ExcitonâExciton Annihilation in Polysilanes - Advances in Chemistry

25 Exciton-Exciton Annihilation i n Polysilanes Downloaded by TUFTS UNIV on June 20, 2017 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch025

R. Glen Kepler and John M. Zeigler1 Sandia National Laboratories, Albuquerque, NM 87185 The exciton-exciton annihilation rate constant for singlet excitons in solid films of poly(n-propylmethylsilane) was determined by measur ing the fluorescent intensity from the films as a function of incidentlight intensity in two types of experiments: one in which the excitons were created by single-photon transitions and one in which the ex citons were created by two-photon transitions. The rate constant is ~10-7 cm /s. 3

THE TRANSPORT OF BOTH CHARGE CARRIERS

and neutral excited states in organic molecular crystals and polymers has been studied extensively in recent years (1-6), Almost all of these studies have been on molecules containing delocalized, conjugated IT electrons and have focused on the role of these electrons in the transport. Very recently, silicon-backbone polymers, polysilanes, were found to exhibit many of the same electronic properties as those previously thought to arise exclusively from conjugated ττ electrons, even though many of the σ-bonded polysilanes contain no IT electrons (7). In both solution and the solid state, these molecules exhibit high quantum efficiencies for fluorescence (8-10) and absorption spectra that depend strongly on molecular weight (8) and conformation (8-15). Solid films of polysilanes are excellent photoconductors (16, 17) and transport charge ef ficiently (18, 19). These properties are believed to result from σ electrons delocalized along the Si backbone, but relatively little is known presently about the theoretical description of the derealization of these electrons and their excited states. In this chapter, we report some measurements of energy transport by Current address: 2208 Lester Drive, NE, Number 421, Albuquerque, NM 87112

0065-2393/90/0224-0459$06.00/0 © 1990 American Chemical Society

Zeigler and Fearon; Silicon-Based Polymer Science Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

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SILICON-BASED POLYMER SCIENCE: A COMPREHENSIVE RESOURCE

singlet excitons (8, 16, 17) in poly(n-propylmethylsilane). We studied exciton-exciton annihilation, a process that occurs at relatively high exciton concentrations, by using two experimental techniques to create the excitons: single-photon and two-photon transitions. We found that exciton-exciton annihilation is an easily observed phenomenon that becomes the dominant process for exciton loss at a concentration in the order of 1016 excitons per cubic centimeter, even though the exciton lifetime is only 0.6 ns.

Downloaded by TUFTS UNIV on June 20, 2017 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch025

Experimental Procedures Crude poly(n-propylmethylsilane) was obtained by adding sodium dispersion to a solution of purified n-propylmethyldichlorosilane in refluxing dry toluene or in dry toluene mixed with heptane (20, 21) under well-controlled conditions. Two precip itations of the crude material from toluene with ethyl acetate and two from tetra hydrofuran with methanol afforded a pure white rubbery solid in 25% overall yield. The weight-average molecular weight (Mw) of this solid was found to be 2.7 X 105 daltons by gel permeation chromatography (calibrated with polystyrene), a value that corresponds to a polymer containing 3140 Si atoms in the backbone chain. The polymer was established (22) to be essentially atactic, that is, it has random ster eochemistry about the backbone silicon atoms. Films of various thicknesses were prepared by solvent casting, spin casting for films less than 1 μπι, and multiple-layer solvent casting for thick films. UV quartz was used as the substrate. The samples were mounted on a cold finger in a vacuum chamber. Most experiments were con ducted at room temperature, but a few were conducted at temperatures as low as 20 K. Excitons were created in the films in two ways: by single-photon transitions using strongly absorbed light and by two-photon transitions using photons with energies well below that required to create an exciton directly. The two-photontransition exciton-exciton annihilation experiments were conducted with frequencydoubled light from a neodymium-doped yttrium-aluminum-garnet (YAG) laser with a pulse width at half maximum of about 5 ns. Most of the single-photon experiments were conducted at 320 nm, but some were conducted at 280 nm. In both cases, the light was obtained by pumping a dye laser with the frequency-doubled neodymiumdoped YAG laser light. Excitons for this exciton lifetime experiment were created by two-photon transitions using frequency-doubled light from a neodymium-doped YAG laser with a pulse width of approximately 200 ps. An experiment consisted of measuring the peak fluorescent light intensity during a pulse as a function of the intensity of the incident light. The incident light intensity was measured by using a pellicle to reflect a fraction of the beam into a light meter (Laser Precision Corporation energy ratiometer, model Rj-7200). The intensity was varied by using a series of filters. The intensity of the fluorescent light was measured with a gated microchannel plate photomultiplier (Hamamatsu, model R2024V). The light intensity incident on the photomultiplier was maintained in the linear range of the photomultiplier by using a series of calibrated neutral density filters. The intensity of the incident light was limited to those intensities that did not damage the sample, as evidenced by the repeatability of experimental results.

Results Typical experimental results obtained on 50^m-thick samples are shown in Figures 1 and 2 for single-photon excitation and two-photon excitation, re-


25.

KEPLER .& ZEIGLER

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Figure 1. Fluorescence intensity versus incident laser light intensity at 320 nm. The straight line was fit to the low-intensity data and is drawn with the assumption that the fluorescence intensity is proportional to the intensity of the incident laser light. The curved solid line is the result predicted by the phenomenological equation for single-photon excitation with 7 = 4.2 X 10 cm 1 s. The area of the exciting laser beam was about 0.1 cm . 8

3

2

spectively. The solid lines are theoretical best fits to the experimental data, which were determined by using the following phenomenological equations and the exciton-exciton annihilation rate constant as a parameter. —

at

= al e~ 0

ax

- βη - 7η

dît — = κί02 - β η - yη

2

at

2

(single-photon excitation) (two-photon excitation)

(1) (2)

In these equations, η is the exciton concentration, t is time, α is the absorption coefficient for the incident light, I is the intensity of the incident light, κ is the two-photon absorption rate constant at 532 nm, β is the reciprocal of the exciton lifetime, and 7 is the exciton-exciton annihilation rate constant. The absorption coefficient α was determined to be 2.4 Χ 105 c m - 1 at 320 nm and 9.2 Χ 104 c m - 1 at 280 nm by measuring the optical density and thickness of several films. The exciton lifetime t (t = l / β ) was measured by using frequency-doubled light from a 200-ps neodymium-doped YAG laser 0



462


LIGHT INTENSITY (PHOTONS/SEC) Figure 2. Fluorescence intensity versus incident laser light intensity at 532 nm. The straight line was fit to the low-intensity data and is drawn with the assumption that the fluorescence intensity is proportional to the square of the intensity of the incident laser light. The curved solid line is the result predicted by the phenomenological equation for two-photon excitation with y = 10~ cm Is. The area of the exciting laser beam was about 0.1 cm . 7

3

2

to create excitons in a thick, approximately 50-μπι film, and the time de pendence of thefluorescencewas measured with a fast photodiode. We used this technique to measure the fluorescent lifetime for three types of poly silane with the following results: for poly(n-propylmethylsilane), t = 0.6 ns; for poly(di-n-hexylsilane), t = 1.0 ns; and for poly(phenylmethylsilane), t < 0.3 ns. For both experiments, we assumed that dn/dt = 0, because the exciton lifetime is considerably shorter than the excitation light pulse width. There fore, for the two-photon experiment at light intensities such that yn « βη, κ = β η / Ζ 0 2 . We found k = 10"26 cm3/s at 532 nm. The solid curve in Figure 2 was determined by using the constants just mentioned and 7 = 10~7 cm3/s. For the single-photon-transition experiment, the exciton con centration η is a strong function of depth in the sample, and thus /ndx is plotted as the solid line in Figure 1 with 7 = 4.2 Χ 10"8 cm3/s. Because the incident laser light intensity was not uniform over its area, the theoretical curves in Figures 1 and 2 were calculated by first measuring the incident laser beam intensity at 900 equally spaced points over its area. 2


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Exciton-Exciton

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We then assumed that the light intensity was uniform within each of these 900 equal-area segments. The total number of excitons present at equilibrium was then calculated for a given total number of excitons in a pulse by summing the theoretically calculated equilibrium density in each of the segments. The variation in light intensity over the area of the beam was taken into account in a similar fashion when we calculated the two-photon-absorption rate constant κ. Preliminary experiments conducted at 20 Κ indicate that the value of 7 at 20 Κ is within our experimental error of about a factor of 3 of its value at room temperature.

Discussion The possibility that our observations are the result of some process other than exciton-exciton annihilation should be examined. The most obvious experimental observation that will establish exciton-exciton annihilation as the process would be a decrease in the exciton lifetime at high concentrations. We have been unable to carry out this experiment so far. The most obvious possible alternative process that might explain the experimental results is exciton photoionization. It is highly unlikely that our results can be explained by this process for two reasons. First, the exciton photoionization coefficient at 320 nm would have to be unrealistically high to account for the obser vations. If σ is the exciton photoionization cross-section, then σ ί = β at the intensity at which the rate of exciton loss by the intensity-dependent process equals the rate of loss at low intensities. Because the intensity at which this occurs is about 1022 photons per square centimeter per second, σ would have to be about 10~13 cm 2 , an unreasonably large number. Second, the cross-section for photoionization at 532 nm would have to be about 3 orders of magnitude lower and fortuitously of just the right magnitude to allow the two different experiments to give results that are almost consistent with a single exciton-exciton annihilation rate constant. These results are strong evidence that excitons in polysilanes are highly mobile. The exciton concentration when the rate of loss by exciton-exciton annihilation equals the rate of loss by other nonannihilation processes can be determined by setting β η = 7 η to give η = β/y ~ 1016 excitons per cubic centimeter. At this concentration, the excitons are, on the average, about 400 Â apart. If excitons are assumed to be particles that diffuse with a diffusion coefficient D in three-dimensional space and that annihilate one another if they come within the distance R of each other, the rate constant for exciton-exciton annihilation is given (23) by 7 = 8uDR. If R is assumed to be 20 Â, D is about 0.01 cm2/s. This value is surprisingly large, because the diffusion coefficient for singlet excitons in anthracene single crystals is thought to be (24) about 10 3 cm2/s. The reported values of the exciton-exciton 2



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annihilation rate constant in anthracene single crystals at room temperature (24) range from 2 X 10~9 to 4 X 10~8 cm3/s. The excitons in the polysilane, however, almost certainly move quite rapidly along the chain on which they exist and then frequently hop from chain to chain. The consequences on exciton-exciton annihilation of this type of motion have not been discussed, to our knowledge. In these experiments, the values of y in the single-photon-excitation experiments were consistently lower than those in the two-photon-excitation experiments. We are presently investigating the possibility that neglect of exciton diffusion in the single-photon-excitation experiment might account for this discrepancy. Finally, because polysilanes show promise as photoresists (25, 26) and nonlinear optical materials (27), the fact that the rate of loss of excitons in poly(n-propylmethylsilane) by exciton-exciton annihilation becomes equal to the monomolecular loss rate at laser intensities of only 10 6 J/cm 2 in a 5-ns pulse is significant. Because exposure levels are typically much higher for photoresist and nonlinear optical studies, exciton-exciton annihilation must be considered when attempting to understand the underlying photochemical reactions, because annihilation may dominate other photophysical and photochemical processes.

Summary By measuring the intensity of fluorescence versus exciton concentration in solid films of poly(n-propylmethylsilane), the exciton-exciton annihilation rate constant was determined to be ~10" 7 cm3/s. These results show that excitons are highly mobile in these materials. One theoretical interpretation of the rate constant indicated that the diffusion coefficient is about 10~2 cm2/s, an exceptionally high value. These results also show that exciton-exciton annihilation is an important process that will have to be taken into account when attempting to interpret experiments designed to investigate fundamental photochemical and photophysical processes in these materials if the exposure light intensity is higher than —100 W/cm 2 .

Acknowledgments This work was supported by the U.S. Department of Energy under contract number DE-AC04-76DP00789. The technical assistance of P. M . Beeson and L. I. McLaughlin is gratefully acknowledged.

References 1. Wudl, F. Acc. Chem. Res. 1984, 17, 227. 2. Tanaka, K.; Yamabe, J. Adv. Quantum Chem. 1985, 17, 251.


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3. Handbook of Conducting Polymers; Skotheim, Α., Ed.; Marcel Dekker: New York, 1986. 4. Polydiacetylenes; Bloor, D.; Chance, R. R., Eds.; Maritimes Nijoff: Netherlands, 1985. 5. Chien, J. C. W. Polyacetylene; Academic: New York, 1984. 6. Hayes, W. Contemp. Phys. 1985, 26, 421-441. 7. West, R. J. Organomet. Chem. 1986, 99, 300.


8. Harrah, L. Α.; Zeigler, J. M . Macromolecules 1987, 20, 601-608. 9. Harrah, L. Α.; Zeigler, J. M . In Photophysics of Polymers; Hoyle, C. E.; Torkelson, J. M . , Eds.; ACS Symposium Series 358; American Chemical Society: Washington, DC, 1987; pp 482-498. 10. Johnson, G. E.; McGrane, Κ. M . In Photophysics of Polymers; Hoyle, C. E.; Torkelson, J. M . , Eds.; ACS Symposium Series 358; American Chemical Society: Washington, D C , 1987; pp 499-515. 11. Harrah, L. Α.; Zeigler, J. M . J. Polym. Sci., Polym. Lett. Ed. 1985, 23, 209.

12. Trefonas, P.; Damewood, J. R.; West, R.; Miller, R. D. Organometallics 1985, 4, 1318-1319. 13. Miller, R. D.; Hofer, D.; Rabolt, J.; Fickes, G. N. J. Am. Chem. Soc. 1985, 107, 2172-2174. 14. Miller, R. D.; Farmer, B. L.; Fleming, W.; Sooriyakumaran, R.; Rabolt, J. J. Am. Chem. Soc. 1987, 109, 2509-2510. 15. Kuzmany, H . ; Rabolt, J. F.; Farmer, B. L.; Miller, R. D. J. Chem. Phys. 1986, 85, 7413-7422. 16. Kepler, R. G.; Zeigler, J. M . ; Harrah, L. Α.; Kurtz, S. R. Phys. Rev. B.: Condens. Matter 1987, 35,

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17. Kepler, R. G.; Zeigler, J. M . ; Harrah, L. Α.; Kurtz, S. R. Bull. Am. Phys. Soc. 1983, 28, 362. 18. Stolka, M . ; Yu, H . J.; McGrane, K.; Pai, D. M . J. Polym. Sci., Part A 1987, 25, 823-827. 19. Abkowitz, M.; Knier, F. Ε.; Yu, Η. J.; Weagley, R. J.; Stolka, M . Solid State Commun. 1987, 62, 547-550.

20. Zeigler, J. M . Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1987, 28,

424-425.

21. Zeigler, J. M . Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1986,

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109-110. 22. Schilling, F. C.; Bovey, F. Α.; Zeigler, J. M . Macromolecules 1986, 19, 2309-2312.

23. Agranovich, V. M . ; Galanin, F. D. Electronic Excitation Energy Transfers in

Condensed Matter; North-Holland: New York, 1982.

24. Kepler, R. G. In Treatise on Solid State Chemistry; Crystalline and Non-Crys

talline Solids; Hannay, Ν. B.; Ed., Plenum: New York, 1976; Vol. 3, ρ 615.

25. Zeigler, J. M . ; Harrah, L. Α.; Technol. Process. II 1985, 537, 26. Hofer, D. C.; Miller, R. D.; Technol Process. I 1984, 469,

Johnson, A. W. Proc SPIE Conf., Adv. Resist 166-174. Willson, C. G. Proc. SPIE Conf., Adv. Resist 16-23.

27. Kajzar, F.; Messier, J.; Rosilio, C. J. Appl. Phys. 1986, 60, 3040-3044.

RECEIVED for review May 27, 1988. ACCEPTED revised manuscript October 20, 1988.


ExcitonâExciton Annihilation in Polysilanes - Advances in Chemistry

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