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Medium effects in the electroreduction of cyanobenzenes
185
J. Electroanal. Chem., 100 (1979) 185--196 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
MEDIUM EFFECTS IN THE ELECTROREDUCTION OF CYANOBENZENES
A. BAR.~NSKI * and W.R. FAWCETT **
Guelph-Waterloo Centre for Graduate Work in Chemistry (Guelph Campus), Department of Chemistry, University of Guelph, Guelph, Ontario NIG 2W1 (Canada) (Received 29th January 1979)
ABSTRACT The kinetics of electroreduction of eyanobenzene, o-dicyanobenzene and p-dicyanobenzene at a dropping mercury electrode have been studied in various perchlorate salt solutions in dimethylformamide and hexamethylphosphoramide using a phase sensitive a.c. admittance technique. The standard rate constants, ks, were found to depend on the nature and concentration of the salt but there was no evidence for ion pair formation between the product anion radical and the cation of the electrolyte. The heat of activation for the electroreduction of the dicyanobenzenes determined by measuring the temperature dependence of k s in the range --12 to 36°C was independent of cation nature in the case of the ortho-compound but varied with electrolyte cation in the case of the para-compound. On the basis of a detailed analysis of medium effects it is concluded that the reaction site for these species is close to the outer Helmholtz plane, the dipolar reactants being oriented in the electrode's field. The dependence of the free energy of activation on the size of ions in the reaction environment, on their interaction with the transition state, and on polarization energy is discussed in detail.
INTRODUCTION
It has been shown [1 ] that the electroreduction of aromatic nitriles in aprotic solvents involves a one,electron reduction to the anion radical which is sufficiently stable in most cases to give an e.s.r, spectrum. This group of conpounds was among those considered b y Bard et al. [2,3] in their study of the kinetics of homogeneous and heterogeneous electron transfer to aromatic molecules. Kojima and Bard [3] discussed the kinetic data within the context of the Marcus-Levich-Hush models [4--6] for electron transfer and concluded that the free energies of activation for the homogeneous and heterogeneous processes are approximately equal when medium effects for the heterogeneous
* On leave from the Department of Chemistry, University of Warsaw, Warsaw, Poland. ** To w h o m correspondence should be addressed.
186
process are estimated on the basis of the Frumkin model [7]. However, the Frumkin model ignores the effects of ion-ion interactions at the reaction site [8], and of the polarization energy of dipolar species [9] on the rate constant and its variation with potential. These effects are difficult to estimate quantitatively b u t would be expected to result in a change in rate with the nature of the base electrolyte and the magnitudes of the dipole m o m e n t s of the reactant and product. Accordingly, the free energy of activation for the heterogeneous process estimated by the Frumkin model is not entirely due to solvent reorganization b u t contains an undetermined contribution from local ion-ion interactions and dipolar effects. One way of obtaining an estimate of these effects is to compare kinetic data for the various isomers of disubstituted benzenes. A convenient pair of reactants are o-dicyanobenzene and p
Heterogeneous rate data were obtained using the phase sensitive a.c. impedance technique described elsewhere [10]. The reference electrode system was redesigned in order to reduce the resistance in the potentiostat circuit and eliminate the requirement for two reference electrodes [10]. The reference electrode consisted of a silver wire dipping into a solution of 0.05 M AgNO3 and 0.05 M tetraethylammonium perchlorate (TEAP) in an aprotic solvent (dimethylformamide (DMF) or hexamethylphosphoramide (HMPA)), the liquid-liquid junction with the working solution being made in a fine fritted glass disc. The silver solution in DMF was replaced daily because of the instability of Ag * to photoreduction in this solvent. The Luggin capillary at the end of the reference electrode system was designed so that its tip could be placed reproducibly at a position approximately 1 mm away from the working electrode (dropping mercury electrode). There was no evidence that Ag ÷ had diffused from the reference electrode c o m p a r t m e n t to the main b o d y of the cell during the period for which current-voltage measurements were made. The counter electrode was platinum foil with an area of - 5 cm 2. Current-potential data were obtained at the peak potential as a function of frequency of the a.c. signal (160 ~< f~< 860 Hz-'), and in the vicinity of the peak potential (--50 mV ~< ~ ~< 50 mV) at a fixed frequency. The solution resistance and double layer capacitance were found b y estimating the a.c. admittance of the system in the potential range of interest b y interpolation from values obtained at potentials where no faradaic current flowed. Admittance data at peak potential were analyzed b y Randles' m e t h o d [11], and those obtained as a function of potential b y the m e t h o d of the Levie and Husovsky [12] as described previously [10].
187 Procedures for purification of the salts and DMF are described elsewhere [13]. The HMPA was dried over 4A molecular sieves and distilled at a reduced pressure (~3 mm) under a nitrogen atmosphere. The dicyanobenzenes (DCB) were purified by recrystallization from ethanol and cyanobenzene (CB) or benzonitrile by distillation. All experiments were carried out in a controlled atmosphere chamber maintained at 25 + 0.5 ° C. Experiments at other temperatures in the range --12 to 36°C were conducted in a cell in which the working compartment was surrounded by a glass chamber through which methanol maintained at the desired temperature was circulated. The reference electrode compartment was always kept at 25 ° C. The concentration of depolarizer was 5 × 10 -4 M in DMF solutions and 2 X 10 -3 M in HMPA solutions. RESULTS The reversibility of the electroreduction of the cyanobenzenes was ascertained by cyclic voltammetry performed at a hanging mercury drop electrode. The current-potential curves for CB, o-DCB, and p-DCB had a peak current on the reverse anodic sweep approximately equal to that for the forward cathodic sweep indicating t h a t the radical anion formed on reduction of the parent molecule is stable within the time scale of the experiment. In the case of m-DCB, the anodic peak current was considerably less than the cathodic peak cdrtent indicating t h a t some of the radical anions underwent chemical reaction. A similar conclusion was reached earlier by Rieger et al. [1] on the basis of their e.s.r, study of nitrile radicals. For this reason, m-DCB was n o t included in the kinetic study. The absence of significant ion pairing between anion radicals and the cation of the base electrolyte was ascertained by determining the dependence of the polarographic half-wave potential El/2 on cation nature and concentration for solutions of 1--1 electrolytes in DMF. E1/2 was independent of cation nature within experimental error (-+2 mV) for 0.1 M solutions of TEAP, tetrapropyla m m o n i u m perchlorate (TPAP), t e t r a b u t y l a m m o n i u m perchlorate (TBAP), LiCIO4, and NaCIO4. The values observed, --2.025 V for p-DCB, --2.085 V for o-DCB, and --2.775 V for CB agree well with those reported by Rieger et al. [1]. Variation in the concentration of the electrolyte in the range 0.01 and 0.1 M resulted in a shift in E,/2 by ~16 mV in the positive direction; this observation can be attributed to a change in the liquid junction potential between the working and reference electrode compartments and in the activity of the anion radical with change in ionic strength [13]. The kinetic data obtained in 0.1 M solutions in DMF and HMPA are summarized in Table 1. In all cases, the standard rate constant ks for p-DCB is less than that for o-DCB, the ratio of these rate constants depending on both electrolyte and solvent nature. The rate constant for reduction of CB, which can only be measured in tetraalkylammonium (TAA÷) salt solutions because of its negative reduction potential, lies between those for o-DCB and p-DCB. The rate constants for a given cyanobenzene decrease with increase in the size of the TAA* cation. In the case of Na+and Li+electrolytes, the rate constants are approximately equal for a given reactant, but they are significantly larger in MgCIO4. Unfortunately, kinetic data obtained in the presence of K÷and Cs*
188 TABLE 1 A summary of kinetic data for the electroreduction of cyanobenzenes at mercury in dimethylformamide (DMF) and hexamethylphosphoramide (HMPA) with various electrolytes (concentration = 0.1 M) at 25°C Electrolyte
p-DCB
TEA1) in DMF TPAP in DMF TBAP in DMF LiCIO4 in DMF NaC104 in DMF MgC104 in DMF LiCl04 in HMPA
o-DCB
CB
ks/cms-I
~
k s / c m s -1
~
k s / c m s -1
0.57 0.30 0.22 0.13 0.12 0.36 0.006
0.49 0.49 0.50 0.57 0.57 0.47 0.53
0.75 0.44 0.32 0.33 0.33 0.80 0.039
0.49 0.51 0.53 0.57 0.57 0.50 0.67
0.58 0.34 0.30 -----
0.48 0.53 0.53 -----
cannot be compared directly with those presented in Table 1 because these cations are specifically a d s o r b e d at m e r c u r y in the p o t e n t i a l range of in te r e s t [ 1 4 , 1 5 ] . W h e n t h e s o l v e n t is c h a n g e d f r o m D M F t o H M P A , a c o n s i d e r a b l e r e d u c t i o n i n t h e r a t e Of r e a c t i o n is o b s e r v e d . T h e t r a n s f e r c o e f f i c i e n t ~, d e t e r m i n e d f r o m t h e v a r i a t i o n i n t h e r a t e c o n s t a n t w i t h e l e c t r o d e p o t e n t i a l , is c l o s e t o 0 . 5 f o r m o s t s y s t e m s . A n i n c r e a s e i n a is f o u n d w h e n T A A ÷ salts are
t
!
i
l
|
p - DI CYANOBENZENE
E
£
\ °°\\o --.<-.
\ o
!
- 0.12
I
!
- 0.16
I
-0.12
!
\o - 01.16
Fig. 1. Logarithm of the standard rate constant, log ks, for the electroreduction of o-dicyanobenzene and p-dicyanobenzene obtained in dimethylformamide at a Hg electrode in the presence of various tetraalkylammonium perchlorate salts plotted against the potential drop across the diffuse layer ~bd. The nature of the tetraalkylammonium cation is indicated adjacent to each plot.
189
replaced by LiC104 or NaCIO4 in DMF. In the case of LiC104 in HMPA, e is significantly larger for the polar reactant o-DCB. The variation in standard rate constant with salt concentration, and thus, with the potential drop across the diffuse layer ~d is illustrated in Fig. 1. Values of ~d were calculated from charge-potential data for the Hg/DMF interface at equilibrium [15] using the Gouy-Chapman theory. Since the electrode reaction
(I)
R+e~R-"
involves a negatively charged product, the reaction rate decreases as ~bd becomes more negative. According to the Frumkin model for double layer effects [ 7], the variation in ks with ca for a reaction involving an uncharged reactant is given by In k s
:
In ho + af(dP d - - dPTM)
(2)
where k 0 is the potential independent contribution to ks, 0F, the inner potential of the electrode and f = F / R T . Thus, when the ionic strength is changed, the electrode potential being maintained at the standard potential, 1 [a In ks~
=
(3)
Values of ~ determined from the slopes of plots like those in Fig. 1 are approximately 20% higher than those reported in Table 1 but follow the same trends. They are definitely not as reliable quantitatively because estimates of a from the double layer effect rely heavily on the estimate of cd which are based on 1
i
i
-0.2 O~TEA*
o-
TEA*
o
E
TBA*
U~O~
o -1.0 p -DICYANOBENZENE o ~ , ~
o- DICYANOBENZENE I
'
I 3.4
I 3.8
10 3 T ~ 1 / K -1
Fig. 2. Arrhenius plots of kinetic data for the electroreduction of dicyanobenzenes at Hg in various 0.1 M perchlorate salt solutions in dimethylformamide. The nature of the cation is indicated adjacent to each plot.
190 Gouy-Chapman theory, and on the assumptions of the Frumkin model. These assumptions are discussed in more detail below. The variations in ks with temperature is shown in Fig. 2 for o-DCB and p-DCB. In the case of the ortho-compound the slope of the Arrthenius plots is approximately independent of the nature of the base electrolyte cation whereas for p-DCB, it increase in the order TEA + < TBA ~ < Na +. This indicates a corresponding decrease in interaction of the surrounding cation with the transition state of the reaction. On the basis of the simple theory of double layer effects, the real heat of activation [16], AH~¢ is given by [10] A/-/~ = --R ~ In ks ~(1/T)
RT + ~F~(¢d/T) 2 ~(1/T}
(4)
As shown previously [10], the variation in cd with temperature on the basis of the appropriate double layer data [15] is such that ~(~)d/T)/a(1/T) = 0.010 V. The estimated real heat of activation for o-DCB assuming ~ = 0.5 is 10.0 + 0.2 kJ mo1-1. In the case o f p - D C B , AH~¢ increases from 9 kJ mo1-1 in the presence of TEA + in DMF to 17 kJ mol -~ when NaC104 is the electrolyte. These results suggest that the ortho-compound is oriented in the double layer such that its interaction with surrounding cations does n o t vary significantly with cation nature; on the other hand, the transition state for the reduction of p-DCB is affected by surrounding cations such that the barrier height increases with solvated cation size, that is, with an increase in distance between the interacting species. DISCUSSION
Tke kinetic parameters Kojima and Bard [3] obtained kinetic data for the electroreduction of cyanobenzenes in 0.5 M TBAP in DMF. As one would expect, the standard r a t e constants are higher than those reported in Table 1 because of the change in ionic strength. Estimates of ks at 0.5 M obtained b y extrapolating the data in Fig. 1 agree reasonably well with those of Kojima and Bard [3] except in the case of o-DCB. The values of ~ reported by these authors for CB and o-DCB are significantly higher than those presented in Table 1. These differences can be attributed to different methods of data analysis, the earlier m e t h o d [3] being based on a determination of the potential Emax at which the cotangent of the phase angle of the a.c. current is a maximum. It is easily shown from a statistical analysis of the functional relationship between ~ and Emax that one would expect greater scatter in values of ~ determined this way than b y the m e t h o d used here and described earlier [10]. Assuming that ion-ion interactions at the reaction site are minimal in the presence of Li + and Na +, these kinetic data are the most appropriate to consider within the context of the Marcus-Levich-Hush t h e o r y of electron transfer [4--6]. The standard free energy of activation is given b y [3,10]
AGCo = R T ln(~Ze/ks) + (~F¢ d where ~ is the transmission coefficient assumed to equal unity and Ze, the
(5)
191
heterogeneous collision frequency. Following Marcus [25], Ze is assumed to equal (R T/27rM)'/2 where M is the molecular weight of the reactant. For o-DCB and p-DCB, Ze = 5.55 × 103 cm s -1, and AG0¢ = 17.5 and 20 kJ m o l - ' , respectively. According to the same model, the solvent reorganization energy E s is equal to 4AG0¢ and the transfer coefficient at the standard potential is given by = 0.5 -- FCd/2Es
(6)
Accordingly, the predicted values of a, 0.64 for p-DCB and 0.66 for o-DCB, are somewhat higher than those obtained experimentally. No potential dependence of a which is predicted b y these theories was observed in the small potential range in which reliable data could be obtained. Kojima and Bard [3] concluded that the free energies of activation for homogeneous electron transfer involving systems similar to those considered here are equal, and therefore, that the contribution of imaging to AG0¢ (het) is negligible. According to their data, AG0¢ is 16.4 kJ mol -~ for o-DCB and 18.8 kJ mol -~ for p-DCB; these results agree reasonably well with those presented above. One may estimate the work of solvent reorganization, and thus AG0~, independently on the basis of a simple extension of the Born model [17,18] provided that the charge distribution on the anion radical is known. From the calculations of Rieger and Fraenkel [19], 70% of the spin density on the anion radical is associated with the benzene ring and 15% with each of the cyanogroups for b o t h o-DCB and p-DCB. Thus, neglecting steric effects and imaging, one would expect Es to be approximately equal for the t w o isomers. On the basis of the results presented in Table 1, this is clearly not the case, unless the double layer effects are significantly different from those assumed in the Frumkin model and n o t the same for the t w o reactants. The above estimates of AGo~ are b o t h larger than the corresponding values of the real heat of activation. The difference is largest for o-DCB where AG0¢ = 17.5 kJ mo1-1 and ~ = 10 kJ mo1-1. This can be attributed to a negative entropy of activation reflecting the fact that the ortho-compound which possesses a high dipole m o m e n t is oriented b y the field of the electrode in the transition state. In the case of p-DCB the difference is smaller, AG0¢ being 20 kJ mol -~ and AH~¢, 17 kJ mo1-1 when NaC104 is the electrolyte. Although this molecule is probably oriented at the electrode because of its high polarizability along the axis through the cyano-groups [23], it can assume t w o equivalent orientations so that a less negative entropy of activation is expected. The above results serve to emphasize that the medium effects discussed here on the basis of the Frumkin model are actually much more complex.
Medium effects In a more complete description of medium effects one should consider (a) the possibility that the reaction site in the double layer is n o t on the outer Helmholtz plane (o.H.p.) [20], (b) ion-ion interactions involving the activated complex [8], and (c) the polarization energies of dipolar reactants and products [9]. These effects may be quantitatively included in the expression for the potential dependence of the rate constant for the simple reaction A+e-~B
(7)
192
in the following way: I n k = In ko -- (1 --~)(~A + H A ) / R T - - o ~ ( ~ B + I I B ) / R T + (cL --ZA)f(p r --afdp m
(8)
EA and "%B are electrostatic energies accounting for the interaction of A and B when t h e y are ions with other ions in their environment and with images formed in the conducting electrode; these terms account for the so-called discreteness-of-charge effect [8,21]. HA and HB are electrostatic polarization energies accounting for the fact t h a t A and B when t h e y are dipoles react in a region of non-zero field [9]. Cr is the average potential on the plane parallel to the electrode containing the charge centers of reactants A and B, and ZA is the valence of reactant A. ¢~ is related to the electrode potential ~m and the potential drop across the diffuse layer ~d by the expression [20] (9)
cr = cd + •(¢m __ c d )
where % is a dimensionless fraction depending on the average potential profile perpendicular to the electrode; % is positive when the reaction site is in the inner layer and negative when it is in the diffuse layer. Keeping in mind that the reactions being considered involve neutral reactants, EA and ZA are zero, and eqn. (8) m a y be written I n k = In k0 - - ( 1 -- o O I I A / R T - - a(EB + F I B ) / R T + ~f(1 -- ~)(¢d _ ~m)
(10)
If discreteness-of-charge and polarization effects are neglected (HA = FIB = ~B = 0) and the reaction site is assumed to be on the o.H.p. (~ = 0), it is apparent that eqn. (10) reduces to the relationship given by the Frumkin model (eqn. 2 at the standard potential). According to eqn. (10), the apparent transfer coefficient is given by 18 In k
~a =
~¢d
f 8¢m -~(l--l) --a(l--k) 8¢m +
(1 -- a) 8H A
F
8¢~+F
(x 8(EB + F[B)
~¢m
(II)
and is in general different from the true or intrinsic transfer coefficient a. The magnitude of the m e d i u m effects and their influence on the kinetic parameters reported above are n o w discussed in more detail. The electrode is assumed to be converted by a monolayer of solvent molecules approximately 0.4 n m thick. Non-adsorbed ions and reactant molecules approach the surface of the electrode such that their centers of mass are a distance (r + 0.4) n m from the electrode wall where r is the radius of a given species represented as a hard sphere. Since r is characteristic of molecular or ionic dimensions, it is obvious that the distance of closest approach of a given reactant x~ does n o t coincide in general with the distance of closest approach of the predominant counter ion Xd. Since the electrode is negatively charged and cations predominate at the o.H.p., increasing the solvated size of the cation for a fixed potential drop across the inner layer, Cm __ Ca results in the average potential at the reaction site becoming more negative, that is, an increase in (Fig. 3). This argument is valid both for reaction sites in the inner layer and in diffuse layer. Thus, as the size of the cation is increased in the series TEA * < TPA ÷ < TBA ÷, the electrostatic energy of the anion radical produced in reaction (1) becomes higher and the rate of reaction decreases (Fig. 1). At the s a m e time one would expect the apparent transfer coefficient to decrease in this
193
DIFFUSE LAYER
J J J J J
\-I
J J J J J J
¢'
~!
I i
l
DIFFUSE
LAYER
oJ
,,-j
- X d-----~ ~
J
S
J J
J
OHP
i OHP
Fig. 3. Variation in the p o t e n t i a l q~ at a reaction site n o t c o i n c i d e n t w i t h the o u t e r Helmh o l t z plane ( o . H . p . ) w i t h the p o s i t i o n o f the o.H.p, for a f i x e d p o t e n t i a l drop across the inner layer, (~m __ ~)d. The p o s i t i o n o f the o.H.p, at x = x d is varied b y changing the nature o f the c o u n t e r ion at the electrode.
series due to the corresponding increase in k (eqn. 11). The fact that a small increase is observed suggests that other factors are more important in determining the magnitude of ~,. Comparison of size effects between the TAA + cations and the alkali metal cations is difficult because these two groups of ions have quite different;effects on the local value of the dielectric constant and thus, on the average potential profile in the region of the o.H.p. Finally, it should be noted that cd is approximately independent of cation nature and that it varies little with potential in the region where o-DCB and p-DCB are reduced. For Na +, Li ÷, TPA ÷ and TBA+, ~d ~ --0.12 V at the standard potential for these reactions in 0.1 M salt solutions. This means that the corresponding kinetic data are being compared at the same values of ~bTM -- ~d so that the observed variation in k S cannot be attributed to a corresponding variation in Ca. The effects of ion-ion interactions are clearly evident from the variation in the slope of Arrhenius plots with cation nature (Fig. 2). If it is assumed that the reactants are in the orientation of minimum energy at the reaction site (Fig. 4), the ortho- and para-compounds could behave quite differently as far J J J
I ~
c-=N C=-N
p = 6,2 D
J
~J oj ~J ~w J
~
C---N
p = 4.0 D
J J
N;C ~ )
C;N
P: 0
J J
Fig. 4. Orientation o f various c y a n o b e n z e n e s at a negatively charged electrode. T h e d i p o l e m o m e n t in D e b y e s is indicated adjacent to the m o l e c u l e .
194
as interactions with neighbouring cations are concerned. From the calculations of Rieger and Fraenkel [19], the ring carbon atoms adjacent to the cyanogroups are the sites of highest spin density (~20% each) in the anion radicals of both compounds, and therefore, the most probable sites of interaction. In the case of o--DCB, this part of the molecule is furthest from the electrode in the region of lower electric field. Since the cyano-groups are probably located in the diffuse layer where the electric constant is approximately that in the bulk, ion-ion interactions are not strong. Thus, it follows t h a t the apparent heat of activation is independent of cation nature because these interactions are not an important factor in determining the activation barrier profile for electron transfer. In the case of p-DCB, one of the sites of high spin density is close to the electrode, presumably in the vicinity of the o.H.p, where the dielectric constant will be lower than in the bulk, and interactions with adjacent cations stronger. As the solvated size of a neighbouring cation decreases, its distance of closetst approach to the anion radical decreases and the interaction energy ~B becomes more negative [ 8]. The increase in AH~¢ observed experimentally ( T E A t < TBA ÷ ~ Na ÷) approximately follows the increase in solvated cation size estimated from Stokes' radii [22] (TEA ÷ < Na ÷ < TBA÷). The reversal in ordering of TBA ~ and Na ~ is probably due to the different influences of these ions on the dielectric permittivity of the medium in their vicinity; however, the Stokes' radius which is based on non-equilibrium measurements may n o t be a good estimate of ionic size in the double layer. The rate of reduction of p-DCB in the presence of TEA + is faster that it would have been in the absence of electrostatic interaction. Thus, data obtained in the presence of TEA ÷ are n o t suitable for comparison of free energies of activation since the reactants are affected to differing degrees by their environments. The same is true to a lesser e x t e n t for TBA ÷ and perhaps, also for Na ÷. Finally, on the basis of previous calculations [8], the interaction energy ~B probably does n o t change significantly with potential in the negative region where these reactions occur. It follows t h a t this effect has little influence on the value of the transfer coefficient ( ~ B / a cm ~ 0). The third effect considered here is the polarization energy of the molecular dipole in the field of the electrode. The energy of a molecule with dipole moment p in a local field ~e is equal to --P~e when the dipole is in the orientation of minimum energy. Since the field decreases rapidly with distance from the electrode this effect is only important for reactions which occur at the o.H.p. or closer to the electrode [9]. p-DCB has no permanent dipole m o m e n t but it is highly polarizable along the axis through the cyano-groups [23]. Therefore, the most probable orientation of the molecule is that shown in Fig. 4, but one may assume that the polarization energies HA and IIB are negligible for this reaction. On the other hand, o-DBC has a large permanent dipole m o m e n t 2.06 × 10 -29 Cm (6.2 Debyes). At the standard potential for this reaction, the charge density on the electrode is ~ --13 pC cm -2 and the field at the o.H.p., ~ 4 × 10 ~ V cm -1. The corresponding polarization energy for an o-DCB molecule experiencing this local field is 5 kJ mo1-1. The estimated dipole m o m e n t of the anion radical is 1.7 × 10 -29 Cm (5.2 Debyes) on the basis of Huckel molecular orbital t h e o r y [24], and the corresponding polarization energy, 4 kJ mo1-1. The revised estimate of AG0¢ on the basis of these polarization energies is 22 kJ mo1-1. On the other hand, assuming that the free energies of activation
195 for the ortho- and para-compounds are equal, o-DCB experiences a lower local field ( ~ 2 × 106 V cm-1), the contribution of polarization energy to AG0¢ being 2.5 kJ mo1-1 . Obviously, the magnitude of the dipolar effect is extremely difficult to estimate because of the rapid change in field with distance from the electrode, b u t the latter estimate seems reasonable on the basis of the data obtained in DMF. As the size of the cation at the o.H.p, increases, the local field at the reaction site increases (Fig. 3), and the rate constant for o-DCB increases with respect to that for p-DCB. Thus, the standard rate constant for o-DCB is 1.3 times larger than that for p-DCB when TEA* is the counter ion, b u t 2.5 times larger in the case of Li*. This effect is most pronounced in HMPA where the inner layer is thicker because of the increase in solvated counter ion size. When the dipolar effect is large, one expects a significant increase in the apparent transfer coefficent (eqn 11). Thus, the apparent transfer coefficient for electroreduction of o-DCB in HMPA is considerably larger than that for p-DCB. The dipolar effect u n d o u b t e d l y also affects the values of aa observed in DMF; for example, an increase in aa with cation size is observed for o-DCB with TAA* counter ions at the electrode. However, the effect is small and therefore, partially hidden by other effects such as the change in average potential at the reaction site with counter ion nature. Finally, since the double layer capacity is approximately independent of temperature for the Hg/DMF interface [15], HA and IIB should n o t vary significantly with temperature. Therefore, the revised estimate of ~ for o-DCB is 12.5 kJ mo1-1 after correction for dipolar effects.
Comparison with data for homogeneous electron transfer Kojima and Bard [3] estimated the free energies of activation for homogeneous electron transfer between a series of organic molecules and their anion radicals on the basis of data obtained earlier [2]. In the case of o-DCB and p-DCB, the values of AG0¢ (homo) were 13 kJ mo1-1 and 12 kJ tool -1, respectively. These estimates are considerably less than the values for the heterogeneous process obtained above and earlier [3]. According to the theories of electron transfer [4--6], one expects the heterogeneous free energy of activation to be less than or equal to the homogeneous value. It can be argued that this conclusion is based on an oversimplified model for the work of solvent reorganization Es in which it is assumed that the reactant or product may be represented as a sphere with charge distributed uniformly on its surface in a dielectric continuum. In more detailed models, the non-uniform charge distribution on the anion radical is accounted for b y representing this species as a collection of contiguous spheres, each of which bears a fraction of the total charge [17.18]. Calculations on the basis of a multiple sphere model with consideration of imaging effects according to Marcus [4] would result in values of Es (het) and E s (homo) which are much closer to one another than those obtained b y the simple model. This follows from the fact that imaging effects are greatly reduced because an oriented anion radical would have the majority of spin density on the part of the molecule which is furthest from the negatively charged electrode. Thus, the conclusion of Kojima and Bard [3] that AG0¢ (het) ~- AG0¢ (homo) is correct within the c o n t e x t of Marcus' theory [4] on the basis of
196 more detailed models for Es. However, electron transfer theory does not consider the contribution of orienting effects to AGo¢. Kowert et al. [2] argued that these effects play a role in the h o m o g e n e o u s process. They are undoubtedly more important in the heterogeneous process because of the high field at the reaction site. The resulting negative contribution to z~S0¢ may be the reason why AGo¢ (het) is somewhat larger than AG0¢ (homo) for the reactions considered here and those involving dipolar reactants studied earlier [3]. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
P . H . R i e g e r , I. B e r n a l , W . H . R e i n m u t h a n d G . K . F r a e n k e l , J . A m e r . C h e m . S o c . , 8 5 ( 1 9 6 3 ) 6 8 3 . B . A . K o w e r t , L. M a r c o u x a n d A . J . B a r d , J. A m e r . C h e m . S o c . , 9 4 ( 1 9 7 2 ) 5 5 3 8 . H . K o j i m a a n d A . J . B a r d , J. A m e r . C h e m . S o c . , 9 7 ( 1 9 7 5 ) 6 3 1 7 . R.A. Marcus, Ann. Rev. Phys. Chem., 15 (1964) 155. V.G. Levich, Advan. Electrochem. Eng., 4 (1966) 249. P.P. S c h m i d t in H . R . T h i r s k ( E d . ) , E l e c t r o c h e m i s t r y , S p e c i a l i s t P e r i o d i c a l R e p o r t s , V o l . 5, C h e m i c a l S o c i e t y , L o n d o n , 1 9 7 5 , C h . 2. P. D e l a h a y , D o u b l e L a y e r a n d E l e c t r o d e K i n e t i c s , W i l e y - I n t e r s c i e n c e , N e w Y o r k , 1 9 6 5 , C h . 9. W . R . F a w c e t t a n d S. L e v i n e , J . E l e c t r o a n a l . C h e m . , 6 5 ( 1 9 7 5 ) 5 0 5 . W.R. Fawcett and C.L. Gardner, J. Electroanal. Chem., 82 (1977) 303. W . R . F a w c e t t a n d A . Lasia, J . P h y s . C h e m . , 8 2 ( 1 9 7 8 ) 1 1 1 4 . J.E.B. Randles, Discuss. Faraday Soc., 1 (1947) 11. R. de Levie and A.A. Husovsky, J. Eleetroanal. Chem., 22 (1969) 29. B . G . C h a u h a n , W . R . F a w e e t t a n d A . Lasia, J . P h y s . C h e m . , 8 1 ( 1 9 7 7 ) 1 4 7 6 . Y a . D o y l i d o , R . V . I v a n o v a a n d B.B. D a m a s k i n , E l e k t r o k h i m i y a , 6 ( 1 9 7 0 ) 3. W . R . F a w c e t t , B.M. I k e d a a n d J . B . Sellan, C a n . J. C h e m . , i n press. M. T e m k i n , Z h . Fiz. K h i m . , 2 2 ( 1 9 4 8 ) 1 0 8 1 . M.E. P e o v e r a n d J . S . P o w e l l , J . E l e c t r o a n a l . C h e m . , 2 0 ( 1 9 6 9 ) 4 2 7 . W . R . F a w c e t t a n d Y u . I. K h a r k a t s , J . E l e c t r o a n a l . C h e m . , 4 7 ( 1 9 7 3 ) 4 1 3 . P . H . R i e g e r a n d G . K . F r a e n k e l , J. C h e m . P h y s . , 3 7 ( 1 9 6 2 ) 2 7 9 5 . W . R . F a w c e t t , J. E l e c t r o a n a l . C h e m . , 2 2 ( 1 9 6 9 ) 2 2 . W . R . F a w c e t t , J . C h e m . P h y s . , 61 ( 1 9 7 4 ) 3 8 4 2 . N. MatSuu~a, K . U m e m o t o a n d Y. T a k e d a , Bull. C h e m . S o c . J a p . , 4 8 ( 1 9 7 5 ) 2 2 5 3 . I.E. Coop and L.E. Sutton, J. Chem. Soc., (1938) 1269. C.L.Gardner, private communication. R.A. Marcus, J. Chem. Phys., 43 (1965) 670.
J. Electroanal. Chem., 100 (1979) 185--196 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
MEDIUM EFFECTS IN THE ELECTROREDUCTION OF CYANOBENZENES
A. BAR.~NSKI * and W.R. FAWCETT **
Guelph-Waterloo Centre for Graduate Work in Chemistry (Guelph Campus), Department of Chemistry, University of Guelph, Guelph, Ontario NIG 2W1 (Canada) (Received 29th January 1979)
ABSTRACT The kinetics of electroreduction of eyanobenzene, o-dicyanobenzene and p-dicyanobenzene at a dropping mercury electrode have been studied in various perchlorate salt solutions in dimethylformamide and hexamethylphosphoramide using a phase sensitive a.c. admittance technique. The standard rate constants, ks, were found to depend on the nature and concentration of the salt but there was no evidence for ion pair formation between the product anion radical and the cation of the electrolyte. The heat of activation for the electroreduction of the dicyanobenzenes determined by measuring the temperature dependence of k s in the range --12 to 36°C was independent of cation nature in the case of the ortho-compound but varied with electrolyte cation in the case of the para-compound. On the basis of a detailed analysis of medium effects it is concluded that the reaction site for these species is close to the outer Helmholtz plane, the dipolar reactants being oriented in the electrode's field. The dependence of the free energy of activation on the size of ions in the reaction environment, on their interaction with the transition state, and on polarization energy is discussed in detail.
INTRODUCTION
It has been shown [1 ] that the electroreduction of aromatic nitriles in aprotic solvents involves a one,electron reduction to the anion radical which is sufficiently stable in most cases to give an e.s.r, spectrum. This group of conpounds was among those considered b y Bard et al. [2,3] in their study of the kinetics of homogeneous and heterogeneous electron transfer to aromatic molecules. Kojima and Bard [3] discussed the kinetic data within the context of the Marcus-Levich-Hush models [4--6] for electron transfer and concluded that the free energies of activation for the homogeneous and heterogeneous processes are approximately equal when medium effects for the heterogeneous
* On leave from the Department of Chemistry, University of Warsaw, Warsaw, Poland. ** To w h o m correspondence should be addressed.
186
process are estimated on the basis of the Frumkin model [7]. However, the Frumkin model ignores the effects of ion-ion interactions at the reaction site [8], and of the polarization energy of dipolar species [9] on the rate constant and its variation with potential. These effects are difficult to estimate quantitatively b u t would be expected to result in a change in rate with the nature of the base electrolyte and the magnitudes of the dipole m o m e n t s of the reactant and product. Accordingly, the free energy of activation for the heterogeneous process estimated by the Frumkin model is not entirely due to solvent reorganization b u t contains an undetermined contribution from local ion-ion interactions and dipolar effects. One way of obtaining an estimate of these effects is to compare kinetic data for the various isomers of disubstituted benzenes. A convenient pair of reactants are o-dicyanobenzene and p
Heterogeneous rate data were obtained using the phase sensitive a.c. impedance technique described elsewhere [10]. The reference electrode system was redesigned in order to reduce the resistance in the potentiostat circuit and eliminate the requirement for two reference electrodes [10]. The reference electrode consisted of a silver wire dipping into a solution of 0.05 M AgNO3 and 0.05 M tetraethylammonium perchlorate (TEAP) in an aprotic solvent (dimethylformamide (DMF) or hexamethylphosphoramide (HMPA)), the liquid-liquid junction with the working solution being made in a fine fritted glass disc. The silver solution in DMF was replaced daily because of the instability of Ag * to photoreduction in this solvent. The Luggin capillary at the end of the reference electrode system was designed so that its tip could be placed reproducibly at a position approximately 1 mm away from the working electrode (dropping mercury electrode). There was no evidence that Ag ÷ had diffused from the reference electrode c o m p a r t m e n t to the main b o d y of the cell during the period for which current-voltage measurements were made. The counter electrode was platinum foil with an area of - 5 cm 2. Current-potential data were obtained at the peak potential as a function of frequency of the a.c. signal (160 ~< f~< 860 Hz-'), and in the vicinity of the peak potential (--50 mV ~< ~ ~< 50 mV) at a fixed frequency. The solution resistance and double layer capacitance were found b y estimating the a.c. admittance of the system in the potential range of interest b y interpolation from values obtained at potentials where no faradaic current flowed. Admittance data at peak potential were analyzed b y Randles' m e t h o d [11], and those obtained as a function of potential b y the m e t h o d of the Levie and Husovsky [12] as described previously [10].
187 Procedures for purification of the salts and DMF are described elsewhere [13]. The HMPA was dried over 4A molecular sieves and distilled at a reduced pressure (~3 mm) under a nitrogen atmosphere. The dicyanobenzenes (DCB) were purified by recrystallization from ethanol and cyanobenzene (CB) or benzonitrile by distillation. All experiments were carried out in a controlled atmosphere chamber maintained at 25 + 0.5 ° C. Experiments at other temperatures in the range --12 to 36°C were conducted in a cell in which the working compartment was surrounded by a glass chamber through which methanol maintained at the desired temperature was circulated. The reference electrode compartment was always kept at 25 ° C. The concentration of depolarizer was 5 × 10 -4 M in DMF solutions and 2 X 10 -3 M in HMPA solutions. RESULTS The reversibility of the electroreduction of the cyanobenzenes was ascertained by cyclic voltammetry performed at a hanging mercury drop electrode. The current-potential curves for CB, o-DCB, and p-DCB had a peak current on the reverse anodic sweep approximately equal to that for the forward cathodic sweep indicating t h a t the radical anion formed on reduction of the parent molecule is stable within the time scale of the experiment. In the case of m-DCB, the anodic peak current was considerably less than the cathodic peak cdrtent indicating t h a t some of the radical anions underwent chemical reaction. A similar conclusion was reached earlier by Rieger et al. [1] on the basis of their e.s.r, study of nitrile radicals. For this reason, m-DCB was n o t included in the kinetic study. The absence of significant ion pairing between anion radicals and the cation of the base electrolyte was ascertained by determining the dependence of the polarographic half-wave potential El/2 on cation nature and concentration for solutions of 1--1 electrolytes in DMF. E1/2 was independent of cation nature within experimental error (-+2 mV) for 0.1 M solutions of TEAP, tetrapropyla m m o n i u m perchlorate (TPAP), t e t r a b u t y l a m m o n i u m perchlorate (TBAP), LiCIO4, and NaCIO4. The values observed, --2.025 V for p-DCB, --2.085 V for o-DCB, and --2.775 V for CB agree well with those reported by Rieger et al. [1]. Variation in the concentration of the electrolyte in the range 0.01 and 0.1 M resulted in a shift in E,/2 by ~16 mV in the positive direction; this observation can be attributed to a change in the liquid junction potential between the working and reference electrode compartments and in the activity of the anion radical with change in ionic strength [13]. The kinetic data obtained in 0.1 M solutions in DMF and HMPA are summarized in Table 1. In all cases, the standard rate constant ks for p-DCB is less than that for o-DCB, the ratio of these rate constants depending on both electrolyte and solvent nature. The rate constant for reduction of CB, which can only be measured in tetraalkylammonium (TAA÷) salt solutions because of its negative reduction potential, lies between those for o-DCB and p-DCB. The rate constants for a given cyanobenzene decrease with increase in the size of the TAA* cation. In the case of Na+and Li+electrolytes, the rate constants are approximately equal for a given reactant, but they are significantly larger in MgCIO4. Unfortunately, kinetic data obtained in the presence of K÷and Cs*
188 TABLE 1 A summary of kinetic data for the electroreduction of cyanobenzenes at mercury in dimethylformamide (DMF) and hexamethylphosphoramide (HMPA) with various electrolytes (concentration = 0.1 M) at 25°C Electrolyte
p-DCB
TEA1) in DMF TPAP in DMF TBAP in DMF LiCIO4 in DMF NaC104 in DMF MgC104 in DMF LiCl04 in HMPA
o-DCB
CB
ks/cms-I
~
k s / c m s -1
~
k s / c m s -1
0.57 0.30 0.22 0.13 0.12 0.36 0.006
0.49 0.49 0.50 0.57 0.57 0.47 0.53
0.75 0.44 0.32 0.33 0.33 0.80 0.039
0.49 0.51 0.53 0.57 0.57 0.50 0.67
0.58 0.34 0.30 -----
0.48 0.53 0.53 -----
cannot be compared directly with those presented in Table 1 because these cations are specifically a d s o r b e d at m e r c u r y in the p o t e n t i a l range of in te r e s t [ 1 4 , 1 5 ] . W h e n t h e s o l v e n t is c h a n g e d f r o m D M F t o H M P A , a c o n s i d e r a b l e r e d u c t i o n i n t h e r a t e Of r e a c t i o n is o b s e r v e d . T h e t r a n s f e r c o e f f i c i e n t ~, d e t e r m i n e d f r o m t h e v a r i a t i o n i n t h e r a t e c o n s t a n t w i t h e l e c t r o d e p o t e n t i a l , is c l o s e t o 0 . 5 f o r m o s t s y s t e m s . A n i n c r e a s e i n a is f o u n d w h e n T A A ÷ salts are
t
!
i
l
|
p - DI CYANOBENZENE
E
£
\ °°\\o --.<-.
\ o
!
- 0.12
I
!
- 0.16
I
-0.12
!
\o - 01.16
Fig. 1. Logarithm of the standard rate constant, log ks, for the electroreduction of o-dicyanobenzene and p-dicyanobenzene obtained in dimethylformamide at a Hg electrode in the presence of various tetraalkylammonium perchlorate salts plotted against the potential drop across the diffuse layer ~bd. The nature of the tetraalkylammonium cation is indicated adjacent to each plot.
189
replaced by LiC104 or NaCIO4 in DMF. In the case of LiC104 in HMPA, e is significantly larger for the polar reactant o-DCB. The variation in standard rate constant with salt concentration, and thus, with the potential drop across the diffuse layer ~d is illustrated in Fig. 1. Values of ~d were calculated from charge-potential data for the Hg/DMF interface at equilibrium [15] using the Gouy-Chapman theory. Since the electrode reaction
(I)
R+e~R-"
involves a negatively charged product, the reaction rate decreases as ~bd becomes more negative. According to the Frumkin model for double layer effects [ 7], the variation in ks with ca for a reaction involving an uncharged reactant is given by In k s
:
In ho + af(dP d - - dPTM)
(2)
where k 0 is the potential independent contribution to ks, 0F, the inner potential of the electrode and f = F / R T . Thus, when the ionic strength is changed, the electrode potential being maintained at the standard potential, 1 [a In ks~
=
(3)
Values of ~ determined from the slopes of plots like those in Fig. 1 are approximately 20% higher than those reported in Table 1 but follow the same trends. They are definitely not as reliable quantitatively because estimates of a from the double layer effect rely heavily on the estimate of cd which are based on 1
i
i
-0.2 O~TEA*
o-
TEA*
o
E
TBA*
U~O~
o -1.0 p -DICYANOBENZENE o ~ , ~
o- DICYANOBENZENE I
'
I 3.4
I 3.8
10 3 T ~ 1 / K -1
Fig. 2. Arrhenius plots of kinetic data for the electroreduction of dicyanobenzenes at Hg in various 0.1 M perchlorate salt solutions in dimethylformamide. The nature of the cation is indicated adjacent to each plot.
190 Gouy-Chapman theory, and on the assumptions of the Frumkin model. These assumptions are discussed in more detail below. The variations in ks with temperature is shown in Fig. 2 for o-DCB and p-DCB. In the case of the ortho-compound the slope of the Arrthenius plots is approximately independent of the nature of the base electrolyte cation whereas for p-DCB, it increase in the order TEA + < TBA ~ < Na +. This indicates a corresponding decrease in interaction of the surrounding cation with the transition state of the reaction. On the basis of the simple theory of double layer effects, the real heat of activation [16], AH~¢ is given by [10] A/-/~ = --R ~ In ks ~(1/T)
RT + ~F~(¢d/T) 2 ~(1/T}
(4)
As shown previously [10], the variation in cd with temperature on the basis of the appropriate double layer data [15] is such that ~(~)d/T)/a(1/T) = 0.010 V. The estimated real heat of activation for o-DCB assuming ~ = 0.5 is 10.0 + 0.2 kJ mo1-1. In the case o f p - D C B , AH~¢ increases from 9 kJ mo1-1 in the presence of TEA + in DMF to 17 kJ mol -~ when NaC104 is the electrolyte. These results suggest that the ortho-compound is oriented in the double layer such that its interaction with surrounding cations does n o t vary significantly with cation nature; on the other hand, the transition state for the reduction of p-DCB is affected by surrounding cations such that the barrier height increases with solvated cation size, that is, with an increase in distance between the interacting species. DISCUSSION
Tke kinetic parameters Kojima and Bard [3] obtained kinetic data for the electroreduction of cyanobenzenes in 0.5 M TBAP in DMF. As one would expect, the standard r a t e constants are higher than those reported in Table 1 because of the change in ionic strength. Estimates of ks at 0.5 M obtained b y extrapolating the data in Fig. 1 agree reasonably well with those of Kojima and Bard [3] except in the case of o-DCB. The values of ~ reported by these authors for CB and o-DCB are significantly higher than those presented in Table 1. These differences can be attributed to different methods of data analysis, the earlier m e t h o d [3] being based on a determination of the potential Emax at which the cotangent of the phase angle of the a.c. current is a maximum. It is easily shown from a statistical analysis of the functional relationship between ~ and Emax that one would expect greater scatter in values of ~ determined this way than b y the m e t h o d used here and described earlier [10]. Assuming that ion-ion interactions at the reaction site are minimal in the presence of Li + and Na +, these kinetic data are the most appropriate to consider within the context of the Marcus-Levich-Hush t h e o r y of electron transfer [4--6]. The standard free energy of activation is given b y [3,10]
AGCo = R T ln(~Ze/ks) + (~F¢ d where ~ is the transmission coefficient assumed to equal unity and Ze, the
(5)
191
heterogeneous collision frequency. Following Marcus [25], Ze is assumed to equal (R T/27rM)'/2 where M is the molecular weight of the reactant. For o-DCB and p-DCB, Ze = 5.55 × 103 cm s -1, and AG0¢ = 17.5 and 20 kJ m o l - ' , respectively. According to the same model, the solvent reorganization energy E s is equal to 4AG0¢ and the transfer coefficient at the standard potential is given by = 0.5 -- FCd/2Es
(6)
Accordingly, the predicted values of a, 0.64 for p-DCB and 0.66 for o-DCB, are somewhat higher than those obtained experimentally. No potential dependence of a which is predicted b y these theories was observed in the small potential range in which reliable data could be obtained. Kojima and Bard [3] concluded that the free energies of activation for homogeneous electron transfer involving systems similar to those considered here are equal, and therefore, that the contribution of imaging to AG0¢ (het) is negligible. According to their data, AG0¢ is 16.4 kJ mol -~ for o-DCB and 18.8 kJ mol -~ for p-DCB; these results agree reasonably well with those presented above. One may estimate the work of solvent reorganization, and thus AG0~, independently on the basis of a simple extension of the Born model [17,18] provided that the charge distribution on the anion radical is known. From the calculations of Rieger and Fraenkel [19], 70% of the spin density on the anion radical is associated with the benzene ring and 15% with each of the cyanogroups for b o t h o-DCB and p-DCB. Thus, neglecting steric effects and imaging, one would expect Es to be approximately equal for the t w o isomers. On the basis of the results presented in Table 1, this is clearly not the case, unless the double layer effects are significantly different from those assumed in the Frumkin model and n o t the same for the t w o reactants. The above estimates of AGo~ are b o t h larger than the corresponding values of the real heat of activation. The difference is largest for o-DCB where AG0¢ = 17.5 kJ mo1-1 and ~ = 10 kJ mo1-1. This can be attributed to a negative entropy of activation reflecting the fact that the ortho-compound which possesses a high dipole m o m e n t is oriented b y the field of the electrode in the transition state. In the case of p-DCB the difference is smaller, AG0¢ being 20 kJ mol -~ and AH~¢, 17 kJ mo1-1 when NaC104 is the electrolyte. Although this molecule is probably oriented at the electrode because of its high polarizability along the axis through the cyano-groups [23], it can assume t w o equivalent orientations so that a less negative entropy of activation is expected. The above results serve to emphasize that the medium effects discussed here on the basis of the Frumkin model are actually much more complex.
Medium effects In a more complete description of medium effects one should consider (a) the possibility that the reaction site in the double layer is n o t on the outer Helmholtz plane (o.H.p.) [20], (b) ion-ion interactions involving the activated complex [8], and (c) the polarization energies of dipolar reactants and products [9]. These effects may be quantitatively included in the expression for the potential dependence of the rate constant for the simple reaction A+e-~B
(7)
192
in the following way: I n k = In ko -- (1 --~)(~A + H A ) / R T - - o ~ ( ~ B + I I B ) / R T + (cL --ZA)f(p r --afdp m
(8)
EA and "%B are electrostatic energies accounting for the interaction of A and B when t h e y are ions with other ions in their environment and with images formed in the conducting electrode; these terms account for the so-called discreteness-of-charge effect [8,21]. HA and HB are electrostatic polarization energies accounting for the fact t h a t A and B when t h e y are dipoles react in a region of non-zero field [9]. Cr is the average potential on the plane parallel to the electrode containing the charge centers of reactants A and B, and ZA is the valence of reactant A. ¢~ is related to the electrode potential ~m and the potential drop across the diffuse layer ~d by the expression [20] (9)
cr = cd + •(¢m __ c d )
where % is a dimensionless fraction depending on the average potential profile perpendicular to the electrode; % is positive when the reaction site is in the inner layer and negative when it is in the diffuse layer. Keeping in mind that the reactions being considered involve neutral reactants, EA and ZA are zero, and eqn. (8) m a y be written I n k = In k0 - - ( 1 -- o O I I A / R T - - a(EB + F I B ) / R T + ~f(1 -- ~)(¢d _ ~m)
(10)
If discreteness-of-charge and polarization effects are neglected (HA = FIB = ~B = 0) and the reaction site is assumed to be on the o.H.p. (~ = 0), it is apparent that eqn. (10) reduces to the relationship given by the Frumkin model (eqn. 2 at the standard potential). According to eqn. (10), the apparent transfer coefficient is given by 18 In k
~a =
~¢d
f 8¢m -~(l--l) --a(l--k) 8¢m +
(1 -- a) 8H A
F
8¢~+F
(x 8(EB + F[B)
~¢m
(II)
and is in general different from the true or intrinsic transfer coefficient a. The magnitude of the m e d i u m effects and their influence on the kinetic parameters reported above are n o w discussed in more detail. The electrode is assumed to be converted by a monolayer of solvent molecules approximately 0.4 n m thick. Non-adsorbed ions and reactant molecules approach the surface of the electrode such that their centers of mass are a distance (r + 0.4) n m from the electrode wall where r is the radius of a given species represented as a hard sphere. Since r is characteristic of molecular or ionic dimensions, it is obvious that the distance of closest approach of a given reactant x~ does n o t coincide in general with the distance of closest approach of the predominant counter ion Xd. Since the electrode is negatively charged and cations predominate at the o.H.p., increasing the solvated size of the cation for a fixed potential drop across the inner layer, Cm __ Ca results in the average potential at the reaction site becoming more negative, that is, an increase in (Fig. 3). This argument is valid both for reaction sites in the inner layer and in diffuse layer. Thus, as the size of the cation is increased in the series TEA * < TPA ÷ < TBA ÷, the electrostatic energy of the anion radical produced in reaction (1) becomes higher and the rate of reaction decreases (Fig. 1). At the s a m e time one would expect the apparent transfer coefficient to decrease in this
193
DIFFUSE LAYER
J J J J J
\-I
J J J J J J
¢'
~!
I i
l
DIFFUSE
LAYER
oJ
,,-j
- X d-----~ ~
J
S
J J
J
OHP
i OHP
Fig. 3. Variation in the p o t e n t i a l q~ at a reaction site n o t c o i n c i d e n t w i t h the o u t e r Helmh o l t z plane ( o . H . p . ) w i t h the p o s i t i o n o f the o.H.p, for a f i x e d p o t e n t i a l drop across the inner layer, (~m __ ~)d. The p o s i t i o n o f the o.H.p, at x = x d is varied b y changing the nature o f the c o u n t e r ion at the electrode.
series due to the corresponding increase in k (eqn. 11). The fact that a small increase is observed suggests that other factors are more important in determining the magnitude of ~,. Comparison of size effects between the TAA + cations and the alkali metal cations is difficult because these two groups of ions have quite different;effects on the local value of the dielectric constant and thus, on the average potential profile in the region of the o.H.p. Finally, it should be noted that cd is approximately independent of cation nature and that it varies little with potential in the region where o-DCB and p-DCB are reduced. For Na +, Li ÷, TPA ÷ and TBA+, ~d ~ --0.12 V at the standard potential for these reactions in 0.1 M salt solutions. This means that the corresponding kinetic data are being compared at the same values of ~bTM -- ~d so that the observed variation in k S cannot be attributed to a corresponding variation in Ca. The effects of ion-ion interactions are clearly evident from the variation in the slope of Arrhenius plots with cation nature (Fig. 2). If it is assumed that the reactants are in the orientation of minimum energy at the reaction site (Fig. 4), the ortho- and para-compounds could behave quite differently as far J J J
I ~
c-=N C=-N
p = 6,2 D
J
~J oj ~J ~w J
~
C---N
p = 4.0 D
J J
N;C ~ )
C;N
P: 0
J J
Fig. 4. Orientation o f various c y a n o b e n z e n e s at a negatively charged electrode. T h e d i p o l e m o m e n t in D e b y e s is indicated adjacent to the m o l e c u l e .
194
as interactions with neighbouring cations are concerned. From the calculations of Rieger and Fraenkel [19], the ring carbon atoms adjacent to the cyanogroups are the sites of highest spin density (~20% each) in the anion radicals of both compounds, and therefore, the most probable sites of interaction. In the case of o--DCB, this part of the molecule is furthest from the electrode in the region of lower electric field. Since the cyano-groups are probably located in the diffuse layer where the electric constant is approximately that in the bulk, ion-ion interactions are not strong. Thus, it follows t h a t the apparent heat of activation is independent of cation nature because these interactions are not an important factor in determining the activation barrier profile for electron transfer. In the case of p-DCB, one of the sites of high spin density is close to the electrode, presumably in the vicinity of the o.H.p, where the dielectric constant will be lower than in the bulk, and interactions with adjacent cations stronger. As the solvated size of a neighbouring cation decreases, its distance of closetst approach to the anion radical decreases and the interaction energy ~B becomes more negative [ 8]. The increase in AH~¢ observed experimentally ( T E A t < TBA ÷ ~ Na ÷) approximately follows the increase in solvated cation size estimated from Stokes' radii [22] (TEA ÷ < Na ÷ < TBA÷). The reversal in ordering of TBA ~ and Na ~ is probably due to the different influences of these ions on the dielectric permittivity of the medium in their vicinity; however, the Stokes' radius which is based on non-equilibrium measurements may n o t be a good estimate of ionic size in the double layer. The rate of reduction of p-DCB in the presence of TEA + is faster that it would have been in the absence of electrostatic interaction. Thus, data obtained in the presence of TEA ÷ are n o t suitable for comparison of free energies of activation since the reactants are affected to differing degrees by their environments. The same is true to a lesser e x t e n t for TBA ÷ and perhaps, also for Na ÷. Finally, on the basis of previous calculations [8], the interaction energy ~B probably does n o t change significantly with potential in the negative region where these reactions occur. It follows t h a t this effect has little influence on the value of the transfer coefficient ( ~ B / a cm ~ 0). The third effect considered here is the polarization energy of the molecular dipole in the field of the electrode. The energy of a molecule with dipole moment p in a local field ~e is equal to --P~e when the dipole is in the orientation of minimum energy. Since the field decreases rapidly with distance from the electrode this effect is only important for reactions which occur at the o.H.p. or closer to the electrode [9]. p-DCB has no permanent dipole m o m e n t but it is highly polarizable along the axis through the cyano-groups [23]. Therefore, the most probable orientation of the molecule is that shown in Fig. 4, but one may assume that the polarization energies HA and IIB are negligible for this reaction. On the other hand, o-DBC has a large permanent dipole m o m e n t 2.06 × 10 -29 Cm (6.2 Debyes). At the standard potential for this reaction, the charge density on the electrode is ~ --13 pC cm -2 and the field at the o.H.p., ~ 4 × 10 ~ V cm -1. The corresponding polarization energy for an o-DCB molecule experiencing this local field is 5 kJ mo1-1. The estimated dipole m o m e n t of the anion radical is 1.7 × 10 -29 Cm (5.2 Debyes) on the basis of Huckel molecular orbital t h e o r y [24], and the corresponding polarization energy, 4 kJ mo1-1. The revised estimate of AG0¢ on the basis of these polarization energies is 22 kJ mo1-1. On the other hand, assuming that the free energies of activation
195 for the ortho- and para-compounds are equal, o-DCB experiences a lower local field ( ~ 2 × 106 V cm-1), the contribution of polarization energy to AG0¢ being 2.5 kJ mo1-1 . Obviously, the magnitude of the dipolar effect is extremely difficult to estimate because of the rapid change in field with distance from the electrode, b u t the latter estimate seems reasonable on the basis of the data obtained in DMF. As the size of the cation at the o.H.p, increases, the local field at the reaction site increases (Fig. 3), and the rate constant for o-DCB increases with respect to that for p-DCB. Thus, the standard rate constant for o-DCB is 1.3 times larger than that for p-DCB when TEA* is the counter ion, b u t 2.5 times larger in the case of Li*. This effect is most pronounced in HMPA where the inner layer is thicker because of the increase in solvated counter ion size. When the dipolar effect is large, one expects a significant increase in the apparent transfer coefficent (eqn 11). Thus, the apparent transfer coefficient for electroreduction of o-DCB in HMPA is considerably larger than that for p-DCB. The dipolar effect u n d o u b t e d l y also affects the values of aa observed in DMF; for example, an increase in aa with cation size is observed for o-DCB with TAA* counter ions at the electrode. However, the effect is small and therefore, partially hidden by other effects such as the change in average potential at the reaction site with counter ion nature. Finally, since the double layer capacity is approximately independent of temperature for the Hg/DMF interface [15], HA and IIB should n o t vary significantly with temperature. Therefore, the revised estimate of ~ for o-DCB is 12.5 kJ mo1-1 after correction for dipolar effects.
Comparison with data for homogeneous electron transfer Kojima and Bard [3] estimated the free energies of activation for homogeneous electron transfer between a series of organic molecules and their anion radicals on the basis of data obtained earlier [2]. In the case of o-DCB and p-DCB, the values of AG0¢ (homo) were 13 kJ mo1-1 and 12 kJ tool -1, respectively. These estimates are considerably less than the values for the heterogeneous process obtained above and earlier [3]. According to the theories of electron transfer [4--6], one expects the heterogeneous free energy of activation to be less than or equal to the homogeneous value. It can be argued that this conclusion is based on an oversimplified model for the work of solvent reorganization Es in which it is assumed that the reactant or product may be represented as a sphere with charge distributed uniformly on its surface in a dielectric continuum. In more detailed models, the non-uniform charge distribution on the anion radical is accounted for b y representing this species as a collection of contiguous spheres, each of which bears a fraction of the total charge [17.18]. Calculations on the basis of a multiple sphere model with consideration of imaging effects according to Marcus [4] would result in values of Es (het) and E s (homo) which are much closer to one another than those obtained b y the simple model. This follows from the fact that imaging effects are greatly reduced because an oriented anion radical would have the majority of spin density on the part of the molecule which is furthest from the negatively charged electrode. Thus, the conclusion of Kojima and Bard [3] that AG0¢ (het) ~- AG0¢ (homo) is correct within the c o n t e x t of Marcus' theory [4] on the basis of
196 more detailed models for Es. However, electron transfer theory does not consider the contribution of orienting effects to AGo¢. Kowert et al. [2] argued that these effects play a role in the h o m o g e n e o u s process. They are undoubtedly more important in the heterogeneous process because of the high field at the reaction site. The resulting negative contribution to z~S0¢ may be the reason why AGo¢ (het) is somewhat larger than AG0¢ (homo) for the reactions considered here and those involving dipolar reactants studied earlier [3]. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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