Quantitative Chemically Induced Nuclear Polarization (CIDNP) Study of the Kinetics of the Photolysis of Pivalophenone in Various Solutions BY P. G. FRITHAND K. A. MCLAUCHLAN* Physical Chemistry Laboratory, Oxford University, South Parks Rd., Oxford OX1 342 Received 19th May, 1975 A simple mechanistic study of the photolysis of pivalophenone in a series of solvents showed that under suitable conditions a unique reaction mechanism obtains. In all the solvents investigated benzoyl and t-butyl radicals are produced which undergo two competitive cage reactions, recombina- tion and disproportionation. In chloroform at 310K 15 % of the radicals recombine and 85 % disproportionate ; in the fluorocarbon PP9 with added tetrachloromethane the figures at 310 K are 17 % and 83 % respectively and the activation energies of the two processes differ by 16.322.0 kJ mol-'.This observation is used to rationalise unusual behaviour in the electron polarization phenomena of the radicals. The overall pseudo first-order rate constant for the scavenging of t-butyl radicals in neat chloro- form was measured directly by flash-photolysis e.s.r. techniques as 5.44f 0.13 x lo3s-' ; CIDNP exposed that two scavenging routes occur: hydrogen abstraction with a rate constant kk = 2.54 -+0.07 x lo2dm3 mol-' s-l and chlorine abstraction with a rate constant kE, = 1.842 0.07 x lo2dm3 mol-' s-l. In PP9 the second order rate constant for reaction of t-butyl radicals with tetrachloro- methane is 4.9 x lo4 dm3 mol-i s-l, with an activation energy of 13.844.2kJ mol-'.These kinetic results are compared with literature values and shown to be consistent with previous observa- tions of the t-butyl radical. The spin-lattice relaxation time of the protons in this radical is 2.22 0.7 x s in chloroform solution and its diffusional correlation time is 41t_:1 x lo-'' s ; this is consistent with theoretical predictions of the time required to produce polarization in a solution having the viscosity of chloro-form. The whole provides a stringent test of kinetic CIDNP theory as applied to radical reactions in solution. In a recent paper we demonstrated that a kinetic analysis of the time-dependence of CIDNP signals treated on the diffusion model produced sensible results ; it is the object of this communication to investigate this model in more depth and to expose the detailed kinetic information which can be obtained from CIDNP studies of care- fully-chosen systems under controlled conditions.As before, a quantitative analysis is possible only after the mechanism is established and this results from an initial qualitative study. The molecule investigated was pivalophenone in which reaction proceeds via an excited triplet state produced on light absorption. Although photoreduction occurs in hydrogen-donating solvent^,^ Norrish Type 1scission of the carbonyl-t-butyl bond occurs with high quantum efficiency in other solvents. A time-resolved e.s.r. study identified the benzoyl and t-butyl radicals which result and confirmed the triplet as their source by using naphthalene as a quencher.The electron polarization behaviour was complex but the CIDNP observations can be interpreted in terms of S-To mixing alone (at high magnetic field values). Pivalophenone constitutes a suitable molecule for detailed study since t-butyl derivatives give simple n.m.r. spectra and reaction can be restricted to one well-defined mechanism. In chloroform solution the rate of dis-87 CIDNP STUDY appearance of t-butyl radicals was determined by direct observation from flash- photolysis e.s.r. studies and with the CIDNP results this led to a value of the proton spin-lattice relaxation time in the free radical. This provided an internal time- standard and allowed a detailed investigation of the rates of competitive atom abstrac- tion reactions in this solvent.The activation energies for these processes were obtained from a study of the temperature-dependence of the time-evolution of nuclear polariza- tions observed in fluorocarbon solvents with added scavengers. Two competitive cage reactions of the radicals were also studied. The experiments have been performed at low concentrations of reactant and radical to ininimise radical re-encounter reactions and reactions of photolysis products. EXPERIMENTAL Experiinents were performed using the n.m.r.5 and e.s.r. spectrometers described previously. Pivalophenone was prepared by a standard method and vacuum-distilled, and its purity (>98 %) was confirmed by g.1.c. and n.m.r.observations (refractive index, ,u = 1.510 8) ; a small quantity further purified by preparative g.1.c. gave identical results to the bulk. The e.s.r. observations showed the presence of peroxyl radicals in oxygenated solu- tions and so all samples were purged of oxygen, manipulated under nitrogen and irradiated (with unfiltered high pressure mercury light) as described before. The quantitative studies were performed in chloroform at pivalophenone concentrations of 0.01 mol dm-3 at 310 K, in the fluorocarbon solvent PP9 at 0.004-0.007 mol dm-3 (in the presence of 0.005-0.120 rnol dm-3 tetrachloromethane) at temperatures 243-343 K, and in silicone oils (y = 1-1000cP) at 0.003mol dm-3 in the presence of 0.02-0.07 mol dm-3 tetrachloromethane.The probe temperature was obtained by chemical shift measurements before and after each experiment by substituting a tube containing ethylene glycol, the two samples each being allowed 10min to attain thermal equilibrium before each measurement. The rate of disappearance of the t-butyl radical was measured by flash-photolysis e.s.r. using a 0.01 mol dm-3 solution of pivalophenone in chloroform; a pseudo first-order rate constant k, = 5.44k0.13x lo3s-l was obtained. Low solubility of reactant and scavenger precluded direct observation of this decay in the fluorocarbon solvent. RESULTS QUALITATIVE OBSERVATIONS The polarized spectrum observed on irradiation of pivalophenone in chloroform is shown in fig. l(a). The lines were assigned on the basis of their chemical shifts and by the sign of polarization predicted from S-To mixing in a benzoyl (g = 2.000 8, A,(meta) = 0.15 mT)-t-butyl (g = 2.002 7, AH = 2.3 mT) radical pair obtained from a triplet precursor.The methyl groups of pivalophenone formed by cage recombina- tion are in enhanced absorption as are the aldehyde groups of the cage-disproportiona- tion product benzaldehyde and the methyl and methylene protons of the other disproportionation product, isobutene. The methyl groups of the two scavenged products isobutane and t-butyl chloride formed by abstraction of hydrogen and chlorine atoms respectively from the solvent are in emission. The reactions are suminarized in fig. 2. Experiments in tetrachloromethane [fig. 1(b)] and PP9 with added tetrachloro- methane confirm this overall mechanism but yield additional information.Thus the absence of the isobutane methyl doublet confirms its production by hydrogen- abstraction from the solvent and a decrease in the absorption at 6 7.2 due to produc- tion of negatively-polarized aromatic protons from pivalophenone and benzaldehyde in the cage is observed. Apart from this region, whicli is obscured, the polarizations observed in the irradiation of solutions in benzene, paraffins and silicone oils are also P. G. FRITH AND K. A. MCLAUCHLAN CHC l3 FIG.1.-The polarized n.m.r. spectrum of photolysed pivalophenone : (a)in CHC13, (6) in CCI, and (c) in C2HC13. CIDNP STUDY consistent with the mechanism given in fig.2. An important absence from the spec- trum obtained from the reaction in tetrachloromethane is that of chloroform which might be formed from disproportionation reactions between, for example, t-butyl and trichloromethyl radicals. Similarly a pair of t-butyl radicals might produce multiplet polarization in the disproportionation product isobutane and isobutene ;the lack of such behaviour confirms that in our experiments, in contrast to those reported with the use of higher irradiation intensities,* the polarizations observed derive solely from interactions of the primary radicals. This is an important simplifying feature in the extraction of kinetic information. Thus polarized benzaldehyde originates in a spin-conserved hydrogen transfer within the cage from polarized t-butyl radicals to benzoyl, and this also produces polarized isobutene.hv, I.s. c. C H COC(CH3)3--b5 ** C6H5COC (CH3) * C6H5COCl recombination diffusion disproportionation CHCl (CH;) 3CH (E) CHCl * 3-(CH3I3CC1 FIG.2.-The reactions of pivalophenone in chloroform. Protons which are polarized are marked with an asterisk. In PP9, increasing the concentration of tetrachloromethane increases the intensity of the t-butyl chloride line as the scavenging rate increases and competes more effec- tively with spin relaxation. Use of the alternative scavenger bromotrichloromethane produces t-butyl bromide in emission but the line coincides with an absorption from the isobutene methyl protons and makes the system unsuitable for kinetic study.With no scavenger added, no polarized lines are observed from scavenged products, which confirms the inertness of the fluorocarbon solvent. However cage polarizations are still observed and this indicates that a competitive reaction pathway still exists; this may be reaction with a photoproduct. A complete absence of multiplet polariza- tions implies that formation of secondary radical pairs is insignificant even in the absence of scavenger. Final confirmation of the reaction scheme was provided in deuterochloroform solution [fig. l(c)]. On irradiation the intensity of the aromatic region was reduced from its equilibrium value but it was restored on cessation of irradiation :molecules with negatively-polarized aromatic protons were produced in the reaction.The iso- butene doublet of the spectrum in chloroform appears in deuterochloroform as a triplet due to coupling to the deuteron, thus confirming that isobutane is produced by hydrogen abstraction from the solvent. P. G. FRITH AND K. A. MCLAUCHLAN QUANTITATIVE STUDIES IN CHLOROFORM On photolysis, pivalophenone yields two radicals which undergo two cage reactions (recombination and disproportionation) and two scavenging reactions, in each of which each product derives from a single reaction pathway. The simultaneous obser- vation of the time-dependence of the methyl polarizations from isobutene, t-butyl chloride, pivalophenone and isobutene provides sufficient information to test the most general form of our kinetic model and, in conjunction with the flash-photolysis e.s.r. rate constant for the disappearance of t-butyl radicals, to evaluate all the kinetic parameters.As in our previous study of benzaldehyde,' the triplet molecule is formed with unit quantum yield at the rate of absorption of photons. In the low concentration ~~limit (ECZ -g 1)chosen in our experiments (E nm~= 2.2 m2 mol-', c < 0.01 mol dm-3) the rate of formation of triplet is once again first order in pivalophenone. Radicals generated in pairs from the triplet (3) diffuse apart and re-encounter with a nuclear-spin (j)dependent probability 3w, of being in a singlet state; we suppose a fraction of fR undergoes re-combination whilst the fraction fT( = 1-fR) experiences the dis- proportionation (hydrogen transfer) reaction.We assume that the overall probability of reaction of radicals which re-encounter in a singlet state is unity. Radicals escape from the cage with an overall probability (1 -3wj) and abstract hydrogen or chlorine from the solvent with pseudo first-order rate constants kHand kcl respectively. These are related to the rate constant for the overall disappearance of t-butyl radicals ks by the equation ks == kH+kcl. (1) Since ks was determined from e.s.r. measurements, it follows that a measurement of the ratio kH/kC1 suffices to determine them absolutely. From the reaction mechanism given in fig. 2, the rates of change of the nuclear spin state populations of the methyl groups in ground-state pivalophenone (A), its triplet (B), t-butyl radicals (C), isobutene (D), isobutane (E) and t-butyl chloride (F) are given by Eqn (2)-(7) contain relaxation terms which compete with reaction in removing polarization, with spin-lattice relaxation times TIA,etc.; the concentration terms with superscript O denote the thermal equilibrium populations of each substance in nuclear spin state j. The factor 2/3 occurs in eqn (5) to allow for the fact that only six of the nine protons in the t-butyl radical become methyl protons in isobutene. With a steady state concentration of triplet, [Aj] = kl[Bj]/kZ and This equation concerns the time-evolution of the concentration of a specific nuclear state of (A); the change of its overall concentration is given by 92 CIDNP STUDY where the relaxation term disappears in the summation because it causes no change in the total number of molecules.The reaction probabilities 3wjcan be calculated approximately from the known e.s.r. parameters of the radical pair and an estimated correlation time (z, "N s) and are found to be very small :fR3wj+ 1 and so d[A]/dt = -kl[A]. (10) The apparent difference between this equation and eqn (8) arises because although the selective population of nuclear states in the reaction may create a population difference large compared with that at thermal equilibrium, the total number of radi-cals which recombine is so small (<1 %) that no significant deviation of the decay of (A) from first-order kinetics is obtained.The rate of depletion of pivalophenone was measured in a series of experiments in which separate aliquot portions of solution were irradiated for different lengths of time and the pivalophenone concentration was measured directly from the n.m.r. spectrum at equilibrium with the light off. Four determinations consisting of fifteen observations at one minute intervals gave kl= 2 1 x s-l. (This justifies our previous calculation of the corresponding rate constant for benzaldehyde : under the conditions of our experiments and at equal concentrations the ratio of the first-order decay constants in the two solutions should be equal to the ratio of the extinction coefficients of benzaldehyde and pivalophenone ; this yields for benzaldehyde kl z s-'.) The half-life of pivalophenone molecules in solution (-350 s) is much greater than the nuclear relaxation time of the methyl protons (4.7 s) and the polarization decays completely before further light quanta are absorbed.Consequently, CAjl = gj[Al/G (11) where gj is the degeneracy of the level and there are G levels. Hence from integration of eqn (9) PI = [A10 exP(-k;o (12) where [A], is the initial concentration of yivaloplienone and The intensity of a transition between states i andj is proportional to their popula- t icn difference, which can be obtained from the appropriate differential equations (2)-(7). The total intensity (I)obtained from a t-butyl group in a product is calculated by summation of these population differences over all the states i and j connected by a spin transition.The spin-dependent part is contained in a quantity D, which is common to all the polarized intensities. With nine equivalent protons there are 29 nuclear hyperfine states which can be divided into ten groups of overall magnetic quantum number m,= 9/2, 7/2, . . . -7/2, -9/2, which we label 1 to 10. Taking into account the selection rule Am, = &I and the degeneracies of the ten groups of Zeeman states we obtain 9 where Ci-* is the coefficient of the term in x9-"in the binomial expansion of (I +x)~, and we have neglected the small coupling to the meta protons in the benzoyl radical. Using our previous methods and eqn (2)-(7) the polarized intensities of the four products (A), (D), (E,) and (F) are given as a function of time by FRITK AND K.A. MCLAUCHLAN where Q is an instrumental constant. Similarly for the aldehyde protons (G) in benzaldehyde, and for the olefinic ones (D') of isobutene, These equations contain statistical factors of 1/9 and 2/9 for similar reasons to that in eqn (5). Evaluation of the parameter D, requires the intensity of the pivalophenone methyl line at equilibrium; it is given by I,(A)" = 36Qno[Alo exp(-kit), (21) where 36n, represents the total thermal equilibrium polarization of three methyl groups each with four Zeeman states and twelve degenerate transitions. These equations contain six quantities of interest,fR,fT, kH,kcl,TICand D,,which can be obtained by taking appropriate ratios of the foregoing equations.Thus from eqn (15) and (16), which yieldsfJf, if TIDand T,, are known. Similarly the ratio of eqn (17) and (18) gives a relationship between the two scavenging rate constants : TIC, the nuclear spin-lattice relaxation time in the t-butyl free radical, appears in the equations together with k, in the term (Tc2+k,) which can be obtained from any of the ratios It(F)/It(D), It(F)/lt(A), It(E)/It(D) and 1,(E)/It(A). Typically, In general an independent measurement of either k, or TI, is required to evaluate the other ;in this case k, is known from the e.s.r. determination. D, is proportional to 72 (see below) and should allow its determination. It can be obtained from ratios of polarised intensities recorded during reaction and the intensity of the same transi- tion at equilibrium. In practice only the intensity of the pivalophenone methyl signal CIDNP STUDY could be measured accurately throughout the experiment and D, was evaluated from intensity ratios of the polarized lines of species (A), (D), (E) and (F) with respect to it.Again a typical equation is The form of eqn (22)-(25) shows clearly the role of spin-lattice relaxation in these kinetic experiments : the relaxation times provide internal standards of time with respect to which the reaction rate is measured. In general the observed intensity of a polarized line should be corrected for a contribution due to equilibrium absorption ;in our experiments the cage products benzaldehyde and isobutene were not observed at equilibrium and no correction was necessary, but the converse was true for the scavenged products t-butyl chloride and isobut ane.KINETIC PARAMETERS The rate constant k; can be evaluated from many of the expressions listed above by fitting experimental line intensities to an exponential time dependence; this is particularly straightforward for the cage products. It also follows from eqn (15) and (21) that the observed intensity of the pivalophenone methyl signal, made up of both equilibrium and polarized contributions, varies with the same rate constant. The time-dependences of the methyl polarizations in isobutene, t-butyl chloride, pivalo- phenone and isobutane are shown in fig. 3 and values of k; derived from various sources are listed in table 1, together with statistical factors of curve-fitting.0 30 60 120 I80 240 300 360 420 480 tls FIG.3.-The time-dependence of resonances observed in the methyl region of the spectrum. Since depletion of pivalophenone is rate-determining, scavenged products accumu- late with the same rate constant k; and the equilibrium absorption intensities I,(P)" of product P increase with time according to the expression I,(P)" = I,(P)(l-exp[-k;t]) (26) where I,@) is the intensity observed after total photoconversion of the reactant. In principle I,(P)" could be measured, as for pivalophenone, but at the low conversions P. G. FRITH AND K. A. MCLAUCHLAN of our experiments the measurement is inaccurate ;rather we have made one measure- ment of I,(P) at the end of a period of irradiation and used an iterative fitting procedure to determine k; and Iw(P).A trial value of k; was inserted in eqn (26) to give a value of IJP) and then the correction for equilibrium absorption was calculated as a function of time to obtain the intensity due to polarization, which decayed with a rate constant k; if this was correctly chosen. Iteration was continued until the decay constant agreed to within 1 % of the trial value. Table 1 contains values obtained in this way from the time behaviour of the t-butyl chloride and isobutane resonances and they are in good agreement with the others. These two estimates do not, how- ever, constitute a test of the kinetic model since it is assumed implicitly in calculating PI,although of course the other estimates do. An independent check is obtained from the ratio Iw(E)/Zm(F)which should equal kH/kC;values of loovaried substantially (25 %) from sample to sample but the ratio remained at 1.3k0.1 whilst kH/kC1is reported below as 1.38 +0.08. TABLEVALUES OF THE FIRST-ORDER KINETIC PARAMETER k', IN CHC13 SOLUTIONS average resonance observed k;/10-3 s-1 correlation coefficient averagestudent's t number of determinations CsHsCHO 3.4+ 0.5 0.996 47 6, (cH3)2 C=CH2 (cB3) 2=CH2 C6H5CO(CH3)3 (CH3)3CH (CH313CCl 3.6k0.3 3.4k0.2 3.1& 0.3 3.1 k0.7 2.7+ 0.6 0.989 0.999 0.997 0.999 0.999 35 375 177 133 217 4 5 5 5 5 The relaxation times of diamagnetic products, needed to evaluate other kinetic parameters, can be determined in principle from observations of polarized intensities at times shorter than TI.If this is itself short few measurements can be obtained and the accuracy of the determination is impaired. Consequently values were also obtained directly in CDC13 solution using a 180-90" pulse sequence on a Bruker HX-90 spectrometer and these are contrasted with the CIDNP values in table 2. Overall the relative magnitudes obtained by the two methods are in reasonable agreement but, even in chloroform, the pulse values were taken as likely to be the more accurate. TABLE2.-sPIN-LATTICE RELAXATION TIMES IN DIAMAGNETIC MOLECULES protons C~HSCZO (CH3)2C=CH_r (C_H3)2C=CH2 (cz3)3ccf (Cg3)3CH C~HSCOC(C~~) CIDNP, t/s 2454 8+2 8+2 9+ 1 7f 3 S+l pulse, t/s 26.1k0.1 4.1k0.1 5.1k0.1 5.0k0.1 -4.7k0.1 The ratio of the fractional cage reaction probabilities in chloroform at 310 K can now be obtained from eqn (22)as 5.9k0.2, givingfT = 0.85 andf, = 0.15.It is of interest that this ratio is sensitive to the ratio of relaxation times but not their absolute magnitudes. In more complex kinetic cases, such as that observed in PP9 with tetra- chloromethane as an added scavenger, such a ratio is implicit in an integration term which must be evaluated numerically (see below). Eqn (1 5), (16), (19) and (20) were derived on the assumption that nuclear spin, and hence polarization, is conserved in hydrogen transfer. This implies that It(G):It(D'):It(D):I,(A)= fTTiG:2fTTiD*:6fTTiD:9fRTIA.Experimentally the ratios observed were 3.7 :1.2 :4.4 :1 whilst those calculated from the determined values offT& and the spin-lattice relaxation times were 3.6 :1.1 :4.2 :1. Agreement is excellent. CIDNP STUDY From eqn (23) and the known values of k; and relaxation times we obtain kH/kCI= 1.38k0.08. Since ks = 5.44+0.13 x lo3 s-l and the concentration of neat chloro- form is 12.4mol dm-3 at 310 K, the second-order rate constant k: = 2.54k0.07x lo2 dm3 mol-1 s-l and kF1 = 1.84+0.07 x lo2dm3 mol-l s-l. We defer discussion of these values until later. Four independent determinations of the proton spin-lattice relaxation time in the radical, Tlc,were made from each set of data using the four equations similar to eqn (24) and the rate constants ks, kHand kcl.Within each set, data values were consistent within 2 % but greater variation was observed between sets : an average of 24 values gave Tlc= 2.2k0.7 x lop3 s. This differs substantially from the value obtained by Fischer et aL9 (2.4 x s) but is that expected for an isolated radical of this size if its relaxation is dominated by dipolar coupling. Fischer’s experiments were performed at higher light intensities, in more concentrated solutions, and pro- duced much higher radical concentrations, as evidenced by observation of polarization from secondary radical pairs. At high radical concentrations, the relaxation rate is roughly proportional to the concentration of paramagnetic species and if this is 40 times that in our system, which seems reasonable from the calculation based upon Fischer’s experimental arrangement, we would expect his value of Tl,to be 40 times smaller than ours, as observed.The translational correlation time zd can be obtained by combining eqn (14) with the expression for the probability 3wjgiven as eqn (26) in our previous paper : where 3w,is a triplet-singlet mixing coefficient which can be calculated from the known e.s.r. parameters of the radical pair; for t-butyl the denominator has the value 1.91 x lo6rad s-l. Four values of D, were obtained from each of six sets of experi- mental data: within each set agreement was within 12 % but the overall variation was 20 %. The mean value of the 24 observations was D, = 2.4k0.4 x giving rd = 4& 1 x lo1 s.This compares well with the correlation time calculated as neces- sary for development of polarization in liquids of the viscosity of chloroform lo (0.5 cP), 2x 10-l’ s. Also, sincef, = 0.15 and xgj3wj/G= 0.091 7, from eqn (13)i we find that k; = 0.99 kl, which justifies the assumption of near-equality. We have seen that in chloroform the product of ksTlc can be obtained from the CIDNP investigation. In inert solvents, the scavenging rate can be expressed as the product of a true second-order rate constant kg and the scavenger concentration [S] and CIDNP then yields the quantity k$[S]Tlc.Its evaluation over a range of scavenger concentration gives an accurate value of the product ktTlc and is a severe test of the kinetic model.Experiments were performed to this end in PP9 solutions with added tetrachloromethane (S = CCl,). QUANTITATIVE STUDIES IN INERT SOLVENTS IN THE PRESENCE OF SCAVENGERS Photolysis in these solutions yielded a single scavenged product t-butyl chloride and the temperature was varied over a wide range to obtain the activation energies (E,) and pre-exponential factors (A) of the cage and scavenging reactions. However the low solubility of reactants prevented e.s.r. observation of radical decay and k: for the t-butyl radical was obtained from the value kgTlc with the value of Tlc calculated from the chloroform results (see below) ;as explained above we believe our value to be that expected for an isolated radical and its value should not change further with P.G. FRITH AND K. A. MCLAUCHLAN falling radical concentration. A further complication is that the scavenger, at con- centrations in the range 0.005-0.10 mol dm-3, was no longer in excess but was con- sumed in reactions with the t-butyl (C) and benzoyl (K) radicals with second-order rate constants kg and kg respectively. The rate constant kg we measure is kc. This yields three additional rate equations for the methyl protons of t-butyl radicals and t-butyl chloride, and the aromatic protons of the benzoyl radical. d[C.jI /dt = kz(1-wj)PjI -k$sI[CjI -([CjI-[CjI")/Tic (28) d[KjI/dt = kz(1- 3~j)[BjI -G[SI[KjI -([KjI -[KjI"] /TlK (29) d[FjI/dt = k2.[SIICjI-([FjI -[FjI")/TlF* (30) In the steady state, and remembering that relaxation does not change the concen- tration of molecules, [C] = ki[AlO exP(-k;t)lk:CSI (31) and [K] = kl,[Al0 exp(-k',t)/kg[S] .(32) The absence of polarization from secondary radical pairs implies that each radical consumes one molecule of scavenger and we eliminate expressions in K by a simple manipulation : d[S]/dt = -kz[S][C]-ki[S][K], = -2k; [AI0 exp(-k;t). (33) Integration over time gives [S] = [Sl0 +2[Alo(exp( -kit)-1). (34) Assuming steady state conditions, ignoring thermal equilibrium population differences, combining eqn (28), (30) and (34) and integrating gives IdF) = -Qk~[Al~Dwyr~xP(-~/TIG) (35) KINETIC PARAMETERS IN INERT SOLVENTS Solutions containing different concentrations of pivalophenone (0.004 4-0.006 6 mol dm-3) and tetrachloromethane (0.004 7-0.12 mol dm-3) corresponding to eighteen different values of [S]/[A] were investigated. It is shown below that the kinetic model was only applicable to a certain range of this ratio.No correction of observed inten- sities was necessary for the cage product isobutene but for pivalophenone the equili- brium intensity at any time It(A)"was calculated from the known initial concentration and the first-order rate constant PI. Values of this parameter obtained from the time evolution of the signals of the isobutene (D) and pivalophenone (A) methyl protons in a series of solutions of different concentration and at different temperatures are given in table 3 ;within a single sample values obtained varied by <7 % but a total variation of 14 % occurred between samples.Good agreement with the data in table 1 is evident. As in chloroform, the observed intensity of the line due to t-butyl chloride was corrected for an equilibrium signal. However, the complexity of the equations describing its time-dependence precluded the use of the iterative method alone. Instead, since the values obtained directly and indirectly in chloroform agree within I14 CIDNP STUDY experimental error, the corrections to I,(F) in PP9 were obtained by using the mean value of ki from above and the equilibrium absorption at one given time to evaluate Im(F),and then calculating I,(F) at any other time from this. The relaxation times of the diamagnetic products in the new solvent and at various temperatures were not determined, for as described above, our equations are sensitive only to the ratios of relaxation times ; since 1/T, cc q/T these ratios are independent of viscosity and temperature.TABLE3.-vALUES OF k', IN PPg/Cc14 SOLUTIONS OF VARIOUS CONCENTRATIONS AND TEMPERATURES average average number [A1I [Sl/ k;/10-3 S-1 correlation student's of deter-mol dm-3 mol dm-3 T/K from Zt(F) from Zt(A) coefficient t minations 0.004 4 0.010-0.043 310 3.5k0.4 3.050.4 0.997 121 12 0.005 2 0.015-0.120 310 3.7k0.4 3.4k0.5 0.996 110 15 0.006 6 0.004 7-0.013 310 3.1k0.3 3.0k0.4 0.995 102 10 0.005 4 0.053 296-3.8k0.5 3.6k0.5 0.997 112 14344 0.006 5 0.061 296-3.450.4 3.550.4 0.998 162 15334 The fractional cage-reaction probabilities fR and fT were obtained from the iso- butene and pivalophenone polarizations, as before, and are listed as a function of temperature in table 4.Their ratio was independent of scavenger concentration over TABLE4.-THE TEMPERATURE DEPENDENCE OF f~/f~ number of TIK fT/fR fT( %) fa( %) determinations 344 2.85 74.0 26.0 6 334 2.97 74.8 25.2 6 325 3.26 76.5 23.5 6 314 3.78 79.1 20.9 6 310 4.75 82.6 17.4 37 307 4.11 80.4 19.6 6 296.5 5.06 83.5 16.5 6 288 5.54 84.7 15.3 6 the range of concentrations investigated and at 310 K the mean values obtained, fT = 0.826 andf, = 0.174 differed little from their values in chloroform. Expressing the rate constants in Arrhenius form, A semi-log plot against inverse temperature is shown in fig.4. It yields the para- meters (ER-ET)= 16.3k2.0kJ mol-' and AT/& = 5.4k2.4x lop3. Thus the re- combination reaction has a higher activation energy than the disproportionation one and requires a smaller entropy decrease in forming the transition state. Two independent determinations of the parameter D, were made in each experi- ment from the ratios of the intensities of the polarized isobutene and pivalophenone methyl lines to the equilibrium absorption of pivalophenone. From these values the diffusional correlation times were calculated using eqn (27) and values are listed in table 5 for solutions of various concentration and temperature. This table also con- tains values calculated as being necessary to observe polarization from the theory of Evans, Fleming and Lawler ;lo agreement is remarkably good. This theory predicts that at high viscosities and low temperatures D, becomes a power series in T$ and P.G. FRITH AND K. A. MCLAUCHLAN attempts were made to observe deviations from a simple square-root dependence in PP9 over a range of temperatures and in silicone oils (y = 1-1OOOcP). Unfortu-nately experimental errors were too large to allow significant conclusions in the former, whilst in the latter, overlap from resonances originating in the methyl groups of the silicones also made accurate measurement impossible. With a knowledge of D, (taken as the average of the two values from the same experiment), intensity ratios can be written to involve the intensity of the t-butyl chloride line in which the only unknown is the product kcTlc: It(D)/It(F)= -2fRTlD/3(1-k;TID)Ytexp(k; -T;$)t (38) 6 4 I 3.0 3.2 3.4 103 KIT FIG.4.-An Arrhenius plot of the cage fractionation ratio.TABLE5.-vALUES OF DwAND rd IN PPg/Cc14 SOLUTIONS [A1Imol dm-3 mol dm-3[Sll TK DUlX 102 2d/10-10 S (obs.) 2d/10110 S (calc.) 0.004 4 0.005 0-0.043 310 5.7k0.5 2.3k0.5 2.4 0.006 6 0.004 7-0.030 310 4.550.5 1.5f0.3 2.4 0.005 2 0.004-0.120 310 5.4f0.5 2.1f0.4 2.4 0.006 5 0.061 296-344 4.8f0.8 1.7f0.5 4.1-1.3 0.005 4 0.053 296-344 5.4k0.5 2.1k0.4 4.1-1.3 kETl,, which is included in Yt,was obtained by minimizing the sum of the squares of the differences between experimental ratios and those calculated at the correspond- ing times by inserting trial values in 9t,which was evaluated numerically and used in eqn (38)-(40) with the values off,, D, and k; taken from the same experiment.Typically 30-40 trial values were used to produce root mean square differences in the range 2-8 %. The values of kzTlc obtained as a function of the ratio of tetrachloro-methane to pivalophenone concentration are shown in fig. 6 which combines the results from three series of experiment ([A] = 4.9 x low3,5.2 x and 6.6 x mol dm-3, [S]/[A] = 0.7-23) with a total of twelve determinations at each concentration ratio. It is apparent that it is constant only over a certain range of concentration ratios, and this defines the solutions to which our kinetic model is applicable. At [S]/[A] > 10, the solubility limit of tetrachloromethane in PP9 was exceeded (sensitivity did not allow work at lower pivalophenone concentrations) and the overestimation of [S] 100 CIDNP STUDY forced kETlc to lower :dues.As the scavenger concentration is decreased on the other hand, radical recombinations become significant but our model required scaveng- ing to consume all the radicals ;in our experiments this is noticeable where [S]/[A] < 2, although it is the absolute concentration of scavenger that is important. This explana- tion is reasonable numerically; in both chloroform and PP9 the systems were both in the fast-motion limit for nuclear relaxation, in which TI cc i?/T:in PP9 at 310 K we calculate T,, as 2.27 x s and hence kz = 4.9 x lo4 dm3 11101-I s-l.If the 'ciom --I ~7-,-7m-,T--*--.---0~r-0 I r1 2 4 fl 8 1'3 13, 14 !e 18 29 22 21 [SI/"AI FIG. 5.-The variation of the parameter kETlc with [S]/[A]. Our kinetic model applies to the concentration range 2-10. 103 KIT FIG.6.-A plot of log (kETlc/T)against 1/T. description above is correct and the abstraction reactions are faster than recombina- tion, k~[Bu*][CCl,] > kz[But][R], where k%is a recombination rate constant w109 dm3 mo1-l s-, and [R] is the total concentration of radicals (N mol dm-3) ; since [CCl,] = 2[A] M 0.012 mol dm-3, k$ > 8 x lo3dm3 mol-l s-l, which is con- sistent with the value deduced. kZTlc was studied as a function of temperature in two separate series of experi-ments ([A] = 5.4 x 6.1 x lov3mol dm-3, [S]/[A] = 9.4, 9.8).Assuming an Arrhenius form of k& with activation energy E,, and fast-motion limit relaxation, with a viscosity activation energy E,, k$Tlc/T = const. x exp -(Ec+ EV)/RT. (41) P. G. PRITH AND K. A. MCLAUCHLAN A plot of log(kETl,/T) against 1/T(fig. 7) gives (E,+E,) = 27.224.2 kJ inol-'. Ev = 13.4 kJ niol-' and so Ec = 13.8k4.2 kJ mol-I ; this implies that the pre-exponential factor Ac = 1.04x lo7 dm3 mol-1 s-l. DISCUSSION The study of the photolysis of pivalophenone under specific experimental condi- tions has provided a detailed test of the diffusion kinetic theory of CIDNP. Frequently a parameter has been obtained from a series of quite separate experimental observa- tions and the consistency of values obtained has provided strong support of the model.Furthermore other checks for consistency have been performed and found good. The care with which experimental conditions must be chosen has been emphasised and it has been shown, not surprisingly, that the detailed kinetics which we have analysed are applicable only over a certain concentration-ratio range in inert solvents with added scavenger. The kinetics have been exposed in a detailed manner and direct measurements made of the fractional probabilities of competing cage processes, which have shown a disproportionation reaction of two radicals to be more favourable than recombina- tion. A variable temperature study has allowed measurement of the difference in activation energies of the two processes and of the ratio of their pre-exponential factors.Two competitive scavenging reactions, namely hydrogen- and chlorine-abstraction, have also been studied in detail. It remains to be discussed whether the values we have obtained are reasonable and what is their significance. The values OffT/Jk, AT/ARand (ER-ET) obtained for the reaction of benzoyl and t-butyl radicals arc consistent with the general trends observed in the data for similar reactions.12 Thus in all cases except those which involve t-butyl,fT/fR < 1, but for t-butyl the ratio is in the range 4.5-27. Although the information is not extensive, fi/fRvaries little with solvent and this implies that the recombination and dispropsr- tionation reactions involving the same species have similar transition states.In all casesfT/fR decreases with increasing temperature, implying ER > ET;for simple alkyl radicals (ER-ET)is small but it increases with substitution and steric hindrance at the radical centre, although the effects of solvation are significant. AT/AR tends to decrease with increasing substitution but it is difficult to assess accurately ;assuming free rotation and that hydrogen-transfer requires a specific relative orientation of the radicals, the smaller Avalues for disproportionation imply this to be a more stringent steric requirement in the transition state than is avoidance of crowding in recom- bination.As the temperature is lowered, the rates of both cage reactions decrease but dis-proportionation becomes relatively more favoured. At some point the more activated process may become so slow that not all the singlet radical pairs produced in the initial S-To mixing react but may emerge from the cage to yield oppositely-polarized transi- tions than those from their triplet counterparts. This implies that in a time-resolved e.s.r. study the polarization might change sign whilst approaching equilibrium when §-To mixing in the singlet radical pairs which do not recombine succeeds in time that in the initial triplet pairs. Electron polarization of this type has been observed below 273 K in viscous solvents but at higher temperatures and lower viscosities only normal polarizations are observed in both e.s.r.and n.m.r. :our previous assumption of unit probability of reaction of radical pairs in singlet configurations appears valid in our experiments. Literature data for the rates of atom abstraction reactions are sparse and those for abstraction of hydrogen and chlorine atoms are summarized in table 6. Most of this 102 CIDNP STUDY information was obtained in the gas phase and it is not possible to estimate the effect of a change of phase with any reliability. However, the values we report for kHand kcl seem reasonable. In the gas phase reaction of methyl radicals and chloroform kH/kC1= 15 and for such a reactive radical this is probably about the same in solution. For plienyl radicals reacting with chloroform in solution the ratio is four.The lower selectivity of t-butyl is surprising at first sight but a study of the relative rates of hydro-gen abstraction from a series of toluenes as a function of the substituents’ Hammett- cr parameter showed that for t-butyl radicals the rate increased with the ability of the substituent to stabilize negative charge; this is opposite to the behaviour of other radicals. The t-butyl radical is unique in possessing a significant contribution from structures such as the following to its transition state :But+ He CCl; ti), But+ H-CCl; (ii), But+ Cl- CHCl; (iii), But+ C1- CHCl., (iv). Structure (ii) is of high energy and its contribution is small. Since CCl; is better able to stabilize negative charge than CHCl;, the contribution of (i) is likely to be greater than that of (iii) but (iv) probably makes a similar one.This may cause a marked increase in the rate of abstraction of chlorine relative to that of hydrogen owing to the juxtaposition of charges in the transition state which is not available to hydrogen transfer. TABLE6.-RATE CONSTANTS FOR ATOM ABSTRACTION REACTIONS atom reactants abstracted k/dm3 molt1 s-1 ref. (CH3),Sn*+ CtjHiiC1 c1 5x lo2 13 n-Bu3Sn-+CH3(CH2)&H2C1 c1 9x lo2 13 CH3*+ CC14 c1 2~ 103 14 CH3*+ CHC13 H 5~ 103 15 But*+CH, H 1 16 But-+cyclohexadiene H 5x lo3 16 But*+ ButCHO H 4~ 103 16 But*+CHC13 I3 1o2 16,17 In the inert solvent, the value of As is comparable with those observed in the gas phase but the activation energy is less and the rate of chlorine abstraction from tetra- chloroniethane is higher than expected by comparison with the chloroform results.Here contributions from the structures But+ C1- CCl; and But+ C1- CCh, are more probable 2o than (iii) and (iv) in chloroform since the stability order is CCl; > CHCl, and CCb, > CHCl-, :the transition state is more ionic and lowers the activation energy for the abstraction of chlorine. This type of explanation has been invoked previously in an analogous case.21 It should not be overlooked that the detailed information reported in this study is the result of several particular features of the experiment. First, all the products of reaction emanate from single reaction mechanisms and give some n.m.r.lines which are singlets. Secondly, this description is true only under certain experimental condi- tions of concentration range and radical concentration. As in our previous work, a major simplification has resulted from the use of low light intensities in illuminations. We thank the Salters’ Company for the support of P. G. F. and Dr. A. J. Dobbs for assistance with the e.s.r. experiments. P. G. Frith and K. A. McLauchlan, J.C.S. Faraday 11, 1975, 71, 1984. P. G. Frith and K. A. McLauchlan, Nuclear Magnetic Resonance (Chem. SOC.Spec. Periodical Rep., London, 1974), vol. 3, p. 378. H. G. Heine, Annulen, 1970, 732, 165. B. G. FIRTH AND K. A. MCLAUCHLAN * P. W. Atkins, A. J. Dobbs and K. A. McLauchlan, J.C.S.Faraday II, 1975, 71, 1269. P. W. Atkins, J. M. Frimston, P. G. Frith, R. C. Gurd and K. A. McLauchlan, J.C.S.Faraday zr, 1973, 69, 1542. P. W. Atkins, K. A. McLauchlan and A. F. 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Suc., 1963, 85, 3754. 2o W. A. Pryor, W. H. Davis and J. P. Stanley, J. Amer. Chem. Sac., 1973, 95, 4754. 21 R. L. Huang, T. W. Lee and S. H. Org, J. Clzem. SOC.C,1969,40. (PAPER 5/947)