# CHAPTER 1: INTRODUCTION

## 1.1 Bimolecular Reactions in Solution

Several similarities and several striking differences are encountered in comparing reactions in the gas and liquid phases. The rate constant for a given reaction between free radicals and molecules is usually not greatly different in the two phases. However, certain thermal reactions of ions and photochemical primary processes involving ion formation and electron transfer become energetically far more favourable and are important in solutions of high dielectric constant. In the case of photochemical solution reactions, if homogeneous light absorption is maintained, the liquid phase systems are usually less complicated by wall reactions than are their gas phase counterparts because of much lower diffusion rates for liquid systems.

From a theoretical point of view, rates of reactions in solution have been satisfactorily interpreted in terms of both Collision and Transition State Theories. The uses and limitations of the former have been dealt with by Noyes[1] and North[2] and of the latter by North[2] and Benson[3].

Many reactions with an activation energy $$E_a$$ of about 10Kcal/mole are fast in the sense that special techniques are needed to measure their rates, but the temperature variation of the rate constant, k, is given by the usual Arrhenius Equation

$$k = Ae ^{\bigl(-{E_a \over RT} \bigl)}$$

in which the fraction of effective collisions, $$e ^{\bigl(-{E_a \over RT} \bigl)}$$, is quite small. Such reactions may be called activation-controlled and taking the value of the pre-exponential factor, A, to be 1011 M-1s-1 ( a value representative of many reactions between an ion and a molecule) bimolecular rate constants in the range 103 - 106 M-1s-1 are found to be typical of such reactions.

For reactions that occur on practically every collision in the gas phase (e.g. free radical recombination and disproportionation, fluorescence quenching, and allowed energy transfer reactions), their rates in solution are frequently limited by the rate of diffusion of the reactants. Such diffusion-controlled reactions have apparent activation energies of 2-3 Kcal/mole and bimolecular rate constants in the region of 109 - 1011 M-1s-1, values which may be estimated from the modified Debye Equation[4,5]

$$k_{diff} = {2RT \over 3 \eta} \Biggl(2 + {d_1 \over d_2} + {d_2 \over d_1} \Biggl)M^{-1}s^{-1}$$

$$= {8RT \over 3 \eta} M^{-1}s^{-1} \quad (\text {if} \; d_1 = d_2)$$

where $$d_1, d_2$$ are the diameters of the reacting species (assumed spherical) and η is the viscosity of the solvent. Many refinements of this simple treatment have been made, giving better quantitative agreement with observed rate constants[1,6,7].

Perhaps the most striking of the effects encountered in solution phase reactions that is observed in the (dilute) gas phase is the cage-effect[8]. Free radical partners formed on homolytic bond rupture are encircled or caged by solvent molecules and, owing to slowness of diffusion in liquids, remain together for about 10-10 s, and this greatly increases the probability of mutual interaction. Two events now become possible:- (a) recombination to the parent molecule, which slows down the overall decomposition rate and (b) formation of new species e.g.

C6H5CH2CO2CH2C6H5 hv(C6H5CH2)2 + CO2

which is unaffected by the presence of a scavenger. The theoretical aspects of this effect have been treated by several workers[1,9-14].

The particular case of free radical recombinations has been widely studied both in the gas phase[15-29] and in solution[28-44], and rate constants of the order of 1010 M-1s-1 are reported, showing such reactions to be diffusion-controlled processes. The radicals may be generated thermally (e.g. pyrolysis of acyl peroxides) or photochemically (e.g. from azo compounds) in a wide variety of solvents, and methods of monitoring the reaction are spectroscopic (ESR and UV) or by the rotating sector technique[42-44], and this has led to a large body of information concerning such reactions in solution.

## 1.2 Electron Transfer Reactions

In general, the mechanism of redox reactions may involve either (a) atom or group transfer or (b) electron transfer, both of which may occur by one of two mechanisms. Firstly, there is the inner-sphere mechanism[45-47]in which two metal ions are connected through a bridging ligand common to both co-ordination shells; and secondly, the outer-sphere mechanism[48-52]in which the inner co-ordination shells of both metal ions remain intact in the transition state.

Electron transfer reactions are well-characterized in the gas phase[53]. The situation in solution is more complex, and, from a quantum mechanical aspect, not even approximate calculations can be made because of the large numbers of particles to be considered. Two important restrictions are applicable to electron transfer processes in solution: firstly, rearrangement of co-ordinated groups cannot occur simultaneously with the transfer of the electron (a result of the Frank-Condon Principle) and, secondly, no overall change in electron spin can occur.

For many of these reactions it has been observed that ΔS, the entropy of activation, is large and negative. Reorganization of the solvation spheres gives a positive contribution to ΔS since it involves partial melting of the solvent attached to its ions, and so there must be some larger negative term involved. This problem can be resolved by assuming an electron tunnelling mechanism for the electron transfer process in solution. The theory was initially developed by R.J.Marcus, Zwolinski, and Eyring[54,55] and utilizes Transition State Theory to derive an expression for the rate constant of the form $$k = K{RT \over Nh}exp \Biggl(-{\Delta G^‡ \over RT} \Biggl)$$

where Κ is the electron tunnelling transmission coefficient and ΔG the free energy of activation, includes the free energy of rearrangement and electrostatic repulsion terms. The theory then shows that the origin of the large negative value of ΔS is due to a contribution to ΔS of R ln. Κ by virtue of the tunnelling process, and since Κ is always less than 1, this will give the required negative term, the magnitude of which is calculated to be about 13e.u.[54]

The treatment of Marcus, Zwolinski and Eyring is based on a non-adiabatic process in that the electron jumps from one potential energy surface to another. R.A.Marcus[56], retaining the electron tunnelling hypothesis but now assuming an adiabatic process based on the idea of a single potential energy surface was then able to formulate a theory of electron transfer processes in solution. He assumed that the degree of spatial overlap of the orbitals of the reacting species in the activated complex is small and was able to show that the electron can transfer at distances considerably greater than that corresponding to the actual collision of the reactants i.e. it is related to the spatial extension of electronic orbitals. According to Marcus Theory, the rate constant for an electron transfer reaction may then be expressed in the form $$K = Ze^{ \bigl(-{W(R) + m^2 \lambda \over RT} \bigl)}$$

where Z is the collision frequency between two uncharged reactants in solution, W(R) is the coulombic work term involved in bringing the reactants together in the transition state, and m2λ is related to the work necessary to reorganize the co-ordination shell around the reactant ion. This theory, although quite useful, has been refined by Marcus and Hush[57-62] to give more accurate correlations with observed results.

## 1.3 The Use of Free Radicals in Electron Transfer Studies

Free radicals may take part in redox process of the type[63,64] $$R^ \bullet + Cu(II) \Rightarrow RX + Cu(I) +H^+ \qquad (A)$$ $$R^ \bullet + Cu(II) \Rightarrow olefin + Cu(I) +H^+ \qquad (B)$$

where HX = H2O, HCl, CH3COOH, and such reactions may be examined to determine any relationship existing between observed rates and thermodynamic properties of the metal species (e.g. redox potentials). Studies can be made in both aqueous and non-aqueous solutions, and particular advantages of the use in aqueous solutions are (a) otherwise-dominant coulombic interactions are minimized and (b) changes in pH or nature and concentration of other solutes affect only one reactant (both advantages being due to the absence of charge on the free radical).

Dainton et al.[65,66] have measured the combined rates of reactions (A) and (B) in the particular case where R• is the growing radical chain in the polymerization of acrylamide and the metal ion is varied. A table containing some of their results is shown below. These kinetic parameters are in better agreement with an electron-tunnelling mechanism than with an atom transfer process since they give rise to negative activation entropies[65].

Rate constants for the reaction between Cu(II) and simple alkyl radicals in aqueous acetic acid have been determined by Kochi and Subramanian[67] and typical values are shown below.

Oxidation Of Polyacrilamide Radicals
Metal ion Rate constant (M-1s-1) Ea (Kcal Mole-1) A
Fe3+aq. 2.8 × 103 2.35 1.45 × 105
2.6 × 103 2.44 1.57 × 105
Cu2+aq. 1.17 × 103 5.4 1.1 × 107
1.4 × 103 5.3 1.0 × 107
Hg2+aq. 1.05 6.2 4.2 × 104
Ti3+aq. 0,34 2,5
VO2+aq. 1.1 × 103
Estimated Rate Constants for the Oxidation of Alkyl Radicals by Cu(II) at 57°C
Radical Ea (Kcal Mole-1) Log A Log kox
C2H5 5.9 8.1
n-C3H7 6.7 8.3 7.64
CH3CHCH3 6.3 8.3 7.70
n-C4H9 5.4 7.9 8.05
CH3CH(CH3)CH2 6.5 8.7 7.70
(CH3)3C• 4.3 7.5 8.74
CH3CH2CHCH3 4.9 7.7 7.88

## 1.4 The Benzyl System

The benzyl radical (C6H5CH2• = Bz•) was first observed by Porter and Wright[68] in the flash photolysis of toluene, ethyl benzene, and benzyl chloride vapours, and subsequently in the solid[69] and liquid[70] phases. Details of the UV spectrum are shown in Figs. 1.1 and 1.2.

Bands are found with peaks at 258nm, 307 and 318nm, and a weaker system whose most intense peak is at 452.7nm. These correspond to the transitions 32B212B2[71], 22A212B2[71], and 12A212B2[72] respectively.

The peak at 318nm Is of highest intensity and is thus useful for monitoring reactions of the benzyl radical by a spectrographic method. However, widely divergent values of the extinction coefficient have been reported: 1.1 × 103 [73], 1.9 × 104 [74,75], and 1.2 × 104 M-1cm-1[41]. Higher values appear more likely (since low values suggest a symmetry-forbidden transition) but involve several assumptions, and were also determined in low-temperature glasses.

Porter and Windsor[70] showed that the radical disappears in liquid paraffin by a diffusion-controlled reaction and suggested a bimolecular collision leading to dibenzyl. This was verified and the second-order rate constant evaluated in cyclohexane and benzene, giving values of 2-4 × 109 M-1s-1 [41,42,76].

## 1.5 Aims of present work

Several aims exist in the work undertaken here. The chief aim is to determine the usefulness of studying redox reactions involving free radicals (in particular the benzyl radical) by a flash photolytic procedure. The benzyl radical is particularly suited to studies of this kind utilizing the flash photolytic procedure (see Experimental section) since the strong absorption band at 318nm. Can be used to monitor concentration changes of the radical in a given reaction, and the radical has a relatively long half-life (of the order of milliseconds for micromolar initial concentrations of the radical) and is thus in the range of conventional flash photolysis systems. Rate constants for redox reactions between benzyl radicals and various metal species are then possibly opened to a quick and simple method of determination.

Using the photolysis of benzyl phenylacetate (φCH2CO2CH2φ) as a source of benzyl radicals, it should also be possible to undertake a study of the cage effect in various solvents (e.g. methanol/water, cyclohexane) since the analogous compound azotoluene (φCH2N2CH2φ) is known to undergo cage recombination of benzyl radicals to a very great extent[77]. A study of the temperature dependence of cage recombination versus non-cage recombination should be particularly easy using the flash photolysis technique.