Polysilane excited states and excited state dynamics

Chemical Physics 146 (1990) 315-325 North-Holland

Polysilane excited states and excited state dynamics J.R.G. Theme,

S.T. Repinec, S.A. Abrash, J.M. Zeigler ’ and R.M. Hoohstrasser

Department of Chemistry, University ofPennsylvania, Philadelphia, PA 19104, USA Received 26 January 1990

Femtosecond time-resolved excited state absorption spectroscopy is used to reveal excited states of linear-chain poly(di-nhexylsilane) about 1 eV and in the range of 3.5 eV above the lowest excited state. A description of the excited state dynamics following optical excitation in polysilanes is presented. The concept of conjugation length is discussed in relation to experiments on the saturation of excited state absorption signals observed at high excitation density.

1. Introdactlon Interest in the nature of the excited states of o-conjugated polysilane polymers, (RR’Si),, has several sources. Theoretical interest centers on the nature of low-dimensional excitations and in particular comparison with the x-conjugated polydiacetylenes. Nonlinear spectroscopies [ I-31 are being applied to investigate the large third-order polarizabilities reported for this system [ 4,5 1. The complex nature of the photochemistry in these materials and the need to understand spatial and spectral diffusion of excitations for photoresist applications, have led to studies of fluorescence depolarization [ 6-8 1, excitonexciton annihilation [ 9 ] and hole burning [ lo,11 1. Poly (di-n-hexylsilane ) is the most extensively studied of the polymers. The absorption spectrum in room temperature solution has a peak at 3 17 nm having a linewidth of x 35 nm. The fluoresence is redshifted and peaks at * 340 nm, with a width of x 20 nm. The position of this latter maximum depends slightly upon excitation wavelength [ 71. The absorption spectrum has been understood in terms of an inhomogeneous distribution of segments having a range of excitation energies [ 12,131. Emission originates from the lower energy segments following energy transfer. The origin of the segment length distribu’ SandiaNational Laboratories,Albuquerque, NM 87185, USA. Present address: Silchemy Inc., 2208 Lester Dr., Albuquerque, NM 87112, USA.

tion is unknown. The solution absorption spectrum has been fairly successfully numerically modelled under the assumption of segmentation using Htickel linear-chain theory and an average segment length of B 10 silicon atoms corresponding to a defect probability of = 0.1 [ 13 1. It has been proposed that disorder can be introduced in the chain by random introduction of trans-gauche links in an otherwise perfect all-trans chain [ 12 1, Recently it has been shown [ 111 that the spectrum can be modelled by introducing a small random Gaussian energy disorder at every site in a linear chain. Application of this model to observed spectra also leads to the conclusion that the lowest energy states of the chain have extents of about 10 silicon atoms. This model explains the effects of energy transfer prior to photochemistry on the holeburning spectrum [ IO]. We refer to these alternative views of polysilane excitations as the “segmented chain”, and “disorder” models. The latter may be “intermittent” [ 12 ] or “random” [ 111 disorder. The process of energy transfer in the polymers has been followed. by the technique of time-resolved fluorescence depolarization [ 61; a fast initial decay of x 1O-20 ps followed by a slow decay of z 2 ns was observed [ 81. The amount of residual anisotropy after fast decay depends upon the excitation wavelength; it is near the theoretical maximum of 0.4 for, excitation on the low energy side of the line (340 nm) [7,81. We have previously made a study of the photoproduct absorptions induced in poly (phenylmeth-

0301-0104/90/S 03.50 0 1990- Elsevier Science Publishers B.V. (North-Holland)

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J.R.G. Thorne et al. / Polysilaneexcitedstates

ylsilane) in solution upon excitation at 355 nm with a 30 ps pulse [ 141. We were unable to identify the precursor state to photochemisty nor to observe excited state absorptions because these were apparently dominated by the photochemistry. In this study we use much improved instrumental time resolution and the polymer, poly ( di-n-hexylsilane ) , which has a longer excited state lifetime, greater quantum yield for radiative decay and reduced photochemical activity compared to poly ( phenylmethylsilane ) , to try to circumvent these photochemical problems. High-lying excited states may be revealed in a transient absorption spectrum where they are very weakly allowed or even strictly forbidden by a dipole mechanism in a single-photon spectrum. In addition, the possibility exists that new structures having absorptions may be induced by the presence of the excitation; polaron and soliton intra-gap transitions in semiconductors may be regarded as examples of this phenomenon. We have observed in our studies of the two-photon excitation spectra of polysilanes [ 1 ] a state x 0.9 eV above the first excited state. Selection rules for this transition render it forbidden with linear absorption. Such selection rules may derive from symmetry, for example the parity in centrosymmetric systems, or may be a result of a nearly vanishing oscillator strength from the electronic nature of these transitions, for example small overlap of wavefunctions involved in the transition. It is our aim in this work to identify and further characterize states by excited state absorption spectroscopy, and to test predictions for the presence of other high-lying electronic levels based on an excitonic model. A preliminary report of the infrared excited state absorption has already been published [ 21. Following the discussion of the states observed, we make use of the transient absorption at x 375 nm as a probe of ultrafast excited state dynamics and discuss possible relaxation mechanisms for the polymer. The final section deals with the saturation of the transient signal and leads to conclusions about the spatial extent of polysilane excitations.

2. Experimental Poly (di-n-hexylsilane ) samples of molecular weight 420000, having an average chain length of 2 100 sili-

cons, were prepared by the methods of Zeigler [15,16].Solutionsinhexanewere 1.2X10-3Mona per silicon basis. The optical density in the 1 mm flowing-cell used was 1.Oat room temperature, for an excitation wavelength of 3 12 nm. A complete description of the apparatus used for femtosecond transient absorption studies is given elsewhere [ 17 1. Laser pulses of = 70 fs fwhm at 624 nm from a CPM laser were amplified at a repetition rate of 20 Hz. The beam was split into pump and probe pulses. The former was doubled in a KDP crystal to generate 3 12 nm light focused to a spot size of 0.5 mm diameter at the sample. The pump energy per pulse was 15 pJ. The probe pulse was passed through a variable length delay line, through a D20 cell to generate broadband continuum radiation from which a frequency slice was selected using interference tilters, and overlapped with the pump at the sample. Ultraviolet probe pulses were generated by selecting a visible frequency, amplifying it and doubling in a KDP crystal. Photodiodes were used to monitor the intensities of pump, probe before sample and probe after sample. Polarization experiments were performed by rotating the polarization of the pump beam at the desired angle with respect to the probe.

3. Results Fig. 1 shows the loss/gain optical density, probed immediately following, and 4 ps after, a 3 12 nm pump laser pulse, as a function of probe pulse wavelength in the ranges 335-405 and 800- 1100 nm. A net gain in the probe wavelength region corresponding to the tail of the absorption peak, extending from 335 to 350 nm was observed and is shown as a negative-going peak in this (and all other) figures. Absorption and fluorescence spectra are shown inverted for comparison with the gain spectrum. Two high-lying excited state absorptions are visible at probe wavelengths of 375 nm (27000 cm-’ above the first state) and > 1100 nm ( < 9000 cm-’ above). Fig. 2 shows the time evolution of the absorption and gain signals at four different ultraviolet probe wavelengths for the first 4 ps following excitation at 3 12 nm. Fig. 3 shows representative short-time fitted data for the rise of the gain at 340 nm and the fast decay of the transient absorption at 920 nm. A summary of the results with

J.R.G. Thorne et al. / Polysilane excited states

AOD

i--L _

0.06

TRANSIENT

317

ABSORPTION

0.04 0.02 0

26000

-1

24000

1

-0.02 -004

TRANSIENT

:

GAIN

1 A

900

400

1000 1100 “Ill

FLUORESCENCE ABSORPTION

Fig. 1. Poly( di-n-hexylsilane) in hexane solution at room temperature, excitation wavelength 3 12 nm. (Upper) Excited state absorption and gain spectra. (Lower) Absorption and fluorescence spectra (inverted).

0.07 340

AOD

o-

%0

nm PROBE

~~=Da0W00000000 -0.02

-0.07

AOD

AOD

-0.03

0 TIME (ps)

0.02 AOD 001

012345 TIME (ps) TIME

(ps)

Fig. 2. Time evolution of transient absorption and gain for probe wavelengths 340-375 nm.

Fig. 3. Cain evolution at 340 mu (upper) and transient absorption evolution at 920 nm (lower). Curves are fitted to eq. (5 ) and have inverse rate constants k& of 500 and 760 fs respectively. Instrumental fwhm 500 fs.

J.R.G. Theme et al. / Polysilane excited states

318

Table 1 Lifetime of transient gain ( - ) and absorption ( + ) Probe energy

Fast kinetics

(nm)

(cm-‘)

&.I

&I,

335 340 345 350 355 360 375 380 390 405

29900 29400 29000 28600 28200 27800 26700 26300 25600 24700

-0.038 -0.01 0.015 0.015 0.005 0.07 0.06

- 0.038 -0.038 -0.015 -0.005 0.02 0.04 0.06 0.035 0.03 0.01

440-800

0.5 0.6 0.9 0.9 0.7

Transient decay time (ps) obscured by photoproduct absorption 53 98 150

photoproduct absorption dominates

920 1000 1100

10900 10000 9100

0.022 0.014

0.01 0.014 0.017

Table 2 Fluorescence lifetimes with 3 12 nm excitation Decay time

Emission wavelength (nm) 330 335 340 345 350 355 360 365

k& (ps)

(96)

r(ps)

W)

7

71 60 60 6

37 45 66 34

29 40 40 94 LOO 100 100 100

99 115 138 126 136 142 155 155

(ps)

fitted rise and decay parameters is given in table 1. Table 2 shows the luminescence lifetimes of the material as a function of detection wavelength when excited at 312 nm, fitted by a two-exponential decay model. The visible region of the spectrum (the region omitted from fig. 1) is dominated by photoproduct absorptions having risetimes of the order of the excited state lifetime. Excited state absorptions with optical density changes less than about 0.005 ( C,,S 100) would not be easily detected. In the spectral range > 27000 cm-’ excited state absorption or gain dominates over photoproduct absorp--

0.76

50 51

tions by a factor of two or more; at early times the effect of the latter is negligible but at long times “permanent” photoproduct absorptions make it difficult to determine the exact lifetime of long-lived excited state absorptions. Fig. 4 gives the decay of anisotropy of the excited state absorption coefficient a, defined as r(t) = (or-a,)/(2a1+u,),recordedwitha375nmprobe having 2 p.l energy, with electric vector parallel ( 11) and perpendicular ( _L) to the pump. For comparison the fluorescence anisotropy when excited by light of the same wavelength, 3 12 nm, is also shown. The transient absorption at 375 nm as a function of incident laser intensity appears in fig. 5.

4. Dlacussion 4.1. The first excited state In order to understand the excited state spectra, it is necessary to first discuss the composition of the absorption spectrum. Of particular importance, for it will occur repeatedly in our discussion, is the homogeneous linewidth (or linewidths) for the transition in solution at room temperature; this quantity is not known. It seems probable that the homogeneous line-

JAG. l%orneet ai. / Polysiianeexcited states

0

2

4 TIME

b)

0

0

200 TIME

6 (ps)

400 (ps)

8

10

600

800

Fig. 4. (a) Anisotropyof transient absorptionat 375 nm. (b) Anisotropyof fluorcaenccat 340 am. Pumpwavelength3 12 nm.

width represents an appreciable fraction, yet not the whole, of the observed linewidth at 300 K; we have several indications, in addition to the kinetics to be

319

discussed in the next sections, that this is the case. In poly(di-n-hexylsilane) glass at 78 K the homogeneous linewidth is known through hole-burning measurementstobe z120cm-’ [lO].Assumingaquadratic dependence of linewidth on temperature characteristic of Raman dephasing by weakly coupled phonons [ 18 1, we would predict a room temperature value of s 1700 cm-’ or B 20 nm; the observed spectrum has a width of k: 35 nm. In addition, the luminescence linewidth of ~22 nm may give a reasonable estimate of the homogeneous linewidth, in the limit that emission originates from only a narrow distribution of the lowest energy states. Perhaps the closest experimental determination of this quantity comes from the bleaching of the absorption transition in poly ( phenylmethylsilane ) [ 14 1, where “permanent photochemical hole burning” was possible on the low energy side of the absorption line in room temperature solution; the width of this hole was of the order of 10 nm. It is probable also that there may be a variation in the homogeneous width across the inhomogeneous profile. This has been found to be the case in poly(di-n-hexylsilane) glass at 1.6 IC where the homogeneous width measured by hole burning varied from 1.5 to 5 cm-’ on going from the low to the high energy side of the line [ 111. A related question concerns the peak absorptionpeak emission shift of k: 2000 cm-‘. There is strong evidence both from the hole-burning studies and the fluorescence depolarization measurements that energy transfer within the inhomogeneous line populates low energy centers. In addition emission at low temperature in the glass is nearly resonant with absorption [ 11. It is thought that a particular center on excitation does not strongly relax due to coupling to the lattice, shows negligible phonon structure in absorption and emission, and does not have the character of a strongly bound bipolaron. 4.2. Higher excited states

I

OO

2_ FLUENCE

I

I

4 J cme2x

6 lo3

FiB.5. Non-lineardependenceof transientabsorptionat 375 run upon pump energy, I, with theoretical curve for gruund state depletion.

We turn now to a discussion of the two higher excited states identifiable in poly (di-n-hexylsilane ) . We note fast the general trends in the transient signal decay times observable in the last column of table 1 and in table 2. For the ultraviolet transient, on moving from the high to the low energy side of the peak in fig. 1, the decay is rapid ( < 1 ps) at 340 nm probe wave-

320

J.R.G. Thorne et al. / Polysilane excitedstales

length, and becomes slower at 355 nm ( k: 50 ps), a value corresponding to the fluorescence lifetime for states at z330 nm. The transient at longer wavelengths than the peak maximum at 375 nm has the lifetime characteristic of the majority of the emitting states ( 150 ps). A similar pattern is shown by the infrared transient. At 920 nm it has a fast component; at 1100 nm it has a lifetime of x 50 ps. The width of the ultraviolet transient is z 4000 cm- ‘, similar to that of the lowest energy electronic transition in absorption; the width of the infrared absorption is not known since measurements were not extended beyond 1100 nm. We interpret these observations to mean that the low energy states of the first excited manifold have low energy transient absorptions, the high energy (short lifetime) states have high energy transients. This implies that the inhomogeneous spread of levels in the doubly excited state is approximately twice that in the first excited state. Energy transfer dynamics observed as time-dependent luminescence and luminescence depolarization signals are generally paralleled in the time dependence of excited state absorption and excited state absorption polarization decays. This is the basis of the discussion of dynamics in section 4.3. A postulated energy diagram for states of the polymer backbone labelled B, incorporating the above features, is shown in fig. 6. We note that the shape of the ultraviolet transient loss on the high energy edge is distorted by the gain signal expected in the region of the fluorescence and its peak could be higher in energy than 375 nm. The final state of the infrared transient (designated B2 in fig. 6) could represent the high energy edge of the very strong two-photon absorption transition, not seen in one-photon absorption, that we have observed to occur in all phases of poly (di-nhexylsilane), 7000 cm- ’ above the first excited state, Bl. The nature of this excited state has been discussed at length [ 1,2]. To summarize, we have suggested that it is an excitonic state having a higher degree of charge transfer character than the lowest excited state, in accordance with theoretical models for charge transfer excitons in delocalized systems [ 19,201. Consider a three-silicon, two-bond unit cell, with bonds labelled a and b. Introduction of charge delocalization into a valence-bond or Frenkel exciton model can be simplistically achieved by allowing

Energy cm-’

Energy eV

60000

IBOI

1

Fig, 6. Postulated energylevel diagramfor poly(di-n-hexylsilane).

either the excitation of an electron from bonding orbital a to antibonding orbital a* (bond excitation, B,) or to antibonding orbital b* (charge transfer excitation, CT,). If the energy of either excitation is ccl, the one-electron coupling /3,, and the exciton transfer interaction is a, then the symmetrized wavefunctions and energies for the system are: ci(&,+Bi,)+c~(CTa+CTi,)

3

~,=o,+(B~/2)-(8~/4+8:)“2;

(1)

m

(2)

(CT,-CT&

Ez=~I ;

cz(Ba+Bb)-c,(CT,+CTt.), E,=w, + (pE/2)+ (~8/4+8:)‘/2 m

(B,-B,),

Ed=01 -&.

;

(3) (4)

Level ( 1) is suggested to correspond to the onephoton dipole accessible state B 1; level (2) to the dipole-forbidden two-photon accessible state B2. The intermediate state in the two-photon transition is suggested to be the first excited state, B 1. The charge transfer exciton model predicts the first-to-second excited state absorption (Bl-B2) will have a large transition dipole, equal to $ c2,u,where p is the permanent dipole set up by moving an electron between neighbouring bonds. There is no transition dipole for one-photon absorption (BO-B2 ) in this model.

J.R.G. Thorne et al. / Polysilane excitedstates

In an excitonic description of the excited states of a system it is predicted that an electronic state will occur at about twice the energy of the exciton. The state corresponds to a two-electron, doubly excited or biexciton state and may have a stabilization energy associated with the gain in energy due to the net attraction of two nearby partially charged separated excitations. In this model we could associate the ultraviolet transient with a biexciton state, B5, having an exciton-exciton interaction energy, given by the difference between twice the exciton energy and the biexciton energy, of x 3 1000 - 27000 = 4000 cm-’ or x 0.5 eV. 4.3. Dynamic responses 4.3.1. Causes

States of the polymer are excited on the high energy side of the absorption peak at 3 12 nm (see fig. 1). We now examine in detail the kinetics of the energy transfer process following excitation, as represented by the wavy arrow in fig. 6. We have two indicators of the dynamics, the transient gain and the transient absorptions. The gain of the probe observed at energies greater than 28200 cm-’ (355 nm) has two causes: The first is a depletion of the ground state population of centers absorbing at these wavelengths. This may be direct depopulation or may occur following energy transfer. The second cause is an excited state population that emits at a probe wavelength. Both the ground state bleaching and the gain will contribute to the net gain signal. When absorption and emission are resonant in energy, bleach and gain have the same spectral profiles. If the fluorescence of a particular chromophore is Stokes shifted with respect to its absorption, the gain signal should be proportional to the fluorescence signal, the bleach should follow the absorption profile. We assume in the following discussion that absorption and emission by a particular component of the inhomogeneous distribution are nearly resonant. Negative optical density changes are a combination of ground state bleach and excited state gain and are a direct indication of the excited state population emitting and the ground state population being depleted at any probe wavelength.

321

4.3.2. Energy transfer kinetics All the short time ( ~6 ps) gain and loss optical density (D) data of figs. l-3 are described by a simple two-component model, km

Bl -

Bl’ ,

fitted to a response function of the form

(5)

convoluted with a 500 fs fwhm instrument function and with DB,(Iz), DBIS(Iz) given in table 1. The nature of this response as a function of 1 is most clearly seen in fig. 2. For all wavelengths between 340 and 360 nm and at 920 nm the inverse rate constant l/km has a value of 0.7f0.2 ps. The transients at 335 and 375 nm show no short time kinetics (have instrument limited rise times) and are near isosbestic points for which DBI (2.) m DBIr(A) and no value of 1/km is derivable. It is suggested that Bl represents the species absorbing directly at 3 12 nm (those components of the inhomogeneous distribution whose pumped homogeneous line profiles have appreciable amplitude at 3 12 nm); the B 1’ species represents those populated by energy transfer. The latter constitute the population that emits to longer wavelength ( > 325 nm); the lifetime of the former ( x 700 fs) is so short that no fluorescence would have been observed from these states using time-correlated single-photon counting apparatus. The evolution of the bleach over the first 4 ps in fig. 1 in the range 335-350 nm thus reflects the excited state energy transfer from B 1 to B 1’; initially its spectrum resembles the absorption spectrum, after transfer it resembles the fluorescence. A direct result of this analysis is that the red-shifted fluorescence of polysilanes should have a growth time of x 700 fs. It has not as yet been possible to test the prediction that transients at wavelengths longer than 375 nm, characteristic of the indirectly pumped, emitting species B 1‘) should have a risetime of about 700 fs. 4.3.3. Anisotropy decays We have previously observed a fast decay of the fluorescence anisotropy followed by slow decay with

322

JAG. Thorne et al. / Poiysilane excitedstates

a 2 ns time constant, measured using time-correlated single-photon counting apparatus. This loss of polarization was attributed to reorientations of the emitting transition dipole with respect to that of the pump absorption due to spatial energy transfer processes in the excited state. The time scale for the fast anisotropy decay was shorter than the instrument function ( z 50 ps) [ 6 1. Therefore specific values for the decay constants could not be obtained and the range 1O20 ps was suggested by a statistical analysis of the data. The present results show that the excited state anisotropy decays significantly in less than 1 ps; this we attribute to the reorientation of transition dipoles as a result of the energy transfer process Bl-B 1’. Spatial energy transfer need not necessarily cause reorientation of the dipole, but loss of anisotropy is further evidence for fast spatial energy transport in the polymer. The anisotropy of the transient absorption signal, t(t), at 375 nm in fig. 4a shows this fast component decay to a plateau value of ~0.04. Photon counting data with improved experimental resolution (25 ps) (see fig. 4b for r(t) data with 312 nm excitation) have confirmed that the fluorescence anisotropy seems to persist for tens of p&seconds in contrast to the anisotropy decay in transient absorption, but reaches the same plateau value of 0.04 as the anisotropy of fig. 4a. There are two possible interpretations of this different behavior: either the deconvolution required to determine the anisotropy by photon counting has yielded misleading results or the fluorescent population contains a component that maintains its anisotropy for 10-20 ps but has a diminished contribution to the transient absorption at 375 nm. The resolution of differences in absorption and fluorescence anisotropy can be explained if there are variations in the radiative rate within the excited state population. It appears from the discussion in section 4.3.2 that the transient absorption at 375 nm is characteristic of almost the full manifold of excited states, both those directly pumped and those formed by enetgy transfer. The fluorescent signal, on the other hand, optimizes the ~contributions from excitations having the largest radiative rate. All that is required is that those centers also have the longest orientational relaxation times and a slower decay of anisotropy would be expected from the fluorescence experiment. This interpretation, involving a variation of the radiative rate within the excited state population

is consistent with experimental observations of variations in the relative yield of fluorescence with excitation wavelength near the low energy side of the absorption band where the emitting centers would be expected to absorb [ 7 1. 4.3.4. Overall description A number of mechanisms are possible for energy relaxation observable with short pulse laser excitation. We note that the dephasing time ( T2) is very short in solution at room temperature ( = 3 fs for a homogeneous width of z 3000 cm- ’ ) so excitations rapidly become random-phased, and also that the resonance integral Vsfor silicon-silicon site coupling along the chain is large and generally accepted to have values xlOOOOcm-’ [21]. We consider two extreme cases to describe the absorbing states of the polymer which lead to quite different interpretations of the relaxation that follows excitation. In a segmented chain model of the polymer the laser pulse excites approximate eigenstates of chain segments in isolation. In this mechanism the relaxation would be brought about by direct couplings I’,,. for which the coupling frequency V,,. /ti is less than the bandwidth of the laser pulse. Relaxation occurs by energy transfer with a rate constant given by [ 22 ] km = I’&

T&z*[ 1 + ( T2AeB,/2)*] ,

(6)

where dnn, is the angular frequency separation between the donor (B) and acceptor (B’ ) states. An energy transfer time of 700 fs in eq. (6) would imply a coupling between segments Vn,. x 150 cm-’ (for an energy defect ABw= 3000 cm-‘). This would seem to be an implausibly small value for the silicon resonance integral, Vs,of the chain at the site of the “kink” between segments: a single gauche link in an all-trans chain would not effectively localize segments on a 100 fs timescale [ 121. Conceivably I&. involves some structural reorganization (Franck-Condon factor) but there is no evidence of large phonon involvement in the transitions from the spectrum in absorption or emission. On the other hand, the same model (eq. (6) ) would apply if the energy were transferring through space between different regions of a tangled chain. The excitation exchange interaction between two chains separated by 13 A was calculated previously to be 40 cm- l [ 23 1, so is within range to ac-

J.R.G. Thome et al. / Polysilane excitedstates

count for the observations, but this would tend to reduce the anisotropy to zero which does not occur until the elapse of nanoseconds. In a randomly disordered [ 111 or intermittently disordered [ 121 chain model, the pump laser generates a distribution of eigenstates of each disordered chain in the ensemble: there are no independent segments as such in these models. Phonon assisted energy transfer rates between these Born-Oppenheimer states are then determined by the nuclear momentum operators. We consider this the likely relaxation occurring in 700 fs. Strong localization of the excitation to a distortion [ 2 1 ] is improbable in view of the absence of phonon structure in absorption and emission lineshapes so we regard excitations in polysilanes as delocalized and disordered excitons. It will be worthwhile to develop a model for the non-BornOppenheimer coupling of the nearby exciton states of disordered linear chains. Calculation of the rate of such processes is complex and will depend upon the coupling to the relevant promoting phonon mode and the magnitude of the energy defect ABB,. We can, however, address the question of whether 700 fs is a reasonable value for the non-resonant phonon assisted energy transfer time ( 1/kET) in the polymer at room temperature, based on other experimental measurements. Low temperature holes burnt in the polymer in glasses have widths of about 4 cm-’ [ lo], suggesting a dephasing time Tz of = 5 ps. This places an upper limit on the energy transfer rate at low temperature corresponding to an energy loss process having a T, time of 2.5 ps. Single-phonon emission processes, having energy defects ABBPof 1000 cm-’ or more, would be expected to have weak temperature dependences, varying as 1+ n where n is the phonon occupation number [ 18 ] : a room temperature value of the transfer rate a4 times larger than this would not be unlikely. We thus suggest that the timescales for energy transfer reflected in the decays of both fluorescence and excited state absorption and their associated anisotropies represent: (i) Rapid 700 fs phonon assisted relaxations from high energy states of the chain that, in the two disorder models discussed, have direct spatial overlap with low energy states. This would be the primary energy transfer step. The direct intersegment coupling required to rationalize the 700 fs relaxation time is too

323

small to be a nearest neighbour silicon coupling, in the presence of weak electron-phonon interactions. (ii) “Slow” 1 ps-2 ns relaxation from low energy states to those at even lower energy. These energy transfers require tunnelling through high energy regions of the linear chain (superexchange interactions). The lower in energy the excitation, the less probable would be its transfer to one of even lower energy, accounting for the highly dispersive kinetics in this time regime. Direct excitation on the low energy edge of the absorption band populates these lower energy states directly and there is no 1O-20 ps component expected of the fluorescence anisotropy decay, as is indeed observed when the excitation wavelength is > 335 nm [ 6,8]. We intend to carry out femtosecond studies of transient absorption excited at wavelengths longer than 312 nm. Simulation of the evolution of the emission spectrum and the decay of the anisotropy using the random disorder and intermittent disorder models for the linear-chain states of the polymer, is currently in progress. The decay of anisotropy should be particularly dependent upon the change of backbone direction that would occur at a tmns-gauche link [ 6 ] and should allow us to distinguish between these two models. 4.4. Saturation of the transient absorption signal We turn lastly to a discussion of the saturation of the transient absorption signal at high pump intensity seen in fig. 5, which is attributed to a ground state depopulation or bleaching effect. The fitted curve has the conventional saturation form [ 241, 6D= SD,,, [ 2*aZ/ ( 1 + 2*aZ) ] ,

(7)

where Z is the incident pump intensity, a is constant, 2* is a number between 2 and 1 and SO,,=O. 12. The dashed line in fig. 5 is tangent at Z=O. We consider two limiting cases for the saturation phenomenon. For a pure two-level system 2* = 2 and the transition between ground and excited state, as well as the transient absorption associated with the excited state, saturate when half the population is in the excited state. The incident flux required to achieve this is shown by the dashed line in fig. 5 to be 2.2 mJ/ cm’. This corresponds to 3x 10” photons absorbed in an irradiation volume of 0.2 mm3. The total num-

324

J.R.G. Thorne et al. / Polysilane excitedstates

ber of silicon atoms within this volume is 1.5 x 10L4. Thus saturation occurs at a level of one excitation per 50 silicon atoms which implies an average chromophore length of half this number, or 25 silicon atoms. A similar approach, that of phase-space filling, for excited state absorption in a polydiacetylene gives similar excitation lengths ( = 30-40 A) for this polymer [25]. Previous estimates of the conjugation length [ 61 of absorbing chromophores in polysilanes have been made using the ratio of the predicted (on the basis of absorption strength) to the observed radiative lifetimes. This calculation is repeated here. For irradiation at 3 12 nm the quantum yield of emission is 0.3 [ 71 and the majority of the emission decays with a lifetime of 150 ps [ 8 1. This implies a radiative decay rate of 2 x lo9 s-r. The integrated extinction coefficient per silicon atom for the transition, however, implies a decay rate of only 0.077 X lo9 s-r, which suggests a chromophore length of 26 silicon atoms. A problem with the foregoing arguments, which applies equally to both these estimates of the chromophore length, is that the fraction of material excitable at 3 12 nm is unknown. Were the value discussed for the homogeneous width of x20 nm to be accurate, the estimate of the conjugation length above would be reduced to between 10 and 15 silicon atoms, in accord with both kink [ 13 ] and random disorder models [ 111, since only about half of the silicon atoms would contribute to the absorption. There is a further important process to consider in order to interpret the saturation experiment when the absorption line is inhomogeneously broad. If energy transfer away from the initially excited center were to be occurring within the time span of the laser pulse (x 100 fs) the homogeneous linewidth would no longer give an estimate of the excitable fraction of the line. For very rapid energy transfer we obtain the second limiting case ( 2* = 1) in eq. (7) and the ground to excited state transition saturates when all the population is transferred. In those circumstances, we would have an estimate of the chromophore length of 50 silicon atoms. A transient absorption signal associated with the indirectly pumped B 1’ states, might however, saturate when all such “trap” states were populated. The kinetics are then determined by bottlenecking processes at traps and exciton-exciton interactions become of importance. We note that even

at the extremely high excitation densities used, we have observed no evidence of decay kinetics dependent upon laser intensity characteristic of excitonexciton annihilation processes [ 91. The non-instantaneous 500-600 fs risetime of the bleaching of indirectly pumped states is the best evidence that these are not the pertaining circumstances. For slow energy transfer away from the directly pumped B 1 states, in the limit that there is no excited state relaxation (no absorption-emission shift for a particular chromophore), we recover the limit 2* = 2. In practice, we obtain essentially the same estimate of the conjugation length from the fluorescence lifetime shortening as from the saturation experiment with the assumption of two-level kinetics (2* = 2 ) . We conclude that if, as seems probable, there is an appreciable inhomogeneous contribution to the line and the average conjugation length is indeed shorter than 25 silicon atoms, then the initial energy transfer step is probably slower than x 100 fs. This is fully supported by the kinetic evolution of the transient spectra in a time of 700 fs. A comment on the strengths of the transient absorptions is in order here. The ground state transition ( BO-B 1) has an extinction coefficient per silicon esi of about 1.0x 104; the optical density at 312 nm in the solution used was 1.0. Since the width of the ultraviolet transient absorption (B l-B5 ) was similar to that of the first transition we could relate the observed maximum optical density change of 0.1 (corresponding to an excited state B 1 population of 0.5 ) to an extinction coefficient eSi*for excited state absorption (B l-B5) of z 2 x 10’. This represents a minimum value for the extinction of the excited state transition; the estimate again neglects the concept of the excitable fraction of the line. If in reality only half the population is excited at 312 nm, then Esi*would increase by a factor of two.

5. Conclusions We have observed excited states of poly (di-n-hexylsilane) in transient absorption. The state in the infrared correlates well with that seen in two-photon spectroscopic measurements and attributed to a charge transfer exciton. The state in the ultraviolet is tentatively assigned to a biexciton.

J.R.G. Thorne et al. / Polysilane excited states

Fast energy transfer in the linear-chain polymer is observed to occur on a time scale of 700 fs after excitation at short wavelength. We believe this process populates a distribution of lower energy states through phonon assisted relaxations. We estimate an upper limit for the average excitation conjugation length to be 25 silicon atoms and a probable value to be lo- 15 atoms.

Acknowledgement We thank Dr. H.P. Trommsdorff and A. Tilgner for helpful discussions. This work was supported by NSF and by the Sandia National Laboratories, supported by the US Department of Energy under contract number DEAC04-76-DP00789

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