THE OXIDATION AND REDUCTION OF FREE RADICALS BY METAL IONS IN AQUEOUS SOLUTION BY E. COLLINSON, F. S. DAINTON, I>. R. SMITH, G. J. TRUDEL AND (IN PART) S. TAZUKB Dept. of Physical Chemistry, The University, Leeds, 2 Received 8th February, 1960 If Rp is the rate of the radiation-induced polymerisation of acrylamide in aqueous sohtions containing metallic ions, M, which terminate the growth of polymer radicals by oxidizing or reducing them, the graph of R$ against Rp [MI always has a linear portion, of which the negative slope is proportional to the rate constant of this termination reaction. Tn addition, from certain of the graphs may be obtained (i) values of GH/COH or GH~o,/(GH+ GOH) in good agreement with established values, and (ii) relative rate constants for the reactions of metal ions with hydrogen atoms or hydroxyl radicals.The A and E factors for the oxidation of polymer radicals by (i) Fe3+ and Cu2+ in H20 and D20 and (ii) CeOH3+, TP+, Hg2+ and Ag+ in H20 are all very small, whereas for their reduction by Ti3+ in H20 and D20, A = 1012 1 . mole-1 sec-1 and E = 14.6 kcal mole-1. The oxidation of the polyacrylamide radical is considered to be an electron transfer in which the completeness or otherwise of the d-shell is the dominant influence, whereas the oxidation of H-atoms, which probably proceeds through the formation of M-H, is controlled primarily by the d+s orbital energy difference. The reductions of OH and polymer radicals by Ti3+ necessarily involve 0-H bond fission. It has long been known that simple inorganic free radicals such as He, HO., Hop and C1.can enter into oxidation-reduction reactions with inorganic ions in aqueous solution. Although relative values of the rate constants of the reactions of metal ions with a particular radical are known in a very limited number of instances, reliable absolute values of rate constants are difficult to obtain. Recently, and especially in the last decade, it has become clear that the cations of metals of variable valency can be oxidized or reduced by organic free radicals. For a free radical denoted by R. and a metal ion of oxidation number +x, these reactions may be written formally as eqn. (1) and (2) : R. + M ~ + -+M(~- l)+ + R+, (1) R. +M(X-~)+-+M~+ +R-. (2) It was pointed out by Mackinnon and Waters1 that free radicals and their anions (R-) and cations (R+) may be regarded as two redox pairs R.+R++e-, E,,,), (3) R--R.+e-, E(++ (4) having potentials E(-e) and E(+e) as indicated, and that consequentIy whether reaction (1) or (2) will occur, will depend on the relative magnitudes of E(-e), E(+e) and the redox potential EM(^) of the M(x-l)-+/MX+ couple.Thus if E(-e) is more positive than Ep~l(~) ( U . S . convention) then the oxidation reaction (1) will take place. In practice, for many radicals E(-e> and IT(+,) are not measurable under thermodynamically reversible conditions and these quantities can only be evaluated approximately by determining whether reaction (1) or reaction (2), or their anionic counterparts, take place between the same radical and different ions. By this 188COLLINSON, DAINTON, SMITH, TRUDEL, TAZUKB 189 means Haines and Waters2 have assigned an approximate redox potential E(-e)N- 0.4 V to the radicals oC(CH~)(CN)CH~CH~COOH and *c(cN) (CH2CH2COOH)2.Similarly, polyacrylonitrile radicals [R(CH2CH(CN)>,*] are reduced by Ti(III), Mo(III), U(III), W(III), CrUI), V(II), and Eu(I1) ions3 swg- gesting that E(+e) for this radical is more negative than N-0.1 V. This approach to the problem of the assessment of the oxidizability or reduci- bility of free radicals may be objected to on the grounds that, although the actual value of AG? or AGZ may be large and negative, the value of the rate constant ki or k2 may be such that under the experimental conditions chosen the particular reaction (1) or (2) may be undetectable and an erroneous conclusion about E(+=) or will therefore be drawn.The reason for this is that the actual course of the reaction written formally as (1) or (2) may be different for different ions. Thus the oxidation of a free radical may conceivably involve simple electron transfer ( q n (111, hydroxyl radical addition (eqn. (5)), Re + MXf + OH-(or HZO)-,ROH + M(X- ')+(or + H'), Re + MX++R minus H + M(X-')' + H', ( 5 ) (6) or hydrogen-atom abstraction either as a proton (eqn. (6)), or even as a hydrogen molecule, in a reaction in which the radical and the metal ion are both oxidized, Ra+MX++H+-, R minus H+H2+M(X+')+. (7) Furthermore, water molecules of the inner or outer hydration spheres of Mx+ or hydrolyzed or oxygenated or even polymeric forms of MX+ may be involved in the rate-determining step.For a better understanding of these reactions it is necessary to know the kinetic parameters of a series of closely related reactions. As a first step we aim to determine the rate constants of the reactions of a particular radical towards different cations and the effects on them of changes in temperature, ionic strength, nature of the anion, isotopic composition of the solvent, etc. To achieve this it is necessary to know the concentration of R* whilst reaction (1) or (2) is occurring. If R* is the growing polyradical chain carrier mi*, of the polymerization of a vinyl monomer (ml), the propagation step of which may be written the concentration of Re = [mj.], when high polymer is formed, is at all times given by Rp/kp[ml], where Rp is the rate of polymerization. Hence measurement of Rp allows [mi*] to be calculated, provided kp is known, and the larger kp the more sensitive the method.The polymerization of acrylamide (CH2 : CH . CO . NH2) is a very suitable reaction for this purpose, since kp is large (= 1.8 X 104 1 . mole-1 sec-1 at 25°C) and the mechanism of the reaction well understood.4~ 5 This paper is concerned with the determination of the rate constants of the reaction of polyacrylamide radicals with ferric, cupric, ceric, mercuric, thallic and argentous ions in perchloric acid media and titanous ion in sulphuric acid media and the measurement of the relative rate constants of the reactions of hydrogen atoms with argentous and mercuric ions. THE PRINCIPLE OF THE METHOD When a deaerated aqueous solution of acrylamide is irradiated with prays from cobalt-60 the reactions which ensue are :190 REACTIONS BUTWEEN RADICALS A N D CATIONS kio H.+ml-+ml.HQ. +m,-+m,. k i 1 INITIATION PROPAGATION mi. +ml%mj+ 1. (8) TERMINATION 2mj.-+dead kt polymer, (12) where GH and GOH denote the numbers of hydrogen atoms and hydroxyl radicals respectively, which are formed per 100 eV of pray energy absorbed. The steady- state rate of polymerization is then given by eqn. (13). = ([GI%+ Go~I]~abs)*kp[ml]/k~ mole I.-' sec-', (13) where Iabs is the dose rate in units of 100 eV 1 .-I sec-1. An oxidizing cation Mn+, could conceivably oxidize hydrogen atoms and polyradicals according to the formal eqn. (14) and (1 5) : H.+M*f?H+ +M("-')+ (14) inj. + M"+Adead polymer + M("- 'If.I<' (15) Increasing amounts of MX+, by diminishing the extent to which initiation by reaction (10) can occur and by augmenting the termination rate through reaction (15), will cause a progressive decrease in the rate of polymerization which is expressed in eqn. (16) : Rp" = Ri,O(GOH+ GHklO[ml]/(klO[ml] f k14[MX+]))/(GH+ - R,CMX '1 kp[mllk:/kt, (1 6) where Rp, 0 is the rate of polymerization when no metal ion is present (eqn. (13)). Two extreme cases may be distinguished depending on whether reaction (14) is negligible at all the concentrations of MX+ used. If reaction (14) is negligible the graph obtained by plotting RZ against Xp[MX+] will be a straight line of negative slope = k,[ml]/c:/k, and positive intercept on the ordinate = I?$,*.This is illustrated in fig. 1. Since k, and kt are known Ic; can be determined. Moreover at high concentrations of [Mn+] where almost all the chains are terminated by reaction (15), RZ is negligible in comparison with the other terms in eqn. (16) and hence Rp = (GH + G o d l a b s kp Lm 1 CM"+ 1 (17) and (GI,+ GOH)labs = -d[M"+]/dl* (1 8) If, on the other hand, Mx+ competes very effectively with acrylamide for hydrogen atoms, the curve of R: against Rp[Mx+] will show an initial rapid fall and then become a straight line of negative slope = k,[ml]kf//~, as before. This is illustrated in fig. 5. If the straight line portion is extrapolated to Rp[Mx+] = 0, the intercept will be R&o GoH/(GH+ GoH). Eqn. (16) may be rearranged to give eqn.(l9), (19) the whole of the left hand side of which can be evaluated from the straight line portion of the graph, its intercept and the observed values of R,,o and R,. A plot of 0 against [Mx+J/[ml] allows k14//~10 to be determined.COLLINSON, DAINTON, SMITH, TRUDEL, TAZUKE 192 If, instead of using oxidizing ions, reducing ions NJ”- capable of entering into reactions (20) and (21) are used, another set of equations : Ic ; mjo + NY i- -+dead polymer + N‘y ’ I)’, similar in form, and corresponding to (16), (17), (18), and (19) but with the sub- stitutions GH for GOH, kll for klo, k2o for k14, ky for /ti and NU+ for Mx+ are obtained. Clearly, the study of the effect of various metal ions on the rate of polymerization of acrylamide induced by ionizing radiation is of great potential utility for the determination of absolute values of ki, kr, GI* and GOH and relative values of k14 and k20.In addition, if measurements of gaseous hydrogen yields are made and the end-groups in polacrylamide are identified, then, as discussed later, valuable information concerning the precise mechanisms of reaction (lo), (ll), (14), (15), (20) and (21) may, under favourable circumstances, be obtained. EXPERIMENTAL The source of y-rays was 8 Curies of cobalt 60 and the source of X-rays was a 220 kVp G.E.C. Maximar X-ray set. The method of preparing dsaerated solutions for irradiation and the dosimetry wcre similar to those already dcscribed.4 RECORDING DILATOMETER.-The polymerization was followcd dilatometrically, the change in height of the level of the meniscus in the capillary tube being measured by the change in resistance of a 10 % w/w aqueous solution of potassium chloride separated from the irradiated solution by a column of mercury of constant length.The apparatus was essentially that shown in fig. 1 of ref. (4), exccpt that the change in resistance was ‘recorded by making the conducting column of potassium chloride solution part of an A.C. bridge circuit, the out-of-balance e.m.f. of which was alternately fed into a Honeywell- Brown 1 mV strip chart recorder with a full-scalc traverse-time of about 1 sec. At maximum sensitivity a change of 1 0 cm in height of the dilatometer meniscus corresponded to the full width (11 in.) of the chart. PREPARATION OF REAGENm-Water was twice distilled, the second distillation being from alkaline potassium permanganate in a Pyrex apparatus.The deuterium oxide (99-78 % D2O ex Norsk Hydro Elektrisk Akt.) was similarly treated. Acrylaniide as supplied by the American Cyanamid Co. Ltd., was recrystallized once from chloroform, the resultant crystals were washed several times with A.R. benzene and final traces of this substance were removed by evaporation in vucuu. A.R. perchloric was distilled twice under vacuum at 100°C. Ferric perchlorate was made by dissolving spectroscopically pure (British Bureau of Analysed Samples Ltd.) iron wire in perchloric acid and the resultant ferrous perchlorate solution diluted to 0.1 M concentration and oxidized by passage through it of ozonized oxygen. Excess ozone was subsequently displaced by a stream of pure oxygen.During oxidation a faint purple colour of permanganate ion developed which was due to manganese impurity in the iron to the extent of 0.023 %. This was reduced by the addition of an equivalent of ferrous perchlorate solution. In other experiments, G. Frederick Smith reagent-grade ferric perchlorate dissolved in perchloric acid without further purification was used. No difference was detectable between the effects of these ferric perchlorate solutions on the polymerization. Cupric, mercuric and silver perchlorate (G. Frederick Smith reagent grade) were used without further treatment. Thallous perchlorate prepared by dissolution of thallous carbonate in an excess of hot perchloric acid was thrice re- crystallized from doubly distilled water. Cerous perchlorate (G.Frederick Smith reagent grade) and thallous perchlorate, each dissolved in 2 M perchloric acid were oxidized to the ceric and thallic states in the anode compartment of an electrolytic cell of the type described by Biedermann.6 Since titanous ions reduce perchloric acid it was necessary to use sulphuric acid solution as the solvent for trivalent titanium. Approximately 10-2 M titanyl sulphate solution in 0.8 N sulphuric acid was prepared by gentle boiling of potassium titanyl oxalate in con- centrated sulphuric acid, followed by dilution with water. After further dilution with 0.8 N sulphuric acid, the titanyl sulphate solution was de-areated and then shaken under192 REACTIONS BETWEEN RADICALS AND CATIONS vacuum with liquid zinc amalgam from which it was separated by filtration through a sintered-glass disc of porosity no.3. I n order to ensure as high a concentration of deuterium oxide as possible in the heavy water solution, the appropriate acid and salt were added from an Agla micrometer syringe. ANALYTICAL METHODS.-The concentration of the ferric iron in the stock solution was determined gravimetrically as ferric oxide and in dilute solutions containing 0.8 N &SO4 it was deduced from the optical density at 304 mp assuming an extinction coefficient of 2150 1 . mole-1 cm-1 at 20°C. Cupric ion concentrations in stock solutions were deter- mined iodometrically and mercuric ion concentrations by titration with potassium thiocyanate. Any mercurous ion in the latter was estimated from the optical density at 236.5 mp using Higginson's value 7 of the extinction coefficient.Ceric ion concentrations in the stock solution were determined by titration against standardized ferrous sulphate solution, and in dilute solutions the ferric ion produced on addition of excess ferrous sulphate was estimated from the optical density at 304 mp. For the measurement of cerous ion concentration the method of Willard and Young 8 was employed. Thallic ion concentration was measured by reduction to the thallous state by passage of sulphur dioxide through the solution. After removal of the excess sulphur dioxide by boiling the solution was acidified with concentrated hydrochloric acid and titrated potentiometrically against a standard potassium bromate solution. Argentous ion concentration in the stock solution was obtained by titration against potassium chloride solution.The titanium content of the stock titanyl sulphate solution was determined gravimetrically as Ti02 obtained by ignition of the filtered precipitate produced by addition of cupferron. In all these soIutions the hydrion concentration was determined by some appropriate standard method. EXPERIMENTAL PROCEDURE.-The great sensitivity of the acrylamide polymerization to traces of impurity required strict adherence to the rigorous cleaning and de-aeration procedures which are in frequent use in this laboratory and which have often been described. The preparation of the de-aerated solution and their transfer to the dilatometer were by methods already described.4 RESULTS POLYMERIZATION IN THE ABSENCE OF METAL IONS No thermal rates of polymerization or inhibition periods were observed.At an acrylamide concentration of 0.4 M in 0.1 N perchloric acid solution R,, 0 was found to be proportional to I& over the dose rate range 1 . 3 2 ~ 1014 to 2.68 x 1016 eV 1-1 sec-1. Taking the value of GH and GOH in 0.4 M acrylamide solution as equal to 7.5 and to be independent of temperature,g the application of eqn. (13) to the measured values of R,, 0 at 18.6", 25.0", 32.5" and 40.3"C gave APIA; = 45 1.4 mole4 sec-) and Ep-(EJ2) = 1.38 f0.25 kcal mole-1. The value of kp/kj at 25°C was 4.4 I.& mole4 sec-* in good agreement with the value of 4.7 previously reported,4 and the values of kp = 1 . 8 ~ 104 and kt = 1 . 4 5 ~ 107 1 . mole-1 sec-1 given by Dainton and Tordoff.6 An increase in perchloric acid concentration from 0.1 to 1.0 M had no effect on Rp, 0, but replacement of perchloric acid by 0.8 N sulphuric acid halved the value of R,, 0 and replacement of the perchloric acid by 0.8 N sulphuric acid and 0.5 M sodium sulphate decreased Rp, 0 by 30 %.THE EFFECTS OF ADDED FERRIC AND CUPIUC PERCHLORATES The results obtained for 0.1 N perchloric acid solution are given in fig. 1 and the linearity of the graphs indicates that over the whole range of concentrations used, the metal ions present react only with polymer radicals and not with H- or -OH, both of which are captured by acrylamide. Applying eqn. (16) after putting k14 = 0, and substituting for kp and kt with the values given above, the values of k,' for ferric and cupric perchlorate at 25°C in 0.1 N perchloric acid are: k1(Fe(C104),) = 4.1 x 103 and k,'(Cu(ClO&) = 1 .2 ~ 103 1 . mole-1 sec-1. TheCOLLINSON, DAINTON, SMITH, TRUDEL, TAZUKB 193 value for the sum of these rate constants obtained from measurements made on the equimolar mixture is 5.1 x 103 1. mole-1 sec-1. Rp[M(Z+l)+] x l o 9 mole2 1.-2 sec-1 FIG. 1.-The effect of added ferric (-0-) and cupric (-O-) perchlorates and equimolar mixtures of the two (--@-) on the rate of polymerization of 0.4 M acrylamide solution in 0.1 N perchloric acid solution at 25°C. Dose rate = 2.68 x 1011 eV 1.-1 sec-1 for 0 and 0 , slightly less for 0, It has been shown elsewhere that k,' for hydrolyzed ferric ion is larger than that for unhydrolyzed ferric ion.+ s.To determine E: for the latter it is necessary to ensure that this species comprises < 99 % of the total ferric iron at all temperatures at which k;(Fe(ClO&) is measured. This was achieved by raising the perchloric acid concentration to 1 M. The Arrhenius plots for the ferric and cupric per- chlorate systems at this acidity in H20 and D2O are shown in fig. 2. THE EFFECT OF ADDED CERIC PERCHLORATE Ceric salts will initiate the polymerization of water-soluble vinyl compounds even in the dark.10 This thermal polymerization is at least second order with respect to monomer concentration 11 whereas the radiation-induced reaction is first order. Consequently in 0.2 M acrylamide solution the thermal rate can be reduced to a very small fraction of that of the radiation-induced polymerization.However, the radiation-induced reaction in the presence of ceric ions differed from all other systems investigated in that the steady-state was often not attained until several hours had elapsed. During this period, the duration of which increased with increased initial concentration of ceric ions, the polymerization slowly accelerated and the ceric ion concentration decreased initially at a rate corresponding to a large G(- Ce(1V)) value ( ~ 2 0 ) . At the end of this induction period both the concentration of ceric ion and the rate of polymerization became constant and the graph of the square of this steady rate against the product of this rate and the steady-state ceric ion concentration gave the straight line shown in fig. 3. The G1 94 REACTIONS BETWEEN RADICALS AND CATIONS value of kt(Ce(C104)4) obtained from this graph asuming that eqn.(16) with klo = 0, is applicable, is 3.4f0.3 1. mole-1 sec-1. It seems likely that the long induction period is due to reaction of ceric ion with hydrogen peroxide formed in l/T°K x 103 perchloric acid solution in H20 and D20. FIG. 2.-Log10(kpk,'/kt) plotted against T-1 for 0.4 M acrylamide solution in 1.0 N T 1- 0 Fe 011) in H20 I I Fe 011) in D20 1- - I 0 Cu (11) in H20 I I B Cu (11) in D20 1_ the primary act. The oxygen liberated adds to growing poly radicals forming mi02. radicals which either combine with other poly radicals or reduce ceric ions. The polymer peroxides are then oxidized in reactions with ceric ions which involve free radical intermediates and ultimately lead to polymers containing carbonyl groups.Many feasible reactions participate in this mechanism, the net result of which is slow reduction in the oxygen concentration and a rapid conversion of ceric ions to the cerous state. Cerous ions play no part in this process, since addition of cerous ion initially has no effect. The maximum permissible value of G(- Ce IV) based on the known radical and molecular yields is 35 and the observed value is less than this. When the concentration of ceric ions falls below a certain level the rate of regeneration of oxygen from the peroxidic products also diminishes and the concentration of oxygen becomes very low. Polymerization then proceeds at the steady rate (given by eqn. (17)) and the ceric ion concentration decreases at an undetectably small rate.The graphs of loglo (k,k:/kt) against T-* at two different acrylamide concen- trations are curved, as shown in fig. 4. This curvature is undoubtedly due to the increased hydrolysis of ccric ions as the temperature is raised, and to differentCOLLINSON, DAINTON, SMITH, TRUDEL, TAZUKb 195 I I I 5 10 R,, f [Ce LV]fx 1010 mole2 1.-2 set-1 FIG. 3 . T h e relation between the steady rate of polymerization of 0.2 M acrylamide solution in 0.1 N perchloric acid solution and the steady-state ceric perchlorate concen- tration at 25°C. Dose-rate = 2 X 1016 eV 1.-1 sec-1. l/T°K x 103 FIG. 4.---Effect of temperature on k,k,'/kt for ceric perchlorate in 1.0 N HC104. Acryl- :iniidc conccntratiori. 0 0 4 M ; 0 0 2 M ; ordinates separated for clarity.196 REACTIONS BETWEEN RADICALS A N D CATIONS values of E,' for Ce4+ and CeOH3+.In the temperature range used [Ce4+] decreases almost 6-fold whereas [CeOH3+] increases by a quarter and it is possible that the steeper slope at the lower temperatures is due to E,'(C&+)>E:(Ce-OH3+) and that the contribution which Ce4+ makes to linear termination is much smaller at the higher temperatures, in which case the limiting slope at higher temperatures will provide an upper limit for E,'(CeOH3+). THE EFFECT OF ADDED MERCURIC, THALLIC, AND SILVER PERCHLORATES The effect of each of these salts is much less marked than that of any of the salts mentioned above. In addition, the graphs of I?; against RP[Mx+], which are shown in fig. 5, have two distinct sections.The sections corresponding to the 9 0 6 0 3 0 4 a 12 Rp[M2+] x 106 mole* 1.-2 sec-1 FIG. 5.-The effect of added mercuric (-O-), thallic (-a- )and silver (-0-) per- chlorates on the rate of polymerization of 0.4 M acrylamide solution in 0.1 N perchloric acid solution at 25°C. Dose rate = 1 . 8 6 ~ 1016 eV 1.-1 sec-1. higher values of [Mx+] are linear but at low concentrations the plots are curved and of steeper slope. For mercuric and silver perchlorates the results are con- sistent with eqn. (16) when k149k10. Back extrapolation of the linear portions to intersect the ordinate gives values of (GH+GoH)/GoH = 1.93 (HgZ+) and 2-11 (A&) which may be compared with the value of 2.18 obtained for the acryl- amide water system by another method.9 The slopes of the linear portions indicated that at 25"C, k,'(AgCIOd) = 0 and k:(Hg(ClO&) = 1.05 I.mole-1 sec-1 and the plots of 0 (for definition see eqn. (19)) against [Mxf]/[M1] give straight lines corresponding to k14 (Ag+)/klo = 28 and k14 (Hg2+)/klo = 510 at 25°C. Thallic perchlorate is a less effective chain terminator than mercuric per- chlorate and from the slope of the linear part of the curve in fig. 5 we deduce that k,'(Tl(ClO4)3) = 0.34 1. mole-* sec-1 at 25°C. The rapid initial drop in rate of polymerization may be ascribed to a liberation of oxygen from the molecular hydrogen peroxide by reaction with thallic ions (eqn. (22)) T13 .t + H2O2+Tl+ + 2H' + 0, (22) followed by reaction of the oxygen with hydrogen atoms to form HO2 radicals.COLLINSON, DAINTON, SMITH, TRUDBL, TAZUKB 197 Hence, for each 100 eV energy absorbed G H ~ o ~ polymerization chains would be prevented from starting and the ratio of the intercept on the ordinate to Rg, should be (GH+ GOH- GH~o*)/(GH+ GOH) for which the predicted value 9 is 0.935 and the value obtained from the data depicted in fig.5 is 0.92. I 3.2 3.3 3.4 I 1 1/TK x 103 FIG. &-Log (kpkl/kt) plotted against T-1 for 0.4 M acrylamide solutions in 1.0N per- chloric acid : -0- added Hg(C104)~ ; -0- added TI(C104)3. In fig. 6 are shown the Arrhenius plots for the mercuric- and thallic-perchlorate terminated polymerization. THE EFFECT OF ADDED TITANOUS AND SODIUM SULPHATES Titanous sulphate solutions in 0-8N sulphuric acid have a broad, weak, ab- sorption band centred at 525 mp at which wavelength the extinction coefficient is about five.Between 4-00 mp and 280 mp, which is the long-wave absorption edge of the electron transfer band, the solutions are virtually transparent. When acrylamide is added to these solutions a new absorption band with A, = 325 mp, is produced. Measurements of the optical density at 325 mp of solutions con- taining a large, variable excess of acrylamide and a small, fixed, concentration of titanous sulphate indicated that the new absorption band is due to a 1 : 1 complex of acrylamide and titanous sulphate. In a solution containing 0.8 N sulphuric acid and 0.5 M sodium sulphate the equilibrium constant (= [complex]/r]ri 1111 [ml]) is G0.13 at room temperature and the extinction coefficient of the complex is N 285 1.mole-1 cm-1 at 325 mp. At the concentrations of acrylamide used in the polymerization experiments described below, not more than 1.3 % of the total titanous ion exists as the complex. The effects of increasing titanous sulphate concentration on the rate of poly- merization of 0.1 M acrylamide solution (a) in 0.8 N sulphuric acid solution and (b) in 0-8 N sulphuric acid solution also containing 0.5 M sodium sulphate, are shown in fig. 7. The ionizing radiation used was 220 kVp X-rays. This radiation rather than 6ocobalt y-rays was used because a higher dose-rate was desirable to compensate for the decrease in rate due to the lower monomer concentration necessary to minimize complex formation. No thermal rates or inhibition or198 REACTIONS BETWEEN RADICALS AND CATIONS induction periods were observed, and the presence of 1 .2 ~ 10-4 M titanyl sulphate had no effect on the rate of polymerization. The graphs of Ri plotted against Hp [Ti 1111 wcre similar to the corresponding graph for mercuric perchlorate (see fig. 5). The obvious explanation of these graphs is that titaiious ions compete with acrylamide for hydroxyl radicals and also terminate polymer radicals. The values of (GH+GoH)/GH obtained from the ratios of Rg,O to the intcrcept on the ordinate when the linear portions of the graphs are back-extrapolated are (a) in 0.8 N sulphuric acid solution, 1.72 and (b) in the mixed sulphuric acid+sodium sulphate solution, 1.82. This ratio has not previously been determined for 0.1 M acrylamide solution in these media for 220 kVp X-rays.In 0.04 M perchloric acid solution containing 0.1 M acrylamide 9 the ratio for cobalt-60 y-rays is 1.82, and it would be expected that the ratio for 220 kVp X-rays in 0.8 N solution would be close to, but would not exceed this value. I R, [Ti(lII)] x 108 mole2 1.-2 sec-1 FIG. 7.The effect of added titanous sulphate on the rate of polymerization of 0.1 M acrylamide solution at 25°C. Dose rate = 9.6 X 1017 eV 1.-1 sec-1. 0 denotes solvent is 0.8 N H2SO4 in H20 ; -a- denotes solvent is 0.8 N H2SO4+05 M Na2SO4 in H20 ; Qo denotes solvent is 0.8 N H2SO4 in D20. The data for solutions in D20 may be interpreted in a similar way and indicate that (GD+G~D)/GD = 1.87 which may be compared with the value of 1.86 for 0.1 M acrylamide in 0.04 N perchloric acid solution in D20 using y-rays.9 Assuming GH 3 3.95, GOH = 3.21, GD = 4.25 and GOD = 3.6 the values of k,/l/kt for 0.8 M H2S04 solution in H20, 0.8 N H2SO4 in D20 and 0.8 N H2S04+0'5 M Na2S04 are 2.36, 2.45 and 2.96 1.4 mole-* sec-) respectively.These results indicate that substitution of D for H has no effect on k,/kt but that substitution of 0-8 N H2S04 for 0.1 N HClO4 diminishes this ratio by a factor of two and that the addition of 0.5 M Na2SO4 increases k,,/kt by 50 %. It is not yetCOLLINSON, DAINTON, SMITH, TRUDEL, TAZUKk 199 known whether changes in this ratio are due to changes in kp or kt, or both. In the only remotely comparable situation which exists, namely, the polymerization of acrylonitrile in NN1-dimethyl-formamide,l2 the addition of 0.294 M lithium chloride increased the propagation rate constant without affecting the termination constant.Although final values of k," (Ti 111) must await the determination of the values of k, and kt in each of these media, it is instructive to compare the values which kl' (Ti 111) would have assuming that the change in k,/@ is due solely either to (a) a change in k,, or (b) a change in kt These values are tabulated below. TABLE 1 medium 0.8 N . H S04/Hz0 0.8 N . H2S04/D~0 0.8 N HzS04/0.5 M Na2S041HzO kP1kt 2.36 2-45 2.96 Assumption a b a b a b k11 CriIII) 1.14X I03 2.3X 103 1.59X 103 3.27X 103 1 . 1 0 ~ 103 1 . 7 9 ~ 103 The Arrhenius plot of loglo (k,(ml)k:l (Ti IIT)/kt) against 2'-1 gives a value of E,-J?Z~+E)~ (Ti 111) = 16*2 kcal mole-1 and AllAp/At = 8x 1010 1.mole-1 sec-1. Unpublished work in this laboratory 13 suggests that Et = 0 A0.5 kcal mole-1 and hence Ep = 1.38f0.25 kcal mole-1. From these data we calculate that Etl p i III) = 14.652.75 kcal mole-1 and that A i l (Ti 111) lies between 5 x 1010 and 5 x 1014 1. mole-* sec-1 in 0.8 N sulphuric acid. The quantity 8 in eqn. (19) can be evaluated for each titanous sulphate concen- tration from the data given in fig. 7 and hence we may obtain the ratio of the rate constants for the reactions of OH (or OD) with acrylamide and titanous sulphate in the various media. The values of k20 (Ti III)/kll at 25°C are : (a) in 0.8 N H2SO4 in H 2 0 , 650, (6) in 0.8 N H2SO4 in D20, 1600 ; and (c) in 0.8 N H2SO4, 0.5 N Na2S04 in H20, 860. DISCUSSION The results presented in the previous section indicate that the study of the effects of metallic salts on the rate of polymerization of acrylamide initiated by ionizing radiation afford a powerful means of determining (i) the absolute values of the Arrhenius parameters of oxidation-reduction reactions between various cations and the same free radical, namely, the polyacrylamide radical, (ii) relative values of the Arrhenius parameters of the reactions of hydrogen atoms or hydroxyl radicals with various cations and (iii), incidentally, where (ii) is possible, values of GH and GOH.Although it is our intention to study many more of these reactions and final conclusions concerning reaction mechanisms and the influences which control the magnitudes of the Arrhenius parameters must be deferred until this survey is complete, some correlation and tentative conclusions can be reached on the basis of the results obtained for the seven ions with which reactions have already been investigated.Most of the results are given in tables 1, 2 and 3, and the broad conclusions to be drawn from them are : (i) The values derived for the radiation-chemical quantities are in good agree- ment with those derived by an entirely independent method 9 for aqueous solutions of acrylamide of the same concentration. (ii) For the reactions between the radical and ferric, cupric or titanous ions the difference between the values of the rate constants in D20 and H20 are within the experimental error, but there is a genuine solvent isotope effect for the reaction between hydroxyl radicals and titanous ion which is contrary to that usually observed for oxidation-reduction reactions.TABLE 2 REDUCTION OF CATIONS (Mx+) BY THE POLY-ACRYLAMIDE RADICAL (mj*)AND BY A HYDROGEN ATOM (Ha) derived -radiation chemical quantity Fe3+ - 0.77 1 - 17.8 - 9.6 + 26.5 H20,O.l N HClO4 4.1 X lo3 .... .................. too small H20, 1.0 N HClO4 2.8x 103 1 . 4 5 ~ 10s 2.35k0.6 to Nil .................. measure D20, 1.0 N HClO4 2.6 X lo3 1.57X 10s 244kO-3 -3.5 uncertain + 1.7? H20, 1.0 N HC104 1.17%' 103 1.1 X lo7 5.4h1.3 too small .................. to D20, 1.0 N HC104 1.4 x I03 1.0 x 107 5351.3 measure CeOH3+ -1.7 - 39.0 (in 1.0 N HC10,) , HzO, 0.1 N HClO4 3.4 X lo3 .. . . too small .................. to H20, 1.0 N HClO4 3.2 X 103 2 X 105 p2.45 measure Nil Nil Hg2+ (-0.9 forHg;+/Hgz+) (-;I) .. . . HzO. 0.1 N HClO4 1.05 4.2 X 104 6*2&1*0 510 (GH+GoH)/GoH= 1.93 unknown for Hg+/HgZ+ . TI3+ Eo for TP+/TP+ Between . . . . H20.0.1 N HC104 0-34 21 2.5 -1-0.4 too small (GH+ GoH)/(GH+ GOH- GHZO~) unknown but - 18 and to - 1-09 -0*79> E"> - 1*7(e) -40 measure Ag+ +l*8 (f) +41.4 +434 +lS HzO, 1.0N HCIOd 0 .. .. 28 (GH+ GoH)I(GoH = 2-1 1 NOTES (a) Since k,/kt and E,,-(Et/2) have same values in H2O as DzO, A,, A t , Ep and Et are assumed to be the same in each of these solvents. (6) taken from Latimer, Oxidation Potentials. New York. 1952. (c) Bureau of Standards values; heat of formation of H& and H2 taken as zero. ( d ) based on convention SR+ = 0 and taking si&) = 31.2 cal deg. mole-1.(e) From the facts that Eo (TI+/Tl3+) = - 1.24 and both Tl3+ and TP+ oxidize Fe2f.17 ( f ) refers to ~H2(s)+fAga'-Ha's+Ag(6). Ei calculated from AGO. c( 0COLLINSON, DAINTON, SMITH, TRUDEL, TAZUKi! 201 (iii) Whereas the entropy of activation for the oxidation of titanous ion by the radical is nearly zero, the entropies of activation for the reduction of ferric, cupric, ceric, mercuric and thallic ions are all surprisingly large and negative, having the values - 35, - 25, - 3 1, - 38 and - 53 cal deg.-l mole-1 respectively. Moreover, these values have no obvious relation to AS" for the reduction of the ions by hydrogen (see column five of table 2). (iv) The energies of activation for the reduction of cations by the polymer radical are all much smaller than that for the oxidation of titanous ion.(v) The rate constants for reduction by polymer radicals of ferric, cupric and ceric ions are all between lo3 and 104 times larger than the rate constants for reduction of mercuric and thallic ions and bear no relation to AGO for the reduction of these ions by hydrogen. The stability of argentous ions towards the radical may be associated with the very large positive value of AGO for the reduction of this ion to atomic silver by hydrogen. (vi) It is broadly true that those ions which react rapidly with hydrogen atoms react slowly with the polymer radical, and vice versa. Thus argentous and mercuric ions react rapidly with the atom and very slowly or not at all with the radicals, and ferric ions, which oxidize the radical more rapidly than cupric ions, oxidize hydrogen atoms less rapidly.14 TABLE 3.-oXIDATION OF TITANOUS ION (TI3'') IN 0.8 N H2S04 IN H20 AND D20 BY THE POLYACRYLAMIDE RADICAL (mj .) AND BY THE HYDROXYL RADICAL OH) k2l at 25°C A21 E21 k20/kll at 250c derived radiation medium 1.mole-1 sec-1 1. mole-1 sec-1 kcal chemical quantity (a) (6) H20 1.14x lo3 2.3 x l o 3 1012*2 14*6&2*75 N 600 (GH+GoH)/GH = 1.72 D20 1-59 x 103 3.3 x 103 .. .. N 1600 (GD+GoD)/GD = 1-87 RELATED THERMODYNAMIC DATA Reaction AGO OH+TP+-+TiOz++ H+ - 62 Hf HzO+TiJ++H++H2fTi02+- 46 (a) and (b) refer to the assumptions that sulphuric acid alters (a) k, only (b) kt only. (vii) Previous studies 15@) in these laboratories have shown that k2o/lcll for ferrous ions at 25°C is 0.02 and therefore kzo(Ti3+)/~20(Fe2$)-"3x 104 which is the order expected for these ions, since AGO for the oxidation of Ti3+ by OH is e l 4 kcal more negative than that for the oxidation of Fe2+.However, the solvent isotope effect for the Ti3++ OH reaction is opposite to that which probably holds for the Fe2++ OH rea~tion.ls(~) REDUCTION OF CATIONS All attempts to correlate either the rate constants, or the entropies or energies of activation, of these reactions with thermodynamic properties of the redox system including relative free energy, enthalpy and entropy changes, or with changes in solvation heats or entropies, or ionization potentials are unsuccessful, and this suggests that entirely non-thermodynamic influences dominate these reactions. It is very striking that ions with incomplete d orfshells react rapidly with the radical, whereas the ions with complete d shells either react very slowly (Hg2+ and TP+) or not at all (Agf) with the radical and may react (Hg2+ and Ag+) more rapidly with hydrogen atoms than transition element ions such as Fe3-+ and Cu2f.This suggests that the oxidation of the radicaI involves the utilization of one of the vacant d orbitals of the cation. We may envisage the approach of the radical to the cation so as to achieve sufficient overlap of the p-orbital of the202 REACTIONS BETWEEN RADICALS AND CATIONS carbon and a d-orbital of the cation in the transition state for rapid electron transfer to take place. The release of an electron by the radical enabIes it to expel a proton. On this hypothesis the overall reaction might be represented in the case of cupric ion by eqn.(23) : Cu2+ + . C H ( X ) C H ~ ~ ~ - ~ + ( C U . . . CH(x)---CH-mj)2++Cu+ + 3d9 i 3di0 H +CH(x)=CHmj_, (23) H+ transition state (where x = CONHz), and would lead to the predictions : (a) that the energy of activation would have the low value typical of true electron-transfer processes, (6) that ions with completed d shells would not react, (c) that no marked solvent isotope effect should exist since no 0-H bond breakage occurs in the rate determining step, and (d) that the polymer should contain a terminal vinylene group. (a), (b) and (c) have been shown in this paper to be in accord with the facts and (d) will be tested. This model does not indicate that the observed negative entropy of activation is caused by stronger solvation of the transition state.Possibly electron " tunnelling " transfer is involved and the negative AS+ values are due to low permeability of the barrier. For a reaction of the type shown in eqn. (23) to be exothermic, almost complete solvation of the proton is necessary. A long-lived transition state will facilitate the development of this solvation, and the incipient bond formation through an unoccupied d-orbital, which is implicit in the above mechanism, is clearly ad- vantageous. The question then arises as to whether a similar mechanism applies to the reduction of cations by hydrogen atoms. Although in principle this might be the case, it should be remembered that hydride formation involving d-orbitals is unknown, but that a($ hydride bonds involving metals are common.If incipient formation of such a bond is a necessary prerequisite in the reduction of a cation by hydrogen atoms, the magnitude of the energy necessary to promote an electron in the cation to the lowest available s orbital, may be the controlling influence on the rate, in the sense that the larger this energy the smaller k14. This d-s energy interval will be smaller (a) the smaller the charge on the ion and (6) the larger the principal quantum numbers involved, and hence also the greater the atomic number. On this basis it is immediately apparent why the ions Hg2+(5dlO) and Ag+(MlO), having low charge and large principal quantum number should be reduced more rapidly than Fe3+(3d5) and Gi2$-(3d9) which have either high charge or low principal quantum number or both.* For thallic and Eric ions the charge and quantum number influences are in opposition, but further experiment is necessary to establish whether these two ions occupy an intermediate position between A& and Cuz+.Arguments somewhat similar to these have been advanced by Halpern 16 to account for the effectiveness of certain cations as catalysts for the activation of molecular hydrogen. These reactions involve the transfer of either an H. atom or the hydride (H-) ion to the catalyst cation and optimum catalytic activity is observed when the d-shell is filled or nearly filled and the ion can make available an empty d-orbital by promotion. The hydride intermediates proposed include ASH+, HgH+ and CuHf, which will certainly utilize bonding orbitals.OXIDATION OF TITANOUS IONS Titanium (IV) exists in aqueous solution as the Ti02+ ion. Consequently the oxidation of the titanous ion by the OH radical may perhaps be regarded as the * Results of radiation-chemical experiments indicate that H atoms do reduce Fe3+, T13+, Cu2+ and CeSO:+ ions, and that, as would be expected, kl4(Cu2+)>k,4(Fe3+).14COLLINSON, DAINTON, SMITH, TRUDEL, TAZUKE 203 transfer of charge by transfer of 0- from the OH radical and expulsion of the proton. The reaction would be expected to be more rapid than the oxidation of ferrous ion by the OH radical because -AGO is much larger, and the entropy of activation should be more positive since, unliko the ferrous+ OH reaction, no additional charge is developed in forming the transition state.If the reaction mechanism is correctly represented by the equation given in table 3, it might be expected that a change of radical from OH to OD would retard the reaction, whereas the present indications are that the reverse is true. This may be evidence of some net desolvation in forming the activated complex, associated with the decrease in charge on the titanium. Since D20 solvates cations more strongly than H20 this could lead to greater entropy gain in the former solvent than in the latter, an effect which might be sufficiently strong to predominate and to invert the normal specific solvent effect in oxidation-reduction reactions. The oxidation of Ti(II1) by mp necessarily involves the breaking of both the OH bonds of one of the bound water molecules.The reaction can be one of attachment of a hydrogen atom to (eqn. (24)), Ti~OH~++~CH(x)~CH2mj~1+TiOz++H++HCH(x)CH2mj~l, (24) or detachment of a hydrogen atom from (eqn. (25)), the polymer radical. We have some evidence, which will be presented elsewhere, that eqn. (25) is the more correct, but whcther this involves electron transfer from the radical with proton expulsion from it (eqn. (25(a))) Ti3+*CH(x)CH.mj- 1-+Ti2+ + CH(x): CHmj- 0 /OX\ H + H+ 1 H H H2 in a manner which recalIs eqn. (23), or whether there is no charge flow in the radical (eqn. (25(b))), Ti3 +.CH(x), -+Ti2+CH(x) 7 x = CONH, is not yet determined. If the former is true, d-orbital influence may be important, but only experiments with other ions can establish or disprove this. If the latter is correct the hydrated Ti(II1) ion may be regarded as a hydrogen atom capable of entering into a disproportionation reaction with the radical. The zero entropy of activation and the high energy of activation suggest that this may be the case. We are grateful to the General Electric Research Laboratory for some financial aid to S.T. and G.J.T. 1 Mackinnon and Waters, J. Chem. Soc., 1953, 323. 2 Haines and Waters, J. Chem. SOC., 1955, 4256. 3 Dainton and James, Trans. Faraday SOC., 1958, 54, 649. 4 Collinson, Dainton and McNaughton, Trans. Faraday SOC., 1957, 53, 476, 489. 5 Dainton and Tordoff, Trans. Faraday SOC., 1957, 53,499. 6 Biederman, Arkiv. Kemi, 1953, 5, 441. 7 Higginson, J. Chem. SOC., 1951, 1438. 8 Willard and Young, J. Amer. Chem. Soc., 1928, 50, 1379. 9 Armstrong, Collinson and Dainton, Trans. Faraday SOC., 1959, 55, 1375. JOBacon, Trans. Faraday Soc., 1946, 42, 140; Saldick, J. Polymer Sci., 1956, 19, 73.204 REACTIONS BETWEEN RADICALS AND CATIONS 11 Second-order with respect to monomer concentration would be expected if the initiation reaction involved a bimoIecuIar reaction between acrylamide and ceric ions and termination were exclusively by reaction (16). The recent work of Mino, Kaizerman and Rasmussen, (J. Polymer Sci., 1959, 38, 393) suggests that this mechanism is probable. 12 Bamford, Jenkins and Johnston, J. Polymer Sci., 1958, 29, 255. 13 S. A. Zahir, Thesis (Leeds), 1960. 14 Riesz and Hart, J. Physic. Chem., 1959, 63, 858. 15 (a) Dainton and Hardwick, unpublished data. (b) Bunn, Dainton and Salmon, unpublished data. 16 Halpern, J. Physic. Chem., 1959, 63, 398. 17 Higginson and Ashurst, J. Chem. SOC., 1953, 3044.