5 Electronic Energy Transfer in Polymers By J. R. MACCALLUM Chemistry Department University of St. Andrews Fife 1 introduction There are many areas of practical application in which electronic energy transfer (EET) is significant. Transference of electronic energy from the point of photon capture to some other site within a macromolecular structure by non-radiative means is of vital importance in photostabilization of synthetic polymers.’ Non-chemical dissipation of the energy results in effective protection and conversely efficient conversion leading to chemical change gives the basis for synthesizing photodegrad- able plastics. An understanding of the mechanism of electronic energy transfer will result in better design of materials for particular environmental conditions.EET is also one of the essential steps in the process of photosynthesis where a chromophore is situated in conditions more akin to attachment to a polymer molecule than to a small molecule. Diffusional movement is restricted and neighbouring groups are determined by the chemical composition of the macromolecule. The fact that in Nature molecular aggregates are involved in conversion of radiative energy into chemical reactions has prompted some polymer chemists to investigate the feasibility of employing synthetic polymers as media for using solar energy to promote chemical reactions by a mechanism of photon harvesting.* The rather special properties of macromolecules may well endow to attached chromophores some specific advan- tages not possessed by small-molecule analogues.It is reasonable to predict that the behaviour of polymer molecules in EET processes should be somewhere between that of small molecules where the most common mechanism involves random collisions of energy-donor and -acceptor and that of crystalline solids in which exciton migration within the highly ordered structure plays a dominant role. Luminescence of crystalline organic solids has just been re~iewed.~ If the above comparison is restricted to the solid phase then the obvious question is How does electronic energy transfer from a donor to an acceptor both bound to a polymer molecule compare with the same process involving on the one hand fixed randomly distributed small molecules and on the other the same donor-acceptor pair incorporated in a crystalline lattice? Even to attempt to answer that question requires a clear understanding of the significance of donor-acceptor separation and orientation in the efficiency of transfer.’ B. Rhby and J. F. Rabek ‘Photodegradation Photo-Oxidation and Photostabilisation of Polymers’ John Wiley New York 1975. J. E. Guillet Pure Appl. Chem. 1977 19,249. J. 0.Williams Ann Reports (A),1977 51. 99 J. R. Maccallum This Report will attempt first to outline the theories advanced to account for the mechanism of EET and their relation to experimental measurements and then review the work which has been carried out involving solid polymers either as donor or as donor and acceptor. For a variety of reasons much interest in EET has been generated among biochemist^.^ Since this area of research is concerned with macromolecules in solution and therefore under conditions in which translational movement albeit highly restricted of the donor or acceptor group can occur thereby altering the separation/orientation parameters in time it will warrant reference only when proposals are made or conclusions drawn which are relevant to the theories of EET.2 Theory The process under consideration can be described as D*+A + D+A* (1) The transfer of electronic energy from the excited donor D* to the acceptor A takes place by a non-radiative mechanism. The transfer of energy is complete since no back transfer takes place and it is possible to identify on which species the energy resides.Normally D and A are different chemical types but given the correct conditions D and A may be chemically identical molecules. The mechanisms involved in process (1)require that the transition D* + D be of comparable energy to A + A* and that the initial state (D* +A) interacts in some way with the final state (D+A*). Normally the former requirement means that vibrational levels in both species contribute to the transfer of energy. The mechanisms of transfer generally described as resonance transfer processes which are considered to predominate in macromolecules are assumed to involve vibra- tionally relaxed species.’ The implication of such an assumption is simply that the rate of transfer is much slower than the rate of vibrational relaxation.The converse condition of transfer before relaxation requires very fast rates and takes place in organic crystals. This type of EET was covered in Williams’ Report last year and is satisfactorily explained by exciton the~ry.~ 3 Rate of Energy Transfer The conditions for energy transfer being much slower than relaxation are U << AE AE (2) in which U is the interaction energy between initial and final states AE the transition energy and A& the electronic bandwidths. A consequence of these requirements is that the spectral characteristics of donor and acceptor are unchanged in each others’ presence. It can be shown that the probability of transfer from the initial state to the final state depends on the interaction U between the two states and on the density of L.Stryer and R. P. Haugland Proc. Nut. Acad. Sci.,U.S.A.,1967 58 719; J. Eisinger Biochemistry 1969 8 3902. Th. Forster Discuss. Faraday SOC.,1959 27 7. Electronic Energy Transfer in Polymers states ps.6 Thus the probability of EET PDA is expressed in the form where h is Planck's constant. The density of states is measured from the spectral overlap of the donor emission and acceptor absorption both normalized to unity. Two types of interaction are significant in resonance transfer of energy; (i) dip~le-dipole,~ and (ii) exchange.6 4 Dipole-Dipole Interaction The first complete derivation of a relationship between the specific rate of EET and experimentally available parameters was made by For~ter.~ Briefly he proposed that the interaction between D and A would be totally dipolar in nature when D and A were separated by more than approximately 1nm.Thus cJc€[3$5]2 (4) in which UDand UAare the dipoles for the transitions in D and A on transfer and R is the D-A separation. The dipoles are treated as points. UDand UAare related to the radiative transitions of each species i.e. the radiative lifetime of the donor 7D the donor quantum yield QD and the molar extinction coefficient of the acceptor Forster derived the relationship where K is a constant factor to allow for the orientation of UDand UA,n is the refractive index of the medium and B = [FD(u)&A(u)/(u)4] du. A specific D-A separation Ro,is defined such that for this condition the probability of transfer is equal to the probability of decay by radiative and non-radiative processes.Under these circumstances ~ETTD= 1 and then Normally K is averaged over all possible orientations and consequently (K)~ is equal to 0.66. Equation (6)now becomes &/nm = 2.89 x lop5[-(7) Q;B]i The terms on the right-hand side of the equation can be evaluated from the spectroscopic properties of the donor and acceptor thereby allowing a prediction of Ro from such data. Obviously the overlap factor B is the key parameter in determining Ro. Equation (5)can now be rewritten as Th. Forster Ann. Physik 1948 2 55. Th. Forster 2.Naturforsch. 1949 4a 321. J. R. Maccallum It is convenient to define the efficiency of transfer QET in an analogous way to the definition of quantum efficiency thus or Equation (8)gives the specific rate of transfer for a single pair separated from each other by a distance R.Experimentally what is studied is an assembly of D-A pairs involving a distribution of R values for a given sample. Furthermore the D-A distance must remain constant during the lifetime of the donor otherwise allowance must be made for a time-dependent R resulting from spatial diffusion of the chromophores involved in EET.8 Thus the next step in the development of Forster's theory was to average over all the D-A pairs in a given sample. Indeed an averaging procedure has already been operated in allotting a value of 0.66 to (K)~,a situation which has provoked some comment and to which reference will be made later.' The equations derived by Forster in which R is replaced by the concentration of acceptor C are now given QET = Ji x exp(x)*[I -erf (XI] (12) where x = 0.54; (C/Co).Equation (11)describes the decay of donor fluorescence intensity with time and equation (12) relates the efficiency of transfer to varying acceptor concentration; Co is the 'equal probability' value corresponding to a D-A separation of R,. Experi-mentally C is obtained by fitting measured data to either equation (1l),if flash excitation is used or equation (12) if steady-state illumination is used. Ro is calculated from equation (13) which is derived by considering the volume of the sample as comprising uniform spheres each containing one acceptor species. This treatment cannot be applied for intramolecular EET.Ro= 0.7346(Co)' (13) Thus from equation (7)a spectroscopic prediction of Ro is available and can be compared with the value obtained from energy-transfer experiments through equa- tions (13) and (11)or (12). In this way Forster's theory can be tested and in the event of discrepancy between the two approaches the possibility of phenomena such as bulk diffusion and energy migration before or after transfer can be investigated. It is worth making an observation on equation (12). On solving for QET when C=Co a value of 0.72 is obtained. Now Co is the concentration of acceptor corresponding to the D-A separation Ro [equation (13)] and from equation (lo) when ~ET(TD)-' = 1 i.e. R = Ro,then QET= 0.5. The explanation for this apparent disagreement is not available.* D. L. Dexter J. Chem. Phys. 1953,21 836. R. E. Dale and J. Eisinger Proc. Nat. Acad. Sci. U.S.A.,1976 73 271. Electronic Energy Transfer in Polymers 103 Diffusion and Energy Migration.-Forster did not extend his treatment to account for the effect of bulk diffusion of D and A during the lifetime of D. When this occurs R becomes a function of time and as kETK(R)-6,the specific rate can vary considerably. Several papers have been published developing this aspect of Forster's original theory. With regard to bulk diffusion the most notable contributions are those from Yokota and Tanimoto" and more recently from Gosele et al." Since macromole- cules are generally studied in the solid phase and even in solution their diffusion is slow this effect will not be considered in this review.Energy migration on the other hand is a more likely possibility in a macromole- cular environment than in an assembly of small molecules randomly distributed in a matrix. D/A chromophores attached to the same polymer molecule which is itself suspended in an inert medium may have a very low overall concentration and therefore an apparently high R. However at the molecular level the actual separation of the chromophores is governed by their disposition on the polymer molecule and the correct R can be a fraction of the apparent R. In effect each polymer molecule contains a high local concentration of D and A. The number of such pockets is governed by the molecular weight of the polymer and the weight per cent suspended in the matrix.Somewhat more difficult interpretations of concen-tration in relation to R have to be made when the donor species is part of one polymer molecule and the acceptor is part of another. Indeed this example is one which has not been completely resolved. For the case in which the matrix is itself the donor then energy migration may well be significant with the overall efficiency following the predictions of exciton theory rather than single-step resonance-transfer theory. Energy migration is also an important step in photosynthesis. No complete theory has been evolved to relate QET with concentration of acceptor although Zwanzig has proposed an approximate relationship.'* If the mechanism of resonance transfer from one chromophore to another be that considered by Forster then it would seem that the movement of the quantum of energy would be very similar to the anisotropic diffusion of an elec- tronically excited molecule as treated by Gosele,' the anisotropy being introduced by the requirements of orientation of dipoles.Indeed Altmann Beddard and Porter have used computational techniques to analyse the diffusion equation relevant to energy transfer in chlorophyll. l3 Although the computer-simulated results are for a two-dimensional model the agreement with experimental observation is encouraging. On considering the possible mechanisms for EET between like molecules psmust be the governing factor in determining the efficiency [vide equation (3)].Since this parameter is normally very small it is probable that energy migration along polymer chains containing donor species attached to the repeat unit proceeds by the exchange mechanism rather than by the dipole-dipole. 10 M. Yokota and 0.Tanimoto J. Phys. SOC.Japan 1967,22,779. U. Gosele M. Hauser U. K. A. Klein and R. Frey Chem. Phys. Letters 1975,34,519; U. Gosele U. K. A. Klein R. Frey and M. Hauser ibid. 1976 41 139; U. Gosele ibid. 1976 43 61. 12 S. W. Haan and R. Zwanzig J. Chem. Phys. 1978,68 1879. l3 J. A. Altmann G. S. Beddard and G. Porter Chem. Phys. Letters 1978 58 54. J. R.Maccallum 5 Exchange Interaction The exchange interaction arises from the spatial overlap of the donor and acceptor wavefunctions and since normally the molecular electronic wavefunction decreases exponentially the expression for this type of interaction would be expected to include a term exponential in the D-A separation.Dexter has attempted to solve the wavefunctions for overlap and he proposed the following expression for the specific rate of EET;' (14) where Z2is dependent on R such that Z2= Yexp (-2R/L) (15) Y is a constant with the dimensions of energy and L another constant described as 'the effective average Bohr radius'. The overlap integral is normalized such that du (donor emission) = ~~(0) 1FD(u) du (acceptor absorbance) = 1. Using a similar approach as adopted for dipole-dipole interaction a D-A separa-tion Rois defined such that for this value EkET(~D)-l= 1 and consequently EkET= (71-l exp -(R/RO)I} (16) in which d = 2R0/L and Rois the so-called critical transfer distance.The specific rate of EET falls off exponentially with increasing D-A separation; however the theory has not yet reached a stage of development which allows direct estimation of Rofrom spectroscopic properties of D and A. The physical significance of L is not too clear and the application of equation (16) leaves L as an adjustable parameter adjustment being restricted within certain limits. 6 Comparisonof the Two Mechanisms The decrease of specific rate of transfer with increasing D-A separation is less severe for dipole-dipole than for exchange interaction. For this reason EET involving the former mechanism can take place over distances up to 10 nm which in molecular terms is considerable.The efficiency of transfer for the dipole-dipole mechanism is governed by the strength of the transition in the donor and acceptor chromophores particularly the donor whereas for exchange this does not apply as the overlap function is normalized. Thus considering only spin-allowed processes the following transfers can be postulated D*(singlet)+A(sing1et) -D D(sing1et)+A*(singlet) (17) D*(singlet)+A(trip1et) -D D(sing1et)+A*(triplet) (18) D*(triplet)+A(sing1et) + D(sing1et)+A*(triplet) (19) D*(triplet)+A(trip1et) -+ D(sing1et)+A*(singlet) (20) Processes (17) and (18)will be more feasible by the dipole-dipole mechanism as the transitions in both the donor and acceptor are allowed although the exchange Electronic Energy Transfer in Polymers 105 mechanism is possible if less likely.On the other hand (19)and (20)are more likely to proceed through exchange interaction as both the donor and acceptor transitions are forbidden. Since ground-state triplet species are uncommon and transfer to excited acceptors is unusual (18) and (20) are experimentally improbable though possible. However having stated the generalization it is worth noting the exception which involves oxygen a triplet species in the ground state. The lowest singlet form of oxygen has been the subject of much investigation and is responsible for some unusual chemical reactions.14 7 Singlet-Singlet EET As indicated above this type of transfer generally proceeds by the dipole-dipole mechanism.The most common donors are aromatic groups attached to the polymer main chain for example polystyrene poly(vinylnaphthalene) and poly(viny1- carbazole) with small molecule acceptors suspended in the donor itself or with the D-A pair dispersed in an inert matrix usually poly(methy1 methacrylate) for studies at room temperature. No experimental data appear to have been reported for a polymeric acceptor or for both polymeric donor and acceptor. The use of an inert matrix can lead to experimental difficulties in that the theory requires a random distribution of acceptors around the excited donor and the attainment of such a distribution may present problems since donor and acceptor can have quite different compatibilities with the matrix.In this context the actual configuration of the macromolecule within the solid solution must be of some significance. For example a chromophore buried in the centre of a spherical macromolecule will perforce be much farther from an acceptor than the same chromophore on the periphery yet both have the same probability for excitation. A situation could also arise whereby the acceptor species is preferentially distributed within the polymer coils; in effect the converse of the previous condition. Attempts have been made to allow for such possibilities in studies involving fluid but not for solid solutions in which the above theories are applicable. With a homopolymer containing pendant chromophores in close proximity to each other there arises the possibility of same-species transfer along the polymer chain giving the phenomenon of energy migration which must be considered as a possible prior occurrence to EET from polymeric donors.Diffusion of the singlet energy before transfer results in a higher efficiency of transfer and a simple test for energy migration is to compare the spectroscopic value of Ro with that determined by experiment. When the latter is much larger than the former this is considered as good evidence for energy migration. Another somewhat special property of donors attached to addition polymers is that since they are made up of multi-units comprising 1,3-disubstituted propane blocks the possibility of forming excimers is greatly enhanced. The properties of such excited states in polymer and small molecules have been reviewed by Klopf- fer.16 The formation of excimers is raised at this point to illustrate a further possible mechanism for energy migration which does not involve EET by dipole-dipole or 14 ‘Singlet Oxygen’ ed.B. Rhby and J. F. Rabek John Wiley New York 1978. Is J. DanEcEk P. HrdloviE and I. Lukac European Polymer J. 1976 12 513. W. Klopffer ‘Organic Molecular Photophysics’ ed. J. Birks John Wiley New York 1973 p. 357. J. R. Maccallum exchange interactions thus IS* I S I S I cs I Sl* I S CH2 H CH2 H / \y \A/ Excimer/CH2 H CH2\A/ \ I S IS* IS S* represents an excited singlet or triplet substituent aromatic residue. The requirement of a face-to-face conformation in forming the excimer places definite restrictions on the number of transfers possible on a macromolecule held rigidly within a glass.However relatively unrestricted main-chain rotation in solution should enhance this mechanism. Efficient migration over many substituent groups implies that the excimer is not a trap from which the electronic energy is dissipated as radiative or vibrational energy. Polystyrene.-Two excited singlet species are found in polystyrene at room temperature; monomer which has A,, emission at 280 nm with a quantum yield -0.004 and excimer with A,, emission at 330 nm and a quantum yield of approximately 0.02. The first report of EET involving polystyrene as matrix and donor was made by Basile who used tetraphenylbutadiene as acceptor." From the concentration of acceptor at which QET= 0.5 he found Roto be 2.18 nm.His data fitted the Forster equation (12) very well but R (spectroscopic) was not determined. Later Geuskens et al. repeated this work using polystyrene and a styrene-methyl methacrylate copolymer giving Ro (experimental) of 1.95 nm and 2.2 nm respectively for QET = 0.72. They concluded that both monomer and excimer were acting as donors. The agreement between the two sets of results is reasonable and the mechanism would appear to be dipole-dipole transfer. Geuskens and co-workers proposed that singlet energy migration takes place along the polymer chain from phenyl unit to phenyl unit until an excimer-forming site is reached where the migrating energy is trapped." Evidence for this happening is usually based on comparing R (spectroscopic) with R,(experimental).However another method which can be used is measurement of the polarization p of the emitted radiation using polarized exciting radiation. Energy migration provided it is spatially random results in depolarization of the emitted radiation. Two sets of measurements have been performed on solutions of copolymers of styrene and methyl methacrylate in glasses of methyltetrahydrofuran at 77 K.'9*20 The emission studied was that from monomer and it was found that the extent of depolarization increased with increasing styrene content suggesting that the L. J. Basile Trans. Faraday SOC., 1965 42 3163. '* C. David M. Piens and G. Geuskens European Polymer J. 1973,9,533.l9 C.David D. Baeyens-Volant and G. Geuskens European Polymer J. 1976,12,71. 2o R. F.Reid and I. Soutar J. Polymer Sci.,Polymer Phys. Edn. 1978,16,231. Electronic Energy Transfer in Polymers 107 captured photon could migrate from unit to unit before emission. The mechanism of EET must be either dipole-dipole or exchange as no excimer emission was observed. Both investigations also measured the ratio of the intensity of excimer emission to that from monomer in fluid solutions at room temperature and each concluded that the results obtained indicated the presence of energy migration. However the plots on which the conclusions were based differ. Geuskens found IE/IM(emission intensity of excimer to monomer) to be linear with the fraction of styrene-styrene links,lg whereas Soutar obtained a linear plot for IE/IM versus the fraction of styrene-styrene links multiplied by the mean length of styrene seg- ments2’ Somersall carried out similar measurement with styrene/acrylonitrile and his data agreed with the relationship found by Geuskens.The occurrenceof energy migration would in fact be more likely to give a linear plot in the form reported by Soutar. The matter is further complicated by decay measurements performed by Phillips using very sophisticated apparatus.22 The decay of monomer emission in fluid solution follows exponential behaviour which would not be the case when significant EET takes place from one species to another of the same chemical type. Polarization measurements for polymer solutions do not throw any light on the problem as they are not meaningful when the emitting species can move within its own lifetime.The polarization value obtained for excimer the energy trap in thin films of polystyrene was 0.77 indicating that the emitting species is also the absorbing species thus precluding energy migrati~n.’~ However similar measure- ments on the monomer emission in thin films of styrene/methyl methacrylate copolymers pointed to site transfer of the singlet It seems that the occurrence of energy migration within solid polystyrene although frequently proposed is by no means proved. Neither the exchange nor the dipole-dipole mechanism would be expected to be very temperature-dependent yet the available results suggest efficient migration at 77 K but none at room tempera- ture.Phillips’ results for dilute solutions22 give strong support to the room-tempera- ture polarization data from films.23 The matter remains to be resolved. Poly(vinylnaphthalene).-Polymers of both 1-~inylnaphthalene~’ and 2-vinyl- naphthalene26 have been studied and no notable difference in photophysical prop- erties has been recorded. The emission spectrum for poly(vinylnaphthalene) PVN comprises monomer (A,= == 340 nm) and excimer (A,, 400 nm) with no quantum yields reported for either emission. At room temperature the predominant emission is that from excimer. The general interest in the photophysical behaviour of PVN has been directed towards investigating naphthyl-naphthyl rather than naphthyl-acceptor EET.However David Demarteau and Geuskens have studied the system PVN (donor)- benzophenone (acceptor) at 77 K2’ and measured R (experimental) as 1.5 nm compared with Ro (spectroscopic) of approximately 1.4nm an agreement which 2’ A. C. Somersall J. Polymer Sci. Polymer Chem. Edn. 1977 15 2013. 22 K. P. Chiggino R. D. Wright and D. Phillips. J. Polymer Sci. Polymer Phys. Edn. 1978 16 1499. 23 J. R. MacCallum and L. Rudkin Nature 1977 266 338. 24 C. David N. Putman-De Lavareille ,and G. Geuskens European PolymerJ. 1977,13 15. 25 R. F. Reid and I. Soutar J. Polymer Sci. Polymer Letters Edn. 1977 15 153. 26 N. F. Pasch and S. E. Webber Chem. Phys. 1976,16,361. 27 C. David W. Demarteau and G. Geuskens European Polymer J. 1970,6 1397. 108 J.R. Maccallum tends to eliminate significant energy migration. However a number of studies of the homopolymer and copolymers have indicated the likelihood of singlet energy hopping along the polymer chain. Geuskens measured the depolarization ratio for a series of methyl methacrylate copolymers and homopolymer as rigid glasses and as films; the results strongly suggested energy migration.24 Soutar performed similar experiments extending the range of copolymer composition and also measuring IE/IM He for solutions as a function of the naphthyl content in the cop01ymer.~~ concluded that extensive energy migration occurred among the aromatic moieties. A very thorough investigation of the ratio of intensity of excimer emission to monomer emission over a temperature range 4.2-373K was carried out by Frank and Harrah.28 They developed a model which incorporated an element of energy transfer from unit to unit by dipole-dipole interaction accounting qualitatively for the behaviour at low temperatures.A cautionary note should be added to the effect that none of these authors considered the contribution of delayed fluorescence resulting from triplet-triplet annihilation an effect which has been clearly demon- strated (see later). Although this report is primarily devoted to solid-state EET it is appropriate to refer to the use of time-resolved measurements of emission spectra. Using short- and long-time gates following flash excitation of solutions of poly(1-vinyl-naphthalene) Phillips showed22 that the excimer dissociated to produce excited monomer thereby demonstrating that EET could proceed by the third mechanism indicated above.Extension of such measurements to polymer films should help resolve some of the problems associated with assessing the significance of energy migration. Poly(vinylcarbazole).-The fluorescence characteristics of poly(vinylcarbazole) PVK are complicated by the occurrence of two excited states of very similar energies neither of which has a ground-state analogue. Thin films of PVK show a very broad structureless emission centred around 410 nm which comprises two emissions; the low-energy part of the band has a decay time of 20 ns and is due to excimer while the high-energy portion is attributed to dimer structures with a lifetime of 11ns.There is marked overlap of the fluorescence of the two emitting states. No monomer emission has been observed for films of PVK at room ternperat~re,~~ whereas dilute suspensions of PVK in poly(methy1 methacrylate) films show only monomer.3o Since the formation of excimer is due to intramolecular association of pendant groups the macromolecules must be held in the matrix in such a way that face-to-face configurations are eliminated. The first investigation of EET with PVK as donor was reported by Klopffer who used films of the polymer containing small amounts of perylene hexachloro-p- xylene (HCX) and 2,4,7-trinitrofluorenone as acceptor^.^' Addition of small amounts of acceptor resulted in very efficient EET in fact much higher values than could be accounted for by either dipole-dipole or exchange energy transfer.Indeed the absorption spectrum of HCX has no overlap with the polymer emission and yet 28 C. W. Frank and L. A. Harrah J. Chem. Phys. 1974,61 1526. 29 W. Klopfer and D. Fischer J. Polymer Sci.,Symposium Edn. 1973,40,43. 30 A. M. North and M. F. Treadaway European Polymer J. 1973,9,609. 31 W. Klopffer J. Chem. Phys. 1969 50 2337. Electronic Energy Transfer in Polymers this substance was an efficient quencher of polymer excited states. Klopffer inter- preted his results in terms of exciton diffusion following photon absorption until the mobile exciton reached a trap in the form of an excimer-forming site or in the case of added materials a guest trap. He calculated that the exciton ranged over one thousand polymer units intramolecularly and intermolecularly during its lifetime.This proposed mechanism is similar to the type of energy migration which takes place in crystals of aromatic compounds when strong ground-state intermolecular inter- actions favour diffusion of the exciton. In these circumstances the ground-state absorption spectrum of the donor system shows clear differences from that for the same molecules in solution. However films of PVK have the same absorption spectrum as solutions of the polymer and also model compounds. It is not clear what mechanism allows the exciton to move so freely in competition with monomer deactivation. Later Powell made lifetime measurements on films of PVK doped with ~erylene.~* He proposed that as well as exciton migration into excimer dimer and acceptor traps EET took place from dimer structures to closely associated acceptor molecules (perylene) by a dipole-dipole mechanism.The efficiency of this process was almost independent of temperature in the range 13 K to room tempera- ture. North and Treadaway measured EET from the carbazole units in vinylcar- bazole/methyl acrylate copolymers to anthra~ene.~' Following Yokota and Tani- moto," they characterized the energy migration in terms of a migration coefficient analogous to a diffusion coefficient and their results are summarised in Table 1. As Table 1 Electronic energy migration coefficient for vinylcarbazolelmethyl acrylate copolymers." Singlet EET Mole fraction of vinyl- carbazole (donor) Migration coe cient AX 1o9lrnP in polymer Acceptor Matrix' s-' 1 Anthracene PMMA 7.3 1 Anthracene PS 7.8 0.84 Anthracene PMMA 6.2 0.79 Anthracene PS 5.6 0.70 Anthracene PMMA 3.9 0.70 Anthracene PS 4.2 a A.M. North and M. J. Treadaway European Polymer J. 1973 9 609; PMMA is poly(methy1 methacrylate) PS is polystyrene. previously noted an interesting feature of this work is that no significant excimer emission was observed for dilute solutions of PVK in poly(methy1 methacrylate) and polystyrene matrices. Monomer (A,, 350 nm) was the only emission detected and transfer from excimer to the acceptor was discounted. Although neither KlOpfferz9 nor Mika~a~~ observed monomer emission using films of pure PVK this could be explained by self-absorption of monomer fluorescence within the sample.A molecular energy-transfer distance r can be defined such that r = AT^) 32 G. E. Venikouas and R. C. Powell Chem. Phys. Letters 1975 34 601. 33 M. Yokoyama T. Tamamura T. Nakano and H. Mikawa I. Chem. Phys. 1976,65,272. J. R. Maccallum where A is the donor excitation energy migration coefficient and T~ is the donor fluorescence lifetime in the absence of additive. Assuming T~ to be around 11ns yields a value of 12.1 nm for r for the homopolymer. This compares reasonably well with Klopffer’s estimate of a random-walk distance of approximately 20 nm for the exciton in pure PVK films in which intermolecular hopping must extend the range compared with the essentially intramolecular conditions used by North and Treadaway.30 Poly(phenylacetylene).-Macromolecular polyenes are provoking some interest; in particular their unusual electrical properties have led to speculation about the extent of delocalization of electrons within the polymer The photophysical behaviour of one of the more stable polyenes poly(phenylacetylene) PPA and copolymers derived from this monomer has been studied in some detail since the electronic structure might facilitate exciton migration. The absorption and emission spectra of samples of PPA are broad characterless bands with low quantum yields for emission (-0.02) and radiative lifetimes around 5 ns. Using poly(methy1 methacrylate) as matrix North and co-workers measured Ro (experimental) as 4.4nm compared with R (spectroscopic) of 2.5 nm for PPA (donor) and Rhodamine B (a~ceptor).~’ The Ro values for a series of copolymers of styrene and phenylacetylene (donors) with perylene (a~ceptor)~~ are shown in Table 2 giving the Table 2 Comparison of Ro(experimentul) with R,(spectroscopic) for styrenelphenyl- acetylene copolymers.” Singlet EET Mole fraction of phenyl-acetylene (donor) 1experimen ta ,( R ) Ro(spectroscopic) in polymer Acceptor Matrix /nm /nm 0.23 Perylene PMMA 7.80 2.61 0.66 Perylene PMMA 7.52 3.28 0.76 Perylene PMMA 5.90 3.31 0.80 Pery1en e PMMA 6.10 3.29 0.23 BBOT PMMA 12.87 3.86 0.76 BBOT PMMA 8.57 3.81 0.80 BBOT PMMA 10.63 2.98 a L.Rudkin Ph.D.Thesis University of St. Andrews 1976; PMMA is poly(methy1 methacrylate) BBOT is 2,5-bis-[5’-t-butylbenzoxazolyl(2‘)]thiophen. same range of differences between experimental and spectroscopic values as obser- ved by North et al. Later measurements showed that the decay of the fluorescence was non-exponential and using time-resolved spectroscopy Guillet Hoyle and MacCallum were able to prove that the emission from a phenylacetylene/styrene copolymer was due to two emitting ~tates.~’ The value of this experimental tech- nique is illustrated by this particular example for which the demonstration of two excited singlet states was a key factor in interpreting the EET behaviour. The time-resolved spectra for a phenylacetylene/styrene copolymer are shown in Figure 1.34 H. Shirakawa T. Ito and S. Ikeda Makrornol. Chern. 1978 179 1565. ” A. M. North D. A. Ross and M. F. Treadaway European Polymer J. 1974 10,411. 36 L. Rudkin Ph.D. Thesis University of St. Andrews 1976. 37 J. E. Guillet C. E. Hoyle and J. R.MacCallum Chern. Phys. Letters 1978 54 337. Electronic Energy Transfer in Polymers 350 400 450 500 550 Wavelength / nm Figure 1 Time-resolved fluorescence spectra of SPA in polystyrene film. Exciting wavelength is 313 nm. The lower and upper limits for the time-resolved spectra are given as the interval from the lamp maximum (a) upper 0.23 ns (b)lower 1.15 ns; upper 4.37 ns (c)lower 4.6 ns; upper 7.82ns (d) lower 20.2 ns; upper 25.1 ns. Spectra adjusted to fit on same scale. (Reproduced by permission from Chem.Phys. Letters 1978 54 337) North and co-workers concluded that efficient energy migration occurs within the polyene system before EET to the acceptor.35 Comparison of Ro(experimental) and Ro(spectroscopic) in Table 2 gives strong support to this conclusion. However the demonstration that two emitting states are responsible for the polyene emission indicates an alternative explanation. Berlmann has commented on the relationship between natural lifetime and radiative lifetime when fluorescence is due to two emitting states of similar energy.38 For diphenyl-terminated polyenes Dalle and Rosenburg showed that the natural lifetime T~, == ~/20Q,where Tis the radiative lifetime and Q is the fluorescence quantum yield.39 Now in the deduction of the Forster equations the specific rate of EET is shown to be proportional to (natural lifetime)-' and the assumption is usually made that TN = T/Q resulting in the Forster relationship [equation (5)].However for polyenes a modification must be made to accommodate Dalle and Rosenburg's observations. The outcome of the correction is that Ro (spectroscopic) ,as shown in Table 2 and calculated by North must be multiplied by 1.65 i.e. (20)",to yield the real value. The correction factor should be regarded as approximate but when taken into account the process of EET involving PPA as donor can be rationalized by a dipole-dipole mechanism with no energy migration. This explanation is supported by polarization measurements reported by MacCallum and Rudkin on emission from a copolymer of styrene and phenyla~etylene.~~ 38 I.Berlman 'Handbook of Fluorescence Spectra of Aromatic Molecules' Academic Press New York 1971 p. 60. 39 J. P. Dalle and B. Rosenberg Phorochzrn. and Photobiol. 1970 12 151. J. R. Maccallum 8 Triplet-Triplet EET The process of an electronically excited triplet donor producing a triplet-state acceptor [equation (19)] is spin-allowed and most probably proceeds by the exchange mechanism. The possibility of the dipole-dipole mechanism operating is very much reduced by a low molar extinction coefficient and a long natural lifetime for the donor change of state. The spatial requirements for the exchange interaction demand a close approach of a DA pair with the consequent effect of reducing R to within the range 1.0-1.5 nm.This type of transfer has received relatively little attention from polymer chemists and few studies of polymer (donor)-small molecule (acceptor) systems have been reported. Polymers containing Ketone Groups.-Guillet and Dan studying solid solutions of poly(pheny1 vinyl ketone) and poly(methy1 isopropenyl ketone) to which varying amounts of 1-cis,3 -cis- cyclo-octadiene and piperylene had been added as quen- chers found evidence for energy migration in the former but not in the latter polymer.4o They compared the efficiency of quenching of a series of model compounds with equivalent solutions of the polymers and found the aromatic-based polyketone to be more effectively quenched. A number of polymers containing aryl ketones have been investigated by Geus- kens and co-workers.Efficiency of EET to naphthalene as acceptor at 77 K has been measured for poly(vinylben~ophenone),~~poly(pheny1 vinyl ketone),42 and poly(methy1 vinyl ketone),43 with R, values shown in Table 3. For the exchange Table 3 R,(experimental) for ketone-containing polymers. Triplet EET Poly(viny1benzophenone)" Poly(pheny1 vinyl ketone)b Polymer (donor) Naphthalene Naphthalene Acceptor ss ss Matrix* 3.6 2.6 Ro(experimental)/nm Poly(methy1 vinyl ketone)' Poly(vinylnaphthalene)d Naphthalene Penta-1,3-diene ss SS 1.1 1.5 Poly(styrene/vinyl- Naphthalene ss 3.0 benzophenone)' * SS is solid solution at 77 K. C. David W. Demarteau and G. Geuskens European Polymer J.1970 6 537; C. David W. Dernarteau and G. Geuskens ibid.,p. 1405; C. David N. Putman M. Lernpereur and G. Geuskens ibid. 1972,8,409; C. David M. Lempereur and G. Geuskens ibid. p. 417; 'C. David V. Naegelen W. Piret and G. Geuskens ibid. 1975 11 569. mechanism there is no means of estimating Ro (spectroscopic) and thus experimen- tal Re's have to be compared with what could be defined as the range of likely values 1.0-1.5 nm. The distances evaluated from Geusken's data for the triplet-triplet exchange gave strong evidence for energy migration. Polarization measurements on styrene/vinylbenzophenone cop01ymers~~ supported the conclusion that quite extensive migration of the triplet energy was taking place within the polymer chains the extent increasing with increasing benzophenone content.The phosphorescence 40 E. Dan D. C. Sornersall and J. E. Guillet Macromolecules 1973 6 228. 41 C. David W. Demarteau and G. Geuskens European Polymer. J. 1970,6,537. 42 C. David W. Demarteau and G. Geuskens European Polymer J. 1970,6 1405. C. David N. Putnam M. Lempereur and G. Geuskens European Polymer J. 1972,8,409. Electronic Energy Transfer in Polymers 113 decay of the same copolymers was studied at 77 K in glassy solutions and as For the solutions the decay was exponential giving a lifetime of 5 ms for the whole range of copolymers. On examining the phosphorescence decay of the powders it was found that those containing more than 50 mole per cent vinylben- zophenone exhibited bi-exponential decay with lifetimes of 2.2 ms and 20 ms for the two components.It was proposed that the long-living triplet was a trap into which the migrating energy flowed. As the number of traps increased with increasing vinylbenzophenone content the authors proposed that the trap was a benzophenone unit perturbed by neighbouring benzophenone units. 9 Delayed Fluorescence Delayed fluorescence results from triplet-triplet annihilation [equation (20)]. Basically delayed fluorescence is a biphotonic process with a lifetime half that of the sample phosphore~cence.~~ For polymers either in glassy solutions or as films the excited chromophore is incapable of translational motion and therefore the incidence of delayed fluorescence is indicative of triplet energy migration.This phenomenon was first observed by Fox and Cozzens in a solid solution of poly(vinylnaphtha1ene) and was interpreted as being due to triplet-triplet reaction following migration of triplet energy.46 Delayed fluorescence has also been observed at low temperatures from poly(naphthy1 metha~rylate)~’ and poly(vinylcarbaz01e.)~~ Poly(vinylnaphthalene).-Cozzens and Fox explained the emission of delayed fluorescence from solid solutions of poly( 1-vinylnaphthalene) as resulting from intramolecular triplet EET.46 The relatively high efficiency of quenching by addi- tives supported their mechanism. More recently Pasch and Webber have studied solid solutions ( M in chromophore) of poly(2-~inylnaphthalene).~’By measur- ing the efficiency of quenching of phosphorescence by piperylene they showed that sample molecular weight played an important role in the migration mechanism.Their interpretation of this effect was that the probability of a triplet exciton encountering a quencher species increased as its intramolecular diffusion length increased. Once the chain-length of the polymer exceeded the diffusion length (ca. 700 units) then molecular weight made no difference to the efficiency of quenching. Table 4shows the values obtained for A for a range of molecular weights. A very interesting application of the properties of the kinetics of the annihilation process was proposed by Avakian who used magnetic fields to vary the rate of migration.49 From the dependence of the intensity of delayed fluorescence on the strength of the applied magnetic field he was able to derive structural information about the macromolecules.Poly(2-naphthyl methacrylate) PNMA.-Guillet and Somersall observed T-T annihilation leading to delayed fluorescence in solid solutions of PNMA and they 44 C. David D. Baeyens-Volant P. Macedo de Abren and G. Geuskens European Polymer. J. 1977,13 841. 45 C. A. Parker and C. G. Hatchard Trans. Faraday SOC. 1963 59 284. 46 R. F. Cozzens and R. B. Fox,J. Chem. Phys. 1969 50 1532. 47 J. E. Guillet and A. C. Somersall Macromolecules 1973 6 218. 48 N. F. Pasch R. D. MacKenzie and S. E. Webber Macromolecules 1978 11,727. 49 P. Avakian R. P. Groff A. Suna and H. N. Cripps Chem. Phys. Letters 1975 32,466. J. R. Maccallum Table 4 Electronic energy-migration coefficient for series of polymers.Triplet EET Polymer (donor)* Poly(viny1naphthalene)" DP = 100 Acceptor Piperylene Matrix t ss Migration coe cienr ~xlo'*/mBss-l 2.41 DP = 273 DP = 664 DP = 3250 Poly(vinylcarbazole)b Poly(naphthy1 methacrylate)' Piperylene Piperylene Piperylene Naphthalene Piperylene ss ss ss ss ss 5.17 5.50 7.63 320.0 13.0 * DP is degree of polymerization; f SS is solid solution at 77 K N. F. Pasch R. D. MacKenzie and S. E. Webber Macromolecules 1978,11,733;* M. Yokoyama T. Tamamura T. Nakano and H. Mikawa J. Chem. Phys. 1976,65,272; E. Dan A. C. Somersall and J. E. Guillet Macromolecules 1973 6 228. studied the relative transfer rate of triplet energy by the addition of triplet quen- hers.^' The delayed fluorescence was biphotonic but excimers did not involve nearest neighbours.This work was extended by Pasch and Webber who found that the intensity of delayed fluorescence increased with increasing molecular weight while the intensity and lifetime of phosphorescence decreased." The decays of phosphorescence and delayed fluorescence were non-exponential with the 'lifetime' of the latter very much less than half that for phosphorescence while the relative intensities did not follow the biphotonic relationship predicted for straightforward T-T annihilation. The authors suggested that the behaviour was consistent with a model involving two types of triplet a trapped and a mobile species. The relatively slow rate of migration of the triplet exciton governed the decay rate for delayed fluorescence.The effect of increasing molecular weight was primarily to increase the probability of two triplets being simultaneously generated on one chain thus facilitating T-T annihilation following intramolecular energy migration. Fox et al. using a series of copolymers both random and alternating showed that intramolecular triplet exciton migration in alternating copolymers was as efficient as in the corresponding homopolymers.5' They observed that in solid solutions intramolecular migration was the principal mechanism of EET while in films of the pure polymer inter-chain hopping was occurring. Each hop operated on exchange interaction. Copolymers incorporating alternating vinyl aromatic units/methyl methacrylate did not show any excimer emission; this was explained by the existence of charge-transfer interactions between aromatic chromophore and adjacent ester carbonyl groups.Poly(vinylcarbazole).-It was for PVK that the first observation of the significance of chain-length on the ratio of intensity of delayed fluorescence to phosphorescence was noted.31 Solid solutions of a range of molecular weights were investigated at 77 K and it was observed that phosphorescence could not be detected for samples of high molecular weight. In a later paper Klopffer and co-workers used fractionated samples and found that the intensity of phosphorescence was equal to that of delayed fluorescence at a molecular weight of 110 OO0.52 They measured the phos- phorescence decay as a first-order process with a lifetime of 8.2s whereas the N.F. Pasch and S. E. Webber Macromolecules 1978 11,733. " R. B. Fox T. R. Price R. F. Coyzens and W. H. Echols Macromolecules 1974,6 218. '' W. Klopffer D. Fischer and G. Naudorf Macromolecules 1977 10 450. Electronic Energy Transfer in Polymers 115 delayed fluorescence had a lifetime of 34 ms. It was concluded that the triplet population comprised two species; long-living immobile triplets and shorter-lived mobile triplets. Delayed fluorescence resulted from self-annihilation of the latter. A parallel study under comparable conditions was carried out by Yokoyama et al. who used a range of samples of similar molecular weights to Klopffer's They added naphthalene as a triplet quencher and observed that the lifetime of delayed fluorescence decreased but the lifetime of phosphorescence was unchanged at 7.6 s despite a reduction in intensity.It was proposed that phosphorescence was emitted from traps and not from migrating triplet excitons which were responsible for delayed fluorescence and were quenched by naphthalene whereas the trapped triplet was unaffected by this quencher. The molecular weight at which the intensi- ties of phosphorescence and delayed fluorescence were equal was about 40 000 and no delayed fluorescence was detected from samples of molecular weight less than 10 000. For the homopolymer they calculated an energy-migration coefficient A of 3.2 x m2s-'. The kinetics of delayed fluorescence and triplet energy migration in films of PVK have been studied by B~rkhart.~~ Some notable differences in behaviour compared with solid solutions were observed.The relative intensity of delayed fluorescence was Siphotonic and that of phosphorescence monophotonic; the lifetimes were in the ratio 0.5 :1,as predicted by basic theory. The molecular weights of his samples were constant but on varying the temperature from 198 to 123 K the ratio of the intensities of delayed fluorescence and phosphorescence changed markedly with the maximum at 173 K. At this temperature two triplet emitting species were detected one with Amax at 475 nm and T of 475 ms and the other with A,, at 505 nm and T of 574ms. Both decays were first order. The two emissions were explained by postulating the existence of two types of triplet; the lower-energy species was associated with immobile trap sites and the higher-energy emission was attributed to mobile triplets.Burkhart proposed the following annihilation steps (mobile triplet) +(traptriplet) = (singlet)'+ (trap singlet)' Polystyrene.-George investigated the relative efficiency of quenching by added and copolymerized additives.54 Films of polystyrene suffered identical quenching of phosphorescence when naphthalene was present as a free molecule or as a comonomer. For intramolecular energy migration the comonomer quencher would be expected to be more effective. The above author concluded that for the condition of a slow final energy-transfer step following rapid energy migration copoly- merization was no improvement on simple molecular dispersion of an additive.He extended his conclusions to triplet EET in poly(viny1 phenyl ketone). It can be seen that when as in films inter- as well as intra-molecular energy migration becomes significant differences in behaviour are observed. In general terms the process of triplet energy migration is understood but some of the details are still to be unravelled. 53 R.D. Burkhart Macromolecules 1976 9 234. 54 G. A. George,J. Polymer Sci. Polymer Phys. Edn. 1972 10,1361. J. R. Maccallum 10 Orientation Factor In the Forster derivation relating specific rate of energy transfer to measurable parameters [equation (5)] a term K is introduced to allow for D-A spatial orientation. When this is completely randomized during the transfer time K’ takes a value of 0.66.For intermolecular transfer in solutions of low viscosity this is a realistic condition. However for intramolecular transfer and transfer in solids such as films or glasses the appropriate value for K may well be quite different; indeed depending on the disposition of the donor and acceptor moments K may vary from 0 to 4. The question of the appropriate value for K~ and even the applicability of the Forster equation have been discussed in a series of papers by Eisinger.’’ The thrust of his arguments is more directed to biochemical studies of EET but there seems to be a good case for consideration of the relevance of his criticisms to systems involving polymers in films and glasses. None of the papers which have been referred to in this Report and which used the Forster equations made any allowance for possible orientation effects.In Dexter’s treatment of the exchange mechanism for EET there is no explicit term which allows for orientation of the D/A pair [equation (14)]. Judeikis and Siegel proposed that the specific rate of transfer EkET,should be modified such that in which /3 is set equal to cos”8 with 8 the angle between donor and acceptor molecular planes.56 /3 was introduced as an arbitrary factor but the authors designated EkkT as a slow-moving function (m =O) or a fast-moving function (m large) of 8. Polarization measurements have been made on benzophenone-phenanthrene mixtures in poly(methy1 methacrylate).” In the circumstances used triplet EET took place by the exchange mechanism.It was concluded that the function was slow-moving and the dominant factor in determining EET was that of distance dependence. The relevance of orientation requirements in EET processes has been highlighted in theoretical treatments but there seems to be a need for more experimental data to assess the real significance of this factor in both the dipole-dipole and exchange mechanisms of EET. 55 J. Eisinger and R. E. Dale ‘Excited States of Biological Molecules’ Proc. Int. Conf. ed. J. Birks Wiley Chichester 1974 p. 579. s6 H. S. Judeikis and S. Siegel J. Chem. Phys. 1970 53 3500. 57 A. Adamczyk S. W. Beavan and D. Phillips ‘Excited States of Biological Molecules’ Proc. Int. Conf. ed. J. Birks 1974 p.39.