Ionization and Excitation in Non-Polar Organic Liquids Sanford Lipsky University of Minnesota, Minneapolis, MN 55455 Minneapolis, MN 55455 A number of comprehensive reviews concerned with the effect of high-energy radiation on organic liquids were published about ten years ago ( 1 - 4 ) . Rather considerable progress has been made since then, most significantly in our understanding of the nature and behavior of an electron in these liquids. Our purpose here is to describe some of this progress to an audience who have not followed too closely the development of this area. Wherever possible reference is made to articles and reviews more detailed and of wider range than is appropriate here.,Our emphasis will he on the nature of ionized and electronically excited states but will be confined to features having some relevance to radiation chemistry. The first two sections develop some very elementary concepts. Two excellent review articles by Fano (5) and by Franck (6)should be consulted for more detailed discussions.
I. The General Nature of Excited and Ionized States The internal energy states of a molecule are most broadly classified as being either electronically hound or ionized. The demarcation is determined by the minimum energy required to eject the least tightly bound electron (i.e., the first ionization potential). Below this energy lies an infinity of states with discrete electronic energies. The lowest of these is the ground state which may be considered to he indefinitely stable, whereas all others, the excited states, are intrinsically unstable and under isolated conditions will decay either by dissociation or by the emission of light. Above the first ionization potential lies a continuum of ionized states each corresponding to a free electron (with some arbitrary energy equal to the energy initially imparted less the ionization energy) and an ion in its ground state. This continuum is overlapped by an infinity of other ionization continua each corresponding to the ion now in some vibrationally andlor electronically excited state plus a free electron. Overlapping these continua are still other ionization continua corresponding to the production of multiply-charged ions and their concomitant free electrons. If the molecule is supplied with enough energy to generate several different ionized states corresponding, for example, to the ion in some excited state and a free electron with some kinetic energy, or to the ion in its ground state and the free electron with correspondingly more kinetic energy, then quantum mechanics predicts a certain probability for each event. These probabilities will depend on the nature of the molecule and on the energy imparted. The ionization of an atom or molecule may occur either immediately subsequent to the absorption of the requisite energy or after some delay. In the former case one speaks of a direct ionization whereas otherwise the process is referred to as an auto-ionization. In an auto-ionization, the promoted electron, although possessing enough energy to escape the field of the ion, is delayed in its escape by times usually of the order of 10-l2 to 10-14 sec (although much longer times too have been reported) (7). This very metastable situation is sometimes referred to as a resonance. The origin of the delay is, of course, best described via an appropriate quantum mechanical description but a crude picture can be developed in a few cases. In what is referred to as a "Feshhach resonance," two electrons are simultaneously promoted permitting them (if they both can penetrate sufficiently into the attractive ion core) to experience a stronger attraction to the nucleus and therefore to remain bound until their mutual repulsion forces the escape of one of them. In a "shape resonance" the delay
is caused by promoting a single electron to a state of high angular momentum. Conservation of aneular momentum then generates an effective barrier that blocks the passage of the electron to infinitv. Thus if the difference between the enerev .." imparted to the ilectron and the ~onizationpotential is less than the height of this barrier the onlv m w w for electron egress is via tunneling through the barrier. The consequence is again a delay in the electron escape. For both types of resonance the delay is strongly dependent on the energy imparted to the system and is maximal onlv a t certain critical energies. At these critical, or resonant, energies, the cross-section for auto-ionization may become much larger than for direct ionization and thus the spectroscopic signature of auto-ionization is usually a sharp structure (with some characteristic line shane) in the total ionization cross-section that suoerimooses on background due to direct ionization, the crosi-section for which is usually more slowly dependent on excitation energy. If the delays are sufficiently long and decay channels other than electron eiection are available, the ionization nrocess mav be totally thwarted. In isolated atoms, the only ocher possibie decay would he by photon emission, but this usually requires times much longer than the time for auto-ionization. In molecular systems, dissociation into neutral fragments often prevails over electron ejection (7,8). A molecular resonance which for one reason or another does not auto-ionize has been termed a "superexcited state." (9). The energy of a hound state of an atom is often conveniently specified in terms of the lowest energy required to eject an electron from that state. When specified this way, the energy is referred to as the term value of the state. For H atom, as is well known, the term value of the state with principal quantum n is given by T" = En
a
, n
(1)
where EH = 13.6 eV is the ionization potential of the ground state. For more complex atoms, and even for molecules, a similar equation is obeyed for states involving the promotion of a single electron with an energy close to the ionization threshold (10).This, of coune, is not particularly unexpected. For an electron with very large average distance from the center of mass, the force it feels will be very similar to that experienced by a hydrogenic electron so long as the electron never penetrates so deeply into the core as to lose the effective shielding of the nuclei by the inner electrons. For electrons promoted into states of high angular momentum (1 = 1,2, etc.) conservation of angular momentum will indeed prevent the electron from approaching the core too closely whereas for 1 = 0 (i.e., S ) electrons, penetration can he quite severe even for large average distance from the center of mass. Thus eqn. 1 is usually written for complex atoms and molecules as
EH T" = (n
- 61)'
(2)
where 6 , is a parameter referred to as the quantum defect and is approximately independent of n but becomes smaller as 1 increases. Equation 2 is referred to as the Rydberg equation, and excited states of atoms and molecules whose term values fit this equation are called Rydberg states. Alternatively, a Rydberg state may be considered as one involving a single electron promoted to sufficiently large average distance from Supported in part by the U. S. Department of Energy. Volume 58 Number 2
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the remainder of the system to permit satisfaction of eqn. 2. The spatial extent of a Rydberg state can he estimated by using a well-known hydrogenic equation for the average distance, ( r ) , of the promoted electron ( l l ) , i.e.,
- l ( 1 + I)] where a. is the Bohr radius and n* = n - 4, (r)= ;
(3)
[(n*)Z
tum numhers for the two electron system, i.e., S = 1and S = 0, and add each of them in the manner previously prescribed to the S:z = ll', for the third electron. Thus for three electrons. S = 3/2ia &artet state) or lI2 ( a doublet state). If the ground state of a molecular ion is doublet. then all one electron oromotions can be either doublet or quartet. But starting with a singlet molecule, a quartet state can be generated only by promoting two electrons, one of which is ejected. However, quantum mechanical considerations that determine the prohability for generation of a particular quantum state by absorption of energy from a light wave or from the electric field of a fast-moving charge particle are such that simultaneous promotion of two (or more) electrons is a much less nrobable event than a one-electron oromotion (11). Addii from a low density of initial states to ahighe; density of final states (i.e., to increase its entropy). The rates of internal conversion and intersystem crossing are sensitive to the energy separation AE between the two combining electronic states. In the statistical limit the rate appears to decline exponentially as AE increases. Since for aromatics the largest AE usually occurs between the ground (So) and first (S1) electronic singlet states, the SI -So internal conversion rate is normallv small and comparable to the S1 So radiative constant (i.e., =lo7-109 sec-'1. Since the aromatic t r i ~ l estates t (hoth the lowest, TO,and the next highest, TI) lie ;sually much closer to SI than does So, the SI T I and/or SI To intersvstem crossings, even with the proh%ition imdosed by the fact that AS 2 0, remain com~ e t i t i v with e internal conversion and are of comparable rate (18,ZO). For internal conversion from higher excited states of aromatics much less is known, but S, S,-I internal conversion rates should generally be much larger than for SI So and to dominate any intersystem crossing rate from S,. This seems to be borne out by the few studies reported (21). Thus, for example, for p-xylene in isooctane solution, the S3 S p and S2 S1internal conversion rates have been reported to be 2.5 X lot4 sec-I and 1.0 X l O I 3 sec-I, respectively, and similarly large rates have been reported for the total decay constant of naphthalene, pyrene, and some other methylhenzenes. In all of these cases there appears to be no evidence for intersvstem crossine other than from the lowest sinelet state. A ~ electronicall; I excited states with energy higher than that of the weakest chemical bond may dissociate. For complex molecules this dissociation, however, is often slow (i.e., k 2 lot2sec-') unless the excited state has no stable position with respect to some nuclear motion (so that when the nuclei adopt thismotion there is no restorina force) or has such adisparate equilibrium geometry from t h i ground state that excitation to the state leave the nuclei with enouah potential energy to dissociate a bond. In the former case, the-state is referred to as repulsive. If the transition that generates the repulsive state or the strongly distorted state, si<aneously generates the dissociative motion, then dissociation times may he as short as 10-l4 sec. However. more usuallv for a c o m ~ l e xmolecule. it is some other motion which is co;pled strongly to the elec: tronic transition and dissociation is, therefore, subsequent to a redistribution of vibrational energy. In such cases, vibrational relaxation by collisions with other molecules may be expected to, a t least partially, thwart the dissociation. To illustrate some of these ideas, we consider the case of n c ~ liquid t cyclohexane. At photon rx$.ir;*timc.nergies of both X 1 e\' (1'2)and 7.6 eV (23,. H:, is produced with qil:ilirum yield of essentially unity. The distribution of other products (cyclohexene and bicyclohexyl) suggests production mainly via molecular elimination. The fluorescence of cyclohexane has been observed also for excitation a t 8.4 eV and 7.5 eV with quantum yields, respectively, of 3.5 X 10Wand 8.8 X (24). The fluorescence appears to come from the same state.
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Thus 40% of the molecules must evolve from the 8.4 eV state to the 7.5 eV state. To reconcile this with the invariance of the Hz quantum yield, it is most plausible to assume that a t least 40% of the dissociation occurs suhsequent to the transition from 8.4 eV to 7.6 eV. But 7.6 eV is only -0.6 eV above the cyclohexane optical absorption threshold and this energy is 5 thermodynamically insufficient for the reaction (by ~ 0 . eV). Accordingly, a t least 40% of the Hp production must occur from a lower electronic state than is responsible for the fluorescence. ~~~~~-~~~Although ~~" the nature of this state is not vet known. it is most plausibly not the triplet (which would likily not have enough vihrational energy) but rather some high vihrational level of the ground state populated via internal conversion from the first singlet. Clearly, this would possess so much internal vihrational energy that dissociation might occur sufficientlv rapidly to ureclude the effect of other molecules to relax the riqui&e Gihrational energy. The last unimolecular decay channel which properly should he considered here is one that involves an internal rearrangement of the nuclei to generate an isomeric species (25). This is expected to be a relatively slow process in view of the large nuclear distortions that are required. Most bimolecular reactions involvine excited states in the radiation chemistry of neat liquids involve a reaction between the lowest excited state of the solvent and a solute present a t some concentration c. Whatever the nature of the reaction, it usually leads to a quenching of solvent fluorescence and thus can be monitored hy observing the intensity, I, of the fluorescence as a function of c. Almost invariably this function is of the Stern-Volmer form, i.e., lo/I = 1
+ Kc
r
r
r
E
4nRDL'
(5)
where D is the mutual diffusion coefficient and L' = 6.02 X 1020. For henzene, toluene, and p-xylene as solvents, one finds for a wide variety of solutes that K is essentially the same whether the aromatic is excited outicallv into SI,or into higher states, Sn(27). The immediate'implication is that in these liquids, internal conversion from S, to S1is too rapid for reaction of S, with the solute. The magnitude of K, taken together with measured values of k z (for Sd, are in general agreement with the predicted values of r,although R tends to underestimate the geometric encounter radius by a factor of -2-3. In part this isdue to the crudeness of the assumption that there is a unique R rather than a distribution with different reaction probabilities. However, a more important contributor to the discrepancy is the neglect, in this simple treatment. of enerev mieration within the solvent. There exist two&iict mechanisms by which energy can mierate within a hvdrocarbon liquid. The first of these is a and is clas~icallyvery similar to the "lo&-range" non-radiative exchange of energy between two identical electrical oscillators located within their near-zone dipole fields. The first quantum mechanical application of this idea to the non-radiative transfer of energy between two nonidentical molecules was made by Forster in 1947 (28), assuming that (i) the two molecules were sufficiently far apart that the major interaction hetween them was dipole-dipole and (ii) the interaction was sufficiently weak so as to leave 96
Journal of Chemical Education
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(so long as c remains less than 1.10-2 M), l o is the solvent fluorescence intensity in the ahsence of solute, and K is a constant referred to as the Stern-Volmer constant. As is simply verified from a steady state solution to the pertinent kineticequations (which merely involve competition between auenchine and fluorescence). x where is the rate . . K = r l k-. constant for the bimolecular reaction and k z is the decay constant of the excited state in the absence of solute. In the simplest case, the reaction involves a diffusion of the two species together to some distance R and then reaction with unit probability a t R. In such cases the diffusion-limited rate constant (in units of M-'sec-'1 is given by (26)
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unaffected their internal vibrational motions. It was then derived that a nair of coupled non-radiative transitions would occur with the excited donor molecule decaying to some vibrational level of its ground state and simultaneously exciting the neighboring acceptor molecule to some vihrational level of its excited state with a prohahilitv proportional to the ahsorption radiative constant of the kxcited &&-the strength of the acceptor, and the degree of overlap of the emission spectrum ofthe donor with the absorption spectrum of the acceptor. Numerous experiments have quantitatively verified these nredictions (29).For the liauid hvdrocarhons. however, conditions are very unfavorable for "Forster-type" transfer. The radiative constants are small, the absorption strengths are weak, and the spectral overlap is poor. The second mechanism involves a much shorter ranee process and is subsequent to the motion of the two molecules to within distances of the order of 3 4 A and the formation of an excited complex. This complex is referred to as an excimer if the two molecules are identical and as an exciplex if they are dissimilar. These complexes are formed only if one of the species is electronically excited. With hoth in the ground state, no complex formation is observed. Both excimers and exciplexes are normally fluorescent, emitting light a t a lower frequency than that of the uncomplexed pair (30). For the alkyl benzenes, the most rapid decay channel of the excimer is by dissociation to reform the initial pair, and i t is this fast dissociation that makes possihle, as first suggested hy Birks, a mechanism for energy migration. Thus, consider the translation of say A* to A, the formation of an excimer, and its dissociation such that the initially unexcited A now emerges with the excitation, i.e., (6)
A*+A-(AA)*-A+A*
In this manner the requirement in normal diffusion for an activated motion of one molecule past another would partially be subverted. In neat liquid benzene a t 25"C, it can he estimated that a t any instant of time during a continuous irradiation the ratio of excimers to excited monomers is ~ 3 . 3 This . process for enerw .,. mieration amears . . capable of lareelv explaining the discrepancies previously mentioned. For saturated hvdrocarhon solvents there is. however. no evidence for excime; formation (24).
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Ill. The Effect of Environmental Perturbation Molecules excited under isolated conditions (i.e., in a low pressure gas) or excited when present as a guest in some host solvent behave auite differentlv. In the case of non-polar, hgdr~r;url,msolvents, t w o distinct effw t - ~ m ~ t r i h uto t ethis d1116rence. The first of these hus .~lre;idvh e w discussed and a sink for vihrais based on the role of the solvent to tioual enerev therehv altering hoth the rates and the branching r&os of the uon-radiative molecular decay channels (31). Also to be considered here is the effect of the solvent cage to facilitate the recombination of departing fragments. A second very important effect derives from the role of the solvent to alter the entire absorption spectrum by virtue of changing the potential in which the promoted electron moves. (Since the solvent electrons themselves respond "instantaneouslv" to the altered electronic distribution, this potential will in-general be different for different electronic states.) Indeed for very highly excited Rydberg states in which the electron must penetrate deeply into regions extensively occupied by the solvent, this potential may he as strongly controlled by the nature and density of the solvent as by the coulomb field of the core. Thus, rather dramatic differences from eas nhase soectra are expected and are indeed found. staking first with the valence transitions, there is generally observed a slight shift of the spectrum to the red. The magnitude of thisihift increases with increasing polarizahility of the solvent and with increasing strength of the molecular absorption (32). The effect has its origin in a somewhat stronger attractive dispersion interaction of the solvent with
the excited state than with the ground state. The dependence on the polarizahility of the solvent and on the absorption strength of the transition follows from the general theory of disoersion forces. In addition to a shift of the spectrum, there is also observed a hroadening. I n part this is due to solvent enhanced relaxation and to the inverse connection (provided by the Heisenberg uncertainty principle) between lifetime and spectral width. Also, however, some of the broadening is caused hv a statistical effect. Since in a tvpical absorption experim&t many molecules are excited, kach in a slightly different solvent environment, it follows that each is shifted somewhat differently by the solvent perturbation and, accordinelv, each will absorb light of a slightly different frequency. Whereas the valence states shift to the red, the lowest Rvdberg state usuallv s h i i t ilightlq ro the hlue and increaiin&, rhe less polarirahlu is lhe ss
I371 &hen. M. H.. in "Electrons in Fluids? Jortner. J , m d KpsDler,N. R, Springer-Verlag.
P r n ~ in~Radiation s Chemistry..)Audmp. P., lnlcrnianee. 1968. Chapter 1:Shida, 8 , and Hstano, Y..Int. J. Rodiot.Phyr. Chm., 8.171 119761. (6s) ~ P.. ~ and i.ias. ~ S. G.,i~ n '"Chemical l Speetroseopy ~ ~ and Photochemistry ~ . i n the Yarvum l l l t m v i d ~Sandorfy, t~ C.. Audonr. P. J.. and Robin, M. B.. (Edilorsl, D. Rcidel. 1974.1,. 41% (66) Warmsn. J. M.. Aamus. K.-11.. end Schuler. 8. N.. Ada Chem. Ser., 82.25 11968); ~~h~l~~.R.H ..~nd Infelu,P.P..J~Phys.Chom.. 76.3812i1972);Rmd,SS..J.Phrs. Chrm.. 75,8722(19721:7adnr.E., Warman,J.M..and Hummrl,A., J.Chem. Phyr, 62.11197 i19751:Thomas. J. K..Int. J. Radio,. Phys. Chem.. 8.1119761. Msce. 157) Hammel. A..J Chrm. Phue.. 49.4MO ~1968);Abrl1.G.C.,Morumder,AAA~nd
J.L..J C h ~ mPhys.. . 55,5422 11972);Crumb.l. A.,andBainl, J.K., J Phya. Chrm.. R1. L190iL9791:Tschiua.M.. J. Chsm Phvr.. 70.288119791:Friauf.R.J.. . . . . Nmlmdi. H o k K. M../ h e m . P~.vs.. n.iri iis79). (58) Schmidt. Uz.P.,and Alirn, A. 0..J. Phys Chrm.. 72.3730 (1968); Schmidt, W. F.,and Allen.A.O.,J. Chron Phya.. 52,2346 (1970): Allen. A.O.."YioldsofFreo Inns Formed in l.iquidr by Rsdialion." N S R I W N R S 67. 1976. 1591 Stoneham, 7. A , ELhridge. D. R., and Mdselr, C. C.. J Chem. Phya.. 51. 1051
\."..,. ,.S",,
( M W u , K L a n d LipXy,S., J. Chem. Php.. 66,5614 (19771. J. Radial. Phw. Chem. 8.237i1976). 161) IVs1ter.L.. Hiraylms.F..and I.ipsky.S..Int.
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