparent i, be subtracted from the total current to obtain if? Furthermore, because the capacitances of the bare and coated electrodes are very different, background correction would be very pr~blematic.~~ In the conventional chronoamperometric experiment, it is often possible to circumvent the i, problem by waiting for i, to decay.32 However, because the time course of delivery of the large, capacitive-like current at the conductive polymer-coated electrode is unknown, a correction based on temporal discrimination also (3 1) As we shall, the discussion presented applies to chronocoulometry and other large-amplitude methods also. (32) Bard, A. J.; Faulher, L. R. Electrochemical Methods: Theory and Applications; Wiley: New York, 1980; p 143. (33) The question of available electrode area arises because in the oxidized form both the substrate Pt surface and some fraction of the internal surface area of the polymer are available for polymer electrolysis. In contrast, in the reduced form only the substrate Pt electrode is available for polymer electrolysis. (34) Penner, R. M.; Martin, C. R. J . Electrochem. SOC.1986, 133, 310. ( 3 5 ) Tanguy, J.; Mermilliod, N.; Hoclet, M. J . Electrochem. SOC.1987, 134, 795. (36) Tanguy, J.; Mermilliod, N.; Hoclet, M. Synth. Met. 1987, 18, 7.
5276 The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
seems doubtful. Finally, one might suggest that this i, problem could be circumvented by conducting a chronocoulometric experiment, in that double-layer charging is typically observed as an intercept in the Q vs t112 plot.37 Note, however, that this is just another form of temporal discrimination. Again, because the time course of delivery of the capactivie-like charge is unknown, this form of temporal discrimination is also problematic. The third problem associated with the use of large-amplitude methods concerns the drastic changes in the chemical, electronic, and morphological properties that occur when the film is converted from one state to the other. The reduced form of polypyrrole is a neutral, insulating, hydrophobic organic polymer. In contrast, the oxidized form is a conductive polyelectrolyte, which contains a high cationic charge density. These are very different materials, and it would be surprising if they showed equivalent ion-transport rates. Because the large-amplitude method converts the reduced polymer to the oxidized form (or vice versa), this experiment is, in essence, conducted on one material at short times and a very different material at long times. Finally, an examination of the chronocoulometric data for polypyrrole presented in the literature clearly shows that these data do not conform to simple theory.25 Note, for example, that Diaz et al. show Q vs t112plots with negative intercepts; furthermore, the slopes of these plots increased as the positive limit of the potential step increased. We have obtained identical data in our l a b o r a t ~ r y . Note ~ ~ further that the very elegant refinements of Cottrell theory by Lange and D ~ b l h o f e r(which ~ ~ take into account migration effects) will not help here since migration is not the problem. Furthermore, Lange and Doblhofer's theory assumes that the redox active ions are the only mobile charge carriers. We show, below, that reduced polypyrrole contains large quantities of supporting electrolyte. Thus, this theory is not applicable to polypyrrole. The Advantages of the Small-Amplitude Current-Pulse Method. The key features of the method developed here are (1) the experiment is initiated at a potential where the polymer is in its reduced, nonconductive form (-0.4 V vs SCE) and (2) the total potential perturbation during the experiment is so small (usually less than 20 mV) that the polymer remains in the reduced form throughout the experiment. These features solve all of the above problems. First, because the polymer is in the reduced form, the electrode area is just the substrate Pt area and, because this Pt electrode is a disk, diffusion must be linear. Second, because the polymer is never converted to a conductor, the large, unknown "capacitive-like'' current associated with the conductive form is not observed. The only capacitive current is that associated with charging the double layer at the Pt/film interface, and this can be easily measured and corrected (vide infra). Finally, because this is a small-amplitude method, the problem of converting one material into a second, very different, material during the course of the experiment is clearly obviated. However, this feature also has a drawback-the Dappobtained is unique to the reduced form and information about charge-transport rates in the oxidized form of the polymer is not accessible with this method. Fundamental Assumptions. This method requires three fundamental assumptions. The first might be termed the "effective medium theory assumption". Because polypyrrole is microporO U S , ' ~ it , ~ is ~ a biphasic system (i.e., it is composed of solventswollen polymer and solvent-filled pores). We assume, however, that as an ion diffuses through the polymer film, it makes so many transitions between these two microphases that its motion can be described by an apparent diffusion coefficient, Dapp.This Dapp is the diffusion coefficient for the "effective medium" obtained by intimately mixing the two component phases. Recent work by Chien et al. clearly shows that this effective medium theory (37) Bard, A. J.; Faulkner, L. F. Electrochemical Methods: Theory and Applications; Wiley: New York, 1980; p 200. (38) Penner, R. M., Texas A&M University, Dec, 1987, unpublished
__
rewl 1 . -.t.-.
(39) Lange, R.; Doblhofer, K. J . Electroanal. Chem. Interfacial Electrochem. 1987, 237, 13.
Penner et al. TABLE I: Double-Layer Capacitance for Pt/Polypyrrole Various Values of Potential E , V vs SCE C, p F cm-2 E , V vs SCE C, -0.585 22.2 -0.418 -0.530 25.0 -0.388 -0.490 26.0 -0.378 -0.454 30.1 -0.363 -0.443 34.9 -0.358
Interface at pF cm112
35.4 39.0 42.8 47.4 54.4
approach is valid for p~lypyrrole.~' As noted above, the polymer film is an electronic insulator throughout the course of this current-pulse experiment. This is experimentally verified by the capacitance data shown in Table I. The question then becomes the following: if the polymer is not electronically conductive, how is charge transported across the film? We believe that by forcing the polymer to remain nonconductive, we convert the electronically conductive polymer into a redox In analogy to the redox polymer situation, we assume that charge (Le., oxidized monomer equivalents) is transported via electron self-exchange with reduced polymer site^.'^-^^ Thus, the theories developed for diffusional electron hopping in redox polymers apply here.19a41 Finally, we assume that the rate of this diffusional charge transport in polypyrrole is controlled by counterion motion rather than by the actual self-exchange event. This assumption has been experimentally demonstrated for other redox polymers43and, as noted above, is supported by the available data on polypyrro1e.'4-18x44 Note, however, that even if this assumption proves to be incorrect, the Dappvalues reported here are still valid quantitative measures of the charge-transport rate. Background to Current-Pulse Methods. Consider a Pt working electrode which is coated with a thin, electronically conductive polymer film and immersed (along with suitable reference and counter electrodes) into a supporting electrolyte solution. At time ( t ) = 0 a galvanostat is used to inject a small-amplitude anodic into this current pulse of duration i-and amplitude i, (A electrochemical cell. At the termination of this current pulse, the working electrode is returned to open circuit and its potential, E,, is monitored as a function of time. The anodic current pulse drives the reaction shown in eq 1, thus increasing the concentration of Py+ sites at the Pt/film interface. (Note, however, that the magnitude of the pulse is so small that at no time is any portion of the film converted to an electronic conductor.) The Nernst equation says that this increase in [Py'] will cause a corresponding increase in E,. After termination of the current pulse, these Py+ sites will diffuse (i.e., self-exchange) into the bulk of the film. E, will, therefore, decrease with time; this transient will persist until the concentration of Py+ is uniform throughout the film. Because the rate of equilibration is controlled by diffusional transport of the Py+ sites, Dappcan be obtained from the E , vs t transient. A current-pulse method was employed by Worrell et al. to obtain diffusion coefficients in intercalation corn pound^.^^-^* (40) Schlenoff, J. B.; Chien, J. C. W. J . A m . Chem. SOC.1987, 109, 6269. (41) Laviron, E. J. Electroanal. Chem. Interfacial Electrochem. 1980, 112, 1.
(42) Chidsey, C. E. D.; Murray, R. W. Science (Washington, D.C.) 1986, 231, 25. (43) Jernigan, J . C.; Murray, R. W . J . A m . Chem. SOC.1987, 109, 1738. (44) Diaz, A. F.; Castillo, J. I.; Logan, J. A,; Lee, W.-Y. J . Electroanal. Chem. Interfacial Electrochem. 1981, 129, 115. (45) Basu, S.; Worrell, W. L. In Fast Ion Transport in Solids; Vashishta, P., Mundy, J. N., Shenoy, J. K . , Eds.; Elsevier: Amsterdam, 1979. (46) Basu, S . ; Worrell, W. L. In Proceedings of the Symposium on Electrode Materials and Process f o r Energy Canversion and Storage; McIntyre, J. D. E., Srinivasan, S., Will, F. G., Eds.; Electrochemical Society: Princeton, 1977; p 861. (47) Nagelburg, A. S . ; Worrell, W. L. In Proceedings of the Symposium on Electrode Materials and Process for Energy Conversion and Storage; McIntyre, J. D. E., Srinivasan, S . , Will, F. G., Eds.; Electrochemical Society, Princeton, 1977; p 861. (48) Nagelburg, A. S . ; Worrell, W. L. The Electrochemical Society Extended Abstracts; Electrochemical Society: Philadelphia, PA, 1977; Vol. 77-1, p 948.
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5271
Charge-Transport Rates in Polypyrrole
initial concentration-distance profile for the diffusing species (given the symbol cdiff(x’,T))must be calculated (eq 3); Cdiff(x’,T)is the diffusion layer profile extant after termination of the current pulse, at t = T . 5 4 This initial distribution is then plugged into the expression for the Cdiff(x=O)vs t transient for the finite diffusion case (eq 4); this equation is used to calculate the simulated transients. The initial profile, cdiff(x’,T),is calculated assuming a continuous planar source of diffusing species and semiinfinite diff~sion:~~,~~
25 20 15
10 5 -
0
5
10
15
20
t-112 (sec-1/2)
Figure 1. Potential-time transient from current-pulse experiment at polypyrrole-film-coated electrode; data analyzed as per eq 2. AE = measured E - initial E , initial E = -0.4 V, and film thickness = 0.5 Fm. Current-pulse amplitudes were (A) 400, (B) 300, (C) 200, and (D) 100 fiA cm-2.
These authors were able to make a number of simplifying assumptions which yielded the following simple expression for the E , vs t transient mi,T
Eo, =
Because eq 3 assumes semiinfinite diffusion during the pulse, the maximum pulse duration is given by T = (d2/2Dapp),where d is the film thickness.56 Equation 3 was solved by using conventional numerical method^.^' The concentration of diffusing species (for the finite diffusion case) at any distance ( x ) from the electrode surface, for any time ( t ) after termination of the current pulse, and for any initial distribution of diffusing species (cdiff(x’,T))is given bys8
F(irDappt)l12
where t is time (after termination of the current pulse) and m is an experimentally obtained c o n ~ t a n t Equation . ~ ~ ~ ~ 2 predicts that is linear and that Dappcan be obtained from a plot of E, vs the Figure 1 shows that current-pulse data obtained for thin polypyrrole films do not follow the simple theory (eq 2) of Worrell et al. An analysis of these data49indicates that this simple theory fails because it assumes (1) semiinfinite diffusion, (2) an infinitesimally thin initial diffusion layer, after termination of the current pulse, and (3) that a negligible quantity of charge is introduced during the current p ~ l s e . ~While ~ - ~it~is in principle possible to adjust the experimental conditions such that this theory is applicable, this would entail using thicker films, shorter pulse durations, and/or lower pulse amplitudes. Because thicker polypyrrole films become irreversibly o ~ i d i z e d , ~submicron * ~ ~ * ~films ~ must be employed. Furthermore, the current-pulse duration and amplitude are limited by the resolution of the voltage measuring system; values lower than those used in Figure 1 would ultimately yield immeasurably small voltage transients. A Rigorous Theoretical Analysis. Clearly, a more rigorous. theoretical analysis is needed if a current-pulse method is to be applied to electronically conductive polymers. Equations applicable to a finite diffusion situation, starting from a diffusion layer of finite thickness, can be obtained from the heat-transfer l i t e r a t ~ r e . ~ ~ These equations (see below) form the basis of this new theoretical analysis. Because this analysis is mathematically more complex, a simple relationship between E , and time (e.g., eq 2) does not exist. Dappvalues are obtained by matching experimental and simulated E , vs t transients. As we shall see, DaqPis the only adjustable parameter. This new theoretical analysis IS compatible with virtually any combination of experimental current-pulse parameters and film thickness values. Furthermore, this analysis should be applicable to any type of redox active film. The heart of this theoretical analysis is the generation of simulated Cdiff(x‘0) vs t transients, where Cdiff(x=O)is the concentration of the diffusing species (Le., [Py’]) at the Pt/film interface.53 Two discrete calculations are involved. First, the (49). Penner, R. M., Martin, C. R., Texas A&M University, Oct 1987, unpublished results, available upon request. (50) Diaz, A. F.; Castillo, J. I. J . Chem. Soc., Chem. Commun. 1980, 397. ( 5 1 ) Osaka, T.; Naoi, K.; Hirabayashi, T.; Nakamura, S . Bull. Chem. SOC. Jpn. 1986, 59, 2717. (52) Carslaw, J. S.; Jaeger, J. C. Conduction of Heat in Solids; Oxford University: London, 1959.
(4)
Cdiff(x’0) at any time is obtained by solving eq 4 for x = 0; numerical methods were used.59 Equations 3 and 4 contain a total of four variables, i,, T , d , and Dapp Because the pulse parameters are known and the film thickness can be measured with a profilometer,20Dappis the only freely adjustable parameter. As noted above, Dappvalues were obtained by matching experimental and simulated E, vs t transients. Because eq 4 yields simulated Cdiff(x=O)vs t (not E , vs t ) transients, some means of translating from Cdiff(x=O)to E , is needed. A coulometric titration procedure was used to accomplish this translation (see Experimental Section). Experimental Section Materials and Equipment. Tetraethylammonium tetrafluorohrate (99%, Aldrich) was recrystallized from methanol and dried in vacuo at 100 ‘C for ca. 24 h prior to use. Pyrrole (99%, (53) The parameter x is the distance from the electrode/film interface. Thus, x extends from x = 0 to x = d where d is the film thickness. (54) The symbol x’ is used to express distance from the electrcde/film interface for the initial diffusion layer profile. See, for example, ref 56. (55) Carslaw, J. S.; Jaeger, J. C. Conduction of Heat in Solids; Oxford University: London, 1959; p 263. (56) This is not, however, an overly restrictive constraint. For example, if D,,, and film thickness are taken to be 1 X cm2 s-I and 0.5 fim, respectively, the maximum allowable pulse duration is ca. 100 ms. This restriction could be eliminated by using the appropriate finite diffusion equation for the initial distribution. This increase in complexity was not warranted for the experiments performed here. (57) Cdiff(x’,T)values were calculated at each of 200 distance lamina (x’ Gx’where 6x‘= d/200); the erf integral was calculated numerically by the trapezoid rule. See for example: Smith, W. A. Elementary Numerical Methods; Prentice-Hall: Englewood Cliffs, NJ, 1986; p 312. (58) Carslaw, J. S.; Jaeger, J. C. Conduction of Hear in Solids; Oxford University: London, 1959; p 101. (59) Cdif(x=o) was calculated for each of 200 time increments, r + dt where dt = t,,/200. At each time increment, the summation included in eq 4 was evaluated to 100 terms. The integration included in this summation was evaluated for each term by the trapezoid rule and 200 distance increments, x + dx, where dx = d/200. The function of the first integration in eq 4 is to determine the final, equilibrium concentration of diffusing species. Since this concentration is simply equal to ip7d/nFA, the indicated integration was not required.
+
5218 The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
I
v
0.4
0.6
Polymerieatlon charge ( C cm-2)
Figure 2. Plot of film thickness vs charge consumed during polymerization for polypyrrole films.
Aldrich) was distilled under N 2 immediately prior to use. Acetonitrile (UV grade, Burdick & Jackson) was used as received. Pt foil (0.254 mm thick, Alfa) and Kel-F rod (diameter = 1.27 cm, Afton Plastics) were used to construct the Pt disk working electrodes. All electrochemical measurements were accomplished using an EG&G PAR Model 173 potentiostat/galvanostat in conjunction with a PAR 175 programmer. Transients were recorded with a Nicolet 2090 digital oscilloscope. Cyclic voltammograms were recorded on a Houston Instruments Model 2000 X-Y recorder. Simulated data were c a l c ~ l a t e d ~by~ -means ~ ~ of a Compaq Portable I1 computer. Solution conductivity measurements were accomplished with a Yellow Springs Instruments Model 31 ac conductivity bridge and Model 3402 cell (cell constant = 0.1 ohm cm-l). Electrodes and Electrochemical Cells. Working electrodes were prepared as follows: Pt disks (diameter = 3.3 mm) were heatsealed onto the surface of Kel-F cylinders by melting the Kel-F around the disk with a heat gun and the physically pressing the Pt into the heat-softened surface. Electrical contact was made to the back of the Pt disk with silver epoxy (Epo-Tek 410E, Epoxy Technology). The electrodes were then polished as described previously.21 Tin oxide coated glass electrodes (area = 15 cm2) were used to prepare large-area polypyrrole films. These electrodes were cleaned in concentrated H2S04 and washed with water and acetonitrile prior to use. Conventional one-compartment glass cells were employed for all electrochemical measurements. A large-area, Pt gauze counter electrode (25 X 25 mm, AESAR) and a conventional saturated calomel reference electrode (SCE) were used. Potentials are reported vs SCE. All solutions were prepared with acetonitrile as the solvent and were purged with purified N2 prior to use. Polypyrrole Film Deposition. Polymerization solutions were 0.5 M in pyrrole and 0.2 M in Et4NBF4. Pyrrole was polymerized (and deposited) galvanostatically; a current density of 1.0 mA was employed. Reproducible steady-state potentials of 0.84 V f 0.01 V were observed during film deposition at this current density. After deposition, the polypyrrole-film-coated electrode was transferred to monomer-free, 0.2 M Et4NBF4. All subsequent electrochemical measurements were performed in this electrolyte. A Tencor Alpha Step profilometer was used to construct a calibration curve of film thickness vs charge consumed during the polymerization process. As shown in Figure 2, film thickness is linearly related to polymerization charge. While Diaz et al. noted a similar relationship, the slope of their line (4.16 fim cm2 C-l) was substantially greater than the slope in Figure 2 (2.64 fim cm2 C ’ ) ,even though these films were synthesized under identical condition^.^^ Film thicknesses for these studies were calculated from the known polymerization charge and the slope of the least-squares fit (solid line) to the data in Figure 2. Determination of the Quantity of Electrolyte in Reduced Polypyrrole Film. The following conductometric method was used: 0.5-fim-thick polypyrrole films were synthesized (as described above) on 1 5-cm2 Sn02-coated glass electrodes. The freshly
Penner et al. deposited films were transferred to a 0.2 M Et4NBF4solution and quantitatively reduced at -0.8 V . The reduced films were then either rinsed (see below) and exposed to pure acetonitrile or exposed directly to pure acetonitrile. The films were exposed for 20 h. During this time the electrolyte present in the film was leached into the CH3CN. The quantity of electrolyte leached was determined by measuring the conductivity of the leaching solution. The film electrolyte concentration was calculated assuming a film volume of 7.5 x 1 0 - ~cm3. Two different rinsing procedures, “dip rinsing” and “long rinsing”, were employed. The diprinsed films were removed from the 0.2 M Et4NBF4solution, quickly dipped into pure acetonitrile, and then exposed to the leaching solution. The long-rinsed films were removed from the electrolyte solution, stirred in pure acetonitrile for 10 s, and then exposed to the leaching solution. Determination of the Relationship between E , and [Py’]. As noted in the Theory Section, this relationship allows the simulated Cw+(x=O) vs t transients to be translated into E , vs t transients. Because the current-pulse experiment used to evaluate D,, causes the electrode potential to change from -0.4 V to at very most -0.35 V, the relationship between E, and [Py’] needs to be defined only over this narrow potential region. While the Nernst equation should, in principle, define this relationship, these films are non-Nernstian (see Figure 5 ) . Therefore, the relationship between E , and [Py’] was determined empirically by a coulometric titration procedure.6‘t62 The coulometric titration was accomplished as follows: A freshly prepared polypyrrole film was first quantitatively reduced at -1.0 V. Increments of charge, Qi, were then injected into the reduced film. Equilibrium open-circuit potentials were recorded ) after (Ew,i,2) each Qi was injected. The Qi’s before ( E x , i , l and were injected by applying anodic current pulses (500 nA X 1 s). By summing up the individual Qi’s, the above experiment delineated the relationship between total charge injected and E,. However, the relationship between [Py’] and E , cannot be obtained from these data alone. The following equation holds for each Qi: Qi
=
Qf,i
+ Qd,i
(5)
where Qf,iis the portion of Qi which goes to the faradaic process (Le., to the creation of Py+ sites) and Qd,iis that portion which is used to charge the double layer at the Pt/film interface. Since we are interested in [Py’], the faradaic component, Qf,,must be extracted from each Qi. This was accomplished by obtaining the appropriate Qd,ivalues (eq 5). The following method was used. As noted above, each Qi injected caused the potential to increase from to The double-layer charging component of Qj over this potential window can be obtained via Qd,i
= Cd,i(Eoc,i,2- Eoc,i,1)
(6)
where cd,jis the double-layer capacitance of the Pt/film interface over this potential window. The Qd,j values obtained from eq 6 were used in conjunction with eq 5 to calculate the faradaic charge values Qf,i. Faraday’s law was used to convert the cumulative Qzi values into moles of Py’, and these data were divided by the film volume to give [Py’] at each value of E,,i,2. Equation 6 requires that the values of Cd,iover each potential window E,,i,Z to E,,i,, be known. A current-step experiment was d values.63 At very short times ( t < 100 used to obtain these c fils) after the application of a current step, the response of the electrochemical cell approximates that of an RC circuit and the working electrode potential is given by64 E = &i
+ ipt/Cd
(7)
(60) Kaufman, J. H.; Kaufer, J. W.; Heeger, A. J.; Kaner, R.; MacDiarmid, A. G. Phys. Rev. B: Condens. Matter 1982, 26, 2327. (61) Kaufman, J. H.; Chung, T.-C.;Heeger, A. J. Solid State Commun. 1983, 47, 585. (62) Kaufman, J. H.; Chung, T.-C.;Heeger, A. J. J . Elecrrochem. Sac. 1984, 131, 2847. (63) Will, F. G . J . Electrochem. S o t . 1985, 132, 2093.
The Journal of Physical Chemistry, Vol. 92, No, 18, 1988 5279
Charge-Transport Rates in Polypyrrole
v
1
.d
4
T
0 0
20
40
60
80
100
200pA
120
I
Time ( r s e c )
Figure 3. Typical potential-time transients from current-stepexperiment used to obtain the capacitance of the Pt/polypyrrole interface; data analyzed as per eq 7. Initial E = -0.375 V and film thickness = 0.27 pm. Current steps were (from top),l.l7 mA cm-*, 875 pA cm-2, 585 pA
and 290 p A
I
oio
0.4
- 0.4f
I - 0.8 E, V
where i, is the amplitude of the step and R , is the total series resistance of the circuit. According to eq 7, a plot of E vs t over this short time interval is h e a r and gives c d from the slope. Thus, the general procedure for obtaining the requisite (eq 6) cd values was to equilibrate the film-coated electrode at the desired E, apply a current step, obtain the E vs t data for times less than 100 ps, and plot E vs t . In practice, to improve accuracy, we applied four current steps, of different i,, at each potential so that d values at each potential could be obtained. Typical average c plots of E vs t for the four current steps are shown in Figure 3. d data are shown in Table I. These data were used The relevant c in conjunction with eq 6 to obtain the requisite f&values. Determination of Dapp Experimental E, us Time Transients. Freshly synthesized polypyrrole film was quantitatively reduced at -0.8 V vs SCE. The reduced film was then potentiostated at an initial potential of -0.4 V. The working electrode was switched to open circuit and a 50-ms anodic current pulse of the desired amplitude (100-400 pA cm-*) was applied. The ensuing E , vs t transient was recorded with the Nicolet oscilloscope. As was the case in the coulometric titration experiment (above), only a fraction of the total charge injection here goes toward creation of Py+ sites; eq 5 and 6 were used to extract this fraction from d values (eq 6 ) were taken the total charge injected. Again, the c or extrapolated from the data in Table I. Simulated E , us Time Transients. Programs for generating simulated Cpy+(x=O)vs t transients (eq 3 and 4) were written in PASCAL (Turbo Pascal, Borland) and executed on the Compaq Portable I1 computer. These curves were converted to simulated E , vs t transients. Simulated and experimental E , vs t transients were plotted using LOTUS 1-2-3 (Lotus Development Corp.) graphics. Dappvalues were obtained by manually matching6’ the experimental and simulated curves.
Results and Discussion Cyclic Voltammetry of Polypyrrole. Prior to performing other electrochemical measurements, we routinely used cyclic voltammetry to assess the quality of freshly synthesized films. A typical voltammogram for a 0.27-pm polypyrrole film in 0.2 M Et4NBF,, MeCN is shown in Figure 4. Cyclic voltammograms for films up to ca. 1.O pm in thickness were qualitatively similar. Electrolyte Content of Reduced Polypyrrole Film. Electrochemical experiments are usually conducted on solutions containing high concentrations of inert supporting electrolyte. This electrolyte lowers the ohmic resistance of the solvent, eliminates migration problems, and allows for the establishment of a compact and (64) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Theory and Applications; Wiley: New York, 1980; Chapter 1. ( 6 5 ) The reproducibility in the experimental transitions was such that errors introduced by manual (as opposed to nonlinear regression) matching of the transients was negligibly small.
VI.
SCE
Figure 4. Typical cyclic voltammogram for 0.27-pm-thick polypyrrole film. Scan rate = 10 mV s-’. Solution was 0.2 M Et4NBF4in aceto-
nitrile. TABLE II: Concentrations of EtdNBF, in Reduced Polypyrrole Films”
rinse procedure unrinsed
dip-rinsed* long-rinsed*
concn of Et4NBF4 in leaching solution, M 1.68 X IO4 f 8.9 X 4.06 X f 3.8 X 10” 2.15 X lo-’ f 6.0 X IO-’
concn of Et4NBF4in film, M 22.2 f 13.1
5.40 f 0.50 2.86
* 0.08
“ Films were 0.5 pm thick and were equilibrated with 0.2 M Et4BF4 in CH$N.
bSee Text.
well-defined electrical double layer. In the Theory and Experimental Sections of this paper we have assumed that such a double layer exists at the interface between the substrate Pt electrode and the reduced polypyrrole film. This can only be possible if supporting electrolyte is present in the reduced film. The electrolyte content of reduced polypyrrole film was estimated by equilibrating the film with 0.2 M Et4NBF4and then leaching the incorporated electrolyte into acetonitrile. While this sounds easy, there is a problem: how is electrolyte incorporated within the film distinguished from electrolyte present in solution clinging to the surface of the film? Because of this problem, we investigated several rinsing procedures. The data obtained are shown in Table 11. When the films were not rinsed, very high and variable film electrolyte contents were obtained (Table 11). The magnitude and variance of these data undoubtedly reflect contributions from variable amounts of electrolyte solution clinging to the polypyrrole film. Diprinsed films showed lower and more precise salt contents. Films which had been rinsed by stirring in acetonitrile showed even lower electrolyte contents. It seems likely that, in this case, some of the electrolyte which was initially present in the film was leached out during the rinsing step. The data in Table I1 indicate that electrolyte is present in the reduced film and that the concentration is quite high. Because of the uncertainty introduced by the rinsing procedure, we cannot give an accurate value for the concentration of electrolyte in the reduced film; however, the data suggest a concentration somewhere around 3 M. Miller et al. have recently reported similar values for other electrolytes in reduced polypyrrole.66 The surprisingly high concentrations reported in Table I1 indicate that the organic salt Et4NBF4 is not merely included in pores in the film but actually dissolves into the polymer phase. Thus, polypyrrole is acting like a solvent polymer membrane.67 ( 6 6 ) Zho, Q.-Z.; Kolaskie, C . J.; Miller, L. L. J . Electroanal. Chem. Interfacial Electrochem. 1987, 223, 283.
5280
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 -0.3 _
I
_
Penner et al.
~
h
% vi
, 6
-0.4
-
B
v 0
w
/‘D
I
-4.70
-5.10
-4.30
(IPY+]) log (mols cm-3) Figure 5. Typical Nernst plot for polypyrrole-film-coatedelectrode; obtained from coulometric titration experiment. Film thickness = 0.27 bm. See text.
5 0.0
log
Because the supporting electrolyte concentration in the reduced polymer film is high, a compact and well-defined double layer can exist at the Pt/film interface. We will report the value of the capacitance of this double layer in the following section. Finally, the high film salt contents will minimize migration effects in this and other electrochemical experiments. The Double-Layer Capacitance at the PtlFilm Interface. c d must be known if the relationship between E , and [Py’] is to be defined. Ac impedance methods have been used to obtain capacitance values for reduced polypyrrole f i l m ~ . ’ ~ Because 9~~ these capacitances were, in general, obtained from low-frequency ac data,’5s69we cannot use these C values in our studies. A consideration of the relevant equivalent circuit shows why this is so. We and others have shown that when a polypyrrole film is in the reduced (nonconductive) form, the electrochemical cell approximates a Randels equivalent ~ i r c u i t . ~This ~ . ~circuit ~ contains parallel branches; the “upper” branch contains only c d while the “lower” branch contains the series combination of the polarization resistance and the pseudo~apacitance.~~ Since we need to know the value of cd, the time scale of the experiment used must be such that only the upper branch of the Randels circuit contributes to the observed electrochemical response. This means that a high-frequency or fast time scale experiment must be employed. Since the previous were obtained from relatively low frequency ac experiments, the c s reported are not C d k The above discussion shows why the current-step experiment used here is ideally suited for obtaining cd. This method employs a very short time scale (see Figure 3). At these short times, all of the charge injected into the cell goes through the upper branch of the Randels circuit and thus charges cd. The linear relationship between E and t (eq 7 and Figure 3) proves this point. Thus, the current-step experiment is specifically designed to provide only
0.4
0.2
0.6
08
Time ( s e c )
Figure 6. Simulated potential-time transients for the current-pulse experiment: Effect of magnitude of D,, on the transient. Simulation conditions were as follows: film thickness = 0.5 bm;t = 50 ms; i, = 100 FA cm-2; initial E = -0.4 V. D,,pls were as follows: (A) 2 X (B) 2.5 X (C) 3 X and (D) 4 X cm2 s-l.
20
I\
1
?. > Y
Y
5 ’
0.0
0.2
0.4
0.6
0.8
1.o
Time (sec)
Figure 7. Simulated potential-time transients for the current-pulse experiment: Effect of film thickness on the transient. Simulation conditions as per Figure 6 , except Dapp= 1 X cm2 s-l and film thicknesses as follows: (A) 0.20, (B) 0.25, (C) 0.30, and (D) 0.50 bm.
E , us log [Py’] Calibration Curves. As discussed in detail in the Experimental Section, the relationship between E , and [Py+] was determined empirically by using a coulometric titration experiment. Figure 5 shows a typical semilog (or Nernst) plot of these data. Again, data were obtained only over the narrow potential window accessed by the current-pulse experiment used to obtain DaPFOver this window E, varies linearly with log [Py’]; however, the slope is super-Nernstian (0.109 V/log [Py+]). The data in Figure 5 were used to convert calculated Cv+(x=O) values into the corresponding E , values so that experimental and simcd. ulated E , vs t transients could be compared. The cd values obtained are shown in Table I. Note that, at Simulated E , us Time Transients. Figure 6 shows the effect very negative potentials ( E < -0.49 V), cd’sat the coated electrode of Dappon the simulated E , vs t transient. The values of i, 7, are essentially identical with values obtained at a bare Pt electrode and film thickness used in Figure 6 are typical of the experiments Cis are observed at the more positive in this e l e ~ t r o l y t e . Larger ~~ conducted here. These simulated curves predict that the rate of potentials in Table I. This increase in Cd is not due to the confilm equilibration should be very sensitive to the value of the version of the film into an electronic conductor; a very abrupt and dramatic jump in C, at ca. -0.3 V accompanies this t r a n ~ i t i o n . ~ ~ apparent diffusion coefficient. Furthermore, these data suggest that the experimental transients should occur over an easily acRather, the increase in c d with E, observed in Table I, is uncessible time window. doubtedly caused by changes in the structure of the interface The effect of film thickness on the simulated E , vs t transient associated with introduction of the first Py+ sites into the film. is illustrated in Figure 7 . As might be expected, both the rate of relaxation and the value of the final equilibrium potential are (67) Jagur-Grodzinski, J.; Marian, S.;Vofsi, D. Sep. Sci. 1973, 8, 33. strongly dependent on film thickness. While this sensitivity is good (68) Elliot, C. M.; Redenpenning, J. G. J. Electroanal. Chem. Interfacial in the sense that it allows the effect of film thickness on Dappto Elecrrochem. 1984, 181, 137. be accurately assessed, it places a high premium on obtaining a (69) Feldman, B. J.; Burgemayer, P.; Murray, R. W. J . A m . Chem. SOC. reliable measure of the film thickness. 1985, 107, 872. ( 7 0 ) Penner, R. M.; Martin, C. R., to be submitted for publication. Apparent Diffusion Coefficient Values. Experimental E , vs (71) Tanguy, J.; Mermilliod, N.; Hoclet, M. J . Electrochem. S o t . 1987, t transients were obtained for three different polypyrrole film 134, 795. thicknesses and for four different values of the current pulse. These (72) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Theory and curves were matched to simulated curves by using D,, as the only Applications; Wiley: New York, 1980; p 323. (73) Penner, R. M.; Martin, C. R. Anal. Chem. 1987, 59, 2625. adjustable parameter. Typical data are shown in Figure 8. ~~~
~~~
~~
~~
Charge-Transport Rates in Polypyrrole
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5281
film thickness, pm
D~,,, 10-~cm2 s-'
0.35 0.54 0.73
6.2 f 0.3
10.2
8.3 f 0.3
1
4
TABLE 111: Apparent Diffusion Coefficients for Polypyrrole Films
*1
4.2 f 0.5 v
Excellent fits between the experimental and simulated data were obtained; this gives us some confidence in the veracity of the theoretical model. The model can be further tested by evaluating the effect of the magnitude of the current pulse on the value of Dappobtained. The theory predicts that Dappshould be independent of i, provided, of course, that i, is not so large that the film is converted to an electronic conductor. To assess the effect of i, current pulses of 100, 200, 300, and 400 pA were applied to a 0.54-pm-thick film. Dapp)swere obtained from the best match between experimental and simulated transients. An averge value of 6.2 (f0.2) X cm2 s-I was obtained. Since this standard deviation is identical with the standard deviation for replicate measurements at a single value of i,, there is clearly no dependence of Dappon i,. Dappvalues for three different polypyrrole film thicknesses are shown in Table 111. Each Dapprepresents an average of eight determinations (two films, four different current densities for each film). Note first that the D,,, values reported in Table I11 are as much as an order of magnitude larger than values reported by Diaz et aLZ5and Osaka et al.29 Because these previously reported data were obtained by using large-amplitude methods, we believe (see Theory Section) that these Dappvalues are suspect. The theory developed here predicts that, if thin films have the same chemical and morphological composition as thick films, Dapp should be independent of film thickness. In contrast, while excellent matches between experimental and simulated transients were obtained for all of the film thickness reported here (Figure 8), Dappclearly decreases with film thickness (Table 111). These data are in agreement with the often reported qualitative observation that charge-transport rates decrease with film thickness." Furthermore, Osaka et al. observed a similar trend in their data.29 We would like to suggest the following explanation for the dependence of Daw on film thickness. First, it is important to point out that the films studied here were not grown under masstransport-limited conditions. Thus, the concentration of monomer at the electrode surface during polymerization was never dropped to zero. This means that unreacted monomer was incorporated into the nascent polypyrrole films. However, because the polymer is itself electronically conductive, this unreacted monomer could, in principle, undergo polymerization within the bulk of the film at the same time that fresh monomer is arriving and reacting at the polymer/electrolyte interface. If the scenario presented above is correct, the portion of the film in the region near the electrode surface (Le., the oldest part of the nascent film) becomes denser as polymerization proceeds. This explains why thicker films (longer polymerization times, denser inner layers) show lower apparent diffusion coefficients than thinner films. Polypyrrole formed at very positive potentials would not show this densification effect, since little, if any, unreacted monomer would be present in the film during polymerization. In agreement with this prediction, Osaka et al. have found that films prepared at very positive potentials show Dappvalues which are independent of film thi~kness.2~ While this observation supports our densification theory, it is clear that direct experimental evidence will be required before this theory can be accepted. Conclusions We have developed a new small-amplitude electrochemical method for determination of apparent diffusion coefficients associated with charge transport in electronically conductive polymers. For the reasons noted in the Theory Section, this method is ideally suited for investigations of such polymers. In a more general sense, this method should also be a convenient and powerful tool for studying transport in nearly any type of electroactive film. Some of the features which make this an attractive and
Y
a
9.6 m
0 - 0
9.3 9.0 0.0
0.1
0.2
0.3
0.4
0.5
Time (see)
I
B
- -
I 5 0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
C
8
4 1 0.0
0.2
0.4
0.6
0.8
I 1 .o
Time ( s e c )
Figure 8. Comparisons of simulated (curve) and experimental (points) potential-time transients for the current-pulse experiment. Initial E = -0.4 V, i, = 100 pA cm-2, and t = 50 ms; DspP)sa r e presented in Table 111. Film thicknesses were (A) 0.35, (B) 0.54, and (C) 0.73 pm.
powerful method for analysis of transport in thin films are discussed below. First, because this is a small-amplitude method, the electrochemical, chemical, and morphological properties of the film are not greatly perturbed by the analysis. Because electroactive films may show dramatic changes in solvent content, ionic character, morphology, etc., upon oxidation or reduction, the minimally invasive character of this method is an attractive feature. Second, and also related to the small-amplitude nature of this method, by starting at different values of initial applied potential, the effects of the extent of oxidation or reduction on charge transport in the film can be assessed. Thus, for example, the effects of redoxinduced changes in solvent content or morphology can be quantitatively evaluated by using this method. This is not possible with large-amplitude methods. Third, unlike conventional methods for evaluating charge transport in thin films on electrode surfaces,'%24there is no current flow during the data acquisition period. Thus, effects of migration and uncompensated film resistance are minirni~ed'~ or completely (74)As pointed out by one of the reviewers of this paper, while current does not flow during the E-time relaxation, current does flow during the initial current pulse. Thus, migration could contribute to charge transport during the current pulse and this could affect the initial distribution (eq 3). However, the high salt contents should minimize this problem.
J . Phys. Chem. 1988, 92, 5282-5287
5282
eliminated. Fourth, the theoretical model for obtaining Dappis applicable to both the semiinfinite and finite diffusion cases. Thus, unlike many other method^,'^-^^ it is not necessary to adjust the experimental conditions such that the semiinfinite case is obtained. Finally, it should be noted that if the film to be studied is Nernstian, the method would be simplified in that an E , vs concentration of diffusing species calibration curve (Le., Figure 5) would not have to be obtained experimentally. Because of the versatility and power of this new method, we are currently using
this technique to evaluate charge-transport rates in ion-exchange and other polymer films on electrode surfaces. Acknowledgment. This work was supported by the Air Force Office of Scientific Research, the Office of Naval Research, and the NASA Johnson Space Center. We acknowledge valuable discussions with Professor Dan Buttry. Registry No. Pt, 7440-06-4;Et4N*BFc, 429-06-1;BFC, 14874-70-5; pyrrole, 109-97-7; polypyrrole, 30604-81-0; acetonitrile, 75-05-8.
Acidity Constants in the Excited States: Absence of an Excited-State Prototropic Equilibrium for the Monocation-Neutral Pair of 2,3-Diaminonaphthalene R. Manoharan and Sneh K. Dogra* Department of Chemistry, I.I.T. Kanpur. Kanpur-208 016, India (Received: August 26, 1987; In Final Form: February 2, 1988)
The effects of solvents and pH on the absorption and fluorescence spectra of 2,3-diaminonaphthalene indicate that the two amino groups are twisted with respect to the naphthalene moiety. A similar conclusion is drawn for the case of the monocation, formed by the protonation of one of the amino groups. The ground-state pKa value obtained from the fluorimetric titration between the monocation and neutral species indicates that prototropic equilibrium is not established in the excited state. This is mainly caused by the extremely slow proton dissociation rate of the monocation compared to its decay rate ( 5 X 10' s-l). No proton-induced fluorescence quenching is observed for the neutral species prior to formation of the monocation, whereas proton-induced fluorescence quenching is noticed for the monocation, prior to the formation of the dication. This proton-induced fluorescence quenching is static in nature rather than dynamic. pK, values for various prototropic reactions have been determined in the So and SI states and discussed.
Introduction Since Forster' and Weller's2 study of the effect of pH on the electronic absorption and fluorescence spectra of 1-naphthylamine-Csulfonate, considerable study has been carried out on the electronic spectra of aromatic acids and base^,^-^ which are either monofunctional or bifunctional, with one functional group having electron-withdrawing and the other electron-donating properties. It is a well-known fact that in monofunctional molecules, electron-withdrawing groups, e.g., -COOH group or tertiary nitrogen atom, become more basic in the excited singlet state and thus lead R* is the lowest energy to a red shift in the spectra if R transition. Similarly in monofunctional molecules, electron-donating groups such as -OH and -NH2 become stronger acids in the SI state and lead to a red shift or blue shift in the electronic spectra when these groups become deprotonated or protonated. In bifunctional molecules, having electron-donating and electron-withdrawing functional groups, the spectral characteristics of the individual groups are retained. But in some molecules the increase in basicity of the electron-withdrawing group or in acidity of the electron-donating group is so large that the site of protonation is different in the ground and excited states. For example, at pH -2, 5-aminoinda~ole'~ exists as a monocation, formed by protonating the amino group in the ground state. However, in
-
( I ) Forster, Th. 2.Elektrochem. Angew. Phys. Chem. 1950, 54, 42. (2) Weller, A. Ber. Bunsen-Ges. Phys. Chem. 1952, 56, 662; 1956, 66, 1144. ( 3 ) Weller, A. Prog. React. Kine?. 1951, 1, 189. (4) Vander Donckt, E. Prog. React. Kine?. 1970, 5 , 273. (5) Wehry, E. L.; Rogers, L. B. In Fluorescence and Phosphorescence Analysis; Hercules, D. M., Ed.; Wiley-Interscience: New York, 1966; p 125. (6) Schulman, S. G. In Modern Fluorescence Spectroscopy; Wehry, E. L., Ed.; Plenum: New York, 1976; Vol. 2. (7) Schulman. S. G. In Fluorescence and Phosphorescence Spectroscopy; Pergamon: Oxford, 1977. (8) Ireland, J. F.; Wyatt, P. A. H. Adu. Phys. Org. Chem. 1976, 12, 131,
and a number of references mentioned therein. (9) Klopffer, W. Adu. Photochem. 1977, 10, 31 I . (10) Swaminathan, M.; Dogra, S. K. J . A m . Chem. SOC.1983,105,6223.
the lowest excited singlet state, the stable species is also a monocation but is formed by the protonation of the tertiary nitrogen atom. The change in the formation of species in the ground and first excited singlet states is termed phototautomerism because this involves only migration of the proton from one functional group to another. This kind of isomerization is called biprotonic phototautomerism, because the electron-donating and electronwithdrawing groups are widely separated. In the molecules where the electron-donating and electron-withdrawing groups are close to each other, e.g., 2-(2'-hydroxyphenyl)benzimidazole,~~the phototautomerism can occur by intramolecular hydrogen bonding. This is called monoprotonic or intramolecular phototautomerism. Many examples of molecules fall into either of the above categories. However, little systematic study has been undertaken for excited-state protonation and fluorescence phenomena of bifunctional molecules in which both of the functional groups are electron donating.I2-l6 Our recent study on a few system^'^-'^ of these kinds have revealed very interesting features. For example, all the phenylenediaminesI8 (ortho, meta, and para) give rise to a similar sequence of spectral changes when protonation is carried out stepwise, and this agrees with the normal behavior of aromatic amines. However, a small red shift is observed on the protonation of the first amino group (which is an anomalous behavior), followed by a large blue shift in the fluorescence spectrum when second amino group of 2,7-diarninofl~orene'~ is protonated. On (11) (12) (13) (14) (15) (16)
Sarpal, (17) (18)
(19)
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0022-3654/88/2092-5282$0l.50/00 1988 American Chemical Society
