Fast liquid-phase bimolecular reactions of aromatic

'Reviews of Chemical Intermediates, 7 (1986) 271--300

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

271

FAST LIQUID-PHASE BIMOLECULARREACTIONSOF AROMATICFREE RADICALS IGOR V. KHUDYAKOV Institute of Chemical Physics, USSRAcademy of Sciences, I17334, Moscow, U.S.S.R. BORIS I. YAKOBSON Institute of Solid-State Chemistry, Siberian Branch of the USSRAcademy of Sciences, 630091, Novosibirsk, U.S.S.R.

CONTENTS I. II. III.

Vl. VII. VIII.

Introduction ........................................................ 271 Preparation and Absorption Spectra of Aromatic Radicals ............ 272 Aromatic Radical Recombination and Disproportionation Kinetics ...... 273 A. Diffusion-enhanced reactions ..................................... 274 B. Solvent viscosity effect on recombination (disproportionatlon) kinetics ......................................................... 277 C. Pseudodlffusion reactions. Radical reactivity anisotropy ......... 280 D. Rates of H-atom transfer in~aroxyl decay reactions ............... 286 Solvent Effect on Aromatic Radical Recombination and Disproportionation Kinetics ...................................................... 287 A. Effect of "non-solvating" solvents on recombination kinetics ..... 288 B. Effect o f " s p e c l f i c " solvation on recombination and disproportionation rates .................................................. 289 C. Recombination and disproportionation of aromatic radicals in strongly non-ldeal solvent mixtures .............................. 291 Electron Transfer Kinetics in Bimolecular Reactions ................. 291 A. Activation-controlled reactions .................................. 292 B. Pseudodiffusion reactions ........................................ 292 C. Oxidation with copper (II) compounds ............................. 293 Cage Effect Dynamics in Photodissociation to Aromatic Radicals ...... 294 Conclusions ......................................................... 297 References .......................................................... 299

I.

INTRODUCTION

IV.

V.

Aromatic free radicals are important intermediates in a range of chemical, photo- and radiation-induced chemical reactions [1,2]. conjugated r-radicals containing aromatic rings.

Aromatic radicals are

The hyperfine interactions

in them are due to the spin polarization mechanism. Examplesof aromatic radicals are: aroxyl, semiquinone, 2-arylindane-l ,3-dione-2-yl, ketyl, benzyl, aminyl : 6 6 o --~- ~-

0162-7546/86/$10.50

© 1986 Elsevier Science Publishers B.V.

272 In recent years the kinetics of recombination and other bimolecular reactions involving aromatic radicals (aroxyl, 2-arylindane-l,3-dione-2-yl, aminyl) generated by antioxidants and stabilizers in polymeric matrices have been studied thoroughly and comprehensively (cf. e.g. [3,4]!). The rational choice of oxidation inhibitors and the prediction of antioxidant effectiveness in a particular composition is an urgent problem of both scientific and practical importance. For its solution, information on the inhibitor radical reactivities is necessary. At the same time, measurements of the rates of elementary chemical processes are of fundamental importance for chemical kinetics and chemical physics in general. Problems and theories related to solvent effects on th~ reaction rate and equilibrium, and to mechanisms of elementary reactions in liquid phase, can only be resolved on the basis of measured rate constants of elementary reactions, and their dependence on temperature, pressure and solvent properties. What distinguishes bimolecular reactions between radicals is that they are very fast, so fast in fact that their rates are controlled solely by the molecular mobility of the reactants. Today, the theory of diffusion-controlled reactions (including those between chemically anisotropic reagents) is in a welldeveloped stage. Currently, scientists feel the need for an "all-out" experimental investigation of diffusion-controlled reactions with a view to compare theory with experiment and determine the factors which control the rates of fast elementary reactions. An overview of such experimental work is presented here. The authors do not aim to carry out an exhaustive analysis of literature devoted to bimolecular reactions between aromatic radicals, but rather seek to highlight a number of current problems in the kinetics of elementary liquid-phase reactions. Special emphasis will be made on the so-called "pseudodiffusion" reactions between aromatic radicals. II.

PREPARATIONAND ABSORPTIONSPECTRAOF AROMATIC RADICALS

In their pioneering work carried out during the 1950s and 1960s Porter and coworkers [2] used the flash photolysis technique for generating, recording and identifying the absorption spectra of aromatic radicals. In aqueous solutions the kinetics of aromatic radical decay and the absorption spectra were studied using the alternative technique of pulsed radiolysis [5]. Flash photolysis s t i l l remains a very convenient method for generating radicals and recording their decay kinetics by optical density measurements in the absorption maximum. The following photochemical methods are known to produce aromatic radicals [I-3, 6-14]: direct photolysis of phenols, arylacylates, amines with UV light; photolysis of the C-C or C-O radical dimers; photoreduction of quinones and ketones; t r i p l e t carbonyl-sensitized photooxidation of phenols, hydroquinones, amines, 2arylindane-l,3-diones.

Along with photochemical reactions, dark reactions have

273

also been used for generating aromatic radicals [4,12,13], including: thermolysis of radical dimers in solution; quinone reduction to radical-anions in strongly alkaline solutions; oxidation of phenols with lead dioxide, etc.

Many

of the radicals investigated were in solution phase, in equilibrium with the corresponding diamagnetic dimers [4]. The absorption spectra of radicals were recorded with the flash photolysis apparatus or with a conventional spectrophotometer (for the cases of stable radicals and those in equilibrium with dimers). I t has been shown that for radicals, as for molecules, the evolution of the conjugation chain results in a bathochromic shift and a hyperchromic effect in the absorption spectra [15,16].

For example, the unsubstituted phenoxyl radical

has an absorption maximum at X : 400 nm [2].

Addition of at least one substitu-

ent at the ortho- and para-position results in longer wavelength shift to L 500 nm [13,16].

Successive substitution of the h-butyl groups in the stable

galvinoxyl radical with phenyl rings brings about an intensification of the radical color [16]. For the 2-arylindane-l,3-dione-2-yl series the position of the longest wavelength maximum strongly depends on the nature of substituents in the aryl fragment [15].

Introduction of electron donating substituents leads to a bathochro-

mic shift in the absorption spectra of radicals.

A Hammet correlation between

the longest wavelength transition and the a-constants of the substituents has been established [15]. The 2-(4'-dimethylaminophenyl)-arylindane-l,3-dione-2-yl

radical is a posit-

ively solvatochromic compound. The longest wavelength band in the spectrum of this radical has been identified as an internal charge transfer band. The frequency of this transition correlates well with the universal intermolecular interaction functions [17]. For the aromatic ketone, quinone and diphenoquinone molecules investigated, the carbonyl molecule ÷ neutral aromatic radical ÷ radical-anion evolution causes a steady red shift of the long wavelength peak [lO,12]. These results have been used for investigations of aromatic radical reactions in different solvents by kinetic spectrophotometry. III.

AROMATICRADICAL RECOMBINATIONAND DISPROPORTIONATION KINETICS

Aromatic radicals are a class of "stabilized" radicals and are normally inactive in many typical radical reactions. Mainly, they participate in bimolecular reactions with each other and with other radical species, and in reductionoxidation reactions.

Reactions of the following types have been studied most

thoroughly [1,3-8,10-13,18-24]:

274 R'+R"

2kl

, D (2k_l

(I)

RH" + RH" 2k2 ' R+ RH2

(2)

RH" * R; k3

(3)

,

R+ RiH

where Rl is the stable nitroxyl radical [lO]. Bimelecular reactions between radicals are fast and have high rate constants. Before we begin a review of the available kinetic data i t may be helpful to recall the fundamental principles of the theory of diffusion-controlled reactions. A. Diffusion-enhanced reactions This term is used for reactions whose rate depends in some way on the reagent diffusion rate. I f the reaction rate is totally determined by the diffusion rates of the reagents, the reaction is called diffusion-controlled.

Below, we

will give a brief account of the theoretical models used to describe the diffusion-enhanced reaction kinetics [25-28].

Sometimes i t helps to employ simple

geometrical models of reactants which differ as regards size, reactivity and dependence on reactant concentration.

Such models have been termed [26,31-32]

"white sphere", "black sphere" and "grey sphere", corresponding, respectively, to a non-reactive, infinitely reactive (obeying the Smoluchowski boundary condition [25,28]) and moderately reactive reagent (the radiation boundary conditions [25,28]) (Figure l ) .

If a reaction requires not only a simple contact but also

a specific mutual orientation of the reactants, the spheres representing them may be considered to have a "reaction spot" - black or grey, depending on the reactivity (Figure I). the reaction.

The smaller the spot dimensions, the more stereospecific

The statistical weighted mean of such chemically favorable orien-

tations, f, is referred to as the steric factor by analogy with the steric

olo -[ooj-

®1o-[®®] .[ee]-o0, (4)

Figure i. A scheme for reaction between black spheres (I) and between white spheres with black spots (3). The square brackets indicate that the spheres are in the solvent cage; (2) - the polar angle 0 giving the relative size of the black spot; (4) - reagent orientation at the first contact.

275

factor of gas phase reactions. Consider f i r s t the steady-state condition with the reagents being i n i t i a l l y uniformly distributed in the solution.

The spacing r between any two reactants

varies as they mutually diffuse with the total diffusion coefficient D= DA+D B, until they meet when p ~ r ~ p +A, where p is the sum of their van der Waals' radii and A is the thickness of the reaction layer.

(One suggests often that a

chemical reaction proceeds not at a fixed distance between reagents but within a thin reaction layer A; A

f e f f versus f relationships for f e f f ~ I0-2" The experimental and theoretical estimates of the rate constants of pseudodiffusion reactions have been compared [I0,II,26].

To determine f , the reactive

surface area of the radical ~A ) susceptible to attack by the partner was compared with the Van der Waals' surface area of the radical (S).

The radical vol-

ume was calculated using the Van der Waals' increments of its constituent groups and then the surface area of a sphere of equal volume, which was in fact S, was

281 calculated.

From a direct comparison of two molecular models of the reacting

radicals i t was estimated, for example, that for carbon atoms participating in bond formation SA = I/3-S(C), where S(C) is the Van der Waals' surface area of the carbon atom. Then for the recombination of two C-centered radicals forming the C-C bond, f = [S(C)/(3S)] 2.

The f values for recombination of aromatic rad-

icals in which more than one black spot on the radical surface is involved, have been evaluated. Using the resulting f = 10-4 - 10-2, the f e f f values were estimated in terms of the model described in Reference 37.

kD was calculated by the

formula: kD = o4~pD

(13)

The radical diffusivities were calculated using the Stokes-Einstein formula with allowance for the "microfriction" factor [26].

Using the values of kD ob-

tained in Eq. (13) and f e f f ' the pseudodiffusion reaction rate constants were estimated from Eq. (8).

The calculated and experimental rate constants of sel-

ected pseudodiffusion reactions are compared in Table II. Table II.

Calculated and experimental rate constants of selected pseudodiffusion reactions, a

Reaction

2kcalc (M-is-I)

ow ~C'~NPh

QH_~

2 ~ _

P.

p

.}. H3C~CH3

~

C

O,

~--Si--6H2 ak

exp

7.8 x 107

(9.0 +_ 0.5) x 108

9.0X i0 7b

(4.9-+ 1.5) X I08b

2.0 x 108

(1.2 -+ 0.2) x 108

i.i x i0l°b

(4.0 -+ 0.5) x I09b

1.5 X 108

(7.9 X 0.5) X 108

H3C Jo cH3

O"

~

O

2

2kexp (M-is-1)

from References 4,10,26,36,38.

bHere, k calc and k exp are given.

Although the estimated values are very approximate, i t yet appears that there is a reasonable agreement between the calculated and experimental k values. This fact supports the interpretation of the pseudodiffusion behavior of reactions in terms of steric hindrances.

I t is, of course, a notable achievement that the

rate constant of a bimolecular reaction between highly reactive agents in the

282 liquid phase may now be calculated on the basis of their structure with an accuracy within a factor as small as lO-15. The theoretical f e f f versus f relationships and the numerical parameters appearing in such relationships are chosen with a certain degree of arbitrariness [26].

The experimentalist, we believe, faces the inverse problem - to plot the

f e f f versus f relationship departing from the available experimental data. For recombination (disproportionation) of aromatic radicals a plot of this kind is shown in Figure 5. I t is based on Eq. (8), f e f f = k/kD' and the corresponding f values which, as we have described above, are estimated from molecular models. ~

( I t is more convenient to use the angular size of the black spot, 8 = 2 arcsin4~, instead of f ) .

o

-%0

Figure 5.

lo' 2o' 30' ~o' ~" WB

The feff yersus e relationship. Reproduced from Reference Ii with permission by Elsevier, The Netherlands.

From Figure 5 i t follows that reactivity anisotropy averaging due to the reactant motions in the cage is very rapid and already at ® ~ 40° ( f ~ O.Ol) the averaging is complete.

Obviously, the diffusion-controlled reactions between

chemically anisotropic reactants are a special case of the broader pseudodiffusion-controlled class and are characterized by f e f f = l (cf. Eq. (8)). Figure 5 demonstrates a smooth transition from pseudodiffusion- to diffusion-controlled reactions as G increases. These results can be formulated as fo|lows: f e f f : f ( l + x ) / ( f + x) Eq. (14) represents the curve shown in Figure 5 for the case x = 0.00025.

(14) Under

certain assumptions the model proposed in Reference 37 also reduces to Eq. (14), and here x is the squared ratio of the length of the elementary diffusion jump to p.

The fact that x kI , which contradicts the experimentally observed two-step decay of this radical [18].

Consequently, the disproportionation of this particular radical proceeds

by reactions (1) and (19); this mechanism seems to be more probable for the other investigated radicals as well, as compared to disproportionation by the elementary reaction (2). Kinetic and thermodynamic data for the recombination and disproportionation of aroxyl radicals may be useful for predicting the effectiveness of phenolic antioxidants. When [R] > K/4 the decay of phenoxyl radicals obeys first-order kinetics and is characterized by a f i r s t order rate constant, k', s- l .

These

experimental values of k' are necessary, while the disproportionation mechanism is insignificant, for analysis of the kinetic schemes. IV.

SOLVENTEFFECTSON AROMATICRADICAL RECOMBINATIONAND DISPROPORTIONATION KINETICS In the preceding section we have shown that solvent viscosity governs the

rates of many fast bimolecular reactions between radicals. Yet there are cases when one cannot ignore the chemical nature of the solvent and the possible formation of solvation complexes between the radical and solvent (Sol): R" + Sol ~ RSoI

(20)

In order to find out the manner in which the solvent affects the rates of fast reactions, molecular mobility limited ones included, the authors of References 4,8,10,13,22-24 and 42 investigated the kinetics of recombination and

288 disproportionation of aromatic radicals and of dimer dissociation in different solvents. Conventional (usually non-viscous) solvents and binary mixtures of solvents were used. A. Effect of "non-solvating" solvents on recombination kinetics The rate constants, thermodynamic and activation parameters of the reversible recombination of aroxyl and arylindanedionyl radicals in different solvents have been determined. I f the recombination is limited by molecular mobility i t may be expected that the parameter k-n-f t = const

(21)

will be solvent-independent under constant pressure and temperature ( f t is a "microfriction" factor) [26]. Eq. (21) is obeyed by a number of radicals. Figure 8 shows log k for the recombination of 2,6-di-~-butylphenoxyl radicals l as a function of an empirical parameter ET(30)* characterizing the solvent polarity. (Recombination of radical l in the toluene/di-n__-butylphthalate mixture is pseudodiffusion-controlled, cf. Table I). In Figure 8 this relationship appears as randomly scattered points. However, according to Eq. (21), the value log (k.n.ft) is weakly solvent-dependent. The t--butyl-substituted aroxyl radicals ! cannot form complexes with solvent because of steric hindrances.

0

0 0

0

O0

O 4 • Z

O0

0

0 O O

711 o

-00

v I

~0

a -l-

g

w

,

v

T--•

I

~0

Q

w ,

a

Figure 8. The dependence of the rate of reaction (i) for radical I on ET(30) at 293 K. i - k' = k, M-is-l; 2 - k' = k'n'ft, M-is -I dPs. The solvents used are listed below in the order of increasing ET(30): n-hexane, carbon tetrachloride, toluene, benzen--e, tetrahydrofuran, chlorobenzene, chloroform, di-_n-butylphthalate, dlchloromethane, acetone, acetonitrile, acetic acid, formic acid [26].

I

E,(30)

The kinetics of reversible recombination of radical 7 in different solvents have been investigated in detail [23]. Recombinationof Z in non-viscous solvents is an activation-controlled reaction (cf. Table I). From the kinetic and thermodynamic data for this reaction i t has been found that i t s rate and equilibrium are affected only by "nonspecific" solvation. I t has been determined that: I) log k_l is a linear function of the Kirkwood parameter (~-I)/(2~+I); the transition state of this reaction is characterized by a higher dipole moment *ET(30) is the energy (in kcal mol-1) of the longwave transition in the absorption spectrum of the solvatochromic dye 2,6-diphenyl-4-(2',4',6'-triphenyl-l'pyridino)phenolate in a given solvent.

289 than that of the i n i t i a l dimer;

2) kI is weakly solvent-dependent;

3) there

is an isokinetic, for reaction ( - l ) , and an isoequilibrium relationship with the corresponding temperatures: B= 408 K and B° = 651 K [23].

For dissociation

of this dimer i t has beenfound that 6M Ink_l = yaM InK, where aM is the LefflerGrunewald operator and y is constant [23].

The high value of y obtained, 0.8,

suggests, apart from the increase of the dipole moment of the transition state of reaction ( - l ) in comparison with that of the dimer, that the transition state is more l i k e l y a pair of radicals than a molecular dimer [23]. B. Effect of "specific" solvation on recombination and disproportionation rates Eq. (2]) is not followed as closely for the cases of recombination of phenylsubstituted aroxyl and other aromatic radicals.

In this case one has to postu-

late a "specific" solvation of radicals by the solvent, Eq. (20).

Phenyl-

substituted aroxyl radicals have an orderly system of conjugated bonds andthere are no large steric hindrances around the monovalent oxygen, thus favoring the formation of different types of solvation complexes RSoI . Empirically, i t has been found that the log k versus ET(30) relationship is represented by a V-shaped curve for the recombination of phenyl-substituted aromatic radicals [4,13,23]. The recombination of phenyl-substituted aromatic radicals such as 2, 4, 9, has been found to be slowest in chloroform, among other non-viscous solvents*, and that of radical 3 is slowest in pyridine and chloroform [4,13,23].

Chloro-

form and pyridine are known to frequently form solvation complexes with various radicals.

Comparison of the rate constants of the spin exchange and recombina-

tion of radical 4 in several different solvents has led to the conclusion that chloroform solvates 4 at the para-position, yielding in all probability complexes of the ~-~-type [43]. In many cases radical solvation involves participation of free valence carrying atoms.

In the dimer the bond is formed between these atoms.

I t may be ex-

pected, therefore, that in some cases recombination will entail desolvation. Some energy is required for desolvation.

This "some" may in fact be so s i g n i f i -

cant that a reaction which is (pseudo)diffusion-controlled in a "non-solvating" solvent may become activation controlled in a "solvating" solvent of similar viscosity. It has been shown, indeed, for reaction (1) and phenyl-substituted aromatic radicals in chloroform, that specific solvation of radicals changes the (pseudo)diffusion recombination to an activation controlled one [23]. This is manifested by the decreased k, while AHt becomes greater than B. (For radical 9 ~

AHt : 3.5 B in chloroform [23]). Desolvation accompanies the recombination of 9. This is manifested by the measured AVt = AV~ > 0 in chloroform; in addition, the ASt of recombination in this solvent is sizeably higher than in other "non*The solvents that have been used are listed in the caption to Figure 8.

290 solvating" solvents, which indicates increased disorder in the transition state due to desolvation [19,23]. Another illustrative example of the specific solvation effects on the recombination rate is reaction (1) involving ketyl radicals of benzophenone (BPH') in aliphatic alcohols, e.~., ~-propanol [lO].

Recombination of BPH" in water

and water/glycerol mixtures is a diffusion-controlled process (Figure l ) . In npropanol, however, 2k < kD and AHt > B, ~.e. the reaction is activation controlled.

The obvious reason for the reaction being slower in alcohol than in

water is that the radical-H-bond complexes formed in alcohol are less reactive than the starting radicals.

Alcohols are stronger H-bond acceptors than water

owing to the higher negative charge on oxygen induced by the alkyl group. These circumstances, along with the observed decrease of k in going from water to alcohol, allow an unambiguous structural assignment to the complex: Ph2COH...O-R

[io].

Thus, the structure of the solvation complexes RSoI may be identified r e l i ably from recombination or spin-exchange kinetic data in different solvents [10,43]. In most cases solvation reduces the reactivity of radicals. Yet, the decrease in k may also be due to more severe steric hindrances. The radicals may recombine as solvation complexes under these circumstances, as illustrated in Figure 7 where Sol indicates, in this particular case, the "adhering" solvent molecule. A convincing illustration of this kind of solvent effect has been discovered in investigations of disproportionation and electron transfer reactions, (3) and (22): BP + )N-O" k22

BP + )N-O-

involving BPH" and BP: radicals (Figure 2) in different solvents [lO].

(22) In the

water/glycerol mixture both reactions are pseudodiffusion-controlled and k3 = k22 (Figure 2).

I t has been shown that in the n_-propanol/glycerol mixture both

reactions are also pseudodiffusion ones, but in this case k22 > k3. .As noted above, BPH" forms complexes acting as an H-bond donor; naturally, BP- cannot form such complexes. Therefore, the steric factors f and feff in the reaction between BPH'...~-R and ~N-O" are consequently lower than in the corresponding reaction (22), A and this is responsible for the observed k22 > k3 in the n_propanol/glycerol mixture [lO]. Thus, strong specific solvation of radical by the solvent lowers the rate of its (pseudo)diffusion-controlled reaction by: l) converting the reaction to the activation-controlled type; or 2) generating more severe steric hindrances [lO, 26].

291

C. Recombination and disproportionation of aromatic radicals in strongl ~ nonideal solvent mixtures. I f a reaction is much slower in one solvent than in another, then in a binary mixture of these solvents one will often observe a monotonous variation of the bimolecular reaction rate with mixture composition.

Hypothetically, reaction

(20) and bimolecular reactions of RSoI and R" occur in a solvent mixture [4,13]. I t has been shown that this conventional treatment of radical reactions is not valid for strongly non-ideal binary mixtures (methanol/chloroform, methanol/ carbon tetrachloride, carbon tetrachloride/acetic acid; non-electrolytic aqueous solutions) [13,24,44].

In investigations of diffusion-controlled reactions

(1,2) involving aromatic radicals in such solvents i t has been found that the k or k-n versus mixture composition relationships have extrema [13,24,44]. I t does not seem possible to develop a systematic approach to the selection of the "microfriction" factor for radicals in such binary mixtures, so new ideas are needed to establish the k versus mixture composition relationships [24]. Sharper versions of k with solvent composition have been shown to occur in regions enriched with water or some other organized solvent [13,24,44].

In some

cases correlations have been observed between log (k-n) and the heat of mixing AHM of the binary mixture [24].

Investigation of the diffusion-controlled reac-

tion kinetics in non-ideal mixtures is one method of elucidating their structure. V.

ELECTRON TRANSFERKINETICS IN BIMOLECULARREACTIONS With the purpose of detecting any electron-transfer pseudodiffusion reac-

tions, establishing the role of steric hindrances and limitations in electrontransfer processes, assessing the importance of electrostatic interactions in fast bimolecular reactions between charged particles, the authors of References 3, 7, 45-52 studied the electron-transfer kinetics in the following reactions:

R=+R

R+R i

(22)

R: + R{+ ÷ R + Rl

(23)

R: + R=

(24)

÷ R + R2-

R" + CuIIL ÷ products

(25)

The test molecules were radical-anions of quinones, benzophenoneand its derivatives; the W~rster Blue radical-cation; stable nitroxyl and triphenylverdazyl radicals. The diffusion constants of reactions (23, 24) have been theoretically estimated with allowance for the Coulomb interaction kD.X, where x is a Coulomb term depending on the product of the reactant charges ZA.ZB [49,50,52]. The values of k23 and 2k24 tend to decrease with increasing ZA-ZB (-3 ~ ZAZB

292 < 9); in most cases k23, 2k24 < kD-X [49,50,52]. Using the k23 versus n plots i t was possible to identify the fast activated and pseudodiffusion electrontransfer reactions. A. Activation controlled reactions I t has been determined that quinone radical-anions transfer an electron to stable radicals (Reaction (22)) [51].

I f (22) is activation controlled, one ob-

serves a regular decrease in the rate constant with increasing one-electron potential of the quinone (Figure 9).

The slope of the linear plot (13 eV- l , Fig-

ure 9) is close to that predicted by the Rehm-Weller formula [53] (17 ev-l). The increase in the steric hindrances around the ~"N-O" fragment upon transition from the five-membered nitroxyl radicals of the imidazoline or pyrroline series to the six-membered ones of the piperidine series causes a decrease in AS~2_ [I0,

48].

0"

0

8~

7.0 Figure 9.

6.0 -OA

I

-R3

i

-0.2

E',(a/O').V

Dependence of log k22 on the singleelectron potential of the qulnone/ semiquinone pair (in water/~-propanol, 293 K) [48].

On the basis of the measured k22 values i t has been shown that the nitroxyls of the pyrroline and imidazoline series investigated are better electron acceptots than those of the piperidine series [I0,48]. I t has been found that the rate of the relatively slow action controlled electron-transfer in reactions (22) and (24) (k = 103-105 M-Is- l ) increases when glycerol or dioxane is added to the aqueous solutions [I0,48]. This behavior may be explained in terms of the Marcus theory, according to which the addition of glycerol or dioxane increases the optical dielectric constant of the solvent and decreases the reorganization energy, which combine to increase k [lO]. B. Pseudodiffusion reactions Pseudodiffusion electron-transfer reactions have been discovered.

In the

water/glycerol mixture the reactions that are pseudodiffusion-controlled include

293 reaction (22) considered above (Figure 2) and reaction (24) with participation of the naphthoquinone-l,4 radical anions and a sodium salt of 2-sulfoanthraquinone-g,lO radical anions (R:) [54]. In this section we will consider reaction (25) for R: and copper perchlorate in the water/glycerol mixture [51].

In viscous solvents (lO ~ n ~ lO4 cPs)

reaction (25) is a pseudodiffusion reaction and the numerical values of k are about 60 times as small as the corresponding kD-X.

I f we now try to estimate

the steric factor f of this reaction, where only one of the reactants is chemically anisotropic, in the same manner as we did for reactions in the absence of electrostatic interaction (Section I l l ) , we obtain an unrealistically low value f : lO-3-10-4.

It must therefore be assumed that the reagents combine into a

complex in which they are coupled by Coulomb attraction: + Rz + Cu~+ q~ +---- R:, Cu2+ aq kr°t ~ R + CUaq

(25)

The reagents rotate in the complex to attain a mutual orientation favorable for reaction (the CuZ~ ion contacting with the surface of one of the oxygen atoms in the 9,10-positiona~of R:) and then electron transfer occurs "instantaneously". Hence, k25 = K.krot. Correct estimates of K and krot , taking into account the anisotropy of charge "distribution over the radical surface and comparison of the experimental and calculated values for k25 and kD-X, give f = O.Ol, which is in fair agreement with the result predicted by the molecular model of R . It has been shown that, as expected, reaction (25) takes place upon immediate contact of the reagent molecules in media havfng a viscosity n ~ lO4 cPs. C. Kinetics of oxidation with copper(ll) compounds In investigations of the effect of copper(II) compounds on the decay kinetics of different aromatic radicals i t has been found that both the rate and mechanism of copper(II) reactions with the radical are heavily dependent upon the donor properties of the radical and the nature of the solvent.

The observed

phenomena can be conveniently interpreted with the help of the Kochi [55] hypothesis on the formation of an intermediate organo-copper compound between R" and CuI I , and the assumption that the oxidation is confined to the internal sphere: CuII + R" + CuII - R ÷ CuI + R+

(25)

For radicals possessing high electron-donor ability the intermediate complex is very short-lived and the oxidation is a one-step process. I f , on the other hand, the radical is a weakerdonor, i t becomes possible to record the absorption spectrum of the complex; the complex then decomposes to reduction-oxidation products.

For s t i l l weaker donors the reaction stops at the complex formation

stage and the complexes decay through bimolecular reactions with each other.

294 The weakest donors cannot react with copper(II) at all. examples [3,7,45-47,51] are illustrated in Figure IO.

O"

O" complex- e]eetron transler

The investigated

_t=~*

--- products

CuLR " comp1e

CuI + R"

Figure i0.

"OXO"

Schematic representations of the different types of reactions between aromatic radicals and copper(ll) compounds.

E

The observed trend is not a t r i v i a l one (Figure I0) since the redox reactions under discussion are complex. In one study, for example, devoted to the oxidation of hydroxyalkyl radicals with copper(II) salts, i t has been found that the oxidation rate decreases with decreasing oxidation potential of the radical [56]. In order to improve the effectiveness of phenolic antioxidants i t is necessary to remove from solution, as rapidly as possible, the aroxyl (semiquinone) radicals so that they can form molecular products. The results described in this Section indicate that copper(II) compounds can be effective in doing this. Vl.

CAGE EFFECTDYNAMICSIN PHOTODISSOCIATIONTO ARO~TIC RADICALS In Section I l l we have discussed the effect of solvent viscosity on radical

recombination rates in the bulk of the solvent. A logical addendum to these studies is the evaluation of the radical recombination kinetics in the solvent cage (the so-called geminate recombination) and measurements of the viscosity influence on the cage effect values (¢®). Studies on the kinetics of geminate recombination of neutral organic radicals were reported for the f i r s t time in 1980 (Figure l l ) ~ nanosecond laser photolysis of the C-C-dimer in a viscous solvent [57]: 0 n

C\ ~F~C~-~NPh2

0 II

~

C\. 2~ ~ ~ N P h 2 ~

295 "z..,-%

N z

[--,

100-

r

4....:::' ;i:... .... 61 J"-

: ..................

1001

_

Figure ii.

"1 ""t.....

1"10 -6 s,~

Oscillograms of optical density variations due to the formation and decay of 9. a: in vaseline oil at 273 K, ~ = 600 cPs; b: in vaseline oil/toluene mixture at 293 K, n = i00 cPs; c,d: scheme of dimer photodlssociation to two radicals represented as white spheres with black spots in solvents of different viscosity, d is for a smaller viscosity solvent than c. Reproduced from Reference 57 with permission by Elsevier, The Netherlands.

A total of 15 oscillograms were recorded under identical conditions in order to obtain as small an experimental error as possible for the calculation of the kinetic curve.

From the data of Figure II i t follows that 59% of the i n i t i a l l y

formed 9 escaped geminate recombination and therefore, ¢= = 0.41.

As n decrea-

ses, the i n i t i a l concentration of 9 remains practically unchanged, yet the inflection portion of the curve becomes less apparent and ¢= decreases. Under the experimental conditions employed no recombination was observed for 4 ~ 50 cPs. I t is interesting that in liquid polyethylene glycol, which is in fact characterized by a relatively low viscosity (n = 63 cPs), almost all the radicals formed decay in the cage and ~® = 0.91 [58].

Experiments of this kind provide

valuable information on the mobility of low-molecular weight compounds in liquid polymers. The ¢~I versus T/n curve (Figure 12) was plotted from experiments on geminate recombination kinetics in toluene/vaseline oil mixtures of different viscosity.

The reasons why ~= should depend on n (Figure 12), and the kinetic behav-

ior of the geminate recombination (Figure l l a ) , have been analyzed [27].

In

order to render the theoretical models applicable to a description of the geminate recombination kinetics, certain assumptions were made concerning the react i v i t i e s of 9, their mutual orientation at the i n i t i a l encounter, and the nature of their motion in the cage. As a result, the following model, consistent with the experimental data of Figures II and 12 and the investigations of 9 recombination in the solvent bulk (Table I), has been proposed [27].

The radicals are

considered to be white spheres with black spots and the solvent, as an isotropic structureless continuum [27]. Under photodissociation, the surplus of the photon energy over the bond

296

12

Figure 12.

0

,

I

2

,

|

4

I

The #~i versus T/q relationship; T/n, °K/cPs. Reproduced from Reference 57 with permission by Elsevier, The Netherlands.

energy (or a portion of the surplus) is spent on overcoming the viscous drag of the solvent on the internal radical rotation (Figure I I , c,d). As n decreases, the black spots on the radical surface (the trivalent carbons) are more and more distanced from each other and @®drops. Very roughly, the resulting situation may be represented by the well-known formula valid for black spheres: @~ = p/L, where L is, in this particular case, the distance between the black spots. In terms of this model, the geminate recombination kinetics are actually controlled by the variation in the mutual orientation of two Rs due to their rotation.

The conception that under photodissociation the radicals turn while in

contact, so that they can rotate enough to face each other within the time of contact, seems to be altogether tenable for viscous media. Indeed, in a liquid, an increase of n often results in a stronger retardation of the translational, rather than rotational mobility (which is easily interpretable in terms of the vacancy mobility mechanism) [27]. Apart from those of geminate recombination, the kinetics of the bulk recombination of 9 have also been monitored under identical conditions (vaseline o i l , 273 K). The 9s that leave the cage recombine in the solvent bulk within a m i l l i second time span [57]. These experiments demonstrate that the nanosecond laser flash photolysis technique can be used for estimating the effectiveness of photoinitiators in viscous solvents. The literature devoted to experimental investigations of recombination of the same radical species in the solvent bulk and in the cage has been c r i t i c a l l y analyzed [27].

In the decay of di-~-butylperoxyoxalate, 2,2'-azoisobutyronit-

r i l e , and 2,2°-azoisobutane, the value of ~ increases with n.

Conventionally,

this is interpreted as resulting from moderate radical reactivity (grey spheres).

297 On the other hand, i t has been shown convincingly enough that recombination of the ~-butyoxyl, cyanoisopropyl, and ~-butyl radicals is diffusion-controlled. (This means that these radicals may be modeled as white spheres with a sufficiently large black spot, Figure 5).

There is thus a contradiction, or at least

a considerable discrepancy, in the estimates of the reactivity of the same radical species, derived from geminate and bulk recombination data [27]. The reasons for the dependence of @. on n have been discussed [27] for the case of highly reactive particles, on the basis of their diffusion properties and their relative positions as they are generated in the cage, ~.e., the shortrange effects. (The reason for the dependence of @®on n upon photodissociation to chemically anisotropic reactants in viscous media has been discussed above). I t has been postulated, for example, that a certain percentage of radicals could be formed due to bond scission beyond the f i r s t coordination sphere. As the viscosity increases, which often results from addition of larger-sized molecules to solution, this percentage decreases and thus ¢~ increases [27]. Vll. CONCLUSIONS With the help of the flash photolysis technique i t has become possible to obtain direct observations of the formation and decay kinetics of short-lived radicals and study the relationships between the measured rate constants and the radical structure.

Aromatic radicals which absorb in the UV-visible range

are convenient test objects for investigation by this technique.

We will now

summarize the principal conclusions that follow from the subjects described in this review. A previously unknown class of bimolecular reactions between radicals (recombination, disproportionation, electron transer) has been discovered, the rate constants of which are inversely proportional to solvent viscosity and smaller than the diffusion rate constants (pseudodiffusion reactions).

Pseudodiffusion

reactions are characterized by low steric factors and normally occur between reactants having pronounced reactivity anisotropy. Analysis of the wealth of the bimolecular reaction rate and equilibrium data shows that steric hindrances (for activation controlled reactions) and steric limitations (for molecular mobility limited reactions) have the controlling effect on the radical decay rates. I t is shown that for the molecular mobility limited recombination of radicals which do not specifically interact with the solvent, the product of the rate constant, viscosity and the "microfriction" factor is solvent-independent. I t has become possible, knowing the rate constant in one solvent, to predict the rate constants in other solvents. A new approach to the investigation of radical reactivity has been proposed and experimentally assessed. I t has been shown that a change in the structures

298 of highly reactive radicals, or their (de)solvation, affect the rate constant of the molecular mobility limited reaction by affecting its steric factor. An empirical relationship between the geometric and effective steric factors has been obtained which allows, on the basis of the structure of highly-reactive radicals, one to predict the rate constants of bimolecular reactions between them. The theoretical estimates obtained in this manner are in agreement with the experimental results by more than a factor of 2-15 (depending on the geometric factor).

The type of plot is consistent with the predictions of the corres-

ponding theoretical models. On the basis of the rate and equilibrium data obtained i t has been shown that the rate of radical recombination which is (pseudo)diffusion-controlled

in a non-

solvating solvent decreases in a solvating solvent. There are two possible reasons for this: l) the reaction remains pseudodiffusion-controlled

but has a smal-

ler steric factor; and 2) the reaction becomes activation controlled.

The acti-

vation volumes of the cage recombination of radicals, AVe, have been determined, whereby i t was possible to decide on the role of solvation complexes in recombinations.

Situations with AV~ > 0 have been discovered, which have been inter-

preted as a direct manifestation of desolvation of the recombining radicals. The kinetics of diffusion-controlled radical reactions in strongly non-ideal binary mixtures have been investigated.

I t has been found that the reaction

rate versus mixture composition curves have maxima due to variations of the solvent structure.

Correlations between the product of the rate constant and vis-

cosity and the heat of mixing of the binary mixture have been established.

In-

vestigation of diffusion-controlled reactions in non-ideal mixtures of solvents is a means of studying their structure. The mechanism and kinetics of hydrogen atom transfer during recombination and disproportionation of aroxyl radicals have been investigated.

For the f i r s t

time i t has been directly shown that recombination of mono- and disubstituted aroxyl radicals and disproportionation

of a number of aroxyl radicals include a

step involving reversible recombination into labile dimers. Steric hindrances control both the mechanism and rate of the disproportionation process: no intermediate dimer is formed and the disproportionation is a relatively slow one-step process when there are sufficiently bulky substituents in the ortho- and parapositions of the aroxyl radical.

The rate constants of the elementary recombin-

ation of radicals to labile dimers, dimer decomposition to radicals, and enolization of domers have been determined for the f i r s t time.

Such data are useful

in predicting the effectiveness of phenolic antioxidants. The kinetics of the geminate recombination of uncharged organic radicals have been recorded for the f i r s t time for 2-(4'-diphenylaminophenyl)indane-l,3-dione2-yl radicals.

For the f i r s t time the rates of the geminate and bulk recombina-

tion have been recorded under identical conditions.

I t has been found that upon

299 photodissociation of dimer, the cage effect (¢®) is enhanced as the solvent viscosity (n) increases.

An explanation is proposed for the observed dependence of

@, on n and the relationships observed in conventional investigations of i n i t i a ted dissociation to highly reactive radicals.

It is based on the assumption

that upon dimer photodissociation in a viscous solvent, a portion of the liquid quantum energy is spent on overcoming the viscous drag of the solvent toparticle rotation about each other.

As n decreases the distance between the reacting

radical atoms increases and ¢, decreases. VIII. i. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

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