4 The Effect of a Magnetic Field on Chemical Reactions By P. W. ATKINS and T. P. LAMBERT Physical Chemistry Laboratory South Parks Road Oxford 1 Historical Background The ways in which magnetic fields can affect chemical reactions have long been the subject of investigation but only recently with the theoretical insight given by the interpretation of chemically induced magnetic polarization,’ has significant progress been made. The early work which because of the frequency of rebuttal and retraction is very hard to disentangle and even then to rely on has been summarized in a number of Mare recently the subject has been analysed by Buchachenko in his book9 on chemically induced polarization and in a brief simplified artic1e,lo but most of the work we describe has been reported only in primary journals.The magnetic field effects that have been reported (if not substan- tiated) range from the physiological7 to the purely chemical. This review ignores the former but includes in the scope of the latter the effect of magnetic fields on the fluorescence intensity of various types of fluid sample. We shall therefore devote some attention to electrochemiluminescence phenomena but refer elsewhere’ to reviews that assess the field in detail and relate it to its solid-state analogues. The turmoil of the early literature is illustrated very.wel1 by the summary given in the review by Figueras Roca.’ For instance in 1908 Ro~enthal’~ reported an effect of a magnetic field on the hydrolysis of starch but this was rapidly refuted by Cegiel~ky’~ and Heimrod.” Selwood6 came to the conclusion that the catalytic activity of various ions in solutions which according to several reports was modified by the application of a modest was more likely to be due to the local agitation of the ions by the field than by any direct modification of their activity.More 1 ‘Chemically Induced Magnetic Polarization’ ed. A. R. Lepley and G. L. Closs Wiley London 1973. * S. S. Bhatnagar and K. N. Mathur ‘Physical Principles and Applications of Magnetochemistry’ Macmillan London 1935. S. S. Bhatnagar K. N. Mathur and R. N. Kapur Phil. Mag. 1929,8,457. E. Miller Natunviss. 1937 25 545. R. Delhez Rev. Quest. Sci. 1957 18 176; Bull. Soc. my. Sci. Litge 1957,27 161. P. W. Selwood Chem. Rev.1946,38,41. ‘Biological Effects of Magnetic Fields’ ed. M. Barnothy Plenum New York 1964. F. Figueras Roca Ann. Chim. 1967 2 255. A. L. Buchachenko ‘Chemical Polarization of Electrons and Nuclei’ Nauka Moscow 1974. lo P. W. Atkins Chem. inBritah 1976 12 214. l1 P. Avakian and R. E. Merrifield Mol. Cryst. 1968,5 37. l2 P. Avakian Pure Appl. Chem. 1974,37 1. l3 I. Rosenthal Sitzber. Akad. Wiss. Berlin 1908 1 20. l4 R. Cegielsky Ber. Phys. Ger. 1908 15 566. l5 G. W. Heimrod 2.Elektrochem. 1914,19,812. l6 S. N. Basmanova Trudy Inst. prikad. Khim. i Electrokim. Akad. Nauk Gruz. S.S.R. 1962 3 117. A. Krause F. Domka and B. Marcieniec Monatsh. 1966,97 99. 67 68 P.W.Atkins and T.P. Lambert recently' the reported magnetic inhibition of the polymerization of styrene'' appears to be ~ontradicted,'~*~~ although a patent based on a 5% increase in the rate of polymerization of propene21 appears to survive.It is not in the least unlikely that commercially sensitive work continues in this field. Figueras Roca's review' is an excellent source of this type of information for it concentrates on the magnetic influence on catalytic activity. Probably the most poignant summary of the early days of this type of work is provided by Mulay and Mulay,22 who make the following remark on the electrochemical studies carried out over more than a decade by Sh~hukarev~~ at the beginning of this century '. . . .after finding that the phenomena of the action of a magnetic field on chemical reactions [were] more complicated than he had originally suspected and that they were too complex for individual observa- tion he decided to give up his study of the phenomena and to retract his former statements.' The reason for the hope and scepticism of the early years lay in two rules advanced by Bhatnagar et aL,2,3one for predicting the effect of a magnetic field on the equilibrium position of a chemical reaction and one for predicting the effect on its rate.The former although not phrased as such was essentially the recognition of the possibility that the magnetic susceptibility of the reactants and the products might differ and therefore that the standard molar reaction Gibbs function AGE would depend on the strength of the applied field B. If the molar susceptibilities differ by Ax this contributes iAxB2 to AGE,24and in principle leads to some concomitant change in the equilibrium constant through AGZ = -RTIn K.It is not difficult however to dismiss this effect as negligible. Even for a generous difference of susceptibilities it is hard for to exceed ca. 1mJ mol-' in magnetic fields available in the laboratory and the resulting shift in the equilibrium is nugatory. The early explanation of the kinetic effect (if by then it had been observed) is also untenable on the grounds of the weakness of the interaction. It was suppo~ed~*~ that the field favoured some molecular orientations thereby altering the effectiveness of collisions. What experimental results were available at the time and which appeared to support the rules seem to be accounted for either by agitation of the mixture or by some photochemical activity.' There is one further type of magnetic activity which might play a role but it remains to be substantiated by reliable experiments and we shall pay no more attention to it than it receives in this paragraph.It is known that the presence of a magnetic field can influence the band structure of conductors and semiconductors (e.g.the de Haas-van Alphen effect) and some authors have reported changes in the work function of metals by as much as 0.1V in quite low fields25 (can that really be so?),and significant changes in their If these results are depend- H. Schmidt G. Muhr and H. Marek 2. Elektrochem. 1945,51 37. l9 J. Breitenbach and F. Richter Monatsh.1949,80 315. 20 S. Collins and W. A. Bryce J. Chem. Phys. 1950,18 1297. 21 W. B. Reeves U.S.P.2 663 394 1953 (Chem. Abs. l954,48,434OE). z2 I. L. Mulay and L. N. Mulay ref. 7 p. 146. 23 A. N. Shchukarev,J. Russ. Phys. Chem. Soc. 1915-1926. 24 S. Kaneko J. Soc. Chem. Znd. Japan Suppl. 1931,34,133. 25 R. Bedos Compt. rend. 1964,259 1695. 26 E.E. Kolosov and P. V. Sharavski,Fiz.Doklady Nauchn. Konf. Leningrad,lngh. Stroit Inst. Leningrad Sb. 1961,31. z7 E. Weisshaar and H. Welker 2. Nuturforsch.,1958,8a 681. The Effect of a Magnetic Field on Chemical Reactions 69 able they certainly suggest that heterogeneous catalytic activity might be changed by a magnetic field and Figueras Roca' has drawn attention to reports in the literature on the rate of oxidation of iron at 580 "Cand the inhibition of the oxidation of formic acid in the presence of a magnetite-Cu2+ mixture.Nevertheless the actual proof of magneto-catalytic activity remains extraordinarily difficult on account of the irre- producibility of samples and the elimination of extraneous complications. Although these effects are of considerable technological importance we shall devote this review to the effects that have been fully substantiated experimentally and which can be accounted for on the basis of moderately reliable theories. Some magnetic field effects have been known and established for many years. Probably the most famous is the interconversion of ortho- and para-hydrogen this was studied originally by Farkas and Sachsse28 and explained by Wigner.29 The basic idea underlying the explanation is closely related to that behind the modern theories of magnetic field effects and a brief account will set the stage.The interconversion of ortho- and para-hydrogen depends on the relative realign- ment of the two proton spins in the molecule. In ortho-hydrogen the proton spins are mutally parallel and the total nuclear spin is unity this is the nuclear triplet state. In para-hydrogen the nuclear spins are antiparallel and the total nuclear spin is zero this is the nuclear singlet. As a result of the requirements of the Pauli exclusion principle3' only the odd rotational energy levels may be populated if the nuclear spins are arranged as the triplet (we shall call this 'triplet phased') and only the even levels if the nuclei are singlet phased.The rotational energy levels are sufficiently different in energy for the nuclear statistical effects to have significant ther- modynamic consequences and the rate of interconversion is so low that ortho- and para-hydrogen constitute two distinct species. In order for an ortho molecule to be converted into a para molecule (or vice versa) the nuclear spins must be realigned. One way of doing this is to dissociate a collection of molecules and then to allow random recombination. This is the dissociative mechanism and is not the one expected to be influenced by a magnetic field (but see below p. 72). Another way of bringing about relative realignment is to subject the molecule to a magnetic field that is inhomogeneous on the scale of the molecule.In that case the two protons will be in different magnetic fields and will precess at different rates. Precession at different rates means relative reorientation of the two nuclear spins and so ortho switches into para and vice versa. One way of generating a sufficiently inhomogeneous magnetic field is to allow collisions between hydrogen molecules and either paramagnetic specie^^^*^'-^^ (ions or neutral molecules) or magnetic surfaces.34 Theory suggests that the rate of interconversion should be proportional to the square of the magnetic moment of the paramagnetic species and this accords with experiment. The interconversion process has recently been the 28 L. Farkas and H. Sachsse 2. phys. Chem.,1933,23B 1 19.29 E. P. Wigner Z. phys. Chem. 1933,23B 28. 30 P. W. Atkins 'Quanta a Handbook of Concepts' Clarendon Press Oxford 1974. 3' H. Sachsse Z. phys. Chem. 1934,24B 429. 32 W. K. Wilmarth and M.K. Baes J. Amer. Ckm. Soc.,1953,75 2237. 33 G.-M. Schwab J. Voitlander and V. Penka Z. phys. Chem. 1963,36,378. 34 D. D. Eley and D. Shooter J. Catalysis 1'963 2 268. 70 P.W.Atkinsand T.P. Lambert subject of renewed aftenti~n~~-~~ and detailed theories of the process in the gas and liquid phases are now available. One chemical application has been to the estimation of the size of hydration spheres of ions in solution.36 Many important chemical reactions involve two electron spins either paired (as in a singlet) or parallel (as in a triplet).The significance of the ortho-para interconver- sion work should now be clear local inhomogeneous magnetic fields can interchange singlet and triplet electron spin phasings as well as nuclear spin phasings and can thereby affect the course of the reaction. Since the electron spins have much stronger magnetic moments than the protons we can expect the difference in precession frequency to be greater for a given magnetic field difference. There is every hope therefore that the local field inhomogeneities can modify the course of reactions and this is confirmed by experiment. The remainder of this review explores this idea for radical reactions and fluorescent processes involving excited triplet states of molecules. We shall see that the various types of spin rephasing process are the central reasons for the response of chemical reactions to magnetic fields.2 The General Theoretical Background Modern theories of the effects of magnetic are based on two effects and both are related to the interconversion of spin multiplets. The problem can be illustrated by considering the simple case of the homolysis of a bond in the molecule A-B to give two doublet radicals 'A and 2B.We suppose first that the homolysis occurs from a singlet state of AB and that the bond cleavage occurs without alteration of the overall spin of the molecule. This means that the two spins of the bond remain antiparallel even though they are now confined to spatially separated radicals. In other words homolysis leads to a singlet radical pair 1{2A-.-2B}.If the homolysis proceeds through a triplet state of AB (as it might in a photochemical cleavage) the same argument implies the formation of a radical pair in an overall triplet spin state 3{2A***2B}. The components of the radical pair diffuse apart but they have a significant probability of re-encountering each other. If they re- encounter they may form a bond this is geminate recombination and the product is called the cage product. The bond will form however only if the radicals have singlet-phased electron spins when they re-encounter if the electrons are triplet phased (parallel) the bond will not form and the encounter will be unproductive. If a mechanism exists for destroying the initial singlet phasing of the radical pair it follows that the probability of geminate recombination is reduced.In that case the proportion of cage products declines relative to the escape products. If the magnetic field can influence the rate at which the singlet character of the radical pair is lost it will affect the proportions of cage and escape products. The loss of singlet phasing implies a gain in overall triplet phasing. The process by which this comes about is the same as in the ortho-para interconversion process 35 S. E. Nielsen and J. P. Dahler J. Chem. Plays. 1967,46 732. 36 P. W. Atkins and M. J. Clugston Mol. Phys. 1974,27 1619. 37 E.-A. Reinsch Mol. Phys. 1974,28,683. 38 R. Kaptein Thesis Leyden 1971. 39 R. Lawler and G. T. Evans Ind. Chem. Belges 1971,36 1087. 40 R.Sagdeev Yu. N. Molia K. M. Salikhov T. V. Leshina M. A. Kamha and S. M. Shein Org. Magn. Resonance 1973,5,603. 41 A. L. Buchachenko and Sh. A. Markarian React. Kinetics Catalysis Letters. 1974 1 157. The Effect of a Magnetic Field on Chemical Reactions (which was for nuclei -now we deal with electrons) and is illustrated in Figure 1.The singlet state of a pair of electrons can be depicted as in Figure l(u):we see that not only does the state consist of an a and a p spin but their relative azimuth is such that the resultant spin angular momentum is zero.3o On the other hand a triplet state of two electron spins can be constructed in three ways. One uses an equal mixture of a and /3 spins but their relative azimuth is such as to give a resultant spin angular momentum of unity (actually d2R),Figure l(6).The difference between the arrange- ments in Figures l(a) and l(b) illustrates what is meant by the difference of the ‘phasing’ of the a and /.? spin orientations in the singlet and triplet states.There are twoother ways of obtaining a total spin of unity. One is to use two a spins this gives a state with S = 1 M = +1 (Figure l(c)),which is denoted T+l.The other uses twop spins this gives S = 1 M = -1 (Figure l(d)),a state denoted T-l. S Figure 1 A singlet-phased pair of spins can be induced to switch into a triplet if their individual precession frequencies differ. For example if the Larmor precession frequencyof spin A in Figure l(a)differs from that of spin B they will not maintain their initial singlet phasing but will evolve into the phasing characteristic of To.If the (circular) frequencies differ by A@,complete conversion will occur in a time T/Ao.A difference of Larmor precession frequencies about the z-direction depends on the two spins experiencing different fields along z. It is also quite possible for the spins to experience different local fields pointing along the x-and y-directions. Such fields exert torques about their directions (about the x and y axes) and tend to twist aspins into p and p spins into a.It follows that a singlet state may have its (Y spin twisted into p (if the field is sufficiently different at the twoelectrons) and soevolve into T-l or its p spin twisted into a,which takes it into T+l.In summary therefore we see that local magnetic fields different at the two electrons of a radical pair can induce singlet- triplet interconversions and the triplet state generated (its M value) depends on the orientation of the local field inhomogeneity.72 P. W.Atkins and T.P. Lambert This qualitative discussion can be made more quantitative as follows. If the energy of spin A is determined by a termf,*s in a Hamiltonian and that of spin B by a term fB*sB the total Hamiltonian can be written H=fA'SA+fB.SB =g(fA+fB)'(SA+sB) +i(fA -fB)'(sA -sB) (1) For our purposes the important term is the second. This is antisymmetric in the spins and so it contributes to matrix elements (qH(S)because the singlet is antisymmetric in the spins the triplet is symmetric and the whole matrix element must be symmetric if it is not to be zero.The term proportional to S -sBvanishes if fA =fB and this is the basis of the earlier assertion that the individual Larmor precession frequencies (which are proportional to fA and fB) must differ if singlet-triplet transitions are to occur. In order to identify what contributions to the Hamiltonian may induce singlet- triplet rephasing we have to find interactions of the form f-s that are different for the two radicals. One candidate is the Zeeman interaction. If the g-values of the radicals are gA and gB their interaction with the external field B is and the antisymmetric part of this is proportional to (gA-gB)B. Its magnitude increases with B and so the rate of singlet-triplet conversion should increase as the applied field is increased.Notice that this interaction has operators relating to only the z-direction and in terms of the qualitative picture of the process corresponds to a relative rephasing of the two spins around the z-direction. In other words the g-factor differences allow S-To crossing but not S-T,,. (This restriction can be lifted in some special cases.42) In a field of 1 T (10kG) taking gA -gB -loA3(which is a reasonable choice for a range of organic radicals) the time for complete rephasing is about 3 X lo-* s. We shall return to explore the significance of this remark. Another candidate for the spin-rephasing interaction is the hyperfine interaction of each electron with the magnetic nuclei in the radicals. The antisymmetric part of the interaction aAIA*sA+aBIB*sBis H(-) =+(~AIA-MB) * (sA -sB) =;(a,+ ~B)(IA-IB) '(~A-sg) +b(aA-aB)(rA+~g) * (sA-s~) (3) and so this interaction can operate even if the radicals are identical (a = aB)but their nuclear spin orientations differ (I # IB).The rate of interconversion under the influence of H(-)depends on the nuclear spin states of the radicals because of the involvement of nuclear ,spin operators in H(+ and this is the reason why chemical reactions are a potential technique for the separation of isotopes on the basis of their spins rather than their masses.The hyperfine Hamiltonian has components of magnetic field in all three directions (because the nuclear moments can take up various orientations) and so it can induce transitions between the electronic singlet and all three substates of the triplet.At first sight however does not appear to depend on the strength of an external magnetic field. This is indeed true but the effectiveness of H(-)in causing S-T interconversions does depend on the applied field and this introduces one of the most important sources of a magnetic field effect. 42 P. W. Atkins A. J. Dobbs and K. A. McLauchlan Chem Phys. Letters 1973 22 209. The Effect of a Magnetic Field on Chemical Reactions 73 The explanation of the role of the external field in governing the effectiveness of the perturbation H(-)is as follows. When a perturbation acts its success in causing a transition depends on the ratio of its strength to the energy separating the states it is tending to This can be illustrated explicitly by a very simple calculation.Suppose a perturbation of strength k V acts on a system which at t = 0 is known to be in a state $l; then the probability that it will be in another state q52 (the only other state available) at a later time t is p(t) = (2V/u> sin2 Ut (4) where U2= A2+ 4 v‘,A being the separation in energy of q1and q2.If A is very small 2 V/ U -1 and the probability oscillates between 0 and 1 the latter implying total transfer to q2.If A is large in the sense V<cA the value of P(t)does not rise above ca. 2V/A which is small and implies that the perturbation is unable to induce a significant transition into the other state. In the present case the To,T,l substates of the triplet do not lie at the same energy when a magnetic field is present and so the efficiency with which can induce transitions from S to To,T, will be different in each case.The simplest situation that arises is when the singlet and triplet lie at the same mean energy (which is the case if exchange interactions between the components of the radical pair are very small this is often the case for radicals that are significantly separated in the solution but not when they are actually in contact). In this case and in the absence of an external field the hyperfine interaction can induce transitions from S to To,T, at about the same rate (so long as it has non-vanishing matrix elements) because the triplet substates lie at the same energy. When a field is applied the T- substate drops to an energy A -gp,B below To(and therefore below S which remains degenerate with To),and T, rises to an energy A above To.Therefore although the S-To crossing may continue as before the extent of the S -T, crossing is decreased by a factor of ca. 2 V/A (where V-El(-)in this case). Since V-0.1 mTand A -1T it follows that the crossings to and from T, are effectively quenched in a high field. This discussion may be summarized as follows. The proportion of cage and escape products in a radical reaction in solution depends on the rate at which the spins of the radical pair change their relative orientations. The rate of S-T, crossing is decreased on the application of a magnetic field and in regions of high field only the S-To crossing plays a significant role.All three crossings may be induced by hyperfine interactions. The S-To crossing may also be induced by a g-value difference in the two radicals of the pair the strength of this interaction is proportional to the magnetic field and the rate of S-To crossing is increased by a field. Being in an overall singlet is a necessary but not a sufficient criterion for recombination the two radicals of the pair must also be in contact (in some sense). Therefore the probability that the pair is in a singlet at a time t has to be multiplied by the probability that at that time it has a spatial conformation corresponding to If the latter probability is denoted G(t) the total recombination probability depends on the value of the integral gdtG(t)P,(t) P,(t) being the probability of being in a singlet at time t.For simple three-dimensional translational diffusion G(t)a t-9 exp (-t/~),and the integral can be evaluated; this gives the characteristic $ and thence (q/7‘)j behaviour of such diffusional processes and explicit expressions have been reported in several 43 P. W. Atkins ‘Molecular Quantum Mechanics’ Clarendon Press Oxford 1970. 74 P. W.Atkins and T.P. Lambert 3 Experimental Examples Substantial experimental evidence is a~ailable~~.~~ for magnetic field effects along the lines of the theory described so far. For instance Sagdeev et uL40have examined the dependence on a magnetic field ofthe proportions of cage and escape products in the liquid-phase reaction between various fluorinated benzyl chlorides and n-butyl- lithium.The cage product formed from benzyl+ butyl radicals is phenylpentane and the escape products include diphenylethane. The reaction involves a singlet precursor and so we expect the proportion of cage products to increase as the field increases (S-Tinhibited). The report indicates that for benzyl chloride itself the ratio of phenylpentane to diphenylethane does indeed increase and changes from 4.7 f 0.3 to 5.6*0.5 when the applied field is changed from 50 pT (0.5 G) to 1.5 T (15 kG). The same authors also studied the effect of temperature and solvent on the field dependence. Typical results are those relating to pentafluorobenzyl chloride and n- butyl-lithium. The ratio of products rose from 4.5f0.5 to 6.2 h 0.3 when the solvent was n-hexane at 70 "C and the field was increased from 50 pT to 2.5 T (25 kG) an increase of cu.37% but it changed from 4.0h0.3 to 6.1*0.5 in cyclohexane at 70 "C,an increase of ca. 54% (probably the record so far). In cyclohexane at 80 "C the ratio changed from 3.7 f0.3 to 5.3 f0.5. The magnetic field is expected to have a smaller effect at high solvent mobilities because the diffusional trajectory terminates more quickly than at low mobilities and the rephasing effects are less pronounced because they have less time to operate. Another class of examples is pravided by the work of Gupta and Hamm~nd,~~ who reported some intriguing results on the effect of a magnetic field on the photosen- sitized isomerization of piperylene (penta- 1,3-diene) and stilbene (1,2-dip hen yle t hene).They found that the photos ta tionar y state concentrations changed when a 0.9 T field was applied and that the effect depended on the nature of both the substrate and the photosensitizer. For instance the ratio of translcis photostationary state concentrations of the isomeric piperylenes was 1.08 (ben-zophenone as sensitizer) 1.13 (m-methoxyacetophenone) 1.08 (fluorenone) 1.16 (2-acetonaphthone) 1.07 (Michler's ketone) but 0.91 for stilbene (with ben- zophenone) and 0.95 (2-acetonaphthone). They pointed out a number of features of their results which would need to be accommodated by any theory. In the first place they considered that some kind of relaxation time must be involved but that this could not be radiative decay of sensitizer triplets because the substrate concentra- tions are much greater than are needed to capture virtually all the excited triplets and an effect on the sensitizer alone would be unlikely to influence the different isomers to different extents.They concluded that the explanation probably lay in the ability of the magnetic field to influence the relative rates of radiationless decay of triplet exciplexes. An explanation of these experiments which conforms to the suggestions outlined here has been ~uggested.~~ It was proposed that the triplet exciplex should be regarded as having the nature of a radical ion pair. In that case the application of the magnetic field can stimulate an intersystem crossing because the two components of the exciplex have different g-values and therefore different precession frequencies in 44 A.Gupta and G. S. Hammond J. Chem. Phys. 1972,57 1789. 45 P. W. Atkins Chem. Phys. Letters 1973 18 355. The Eflect of a Magnetic Field on Chemical Reactions 75 the same applied field. Furthermore the rate of deactivation of the exciplex (the rate at which it is switched from triplet to singlet) will depend not only on the field strength but also on the nature of the components as the experimental results require. The theory was expressed in simple quantitative and speculations about the g-value differences and the unperturbed lifetimes of the exciplex showed that it could account for the order of magnitude of the effect observed. The crucial difficulty of the theory is the magnitude of the exchange interaction between the two components of the exciplex the theory would fail if it were much larger than the Zeeman interaction energies.Therefore if the theory is valid it points to a structure of the exciplex that has the two components separated by at least one solvent molecule and possibly more. There is clearly room for a closer analysis of the effect and note should be taken of a brief comment46 which suggests that triplet quenching by other radicals produced in the reaction might be another explanation. (Why that should be field dependent we shall explain in Section 4.)If however the orbiting model of the exciplex is tenable the development of the theoretical description could take the form of structuring the relative translational motion of the two components to take into account their mutual Coulomb interaction and some features of their exchange interaction (as has been done for some aspects of chemically induced magnetic p~larization~~).Some crude potential energy surfaces are available4' but it is most doubtful that they would be applicable to the present problem. There has been some peculation^^ about the possibility that a high-frequency magnetic field can play a special role in influencing the rate of recombination of radicals but there appears to be no experimental support for the suggestion. Strong static fields at low temperatures can play a role and the recombination of hydrogen atoms has been The authors showed that the rate of recombination was inhibited by a strong field and accounted for it on the basis that the atoms all tended to adopt /3 as their spin state and the parallel electrons were unable to form bonds.A similar type of problem has been studied in connection with ion recombination processe~,~ as is described below. 1-54 When solutions of aromatic compounds such as naphthalene and anthracene in aliphatic solvents are exposed to high-energy radiation excited states of molecules are produced as a result of the ion-recombination process. At high solute concentra- tions the main reactions are s + S++e-S++M + S+M+ M++M-+ M*+M 46 H. van Willigen Chem. Phys. Letters 1975 33 540. 47 J. B. Pedersen and J. H. Freed J. Chem. Phys. 1963,58,2746. 48 J.N. Murrell and J. Tanaka MoZ. Phys. 1964,7 363. 49 S. I. Kubarev and E. A. Pshenichnov Chem. Phys. Letters 1974,28 66. J. T. Jones and M. H. Johnson U.S. Gout. Res. Reports 1959,32 110. 51 B. Brocklehurst Nature 1969,221 921; Chem. Phys. 1973 2,6. 52 B. Brocklehurst Chem. Phys. Letters 1974 28 357. 52aB. Brocklehurst Chem Phys. Letters 1974 29,635. 53 B. Brocklehurst R. S. Dixon E. M. Gardy V. J. Lopata M. J. Quinn A. Singh and F. P. Sargent Chem. Phys. Letters 1974,28,361. R. S. Dixon E M. Gardy V. J. Lopata and F. P. Sargent Chem. Phys. Letters 1975,30 463. P. W.Atkins and T.P. Lambert where M is the solute and S the solvent. The question that arises is the multiplicity of the excited solute molecule M*. Both singlets and triplets may be formed and Brocklehurst has predicted,” that the proportion of excited states may be altered by the application of a magnetic field.The argument is as follows. If the encounters between the reacting species M’ M- were random then a triplet singlet ratio of 3 would be expected since of the four arrangements of the two electrons three are triplet and one is singlet. Generally however the encounters are not random the low relative permittivity of the solvent in these systems means that in only a few cases do the ions escape from their mutual Coulombic interaction and the majority undergo geminate recombination. In such a situation if the recombination is very fast the triplet singlet ratio will be zero because the initial state is a singlet and there is insufficient time for significant rephasing.On the other hand if the recombination is slow the arguments of Section 2 lead one to expect total relaxation and therefore approach to a triplet singlet ratio of 3. The relative recombination and rephasing times can be discussed in a variety of ways and the theories outlined earlier are applicable. It is helpful for instance to be precise about the meaning of ‘S~OW’ and ’fast’ recombination times. If the time for recombination is TR,by fast recombination is meant TR<<T, T2,where T and T2are the longitudinal and transverse electron- spin relaxation times (the former corresponding to S-T, rephasings and the latter to S-To).Clearly slow recombination is when TR >> T, T2.We can also distinguish an intermediate case when T2<<TR<< T,,and in this case a triplet :singlet ratio of unity is expected because of the S-To equilibration.In summary TR<<T, T2should give a ratio of 0; T, T2<< TRa ratio of 3; and T2<<TR<<T a ratio of 1. In zero magnetic field there is no distinction between T and T2(all three triplet levels are mutually degenerate and degenerate with the singlet at significant separations) but in high fields the situation changes to the intermediate case. (This is the same argument as used in Section 2 but expressed differently.) Therefore we expect the triplet singlet ratio to drop from 3 to 1as high fields are reached. On these arguments and with some consideration of the mobility of the substrates in the solvents Brocklehur~t~’ proposed that magnetic field effects should be observable in solvents with viscosities in the range 1-10 poise.It was found53 that the intensity of emission from the singlet excited state of fluorene in the solvent squalane was enhanced by a magnetic field in accord with the theory. Subsequent experiment~~~ examined the continuous y-irradiation of fluorene. In squalane solutions application of a magnetic field again significantly enhanced the emission from singlet excited fluorene. In cyclohexane solutions a magnetic field effect was also observed but it was much less marked as expected on the basis that cyclohexane is much less viscous than squalane. No magnetic field effect was observed when benzene was the solvent and it is believed that excited states of fluorene are not formed by ion recombination in this case.Brocklehurst has pointed out” that an implicit assumption in this work is that the rates of formation of the singlet state and the triplet substates are all equal. Since Franck-Condon factors and densities of states in the singlet and triplet manifolds are unlikely to be the same this is unlikely to be true and the pure triplet singlet ratios of 0,3 or 1are unlikely to be obtained even when the conditions predict them. There is reason to hope however that deviations from them are likely to be and magnetic field effects should be an acceptable technique of studying the recombina- tion process (and perhaps even of elucidating that very point). The Effectof a Magnetic Field on Chemical Reactions 77 On to the basic account of atom and ion recombination may be grafted a number of significant extra features.In the first place Brocklehurst has e~amined’~*’~~ the problem from the point of view of coherent rephasing of the electron spins rather than stochastic relaxation. If the general ideas of Section 2 are borne in mind it is easy to understand that the S-To rephasing can be brought about by the nuclear hyperfine interaction with the two electron spins. If only one magnetic nucleus were involved the overall state would oscillate harmonically between singlet and triplet in accord with equation (4). In the present case there are many magnetic nuclei in each species of the pair and so the hyperfine interactions have to be summed over.This summation has the practical effect of making the singlet probability decay rather than oscillate (unless the coupling constants happen to be in simple ratios as in perylene52T52a or the magnetic nuclei are sparse) on the time-scale of interest (generally less than the Poincare cycle time). The singlet probability is therefore predicted to fall to an average value (at slightly greater than $) and then to remain constant. In zero field however the rate of decay of the singlet under the coherent but multiple hyperfine perturbation should be greater than in the high-field case for reasons that we have already explained. A quantitative calculation is difficult because the angular momenta are orientated at random but it has been done on the basis of a number of approximation^.^^ The overall result is again that decay rather than oscillation occurs but in this case the singlet population falls to a value of slightly less than $.The difference between the two results one at high field the other at low is the basis of the experimental results for the magnetic field effect on singlet recombination yields.54 The other feature to graft on to this work is the problem of the allowed multiplicities when a number of ions or neutral molecules can take part in a recombination (as in a spur). On the basis that the spins do not relax or rephase there have been two conflicting sets of expressions quoted for the probability that the recombination product is a singlet (or a A recent analysis of the problem5’ shows it to be more complex than either of the earlier results had suggested but the singlet recombination probabilities can be calculated for any number of participants.It is now also possible to account for spin rephasing within the spur and the consequent effects of a magnetic field but that work remains incomplete. There are three examples of the effects of magnetic fields on fluorescence from the molecules in the gas phase but as these lie at the limits of the boundaries of the present report we shall deal with them only briefly. The quenching of the fluores- cence of iodine ~apour’~,’~ is a result of a magnetic-field-induced dissociation of an excited state and arises from the ability of the applied field to mix the 0; state with the unbound 0 state.Similarly the fluorescence from nitrogen(1v) oxide (NO,) is quenched by a magnetic field.60 In that case the field appears to operate in the collisional quenching step NO;(B)+NO2 + 2N02 rate =B2[NO2][N0;] 55 J. L. Magee and J.-T. J. Huang J. Phys. Chem. 1972,76 3801. 56 B. Brocklehurst and T. Higashimura J. Phys. Chem. 1974,78,309. 57 P. W. Atkins and T. P. Lambert in press. 58 E. 0.Degenkolb J. I. Steinfeld E. Wasserman and W. Klemperer J. Chem. Phys. 1969,51,615. 59 L. A. Turner 2.phys. 1930,65 464. 6o R. Solarz S. Butler and D. H. Levy J. Chem.Phys. 1973 58 5172. 78 P. W.Atkins and T.P.Lambert and the Lorentzian field dependence of the overall fluorescence is reproduced by the inclusion of this rate step.It has been suggested that the excited states of NO are heavily perturbed by vibrational levels of the ground 2A1state and magnetic mixing of the quenched state with the ground state followed by radiationless collisional relaxation down the vibrational states of 'A1 would account for the observations.60 Collisions play an essential role because of the low density of states in the small molecules. Matsuzaki and Nagakura61a have reported equally interesting results on the gas-phase fluorescence from carbon disulphide. They recorded the time-dependence of the fluorescent emission from gaseous CS excited by a nitrogen gas laser and observed three band systems of which one was due to the 'Azexcited state. Particular attention was paid to the 'A2(0,5,0)vibronic state and its lifetime and integrated emission intensity were measured for applied magnetic fields of up to 1.5T.They found that both the lifetime and the integrated intensity are reduced by half when the field is ca. 1.3 T; this indicates that the non-radiative processes are enhanced by the magnetic field. They also found that the extrapolated collision-free lifetimes shortened with increasing field strength but the collisional quenching constant remains unchanged within the limits of experimental error. At low magnetic fields (<70 mT 700 G) the opposite effects were observed. Once again the effects can be accounted for in terms of magnetic-field-induced mixing the influence on a singlet molecule being possible because of the large spin-orbit coupling present.Very recent work61b reports virtually the same behaviour for glyoxal. 4 EIectrochemiluminescence Electrochemiluminescence has turned out to be rich in examples of magnetic field effects. The processes that occur are closely related to exciton mechanisms in the solid state and the way that these involve applied magnetic fields has received considerable attention and has been largely elucidated through the work of Mer- rifield,11,62,63 Frankevit~h,~~~~ and others.12 We shall give a brief description of the solid-state processes and then pass on to concentrate on theories and experimental results for fluids. The theory advanced by Merrifield62 and Johnson and Mer~-ifield~~ runs as follows. In a pair of colliding triplets there are nine possible spin states and these will occur with equal probability when the temperature is high.The rate of production of each of the nine composite states is therefore $kln2,where n is the concentration of triplet excitons. There are two possible outcomes of the collision one is scattering the rate being k-l and for which there are no collision rules. The other is annihilation with a rate that may be written k,S where S =I(Slt,hl)l is the modulus of the amplitude of the singlet component in the state labelled 1. It follows that the probability of annihilation from the Z'th composite exciton state is k,S:/[k_ +k2S:].The annihila- tion rate constant k is then the product of the collision rate constant and the total O1 A. Matsuzaki and S. Nagakura (a) Chem.Letters 1974,7,675;(b)Chem. Phys. Letters 1976,37,204. 62 R. E. Merrifield J. Chem. Phys. 1968,48 4318. O3 R. C. Johnson and R. E. Merrifield Phys. Rev. 1970 B1 896. 64 B. M. Rusin and E. L. Frankevitch Phys. Status Solidi 1969,33 885. 65 E. L. Frankevitch B. M. Rurnyantsev and B. I. Lesin Optics and Spectroscopy 1974,37,376. 66 E. L. Frankevitch and B. M. Rusin J.E.T.P. 1972,63,2015. The Efect of a Magnetic Field on Chemical Reactions annihilation probability 9 k =$kl 1 k2S:/[k_,+k2S?] 1=1 The qualitative manner in which k depends on the pair spin states can be seen by considering the two limiting cases. In one limit all nine states have equal singlet character; in the other only one state is a singlet. If the annihilation rates are denoted k(9) and k(l) respectively their ratio is given by the last equation together with the requirement that S? must sum to unity as This indicates that k is greater the more uniformly the singlet character is distributed over the nine pair states.The next problem therefore is the assessment of this distribution and its dependence on an applied field. The spin-Hamiltonian for a triplet exciton consists of two terms one is the Zeeman interaction the other the spin-spin interaction. In the zero-field case the spin vectors of each triplet are aligned along one of the principal directions of the zero-field splitting tensor and we speak of the T, Ty,and T states depending on the orientation of the spin with respect to these axes. The averall singlet state of two triplets can be constructed by analogy with the scalar r2=x2+y2+z2 and is (1/./3){~T,T,)+~T,Ty)+(T~T,)}.Thus at zero field three of the pair states have a singlet component (by inversion of this state). As the field is turned on the zero-field states are contaminated because the Zeeman interaction provides an alternative and increasingly important quantization axis. It follows that the zero-field states begin to mix. This disperses the singlet character over more states and so according to the above discussion the annihilation rate constant should increase in a magnetic field. This behaviour is confined to low magnetic fields where the spin-spin interaction although suffering competition from the Zeeman interaction is dominant.At high magnetic fields the Zeeman interaction is dominant and in the limit of infinite field strength the spins are quantized exactly along its direction. Three of the joint triplet states 10,0),1+1,-l) 1-1 +1) (labelled now as IMs,M>) have a total projection of 0 and so may contribute to a singlet. Nevertheless we have to take not? of the relative phasing of the If 1)states (just as in the case of the construction of singlets and triplets out of spin-; components Figure 1) and only the in-phase combination 1+1 -l)+ 1-1 +1) can contribute to the singlet. (This can be seen explicitly by examining the vector coupling coefficients.) It follows that in the high-field case there are only two states with singlet character and therefore a smaller annihilation rate constant than at zero field.The general dependence of the annihilation rate constant is therefore as fol-low~.~~~~~ At low fields it should increuse with increasing field pass through a maximum and then decrease at high fields to a value lower than the zero-field value. Detailed analysis of the degeneracies and level crossings involved also leads to the conclusion that the high-field annihilation rate constant should be anisotropic with minima in field directions for which the energies of the 10,O) and l*l 71) states are the same. These conclusions conform to experiment11T12 in the solid state and are a basis for explanations of processes in fluids. 80 P.W.Atkins and T.P. Lambert The Johnson-Merrifield scheme has been adapted for fluid solutions by averaging the interactions over a random but stationary en~emble.~' This is obviously a restricted view of the actual dynamical situation and the model based on mobile species has been examined by a different technique.68 The sequence of events treated by Atkins and Evans6' is as follows The triplet species diffuse from their points of generation by charge transfer from pairs of radical ions and encounter each other at some point in the fluid medium.Since each triplet has unit spin the total spin angular momentum of the colliding pair is 0 1,or 2 (giving respectively an overall singlet triplet or quintet). The overall singlet pair may pass on to give fluorescence because the energy transfer step is permitted by the overall spin. This is because the energy transfer takes 3A* +3A* to 'A* +'A and the latter can be only an overall singlet; therefore on the basis of the conservation of spin angular momentum during the energy exchange only the 1{3A* +3A*} can give rise to 'A* +'A.Neither the overall triplet 3{3A* +3A*} nor the overall quintet 5{3A* + * 3A } can redistribute their energy to give '{'A" +'A} without violating spin conser- vation and so pairs in these overall states survive the encounter. There is in fact some possibility that the overall triplets and quintets do change into an overall singlet during the encounter. This can come about because of the different spin-spin dipolar interactions within each triplet (different not because the triplets are not identical but because they are in general at different orientations to the applied field and compete with its quantization direction).The overall quintet can switch into the singlet (the triplet-singlet switch is forbidden by symmetry for this mechanism -the spin-spin interaction is of second rank) and do so with a rate ps(t) =&(1 i-c)D2I,'dt(1+2 cos wt+2 cos 2ot)exp (-t/~& (7) where o =p,B/A is the Larmor frequency of the spins D the spin-spin interaction within each triplet and 7R the rotational correlation time of the pair (c = 1 if they rotate as though stuck together; c =0 if the two triplets rotate independently). The cos ot and cos 2wt terms represent the mixing of the singlet with the M =*1 and M,=*2 states of the quintet and we. see that they contribute less to the integral at high fields (because they oscillate to positive and negative values) than at low fields.This is the effect of the removal of degeneracy already described in the earlier sections. At short times the integrand varies as 1-02t2 and so the crossing rate is inhibited by a field. The expression for P,(t) shows that the magnetic field effect vanishes when the triplets rotate rapidly (because the exponential term quenches the integrand if TR is short) the physical reason for this being that the spin-spin interaction averages to zero and ceases to compete effectively with the Zeeman interaction. The difficulty with this mechanism is that the two colliding triplets might remain together for only a short time and the interconversion rate be so slow that only an insignificant amount switches into the singlet.What we seek is a way of permitting a long interval during which the spins are able to rephase significantly. The same requirement is needed in chemically induced magnetic polarization experiments,' 67 P. Avakian R. P. Groff R. E. Kellogg R. E. Merrifield and A. Suna 'Organic Scintillators and Liquid Scintillation Counting' Academic Press New York 1971,499. 68 P. W. Atkins and G. T. Evans Mol. Phys. 1975,29,921. The Effect of a Magnetic Field on Chemical Reactions 81 where the spin rephasing is allowed to take place during a diffusional trajectory which has a high probability of bringing the two components back to a re-encounter configuration. We therefore consider the following sequence of events.68 During the initial encounter the two triplets may fluoresce if they are relatively singlet phased but will survive as individual triplets if they are overall triplet or quintet.The encounter pair breaks up and the two triplets drift apart. Although separate they still possess their initial phasing but over the whole sample there is a depletion of overall singlet-phased pairs. During the translational diffusion that takes them apart the two triplets rotate. This rotation is a very efficient cause of spin relaxation on account of the strong anisotropic spin-spin dipolar interactions within each triplet. (A few trriplet spin-relaxation times in fluids have been and found to lie in the range 2-20 ns.) The triplet spins relax independently.When therefore their diffusive motion brings them back into contact (or whatever a ‘re-encounter’ involves) there is some probability that they have replenished the depleted overall singlet phasing and have regained more or less the thermal equilibrium distribution which had been distorted by the first encounter. If overall singlet phasing has been replenished contact between the two species may lead to energy transfer and thence to fluorescence. The point to emphasize at this stage is that the observed fluorescence is the totality of emission from the first encounter and the re-encounter and the latter can contribute more effectively if spin relaxation has occurred before it takes place. The magnetic field plays its role during the diffusional excursion.Efficient spin relaxation depends not only on the strength of the perturbative coupling (for example the anisotropy of the dipolar interactions and in particular the spin-spin interaction) but also on the rate at which they are modulated by molecular motion (e.g. molecular rotation). Relaxation between different m states is most efficient when the relaxing perturbations are modulated at a rate comparable to the Larmor frequency. If the Larmor frequency is changed by an alteration of the strength of the applied field the rela,xation rates will change. This is the core of the magnetic field effect on this type of fluorescent reaction the field changes the relaxation rates and so the extent of replenishment of the singlet is changed. This change affects the probability of energy transfer on a re-encounter and so the fluorescence intensity depends on the applied magnetic field.These ideas have been expressed quantitatively68 and the following is a brief outline of the calculation. In the beginning there are two independent triplets with their spins at thermal equilibrium. The state of each is described by the thermal equilibrium density matrix a*.Immediately before the first encounter both triplets are described in this way and the overall state at that instant is p(0J =a*(A)g*(B). Immediately after the collision the overall density matrix is p(0,). This differs from p(0-) in as much as some of the overall singlets have been eliminated. If Psis an operator that selects singlets and A is a parameter that measures the effectiveness with which an overall singlet undergoes energy transfer we can write the final state of the triplet pair just as it breaks up as p(0,) =(1-APs)p(O-).From this point the states of the two triplets evolve independently and each one obeys the equation of motion a(t) =i[u(t),W+ Ru(t) (8) 69 P. W. Atkins A. J. Dobbs and K. A. McLauchlan Chem. Phys. Letters 1974,29 616. P. W.Atkinsand T.P. Lambert 2is the Hamiltonian representing the effect of the applied field and R is an operator that takes relaxation into account. This equation can be solved for each triplet using as initial conditions the joint singlet-depleted density matrix p(0,). In this way it is possible to calculate the probability Ps(t) that the pair of triplets is in an overall singlet at some t>0+.In order to contribute to the fluorescence the two triplets must re-encounter each other at some stage. The probability that they do so G(t),can be evaluated on the basis of a diffusion equation and the total contribution to the fluorescence is determined by the product of probabilities P,(t)G(t) integrated over all possible excursion times. Explicit expressions are given in the original paper,68 and in the limit of rapid molecular motion in a strong magnetic field one finds I(B)/I(O)= 1 -0.61(-)Dd(+,s) A 1-A (9) where D is the spin-spin interaction (zero-field splitting) rR the rotational correla- tion time and r the translational diffusion correlation time. This is the asymptotic behaviour and it predicts that the intensity falls off with increasing field as observed.The role of stable doublet quenchers is easy to explain qualitatively but much more difficult to deal with quantitatively. Once again the solid-state mechanisms are a guide to those operating in the fluid if the rudiutionless quenching by the doublets is inhibited by the application of a magnetic field the fluorescence radiation will be enhanced. We shall describe the qualitative model but not go as far as describing the actual calculation68 (which follows much the same scheme as that outlined above). Consider the collision of a doublet (S= 5) and an excited triplet (S= 1).Their overall spin may be either doublet (S= +) or quartet (S =;). If it is the former radiationless energy reorganization from 2{3A*+ 'Q} to 2{1A+ 'Q} may occur with- out change of total spin angular momentum but 4{3A*+ 'Q} may not so reorganize.When the initial encounter pair breaks up it is depleted in overall doublet. The two components diffuse apart but have a significant re-encounter probability. During the diffusion spin relaxation replenishes the overall doublet and so on re-encounter the quenching is more likely to occur than if no relaxation had occurred. The spin relaxation depends on the Larmor frequencies involved (this time of both doublet and triplet species) and so it depends on the strength of the applied field. It turns out that the significant relaxation is inhibited by the applied field and so the radiationless quenching is also inhibited. That is just the situation necessary in order to lead to enhancement of the fluorescence because more triplets survive doublet encounters and live long enough to meet triplet partners.These triplet encounters are also field dependent (as described earlier) but the observed increase in fluorescence indicates that the quenching responds to the magnetic field in the dominant way. The calculational d@culty in the quantitative formulation of the model is the need to treat it as at least a three-particle collision (doublet triplet and another triplet). Nevertheless the overall effect has been estimated and the observed increase in fluorescence intensity with field strength can be accounted for.68 There are of course many loose ends in both calculations and there is room for a much more detailed analysis of the quenching sequence.Furthermore the descrip- tion of the processes going on during the encounters themselves remain to be unified into a single coherent calculation rather than remaining in their present disjointed The Effect of a Magnetic Field on Chemical Reactions 83 form. When this is analysed in more detail the type of argument used by Perisamy and Santhanam7' on the Marcus description of the electron-transfer step may play a role in the overall scheme. The type of experimental information available can be illustrated by the following selection of papers. For instance Faulkner and Bard71 examined the magnetic field dependence of the chemiluminescence from electron transfer reactions involving the ion-radicals of a variety of aromatic hydrocarbons.In particular they studied the reaction of the radical cation formed from NNN'N'-tetramethyl-p-phenylenediamine (Wursters' Blue WB henceforth) with the anion radicals of anthracene and 9,lO-diphenylanthracene (DPA). From the standard electrode potentials it is clear that the energy available from the ion-radical annihilation involving WB' and a hydrocarbon radical anion is insufficient to produce the hydrocarbon in its first excited singlet (such systems are called 'energy deficient'). This excited state is attainable from the reaction between DPA' and DPA- (an 'energy sufficient' system). In a magnetic field the authors found that for solutions containing WB the emission intensity from the excited singlet increases with applied field (by ca.20% in 0.6 T for anthracene-WB) but in the solution containing only DPA the field had no effect on the emission intensity. Faulkner and Bard draw two conclusions from these first that paramagnetic species are involved in at least one rate-determining step for light emission from the energy-deficient system and that the rate of that step is field- dependent and secondly either that no paramagnetic species are involved in the rate-determining steps for fluorescence in the case of DPA alone or that paramagne- tic species are involved but that behaviour is unaffected by the field. Furthermore unless one supposes that the magnetic field can influence the diffusional characteris- tics (e.g.the diffusion constants) the rate of a diffusion-controlled reaction cannot be altered by the field in the manner observed and the rate-determining steps for the energy-deficient system studied are probably not diffusion controlled.The DPA energy-sufficient system however may or may not have diff usion-controlled rate- determining steps. The results for the energy-deficient system were rationalized by supposing that if the hydrocarbon triplet is formed in the radical annihilation step then triplet-triplet annihilation leads to the first singlet-excited state by the energy-exchange process discussed in the earlier part of this section. In contrast the reaction involving annihilation of DPA' and DPA- is believed to result in the direct formation of an excited singlet DPA molecule.The magnetic field dependence occurs as we have already described and the increase in fluorescence intensity is compatible with the inhibition of radiationless triplet quenching by the presence of stable doublets (WB'). It has also been pointed out in support of this mechanism7' that Parker et aZ.72have provided substantial evidence to support the view that triplet-triplet annihilation is not generally a diff usion-controlled process for aromatic hydrocar- bons and might occur by means of a resonance energy transfer mechanism that can operate over a great distance. 'O N. Perisamy and K. S. V. Santhanam Chem. Phys. Letters in press. 71 L. R. Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91 209. 72 C. A. Parker in 'The Triplet State' ed. A B. Zahlan Cambridge University Press 1967.84 P.W.Atkins and T.P. Lambert This early work was followed by a series of studies on related systems. In the case of anthracene in dimethylformamide (DMF)73 for example it was observed that the fluorescence intensity decreased with increasing field and was proportional to the square of the incident excitation intensity. The intensity of delayed fluorescence under steady-state illumination is expected to obey the expre~sion’~ I = $dfka(1a+t7)* (10) where +fis the fluorescence efficiency k the annihilation rate constant I the rate of light absorption 4 the triplet formation efficiency and r is the triplet lifetime. The three quantities 4f,+t I,,it was argued,73 are unlikely to be field-dependent because they are properties of diamagnetic materials (although the peculiar properties of carbon disulphide referred to above indicate that that may be a false argument in special circumstances).In support of this view Faulkner and Bard draw attention to solid-state results which show that magnetic fields do not affect the intensity of the prompt fluorescence from crystalline anthracene. The concentration dependence of the fluorescence and its magnetic field dependence allows this argument to be taken further. In solutions containing an anthracene concentration of > ca. mol dm-3 anthracene triplet lifetimes are shortened drastically by self- or impurity-quenching. At lower concentrations the lifetime is virtually constant. Any field dependence of the lifetimes would probably be concentration dependent in the range where the quenching term begins to be significant in determining the value of 7.Thus the field effect that arose from this source would be expected to be concentration dependent in this range. Since the experimental results show that the field variation is indepen- dent of concentration in the range where the lifetime begins to change markedly it is most unlikely that the lifetime r is the field-dependent quantity. Faulkner and Bard also go on to eliminate 4t as the field-dependent quantity.73 They examined the fluorescence of a solution of 5 X lo-’ mol dm-3 anthracene plus 7 x mol dm-3 phenanthrene in DMF and found that the field dependence of the anthracene-delayed fluorescence was the same as in the absence of the phenanthrene sensitizer.In this case the anthracene triplet is populated by energy transfer rather than intersystem crossing from anthracene singlet and therefore +t cannot be the field-dependent factor. The elimination of 7 4f,I, and 9 as the field-sensitive quantities leaves only k, and the theoretical reasons for its dependence have already been explained. The role of doublet species in modifying the field dependence of the delayed fluorescence has also been elucidated74 and as indicated previously centres on the suggestion made by Hoytink7’ that ion radicals might be effective triplet quenchers in fluid solution. Faulkner and Bard74 measured the intensities and lifetimes of the delayed fluorescence from anthracene and WE3 perchlorate in methylene chloride solution.The effectiveness of WB’ as a quencher of anthracene triplets was indicated by the shortening of their lifetimes. For example a 1.8X mol dm-3 WB perchlo-rate and 8x lo-’ mol dm-3 anthracene solution showed a delayed fluorescence lifetime of 1.4ms in contrast to a lifetime of 6.4 ms in the absence of WB’. The quenching rate constant was ca. 2 X lo9dm3 mol-‘ s-’ which is comparable to the triplet-triplet energy-transfer rate constant in solvents of similar viscosity. As for the 73 L. R. Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91,6495. 74 L. R.Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91,6497. 75 G. J. Hoytink Discuss. Faraday Soc. 1968,45 14. The Efect of a Magnetic Field on Chemical Reactions 85 magnetic field effect it was found that the fluorescence intensity was enhanced (by ca.2% in 0.8 T) as would be expected on the basis of the theory already explained. The longer lifetimes that result from this effect dominate the opposing effect on the annihilation rate. The results also suggest that the quenching rate is not entirely diffusion contr~lled,~~ and the authors suggest a tentative upper limit of 2.6~ 10" dm-3 mol-' s-' on the rate constant. Magnetic field effects on the fluorescence intensity from anthracene DPA rubrene 1,3,4,8-tetraphenylpyrene (TPP) and fluoranthrene have also been reported.76 Enhancements of the emission to the extent of up to 27% were noted for energy-deficient oxidations of anthracene DPA rubrene and TPP anions by WB+ for the energy-deficient oxidation of fluoranthrene anion by the radical cation of 10-methylphenothiazine and for the energy-deficient reduction of the rubrene radical cation by the p-benzoquinone radical ani~n.'~ In contrast (but in conformity with theory) no field effect was observed for the fluorescence arising from the energy-sufficient DPA'/DPA- reaction.The field enhanced the luminescence from the reaction between the rubrene anion and cation radicals but had no effect on the TPP anion and cation reaction. All these results are compatible with the inhibition of the triplet-triplet step by a magnetic field the inhibition of the triplet-doublet radiationless quenching step and the absence of involvement of triplet species in energy-sufficient systems.The rubrene'/rubrene- and the TPP'/TPP- systems are marginal cases and it was suggested76 that the former gives rise to luminescence predominantly uia the triplet mechanism but the latter is essentially energy- sufficient and forms the emitting state directly. The paper includes a useful list of reaction enthalpies and spectroscopic data and rationalizes the magnetic field effects by reference to the Johnson-Merrifield solid-state mechanism. Oxygen is an obvious candidate for the examination of magnetic field effects on triplet species and its role in the production of delayed fluorescence from anthracene and pyrene in fluid solution has been studied.78 The triplet quenching can be represented by the simple scheme 3~+3~2 + 'M+~O~ and its rate should be field dependent.The authors observed that the usual decrease of fluorescence intensity with applied field was modified when oxygen was admitted to the solution. At first no delayed fluorescence signal was detected but after several minutes its intensity increased to a measurable level. The same kind of time- dependent increase has also been noticed in solid samples and is probably caused by oxygen depletion arising from the formation of a transannular peroxide. The delayed fluorescence signals from both anthracene and pyrene increased with increasing field indicating a magnetic inhibition of the quenching reaction just as in the case of radical ion quenching. On the other hand in acetonitrile solution no change in the fluorescence was observed for either species although oxygen quenching was shown to be occurring by the decrease in lifetime of the aromatic triplet.Further papers in this series deal with a series of related observations. Onen 76 L. R. Faulkner H. Tachikawa and A. J. Bard J. Amer. Chem. Soc. 1972,94,691. 77 H. Tachikawa and A. J. Bard Chem. Phys. Letters 1974,26 10. 78 H. Tachikawa and A. J. Bard J. Amer. Chem. Soc. 1973,95 1672. 79 C. P. Kesthelyi N. E. Tokel-Takvoryan H. Tachikawa and A. J. Bard Chem. Phys. Letters 1973,23 219. 86 P. W.Atkins and T.P. Lambert examines the effect of the supporting electrolyte concentration and the magnetic field effect on a 9,lO-dimethylanthracene (DMA) -tri-p-tolylamine (TPTA) system dissolved in tetrahydrofuran (THF).The magnetic field enhanced the fluorescence for all concentrations of the supporting electrolyte tetra-n-butylammonium perchlo- rate (TBAP) and extrapolation to zero TBAP concentration gave results in accord with those of Weller and Zachariasse." Although quenching of intermediates by TBAP ions might be important the authors believe that the effect on the reaction enthalpy as the concentration of TBAP decreases is probably more important.This increase in AH can be traced either to a decrease in the extent of formation of the ion pairs (TBAP)'. -.(DMA)- or (TPTA)'. * .ClO (formation of ion pairs would facili- tate the oxidation of TPTA and the reduction of DMA and hence reduce AG* for the ion annihilation reaction) or to a change in the nature of the solvent system with an effective increase in relative permittivity at higher TBAP concentrations.Thus at low TBAP the reaction is strongly energy deficient and proceeds through the magnetically sensitive triplet annihilation route but at high TBAP concentrations the reaction may proceed through the direct production of singlets and be less magnetically sensitive. The effect of solvents has been by measuring the emission intensity of rubrene ions generated electrochemically. The intensity increases with applied field and the effect is strongest when the solvent is DMF and then progressively weaker along the sequence acetonitrile benzonitrile THF. The results were interpreted" in terms of a model in which the electron-transfer route produces both singlet and triplet excited states of rubrene with the triplets being quenched by radical ions or oxygen The authors examined the energetics of the reaction on the basis of Marcus's theory of electron transfer and suggest the possibility that two triplet states may be formed in the electron-transfer step.Wyrsch and Labhart,82 Tachikawa and Bard,83 and van Willigen46 have all examined the delayed fluorescence from monomer and excimer species. Wyrsch and Labhart investigated 172-benzanthracene in ethanol van Willigen investigated pyrene in 3-methylpentane and in ethanol and Tachikawa and Bard pyrene and 172-benzanthracene the pyrene-TMPD system and the 9-methylanthracene- TPTA system. Wyrsch and Labhart observed different magnetic quenching behaviour of the monomer and excimer emissions and concluded that there is no common triplet annihilation process generating the two types of fluorescent species.On the other hand van Willigen observed the same behaviour when 3-methylpentane was the solvent. van Willigen ascribes his results to a scheme proposed by Stevenss4 which involves the reaction sequence -B 'M*+ 'M* '&*+ 'M0 'Mg+'Mo+ 'D* '&*+'M -D 'D* A. Weller and K. Zachariasse Chem. Phys. Letters 1971 10 424 590. H. Tachikawa and A. J. Bard Chem. Phys. Letters 1974,26 246. 82 D. Wyrsch and H. Labhart Chem. Phys. Letters. 1971,8 217. 83 H. Tachikawa and A. J. Bard Gem. Phys. Letters. 1974,26 568. 84 B. Stevens Chem. Phys. Letters. 1969,3 233. The Eflect of a Magnetic Field on Chemical Reactions 87 The first step is common to excimer ('D*)and excited monomer ('M,*) formation; it is a spin-selective step and therefore the magnetic field ought to affect the two fluorescent intensities equally.He attempts to account for the discrepancy between the two sets of results on two grounds. First that the mechanism depends on the species involved. Second and much more speculatively that the exciplex formation step (the second of the three steps in the scheme above) depends on the relative orientations of the species orientations that are influenced by the magnetic field. It is hard to believe that this could be the explanation even at low temperatures where rotational correlation times are quite long but it is at least an interesting suggestion.Tachikawa and Bard observe that the magnetic field effects on the excimer and monomer delayed fluorescence intensities are essentially the same for pyrene in cyclohexane and for 1,2-benzanthracene in cyclohexane and also conclude that there must be a common precursor in these systems. van Willigen46 has also reported a peculiar field dependence when ethanol is used as solvent. At low temperatures the monomer and dimer fluorescences increase with magnetic field. He suggests that the reason might lie in the formation of doublet radicals in the system and that these act as triplet quenchers (the remark on p. 75 arose from this suggestion). Magnetic field effects have also been observed in tetracene-TMPD," this energy- deficient system showing an intensity increase of up to 19.5% in fields of up to 0.75 T and the results were interpreted as evidence for the production of triplet tetracene by charge transfer between tetracene radical anion and TMPD cation.The delayed fluorescence of carbazole in DMF with t-butylammonium iodide as supporting electrolyte shows a sharp increase in intensity up to ca. 0.4 T and this is followed by a gradual decline.86 Perisamy and SanthanamS7 have also examined the elec- trochemiluminescence of mixed systems in which phenanthrene and perdeuteriated phenanthrene provide the radical anion and propose a triplet-triplet annihilation step on the basis of the magnetic field effect observed. A magnetic field effect-on an energy-sufficient system has also been reported." The authors studied the rubrene tetracene phenanthrene and cation-anion systems and found an increase in fluorescent intensity of the order of 10% in 1T.The overall scheme can be summarized by the sequence 3M*+3M* -+'M*+M; 'M* + M+hv t (c) 'M*-3M*; 'M* -+ M+hv Step (b) is the conventional magnetic-field-sensitive step but triplet species gener- ated by the singlet step (c)may also take part in it and give rise to an overall magnetic field dependence especially if step (c)is itself magnetic field dependent. Thus if a magnetic field can inhibit the crossing involved in step (c)more of the initial singlets can produce fluorescence. H. Tachikawa and A. J. Bard Chem. Phys. Letters. 1973 19 287. 86 K. S. V. Santhanam Canad. J. Chem. 1971,49,3577. 87 N.Perisamy and K. S. V. Santhanam Canad. J. Chem. 1975,53 76. 88 N. Perisamy S. J. Shah and K. S. V. Santhanarn,J. Chem. Phys. 1973,58 821. 88 P. W.Atkins and T.P. Lambert Finally we report an interesting application of this type of magnetic field effect on a solid polymer (which is as close to true solids as we allow ourselves to come in this review). Avakian et uLg9have found that the rate of fusion of triplet exciton pairs in polymers such as poly(vinylnaphtha1ene) can be changed by a magnetic field of a few kilogauss. The delayed fluorescence following exciton generation was found to increase monotonically to 3% above the zero-field value at 0.09 T (900 G),and then to drop back to its zero-field value at 0.4 T. The emission continues to decrease to an asymptotic value ca.2% below the zero-field value when the field reaches 1.O T. This behaviour contrasts with the observation of a similar phenomenon in naphthalene at 77 K where the low-field peak (of 6%)occurs at 0.06 T the zero-field value is passed at 0.17 T and the saturation value (of -12%) is attained above 1.0 T. The authors explain these observations in terms of the local orientations of the naphthalene units along the polymer chain and reach the significant conclusion that they are spread over a range of orientations such that S:-S; averages to zero but that the normal axes of each naphthalene unit remain approximately aligned. This magnetic field dependence therefore constitutes a novel method for investigating the conformation of polymer molecules.Essentially the technique consists of deducing the fine- structure parameters D and E from the magnetic field dependence of delayed fluorescence Deviations from the known parameters of the isolated molecules can then be accounted for by assuming a conformation and then allowing for the averaging of differently ordered side-groups by the exciton motion. 5 Conclusion It should be clear at this point that there are many well-authenticated examples of the effect of magnetic fields on chemical reactions; effects that range from the inhibition of spin-multiplicity crossings and the consequent effects on fluorescent activity (and presumably on reactions themselves) to the actual modification of the concentra- tions of the product species.A magnetic field is potentially an influence on any reaction involving the change of multiplicity of some intermediate and whether that change of multiplicity leads on to a physical consequence (fluorescence) or to a chemical consequence (cage escape reactions) is not of itself of interest. The rate constants of all the steps in the overall scheme must be appropriate but in many cases that is happily the case. So many reactions involving doublet and triplet (and presumably higher multiplets) are magnetically sensitive that the best advice a theoretician can give to the experimentalist with a likely candidate is try it! Although we have emphasized the academic and theoretical aspects of magnetic field effects it should be clear that they may have considerable industrial significance.We shall have to wait in order to see whether this will emerge through their application to polymerization reactions or to the separation of nuclear isotopes or simply to the warping of a reaction in favour of one stereoisomer or product of a radical reaction. Note added in proof. Although an earlier analysis of the singlet and triplet photosen- sitized decomposition of dibenzoyl peroxide showed no field effect,” a new study using much higher fields’’ has shown that there is one. 89 P. Avakian R. P. Groff,A. Suna and H. N. Cripps Chem. Phys. Letters 1975,32,466. 90 H. Sakuragi M. Sakuragi T. Mishima S. Watanabe M. Hasegawa and K. Tokumaru Chem. Lerfers 1975,8 231. 91 Y. Tanimoto H. Hayashi S. Nagakura H. Sakuragi and K.Tokumaru in press.