20114
J. Phys. Chem. 1996, 100, 20114-20121
Photoelectrochemical Reaction Mechanisms. The Photoelectrocatalytic Reduction of 4-Chlorobiphenyl Wayne M. Leslie and Richard G. Compton* Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, U.K.
Toomas Silk Faculty of Physics and Chemistry, Tartu UniVersity, Jakobi 2, EE2400 Tartu, Estonia ReceiVed: August 2, 1996; In Final Form: October 14, 1996X
Channel electrode methodology is used to study the photoelectrocatalytic reduction of 4-chlorobiphenyl (CBP) in acetonitrile solution using 9,10-diphenylanthracene (DPA) as a mediator. The latter is reduced at a lower potential than is required for the direct reduction of the substrate, and the resulting radical anion, DPA•-, when photoexcited irreversibly transfers an electron to CBP. The mechanism of the reaction is explored, and it is shown that in addition to the catalytic reduction of the biphenyl by excited state DPA•- the latter also undergoes quenching by DPA and photoinduced disproportionation leading to the dianion, DPA2-, which undergoes irreversible chemical transformation. Kinetic parameters are reported.
Introduction It has been argued1 that electrochemical transformations can be beneficially enhanced, or usefully modified, through the introduction of light close to the electrode surface, so giving the possibility of the dual actiVation of target species. Specifically it may be speculated that the sequential use of electrochemical and photochemical activation of organic and organometallic molecules may lead to a wealth of hitherto unsuspected chemistry including novel mechanistic pathways, the discovery of new compounds associated with unusual reactive intermediates, and ultimately new synthetic routes. In our previous studies we have advocated the channel electrode approach (Figure 1) for the kinetic and mechanistic investigation of photoelectrochemical pathways1,2 and reported results in a variety of systems including aryl halides,3 cobalt dithiocarbamates,4 bis(cyclopentadienyl) metal dichlorides,5 iron phosphine complexes,6 and heteropoly anion clusters.7 In particular the variation of the channel electrode photocurrent with mass transport (solution flow rate), coupled to spectroelectrochemical measurementsssuch as ESR or fluorescence1,2smade using the same cell has been shown to be particularly powerful with respect to the characterization of photoelectrochemical mechanisms. In this paper we examine the photoelectroreduction of 4-chlorobiphenyl (CBP) using the radical anion of 9,10-
DPA
loss of the mediator via reactions of DPA2- so that the overall mechanism is
CBP
diphenylanthracene (DPA) as a mediator. The latter is thought to absorb light, and the resulting excited state transfers an electron to CBP. The rapid fragmentation of the latter ensures the irreversibility of the electron transfer, which results in the dechlorination of the substrate.8 It is demonstrated that the channel electrode approach can provide a detailed mechanism for the reaction. Specifically the excited state will be shown, in addition to undergoing electron transfer with CBP, to be quenched by the parent DPA molecule and also to undergo lightinduced disproportionation, leading to the chemically irreversible X
Abstract published in AdVance ACS Abstracts, December 1, 1996.
S0022-3654(96)02341-6 CCC: $12.00
DPA + e- f DPA•-
(i)
DPA•- + hν f [DPA•-]*
(ii)
[DPA•-]* f DPA•-
(iii)
[DPA•-]* + CBP f DPA + products
(iv)
[DPA•-]* + DPA f DPA•- + DPA
(v)
[DPA•-]* + DPA•- f DPA2- + DPA
(vi)
DPA2- + DPA f 2DPA•-
(vii)
DPA2- f products
(viii)
To interrogate this complex system, the theory of catalytic reactions at the channel electrode requires development as addressed in the following section. Theory We consider first the generalized electrode reaction mechanism defined by steps i-viii above and then focus on various limiting cases of interest. To simplify the notation, we denote DPA by A, DPA•- by B, [DPA•-]* by B*, DPA2- by C, and CBP by P. The convective-diffusion equations describing the distributions of A, B, B*, C, and P in time (t) and space (x,y) © 1996 American Chemical Society
Photoelectrocatalytic Reduction of 4-Chlorobiphenyl
J. Phys. Chem., Vol. 100, No. 51, 1996 20115
k(ii)[B] ) k(iii)[B*] + k(vi)[B][B*] + k(v)[A][B*] + k(iv)[B*][P] (8) so that
[B*] )
k(ii)[B]
(9)
k(iii) + k(vi)[B] + k(v)[A] + k(iv)[P]
Similarly for C, Figure 1. Practical channel flow cell for mechanistic photoelectrochemical studies.
k(vi)[B][B*] ) k(vii)[A][C] + k(viii)[C] giving
within a channel electrode flow cell are
∂[A] ∂2[A] ∂[A] ) DA 2 - Vx + k(vi)[B][B*] - k(vii)[A][C] + ∂t ∂x ∂y k(iv)[B*][P] (1) 2
∂[B] ∂ [B] ∂[B] ) DB 2 - Vx + k(iii)[B*] + k(v)[A][B*] + ∂t ∂x ∂y 2k(vii)[A][C] - k(vi)[B][B*] - k(ii)[B] (2) ∂[B*] ∂2[B*] ∂[B*] - Vx ) DB* + k(ii)[B] - k(iii)[B*] 2 ∂t ∂x ∂y k(vi)[B][B*] - k(v)[A][B*] - k(iv)[B*][P] (3)
[C] )
∂[C] ∂ [C] ∂[C] ) DC 2 - Vx + k(vi)[B][B*] - k(vii)[A][C] ∂t ∂x ∂y k(viii)[C] (4)
(k(viii) + k(vii)[A])(k(iii) + k(vi)[B] + k(v)[A] + k(iv)[P])
(
h2
)
(5)
(6)
where h is the half-height of the cell and V0 is the solution velocity at the center of the channel. Equations 1-4 assume that axial diffusion effects may be neglected; this is valid provided the electrodes considered are not of microelectrode dimensions.10 Further simplifications are possible. The first results since we examine the case of steady-state experiments only so that
∂[L] )0 ∂t
+
k(ii)k(iv)[B][P] (k(iii) + k(iv)[P] + k(v)[A] + k(vi)[B]) 0 ) DB
∂2[B] ∂y
2
- Vx
(7)
Second it is possible to locally apply the steady-state approximation to suitably kinetically labile species;11 the following develops the implications of this for the general SID-QC mechanism defined by reactions i-viii above. If we apply the steady-state approximation to B*, then
(k(viii) + k(vii)[A])(k(iii) + k(vi)[B] + k(v)[A]) + k(iv)[P]) k(ii)k(iv)[B][P] (k(iii) + k(iv)[P] + k(v)[A] + k(vi)[B]) 0 ) DP
(12)
∂[B] ∂x 2k(ii)k(vi)k(viii)[B]2
where DL is the diffusion coefficients of species L ()A, B, B*, C or P), k(n) is the rate constant for reaction (n) of the general scheme in the Introduction, and the Cartesian coordinates x and y can be understood with reference to Figure 31 in ref 1. Vx is the solution velocity in the x-direction; the components in the y- and z-directions are zero. Given laminar flow conditions and that a sufficiently long lead-in length exists upstream of the electrodes so as to allow the full development of Poiseuille flow, then Vx is parabolic:9
(h - y)2
(11)
k(viii) + k(vii)[A]
∂2[A] ∂[A] 0 ) DA 2 - Vx + ∂x ∂y k(ii)k(vi)k(viii)[B]2
2
∂[P] ∂ [P] ∂[P] ) DP 2 - Vx - k(iv)[P][B*] ∂t ∂x ∂y
k(vi)[B][B*]
Thus the mass transport equations for the general mechanism simplify under these conditions to
2
Vx ) V0 1 -
(10)
(13)
∂2[P]
k(ii)k(iv)[B][P] ∂[P] - Vx ∂x (k(iii) + k(iv)[P] + k(v)[A] + k(vi)[B]) ∂y (14) 2
The above transport equations can be solved provided appropriate boundary conditions are specified for the different species. For the situation where the transport-limited current for the discharge of A is flowing these are as follows. Boundary Conditions for Species A: x ) 0; 0 < x < xe; all x;
[A] ) [A]bulk [A] ) 0 ∂[A]/∂y ) 0
all y; y ) 0; y ) 2h
Boundary Conditions for Species B: x ) 0; 0 < x < xe; all x;
all y; y ) 0; y ) 2h
[B] ) 0 DB∂[B]/∂y ) -DA∂[A]/∂y ∂[B]/∂y ) 0
Boundary Conditions for Species P: x ) 0; 0 < x < xe; all x;
all y; y ) 0; y ) 2h
[P] ) [P]bulk DP∂[P]/∂y ) 0 ∂[P]/∂y ) 0
The mass transport equations 1-14 can be readily solved for
20116 J. Phys. Chem., Vol. 100, No. 51, 1996
Leslie et al.
the above boundary conditions by direct application of an implicit finite-difference method previously advocated by the authors for the solution of steady-state problems in the channel electrode geometry.12,13 References 12 and 13 contain a full and comprehensive account of the computation of concentration profiles within a channel electrode: this detail is not repeated here as the present computations constitute a direct application of the previously proven successful method. However copies of the programs used are available upon request from the authors. Computer programs were written in FORTRAN 77 and executed on a SUN SPARC IPC workstation. Convergence of the simulation was verified by systematic variation of the size of the finite difference grid used for the computations, as described elsewhere.13 In regular computations 2500 grid points were used over the channel length, and 1000 over the channel height sufficed to produce adequately converged data in the form of currents normalized to the corresponding steady state for a simple one-electron conversion of A to B in the absence of any kinetic complications. Values of “the effective number of electrons transferred”, Neff, were thus computed for various flow rates and for different channel electrode geometries; each transient typically required ca. 10 s of CPU time. For the purposes of interpreting the results obtained we next consider the general mechanism given in the Introduction via progressive stages of complexity. The first of these corresponds to an established mechanistic pathway, while the other two will be shown below to relate specifically to the DPA/CBP experimental system. Limiting Case a: The Simple EC′ (Catalytic Pathway). If attention is simply given to reactions i-iv, neglecting steps v-viii, a simple EC′ (catalytic) mechanism is recovered. The corresponding transport equations are
k(ii)k(iv)[B][P] ∂[A] ∂2[A] 0 ) DA 2 - Vx + ∂x (k(iii) + k(iv)[P]) ∂y ∂2[B]
(18)
k(ii)k(iv)[B][P] ∂[B] ∂x (k(iii) + k(iv)[P])
(19)
k(ii)k(iv)[B][P] ∂2[P] ∂[P] + 0 ) DP 2 - Vx ∂x (k(iii) + k(iv)[P]) ∂y
(20)
0 ) DB
2
∂y
- Vx
The theory of this type of mechanism has been developed for reactions that take place in the absence of any illumination by Matsuda and co-workers.14 The photoelectrochemical problem collapses to their model if k(iii) . k(iv)[P], DA ) DB ) DP, and [P]bulk is considered to be in such excess that B is effectively lost via pseudo-first-order kinetics.14 Under these conditions it can be shown that Neff is a unique function of the single parameter
Λ2 ) {k(ii)k(iv)[P]bulk/k(iii)}{4xe2h4d2/9DVf2}1/3
(21)
provided the Le´veˆque approximation holds, as is the case with almost all experimental flow cells.1,2,14 When the concentration of P is such that the assumption of pseudo-first-order kinetics is compromised, then dimensionless analysis shows that Neff depends on a dimensionless rate constant
Knorm ) {k(ii)k(iv)[A]bulk/k(iii)}{4xe2h4d2/9DVf2}1/3 (22) and the ratio [P]bulk/[A]bulk. Moreover if the equal diffusion coefficient assumption is relaxed, then Neff further depends on the ratios DB/DA and DP/DA.
Figures 2 and 3 between them show the results of simulations carried out for values of [P]bulk/[A]bulk equal to 1 and 10, and for two different values of the ratio of rate constants k(ii)k(iv)/ k(iii). In both sets of figures the progressive depletion of A in the direction of flow is evident, although as the extent of the following catalytic reaction is increased, either by virtue of higher [P]bulk or faster k(ii)k(iv)/k(iii), the concentration profile near the electrode surface is sharper because of the larger regeneration. The same influences can be seen in the plots of B and P. Examination of Figure 3 shows that for [P]bulk/[A]bulk ) 10 the depletion of P is such that the pseudo-first-order limit might be expected to become a realistic description. Accordingly Figure 4 shows a comparison of our simulation results for the case of [P]bulk/[A]bulk ) 10 with the approximate analytical theory of Matsuda.14 Excellent agreement is observed, so vindicating our computational approach and its implementation. Figure 5 shows working curves deduced for various concentration ratios [P]bulk/[A]bulk for the simple EC′ mechanism. As expected, larger relative currents flow under catalytic conditions for higher concentrations of the substrate P. Because of the second-order kinetics in eqs 18-20, the analytical approach to the prediction of the catalytic currents is unfruitful and simulations are essential for [P]bulk/[A]bulk less than ca. 10. Simulations are further valuable in that they can be readily extended beyond the equal diffusion coefficient assumption usually invoked to facilitate unclumsy analytical treatments; this is particularly important in EC′ mechanisms where P may likely have a markedly contrasting diffusion coefficient to that of A or B. Figure 6 shows the results of simulations of Neff for [P]bulk/ [A]bulk ) 1 taking DB/DA ) 0.5, 1, or 2 and DP/DA ) 0.5, 1, or 2. The significant changes between the different data sets can be understood on the basis that a reduced diffusion coefficient for B and/or an increased diffusion coefficient for P have the effect of promoting relatively more reactionsstep ivsin the near vicinity of the electrode surface, thus leading to a greater regeneration of A for further catalytic cycling by the electrode. Limiting Case b: The Photo-EC′ Mechanism with Quenching of B* by A. If attention now extended to reactions i-v, neglecting only steps vi-viii, we consider what is effectively a photo-EC′ (catalytic) mechanism in which the reactive excited state, B*, is quenched by the parent molecule, A. The corresponding transport equations are
k(ii)k(iv)[B][P] ∂2[A] ∂[A] 0 ) DQ 2 - Vx + ∂x (k(iii) + k(iv)[P] + k(v)[A]) ∂y 0 ) DB 0 ) DP
∂2[B] ∂y2
∂2[P] 2
∂y
(23)
k(ii)k(iv)[B][P] ∂[B] - Vx ∂x (k(iii) + k(iv)[P] + k(v)[A])
(24)
k(ii)k(iv)[B][P] ∂[P] ∂x (k(iii) + k(iv)[P] + k(v)[A])
(25)
- Vx
If the proposed quenching step v is the dominant fate for excited B molecules, then k(v)[A] . k(iii) or k(iv)[P]. In this situation dimensionless analysis predicts that the effective number of electrons tranferred will depend on the ratio [P]bulk/[A]bulk and a different dimensionless rate constant,
Knorm,Q ) {k(ii)k(iv)/k(v)}{4xe2h4d2/9DVf2}1/3
(26)
Figure 7 shows two representative working curves for this limiting case. Limiting Case c: Strongly Competitive Disproportionation/Conproprotionation Reactions. Here we focus on the general mechanism presented in the Introduction and retain all
Photoelectrocatalytic Reduction of 4-Chlorobiphenyl
J. Phys. Chem., Vol. 100, No. 51, 1996 20117
Figure 2. Concentration profiles generated for a simple EC′ (catalytic) mechanism for the case of [P]bulk/[A]bulk ) 1. The profiles of A, B, and P are shown for k(ii)k(iv)/k(iii) ) 3.5 × 105 mol-1 cm3 s-1 and 3.5 × 106 mol-1 cm3 s-1. The corresponding values of the normalized rate constant (Knorm, see text) are 0.0383 (upper row) and 0.383 (lower row). The cell geometry was defined by d ) 0.6 cm, w ) 0.4 cm, and xe ) 0.4 cm. The other parameters used were D ) 10-5 cm2 s-1 and Vf ) 0.0177 cm3 s-1. Each profile shows the concentration distribution in x,y space corresponding to the full electrode length and a fraction 0.4 of the full cell depth (2h).
Figure 3. Concentration profiles generated for a simple EC′ (catalytic) mechanism for the case of [P]bulk/[A]bulk ) 10 (upper row) and 1 (lower row). The profiles of A, B, and P are shown for k(ii)k(iv)/k(iii) ) 3.5 × 105 mol-1 cm3 s-1 in each case. These both correspond to a value of Knorm of 0.0383. The cell geometry and other parameters used were as for Figure 2. Each profile shows the concentration distribution in x,y space corresponding to the full electrode length and a fraction 0.4 of the full cell depth (2h).
of the steps i-viii with the exception of step iv. The pertinent mass transport equations are as follows.
the event that k(v)[A] . k(iii), k(vi)[B] and k(vii)[A] . k(viii), then the effective number of electrons passed depends solely on the dimensionless rate constant
∂2[A] ∂[A] 0 ) DA 2 - Vx + ∂x ∂y
KSID2,2-QC ) k(ii)k(vi)k(viii)[B]2
(k(viii) + k(vii)[A])(k(iii) + k(vi)[B] + k(v)[A]) 0 ) DB
∂2[B] 2
∂y
{k(ii)k(vi)k(viii)/k(vii)k(v)[A]bulk}{4xe2h4d2/9DVf2}1/3 (29) (27)
Appropriate working curves are given in ref 15. Experimental Section
∂[B] - Vx ∂x 2k(ii)k(vi)k(viii)[B]2
(k(viii) + k(vii)[A])(k(iii) + k(vi)[B] + k(v)[A]))
(28)
In this case there is obviously zero depletion of P if any is present in bulk solution. This kinetic limit has been explored in detail elsewhere15 and labeled as a “self-inhibiting disproportionation reaction” denoted SID-QC,15 where suffixes Q and C imply both significant quenching and conproportionation. In
All standard photovoltammetry experiments were conducted using a platinum channel electrode made of optical quality synthetic silica to standard construction and dimensions.1,2 Solution (volume) flow rates between 10-4 and 10-1 cm3 s-1 were employed. Working electrodes were fabricated from Pt foils (purity 99.95%, thickness 0.025 mm) of approximate size 4 mm × 4 mm, supplied by Goodfellow Advanced Materials. Precise electrode dimensions were determined using a travelling microscope. A silver pseudo reference electrode (Ag) was positioned in the flow system upstream and a platinum gauze
20118 J. Phys. Chem., Vol. 100, No. 51, 1996
Figure 4. Comparison of the dependence of Neff on Knorm as predicted by the analytical theory of Matsuda (O)14 and by backward implicit simulation (×) as discussed in the text.
Leslie et al. used in conjunction with a Jarrell-Ash 82-410 grating monochromator (maximum incident power 2.0 mW cm-2); this permitted variable light intensity measurements through attenuation of the beam as described elsewhere;3 and (ii) an Omnichrome continuous wave 3112XM He-Cd source (Omnichrome, Chino, CA), which gave light of wavelength 325 nm at 20 mW absolute power with a minimum beam diameter of 1.6 mm. The laser was used in conjunction with a beam expander (Optics for Research, Caldwell, NJ), which gave a 25-fold increase in beam area and a radiative power of 55 mW cm-2. Simultaneous photoelectrochemical EPR experiments used a channel flow cell carefully positioned in the TE102 cavity of an X-band (9.0-10.0 GHz) Bruker ER200D spectrometer as previously described.1,2 Platinum microdisc electrodes of diameter 10-120 µm were supplied by Bioanalytical Systems (West Lafayette, IN). Experiments were performed using solutions of the electroactive substrate (ca. 10-4-10-3 M) in dried16 acetonitrile (Fisons, dried, distilled) or dimethylformamide (DMF, supplied by BDH, HPLC grade) solution containing 0.1 M (recrystallized) tetrabutylammonium perchlorate (TBAP) (Kodak) as supporting electrolyte. Solutions were purged of oxygen by outgassing with prepurified argon prior to electrolysis. 9,10-Diphenylanthracene and 4-chlorobiphenyl were used as received from Aldrich (>99%). Results and Discussion
Figure 5. Working curves for a simple EC′ mechanism, as defined by steps i-iv, for the concentration ratios [P]bulk/[A]bulk ) 1 (a), 5 (b), and 10 (c).
counter electrode was located downstream of the channel electrode. Electrochemical measurements were made using an Oxford Electrodes potentiostat modified to boost the counter electrode voltage (up to 200 V). Other methodological details were as described previously.1-3 Irradiation was provided by one of two sources: (i) a Wotan XBO 900 W/2 xenon arc lamp
We discuss first experiments conducted on the reduction of the catalyst 9,10-diphenylanthracene (DPA) in acetonitrile solution containing 0.1 M TBAP as supporting electrolyte. Channel flow cell voltammetry using platinum electrodes revealed a one-electron reduction at -1.74 V (vs Ag), and measurements of the transport-limited current as a function of solution flow rate gave a diffusion coeficient of 1.15 × 10-5 cm2 s-1. All these observations are in good agreement with literature reports,17,18 which additionally indicate that the radical anion formed as a result of this electrode process,
Figure 6. Working curves simulated for a simple EC′ mechanism with [P]bulk/[A]bulk ) 1 and DB/DA ) 0.5, 1, or 2 and DP/DA ) 0.5, 1, or 2.
Photoelectrocatalytic Reduction of 4-Chlorobiphenyl
J. Phys. Chem., Vol. 100, No. 51, 1996 20119 TABLE 1
Figure 7. Working curves for a photo-EC′ mechanism in the presence of significant quenchingsstep vsshowing how Neff depends on Knorm,Q for [P]bulk/[A]bulk ) 1 (a) and 10 (b).
DPA + e- f [DPA]•is kinetically stable. Experiments were next conducted using irradiation from a He-Cd laser or from a xenon lamp. Appreciable photocurrents were seen to flow for wavelengths between 260 and 500 nm. The resulting action spectrum depicting the variation of the photocurrent with the wavelength of the incident xenon lamp light has been reported elsewhere.15 Comparison of the action spectrum with the UV-visible spectrum of DPA confirmed that the photocurrents are derived from the absorption of light by the radical anion, [DPA]•-.15 Quantitative photoelectrochemical measurements accomplished by measuring the photocurrents as a function of both flow rate and parent DPA concentration confirmed that a SID2,2-QC mechanism (see above) was operative in which we suggest that the dianion of diphenylanthracene ultimately undergoes protonation to form the dihydro species.15,19,20 Experimentaly Neff values in the range 1.0-1.2 were observed, and a value for the ratio of rate constants of k(ii)k(vi)k(viii)/k(vii)k(v) ) 10.3 mol cm3 s-1 was derived for illumination at 320 nm using the xenon arc lamp. Attention was then turned to the study of the photoelectroreduction of DPA in the presence of variable amounts of CBP. The concentration of DPA was changed in the range 0.279 < [DPA]bulk/mM < 1.518, while that of CBP varied as follows: 2.554 < [CBP]bulk/mM < 15.03. Light of wavelengths 320 nm (xenon lamp) and 330 nm (He-Cd laser) were used, and significant photocurrents were seen to flow at voltages corresponding to the one-electron reduction of DPA. Very strong photocurrents were observed under all conditions and were generally such that Neff was in excess of 2; under favorable conditions Neff values as high as 3 could be measured. The magnitude of these Neff values is suggestive of some form of photocatalytic mechanism operating in this case as proposed in simple form by Rusling.8 Systematic channel electrode studies of the photocurrent as a function of solution flow rate under the diverse conditions defined above permitted a thorough mechanistic examination of the DPA/CBP system. The data obtained were examined using the working curves produced for the limiting case b above, in which a simple EC′ mechanism is augmented by step v, corresponding to the quenching of the excited state radical anion of DPA by the parent material. The latter has already been established on the basis of the photoelectrochemistry of the isolated DPA system reported above. Since the photocurrents seen in the presence of CBP were dramatically larger than in its absence, for the purposes of quantitative interpretations the working curves found for the limiting case b were applied directly once the raw photocurrent
λ/nm
[DPA]/mM
[CBP]/mM
(k(ii)k(iv)/k(v))/s-1
330 330 330 330 320 320 320 320
1.032 1.518 1.025 0.473 1.055 1.012 0.515 0.279
1.012 15.03 10.10 4.738 1.028 10.04 4.993 2.554
0.274 0.0654 0.0708 0.0639 0.0521 0.0102 0.0144 0.0111
data had been corrected for the (small) contribution from the SID-QC process. Figure 8 shows the analysis of typical sets of photocurrent/ flow rate data conducted in the way described above. In all cases a very good linear plot of Knorm,Q vs (flow rate)-2/3 that passed through the origin was obtained, suggesting the correct choice of mechanism. Moreover, with each of the sets of data recorded with the same light conditions the kinetic analysis gave closely consistent values of the ratio of rate constants k(ii)k(iv)/ k(v) for a given value of [P]bulk/[A]bulk regardless of the absolute value of [A]bulk as predicted by eq 26 and as reported in Table 1. This is strong evidence in favor of the mechanism selected for the data analysis. In particular if analyses were conducted using a simple EC′ mechanism without any quenching, then the systematic dependence on [A]bulk predicted by eq 22 was not seen. Table 1 shows the results of analyses made using the EC′ mechanism with the inclusion of quenching (limiting case b above) and after allowance has been made for a tiny contribution to the photocurrent from the SID-QC process operating on the parent DPA molecule alone. Examination of Table 1 shows that while the ratio k(ii)k(iv)/k(v) is independent of [A]bulk for a fixed ratio of [P]bulk/[A]bulk, as required by eq 26, nevertheless a significant variation between different [P]bulk/[A]bulk values does emerge. This hints at further mechanistic complexity, and we tentatively suggest the formation of a complex between species B and P. This may not be chemically unrealistic if the electron rich radical anion, DPA•-, has a charge transfer interaction with the CBP species. In this case the following equibrium may be assumed
B + P h BP where Keq ) [BP]/[B][P] and the effect of the complexation is to remove B from the system in the form of the complex BP, which is assumed not to be active in the scheme proposed in the Introduction. Thus as the amount of P is reduced, B is released and relatively greater catalysis is seen to operate. Quantitatively
[B]free ) [B]total/{1 + Keq[P]}
(30)
where the [B]total represents all the B present (whether in the form of the complex or the free ion). It follows that the true value of the ratio of rate constants is related to the value measured and reported in Table 1 by the equation
{k(ii)k(iv)/k(v)}true ) {k(ii)k(iv)/k(v)}measured/{1 + Keq[P]} (31) Significantly, application of this relationship to the data in Table 1 reveals a value of Keq ) 565 M-1 regardless of the light source used. This observation confirms that the origin of the discrepancy noted in the analysis according to the limiting case b must be independent of the photon flux or energy and must derive from some “dark” chemistry, and this is not inconsistent with the mechanism proposed above. Further evidence for a
20120 J. Phys. Chem., Vol. 100, No. 51, 1996
Leslie et al.
Figure 8. Analysis of photocurrent/flow rate data for the DPA/CBP system obtained (a-c) at 320 nm using a xenon lamp and d-e using a He-Cd laser. The following concentrations were used: (a) [DPA] ) 1.032 mM, [CBP] ) 1.012 mM ([); [DPA] ) 1.518 mM, [CBP] ) 15.03 mM (b), (b) [DPA] ) 1.025 mM, [CBP] ) 10.10 mM, (c) [DPA] ) 0.473 mM, [CBP] ) 4.738 mM, (d) [DPA] ) 1.055 mM, [CBP] ) 1.028 mM ([); [DPA] ) 1.012 mM, [CBP] ) 10.04 mM (b), (e) [DPA] ) 0.515 mM, [CBP] ) 4.993 mM ([); [DPA] ) 0.279 mM, [CBP] ) 2.554 mM (b).
complexation reaction of the form proposed was obtained using the substrate 2-fluorobiphenyl (FBP) in conjunction with the DPA photocatalyst. No catalytic currents were seen at any wavelength; moreover the presence of FBP was found to partially suppress the SID photocurrent as compared to the value obtained in the absence of CBP or FBP. This again would be consistent with the formation of a complex between DPA•- and the substrate in the dark chemistry. Conclusions Channel electrode voltammetry has been used to substantially characterize the mechanism of a highly complex photoelectroreduction. The ability of such methodology to probe subtle-
ties of reaction mechanisms including the quenching of excited states is worth emphasizing. Acknowledgment. We thank the Royal Society for supporting a Joint Project between the Universities of Tartu and Oxford. References and Notes (1) Compton, R. G.; Dryfe, R. A. W. Prog. React. Kinet. 1995, 20, 245. (2) Compton, R. G.; Dryfe, R. A. W.; Eklund, J. C. Res. Chem. Kinet. 1993, 1, 260. (3) Compton, R. G.; Dryfe, R. A. W.; Fisher, A. C. J. Electroanal. Chem. 1993, 361, 275. Compton, R. G.; Dryfe, R. A. W.; Fisher, A. C. J. Chem. Soc., Perkin. Trans. 2 1994, 1581.
Photoelectrocatalytic Reduction of 4-Chlorobiphenyl (4) Compton, R. G.; Eklund, J. C.; Hallik, A.; Kumbhat, S.; Nei, L.; Bond, A. M.; Colton, R.; Mah, Y. J. Chem. Soc., Dalton. Trans. 1995, 1917. (5) Compton, R. G.; Booth, J.; Eklund, J. C. J. Chem. Soc., Dalton. Trans. 1994, 1771. (6) Compton, R. G.; Barghout, R.; Eklund, J. C.; Fisher, A. C.; Davies, S. G.; Metzler, M. R. J. Chem. Soc., Perkin. Trans. 2 1993, 39. Davies, S. G.; Metzler, M. R.; Watkins, W. C.; Compton, R. G.; Booth, J.; Eklund, J. C. J. Chem. Soc., Perkin Trans. 2 1993, 1603. (7) Bond, A. M.; Way, D. M.; Wedd, A. G.; Compton, R. G.; Booth, J.; Eklund, J. C. Inorg. Chem. 1995, 34, 3378. (8) Shukla, S. S.; Rusling, J. F. J. Phys.Chem. 1985, 89, 3353. (9) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: New Jersey, 1962. (10) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. J. J. Phys. Chem. 1991, 95, 7538. (11) Pilling, M. J.; Seakins, P. W. Reaction Kinetics; Oxford Science Publications: New York, 1995, p 199.
J. Phys. Chem., Vol. 100, No. 51, 1996 20121 (12) Fisher, A. C.; Compton, R. G. J. Phys. Chem. 1991, 95, 7538. (13) Compton, R. G.; Pilkington, M. B. J.; Stearn, G. M. J. Chem. Soc., Faraday. Trans. 1 1988, 84, 2155. (14) Aoki, K.; Tokuda, K.; Matsuda, H. J. Electroanal. Chem. 1977, 76, 217. (15) Leslie, W. M.; Compton, R. G.; Silk, T. Electrochim. Acta, in press. (16) Coetzee, J. F. Recommended Methods for Purification of SolVents, IUPAC; Pergamon Press: New York, 1982. (17) Maness, K. M.; Bartelt, J. E.; Wightmann, R. M. J. Phys. Chem. 1994, 98, 3993. (18) Wheeler, L. O.; Santhanum, K. S. V.; Bard, A. J. J. Phys. Chem. 1966, 70, 404. (19) Wawzonek, S.; Laitinen, H. A. J. Am. Chem. Soc. 1942, 64, 1765, 2365. (20) Meerholz, K.; Heinze, J. J. Am. Chem. Soc. 1989, 111, 2325.
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