Mendeleev Communications Electronic Version, Issue 1, 2002 1 Prospects for the determination of thermodynamic and kinetic parameters of electrode reaction intermediates by laser photoemission Alexander G. Krivenko,* Vladimir A. Kurmaz and Alexander S. Kotkin Institute of Problems of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow Region, Russian Federation. Fax: +7 096 524 9676; e-mail: krivenko@icp.ac.ru 10.1070/MC2002v012n01ABEH001533 The method of voltammetric time-resolved waves (TRW) based on a comparative analysis of experimental and simulated curves of photoemissionally generated intermediates was used to determine the thermodynamic and kinetic properties of the R/R– redox pairs for the benzyl PhCH2 · and benzhydryl Ph2CH· radicals.Interest in the redox properties of intermediates including free radicals R in liquid media is stimulated by their ability to determine the direction and efficiency of electrode processes, e.g., in organic electrochemistry.1 The thermodynamic characteristics of redox pairs R/R– and R/R+ can be determined from standard potentials E0, e.g., pK and BDE values.2–4 The standard potentials of intermediates obtained by various methods are available.2–11 However, the main drawbacks of many experimental methods consist in their insufficient versatility and the influence of side processes leading to the inconsistency of measured values with thermodynamic characteristics.Therefore, the experimental values should be corrected depending on the life times of intermediates and the rates of their electrode reactions.It is possible to determine the values of E0 for R/R– redox pairs by traditional electrochemical methods such as voltammetry only in rare cases when the rate of the first electron transfer to an organic halide is much higher than that of the second.12 The relative stability of intermediates is a necessary condition for the majority of methods for E0 measurements3,8,10 and a more powerful method of indirect reduction9(a),(b) requires the knowledge of the full reorganization energy of intermediate self-exchange. Laser photoemission (LPE) can be used to overcome such difficulties; in particular, the method of voltammetric time-resolved waves (TRW) of photoemission-generated intermediates was proposed. 13 The values of E0 were determined by this method for a number of organic and inorganic intermediates in aqueous and aprotic solvents.4–7,11 An analysis5(c),7 demonstrated a similarity between E0 and the half-wave potentials E1/2, measured under conditions of the TRW method, i.e., intermediate generation in a thin near-electrode layer is followed by an equilibrium establishment at the electrode between adsorbed intermediates (radicals) Rads and products X of their reduction/oxidation.However, for the development of a complete kinetic model for an electrode process, it is also necessary, along with E0, to know the rate constants of redox reactions W0 and the dependence of rate constants WR of electrode reactions of intermediates on the potential WR = f(E) within a sufficiently broad range and their activation energies Ea, as well as the times of bulk decay of an intermediate tR and a product of its reduction/oxidation tX in a given solvent.All these values can also be determined by TRW. The long-lived benzyl PhCH2 · and benzhydryl Ph2CH· key organic radicals14 were chosen for the study. The redox potentials of their R/R– pairs were reliably determined by various methods,2 and tR and tX parameters may substantially differ.14 The set of R transformations, generated by photoemission current IP, can be represented by the following scheme: where kR, kX, Wd and W'd are the rate constants of adsorption and desorption, respectively; WR and WX are the rate constants of electrode reactions, and GR and GX are the surface concentrations of adsorbed intermediates (radicals) Rads and products X, respectively.A decrease in the surface concentration of stable reagents is compensated by their diffusion from the bulk of a solution during the diffusion-controlled discharge. However, R and X discharge occurs at their zero bulk concentrations and competes with desorption accompanied by the decay of intermediates.The kinetic equations for surface and bulk concentrations of reagents nR and products nX take the form Bulk concentrations obey the diffusional equations where DR and DX are the diffusion coefficients of reagents and products, respectively; Ip f(t) is the impulse of intermediate generation in the near-electrode layer with a characteristic length of x0.4 The boundary conditions determine the continuity of reagent and product streams on the interface (Scheme 1):† The solution of nonstationary diffusional equations (2)–(4) were analysed7 based on ref. 15. A number of parameters of Scheme 1 are estimable. The values of GR and GX are controlled in the photoemission measurements, and they are equal to 1010– 1011 particle per cm2. Such an estimation as kR, kX ~ D/l » » 102 cm s–1 is valid for the rate constants of adsorption if the 7.0 6.0 5.0 4.0 3.0 1.0 1.2 1.4 1.6 lg WR –E/VNHE (a) (b) 0.35 0.30 0.25 0.20 1.25 1.35 1.45 1.55 Ea/eV –E/VSCE Figure 1 (a) Electroreduction rate constants as functions of potential at various temperatures for PhCH2 · .DMSO; supporting electrolyte, 0.4 M LiClO4; stationary mercury electrode. (1) 98, (2) 51 and (3) 22 °C.(b) Apparent activation energy Ea for the electroreduction of the benzyl radical at various potentials determined from the data in Figure 1(a). 1 2 3 † The absence of such boundary conditions led5(c) to a decrease of requirements to the time interval of measured TRWs, which are necessary for the unambiguous interpretation of experimental data, and caused a partial loss of information at their treatment.tR IP R GR GX X kR Wd WR WX W'd kX , (1) tX dGR dt = kRnR(0) – (WR + Wd)GR + WXGX; dGX dt = kXnX(0) + WRGR – (WX + W'd )GX. (2) ¶nR dt = DR – + e–x/x0 f(t); ¶nX dt = DX – , (3) ¶2nR dx2 nR tR Ip x0 ¶2nX dx2 nX tX ¶nR dx DR = kRnR(0) – WdGR, (4) x = 0 ¶nX dx DX = kXnX(0) – WdGX. x = 0Mendeleev Communications Electronic Version, Issue 1, 2002 2 diffusion coefficient D of intermediates is ~ 5¡¿10.6 cm2 s.1 and the diffusional jump l is (2.3)¡¿10.8 cm.For kR and Wd, using the detailed equilibrium principle,4 we can derive We can obtain from (5) that Wd is 102.104 s.1 at standard values of the parameters (G0 = 1014 cm.2, N0 = 6.4¡¿1020 cm.3) and the typical standard adsorption free energy of organic radicals ..G0 a(R) ¡í .(0.3.0.4) eV.4 W'd >> Wd since ..G0 a(R) for radicals is sufficiently lower than the standard adsorption free energy of carbanions ..G0 a(R.).The value of ..G0 a was determined7 for the redox pair CF3 ¡� /CF3 . (..G0 a = 0.3¡¾0.06 eV), and the difference in the standard free energies of adsorption of organic acids and their anions is equal to 0.1.0.15 eV, which may serve as its lower estimation [..G0 a = .(.G0 a(R) ..G0 a(R.))] (see, e.g., ref. 16 and references therein). The parameter tX is relatively controllable, and it can range from 100.10.7 s in aprotic solvents7,8 to 10.8.10.10 s in aqueous solutions.4 The previously developed procedure13 was improved to obtain TRWs. TRWs were recorded by the measurements and numerical Fourier transformation of signals from a photoelectrochemical cell illuminated with modulated light with a period of tm = 1.0. 10.3 s. Converting from the repetition frequency to frequency W was achieved using the relation W = 5.31tm . 1. A program package was elaborated to expand an effective W range, and that allows the recording of TRWs within the range W ~ (4.5)¡¿104 s.1. This enables us to determine E1/2 on the highest harmonics of modulation frequency, up to 10th.The values of WR = f(E,T) were determined for irreversible electroreduction (E < E0) from the kinetics of the electrode charge during electrodeeactions of Rads. The experimental procedure was described elsewhere.4,17 The transition from WR(E) to E1/2(W) dependences is based on the coincidence of E1/2 and the potential, where WR = W for a given W at the irreversible electroreduction of Rads with an accuracy of 0.01 V.The precision of E1/2 determination is no worse than ¡¾0.005 V.5(b) The radicals R were generated by the dissociative electron transfer17 where e. s is a solvated electron, RX is PhCH2Cl or Ph2CHCl, ka is the rate constant of its capture by an acceptor, and kd is the dissociation rate constant of an anion radical.The values of ka for PhCH2Cl and Ph2CHCl are (1.6.4.5)¡¿109 and 9.5¡¿108 dm3 mol.1 s.1, respectively,18 i.e., they exceed the rate constant of e.s capture by a solvent by more than an order of magnitude. This provides an increase in the signal by a factor of 3.4 in comparison with the background signal on the addition of 0.08.0.2 M of acceptors.The experiments were carried out in DMSO because it is much more stable than DMF and, especially, acetonitrile19 with respect to the action of strong bases such as carbanions. The life times of benzyl and benzhydryl carbanions are considered to change oppositely to pKa values of respective CH acids, consisted of 35 and 32.2 in DMSO;19 51.2 and 43.1 in acetonitrile, 3(b) while tX is usually ¡Ì 10.3 s19(b) in this solvent.The WR(E,T) functions are presented in Figure 1(a) for the irreversible reduction of the benzyl radical at E < E1/2.¢Ô They follow the equation of slow discharge with the transfer coefficient a ~ 0.45 at t = 22 ¡ÆC, as well as other organic radicals (a ~ 0.5¡¾0.05).4 Similar functions were also obtained for the benzhydryl radical. Apparent activation energies Ea for various E values were found from these data to estimate the reorganization energy Es of outer-sphere electron transfer by quadratic Marcus equation1 (Es = 4Ea at E = E0).The values of Es are 0.32.0.35 eV in DMSO, which is close to the published data6 for a number of alkyl radicals (Es is 0.34.0.38 eV). The TRWs of benzyl and benzhydryl radicals obtained on a mercury electrode in DMSO.LiClO4 solutions are similar to those described previously4,5(a),(b),6,7.No serious differences were found in the wave forms and their location on the E-axis at transition to DMF and acetonitrile, the use of LiCl as a supporting electrolyte or the replacement of a Hg electrode with Au. The experimental and simulated E1/2(W) functions for the radicals are represented in Figure 2(a),(b).They are plotted in the lg W.E1/2 coordinates. Figure 2 demonstrates a satisfactory coincidence of experimental data and numerical simulation in each case, even in spite of complex character of the dependence and significant range of W change. Hence it follows that the necessary interval of W change has to override all transition region from reversible to irreversible reduction, i.e., not to be less than 5.7 orders (W is 1.107 s.1) to obtain reliable results.It is possible to measure WR(E) and Ea in this case, to determine tR, tX and ..G0 a(R) and to estimate the standard potentials of redox pairs R/R. on the basis of these data with the precision better than ¡¾0.04 V (Table 1). Table 1 Thermodynamic and kinetic properties of benzyl and benzhydryl radicals in DMSO, DMF and acetonitrile.R¡� Es (E = E0)/eV W0/s.1 ..G0 a(R) ¡¾ 0.02a/eV aThis study, DMSO + 0.4 M LiClO4. bRef. 5(a), the illumination period tm = 2¡¿10.6 s; supporting electrolyte 0.1 M Et4NClO4. cRef. 9, ¡¾0.05 V, supporting electrolyte 0.1 M TBABF4 (acetonitrile). dRef. 3(b), ¡¾0.05 V, supporting electrolyte 0.1 M Bu4NClO4, the illumination period tm = 2¡¿10.2 s.eRef. 5(b), supporting electrolyte 0.1 M Et4NClO4 (DMF) and 0.1 M Bu4NPF6 (acetonitrile), the illumination period tm = 10.3 . 3¡¿10.6 s. fRef. 8(d), ¡¾0.05 V, supporting electrolyte acetonitrile + 0.1 M Bu4NClO4, the illumination period tm = 2¡¿10.2 s. gRef. 9(c), quantum-chemical simulation. hRef. 8(d), ¡¾0.05 V, supporting electrolyte acetonitrile + 0.1 M Bu4NClO4, the illumination period tm = 10.2 s.iRef. 8(e), supporting electrolyte 0.1 M Bu4NClO4 (acetonitrile). a,b,c,eHg electrode. e,f,hAu electrode. iGlassy carbon or Hg-electrode. tR¡¿104/s tX¡¿104/s .E0 (.E1/2)/VSCE DMSO DMF Acetonitrile PhCH2 ¡� 0.34¡¾0.01a (2.6)¡¿103 a 0.45 0.05.0.15a 5.15a 1.35¡¾0.03a (1.37)b (1.35)b 0.433,c 0.733g 4¡¿106 e (11.15)¡¾0.3f 0.2e (1.36)b 1.40c (1.45)d 0.925e 0.1.0.001i ~0.0001i 1.215e ~1.42e Ph2CH¡� 0.33¡¾0.015a (1.3)¡¿104 a 0.39 50.150a 500.1500a 0.97¡¾0.02a (1.12)b (1.16)b 0.703e 2.8¡¿107 e (16.20)¡¾0.2f 0.033e (1.07)b 1.07c (1.14)d 0.1.0.001i 1.107e (1.115), f (1.130)h kR Wd = exp.. (5) G0 N0 .G0 a(R) kBT RX + e.s RX.¡� R¡� + X., ka kd (6) ¢Ô Note that the maximum of the measured WR values was ca. 5¡¿106 s.1 and, consequently, kd ©ø 107 s.1 for both ion radicals, and similar values may be considered as typical for such systems.20 For instance, kd value for the anion radical ClC6H4Me.¡� was estimated to be20(b) 7.6¡¿109 s.1. 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.9 1.0 1.1 1.2 1.3 1.4 1.6 1.8 1.2 1.4 lg W .E1/2/VSCE .E1/2/VSCE 7.0 6.0 5.0 4.0 3.0 2.0 1.0 lg W 1 2 (a) (b) Figure 2 The comparison of the experimental E1/2.W relation with the numerical simulation.DMSO; supporting electrolyte, 0.4 M LiClO4; stationary mercury electrode; 22 ¡ÆC. (1) The data of kinetic measurements; (2) TRWs. The areas of E0 dispersion are depicted by vertical dotted lines: the deviation of E0 to anodic direction from the most positive E1/2(W) values is systematic in nature and may consist of 0.025.0.075 V for systems with such parameters.7 (a) The radical Ph2CH¡�.The parameters of calculation: Wd = 104 s.1; W'd = 107 s.1; tR = 10.4 s and tX = 1 s. (b) The radical PhCH2 ¡� . The parameters of numerical simulation: Wd = 104 s.1; W'd = 108 s.1; tR = 10.5 s and tX = 10.3 s.Mendeleev Communications Electronic Version, Issue 1, 2002 3 The results of measurements and the simulated parameters of Scheme 1 were tabulated together with published data.It follows from Table 1 that the available thermodynamic and kinetic characteristics of the radicals are consistent with those determined in this work. 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