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Charge separation and geminate recombination in sensitized photoconducting polymers
Synthetic Metals 109 Ž2000. 39–42 www.elsevier.comrlocatersynmet
Charge separation and geminate recombination in sensitized photoconducting polymers Darius Abramavicius, Vidmantas Gulbinas, Leonas Valkunas
)
Institute of Physics, A. Gostauto 12, 2600 Vilnius, Lithuania Received 26 June 1999; received in revised form 25 August 1999; accepted 10 September 1999
Abstract Dynamics of charge pair photogeneration and recombination in sensitized photoconducting polymers was analysed by means of Monte Carlo simulations of the charge migration in the cubic lattice framework by taking into account the diagonal and off-diagonal disorder. On the basis of the experimental data, which indicate that the mean time of initial charge separation is on the subpicosecond time scale while the random hopping of charges in the geminate recombination process is of a few orders of magnitude slower, the mechanism, by suggesting correlated oscillations of the environment polarisation as a positive feedback in the unrelaxed charge transfer state, is suggested. By assuming wide initial hole distribution over the separation distance it has been demonstrated that faster recombination in the films with higher concentration of the sensitizer can be related to the dynamic scattering of the unrelaxed charge carrier by the sensitizer molecules in the course of the initial separation process. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Photogeneration; Geminate recombination; Sensitization; Monte Carlo simulation
1. Introduction According to the present understanding of charge photogeneration in sensitized organic photo-conductors, at least two steps can be distinguished in this complex process. Immediately after the light quantum absorption, a Coulombically bound electron–hole pair is generated w1,2x. This step is very fast and proceeds on the subpicosecond time scale, while the second step, which describes the subsequent charge separation by overcoming the Coulomb barrier, is much slower w2–4x. The latter process is adequately described by the Onsager theory, however, the initial step of the charge pair generation is not completely clear. A number of models has been suggested to describe the charge separation mechanisms in organic photoconductors w3–5x. However, no one of them can explain recent experimental data demonstrating ultrafast Žsubpicosecond. initial step of charge separation in organic photoconductors. Therefore, the initial charge transfer distance usually is considered as a fitting parameter by describing a subsequent processes of charge carrier separation andror geminate recombination. It is currently accepted that the low energy charge transfer states of the chromophore-sensitizer )
C orresponding author. [email protected]
Fax:
q370-2-617070;
e-m ail:
complexes ŽCT complexes. play the essential role in the first step of the separation process w2x. There are two well-developed models describing the distribution of initial charge separation distances. Photocurrent measurements w6x and field-induced fluorescence quenching w7–9x are explained by postulating the initial separation extended over several chromophores with the ˚ The other mean initial separation distance r M f 30 A. concept denies the assumption of the initial separation over distances larger than the CT complex size, suggesting that the absorbed light quantum initially creates a charge pair only inside the CT complex w10–12x. Further separation is possible because of the disordered arrangement of the mobile charge Žhole. states on the neighbouring monomers w10x. However, by analysing the geminate pair recombination ŽGPR. kinetics, a wide exponential initial distribution containing the mean separation distance of several lattice constants Ž r M ) a. was suggested w13x. Lately, by using the disordered lattice model and assuming the finite recombination rate in the recombination centre, it has been shown that the initial separation over a large distance is required to explain the kinetic recombination measurements in the films with high concentrations of the sensitizer w14x. It was also suggested that the experimentally observed faster GPR in the films with higher concentration of the sensitizer might be explained by assuming that the
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 1 9 5 - 2
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D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
mean initial separation is shorter in the films with high concentration of the sensitizer. In order to understand a possible reason of the initial charge separation reduction and to define its influence on the GPR kinetics, the analysis of this problem based on the Monte Carlo approach is presented in this paper. This consideration, stimulated by the experimental data of the sensitized carbazolyl-containing ŽCz. compounds w2x, is restricted to a specific range of parameters.
2. Charge separation Recently, the evidence of subpicosecond charge separation in sensitized polymers excited into the lowest CT states is presented w2x. Extremely fast charge separation over a large distance is difficult to be understood in terms of the conventional charge separation models w3–5x between the relaxed electronic states since the excess energy in the CT state is absent in these experimental conditions. Sebastian et al. w15x have suggested that polaron formation energy may be utilised for charge separation. However, this mechanism cannot be applied to explain the ultrafast charge separation. Therefore, we suggest that the hole transfer from the CT states to the neighbouring chromophores can be considered as a dynamic process stimulated by the correlated oscillations of the nuclei of the surrounding. As the CT state is excited, a large dipole moment localised on this particular molecular complex immediately appears, inducing changes in equilibrium positions of atoms in a neighbouring environment. As a consequence, coherent oscillations of these atoms with some characteristic frequencies v i are initiated resulting in an oscillating polarisation field. This field in its turn creates a positive feedback on the initially generated dipole moment. Due to the coherent oscillations, maximum values of the polarisation field may significantly exceed its mean value facilitating charge transfer from the CT complex to the neighbouring molecules. However, the coherence of oscillations is lost after some time t coh . Thus, the time scales of the process must obey the relation: t coh ) vy1 i . The long-range separation process may be understood as a sequence of correlated charge transfer steps resulted from the dipole interaction with the coherent oscillations of the environment. However, the unrestricted path for the initial hole separation is required. Therefore, the initial separation can be disturbed by the other molecules of the sensitizer because of the different polarisability, resulting in the mobile charge scattering.
3. Geminate pair recombination The GPR is related to the second step of the photogeneration process already mentioned in the Introduction. By describing the GPR, the initial charge separation being
much faster than the recombination may be treated as an instant event. Thus, the initial condition of the GPR process can be attributed to the set of independent charge pairs where separation distances between the hole and the electron r 0 are described by the initial separation distribution function n 0 Ž r .. The recombination process corresponds to the diffusive motion of the mobile charge over the polymer framework within the Coulomb field of the counterion. Thus, the recombination time is limited by the diffusive approach time of the mobile charge to the immobile one. It should be noted that the recombination rate in the CT complex may be the other limiting factor w14x; however, the current considerations are related to the pairs separated by large distances, thus, making the hopping process overwhelming. The basic concepts of the simulation model are outlined below. The arrangement of the model system is a cubic lattice framework with a diagonal and off-diagonal disorder included. Two types of the sites are created in the lattice: h sites for the hole movement and CT sites Žprobability to find the CT site in the lattice is denoted by pCT . for the electron hopping as well as determining the recombination centres. The h sites correspond to the polymer chromophores, while the CT sites are attributed to the sensitizer molecules or, more precisely, to the CT complexes. The recombination event is included into consideration by allowing the hole to jump on the CT site occupied by the electron. The diffusive motion of the hole after initial separation is simulated by the same scheme as used w16x. The time scale of the total by Ries and Bassler ¨ process is attributed to the mean hole jump rate k in the plain regular lattice. Distances of the model system are normalised to the lattice constant a while the initial charge pair density is equal to 1. The GPR dependence on the disorder has been studied lately w13x. It has been obtained that the diagonal disorder slows down the recombination in the long times, while the off-diagonal disorder speeds up the recombination on the short time scale. The qualitative shape of the GPR kinetics was found to be governed by the initial separation distribution function. Therefore, in the current study the disorder values are suggested to be the same as determined in Ref. w14x. The simplified initial separation model is the following. On the basis of the dynamic separation model, it is supposed that during the charge separation the hole is transferred to the bulk where it becomes localised at a particular distance r 0 ) a from the sensitizer molecule. The sensitizer molecules may be treated as impurities in the polymer framework creating obstacles for the hole transfer. Thus, the hole is scattered elastically by the CT sites. By modelling this initial hole separation, the duration of this process is not considered because the separation proceeds on the time scale, which is by few orders of magnitude faster. The scattering efficiency is described by a scattering radius rs , which is a single fitting parameter.
D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
41
recombination rate of the CT complex must be taken into account on the short time scale w14x.
4. Concluding remarks
Fig. 1. The distribution of the initial electron–hole separation distance and its dependence on the concentration of the sensitizer; rs s 2 a, width of the off-diagonal disorder soff s 0.3. The distance r is presented in the units of lattice constant a.
Fig. 1 demonstrates the influence of the scattering effect on the shape of the initial separation distribution function as the number of the CT sites increases. Thus, even an exponential distribution assumed for initial separation w13x due to a multiple scattering of the mobile charge Žhole. appears to be similar to the Gaussian one with the mean charge separation distance sensitive to the concentration of sensitizers. The mean initial separation distance r M is reduced from 5 to 2.3 of the lattice constants as the pCT is increased from 0.005 to 0.3. Fig. 2 shows the effect of these changes on the GPR kinetics, that are close to the experimental ones w14x. However, the simulation results should be treated only as references, because the finite
Fig. 2. GPR kinetics with the charge scattering effect included; rs s 2 a, width of the diagonal disorder se s 0.04 eV, width of the off-diagonal disorder soff s 0.3. The time t is presented in the units of the mean jump time in the plain lattice.
The overall charge separation–recombination process may be presented by the scheme shown in Fig. 3. According to the experimental results obtained in poliepoxypropylcarbazole ŽPEPCz. Žas well as in other polymeric photoconductors., the charge separation is initiated by low energy quantum corresponding to the lowest intermolecular CT states w2x. The initial separation inside the CT complex involves correlated oscillations of the environment polarisation, which by the positive feedback influences the unrelaxed CT state. As a consequence, the mobile charge — the hole — is transferred over several chromophores. After some time t coh , a relaxed long-range charge pair, is created. The hole transfer distance may be reduced by another sensitizer molecule happened to be in the vicinity of the CT complex. The relaxed hole makes random hopping until the excited CT state is reformed. The last step of the total process is the CT state recombination which is the intrinsic property of the CT complex. Results of the Monte Carlo simulations presented above point out to the sensitivity of the GPR kinetics to the initial electron–hole separation distribution. As revealed in Ref. w13x, the absence of the delay in the GPR kinetics evidences against the simple Gaussian or delta-type initial distributions with the mean value exceeding the interchromophore distance. By including the finite recombination rate of the CT complex into the simulation model, it has been obtained that the fast initial recombination can be attributed to the charge pairs, which initially are nonsepa-
Fig. 3. The scheme of charge separation and recombination in the sensitized photoconducting polymers.
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D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
rated, i.e., to some holes remaining on the CT complexes w14x. In this case, the initial distribution may be represented as a sum of two distribution functions with the peaks corresponding to two different processes: charge pair separation over short rCT and long r 0 distances, the latter exceeding a lattice constant a. The GPR dependence on the sensitizer concentration can be understood as being resulted from the scattering of the initial hole transfer leading to the transformation of the initial hole distribution causing a decrease in the mean separation distance. Acknowledgements The research described in this publication was made possible in part by Grant No. 359 from the Lithuanian State Foundation of Science and Studies. References w1x L.J. Rothberg, M. Yan, A.W.P. Fung, T.M. Jedju, E.W. Kwock, M.E. Galvin, Synthetic Metals 84 Ž1997. 537.
w2x A. Ruseckas, V. Gulbinas, V. Sundstrom, A. Undzenas, L. Valkunas, J. Phys. Chem. B 102 Ž1998. 7365. w3x E.A. Silinsh, V. Capek, Organic Molecular Crystals, Interaction, Localization and Transport Phenomena, AIP Press, New York, 1994. w4x M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals, Clarendon Press, Oxford, 1982. w5x J. Kalinowski, W. Stampor, P.G. Di Marco, J. Chem. Phys. 96 Ž1992. 4136. w6x K. Okamoto, A. Itaya, Bull. Chem. Soc. Jpn. 57 Ž1984. 1626. w7x M. Yokoyama, A. Matsubara, S. Shimokihara, H. Mikawa, Polym. J. 14 Ž1982. 73. w8x M. Yokoyama, Y. Endo, A. Matsubara, H. Mikawa, J. Chem. Phys. 75 Ž1981. 3006. w9x M. Yokoyama, H. Mikawa, Photo. Sci. Eng. 26 Ž1982. 143. w10x K. Watanabe, T. Asahi, H. Masuhara, J. Phys. Chem. 100 Ž1996. 18436. w11x K. Watanabe, T. Asahi, H. Masuhara, J. Phys. Chem. B 101 Ž1997. 5131. w12x Y. Wang, A. Suna, J. Phys. Chem. B 101 Ž1997. 5131. w13x Abramavicius, V. Gulbinas, A. Ruseckas, A. Undzenas, L. Valkunas, Mol. Cryst. Liq. Cryst. 324 Ž1998. 275. w14x Abramavicius, V. Gulbinas, A. Ruseckas, A. Undzenas, L. Valkunas, J. Chem. Phys., accepted. w15x L. Sebastian, G. Weisler, G. Peter, H. Bassler, Chem. Phys. 75 Ž1983. 103. w16x B. Ries, H. Bassler, Mol. Electron. 3 Ž1987. 15. ¨
Charge separation and geminate recombination in sensitized photoconducting polymers Darius Abramavicius, Vidmantas Gulbinas, Leonas Valkunas
)
Institute of Physics, A. Gostauto 12, 2600 Vilnius, Lithuania Received 26 June 1999; received in revised form 25 August 1999; accepted 10 September 1999
Abstract Dynamics of charge pair photogeneration and recombination in sensitized photoconducting polymers was analysed by means of Monte Carlo simulations of the charge migration in the cubic lattice framework by taking into account the diagonal and off-diagonal disorder. On the basis of the experimental data, which indicate that the mean time of initial charge separation is on the subpicosecond time scale while the random hopping of charges in the geminate recombination process is of a few orders of magnitude slower, the mechanism, by suggesting correlated oscillations of the environment polarisation as a positive feedback in the unrelaxed charge transfer state, is suggested. By assuming wide initial hole distribution over the separation distance it has been demonstrated that faster recombination in the films with higher concentration of the sensitizer can be related to the dynamic scattering of the unrelaxed charge carrier by the sensitizer molecules in the course of the initial separation process. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Photogeneration; Geminate recombination; Sensitization; Monte Carlo simulation
1. Introduction According to the present understanding of charge photogeneration in sensitized organic photo-conductors, at least two steps can be distinguished in this complex process. Immediately after the light quantum absorption, a Coulombically bound electron–hole pair is generated w1,2x. This step is very fast and proceeds on the subpicosecond time scale, while the second step, which describes the subsequent charge separation by overcoming the Coulomb barrier, is much slower w2–4x. The latter process is adequately described by the Onsager theory, however, the initial step of the charge pair generation is not completely clear. A number of models has been suggested to describe the charge separation mechanisms in organic photoconductors w3–5x. However, no one of them can explain recent experimental data demonstrating ultrafast Žsubpicosecond. initial step of charge separation in organic photoconductors. Therefore, the initial charge transfer distance usually is considered as a fitting parameter by describing a subsequent processes of charge carrier separation andror geminate recombination. It is currently accepted that the low energy charge transfer states of the chromophore-sensitizer )
C orresponding author. [email protected]
Fax:
q370-2-617070;
e-m ail:
complexes ŽCT complexes. play the essential role in the first step of the separation process w2x. There are two well-developed models describing the distribution of initial charge separation distances. Photocurrent measurements w6x and field-induced fluorescence quenching w7–9x are explained by postulating the initial separation extended over several chromophores with the ˚ The other mean initial separation distance r M f 30 A. concept denies the assumption of the initial separation over distances larger than the CT complex size, suggesting that the absorbed light quantum initially creates a charge pair only inside the CT complex w10–12x. Further separation is possible because of the disordered arrangement of the mobile charge Žhole. states on the neighbouring monomers w10x. However, by analysing the geminate pair recombination ŽGPR. kinetics, a wide exponential initial distribution containing the mean separation distance of several lattice constants Ž r M ) a. was suggested w13x. Lately, by using the disordered lattice model and assuming the finite recombination rate in the recombination centre, it has been shown that the initial separation over a large distance is required to explain the kinetic recombination measurements in the films with high concentrations of the sensitizer w14x. It was also suggested that the experimentally observed faster GPR in the films with higher concentration of the sensitizer might be explained by assuming that the
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 1 9 5 - 2
40
D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
mean initial separation is shorter in the films with high concentration of the sensitizer. In order to understand a possible reason of the initial charge separation reduction and to define its influence on the GPR kinetics, the analysis of this problem based on the Monte Carlo approach is presented in this paper. This consideration, stimulated by the experimental data of the sensitized carbazolyl-containing ŽCz. compounds w2x, is restricted to a specific range of parameters.
2. Charge separation Recently, the evidence of subpicosecond charge separation in sensitized polymers excited into the lowest CT states is presented w2x. Extremely fast charge separation over a large distance is difficult to be understood in terms of the conventional charge separation models w3–5x between the relaxed electronic states since the excess energy in the CT state is absent in these experimental conditions. Sebastian et al. w15x have suggested that polaron formation energy may be utilised for charge separation. However, this mechanism cannot be applied to explain the ultrafast charge separation. Therefore, we suggest that the hole transfer from the CT states to the neighbouring chromophores can be considered as a dynamic process stimulated by the correlated oscillations of the nuclei of the surrounding. As the CT state is excited, a large dipole moment localised on this particular molecular complex immediately appears, inducing changes in equilibrium positions of atoms in a neighbouring environment. As a consequence, coherent oscillations of these atoms with some characteristic frequencies v i are initiated resulting in an oscillating polarisation field. This field in its turn creates a positive feedback on the initially generated dipole moment. Due to the coherent oscillations, maximum values of the polarisation field may significantly exceed its mean value facilitating charge transfer from the CT complex to the neighbouring molecules. However, the coherence of oscillations is lost after some time t coh . Thus, the time scales of the process must obey the relation: t coh ) vy1 i . The long-range separation process may be understood as a sequence of correlated charge transfer steps resulted from the dipole interaction with the coherent oscillations of the environment. However, the unrestricted path for the initial hole separation is required. Therefore, the initial separation can be disturbed by the other molecules of the sensitizer because of the different polarisability, resulting in the mobile charge scattering.
3. Geminate pair recombination The GPR is related to the second step of the photogeneration process already mentioned in the Introduction. By describing the GPR, the initial charge separation being
much faster than the recombination may be treated as an instant event. Thus, the initial condition of the GPR process can be attributed to the set of independent charge pairs where separation distances between the hole and the electron r 0 are described by the initial separation distribution function n 0 Ž r .. The recombination process corresponds to the diffusive motion of the mobile charge over the polymer framework within the Coulomb field of the counterion. Thus, the recombination time is limited by the diffusive approach time of the mobile charge to the immobile one. It should be noted that the recombination rate in the CT complex may be the other limiting factor w14x; however, the current considerations are related to the pairs separated by large distances, thus, making the hopping process overwhelming. The basic concepts of the simulation model are outlined below. The arrangement of the model system is a cubic lattice framework with a diagonal and off-diagonal disorder included. Two types of the sites are created in the lattice: h sites for the hole movement and CT sites Žprobability to find the CT site in the lattice is denoted by pCT . for the electron hopping as well as determining the recombination centres. The h sites correspond to the polymer chromophores, while the CT sites are attributed to the sensitizer molecules or, more precisely, to the CT complexes. The recombination event is included into consideration by allowing the hole to jump on the CT site occupied by the electron. The diffusive motion of the hole after initial separation is simulated by the same scheme as used w16x. The time scale of the total by Ries and Bassler ¨ process is attributed to the mean hole jump rate k in the plain regular lattice. Distances of the model system are normalised to the lattice constant a while the initial charge pair density is equal to 1. The GPR dependence on the disorder has been studied lately w13x. It has been obtained that the diagonal disorder slows down the recombination in the long times, while the off-diagonal disorder speeds up the recombination on the short time scale. The qualitative shape of the GPR kinetics was found to be governed by the initial separation distribution function. Therefore, in the current study the disorder values are suggested to be the same as determined in Ref. w14x. The simplified initial separation model is the following. On the basis of the dynamic separation model, it is supposed that during the charge separation the hole is transferred to the bulk where it becomes localised at a particular distance r 0 ) a from the sensitizer molecule. The sensitizer molecules may be treated as impurities in the polymer framework creating obstacles for the hole transfer. Thus, the hole is scattered elastically by the CT sites. By modelling this initial hole separation, the duration of this process is not considered because the separation proceeds on the time scale, which is by few orders of magnitude faster. The scattering efficiency is described by a scattering radius rs , which is a single fitting parameter.
D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
41
recombination rate of the CT complex must be taken into account on the short time scale w14x.
4. Concluding remarks
Fig. 1. The distribution of the initial electron–hole separation distance and its dependence on the concentration of the sensitizer; rs s 2 a, width of the off-diagonal disorder soff s 0.3. The distance r is presented in the units of lattice constant a.
Fig. 1 demonstrates the influence of the scattering effect on the shape of the initial separation distribution function as the number of the CT sites increases. Thus, even an exponential distribution assumed for initial separation w13x due to a multiple scattering of the mobile charge Žhole. appears to be similar to the Gaussian one with the mean charge separation distance sensitive to the concentration of sensitizers. The mean initial separation distance r M is reduced from 5 to 2.3 of the lattice constants as the pCT is increased from 0.005 to 0.3. Fig. 2 shows the effect of these changes on the GPR kinetics, that are close to the experimental ones w14x. However, the simulation results should be treated only as references, because the finite
Fig. 2. GPR kinetics with the charge scattering effect included; rs s 2 a, width of the diagonal disorder se s 0.04 eV, width of the off-diagonal disorder soff s 0.3. The time t is presented in the units of the mean jump time in the plain lattice.
The overall charge separation–recombination process may be presented by the scheme shown in Fig. 3. According to the experimental results obtained in poliepoxypropylcarbazole ŽPEPCz. Žas well as in other polymeric photoconductors., the charge separation is initiated by low energy quantum corresponding to the lowest intermolecular CT states w2x. The initial separation inside the CT complex involves correlated oscillations of the environment polarisation, which by the positive feedback influences the unrelaxed CT state. As a consequence, the mobile charge — the hole — is transferred over several chromophores. After some time t coh , a relaxed long-range charge pair, is created. The hole transfer distance may be reduced by another sensitizer molecule happened to be in the vicinity of the CT complex. The relaxed hole makes random hopping until the excited CT state is reformed. The last step of the total process is the CT state recombination which is the intrinsic property of the CT complex. Results of the Monte Carlo simulations presented above point out to the sensitivity of the GPR kinetics to the initial electron–hole separation distribution. As revealed in Ref. w13x, the absence of the delay in the GPR kinetics evidences against the simple Gaussian or delta-type initial distributions with the mean value exceeding the interchromophore distance. By including the finite recombination rate of the CT complex into the simulation model, it has been obtained that the fast initial recombination can be attributed to the charge pairs, which initially are nonsepa-
Fig. 3. The scheme of charge separation and recombination in the sensitized photoconducting polymers.
42
D. AbramaÕicius et al.r Synthetic Metals 109 (2000) 39–42
rated, i.e., to some holes remaining on the CT complexes w14x. In this case, the initial distribution may be represented as a sum of two distribution functions with the peaks corresponding to two different processes: charge pair separation over short rCT and long r 0 distances, the latter exceeding a lattice constant a. The GPR dependence on the sensitizer concentration can be understood as being resulted from the scattering of the initial hole transfer leading to the transformation of the initial hole distribution causing a decrease in the mean separation distance. Acknowledgements The research described in this publication was made possible in part by Grant No. 359 from the Lithuanian State Foundation of Science and Studies. References w1x L.J. Rothberg, M. Yan, A.W.P. Fung, T.M. Jedju, E.W. Kwock, M.E. Galvin, Synthetic Metals 84 Ž1997. 537.
w2x A. Ruseckas, V. Gulbinas, V. Sundstrom, A. Undzenas, L. Valkunas, J. Phys. Chem. B 102 Ž1998. 7365. w3x E.A. Silinsh, V. Capek, Organic Molecular Crystals, Interaction, Localization and Transport Phenomena, AIP Press, New York, 1994. w4x M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals, Clarendon Press, Oxford, 1982. w5x J. Kalinowski, W. Stampor, P.G. Di Marco, J. Chem. Phys. 96 Ž1992. 4136. w6x K. Okamoto, A. Itaya, Bull. Chem. Soc. Jpn. 57 Ž1984. 1626. w7x M. Yokoyama, A. Matsubara, S. Shimokihara, H. Mikawa, Polym. J. 14 Ž1982. 73. w8x M. Yokoyama, Y. Endo, A. Matsubara, H. Mikawa, J. Chem. Phys. 75 Ž1981. 3006. w9x M. Yokoyama, H. Mikawa, Photo. Sci. Eng. 26 Ž1982. 143. w10x K. Watanabe, T. Asahi, H. Masuhara, J. Phys. Chem. 100 Ž1996. 18436. w11x K. Watanabe, T. Asahi, H. Masuhara, J. Phys. Chem. B 101 Ž1997. 5131. w12x Y. Wang, A. Suna, J. Phys. Chem. B 101 Ž1997. 5131. w13x Abramavicius, V. Gulbinas, A. Ruseckas, A. Undzenas, L. Valkunas, Mol. Cryst. Liq. Cryst. 324 Ž1998. 275. w14x Abramavicius, V. Gulbinas, A. Ruseckas, A. Undzenas, L. Valkunas, J. Chem. Phys., accepted. w15x L. Sebastian, G. Weisler, G. Peter, H. Bassler, Chem. Phys. 75 Ž1983. 103. w16x B. Ries, H. Bassler, Mol. Electron. 3 Ž1987. 15. ¨