Electrochemical investigations of tetraphenylethylene in dimethylformamide using fourier transform faradaic admittance measurements (FT-FAM)

J Electroanal Chem, 162 (1984) 189-206 189 Elsevier Sequoia S.A, Lausanne - Pnnted in The Netherlands ELECTROCHEMICAL INVEST IGAT IONS OF TETRAPHENYLETHYLENE IN D IMETHYLFORMAMIDE US ING FOURIER TRANSFORM FARADAIC ADMIT 'FANCE MEASUREMENTS (FT -FAM) MARIA GRZESZCZUK * and DONALD E SMITH ** Department of Chemtstry, Northwestern Umverstty, Evanston, IL 60201 (USA) (Received 12th August 1983) ABSTRACT We have investigated the electrochermcal reduction of tetraphenylethylene in dtmethylformannde-0 10 M tetrabutylammonlum tetrafluoroborate electrolyte The array processor enhanced version of the FT-FAM instrumentation was used in these studies Extensive measurements, including temperature and concentration dependence, were performed. Analysis of the data led to the conclusion that the observed wave represents a two-electron reduction with a very small potential separation (AE) between the first and second waves so that the waves overlap and only one admittance peak is observed at all frequencies Ttus electron transfer pair is coupled to a reversible homogeneous redox reaction ("nuance of the EE mechanism") Other mechamsms, such as the simple EE and ECE without "nuances", were inconsistent with one or more aspects of the data arrays obtaaned The mechanism presented is the only one examaned wbach seems consistent with all aspects of the experimental results. The estimation of thermodynamic and lonetlc parameters is discussed, showing that it is possible to obtain reasonably accurate values of all relevant parameters. Three unique theoretical working curves were developed for this study This investigation is especially lllustrauve of the power of the array processor enhanced FT-FAM lnstrumenta- Uon. INTRODUCTION Repor ted s tud ies on the e lec t rochemica l reduct ion o f pheny l subst l t t t ted e thy lenes ifi o rgan ic so lvent -e lec t ro ly te sys tems have ind icated an in teres t ing behav io r fo r te t rapheny le thy lene (TPE) [1 -5 ] *** . In d imethy l fo rmamide , the reduct ion o f te t ra - pheny le thy lene g ives a s ing le " revers ib le" wave on the dc po la rogram [1 -3 ] and dc * On leave from the Institute of Chemastry, University of Wroclaw, Wroclaw, Poland ** To whom correspondence should be addressed. *** In this paper the following symbols wdl be used TPE, TPE T, TPE 2 -= tetraphenylethylene, its radical amon, and its dlamon, respectively, HRR = "nuance" = homogeneous redox reaction (2 TPE- TPE+TPE2- ) , K d = kd/ t r = [TPE][TPE2-]/[TPE~]2; DMF= dlmethylformarmde, HCT-heteroge- neous electron transfer step, ks, , = heterogeneous electron transfer rate constant at the formal potential for t th electron transfer step; k d = rate constant for dlsproportlonatlon step: k r = rate constant repro- portlonatlon step; C = mechamstic symbol for homogeneous chermcal reaction coupled to the heteroge- neous redox reaction; E = mechanistic symbol for heterogeneous charge transfer step. 0022-0728/84/$03.00 © 1984 Elsevier Sequoia S A. 190 cyclic voltammogram [5], which is about two times higher than observed for stilbene under the same experimental conditions. Sirmlar results also were obtained using tetrahydrofuran as the solvent [4]. The observed voltammograms were interpreted quantitatively as due to two reversible one-electron transfers occurring at potentials separated by less than 0.10 V [6]. The two successive reversible one-electron waves observed on the dc cyclic voltammogram for the reduction of TPE in hexamethylphosphoramide have supported the proposed mechanism [5]. Another aspect of the TPE reduction is the possible existence of a competition between the heterogeneous charge transfer (HCT) process and the homogeneous redox reaction (HRR) involving dlsproportionatlon of the radical anion and the reportionation reaction between the neutral and dlanion forms of TPE. Kinetic studies on the disproportlonation of TPE = in ether solvents were done by flash photolysis of an equilibrium mixture of the three reacting species, 2 TPE- ~ TPE 2- + TPE in the presence of small cations such as L1 +, Na +, and Ba 2+, which form ion pairs with the TPE anions [7-9]. The stereochemlcal aspect of TPE reduction is also an interesting subject for electrochemical investigation, although not easy in the context of overlapping waves [6,10-12]. A spectroscopic study supported by theoretical considerations has indi- cated [14-16] that electron transfer to TPE is accompanied by a substantial change in the geometry of the molecule. Conjugation through the ethylene double bond tends to make the TPE molecular planar, but strong steric repulsion by neighboring benzene rings tends to oppose planarlty. The latter effect is diminished in the course of reduction of TPE to TPE ~ and TPE 2-. The conformational rearrangements in the molecule accompanying heterogeneous electron transfer should have a significant effect on these reactions rate parameters. We have undertaken the investigation of the reduction of TPE in aprotic organic solvents using the array enhanced processor enhanced FT-FAM instrument. The results obtained for the TPE reduction at the dropping mercury electrode using dlmethylformamide (DMF) as the solvent are presented in this paper. EXPERIMENTAL TPE (Aldrich Chemical Co.) was recrystallized from methanol prior to use. Solution concentrations used were 1.0, 1.9 and 2.5 mM. DMF ("distilled in glass", Burdick and Jackson Laboratories, Inc.) was passed through a column of activated alumina before use. Tetrabutylammonium tetrafluoroborate (TBATFB) ("electrometric grade", Southwestern Analytical Chemicals, Inc.) was used as the supporting electrolyte (0.10 M) without further purification. The electrochemical cell utilized a DME with a ls mechanically controlled drop life and 0.33 mg s -1 mercury flow rate. The reference electrode was a homemade AglAgII0.10 M tetraethylammonium lodide-DMF ( - 0.40 V vs. SCE) and a platinum wire was the auxiliary electrode. Argon (Matheson Gas Products) was used to degas the cell solution. It was passed through two columns en route to the cell. The first 191 column was filled with molecular sieves and the second with an oxygen scavenger (Ridox). This was followed by a gas bubbler solvent saturator system. All measure- ments were performed under a blanket or argon. Measurements were performed at six temperatures in the range from -10 to + 61°C using an Aminco constant temperature bath. All measurements were performed using the array processor (Floating Point Systems Model AP120B) enhanced FT-FAM instrument [17]. The main benefit of the array processor is prowding cell admittance data m real time and solving the disk overload problem, thus allowing more space for real-time frequency domain averaging [17,18]. SOME EXPERIMENTAL OBSERVATIONS The reduction of TPE at the DME with 0.10 M TBATFB gives a single dc and ac A (12 ~. -1.5- ~ -1.0- £) o x-O 5 o xxxxXXXXXXXXXXXXXX x x x x × x x xxxxxxxxxXX x~x - t .5 -1 .8 -1 .7 -1 .8 - t 9 Potent ie l / V B ~200. 150. "E IO0. o x e 50, 0 o • tb tb ,ib o°O ° o • o o o o .1~ Oo o o ° , l lo o o ° ° o • $o %~o n~an.an~g4p.,.~ °_" . ,, . . . . ., • . .° tl~'°',.a~nt--¢t'' -1.5 -[.S -1.7 -1.8 -1 £ Potent ia l / V Fig 1 Polarograms for the reduction of 1.0 mM solutzon of TPE in DMF-0 10 M TBATFB electrolyte at 298 K (A) Dc polarogram (B) Ac adm3ttance polarogram at 166 Hz, where * = m-phase faradasc admattance and o = quadrature faradalc adtmttance component 192 polarographic wave in the available potential range, as shown in Fig. 1. Comparison of the response magnitudes for TPE and c~s-stllbene systems under identical experi- mental conditions is in accord with previous results [4,5] which indicate that the TPE reduction is a two-electron process. However, the dc polarographic plot of Iog[0d -- t)/1] VS. Edc and the full width at half maximum of the ac polarogram suggest a one-electron process at 25°C. At this temperature a deviation from linearlty m the cot if-t0 ]/2 spectra is observed at potentials negative of ]A(tot)l p potentml. The nonlinearity is small and extends over a rather broad frequency range. It disappears completely at higher temperatures. Examination of the dc potential influence on the cot ~-~01/2 spectra at lower temperatures reveals the complexity of the ac response for TPE (Fig. 2). A final qualitative observation which indicates the existence of a complicated mechanism is the dependence of the cot ~ spectra on the concentration of TPE. Because there is no evidence of adsorption effects, we must conclude that a -0- 0 0 0d -~ 4 0 0 Z" l "dc : r [Alp 0 O50 • o .oo ° / . . . . : . . . . : . . . . : . . . . ; . . . 50 100 150 ZOO CO ~/2/s-~/2 Edc = LIAIp - - . ' * fo / . . . . ., . . . . ; . . . . : . . . . ; . , . 50 l l~ 150 ZOO 1/2 CO ~12/ ~" Fdc : EIAIp +0 0511 O Go ° ' °° o j . . " z- . . < _ . . . . , . . . . . 0 50 100 150 ZOO m I12/S- ,12 F ig . 2 . Cot ~ spectra for reduction of 1.0 mM TPE m DMF-0 10 M TBATFB electrolyte at 273 K Edc values at winch spectra are obtained are g~ven on the figure 193 second order reaction is coupled to the heterogeneous charge transfer process [19]. In the course of this investigation, the foregoing observations did not occur sponta- neously. We have examined theoretical predictmns for the simple EE mechanism [10,11] and the ECE case [12,20-22]. They were unable to explain all aspects of the foregoing observations. Consequently, the model discussed in the theoretical section was accepted for detailed scrutiny. THEORETICAL PREDICTIONS Calculations of theoretmal predictions for the "EE with nuance" mechanism with unresolved waves were performed to examine the sensitivity of the dc and ac polarographic observables to characteristics of the homogeneous redox reaction. The proposed mechanism is TPE + e- ~ TPE ~ E?' , ks.l, o/1 TPE * + e -~ TPE z E~', ks.2, a 2 (I) kd 2 TPE ~ ~ TPE + TPE 2- Kd, k d, k r kf where E, °' represent formal potentials which are related to the reversible half-wave potentials by the expression: E, °t = Ear/2,, -4- (RT /nF) ln(Do.,/DR. , ) and to the K d by the expression: K d = k Jk , = exp[ (F /RT) (E~' - E?')] (1) (2) Symbols used in the above equations have the usual meaning. The available theory [12] encompasses the expanding sphere model of the DME and accommodates differences in diffusion coefficients of the reacting species. The calculations we have performed invoke the assumption of equal diffusion coefficients. The TPE reduction studied here is characterized by unresolved waves which is much more complicated than the situation where the waves are resolved. The possible relations between parameters describing the two-electron transfers which produce a single wave are rather numerous. Nevertheless, experimental observations do allow one to exclude some cases from consideration. The pure reproportlonation case were E~ °' >> E~' can be associated with overlapping waves when E1/2.1 = El~2. 2. In this case a sufficiently irreversible first heterogeneous charge transfer step occurs in comblnanon with a relatively facile second heterogeneous step. Calculation have shown that the homoge- neous redox reaction (HRR) may influence the dc and ac responses in a rather dramatic manner [12] (Fig. 3). Theoretical predictions of the influence of the kinetic parameters, krd~pE, are opposite to what we observe experimentally. Predicted shapes of cot q~ - w a/2 spectra as well as cot q~ polarograms are not an accord with observed ones. The pure disproportionation case where E1 °' 194 kr/M-is-I i Ox lO 7 ~8 l.OxlO 6 5 0 and 10xlO 6" 0 kr/M-is-i 4 l.OxlO 8 4~- ~ l.OxlO 7 0 and 10xlO 6 ° z C0~/2/S-V2 Fig. 3 Theoretical cot ~ spectra for EE with coupled HRR mechanism. Conditions for calculations are DTPE=DTp E-=DTvE 2 =040×10-5 cm 2 s - l , n l=n2=l , ks, 1=0488 cms- I k~,2=00448 cm s I otI = ot 2 = 0 .50 , C~p E = 1 00 mM; T= 298 K, t =1 0 s (using the expanding sphere model) The repro- op o, __ o, __ port,onation reaction rate constants, kr, are indicated on the figure. (A) E 2 -E 1 -AE 21 - -0 10 V, Edc = E~"+0 05 V (B) AE2,1 = 000 V, Edc = E~"= E~' For the E~' = E~' case, the existence of unresolved waves demands either highly facile heterogeneous charge transfer (HCT) for both steps, or comparable (within an order-of magnitude) ks, 1 and ks, 2 values. Consequently, calculations of theoretical predictions for a reversible HRR coupled with dc reversible HCT steps in the context of the EE with nuances mechanism have been done in this study. Comments, but no calculations, characterized the discussion of this case in the original publica- tion [12]. The predicted effects of the HRR for (E~" - E~')= +0.10 V and ks-values in the range of dc reversibility (k s >~ 10 --2 cm s -1) vary from negligxble to significant. Negligible effects of the HRR on calculated ac polarographic responses (e.g., cot 4~, total adrmttance) for k d and k r less than 10 5 M -1 s -1 has been found under conditions considered here. Because we do see effects of the HRR, meaning k a and k r a re > 10 5 M 1 s- l , the assumption that equihbrla for the HRR exist on the dc Ume scale xs validated. Thus, the digital simulation solution of the dc part of the boundary value problem can be simplified by the equihbrium assumption, so that in any volume element the con&tion (3) g d = [TPE] [TPE 2- ] / [TPE ~ 12 (3) 195 can be applied. All dc simulation calculations for the EE with nuance (HRR) invoked these conditions. Because of the assumption of reversible HRR equilibrium on the dc time scale, slope and n-value characteristics of the dc polarographic wave are negligibly in- fluenced by the HRR. Assuming n = 2, the diffusion coefficient of the species involved in the electrode process can be calculated from the dc limiting current. Calculated working curves, as shown in Fig. 4, can be used to determine the difference between standard or formal potentials of the two HCT steps. The dc slope was determined from the calculated dc polarogram in the usual manner [23]. The working curves presented in Fig. 4 were calculated using the solution for the dc current with the pure EE mechanism. The planar diffusion model was employed [11]. Using a more accurate diffusion model (expanding sphere) for the DME has negligible effects on the theoretical slope plots of Fig. 4. The influence of k~-values within the limits mentioned above has a negligible effect on the slope values when (E~' - E;") ~< 0. Values of this parameter > 0 do enhance the HCT rate effect. It is shown later that the specified potential difference value for the TPE system in DMF is negative. Calculations of the theoretical predictions for the ac polarographlc observables (faradaic admittance × AE = ac polarographic current) were performed using the assumptions that ks. , >1 10 -2 cm s -a, andthat HRR is at equilibrium on the dc time scale. The calculations were performed for a wide range of physically significant rate constants for the HRR process (10-5-10 al M -a s a). Attention was primarily focused on the phase angle cotangent which we believe is the best observable for kinetic parameter determination [24]. The influence of the HRR rate on cot ~ varies from negligible to highly significant in this situation, as shown in Fig. 3. The effects of disproportionation and reproportionation can be seen in different frequency 70- g ½0 29~ -60 -qO -20 0 20 qO aE~,~/mv Fig 4. Theoretical dc polarographlc slope vs AE2y for EE at various temperatures Temperatures m&cated on the figure ks, I=ks , 2=10 cm s 1, DTvE=D.rPET=DTPE2_=050×10 .5 cm 2 s i, sta- tionary plane model All other variables are the same as Fig 3 > 60. E 50 196 ranges of one cot q, spectrum under certain conditions [26]. They also are very sensitive to rate and equilibrium characteristics. Our search to find a method for determination of the kinetic parameters of the two HCT steps led to the consideration of the pure EE mechamsm [10,11]. The large number of parameters (k~, ct, E °' for each step) characterizing the quasi-reversible overlapping two-step HCT scheme and the very cumbersome algebraic forms given in the mathematical description of the ac observables clearly establishes that a generalized formulation of experimental data analysis is not available. To elaborate this problem further, the calculations of cot q~ and the total admittance were A 2- -8- 0 -1.5 -1.6 -1.7 -1.8 Potent ial / V 8 -o- B ~.. .~ E 1E 2 2- _ ._ . . - - . - - - - - E 1 0 50 100 150 200 Off/2/5-1/2 Fig 5 Theoretical comparison of EE mechanism cot q~ data with one-electron reduction mechanism for each individual component. Condit ions for calculation are planar diffusion E~'= -1 64, E~'= 1 68 V, ks, l = 0 10 cm s - 1 ks 2 = 0.010 cm s - l Other parameters are the same as m Fig 3 (A) cot q~ polarograms at 50 Hz (B) cot q~ spectra at - 1.75 V. 197 performed and compared with observables predicted for the simple single-step ac quasi-reversible case [24]. Some examples of such a comparison are shown in Fig. 5. Calculations support intuitive expectations that the contribution of the faster HCT step to the total admittance, ]A(wt)l, is larger, but the slower step will have the greatest influence on cot @. The relative k s values have a profound influence on the ac frequency response. Again, the cot @ values are especially susceptible to dif- ferences in these parameters. At low frequencies cot @ manifests a larger contribu- tion of the slower HCT step while the contribution of the faster step increases w~th increasing frequency (Fig. 5B). The possibdity of using these predictions in the experimental data analysis of the TPE system depends very much on the frequency range available for accurate measurements of the ac response. For condit ions where i C 150 0 c E 1oo. O O 5a- x 9 a- -C- O 2 .5 - 2.0 1.5 1 .0 IAq Cot @ ks, 1 =010 cm 5 -1 ks, 2 = 0010 cm s-1 -1 .5 -1 .8 -1 .7 - I .8 Potential / V B • ~ Cot @ IAI c ~> 15n- U c 2.5 O ~ / ks, 1 = 0010 cm s -1 1on. ~)- ks 2= 010 cm s-1 o ~2.0 O "*" 51"1- × 1.5 ~o b O" 1.0 -1" .5 -1 ' .8 -1'.7 -1 ' .8 Potential / V Fig. 6. The influence of k s values on the total admittance and cot e# peak potentials for the EE mechamsm Conditions for calculation are: Area = 040) 198 AEz~" ~< 0, the cot q~ spectrum at the lowest frequencies has a negligible contr ibut ion from the faster HCT step, especially at the negative stde of the cot ~-Eac profi le as shown in Fig. 5A. Another example of the different behavior of tA(wt) l and cot 4~ is the separation between the two peak potentials at a part icular frequency. Relative posit ions of the two peaks can be very useful in the diagnosis of the relative rates of the twQ HCT steps as i l lustrated by a few examples shown in Fig. 6. As the second HCT step becomes slower relative to the first step, the cot q~ maximum ~s shifted to more negative potentials relative to the IA(wt)l peak. When the first step is slower, the opposite effect is predicted. The increase in AE2f ' plays an opposite role to that of the k s value ratio, but lts effect IS small for AE o, < +0.050 V. The influence of 2,1 a-values within the 0.5 _+ 0.1 range also has a small effect on this observable, although in some cases it is not negligible. The HRR coupled to the two-step HCT process can affect the pure EE behavior from a negligible to a significant extent. Nevertheless, the main patterns just revealed remain unchanged in the case of the reversible HRR with its equihbrmm constant close to 1.0. The influence of the HRR can be detected easily using the TPE concentrat ion dependence of the cot ~ spectrum. Figure 7 shows the sensitivity of 5. -o- t9 -It +0.040 O.OnO -0 040 . • . . , • • . , • • • Log (G/ .e s- q4- C ks, 2 /cm s - I II 2 4 Log (G) -O- 0 8 LO +0.040 ~ , , . . . Log (G) -e- o .ooo ~6 0 0 -o 040 -~ -2 D ks, i /c ~ s - I .... °! 6 i 4 Lo9 (G) Fig 7 Theoreucal dependence of HRR rate and frequency (G parameter) for different thermodynam*c and kinetic propertxes of the two HCT steps (A) ks, 1 = 0 1 cm s -1, ks, 2 = 0 010 cm s 1,500 Hz (B) Same as (A), except 5000 Hz (C) 5000 Hz, AE2~'= -0040 V, k~, 1 = 0 10 cm s -1 (D) Same as (C), except ks, 2 = 0 10 cm s -1 Edc = 0.5 (E~'+ E~') and other parameters as in Fig 3, or indicated on the figure 199 this observable on parameters of the HCT steps. The increase in cot q5 values with an increase in the concentration of TPE (disproportionation effect depends strongly on AEzy and on ks, 2. Note that the rate of the second HCT step competes with the HRR in generating the TPE 2- dianion. The "reproportlonatton effect" is the opposite to that just described. It can also be seen on the same cot q~ spectrum, but this effect is much smaller under the conditions considered. The frequency range available for observation is a very important factor as shown in Fig. 7 which compares the sensitivity of cot q~ on the kinetic parameter kdC~pE/~ = G for differ- ent frequencies. The predicted behavior of the cot q~ and IA(0~t)l peak potentials remains generally unchanged compared to the pure EE case, although the frequency dependence of this observable can be changed. The phase angle cot q~ in the frequency range where its concentration dependence occurs was selected as the observable for quantitative analysis of the reversible HRR kinetics. Accurate measurement of this observable over a sufficiently broad frequency range is necessary to accomplish this goal. RESULTS AND DISCUSSION Dc polarographic data were used to determine the equilibrium constant for dlsproporuonation and diffusion coefficients of TPE at each temperature. Limiting currents were used for diffusion coefficient determination while the E~' -E~" (AE2,t) difference vs. dc slope (Fig. 4) served to provide the data for calculating K a using eqn. (2). A specific example illustrating the use of this type of plot for obtaining the AEz, ] value for TPE in DMF-electrolyte at 298 K is shown in Fig. 8. The van 't Hoff type plot is shown in Fig. 9B. Results indicate that an increase in temperature favors the disproportionatlon step. The estimated enthalpy for dlspro- o so. i 4n. . . . . . . . -4o -2o 6 zb 46 ~0 *~× AE~, 1/v Fig 8 Theoretical calculat ion of effect of ks-values on dc polarographac slope at 298 K and experimental apphcat lon to TPE system. Condit ions for calculat ion are. ( ) k~j = ks. 2 =1 0 cm s a, ( . ) ks j = ks, 2 = 0.010 cm s -1, other parameters as m Fig 3 200 port ionat ion (AH a) is + 9.6 k J /mo l . The diffusion coefficients determined for each temperature are presented in Fig. 9A. The activation enthalpy for diffusion of TPE in DMF is 19.2 k J /mo l . These results were used in the analysis of the kinetic parameters for both the HCT steps and the HRR process. Because knowledge of the second HCT step rate is very important in determining d isproport ionat ion kinetics when K d is known, the low frequency range of the cot spectrum was used to determine its magnitude. The experimental ly observed total admittance, IA(wt)J, and cot ~ peak separation favored the situation where the second HCT step was slowest and its contr ibut ion to cot ~ at the lower frequencies is predominant (note Figs. 5 and 6). -11.5. -12.0- ,'7 v 5 -12 .5 - -18 ,0 - A o o o 3.0 3.2 3.4 3.6 3.8 10 +3 X T - I /K -1 B • • -1.0- o. v -1.5. _5 - 2 . 0 ' , • • ~o0 3.2 3.4 3.6 3.8 10 .'.:-3 X T - f /K -1 Fig. 9 Temperature dependence of the equilibrium constant for dlsproportlonatlon, Ka, and diffusion coefficients, D, for the TPE reduction m DMF-0 10 M TBATFB electrolyte. (A) Arrhenlus plot showing temperature effect on D, assuming n = 2 (B) Van 't Hoff plot showing temperature effect on K d 201 5- 4" .9- 2. o x x x 27r,~ x o " ' ' " . . . . : . . . . ; . . . . I . . . . I . . . . : . . . . l tO 20 BO ½0 50 BO 70 ( . .0~/2 /5 -1 /2 Fig 10. Temperature dependence of low frequency porUon of cot ,# spectra at total admittance peak potential for the TPE reducUon in DMF electrolyte Experimental condmons 1 0 mM TPE in 0.10 M TBATFB-DMF soluUon; drop hfe = 1.0 s. Figure 10 presents low frequency segments of the experimental admittance peak potential cot q, spectra for the reduction of the 1 mM solution of TPE at three temperatures. The estimated HCT rate constant, ks, z, is inversely proportional to the slopes of these straight lines. The relevant equation is: k~ = (2D)1/2/[(a cot ~p)/awl/2)E,, (e-'U + e13S)] where: j= (nF/RT)( Edc- E:/2) ~o = 2~r f f = frequency in Hz (4) (5) (6) (7) (8) • Other symbols have their usual meanings. The approximate values of ks,2 determined by this method probably are overestimated, but their temperature dependence should remain true. In a similar manner, high frequency data are used to estimate the faster ks, 1 value• This first approximation is expected to underestimate the true ks, ] value. The overall procedure can be envisioned by examining the experimental data shown in Fig. 2, which clearly show that different slopes will be obtained from low and high frequency data. The net result of such estimates at 278 K is ks, 1 = 0.060 cm s-] and ks, 2 = 0.030 cm s-1. Experimental data for the temperature of 278 K have been chosen for the "reference" analysis. Accurate and precise cot ~ data can still be measured at this temperature over a broad frequency range. Cot ~ spectra nonlinearity at the peak admittance potential is obvious and it increases at the negative side of the wave. This behavior has been compared with theoretical predictions for (E~' -E~")= -0.040 202 a ~ a a V and for ks. 2-.~ (ks,2)w~O, where (ks ,2 )~ 0 ts the estimated HCT rate constant obtained using low frequency cot ~, data and eqn. (4). The ultimate objective is to find a full set of kinetic parameters describing the system at this temperature. An illustration of the working curves used to determine more accurate ks, 1 and k~, 2 values as well as the HRR reaction rate, kd, is given in Fig. 11A. The abscissa of the plot is I og (kdC~pE) and the ordinate is cot ft. The solid curves represent theoretical plots for six different combinations of k~,] and ks, 2, given the original approximate estimates of these HCT rate parameters, knowledge of K d, the frequency "7 cot a t 25mM J "e" ~ cote a t lOmN 0 ' s ,__2___.~ ? 2 ~ A ½ 5 Log (k d * c) ks j [ ks ,2 cms 1 c, .6 n ,,~ i, ~ L, n: n e~ u u3 n12 n io o ~3 6 7 8 6, ~ 7 ~...........~ 22:3 ,z 3320 Hz 5' -O-½. % O 3 2 _ ~ I%1 / / ,// 29 3 Hz 7 8 2 3 ½ 5 6 Lo 9 (1% , c) Fig. 11 Theoretical cot ff worlong curves for EE with HRR mechanism winch are used to determine k s 1, ks.z, and k d. Condit ions for calculations DTp E = DTPET ~ DTPE2-= 0.32)< 10 -5 cm 2 S 1, T= 278 K, E~ = -1 .64 V, E~ = -1 68 V; Edc = ElA(~ot)[ p -0 .100 = -1 66 V, frequency = 5273 Hz, t = 1.0 s (using the expanding sphere model) Other parameters are given on Figure 3 (A) Work ing curves for different values for ks, 1 and ks, 2 (see text for full detads). (B) Wor long curves for different frequencies using k, 1 and ks, 2 values determined m Fig. 11A. 203 (5273 Hz), temperature (278 K), and other fixed experimental parameters. Included in Fig. l lA are two experimental cot ~ values obtained at Edc = EIA(,~t)I p -- 0 .010 V at two different concentrations, 2.50 mM and 1.00 mM. It is important to recognize that knowledge of the two concentrations allows one to define a distance on the abscissa because A 1og(kdCvpE) = log(k d × 2.5 × 10 -3) - log(k d × 1.0 × 10 -3) = log(2.5) = 0.40 abscissa units. This is indicated on the lower right side of Fig. 11A. Thus, if both experimental values of cot q~ intersect a single working curve, one then examines the corresponding abscissa values to see if they differ by 0.40 units. The procedure is illustrated in the Fig. l lA by horizontal lines representing the two cot values and vertical lines, using different symbols for different working curves, to indicate corresponding abscissa values. An almost ideal fit is obtained for the theoretical working curve for ks. ] = 0.10 cm s ] and ks,: = 0.008 cm s -1. One then can use the actual abscissa magnitudes to calculate k d at each concentration. One obtains k d = 2 × 107 M-1 s-]. It is interesting to note that the theoretical curve for the onginal estimates for ks, 1 and ks, 2 (top curve) does not overlap either experimen- tal cot ~ value. Nevertheless, the estimation was valuable because it designated values within a factor of three of the more refined values obtained in Fig. l lA. This type of procedure was used at several other frequencies. Data obtained were in good agreement with that obtained in Fig. l lA. This is illustrated in Fig. l lB where all parameters are fixed except k d and theoretical working curves are shown for three different frequencies. The same procedure used in Fig. l lA is employed. The fact that all three frequencies yield the same A1og(kdC~-pE ) values located identically along the origin shows that the same k d values are obtained at each frequency. This may not be obvious for the 29.3 Hz case where the HRR effect is small. However, numerical data support this statement. In the course of this investigation the formal potentials of the two HCT steps were detern~ned to be E~ ° '= -1.64 V and E~" = -1.68 V vs. our nonaqueous reference electrode at 278 K. 2 5ra~ 6 lCrc~ "O- 0 50 100 150 200 001/2/S -~/2 Fig. 12 Theory-experiment comparison of cot ~ spectra for TPE reduction in DMF-0 10 M TBATFB electrolyte at 278 K. Relevant conditions are the same as Fig 11A (*) Expenmental spectrum for 1 0 mM TPE, (O) experimental spectrum for 2 5 mM TPE, ( ) theoretical spectra for each concentra- tion. 204 6- 84- A 278K o • ° ° °°°4) kd= 2x107M-1s ~ o ~ k d = 0 o o n o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , , | J 5o too tso zoo (0112/S-~12 B 4- -0- ~:1- 0 tJ Z" 1 0 298K o O kd=lX~O8M-ls-~ ~ kd=O . . . . . . . . . ; . . . . . . . . . : . . . . . . . . . : . . . . . . . . . :~ 50 tOO 15O ZOO LO ~/2/5- 1/2 Fig. 13 Theory-experiment companson of cot q~ spectra showing theoretical predictions with and without the HRR. (O) Experimental data for 1 mM solution of TPE ( ) theoretical spectra for (a) ks,l=0.10 cm s -1, k~,2=0008 cm s-]; (B) k~,l=020 cm s -1, ks,2=0,020 cm s ] DTPE=DTPE. = DT1,E 2- = 0 52 × 106 cm 2 s -1, kd-values given m the figure; cot q, values measured at adrmttance peak potent]als, EIA(wt)I p. Other cond]tlons as in F]g. 11 and Table 1 A final check on the kinetic parameters is to obtain theory-exper iment compari - son of cot ~ spectra under different condit ions. Figure 12 shows such a comparison at two concentrations. Theory-exper iment agreement is reasonable for both con- centrations. It is evident from Fig. 12 that major effects of concentrat ion changes are evident only at higher frequencies (> 1.5 kHz). Experimental data are accompanied by theoretical cot ~ spectra with and without the HRR in Fig. 13. Figure 13A gives data at 278 K and Fig. 13B at 298 K. It should be noted that the theoretical and experimental cot (/, spectra at ElA(o~t)lp are l inear at 298 K. This helps explain why previous investigators using small ampl i tude ac measurements [3] have considered this mechanism to be a simple quasi-reversible case. A l inear cot (/) spectrum also is 205 obtained (and predicted) at higher temperature (318 K and 334 K). Although hnear cot ~ spectra exist, concentration dependences are still found at these higher temperatures. Consequently, this work shows the importance of examining the effect of concentration before concluding that the electrode process is a simple quasire- versible process. This is especially important when the literature contallaS studies of homogeneous disproportionatlon [7-9] of a component in the electrode process under investigation. The results obtained for the TPE reduction at Hg in DMF-0.10 M TBATFB electrolyte according to the mechanism Ef ' TPE + e- ~ TPE ~ E~' TPE ~ + e- ~ TPE E- ks2 ko 2 TPE ~ ~ TPE + TPE 2- kr at two different temperatures are compiled in Table 1. Analysis of the experimental data was performed assuming equal charge transfer coefficients of 0.50. Calculations show that t~-values in the range 0.40 to 0.60 have negligible effect on the observables employed in this investigation, particularly in view of the low resolution with which rate and thermodynamic data are reported. Structural studies for TPE, TPE ~, and TPE 2- indicate clearly that both steps of the TPE reduction are connected with changing the geometry of the molecule [13-16], but the second step is predominant in this respect. Releasing steric hindrance imposed by the central ethylene bond leads to a substantial increase in the conjugation of phenyl groups attached to the same central carbon atom [25]. This effect is reflected in the lower HCT rate constant for the second step. Also, the rate of the less sterically hindered first HCT step is lower than for the stilbenes [3] suggesting it also contains a nontrivaal steric effect. Studies of disproportionation of TPE T in DMF are not reported in the literature. The results of studies of this reaction in ether solvents [7-9,25] indicate that steric strain in TPE- favors disproportionation relative to reproportlonation. The opposite is observed in this study where reproportionation is favored. One might attribute this difference to conditions in previous studies [7-9,25] where radical anions were formed by alkali metal reduction in ether solvents. In this case stabilization of the TABLE 1 Results obtained for the TPE reduction at Hg m DMF-0.10 M TBATFB electrolyte at two different temperatures - E~' = - 1.64 V T/K E~' - E~' /V ks,1/cm s -1 ks,z/cm s -1 kd/M -1 s -1 K d 278 - 0 040 0 10 _+ 0.01 0 008 _+ 0 002 2 >( 107 0.19 298 -0.035 0 20_+0.01 0 020_+0.002 1 × 108 0.26 206 TPE 2- dianion by ion pairing should favor dtsproportionation. Our DMF electro- lyte has much smaller ion pairing character [27]. We do not believe this argument is sufficient to complete the picture. The effect of solvent characteristics are also significant. Preliminary data obtained in this laboratory for TPE in dimethylsulfo- xlde electrolyte suggest that K d = 1. This indicates that a considerable solvent effect is also operative. At this point we only wish to note these effects. Too little information is available to speculate further. ACKNOWLEDGEMENTS The authors gratefully acknowledge financial support from the National Science Foundation through Grants CHE77-15462 and CHE82-10831. We also thank Dr. John H. Begemann for helpful suggestions in programming and computerized instrumentation use. REFERENCES 1 S. Wawzonek, E W. Blaha, R. Berkey and M.E. Runner, J Electrochem Soc, 102 (1955) 235 2 P G. Grodzka and P.J. Elvmg, J. Electrochem. Soc., 110 (1963) 231 3 R. Dletz and M.E. Peover, Discuss. Faraday Soc., (1968) 154 4 B L Funt and D G. Gray, J. Electrochem. Soc, 117 (1970) 1020 5 T. Troll and M M Baazer, Electrocbam. Acta, 19 (1974) 951. 6 D.S. Polycyn and I Sham, Anal Chem., 38 (1966) 370. 7 G. Lexan, S. Claesson and M. Szwarc, J. 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