556 R. Frank, H. Ruu / Tris(2,2'-bipyridine)ruthenium (11) complex by 2-methylanthruquinone

Recl. Trav. Chim. Pays-Bas 114,556-564 (1995) SSDI 0165-0513(95)0068-2

01 65-05 13 /95 / 1 1 / 12556-09$9.50

Kinetic salt effects in the quenching of the excited state of the tris(2,2'-bipyridine)ruthenium(II) complex by 2-methylanthraquinone

Rudolf Frank and Hermann Rau

Universitat Hohenheim, Institut fur Chemie - 130, Fachgebiet Physikalische Chemie, Garbenstrape 30, D- 70599 Stuttgart, Germany (Received February 26, 1995)

Abstract. In the title system, quenching rate constants k , were determined as a function of c(Et,NCIO,), c(NaC10,), and c(LiC10,) in acetonitrile solution. A general and a specific salt effect on k , can be distinguished. The 2-methylanthraquinone radical anion produced by the photoinduced electron transfer forms strong associates with Na+ and even stronger ones with Li+, the formation constants of these complexes being determined from electrochemical measurements. Transient absorption spectra of the methylanthraquinone radical anion and of its associates with Na' and Li+ are presented. The rate constant of the electron transfer step could be determined in selected systems and effAGo values of the electron transfer step were developed. Apparent activation parameters A H ' , A S ' , and AG # were determined from the k , data. The negative values of A H ' can be rationalized by the mechanism of the photoinduced electron transfer reaction. The back electron transfer in the successor complex to the ground state molecules shows Marcus-inverted behaviour.

1. Introduction

The excited state of the tris(2,2'-bipyridine)ruthenium(II) complex ('Rubpy) can be quenched by oxidative and reductive electron transfer reactions. Although a large variety of compounds has been used in these reactions, relatively few investigations have been performed with quinones, especially anthraquinones'-8. For 2-methyl- anthraquinone (MAQ), a more negative reduction poten- tial has been reported than for methylviologen, which is a molecule often used in studies of the oxidative quenching of * Rubpy9-16. According to these values the quenching reaction between * Rubpy and MAQ could be expected to show a free enthalpy of reaction (AGO = AG,, according to Scheme 1) which is near to zero and therefore, it should be possible to transform a larger fraction of the light energy initially absorbed by the Rubpy into chemical energy. When we started to use MAQ as a quencher we observed a kinetic salt effect on the rate constant k , of the oxidative quenching reaction. At first glance, no such effect is expected, as MAQ is not a charged species. In addition, Tuzuke et al. reported negative enthalpies of activation for the oxidative quenching reaction of * Rubpy by benzoquinone and naphthoquinone derivatives [8,17,18]. Using MAQ as a quencher, we also observed negative enthalpies of activation. In order to gain a better insight into the reaction mecha- nism, we studied the reaction as a function of ionic strength. In the course of the work, it became clear that the reaction is governed by two effects: ( i ) change of AGO due to variation of the ionic strength, and ( i i ) strong

' Dedicated to Prof. Dr. Heinz Mauser.

association of the reaction product, 2-methylanth- raquinone radical anion (MAQ'-) with alkali cations of the supporting electrolyte.

2. Experimental section

2.1. Materials

Acetonitrile (AN) for DNA synthesis (Roth) was used as a solvent in all experiments without further purification. 2-Methylanthraquinone (MAQ) from Fluka was recrystallized several times from ethanol. Electrolytes NaCIO,, LiCIO,, Et,NCIO,, and Bu,NCIO, from Fluka or Aldrich were of p.a. grade and used without further purification. NaCIO, and LiCIO, are hygroscopic and were dried for at least 6 h at a temperature of ca. 200°C and a reduced pressure of ca. 10 Pa.

2.2. Quenching experiments

All experiments were performed in oxygen free solutions at 25°C. For the determination of activation parameters, the temperature was varied between 15 and 45°C. Argon was bubbled through the solu- tions for at least 45 min. Quenching rate constants were determined by laser flash experiments, using the 460 nm radiation from a Lambda Physics FL 2000 dye laser to excite the Rubpy. The pulse width of the laser is 15 to 20 ns. The FL 2000 itself was pumped by a Lambda Physics EMG 101 excimer laser, 308 nm. Evaluation of the rate constants k, was performed according to the Stern Volmer treatment from plots of T , / T us. c(MAQ). The concentration of Rubpy was varied in the range (1.10-5 to 1.10-4) mol/l. Stern Volmer plots were linear up to c(MAQ)= 0.112 mol/l. Transient spectra were recorded with the excitation and analysing beams perpendicular to each other. All these experiments were performed at c(Rubpy) = 1. lo-, mol/l and c(MAQ) = 3.10-3 mol/l and laser flash intensities of the order of 5 mJ. The maximum of the transient absorbance occurred approximately 1.3 ps after the

Recueil des Trauaux Chimiques des Pays-Bas, 114 / 11-12, Nouember/December 1995 557

A

0.8

0.6

0.4

0.2

I 250 300 350 400 450 500

A l n m

Figure 1. Absorption spectra of - 2-methylanthraquinone (c(hL4Q) = 3.1.10- perchlorate [c(Rubpy) = 6.7.10- mol / I ] in acetonitrile solution.

m o l / l ) and of - - - tris(2,2‘-bipyridine) ruthenium(II)

laser flash. Photomultiplier outputs (Hamamatsu R 928) were mea- sured with a Tektronix 11302 oscilloscope. The signals on the oscillo- scope screen were recorded by a video camera and digitized by a Tektronix hardware and software system (“digital camera system”) using an 1BM personal computer.

2.3. Electrochemical measurements

A metrohm polarograph (Polarecord 626 with VA scanner E 612) was used for the determination of redox potentials. Redox potentials of MAQ were measured using a dropping mercury electrode. The half-wave potentials were determined by the differential pulse tech- nique relative to an Ag/AgNO, electrode in AN. Using c(AgN0,) =0.1 mol/l and c(Et,NCIO,)= 0.1 mol/l as a supporting elec- trolyte, the potential of this electrode is 0.579 V us. the normal hydrogen electrode (NHE)I9. This electrode was connected to the MAQ solution by a bridge containing a solution of Et,NCIO, in AN, c(Et,NCIO,) = 0.1 mol/l. The advantage of this special reference electrode is that it is not necessary to use any aqueous solutions. The redox potential of Rubpy in AN was determined by cyclic voltarnrne- try using a glassy-carbon electrode as a working electrode and the same reference electrode as before. These measurements were per- formed using a Zahner electric IM5d impedance unit. From these data, the oxidation potential of Rubpy was calculated by subtract- ing 2.1 V ’ O . ~ ’ .

2.4. Spectroscopic measurements

Absorption spectra were recorded with a Zeiss DMR 10 or a Hewlett Packard 8452A diode array spectrophotometer, fluorescence spectra with a Perkin Elmer LS 50 fluorimeter. The absorption spectra of Rubpy and MAQ are shown in Figure 1.

The values of the diffusion-controlled rate constants k 12 and k,, can be estimated by Eqns. 1 and 2i,’7723.

Reasonable values”720 of r D and rQ, which are the radii of the donor Rubpy and the quencher MAQ, are r D = 0.71 nm and rQ = 0.38 nm. qo = 0.341 CP is the viscosity of A N at 25°C. In the temperature range 15 to 40”C, the viscosity of pure AN, q(AN), can be described by Eqn. 3.1, and the viscosity of AN with c(Et,NCIO,) = 0.107 mol/l, q(AN,Et,NClO,), by Eqn. 3.224,25. The viscosity of AN is changed considerably if electrolytes are added. The rela- tive viscosity 77, of AN containing NaClO, at 25°C can be described by Eqn. 3.325926.

7(AN) =3.562- 18.258.10-3.T+25.0.10-6.T2 (3.1)

(3.2)

77(AN,Et4NC104) = 13.283 - 82.149. T

+ 1.3022.10-4.T2 77

770 7, = - = 1 + 0.018. [ c(NaClO,)] + 0.73 . c(NaC10,)

(3.3)

The increase of the viscosity of solutions containing LiClO, is essentially the same as that given by Eqn. 3.326. For solutions containing Et,NCIO, no published data of mea- surements at higher salt concentrations could be found. At low salt concentrations viscosities calculated by Eqn.

3. Kinetic model

The quenching experiments can be described by the com- mon reaction Scheme 1, which determines the rate con- s t an t s k,!fo,22.

k12 k23 * Rubpy2++ MAQ [ * Rubpy2+ . . . MAQ] I [Rubpy3+ . . . MAQ.-]

hu 11 I / T lkb Rubpy3+M:’-

back Rubpy2++ MAQ

Scheme 1.

558 R. Frank, H. Rau / Tris(2,2'-bipyridine)ruthenium ( I I ) complex by 2-methylanthraquinone

3.3 deviate less than 2% from measured data42. There- fore, whenever measured values of k , were corrected for viscosity effects, relative viscosities according to Eqn. 3.3 were used. k , is the Boltzmann constant, R, and T have the usual meaning. Due to the increase in viscosity, k,, decreases from 2.1 . 10" in pure AN to 1.31.10" at c(NaC10,) =

0.8 mol/l; in the same range of concentration variation, k,, decreases from 6.53 . lo9 to 4.08 . lo9. The formation constant of the precursor complex ( K , 2 = k12/k21) is 3.22, independent of salt concentration. At the moment, we have no possibility to estimate the monomolecular rate constants k23 and k32. According to the Marcus theory, Eqn. 4, they are correlated to the free enthalpy AGO = AC23, the solvent reorganization energy A , and the nuclear Y, and electronic K , ~ factors of the electron transfer reactionz2. Of these variables only AC,, (in eV) can be estimated by Eqns. 4.1 to 4.3.

(4) AGO = AC23 = El/,( Rubpy3+/ * Rubpy2+)

- EIl2(MAQ/MAQ'-) + wP - W R (4.1) with

(4.3) 2 . NA .e:. 1.1000

'= ( E g . E ; k g ' T

The El/, are the redox potentials of MAQ and *Rubpy, which is the oxidation potential of Rubpy2+ minus the energy of excitation; wp is the electrostatic work which is necessary to bring the product ions to their contact dis- tance; w, is the same work for the reactants and it is essentially zero as MAQ is not a charged species. The zi are the charge numbers of the oxidized donor (Rubpy3+) and the reduced acceptor (MAQ") and I is the ionic strength of the solution. With eO = 8.85 . lo-'' As/(Vm), eo = 1.6. As, E , = 36.12', the Avogadro constant, the Faraday constant and the foregoing information, the value of wp can be esti- mated. For the donor-acceptor pair of this investigation E,/,(Rubpy3+/ * Rubpy2+) - E,/,(MAQ/MAQ '-) is near to zero and therefore, the contribution of wp to AGO cannot be omitted as is often possible for exergonic elec- tron transfer reactions. The rate constants k, and k , are often combined into a single rate constant k,, = k , + k,,. The rate constant, k,, of the back electron transfer in the successor complex, or the contact ion pair, to the ground-state molecules should also obey Eqn. 4. The rate constant k,, is diffusion-con- trolled and can be estimated. The equation for the esti- mation of k,, is far more com lex than Eqn. 2, as in this case charged species (Rubpy'! and MAQ'-) are con- cerned. A detailed treatment of the calculations is given by Chiorboli et a1.". We estimated k,, according to Eqn. 10 in that publication as well as a diffusion-controlled limit of kback using Eqn. 3 from that work. The observed rate constant of the quenching reaction, k,, is a complex function of the single-rate constants of the elementary steps concerned in Scheme 1. Assuming con- tinuous irradiation and equilibrium kinetics for the short- lived species, k , is given by Eqn. 5.

k, = (5) k l Z ' kZ3' ( k b + k 3 4 )

k21 ' k32 + k21 ' ( b + k34) + k23 ' ( b + '34)

If we assume that k , , B k23, Eqn. 5 reduces to Eqn. 6.

k 1 2 ' k 2 3 ' ( k b + k 3 4 )

k,l ' k32 + k Z l ' ( k b + '34) k , =

This assumption appears to be reasonable, as k , is much smaller than k , 2 . However, Eqn. 6 is still too complex to estimate k23 and the other unknown rate constants of the elementary reaction steps. If we assume further k,, -=K (k, + k3,) Eqn. 6 reduces to Eqn. 7.

k 1 2 . k 2 3 k , = - = K , , . k Z 3 k21

(7)

Both k,, and k,, as well as k! , can be estimated and therefore, in this case, we get estimated values of k,, and of k3, when we use Eqns. 8 and 9.

23 K 2 3 =

with

AG23 = - R . T . In( K23) (9) On the same assumption as before, k32 << ( k b + k,,), Eqn. 5 reduces to Eqn. 10.

k12 ' k23

k21 + k23 k , =

Eqn. 10 offers another possibility to estimate k2, and k32. If k,, >> k23- both Eqns. 7 and 10 should give the same results, within numerical error, as will be discussed later. From the data given in this work it is not possible to determine k , but, as will be shown later, we do gain some information about the variation of k , when the elec- trolyte concentration is varied.

4. Redox potentials and association constants

4.1. Results

The redox potentials of MAQ/MAQ'- have been deter- mined by differential pulse polarography at various salt concentrations of Et,NCIO,, NaCIO,, and LiCIO, in AN solutions. The results are shown in Figure 2. MAQ is reduced at less negative potentials when the concentra- tion of the supporting electrolyte is increased. This varia- tion can be attributed to changes of the activity coeffi- cients of MAQ and MAQ'- as a function of ionic strength. If NaClO, or LiC10, is used as a supporting electrolyte instead of Et,NCIO,, a new, much larger shift of the redox potential is observed. This difference A E , which is the redox potential in the presence of Na' or Li' ions minus the redox potential in the presence of Et,NCIO,, can be attributed to an association of Na' or Li+ cations with MAQ'- anions29,30-33 . Us ing Eqn. 11, K = (eAE/25.6 - 1

association constants K,,, of MAQ'- with Na+ or Li+ have been determined from the differences of the redox potentials A E (in mV) and the concentrations of the associating cations. A second method for the determina- tion of association constants is to vary the ratio of c(Et ,NC1O4)/c(NaC10,) or c(Et ,NC10,)/c(LiCIO4) at constant ionic strength. In this case too, a change of the redox potential is observed and using Eqn. 11, association constants can be determined from a plot of exp(AE/25.6) uersus the concentration of the associating salt at constant ionic strength. For the couple Na+/MAQ '- we obtained association constants of 370 and 90 at ionic strengths of

)/c(salt> (11) ass

Recueil des Travaux Chimiques des Pays-Bas, 114 / 11-12, November/December 199.5 559

400

4 5 0

-500

-550 > E - 600 w- r!

-650

-700

-750

800 ,

...... A A ........... * ................ * ................

...... ...........

0.0 0.1 0.2 0.3 0.4 0.5 0.6

ionic strength I rnol I-' Figure 2. Half-wave potentials of Rubpy and MA& in acetonitrile solution us. NHE. 0 Rubpy3+/'Rubpy2+; M A Q / M A Q ' - with Et,NCIO,; t MAQ/MAQ' - with NaCIO,; A M A Q / M A Q ' - with LiClO,.

0.1 mol/l and 0.5 mol/l by these methods. For the couple Li+/MAQ'- we obtained an association constant of 35 000, the dependence of this association constant on the ionic strength could not be determined. K, , determined by the two methods agreed, within experimental error, which is 10 to 20%, when NaCIO, is used. If A E becomes larger according to Eqn. 11, small changes in A E cause much larger changes in Ka,. Therefore, the association constants in the case of LiCIO, are less reliable and consequently it was not possible to determine K,, as a function of ionic strength.

4.2. Discussion

Reported values of the redox potential of anthraquinone vary between -658 mV and -718 mV in acetonitrile (AN) and -618 mV and -738 mV in DMF. For MAQ, only a few values have been reported, varying between - 528 mV in dichloromethane and - 604 mV in DMF9-16. The redox potentials determined in this laboratory fall into this range. The values given in the section Results are mean values, they vary by approximately 20 mV. This variation may be due to the water content of the AN. Several authors have reported on the association between anthraquinones and alkali cations. Association constants have been determined by optical and polarographic meth- ods. It is generally accepted that no association occurs between MAQ'- and Et,N+ ions. Reported association constants in DMF for the couple AQ'-/Li+ vary between 11.5 and 4890, while for the couple MAQ'-/Na+ and MAQ'-/Li+ association constants of 848 and 4950 have been If it is assumed that only electrostatic interactions are active between the ions, association con- stants can be calculated according to the Fuoss treat- ment23. Such calculations yield association constants of approximately 2 for the couples MAQ'-/Na+ and MAQ'-/Li+, 3 for the couple MAQ'-/Et,N+ and 4 for the couple MAQ'-/Bu4N+ in AN. The association con- stants given in the Results section deviate considerably from the calculated ones and those reported for DMF solutions. This indicates that the non-electrostatic interac- tions between MAQ.- and the alkali cations are essential and thus that the influence of AN and DMF on the

association is not related to the dielectric properties of these solvent^^^^^^. Even so, the association constants are astonishingly high, especially between MAQ'- and Li+. Here we may see parallels to the formation of stable sandwich complexes between Li+ and the cyclopentadi- enyl anion36. With this information we can try to assess to what degree MAQ'- is associated with alkali cations after the photoin- duced electron transfer process. Assuming equilibrium kinetics between associated and free MAQ'- we can estimate the fraction of associated MAQ'- as a function of K, , and the concentration of the alkali cations. At an alkali concentration of 0.1 mol/l and assumed K, , val- ues of 3, 10, 90, 370 and 35 000, we obtain values of 0.23, 0.50, 0.90, 0.97 and 1.0, respectively, for the fractions of MAQ'- ions that are associated with the cations of the supporting electrolyte. At higher alkali concentrations, these fractions approach 1, whenever K, , is assumed to be 10 or higher. This means that in almost all of our experiments the formation of MAQ ' - ions associated with cations of the supporting electrolyte will finally oc- cur. It does not mean, however, that these associates are present immediately after the electron transfer step, as will be shown in the next section.

5. Quenching experiments

5.1. Results

5.1.1. Absorbance of transients. According to the kinetic model, MAQ radical anions (MAQ'-) should be formed in the quenching process. MAQ'- absorbs in the 500-to- 600-nm wavelength range13-15*29*37-42. The transient ab- sorption spectra after the quenching process are shown in Figure 3. The peak wavelength is 535 nm in pure AN and in the presence of Et,NClO,, it is shifted to 515 nm in the presence of NaClO, and to 505 nm in the presence of LiCIO,. As we do not have exact absorption coefficients for the MAQ '- radical anion, normalized transient-ab- sorption spectra are given in Figure 3.

I 1 I I I I

460 480 500 520 540 560 580 600

wavelength I nm Figure 3. Normalized transient absorption spectra of MAQ'- in AN solution after the quenching process. All absorbances were measured approximately 1.3 ps after the laser flash. Absolute values of the absorbance v a y between 0.01 and 0.05. Absorbance in the presence of:

Et,NCIO,; + NaClO,; A LiClO,.

560

-20

21 .o

20.5

- 9 I+

- 20.0

Y

C

19.5

-1 0 0 10

AG I kJ mot-'

R. Frank, H. Rau / Tris(2,2'-bipyridine)ruthenium ( I l ) complex by 2-methylanthraquinone

(0.037) 0.069 0.126 0.158

0.101 0.235 0.331

0.091 0.141 0.190 0.295

(13.1) 3.10 1.40 0.87

2.20 0.75 0.45

2.50 1.38 0.92 0.49

Figure 4. Quenching rate constant k , corrected for viscosity effects us. AC of the quenching reaction. Filled symbols represent values us. AC,, according to Eqn. 4.1, hollow symbols us. AC2, + wp. Electrolyte is: 0

Et,NCIO,; + NaCIO,; A LiClO,.

5.1.2. Rate constants. In Figure 4, the quenching rate constant k,, corrected for viscosity effects, is given as a function of AG of the quenching reaction. As expected the k , values are relatively small, in the order of 1 to 5% of the diffusion-controlled value. Corrected for viscosity effects, they vary between 0.24. lo9 at c(Et,NClO,) = 0.1 mol/l and 1.4. lo9 at c(NaC10,) = 0.5 mol/l. When the kind of electrolyte is not changed, ln(qrkq) increases almost linearly when AG becomes more negative. The slopes in the presence of Et,NClO,, NaClO,, and LiClO, are almost identical and their values are close to -0.2 mol/kJ, equal to - 1/(2 * R * T ) . When the kind of elec- trolyte is changed, AC becomes much more negative but the k , values are not changed in an equivalent manner. For the calculation of the rate constants k23 and k,, an effective free enthalpy of reaction effAG23 was used in- stead of the electrochemically determined AG23 when alkali cations were present in the solutions. The reasons for which we introduced this new quantity will be dis- cussed. In Figure 4, one example is given of how we

1.4

1.2

- 2 1.0

$ 0.8 0.6

3 5 0.4

0.2

0.0 I I I I I

0.0 0.2 0.4 0.6 0.8

c(Et,NCIO,) I moll1

Figure' 5. Normalized quenching-rate constant k , and transient ab- sorbance A A of Me'- in the presence of Et,NCI04. Lines are drawn to aid the viewer and are not calculated.

determined effAG2,. Following the methods described in the section 3 (kinetic model), the rate constants k?,, k,, and k3, can be calculated. These data are compiled in Table I. For pure AN solutions, no AC23 is available from electro- chemical measurements and therefore, no estimate of k,, can be calculated. Tentatively, we determined a value of AG23 by extrapolation from the measured dependence of k , on AG as given in Figure 4. The resulting values are given in parentheses in Table I. Figures 5, 6 and 7 show the variation of k , and of A A , as a function of the various salt concentrations. A A , is the transient absorbance of the MAQ'- at the peak wave- length after the laser flash. k , and AA, differ by several orders of magnitude, therefore, they are normalized to the data corresponding to a ionic strength of 0.5. Using Et,NClO, as an electrolyte, the dependence of the ratios of kq/k,(0.5) and A A , / A A,(0.5) on the salt concentra- tion is the same. The plots of the ratios k,/k,(0.5) and A A , / A A,(0.5) us. salt concentration deviate increasingly if NaClO, or LiClO, is used.

Table I regarded as rough estimates of the true values only, for details see text.

Rate constants and thermodynamic data of the quenching reaction. Rate constants of k,, and k , , at c(sa1t) < 0.3 m o l / l have to be

Salt, c(salt) /(moI/I)

Et, NCIO, 0.0 0.1 0.3 0.5

NaQO, 0.1 0.3 0.5

LiCIO, 0.1 0.2 0.3 0.5

k , /(lo9 1. rno1-I.s- '1

0.12 0.22 0.40 0.50

0.32 0.74 1.03

0.29 0.45 0.60 0.92

(13.0) 9.44 5.96 4.23

7.63 2.88 0.75

8.22 5.65 3.92 1.24

0.18 1.82 2.86 3.09

1.82 2.86 3.09

1.82 2.53 2.86 3.09

Recueil des Travauw Chimiques des Pays-Bas, 114/ I1 -12, November/ December 1995 561

1.4 -

1.2 - - 2 1.0 - 3 2 0.6 -

3 0.8 - b

5 0.4 -

0.0 0.0 0.2 0.4 0.6 0.8

c(NaCI0,) I mol I-' Figure 6. Normalized quenching-rate constant k , and transient ab- sorbance AA of [We'- ... N a + ] in the presence of NaClO,. Lines are drawn to aid the viewer and are not calculated.

5.1.3. Activation parameters. The activation parameters of the quenching reaction are compiled in Table 11. The parameters were determined from the measured k, data. The enthalpies of activation are negative. No data on the viscosity of solutions of Et,NClO,, NaClO,, o r LiCIO, in AN as a function of temperature were available at salt concentrations of 0.5 mol/l. Therefore, temperature-de- pendent k23 values according to Eqns. 10 or 7 could be calculated from k, data only for pure AN solutions and at c(Et,NClO,) =0.1 mol/l. These data of k23 were also used for the determination of activation parameters, the results of these calculations are included in Table 11. In pure AN solutions the enthalpy of activation of the quenching process is almost the same whether we use k, or k23. If k23 instead of k is used in solutions with c(Et4NC10,) = 0.1 mol/l t i e enthalpy of activation

1.6 1

1.4 -

2 l2 -

j b ::I 2 0.6 -

0.4 -

0.2 7

0.0 ' I I I I I I 0.0 0.2 0.4 0.6 0.8

c(LiCI0,) / mol I-'

Figure 7. Normalized quenching-rate constant k , and transient ab- sorbance A A of [MAQ'- ... Li +] in the presence of LiClO,. Lines are drawn to aid the viewer and are not calculated.

Table II Apparent activation parameters of the quenching reaction.

- 13.1 f 4 . 6 0.0 ") - 13.3

0.1 ") - 16.0 - 17.6f 1.0

- 16.5 1.0

-6 .7k1.6

LiClO, - 0.3 f 0.7

a Data determined using k,,,

-137f15

-142+2

- 1 3 4 f 2

-95*5

- 7 5 f 2 4

ir details see text.

27.6 f 9.2 29.8 25.3 f 1.2 28.2 23.6f 1.8

21.7

22.0* 1.5

changes slightly from -17.6 kJ/mol to -16.0 kJ/mol, but it remains negative.

5.2. Discussion

5.2.1. Absorbance of transients. Absorption spectra of the anthraquinone radical anion have been reported in both DMF and AN s o l ~ t i o n s ~ ~ - ' ~ ~ ~ ~ ~ ~ ~ - ~ ~ . In DMF solutions, the longest-wavelength maximum of the absorbance is at 555 nm, in AN solutions at 544 nm. For MAQ, the absorbance maximum in AN has been reported to be at 535-544 nm14,38. The reported absorption coefficients vary between 11000 and 12000 1 mol-' cm-' in DMF and 8500 and 8900 1 mol-' cm-' in AN. Most of the measure- ments have been performed in optically transparent thin- layer cells. The radical anion in these cells is produced by electrochemical reduction of the anthraquinone. The radi- cal anions are reported to be stable on the electrochemi- cal time-scale. In most studies Bu,NCIO, or Et,NClO, were used as supporting electrolytes, although in one investigation different supporting electrolytes were used29. The latter paper reports that the absorbance maximum of the anthraquinone radical anion (AQ'-) in DMF solution shifts from 553 to 530 nm when LiCIO, is used as an electrolyte. Correspondingly, the absorption coefficient drops from 12000 to 9320. In our experiments MAQ'- should be produced as a transient by photoinduced electron transfer. We observe an absorbance maximum of the transient which depends on the nature of the added electrolyte. The observed wavelength' maxima of the transient in our experiments agree with the available data on the maxima of electro- chemically produced AQ '-. The differences in ab- sorbance in the presence of NaClO, and of LiClO, have not previously been reported. The larger shift of the absorbance maximum in the presence of LiClO, corre- sponds well with the higher association constant of MAQ'- and Li+. Although k, increases if NaClO, or LiClO,, is used as an electrolyte instead of Et,NCIO,, the transient absorbance at the peak wavelength remains al- most the same. This observation corresponds to the re- ported decrease of the absorption coefficient of AQ ' - in the presence of LiC10:9. Electrochemical and transient-absorbance measurements confirm the reaction mechanism suggested in the section 3 (kinetic model). Although electrochemical and tran- sient-absorbance measurements are performed on differ- ent time scales, both measurements reveal that there is a strong tendency for associates to be formed between MAQ .- and alkali cations. In electrochemical experi- ments the association takes place under equilibrium reac- tion conditions, while in the flash experiments the forma- tion of associates cannot start before the photoinduced

562 R. Frank, H. Rau / Tris(2,T-bipyridine)ruthenium ( I I ) complex by 2-methylanthraquinone

electron transfer process. The formation of these associ- ates appears to be complete by the time the transients are observed, approximately 1.3 ps after the laser flash. The electron-transfer process itself should be almost indepen- dent of this association. This problem will be discussed in more detail in the next section.

5.2.2. Rate constants. According to the Marcus theory, k23 and, according to the equations given in section 3 (kinetic model), k should both increase with decreasing AGO of the quenciing reaction. Obviously, that was only partly observed in our experiments; k , increases in the expected manner if the variation of AGO can be attributed to changes of El, , which are due to changes in the electro- chemical activity of the Rubpy and MAQ species with salt concentration. For different salts, however, when the changes of El, , and AGO are caused by the association between the alkali cations and MAQ'-, k , is not very dependent on AGO. That means that for our experiments Eqn. 4.1 is not a valid expression for AG23 as a function of the electrochemical redox potentials. El, , , and corre- spondingly the electrochemical AGO, reflect an equilib- rium in an ensemble of MAQ, MAQ'-, and associated MAQ'- species at the electrode. But the photoinduced oxidative quenching process occurs between one * Rubpy and one MAQ molecule, and the association of the MAQ'- with alkali cations takes place after this electron transfer. It appears that the quenching process and the subsequent association between the MAQ radical anion and the alkali cation are independent processes, which are not coupled thermodynamically. Therefore, the proba- bility of the electron transfer, described by k , and k,, is not changed by the association. For the estimation of rate constants k,, and k3, we therefore assumed that the correlation between k , and AC,, in the presence of Et,NCIO, is the most correct one to describe the electron transfer in our system. Thus we use a new quantity,

AG23, shown in Figure 4, for the description of the quenching processes in the presence of alkali cations. If Eqn. 7 is valid, according to Eqn. 4 it should be possible to fit the data in Figure 4 to a parabola and to determine A from the regression parameters. The curves shown in Figure 4 represent such parabolas, but AGO in our system is rather small and therefore the curves are only slightly bent, so we cannot expect to obtain reliable values of A by this method. Therefore, it would appear to be more appropriate to test whether the slopes of the curves are near to - 0.2 mol/kJ equal to - . R . T , according to Eqn. 4. This expectation is fulfilled in all experiments. From other experiments, it is known that A is of the order of 100 kJ/mol for polar solvents like AN2'. Using Eqns. 7 and 10, measured k , data, and estimated diffusion-controlled rate constants k ,, and k, , , we can calculate the values of k23 given in Table I. The values determined from Eqns. 7 and 10 agree, within numerical error. Using the effAG23 to calculate k , according to Eqn. 9, k3, can also be calculated according to Eqn. 8. We used k,, x=- k23 and k3, -=zz ( k , + k,,) in order to derive Eqn. 7. k,, decreases from 6.53.109 in pure AN to 4.73. lo9 at a salt concentration of 0.5 mol/l. Comparing the data of k,, and k , reveals that k,, >> k? is a fair assumption to describe the experiments in dilute solu- tions, but at higher salt concentrations k,, > k23 seems to be more appropriate. In order to derive Eqn. 10, we used k3, -=K ( k , + k 3 4 At the moment we have no exact data upon which to judge the validity of this assumption, as we have no data on k b . According to the Marcus theory, the back electron trans- fer to the ground-state molecules in the successor com- plex or contact ion pair (CI), which is described by k, , takes place in the inverted region. Therefore, k , in our

eff

experiments should increase with increasing ionic strength. Taking into account only k3, and k3, the assumption k3, -=K ( k , + k,,) does not hold at low salt concentrations, at higher salt concentrations k3, < ( k , + k,,) seems to be more appropriate than k3, << ( k , + k,,). If we accept that k , > 1 .10" holds in our experiments, the assump- tion k3, << ( k , + k?,) will become valid at salt concentra- tions equal to or higher than 0.3 mol/l. This also means that Eqns. 7 and 10 are valid in this range of concentra- tion. In any case, the rate constants k23 determined by the methods described have to be treated with great caution. Especially when the ionic strength used in the experiments was lower than 0.3 mol/l, the determined values of k,, should be taken as rough estimates rather than as exact values which describe the electron transfer process. In Figures 5, 6, and 7 the dependence of k,/k,(0.5) and of AA/AA(O.5) on ionic strength is compared. If k,, ( k , + k3,) according to Eqn. 10, the rate of formation of the successor complex is proportional to k , and, in conse- quence, the amount of MAQ'- produced in the quench- ing process is given by Eqn. 12, where p stands for a unknown proportionality factor. The observed transient absorption AA should be proportional to the amount of MAQ'-, so with Eqn. 12 we finally get Eqn. 13, which is suitable for a comparison of k,/k,(0.5) and AA/AA(0.5).

k , . k34 n(MAQ'-) = p .

( k b + k 3 4 )

kij(0.5) and AA(0.5) are the rate constants and the tran- sient absorbance at ionic strength 0.5 mol/l, respectively; the same symbols without the index are the corresponding values at any ionic strength. From Eqn. 12, it becomes clear, that k,/k,(0.5) and AA/AA(O.5) can differ from one another. If the changes of k , and k,, with ionic strength are identical, k,/k,(0.5) and AA/AA(O.5) curves are identi- cal. If the increase of k , with increasing ionic strength is larger than that of k3, then k,/k,(0.5) and AA/AA(0.5) deviate from one another in such a way as that observed in our experiments in the presence of NaCIO, and LiC10,.

In the presence of Et,NCIO, no association occurs between MAQ'- and the electrolyte cation. The separa- tion of Rubpy3+ and the MAQ'- is supported by the increasing ionic strength and k3, increases. From the considerations discussed above and the observed be- haviour of k /k,(0.5) and A A AA(0.9, it follows that k ,

concentrations of Et,NCIO,. This increase obeys the pre- dictions of the Marcus-inverted region, i .e . k , increases although AG,, the free enthalpy of the back electron transfer in the successor complex, becomes less negative with increasing ionic strength. In the presence of NaCIO, and LiCIO, association occurs between MAQ'- and the alkali cations. If the formation of "a+ ... MAQ'-] and [Li+ ... MAQ .-I starts immediately after the electron-transfer step then the separation step '34' no longer takes place between molecules of opposite charge. The value of the rate constant of the separation step k,, will deviate from that given in Table I. Now, the attractive electrostatic interactions no longer dominate the separation process and the corresponding rate con- stant k3, has to be estimated by Eqn. 2. According to this equation, due to the increase in viscosity with increasing salt concentration, the rate constant of the separation process of Rubpy3+ and "a+ ... MAQ '-1 or [Li+ ... MAQ '-1 decreases with increasing ionic strength. According to

increases in he system Rubpy /+ /MAQ'- with increasing

Reccieil des Trauaux Chimiques des Pays-Bas, 114 / 11 -12, Nouember/December 1995 563

Eqn. 13 this change of k,, (in a first assessment k , is assumed to remain unchanged) also causes a deviation between k,/k,(0.5) and AA/AA(O.5) in such a manner as that observed in our experiments. AA/AA(O.S) is larger than k,/k,(0.5) if the ionic strength is lower than 0.5 mol/l and it is lower than k,/k,(0.5) if the ionic strength exceeds 0.5 mol/l. This, of course, is a conse- quence of the normalization, the essential feature of the plots is the difference in curvature. If in addition to the decrease of k,, (according to Eqn. 2), k , increases, the difference between k,/k,(0.5) and A A/AA(O.5) becomes even larger. Following these considerations, the more pronounced difference between k , / k , ( 0 . 5 ) and AA/AA(OS) in the presence of LiC10, can be caused by two reasons. (i) Due to the larger association constant between MAQ’- and Li+ the formation of [Li +... MAQ‘-] is more expressed and/or (ii) the increase of k , with increasing ionic strength is more expressed. It is reason- able that both processes are acting. Which one is domi- nant cannot be determined by the results of our measure- ments, although we guess that the action of the associa- tion prevails.

5.2.3. Activation parameters. If k , is used for the determi- nation of activation parameters of the quenching reaction the data in Table I1 result. In this case negative enthalpies of activation are observed. The phenomenon of negative enthalpies of activation has been observed mainly in ox- idative quenching reactions of *Rubpy and has been discussed in some detail e l s e ~ h e r e ~ * ’ ~ ~ ’ ~ ~ ~ ~ ~ ~ ~ . Negative val- ues can result whenever the observed rate constant k , describes a complex reaction series and not the single elementary reaction of the electron transfer step. Espe- cially if AG23 is small and as a consequence reverse electron transfer from the successor complex to the pre- cursor complex becomes possible, apparent negative en- thalpies of activation are observed. In order to obtain more reliable information about the activation parameters of the electron transfer step, k,, should be used instead of k, . When we used data of k , determined according to the methods described above, we still observed negative enthalpies of activation. This holds for pure AN solutions and at c(Et,NCIO,) = 0.1 mol/l. This observation rein- forces our doubts, mentioned above, as to whether the simplification k , , << ( k , + k,,) holds at low ionic strengths. So the evaluation of activation parameters also supports the assessment that the data of k23 given in Table I should be taken as only rough estimates of the true values. At higher salt concentrations no evaluation of the data was possible, due to missing information about the temperature dependence of the viscosity of the solu- tions.

6. Conclusions

Electrochemical measurements and transient spectra con- firm a strong tendency of MAQ’- to form associates with alkali cations in acetonitrile (AN) solution. This tendency increases from Na+ to Li+. The further experiments and methods described in this work offer a better insight into the complex mechanism of the electron transfer reaction in a system with low AC,,. They show that photoinduced electron transfer is possible in such systems, even uphill, and that reverse electron transfer, process ‘32’ according to the reaction mechanism given in section 3 (kinetic model), has to be taken into account in all cases. Testing various methods to simplify the complex expression of k , revealed that assumptions such as k3, e ( k , + k,,) should be used with great cau- tion. The results following from such simplifications should

be tested very carefully. The experiments show further that Eqn. 4.1 cannot be used in order to estimate the AC,, when the redox potentials observed in electrochemi- cal measurements are governed by consecutive processes at the electrode. The comparison of the k,/k,(0.5) and AA/AA(O.5) data supports the prediction of the Marcus theory that the back electron transfer in the successor complex or contact ion pair to the ground-state molecules should show an inverted behaviour. Further experiments to confirm these results and to get more information on k , are underway.

Acknowledgement

Helpful discussions with Dr. G. Greiner, who designed the program for the calculation of the rate constants k,,, are gratefully acknowledged.

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