Self-termination rate of para-substituted benzyl radicals in aqueous solutions: a time-resolved study

215

1. Photo&em. Photobid A: Chwn., 70 (1993) 215-221

Self-termination rate of para-substituted solutions: a time-resolved study Ahmed M. Mayouf, Helge Lemmetyinen

benzyl radicals

in aqueous

and Jouko Koslcikallio

Laboratory of Physical Chemistty, Universityof Heisinki, Meritulinkur~ XC, SF-00170 Hdsinki {Finland)

(Received July 24, 1992; accepted October 8, 1992)

Abstract The self-termination rates of the benzyl radical (CJ-&-CH,‘) and para-substituted benzyl radicals (X-CJ&-CH~~) were studied in aqueous solutions. The Arrhenius parameters and activation energies were determined in the temperature range 275.5-328 K. The kinetic activation energies of these radicals were close to the dynamic activation energy of the solvent, indicating that the termination rate is controlled by diffusion. The values for the rate constants (UC, (log dm3 mol-’ s-l)) and the activation energies (E (kJ mol-I)) were 5.94kO.52 and 14.69k0.61 for CH@-C&-CH~~, 4.52kO.2 and 17.65 k1.16 for CH&J-I.&H~‘, 3.07~kO.45 and 17.58f0.97 for H-C&.,-C&~,‘, 4.13&0.81 and 19.10&1.20 for Cl-C&I&Hz and 4.17kO.44 and 14.62*0.52 for NO&J&I,-C&‘.

1. Introduction The bimolecular

self-termination reaction radicals in solution has

rate

been shown to be controlled by radical diffusion [l-5] and follows the van Smoluchowski equation

constant

of

alkyl

UC,= (87r/lOOO)aNpD

(1) where u is the pin factor, p is the reaction diameter, N is Avogadro’s number and D is the diffusion coefficient of the corresponding stable hydrocarbon molecule. For small a&y1 radicals, in the absence of steric hindrance, the rate has been found to vary in the range 109-10” dm3 mol-’ s-l at room temperature in solvents of low viscosity. In general, the fate is influenced by many factors such as mutual diffusion [6, 71 and self-diffusion [8, 91 coefficients, and the presence of coulombic forces [lo, 111. Experimental difficulties may arise in the accuracy of molar extinction coefficient measurements of radicals in different solvents and in estimations of the diameters and diffusion parameters of radicals [8]. Reactions of tert-butyl radical [12-U] and benzyl radical [IO, 151 have been studied intensively, both experimentally and theoretically, in different solvents and over wide ranges of temperature. Most of the data in the literature concerning these two radicals and their termination lOlO-6030/93/$6.00

rates are inconsistent with the van Smoluchowski equation. In this work, self-termination reaction rates of para-substituted benzyl radicals, generated by 308 nm laser flash photolysis of para-substituted phenylacetatocobalt(II1) complexes, were measured in aqueous solutions in order to determine the influence of the substituent on the selftermination rate. 2. Experimental

details

2. I. Synthesis of aquopentaaminecobalt(IIZ) perchlorate

Aquopentaaminecobalt(II1) perchlorate ([IW3)5(H20)(Co3+)](C104)3) was synthesized 1161 from carbonatopentaaminecobalt(II1) nitrate ([(NH3),(C03)(Co3+)](N03)~) which was in turn prepared by air oxidation of an aqueous solution of cobalt nitrate (Co(NO&) ammonium hydroxide (IQ&OH) and ammonium carbonate ((NH&C03). The oxidation was slow and was carried out overnight. The [(NH3)&03)(Co3+)](NO& formed was converted to aquopentaaminecobalt(II1) perchlorate by dissolving in hot water and then adding hot concentrated perchloric acid (HC104) until the effervescence of the mixture ceased and further addition of concentrated perchloric acid caused 0 1993 - Elsevier Sequoia. AU rights reserved

216

A. M. Mayouf et al. I Self-tcmzination of benzyi mdicak in aqueous solution

no further precipitation. An additional treatment with HClO* was necessary to remove the remaining traces of nitrate from the complex. 2.2. Preparation of carboxylatopentaaminecobalt(IIZ) perchlorate [(NH,),(RCOO-)(Co” +)wO4)2 Organic acid (X-C,H&H~OOH, Xm C&O, CH,, H, Cl or NOa) (20 mmol) was treated with 10 ml of 1.75 N NaOH, heated to 80 “C for 10 min, and then filtered. To the filtrate (pH <6.5) a solution of 1.0 g of [(NH,),(H,O)(Co)](ClO,), in 2 ml of hot water was added. The mixture was left for 2 h at 75-80 “C, cooled to about 40 “C and added to a separation funnel containing 5 ml of water, 5 ml of 60% HClO, and 150 ml of diethyl ether. The ether was used to dissolve and remove the unchanged organic acid. The aqueous layer separated after about 15 min and was treated again with another portion of 150 ml of ether. The aqueous layer was then bubbled with air for 10 mm to remove the ether, treated further with 10 ml of 60% HClO,, and finally allowed to stand for about 2 h at a temperature below 0 “C. The precipitate was filtered and dissolved in a small quantity of hot water and cooled to 0 “C. The crystals [(NH~)(X-C&&-CH,COO -)(Co”‘)](CIO,), were filtered and dried in vacua at 30 “C for 10 h. All the chemicals used in this work for the preparation of organocobalt complexes were of analytical grade and were used as received. 2.3. Laser flash photoljvis The flash photolysis experiments were carried out with a 308 nm excimer laser (ELIM 72, Special Design Bureau of Estonian Academy of Science) focused on the sample. The laser pulse width was about 10 ns full width at half-maximum (FWHM) with a maximum energy of about 50 mJ per pulse. Transient absorptions were monitored with a 100 W xenon lamp. The width of the xenon lamp pulse was 2 ms and was stable at its maximum height to within 2% for a period of 100 JJ,s.The excitation and monitoring pulses were at right angles to each other. The detection wavelength was selected before reaching the sample by a monochromator (MDR 23). The monitoring beam was focused on the sample in an area of about 5 mm’ coinciding with the region excited by the laser. Beyond the sample the monitoring beam was focused on the entrance slit of a second monochromator (MDR 23). The signal was -detected by a photomultiplier (FED-l(M), which was connected to a differential amplifier (Tektronix 7 A 7) of a 500 MHz transient

digitizer (Tektronix 7912 AD). The data were stored in a computer (Olivetti 24 M) for further manipulation. A least-squares fitting procedure was used to calculate the rate parameters from the experimentaI decay curves. The concentration of the organocobalt complex was varied from 0.4 x low3 to 1.2~ 10m3mol dmm3. The samples were degassed for at least three freeze-pump-thaw cycles. The concentration limit of the samples was restricted by the useful transmittance of the solution at the monitoring wavelength.

3. Results and discussion The photolysis of pentaaminecarboxylatocobalt(II1) perchlorate, [(NH&RCOO)(Co)](ClO,),, in aqueous solution yields alkyl and carboxylato radicals. Carboxylato radicals produce alkyl radicals by fast decarboxylation [17-191. The alkyl radicals dime&e by a diffusion-controlled selftermination reaction to dialkylethane.

5NH, + W + + XGH&H, [(NH,),(X~H&H,-cOO)(Co3+)~+

+ CO, 2

5NH, + co2 + + X-c,H&H,-COO X
=

X-C&&H,

+ X-CJ&-CH,

(2a)

+ C@

(2b) (3)

2

X-&H&H&Hz-C&-X

(4)

Scheme 1.

The photolysis of a pentaaminecarboxylatocobalt(IJ1) complex (Scheme I), in which the acid ligand is a phenylacetato or contains a para substituent, produces a benzyl radical or a parasubstituted benzyl radical (X-W%-CI%, X= CH30, CH3, H, Cl or NO,) which dimerizes to para-substituted diphenylethane (X-C.&-CH,CH,Q,&-X). The absorption of the para-substituted benzyl radical (Fig. 1) was monitored at its maximum absorption wavelength (Table 1). It decayed according to a second-order rate law (see inset in

Fig. 1) shown by the following equation d[R]/df = 2k,[R]’

(5) where [R] is the concentration of the radical and 2k, is the termination rate constant.

A. M. Mayouf et al. / Self-lmnination

of bemyl

radlcah

217

in aqueoussolution

TABLE 2. Experimental rates of the second-order decay of parasubstituted benzyl radicals at different temperatures Temperature

I+, (105 s-l)

(“C)

u

I

1 1.80 -’

2.5 15.0 25.0 35.0 45.0 55.0 65.0

I

m

n i

I

0.00 4 I

C&O

CH,

H

cl

N4

12.95 16.26 19.05 28.49 31.31 35.50 46.98

3.45 5.33 6.20 7.77 8.48 13.10 16.09

1.82 2.59 3.92 4.20 5.22 6.29

3.02 4.31 5.56 8.87 8.84 9.89 15.95

8.38 14.53 15.11 19.70 23.91 23.33

I

0.20 0.60 1.00 1.40 1.80

TABLE 3. Arrhenius termination reaction

parameters and rate constants of substituted benzyl radicals

of the self-

T / lXlO-'S Fig. 1. Decay curve of benzyl radical formed by laser excitation of a 4.73X10-’ mol dm-’ aqueous solution of [(NH&(C&-CH&!OO-)(CQ~+)](C~O~)~ The monitoring wavelength was 315 nm. The second-order rate fitting is shown in the inset. TABLE 1. Maximum wavelength (A), molar absorptivities (6) and relative quantum yields (@#a) for substituted benzyl radicals formed from the laser excitation of cobalt complexes in aqueous solution Substituent

cH,O a3

H Cl NOz

A,,,

(WW

(nm)

Fdn? mol-’

321 320 315 317 3m

2900 74Nl 9oocl 7200 3oMx)”

‘From ref. 10. bQuantum yield of b enzyl radical ‘Estimated value.

cm-‘) 0.372 k 0.003 0.292 * 0.002 1.OOD*o.OOa 0.305 f0.016 0.372 *0.003

considered

to be unity.

The experimental data were based on the optical absorption of the transient radicals, where the absorption (A) is related to the concentration [R] by [R]=A/d and the rate constant of the termination is related to the experimental rate by UC,= elk_,; E is the molar absorption coefficient of the radical and 1 is the path length of the reaction cuvette. Thus d(A)/dz = (l/e&!~&(A)~

(6)

Bimolecular rate constants of the combination reaction of substituted benzyl radicals were calculated from the experimental rate constants (Table 2) measured in the temperature range 275.5-335 K. They are listed in Table 3 together with the Arrhenius parameters which were determined by plotting log 2k, against l/T (Figs. 2a-2e).

Substituent

cH,O a3 H cl N4

log

A

12.35 12.75 12.57 12.97 12.18

10.07 f0.30 f 0.07 +0.05 +0.03

E (kJmol-‘)

UC,

14.68 f. 0.61 17.65 &1.16 17.58 f 0.97 19.11 f 1.20 14.62+0.52

5.94 f 0.52 4.52iO.20 3.07 *0.47 4.13 kO.81 4.17*0&l

(lo9 dm3 mol-’

s-l)

The diffusion rates of the radicals were also calculated using the van Smoluchowski equation (eqn. (1)). In order to estimate the diffusion coefficients and reaction diameters, the molecular volume of the corresponding stable hydrocarbon molecule of the radical was determined by the atomic increment method [20]. The values of the radii were determined from the formula for a sphere, and the diffusion coefficients were estimated from the approximated Stokes-Einstein relationship as r= (3V,/4#n

(7)

D =kTIthrrq

(8)

where V,,, is the molecular volume of the radical, k is the Boltzmann constant, T is the absolute temperature, 17is the viscosity of the solvent and r and D are the molecular radius and molecular diffusion coefficient respectively. The second-order rate constants (UC;3 for diffusion-controlled reactions calculated from the van Smoluchowski equation for the substituted compounds are almost equal to 1.65~10’ dm3 mol-’ s-l. Replacing 6~ in eqn. (8) by 4~ to allow for the “slip” rather than “stick” boundary condition increases the rate of diffusion to avalue of 2.48 X 10’ dm3 mol-’ s-‘. The diffusion coefficients were reformula of estimated from the corrected Wilke-Chang 121, 221, in which D=

7.4x lO’*(?JCM,,,)‘“(T/~)(1/V’““)

(9

218

A. M. Mayouf et al. I Self-tminath

9.0

I

1 3.0

3.2

3.4

I

9.0 1 3.0

3.6

LTx103 degree K

3.0

3.2

3.4

of bemyl mdicals in aqueous sol&on

3.2

3.4

3.6

LTx103 degree K

3.0

3.6

3.2

3.4

3.6

1/Tx103 degree K

lfl’xl@ degree K e

10.0

liTx103

degree K

Fig. 2. Arrhenius plots for the combination (c) X=Cl, (d) X=CH,O and (e) [(NH~),(X-C~~~OO-)(~3+)l(CI0,),.

reaction rate of the para-substituted X=N02) produced by laser

where ?P is the association factor of the solvent (this factor is equal to 2.6 for water) and M, is the molecular weight of the solvent. The calculated values of the diffusion coefficients and the van Smoluchowski diffusion rates are presented in Table 4. As can be seen in the table, the reaction rate decreases as the reaction diameter increases. The transient electronic spectra of substituted benzyl radicals are similar to that of benzyl radical, except for a slight shift of a few nanometres to a longer wavelength [23-251. The paru-methylbenzyl radical spectrum is essentially identical with that of the benzyl radical [23-271. The absorption spectrum of the para-chlorobenzyl radical shows [lo] that the chlorine substituent, like the methyl substituent, causes only a minor perturbation in

(X) benzyi radicals ((a) X =H, photolysis of an aqueous

(b) X=CH,, solution of

the electronic level of the benzyl radical. The methoq group changes the spectrum more, although the main bands are still very similar [lo, 281. The effects of the substituents on the hypefine constants [29] of the ring protons in the electron spin resonance (ESR) spectra of the benzyl radicals are extremely small, which indicates a limited perturbation of the electron spin distribution in the aromatic ring caused by the substitution. However, this may influence the rates of the combination reactions. In general, the substitution alters the electron a&&y at the central carbon due to the delocalization of IT electrons over the substituent, and increases the resonance stabilization of the benzyl

A. M. Mqouf

et al. / Self-termination

of ben& radicals

219

in aqueous solution

4. Molecular volumes (V, (lo-‘I cm’)), reaction diameters (7~ (lo-’ cm)), diffusion coefficients (D (lo-’ cm2 s-l)) and van Smoluchowski rate constants (UC(109 dm3 mol-’ s-l)) for the reactions of para-substituted benzyl radicals in aqueous solution

TABLE

CH,O CH3 H Cl NOZ

115.3 109.1 92.1 106.6 114.7

6.036 5.928 5.608 5.882 6.028

0.723 0.737 0.779 0.742 0.724

1.OM 1.105 1.169 1.114 1.087

1.185 1.225 1.356 1.242 1.189

1.651 1.653 1.653 1.652 1.651

2.478 2.479 2.481 2.479 2.479

2.710 2.748 2.878 2.764 2.712

‘Stick boundary condition. $lip boundary condition. CAccording to the Wilke-Chang formula.

radical, consequently increasing the tendency to dimerization of the substituted beuzyl [30]. Self-termination rates (Uc,(dm3 mol-l s-l)) of benzyl radicals in solution have been measured by several workers. Reported values for the dimerization reactions of benzyl radicals include 5.5 x lo9 in 50% AN-H20 (E = 9000 dm3 mol- ’ -I and AE=6.7 kJ molP1) [31], 3.6X109, :2x lo9 and 5.2X lo9 in cyclohexane [5, 10, 151 and 4.1X109 in toluene [5]. In this work a rate constant of 3.07X lo9 dm3 mol-1 s-l for the dimerization of benzyl radicals was obtained using a value of 9000 dm’ mol-’ cm-’ for E. Avalue of 17.58 kJ mol-’ was obtained for the activation energy. This value is close to the dynamic activation energy of water determined from Andrade’s relationship+. The satisfactory agreement between these two values indicates the reliability of the results for substituted benzyl radicals. The reaction rate constant for substituted benzyl radicals are larger than for unsubstituted benzyl radicals. According to the theoretical calculation for diffusion coefficients, we would expect a decrease in the rate with substitution (Table 5). TABLE 5. Ratio of the experimental rate constant to that calculated theoretically from the van Smoluchowski equation Substituent

(2&v%?

(ucPlus;3b

CKO CH3 H Cl NO?

2.19 1.64 1.07 1.49 1.54

0.970 1.040 1.230 1.100

‘This work. “Reference 10. +L.og?J= log A, + (AEJ2.303 RT). Data for water viscosity (q) and corresponding temperature were taken from ref. 32. The calculated value of AE, was 17.73 kl mol-’ and log A., = - 3.141 (see ref. 33). The self-diffusion coefficient of water is 2.27 X lo9 m’ s-l (see ref. 34).

The experimental rate constants are higher than those calculated using the van Smoluchowski equation. (Most of the reported values of the selftermination rate constants are higher than that calculated using the van Smoluchowski equation (see ref. 33).) The benzyl radical is the only carbon radical that diffuses with a rate approximately equal to the rate of diffusion of the corresponding hydrocarbon molecule [35], and thus the experimental rate of diffusion of the benzyl radical should be close to the theoretical rate. It was conclusively observed that the ratio of the experimental rate to the theoretical rate is close to unity (see Table 5). Few data are available on species possessing dipole moments. Dipole moments do not affect the experimental diffusion coefficients of pseudospherical molecules in the same solvent [36], but changes are observed when the diffusive medium is changed from a hydrocarbon solvent to protic or aprotic solvents. The highest coefficients are seen for aprotic solvents and the lowest for hydrocarbon solvents [36]. This observation may support the present results obtained in water relative to those obtained in cyclohexane [lo] (see Table 5). In general, mutual diffusion depends on the form of the direct interparticle potential. Since the electron is completely delocalized over the whole radical, and thus the reaction should be equally probable at any location [37], the existence of a further step in the mechanism of the reaction is proposed in order to interpret the results obtained. The step suggested is a head-totail (or (Y to para coupling) dimerization step (Scheme 2) similar to cross-reactions of different radicals. The dimerization rate is the rate-determining step, and can be calculated .from Scheme 2 as 2k, = (2k,“f3(k,/k - D+ k,) Since k-, Q: kf

(12a)

220

A. M. Mayouf et al. / Self-termination of benzyl radicals in aqueous solution

References

Scheme 2.

2k, = 2kDeif

112b)

rate constant of Here 2kDeffis the effective diffusion, which corresponds to the case in which the interparticle potential is minimized due to partially opposite charges of the reacted centres (a and para positions) of the combined radicals. These types of intermediates have been observed for the triphenyhnethyl radical [38], which dimerizes to 1-diphenyhnethylene-4-trityl-2,5cyclohexadiene but not hexaphenylethane, and in the dimerization processes of substituted phenoxyl radicals [39], in which the reaction is mainly the headto-tail type [40]. Relatively few rate constants have been measured for reactions between two different free radicals in solution [41]. It should be noted that the reaction rate of different radicals is higher than the reaction rate of identical radicals [42]. Even though there have only been a few measurements of cross-reaction rates, it has been observed that the photolysis of asymmetric diketones produces cross-reaction products in yields which are twice as high as those of the products of the combination of symmetric radicals [43]. The same ratio is obtained in solvents of either low or high viscosity, which proves that the reaction is not a cage reaction, and the rate of the crossreaction [43] is twice the rate of combination. If two radicals have a self-reaction rate of the diffusion-controlled limit, the cross-reaction of these two radicals will be equally fast [42]. In conclusion, we believe that the dipoie moment influences the reaction rate such that the partial charge created at the dipoles of the radical increases as the electron affinity of the substituent is increased. Consequently, the reaction rate will increase as the dipole moment increases. The activation energy is also influenced by polar effects, as shown in Table 3. Further investigations of the substituent effects on the oxidation-reduction reactions of these radicals are in progress.

1 D. F. Calef and J. M. Deutch, Annu. Rev. Phys. Chem., 34 (1983) 493. 2 J. P. Lorand, Z%g. 1~10%. Gem, 17 (II) (1972) 213. 3 D. Griller and K U. Ingold, Inf. I. Chem. Kin&., 6 (1974) 453. 4 H. Paul, In& 1. Chem. Kiner., 10 (1979) 495, and references cited therein. 5 M. Lehni, H. Schuh and H. Fischer, Int. I. Chem. Kinel.., 10 (1979) 705. 6 R. Zwanzing, Adv. Chem. Phys., 15 (1969) 325. 7 J. M. Deutch, J. Chem Phys., 73 (1980) 5396. 8 P. G. Wolynes and J. M. Deutch, I. C&m. Phys., 65 (1976) 450. 9 J. M. Deutch and B. U. Felderhof, 1. Chem. Whys., 59 (1973) 1669. 10 R. F. C. Claridge and H. Fischer, 4 Phys. Chem., 87 (1983) 1960. 11 P. G. Wolynes, Annu. Rev. Phys Chem., 31 (1980) 345. 12 H. &huh, E. J. Homiton, H. Paul and H. Fischer, Heh. Chim. Acta, 57 (1974) 2011. 13 J. E. Bennett and R. Summers, .l. Chem. Sot. Perkin Tram. II (1977) 1504. 14 J. Bennett, J. Eyre, C. Rimmer and R. Summers, Chem. Whys. Lett., 26 (1974) 69. 15 C. Huggenberger and H. Fischer, Helv. Chim Acta, 64 (1981) 338. 16 R. D. Butler, PhD Thesis, Stanford University, 1964, p. 23. 17 E. R. Kantrowith, M. 2. Hoffman and J. F. Endicott, J. Phys. Chem., 75 (1971) 1914, 18 G. J. Ferraudi, Inorg. Chem., 17 (1978) 2506. 19 J. C. Scaiano, W. J. Leigh and G. Ferroudi, Can. J. Chem., 62 (1984) 2355. 20 J. T. Edward, J. Chem. Educ., 47 (1970) 291 and references cited therein. 21 C. R. Wilke and P. Chang, Am Inst. Chem. Eng. J., l (1955) 246. 22 P. Chang and C. R. Wilke, J. Phys. Chem., 59 (1955) 592. 23 T. Izumida. T. Ichikawa and H. Yoshida. J. Phvs. Chem.. 8# (1980) 60. ’ 24 J. E. Hodgkins and D. Megarity, I. Am. Chem. Sot., 87 (1965) 5322. 25 K. Tokumura, T. Ozaki, H. Nosaka, Y. Saigusa and M. Itoh. I. Am. Chem. Sot.. 113 (1991) 4974. 26 D. M. Friedrich and A. C. Albrecht, 1. Chem. Phys., 58 (1973) 4766. 27 H. Hiratsuka, T. Okamura, I. Tanaka and Y. Tanizaki, 1 Phys. Chem., 84 (1980) 285. 28 K. Tokumura, H. Nosaka and Y. Fujiwara, Chem Phys. Let& 177 (1991) 559. 29 P. Neta and R. H. Schuler, 1. Whys Chem., 77 (1973) 1368. 30 H. Hunng and P. K. Lim, 1. Chem. Sot. (C), (1967) 2432. 31 A. M. Mayouf, H. Lemmetyinen and J. Koskikallio, Acta Chem. Scan& 44 (1990) 336. 32 R. C. Weast and M. J. Astle, CRC Handbook of Chemistty and Physics, CRC Press, Boca Raton, FL, 60 edn., 19791980. 33 H. Shuh and H. Fischer, Helv. Chim. Acta, 61 (1978) 2130. 34 K. Tanaka, J. Chem. Sot., Faraday Trans. 2, 71 (1975) 1127. 35 R. D. Burkhart and R. J. Wang, J. Am Chem. Sot., 95 (1973) 7203. 36 T. C. Ghan, 3. Chem. Phys, 79 (1983) 3591. 37 G. B. Watts and K. U. Ingold, ): Am. Chem Sot., 94 (1972) 491. <

A. M. Maymfet

al J Self-termination ofbenzyl radicals in aqueous solution

38 H. Landkemp, W. Th. Nauta and C. MacLean. Tetrahedron Lett., 2 (1968) 249. 39 L R. Mahoney and S. A. Weiner, J. Am. Chem. Sot., 94 (1972) 585. 40 V. D. Pokhodenko, V. A. Khiihnyi and V. A. Bidzilya, Russ. Chem. Rev., 37 (1968) 6.

221

41 E. T. Denisov, Rus. Chem. Aev., 39 (1970) 31. 42 K. W. Ingold, in J. Kochi (ed.), Free Radical, Vol. I, WileyInterscience, New York, 1973, Chapter 2, p. 65. 43 W. K. Robbins and R. H. E&man, J, Am. Chem. SOC., 92 (1970) 6077.