- Email: [email protected]
Yields of excited states from geminate recombination of hydrocarbon radical ions
CHEMICAL PHYSICS LETTERS
Volume 28, number 3
I Qctober
1974
‘. .,
YIELtiS
OF EXCITED STATES FROM &MINATE RECOMBINATION OF HYDROCARBON RADICAL IONS BrianBROCIkEHURST Department of Chz-iwy,
The tiniversity, Sheffield
S3 711F, UK
Received 24 April 1974
A theory similm :o the mdical pair modei for CIDNP, etc., is used to describe the rate of loss of spin correlation geminate pairs of radical ions produced by rndiolysis. The ratio of the yields of triplet and sinL,eletexcited states and the effects of mqnetic fields are discussed.
in
-- When solutions in alkanes are exposed to high energy radiation, excited states of the solute are formed by recombination of radical ions [l]. At high concentrations (a 10B2M), the main reactions are:
S. -f=+
S+te-,
(1)
S+bl+,
.(2)
s++hl
+
e- tM
AM-,
M’tM-
+
c31
M’tM.
6)
The solvent, S, in typical experiments is cycle-hexane; ths solute, M, may be biphenyl, naphthalene, &hracene, etc. MC includes singlet (S) and triplet(T) excited states. Observed T/S ratios are in the range l-2 [2,3] - rather less than the value, of 3 expected for random spin orientatjons. The recombination process is mainly geminate, however, not. iandom: the initial separation of the charges is,large (50-150 A) compared to, molecular diameters but small compared with the Onsager escape distance (- 300 _CJin such a solvent. The odd electrons on Mf and-M- were initiaily paired in a singlet solvent molecule. If the relative orientations and phase of the two spins do not change, then dnly [email protected] be formed. This letter deals with the rate of change of the correlation of the two spins after separation. The aim is to calculate the probability, p,(t), of regaining,a singlet state’after a time, r; itjs assumed that the initial processes produce a ‘puie’ singlet state :
;.: .
‘of the ion pair - a nor.-stationary state. The 0verZl wavefunction thei oscillates between singlet and triplet because of interaction with the nucIei. It is a coheient oscillation not 2 relaxation because the time scale is short compared to the e!ectron spin relaxation times. The initial process - separation and them&a. tion of the electron - is extremely fast (< I ps). Processes (2) and (3) are also fat at high concentrations (= 100 ps); there is a wide range of ion lifetimes - very roughly 1-l 00 ns - in mobile solvents (corresponding to the range of initial separations) [ 1,2] *; ‘an initial rapid decay is followed by a long ‘tail’. The final step - the actual electron transfer in (4) - is also Iikely to be fast because there is no potential barrier due to solvent polarisation; it, will probably take place while the ions are stti separated by solvent [6]. Therefote, interactions before Mf and M- are formed or during their recombination can 5e negected: only the evolution of the overall wavefunction during the ion lifetime is important. The ion Iifettie is short but it is much l,onger than the rotatianal correlation time of the molecules;ihis means that interactions with the solvent and the anisotropic hyperfme interaction with the. nuclei of&F and M- will average to zero, Only the.isotropic hyperfine interaction will be considered. me’two ions wilLbe IabelIed I a.qd 2, the si.ngIet * For recent expetimental
work, sic ref. 141; for theoreticti work, see ref. [S], and recerencs therein
: _.
357
Volume 23,~number 3
CHEMICAL PHYSICS I,ETTERS
”
state, S and the three triple? states, 0, f and -. For the case of only one set ‘ofprotons on each molecule, the hamil?onian, V, may,be written:,
1 October 1974
(9) and the time debendence has’the simple form p 5(1)= c~s2&alnll -a,m,>t} ;
(101
Td .lescribe the overall behaviour, one must sum over
all r-9value and this can be done for the general case of s:veral.types.of proton, on each molecule [S] to nive .. [. 1 + 1 1 co& P,HW =$ 1
+~(si+S2>‘(all~+a21~) ._
(5)
Sf, S-, etc., are shift operators. The first three terms mix the singlet state~withTo, T, and T_, respectively, the ME.. andsixih mixTO with T,. and T while the fourth gives non-zero diagonal elements &_h T, and T_; The matrix of V is, in simple cases,
{v_,-v_, 0
v__ i
(In general, a larger matrix is required since a s@flip one way of a proton‘on one molecule may be followed by a reverse spin-flip on the other; ~1similar problem arises if there is more than one type of nucleus on each molecule.) Since V is independent of time, the time-evolut.ion of the system is @en by 173 p(r)
= e-ivy
p(0)
e+ivf
(7)
(Vf andat amin units of tl). p(O) is a density matrix with.unity for the initial population of the singlet state and all o&her elements zero. Therefore
To proceed, one h;ls to obtein the eigenvalues and eigenfunctions of (6), to express 1s) in terms of these eigenfunctions and to substitute in (8). These equations are easily solved in some simple cases. First, suppose that the experiment is carried out in a strong external magnetic field; if the Zeernau splittin$js much larger than that due to the hyperflne interact&r (fie& s 10OGgauss), then no mixing with T, and T_ occurs 2nd the only relevant matrix ele- : ments are ‘. 358
‘-,
.
~.. l-rcos”~ Ly
-2
1
a$ . .. ,(I 1)
where n1 is the number of protons with hyperfine coupling constant al on molecule 1, etc. Deuterium has 3 spin of I,mstead of+: calculations for deuterium compounds can be made by substituting{2 cosot+l)/3 for cosal in (11) [S]. Fig. la shows results calculated for some anthracenes, usin experimental a values [9] for protons, and the same values nlultiplied by 0.1552 - the ratio of the magnetic moments - for deuterons. For C,,H,o and C,,D,,, p,(f) falls rapidly’to the average value (slightly greater than? because no change occurs if nzl = m2 = 0) and then remains essentially constant. Though coherent oscillation is postulated, the curve lnak; like a random decay (apart from the initial . nc;gaiive~curvature): this is due to the six different o’s (3 for the cation, 3 for the anion). Oscillatory behaviour Lmightbe observed if the 12values are in simple ratios: e.g., for perylene, one can predict peaks in the curve at = 50 (ps rises to O.SS), 350 (0.75) and 400 ns (0.66) but other effects may intervene on the longertime scale. It would be better to use solute molecules with fewer magnetic nuclei: this requirement can be partly met by using compounds such as C,,HD9 (fig. la). Qualitatively; behaviour in the absence of a field should be very similar, except that the rate of change shoull be greater: however, quantitative treatment of the problem is more complicated. One difficulty is tha,! the nuclear angular momentum vectors of the two.molecules are now oriented at random. Eq. (11) shows that ifall the protons (20 for anthracenc) were,on one ion,.none on the other, the same result for p,“(t) is obtained: -this is not’true for>:(t) (field. off) but this approximation is made to simplify the calculation. if, further, the protons all have the “.
V&me 28, number 3
CHEM[CAL PHYSICS LETTERS
1 October 1974
.
1.0
p,(t)
0.5,
I
0
t
'10
:
ty+ir
r 20
Fig. 1. Dependence of the probability of recovering a singlet time: (a) anthracene in a magneiic field: -, Cr4H1e; - - -, CiJDre; *.., Ci4HDa (proton in position 9); cb) ---, Mphenyl in a field; -) in zero field. State on
same u vaiuc, then 8 simple exact solution of eqs. (6) and (7) can be obtained;
:
Py(t>=(~++)-2{$ i-1(1+1) cos2(I+$?t3.
(12)
The further approximation of using only the singIettriplet matrix eIements in (6) gives p,o(r) = cos2 (I {!(I f 1)}“2f .
I131
This iS similar to (10) except that a.reploces a/2 - ‘&e rate of change is greater in zero field Y and p depends on I rather than m (undefined in the absence of a field). Rqs,<12) and(l3) are identicaI when f is very large, but they differ sigticantly when fis small, When I =$, the average value of p:(t) is 518, i.e., greater L than pg”(t): this result has been obtained previously by Lawter and Evans [l O] in discussing possible effects of’magnetic fields on reactions invoIvi.ng pairs of neutral radicals. Siphenyl is a convenient solute molecule for p&e radiolysis studies [l-5] of ion recombination and for trial calculaths, though, U~o~n~teIy, 4 values have .’
not been reported for the cation; they are assumed here’to be the same as for rhe anion: they are probably somewhat larger, in fact. In the anion [ 101, four protons ha% a small Q, 0.370 gauss (these are neglected in what follows); another set of four h.ave a = 2.642 gauss, while two have a = 5.32 gauss -- aI.most exactIy doublie. An average value of 3.76 gauss was obtained by scaling $(I + cosl?~} to +(I scas~xr cas”2xt), cf. eq. (11). This value was ‘aserted irt( L2) which was then summed over values off from U-6. Results are’ given in fig. I b. Because of the assumption made, this function would oscillate, but for the reasons given abovk, it is more likely to fail smoothiy to e $ as shown. The theory given here is very similar to the radicdl pair model currently used to describe CID%? and CIDEP [ 121. It is simpler in so far as both exchange effects and differences in g values (* IW4 for aromatic hydrocarbon ions [ 131) can be n:gIected: it is more complicated because of the large numbers of protons in molecules studied’to date, The experimental situation is different in many respects: ion pairs separate but they necessarily recombine - on& a small proportion of neutral radic& do this: 50th singIet and triplet produtts can be observed directly and the possibIe ti.rne.resolution is limited onIy by the Iifetimes of the excited states (long for triplets, but onhf a few nanoseconds, for singlets in some cases). Some qu~ita~ive conclusions and predictions foIIow. (i) In previous discussions of this probIern (6,141, *he loss of spin correlation was assumed ta be a relaxation process and magnetic field effects were predicted for systems in which the ion lifetime was in between T2 and T, (e l-100 fls); that discussion remains valid but ion lifetimes are much shorter in mobile liquids. The present theory predicts muchmore rapid changes - roughIy in the ratio of the band-width to the line-width of an ESR spectrum: the decay time is comparable with the fastest ion recomb~ation times. @e&I T/S ratios can be estimated by integrating over the ion fifetime d&Mb&on: cs.Ioulations of this type are inprogress [8] ; it is already cIear that a sig. nificant part of the triplet yield [.2,3] can be accounted for in this way, but it must be noted that there are otherprocesses contributingto the yield of triplets from i&s [IS] and that the probabifities caIculated here omit the effects of energy Ievef densities in ,. product molecules 161. 1 ..
Volume 28,number 3
CHEMICALPHYSICS
.’ (ii) The rate of decay will-be increased
siderable,
but an enhancement
of fluorescence
and a
decrease in the triplet .yield took place of&r the eiectron pulse; (iv) Molecules‘containing
only
a few magnetic
nuclei (or, e.g., partly dzuterated compounds) should show reverse
oscillatory effect
behatiour.and, of magnetic
at certain
times,
field on the excited
a
sta?e
yield. No observations have been made. (v) CIDEP effects in pulse radiolysis have been reported [18] but only radicals have been studied and these would not have resulted from ion recombination. According to the present proposals, triplets should only be formed in the To state in 2 magnetic field: the Am, = 2,transition should be absent initially, while Ants = +‘I and - 1 should be. e.normously enhanced in absorption and emission, respectively.. These effects wih decay rapidly (T1), but they might be large enough to be detectable even in the presence of large numbers of relaxed triplets in steady state experiments. The erect on the nuclear spin states depends on the ion lifetim!: if this is long, then all molecules will reach ‘equilibrium’ between singlets and triplets except in ion pairs with mr = 0 for all types of proton - i.e., the central ESR line should be .weaker. If the ion lifetime is very shcrt then the few triplets formed should show a? enhancement of interisity of the hyperfine lines with increasing .m. (vi) The same ideas apply.equajly to photoionisation except that if ionisation bccurs from an excite,d triplet (common G biphotomc processes) then the arguments must be reversed. Fuchs et al. [19]
:
360
..
1 October
1974
ha-/e shown .&at in(sin&j photqionisation of be& zene solutions very little spin relaxation 0ccurS: this is 1:obe expected since recombination is much faster inaromatic solvents. ; ‘.
by large
numbers of protons and large avahres. Methyl substitution ,should,increase the rate.of decay(cf. Q values [9]):. there seems to be some indication of this in the published results [3] but itis not conclusive. Differ-‘ences between unsubstituted tiaphthalene, tithracene, .etc;, shc~uldbe small. 4 striking reduction in the triplet yield should result from deuteration: no results appear to be available. ’ (iii) Enhancement of the total fluorescence yield by an applied magnetic field has recently been observed: the enhancement is affected by deuteration [16]. Some time-resolved measurements have been made [17]; the experimental difficulties were con-
,,
LETTERS
...
The author is grateful to Dr. N.M. Atherton, Dr. P.W: Atkins, Professor G.J. Hoytink and Professor R. McWeeny for many helpful comments.
Re Ferenies [l] J.K. Thomas, Ann. Rev. Phys. Chem. 21 (1970) 17;. A. Sin& Radiation Res. Rev. 4 (1972) 1. [2) I.H. Bxxendale and P. Wardman, Trans. Faraday SOC. 67 (1971) 2997. j3] F.S. Dainton, MB. Ledger, R. May and G.A. Salmon, J. Phys. Chem. 77 (1973) 45. [4] E. Zador, J.M. Warman, L.H. Luthjens and A. IInmmel, J. C%em.Sot. Faraday Trans. I70 (1974) 227. IS] S.J. Rzad, J. Phys. Chem. 76 (1972) 3722. [6] E. Brocklehurst, Chem. Phys. 2 (1973) 6. [7] R.C. Tolman, The principles oi statistical mechanics (Oxford Univ. Press, London, 1938)ch. 9. VV B. Brocklehurst, to be published. 19: G. Vincow, in: Radical ions, eds. E.T. Kaiser and L. Kevan (Interscience, New York, 1966) p. 151. [lOi R.G. Lawler and G.T. Evans;Ind. Chirn. Beige 36’ (1971) 1087. 1111 R. Biehl, K.-P. Dinse and K. M6bius, Chem. Phys. Letters 10 (1971) 605. 1121R. Kaptein, J. Am. Chem. Sot. 94 (1972) 6251 et seq.; F.J. Adrian, I. Chem. Phys. 54 (1971) 3912, 3913; R.G. Lawler and H.R. Ward, in: Determination of organic structures by physical methods, Vol. 5, eds. F.C. Nachod and J.J. Zuckerman (Academic Press, New York, 1973) p. 99. 1131D.J.M:Fassaert and E. de Boer, Mol. Phys. 21 (1971) 485. [141 B..BrockIehurst, Nature 221 (1969) 921. .[I51J.L. Magqe and J.-T.J:,Huang, J. Phys. Chem. 76 (1972) 3801;73 (1974) 310; B. Brocklehorst and T. Higashimura, J. Phys. &rem. 78 (1974) 309. I161 R.S. Dixon, F-P. Sargent and V.J. Lopats, unpublished work. 1171 B. Brocklehurst, R.S. Dixon, E.M. Gsrdy, V.J. Lop&, M.J. Quinn, A. Sir@ and F.P. Sargent, Chem. Phys. Letters 28 (1974) 361. Wl R.W. Fessenden, J. Chem. Phys. Se (1973) 2489. ,I191 C. Fuchs, F. Heisel and R. Voltz, J. Phys. Chsm. 76 (1972) 3867.
:
Volume 28, number 3
I Qctober
1974
‘. .,
YIELtiS
OF EXCITED STATES FROM &MINATE RECOMBINATION OF HYDROCARBON RADICAL IONS BrianBROCIkEHURST Department of Chz-iwy,
The tiniversity, Sheffield
S3 711F, UK
Received 24 April 1974
A theory similm :o the mdical pair modei for CIDNP, etc., is used to describe the rate of loss of spin correlation geminate pairs of radical ions produced by rndiolysis. The ratio of the yields of triplet and sinL,eletexcited states and the effects of mqnetic fields are discussed.
in
-- When solutions in alkanes are exposed to high energy radiation, excited states of the solute are formed by recombination of radical ions [l]. At high concentrations (a 10B2M), the main reactions are:
S. -f=+
S+te-,
(1)
S+bl+,
.(2)
s++hl
+
e- tM
AM-,
M’tM-
+
c31
M’tM.
6)
The solvent, S, in typical experiments is cycle-hexane; ths solute, M, may be biphenyl, naphthalene, &hracene, etc. MC includes singlet (S) and triplet(T) excited states. Observed T/S ratios are in the range l-2 [2,3] - rather less than the value, of 3 expected for random spin orientatjons. The recombination process is mainly geminate, however, not. iandom: the initial separation of the charges is,large (50-150 A) compared to, molecular diameters but small compared with the Onsager escape distance (- 300 _CJin such a solvent. The odd electrons on Mf and-M- were initiaily paired in a singlet solvent molecule. If the relative orientations and phase of the two spins do not change, then dnly [email protected] be formed. This letter deals with the rate of change of the correlation of the two spins after separation. The aim is to calculate the probability, p,(t), of regaining,a singlet state’after a time, r; itjs assumed that the initial processes produce a ‘puie’ singlet state :
;.: .
‘of the ion pair - a nor.-stationary state. The 0verZl wavefunction thei oscillates between singlet and triplet because of interaction with the nucIei. It is a coheient oscillation not 2 relaxation because the time scale is short compared to the e!ectron spin relaxation times. The initial process - separation and them&a. tion of the electron - is extremely fast (< I ps). Processes (2) and (3) are also fat at high concentrations (= 100 ps); there is a wide range of ion lifetimes - very roughly 1-l 00 ns - in mobile solvents (corresponding to the range of initial separations) [ 1,2] *; ‘an initial rapid decay is followed by a long ‘tail’. The final step - the actual electron transfer in (4) - is also Iikely to be fast because there is no potential barrier due to solvent polarisation; it, will probably take place while the ions are stti separated by solvent [6]. Therefote, interactions before Mf and M- are formed or during their recombination can 5e negected: only the evolution of the overall wavefunction during the ion lifetime is important. The ion Iifettie is short but it is much l,onger than the rotatianal correlation time of the molecules;ihis means that interactions with the solvent and the anisotropic hyperfme interaction with the. nuclei of&F and M- will average to zero, Only the.isotropic hyperfine interaction will be considered. me’two ions wilLbe IabelIed I a.qd 2, the si.ngIet * For recent expetimental
work, sic ref. 141; for theoreticti work, see ref. [S], and recerencs therein
: _.
357
Volume 23,~number 3
CHEMICAL PHYSICS I,ETTERS
”
state, S and the three triple? states, 0, f and -. For the case of only one set ‘ofprotons on each molecule, the hamil?onian, V, may,be written:,
1 October 1974
(9) and the time debendence has’the simple form p 5(1)= c~s2&alnll -a,m,>t} ;
(101
Td .lescribe the overall behaviour, one must sum over
all r-9value and this can be done for the general case of s:veral.types.of proton, on each molecule [S] to nive .. [. 1 + 1 1 co& P,HW =$ 1
+~(si+S2>‘(all~+a21~) ._
(5)
Sf, S-, etc., are shift operators. The first three terms mix the singlet state~withTo, T, and T_, respectively, the ME.. andsixih mixTO with T,. and T while the fourth gives non-zero diagonal elements &_h T, and T_; The matrix of V is, in simple cases,
{v_,-v_, 0
v__ i
(In general, a larger matrix is required since a s@flip one way of a proton‘on one molecule may be followed by a reverse spin-flip on the other; ~1similar problem arises if there is more than one type of nucleus on each molecule.) Since V is independent of time, the time-evolut.ion of the system is @en by 173 p(r)
= e-ivy
p(0)
e+ivf
(7)
(Vf andat amin units of tl). p(O) is a density matrix with.unity for the initial population of the singlet state and all o&her elements zero. Therefore
To proceed, one h;ls to obtein the eigenvalues and eigenfunctions of (6), to express 1s) in terms of these eigenfunctions and to substitute in (8). These equations are easily solved in some simple cases. First, suppose that the experiment is carried out in a strong external magnetic field; if the Zeernau splittin$js much larger than that due to the hyperflne interact&r (fie& s 10OGgauss), then no mixing with T, and T_ occurs 2nd the only relevant matrix ele- : ments are ‘. 358
‘-,
.
~.. l-rcos”~ Ly
-2
1
a$ . .. ,(I 1)
where n1 is the number of protons with hyperfine coupling constant al on molecule 1, etc. Deuterium has 3 spin of I,mstead of+: calculations for deuterium compounds can be made by substituting{2 cosot+l)/3 for cosal in (11) [S]. Fig. la shows results calculated for some anthracenes, usin experimental a values [9] for protons, and the same values nlultiplied by 0.1552 - the ratio of the magnetic moments - for deuterons. For C,,H,o and C,,D,,, p,(f) falls rapidly’to the average value (slightly greater than? because no change occurs if nzl = m2 = 0) and then remains essentially constant. Though coherent oscillation is postulated, the curve lnak; like a random decay (apart from the initial . nc;gaiive~curvature): this is due to the six different o’s (3 for the cation, 3 for the anion). Oscillatory behaviour Lmightbe observed if the 12values are in simple ratios: e.g., for perylene, one can predict peaks in the curve at = 50 (ps rises to O.SS), 350 (0.75) and 400 ns (0.66) but other effects may intervene on the longertime scale. It would be better to use solute molecules with fewer magnetic nuclei: this requirement can be partly met by using compounds such as C,,HD9 (fig. la). Qualitatively; behaviour in the absence of a field should be very similar, except that the rate of change shoull be greater: however, quantitative treatment of the problem is more complicated. One difficulty is tha,! the nuclear angular momentum vectors of the two.molecules are now oriented at random. Eq. (11) shows that ifall the protons (20 for anthracenc) were,on one ion,.none on the other, the same result for p,“(t) is obtained: -this is not’true for>:(t) (field. off) but this approximation is made to simplify the calculation. if, further, the protons all have the “.
V&me 28, number 3
CHEM[CAL PHYSICS LETTERS
1 October 1974
.
1.0
p,(t)
0.5,
I
0
t
'10
:
ty+ir
r 20
Fig. 1. Dependence of the probability of recovering a singlet time: (a) anthracene in a magneiic field: -, Cr4H1e; - - -, CiJDre; *.., Ci4HDa (proton in position 9); cb) ---, Mphenyl in a field; -) in zero field. State on
same u vaiuc, then 8 simple exact solution of eqs. (6) and (7) can be obtained;
:
Py(t>=(~++)-2{$ i-1(1+1) cos2(I+$?t3.
(12)
The further approximation of using only the singIettriplet matrix eIements in (6) gives p,o(r) = cos2 (I {!(I f 1)}“2f .
I131
This iS similar to (10) except that a.reploces a/2 - ‘&e rate of change is greater in zero field Y and p depends on I rather than m (undefined in the absence of a field). Rqs,<12) and(l3) are identicaI when f is very large, but they differ sigticantly when fis small, When I =$, the average value of p:(t) is 518, i.e., greater L than pg”(t): this result has been obtained previously by Lawter and Evans [l O] in discussing possible effects of’magnetic fields on reactions invoIvi.ng pairs of neutral radicals. Siphenyl is a convenient solute molecule for p&e radiolysis studies [l-5] of ion recombination and for trial calculaths, though, U~o~n~teIy, 4 values have .’
not been reported for the cation; they are assumed here’to be the same as for rhe anion: they are probably somewhat larger, in fact. In the anion [ 101, four protons ha% a small Q, 0.370 gauss (these are neglected in what follows); another set of four h.ave a = 2.642 gauss, while two have a = 5.32 gauss -- aI.most exactIy doublie. An average value of 3.76 gauss was obtained by scaling $(I + cosl?~} to +(I scas~xr cas”2xt), cf. eq. (11). This value was ‘aserted irt( L2) which was then summed over values off from U-6. Results are’ given in fig. I b. Because of the assumption made, this function would oscillate, but for the reasons given abovk, it is more likely to fail smoothiy to e $ as shown. The theory given here is very similar to the radicdl pair model currently used to describe CID%? and CIDEP [ 121. It is simpler in so far as both exchange effects and differences in g values (* IW4 for aromatic hydrocarbon ions [ 131) can be n:gIected: it is more complicated because of the large numbers of protons in molecules studied’to date, The experimental situation is different in many respects: ion pairs separate but they necessarily recombine - on& a small proportion of neutral radic& do this: 50th singIet and triplet produtts can be observed directly and the possibIe ti.rne.resolution is limited onIy by the Iifetimes of the excited states (long for triplets, but onhf a few nanoseconds, for singlets in some cases). Some qu~ita~ive conclusions and predictions foIIow. (i) In previous discussions of this probIern (6,141, *he loss of spin correlation was assumed ta be a relaxation process and magnetic field effects were predicted for systems in which the ion lifetime was in between T2 and T, (e l-100 fls); that discussion remains valid but ion lifetimes are much shorter in mobile liquids. The present theory predicts muchmore rapid changes - roughIy in the ratio of the band-width to the line-width of an ESR spectrum: the decay time is comparable with the fastest ion recomb~ation times. @e&I T/S ratios can be estimated by integrating over the ion fifetime d&Mb&on: cs.Ioulations of this type are inprogress [8] ; it is already cIear that a sig. nificant part of the triplet yield [.2,3] can be accounted for in this way, but it must be noted that there are otherprocesses contributingto the yield of triplets from i&s [IS] and that the probabifities caIculated here omit the effects of energy Ievef densities in ,. product molecules 161. 1 ..
Volume 28,number 3
CHEMICALPHYSICS
.’ (ii) The rate of decay will-be increased
siderable,
but an enhancement
of fluorescence
and a
decrease in the triplet .yield took place of&r the eiectron pulse; (iv) Molecules‘containing
only
a few magnetic
nuclei (or, e.g., partly dzuterated compounds) should show reverse
oscillatory effect
behatiour.and, of magnetic
at certain
times,
field on the excited
a
sta?e
yield. No observations have been made. (v) CIDEP effects in pulse radiolysis have been reported [18] but only radicals have been studied and these would not have resulted from ion recombination. According to the present proposals, triplets should only be formed in the To state in 2 magnetic field: the Am, = 2,transition should be absent initially, while Ants = +‘I and - 1 should be. e.normously enhanced in absorption and emission, respectively.. These effects wih decay rapidly (T1), but they might be large enough to be detectable even in the presence of large numbers of relaxed triplets in steady state experiments. The erect on the nuclear spin states depends on the ion lifetim!: if this is long, then all molecules will reach ‘equilibrium’ between singlets and triplets except in ion pairs with mr = 0 for all types of proton - i.e., the central ESR line should be .weaker. If the ion lifetime is very shcrt then the few triplets formed should show a? enhancement of interisity of the hyperfine lines with increasing .m. (vi) The same ideas apply.equajly to photoionisation except that if ionisation bccurs from an excite,d triplet (common G biphotomc processes) then the arguments must be reversed. Fuchs et al. [19]
:
360
..
1 October
1974
ha-/e shown .&at in(sin&j photqionisation of be& zene solutions very little spin relaxation 0ccurS: this is 1:obe expected since recombination is much faster inaromatic solvents. ; ‘.
by large
numbers of protons and large avahres. Methyl substitution ,should,increase the rate.of decay(cf. Q values [9]):. there seems to be some indication of this in the published results [3] but itis not conclusive. Differ-‘ences between unsubstituted tiaphthalene, tithracene, .etc;, shc~uldbe small. 4 striking reduction in the triplet yield should result from deuteration: no results appear to be available. ’ (iii) Enhancement of the total fluorescence yield by an applied magnetic field has recently been observed: the enhancement is affected by deuteration [16]. Some time-resolved measurements have been made [17]; the experimental difficulties were con-
,,
LETTERS
...
The author is grateful to Dr. N.M. Atherton, Dr. P.W: Atkins, Professor G.J. Hoytink and Professor R. McWeeny for many helpful comments.
Re Ferenies [l] J.K. Thomas, Ann. Rev. Phys. Chem. 21 (1970) 17;. A. Sin& Radiation Res. Rev. 4 (1972) 1. [2) I.H. Bxxendale and P. Wardman, Trans. Faraday SOC. 67 (1971) 2997. j3] F.S. Dainton, MB. Ledger, R. May and G.A. Salmon, J. Phys. Chem. 77 (1973) 45. [4] E. Zador, J.M. Warman, L.H. Luthjens and A. IInmmel, J. C%em.Sot. Faraday Trans. I70 (1974) 227. IS] S.J. Rzad, J. Phys. Chem. 76 (1972) 3722. [6] E. Brocklehurst, Chem. Phys. 2 (1973) 6. [7] R.C. Tolman, The principles oi statistical mechanics (Oxford Univ. Press, London, 1938)ch. 9. VV B. Brocklehurst, to be published. 19: G. Vincow, in: Radical ions, eds. E.T. Kaiser and L. Kevan (Interscience, New York, 1966) p. 151. [lOi R.G. Lawler and G.T. Evans;Ind. Chirn. Beige 36’ (1971) 1087. 1111 R. Biehl, K.-P. Dinse and K. M6bius, Chem. Phys. Letters 10 (1971) 605. 1121R. Kaptein, J. Am. Chem. Sot. 94 (1972) 6251 et seq.; F.J. Adrian, I. Chem. Phys. 54 (1971) 3912, 3913; R.G. Lawler and H.R. Ward, in: Determination of organic structures by physical methods, Vol. 5, eds. F.C. Nachod and J.J. Zuckerman (Academic Press, New York, 1973) p. 99. 1131D.J.M:Fassaert and E. de Boer, Mol. Phys. 21 (1971) 485. [141 B..BrockIehurst, Nature 221 (1969) 921. .[I51J.L. Magqe and J.-T.J:,Huang, J. Phys. Chem. 76 (1972) 3801;73 (1974) 310; B. Brocklehorst and T. Higashimura, J. Phys. &rem. 78 (1974) 309. I161 R.S. Dixon, F-P. Sargent and V.J. Lopats, unpublished work. 1171 B. Brocklehurst, R.S. Dixon, E.M. Gsrdy, V.J. Lop&, M.J. Quinn, A. Sir@ and F.P. Sargent, Chem. Phys. Letters 28 (1974) 361. Wl R.W. Fessenden, J. Chem. Phys. Se (1973) 2489. ,I191 C. Fuchs, F. Heisel and R. Voltz, J. Phys. Chsm. 76 (1972) 3867.
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