Transient internal temperature of anthracene after picosecond infrared excitation

Volume 1 11. number

4.5

CHEMICAL

PHYSICS

LEITERS

9 November

1983

TRANSIENT INTERNAL TEMPERATURE OF ANTHRACENE AFTER PICOSECOND INFRARED EXCITATION

N.H. GOTTFRIED, Pigaik Deprtntcn

A_ SEILMEIER

and W. KAISER

t der Te~hnid~e~~ LJtliwrsit& M~nclren. Munich, West Getmany

Received 3 August 1983; in fmzd form 71 August

19S4

The trunsicnt So-S1 spectrum of anthnccne following excitation of CIi-stretching modes in the electronic ground state WJS studied by time-resolved spectroscopy. Evidence is presented for the redistribution of energy over the many vibrational degrees of freedom. A temporxy intern4 tcmperdture is assigcd to the exited molecules. The slower enegy dissipation

due 10 solvent-solute

interactions

MIS observed to occur within approximately

1. Introduction

a different

The vibrational dynamics of polyatornic molecules in solution play a central role iu many clleriiical and biophysical proccsscs. The careful study of vibrationally e_xcited molecules is expected to contribute to a better understanding of a series of Inolecular phe-

nomcna. Experimental

data suggest that the relaxation of vibrational energy differs substantially for small and large n~olcculcs. In small molecules (and for not too high vibrational energies), specific relaxation channels esnt, which depend on the details of the molecular structure, ix. on specific vibrational energy states and on anharmonic coupling [I 1. On the other hand, a statistIca relaxation mechanism is expected for large molecules. where the density of vibrdtional states forms 3 quasi-continuum [2] _

Previously, we reported on the transient population and decay of normal modes of naphthalenc and nnthracene. The data were obtained by measuring antI-Stokes Raman scattering on a picosecond timescale [3] _ Ill IldpllthalCIlC. the smaller of these two molcculcs. evidence was presented was redistrIbutcd statistically after ps. For anthraccne. the data were d more rapid randoInisation of tbc energy. More recently. WC dcmonstrsted

that the energy approximately IO limited but indicated vibrational excess the potential

of

15 ps.

experimental

technique.

The change

of the

electronic absorption edge was used as a probe for studying the transient excess population of vibrational modes in the electronic ground state [4]. In the present investigation, this technique is applied to anthracene. New information is obtained on the vibrational dynamics of this molecule_ First, CHstretching modes of anthracene at F = 3052 cm-l are resonantly excited by a picosecond IR pulse. The induced changes of the electronic absorption edge are subsequently monitored by UV probe pulses. The absorption change is tested either by measuring the sample transmission directly or by monitoring the fluorescence_ Our experiments yield the transient electron-

ic absorption spectrum of anthracene immediately after IR excitation. Comparing the data with a model calculation, we can assign an internal temperature to the vibrationally excited molecules. The observed vibrational states are temporarily populated as if the molecules have acquired a higher temperature. The excess energy of the anthracene molecules decreases quickly due to interactions with the cold solvent molecules_ Our resulrs allow the determination of the corresponding intermolecular relaxation times.

2. Experimental The investigations 0 009-2614/S4//s (North-Holland

were performed

03.00 0 Elsevier Physics Publishing

with a mode-

Science Publishers Division)

B-V.

Volume

11 I, number 4,s

CHEMlCAL

PHYSICS

LETTERS

locked Nd : glass laser. The infrared exciting pulses and the ultraviolet probe pulses are generated by parametric three-photon mixing in different non-linear crystals. The duration

of both pukes was 5 ps. Exper-

imental details of the generation of these tunable pico-

second pulses were given eisewhere [5]. For frequencies of the probe pulse i; > 25400 cm-l, the absorption change of anthracene is determined by measuring the difference of the transmission of two equal samples, one of which is excited by an infrared pulse. For frequencies below 25700 cm-l, the S, fluorescence of anthracene is measured with and without infrared excitation. The fluorescence is proportional to the SO--S, transition probabj~ity (i.e. to the instantaneous absorption coefficient). In the present experiment, special attention was paid to an accurate overlap of the infrared excitation and ultraviolet probing beams. From the energy of the exciting pulse, E = 40 /JJ, the infrared absorption cross section of anthracene, and the focal area in the sample, we estimate a fraction of 0.20 z!z0.05 of the anthracene molecules to be vibrationally excited in the probed volumes_ Anthracene, C,IH,o, is dissolved in Ar-saturated C$&_ A concentration of 1 X 30m3 M is chosen in most experinlents- A few data points were taken at an increased cox~ce~ltration of I X 1O-3 M because of the low absorption cross section at 25400
3. Experimental

results

First we discuss the low-frequency end of the electronic absorption spcctruR1 ofanthracenc in C&f4 (see curve 1 in fig. I). The peak absorption of the O-O transition band is found at 26380 cm-l_ In the frequency range 25400 < Z < 26000 cm-l, the absorption of anthracene decreases steeply. Numerous weak transitions contribute to the absorption at these frequencies. They cannot be resolved individually because of congestion, Of special interest is the absorption around 25000 cm -I, where a pronounced hot band is observed.-This

i

25,000

Frequency

I

I

26,000 ii

27,000 bxi’3

Q. 1. X&r extinction coefficient of antlu-wene in CzC4. Curve I: room-ten~pcr~~ureextinction coefficient. Curve 2: transient eXtinction coefficient of anthraecne 7 ps after IR e.\citation. Note the&n in in&n&F of the hot band at 2 = 25000 cm-1 _

belongs to a group of vibrations with frequencies of 1400 cm -l_ It should be recalled that 1400 cm-l progressions determine the absorption spectrum of anthracene [6] for frequencies exceeding 27000 cm- 1 _Anthracene has three totally symmetric modes with large Fran&-Condon factors near 1400 cm-l f7]: ?a = 1557, sG = 1403, and F7 = 1255 cm-l _The Franck-Condon factors of these three modes add up to a transition probabBity slightly larger than that found for the O-O transition, At room temperature- the thermal population of the three modes is approximately lOA3 and - as expected - the hot

approximately

band appears with an extinction coefficient three orders of magnitude below the peak (see curve 1). We now turn to our picosecond experiments. The absorption change around the absorption edge is measured 7 ps after IR excitation. in curve 2 of fig. 1 the 327

Volume I1 1. number 4.5

CHEMICAL

PHYSlCS

transient molar extinction coefficient versus frequency of the probe pulse is shown. The data were obtained taking into account the experimentally estimated excitation of 20% of the anthracene molecules_ Curve 2 differs markedly from the room-temperature spectrum (curve 1). Most significantly, the hot band at 25000

cm-*

gained

intensity

by a factor

of approx-

imately IO. In addition, the transient molar extinction coefficient has a peak absorption reduced by approximately 10% compared with the room-temperature value and the absorption maximum is shifted to lower frequencies by 60 i 20 cm-’ _ For an analysis of the data,it is convenient to plot the relative absorption change AC&Q of the sample versus the frequency of the probe pulse. The result presented in fig. 2 does not involve a correction for the average vibrational excitation of the sample. Quite differently from fig. 1, this plot gives no indication of individual bands. The relative absorption change is seen to rise smoothly with decreasing probing fre-

2L,OOO Probe

1 Pulse

7.00IO

, Frequency

i?

tcmi’3

1 g:- 2. The rdntiw chnngc of absorption of tbc sample obtoined 3t a d&y time TV = 7 ps. ,%r/ag is ~ccn IO vary smoothly wtti the frequency of Ihe probe p&c. a0 = a(300

328

Ii).

LETTERS

9 November

1984

quency. A change of sign of the transient absorption occurs at F = 26270 cm-l_ The dependence of Am/a0 on i3~ of the exciting IR pulses was studied for 2950 < F1;R < 3 150 cm-l in a separate experiment. AoJao was found to be proportional to the known IR spectrum of anthracene. This observation indicates that the measured change of the electronic absorption spectrum of anthracene is caused by energy supplied via vibrational excitation of the molecules in the electronic ground state. The temporal evolution of the change of the electronic absorption was investigated for several frequencies of the UV probe pulse. In fig. 3, the normalized change of absorption is plotted versus delay time for two probe frequencies. Actually, the change in fluorescence was measured and it is proportional to the change in absorption_ In fig. 3a, data are taken at a probing frequency of F = 24760 cm-l. The correlation curve of the IR and UV pulses is also shown by a broken line. At this frequency, the dynamics of the hot bands of skeletal modes are studied by observing the S, fluorescence. We find a rapidly rising signal which reaches a maximum at a delay time of about 7 ps. This delay reflects the duration of exciting IRpuIses. The absorption decays for later delay tunes with a time constant of 20 +- 3 ps. In fig. 3b, the fluorescence signal for a probe pulse frequency of 23530 cm-1 is depicted_ Now the temporary excess fluorescence for a frequency difference from voo of approximately 2800 cm-l is observed_ The signal may be resolved into two independent contributions. (i) A very fast component closely follows the correlation curve (broken line). This signal, found in previous investigations [4], is due to an instantaneous two-photon or two-step excitation of the molecule; it is considerably smaller than the signals found in fig. 3a and thus not visible there. (ii) For delay times tD > 10 ps, a second component with a time constant of 9 + 2 ps is observed. This signal belongs to the transient population of vibrational states approximately 2800 cm-l above the ground state. The risetime of the change of absorbance or fluorescence (see fig. 3a) is very fast, within the temporal resolution of our apparatus of 2 ps. We conclude that the energy redistribution within the excited molecule, occurs within a time of less than 2 ps. On the other hand, the “cooling” of the excited molecule, i.e. the energy transfer to the solvent molecules, proceeds

CHEMICAL

Volume 111, number 4,5

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0 1

10 I

20 I

30 I

LO I

PHYSIC-S LElTER.5

9 November

1984

suggest a rapid redistribution of the added vibrational energy of 3050 cm-r within the antlrracene molecules_ The observed vibrational states suggest a temporary population similar to an increased temperature. To some approximation (see below), we may interpret our observations with the concept of an internal temperature. The following model relates the electronic absorption spectrum to an internal vibrational temperature T of the mo!ecule. The electronic molar extinction coefficient e(v. 7) may be approximated for frequencies v lower than the O-O transition frequency

50 I

)l-

E(Y, n = e*=, (T) S(v) exp [NV - VmaJx-Tl

-

(1)

e,,(T) 1

I

I

I

1

I

I

I ii p,obe= l-

23.530

T’=

3 =

denotes the maximum extinction coefficient dependence at frequency vmz,_ A small temperature

I

I

ofe mz,_(7) is necessary to maintain the electronic oscillator strength when temperature broadening occurs. A spectral shape function S(v) is introduced to

cm‘ 2 ps

describe the structure of the absorption tail of the electronic absorption spectrum_ S(v) is determined by the density of totally symmetric vibrational states and by their corresponding Franck-Condon factors. The exponential function in eq. (1) denotes the Boltzmann distribution of vibrational modes in the

IS-

electronic

Ol-

I

I

-10

0

I

10 Oeloy

I

I

I

I

20

30

co

50

Time

NJ.

tPS3

Fig. 3. Temporal evolution of the cxess fluorescence versus delay time. (a) Frequency of the probe pulse T = 24760 cm-‘_ The signal (full line) rises rapidly with IR excitation and falls off more slowly. The correlation curve of both pulses is shown

by the broken line. (b) Frequency of the probe pulses = 13530 cm-l _ The signal (full lme) shows B fast and a slow component.

ground state with energy lr(~ max -v).

Eq. (1) is an extension of a previously model [4] _ The relative change of e(v, 7) perature is readily calculated from eq. (1) the minor temperature dependence of v,, in our experiment_ For two temperatures with Tr > To, we obtain T1) - e(v,

= exp[Iz(v

proposed with temif we neglect as observed T, and To

qJ /44 T(J)

- vo)(l/kTr

-

l/X-T,)]

-

1 ,

co

where

kT,T, vo = ~mzt_-% - ir(Tl _ To> 111t%,,,(~oklxl~(~l)~

- (3)

discussed in the text

considerably slower, within approximately 25 ps. Thus we may discuss these two important processes separately.

4. Mrarnolecular

redistribution

In this section we show that the experimental

&z/e may be related to the change of the absorption coefficient - which is measured in our experiment - by considering the fraction y < 1 of vibrationally excited anthracene molecules in the probe volume_ From eq. (2). we get, I+*

data

T,) - a(% To)1 /0(v. To)

= -y{exp[Iz(v - ~~)(l/kT,

- l/We)]

-

1) .

(4) 329

Vofurnc I I 1. nuntbsr 4.5

ClII:hllCAL

1’LlYSiCS LIXTI:RS

Eq. (4) predicts the change of absorption of a sample after a tcmpcrature rise from To to T1. Since the CXpcrimcnts are performed at room tcmperaturc, WC take To=300 K. Several conclusions may be drawn from this model: (‘1) AC& IS predicted to increase strongly with decreasing frecp~er~cy v. In addition, details ofthe absorplion spcclrun~ incorporated in Lhe shape function S(V) lost m eq. (4). Both results are in agreement with

xc

our experimental findings in fig. 2. (2) The frequency depcndcncc of A&Y is very sensitive to the parameter T, _ Fitting eq. (4) to the expcrimentaI data of fig_ 2 gwcs an internal temperature T, of450 * 40 K and a value of the fractional excita-

tion y = 0.23 F 0.03. The following points should be noled: (i) The agreement ofcq. (2) and our cxpcrimental data is very satisfactory for c, < v. (see solid line in tig. 2). (ii) The value for T, agrees quite well with a previously [3] deduced temperature of 477 K. In the latter case, the exact calculation of the specific heat of the anthraccne molcculcs leads to the quoted temperature. This fact is important. It suggests a redistrrbution of the excess vibrational energy over all degrees of freedom of rhe n~ofeculc. (iii) The value of y is in good accord with the experimental estimate, y = 0.20 * 0.05, tcported above.

5. The concept

of internal

temperature

0

0 Total

I 0

WC hrfve introduced a transient internal rcmperature for the dnthraccne molecules after redistribution of the vibrational energy in the electronic ground state. The question may be raised as to what extent we are dillowed to t&k of an internal vibrational temperature .ifter fR excitation of the niolecules. In fig. 43, WC present the probability J’(E) of finding antflraccnc n~olecuIes with a total vibrational cncrgy C within an cncrgy interval of 1 c~n-~. Curve 1 IS calculrttcd from the exact density of states of anthracene weighted by the Boltzmann factor at 300 K. The peak of the djstribution occurs at an energy of approximately 1200 c~t;-~, i.e. molecuies with this tot31 energy exist most frcqucntly before excitation. After excitation of the anthracene molecules by IR photons of 3050 crnwl via CI-l-stretching modes, one

has 10 consider the IKW probability distribu&on 2_ Curve 2 is obtained by shifting curve 1 by 3050 cm-l_ 330

3000 Vabrotronal

6000 Energy

1 I

1000

Vibrotlonol

1

9000 E Ccrii’3

I

zooil

3000

Frequency

~,Ccni’3

1‘~. 4. (a) Distribution HE) of the number of anthrxme n~A~~les with a total vibrational energy E. Curves 1 and 3: Cquilibrium distributions for 300 and 470 K. respectively. Curve 2: Distribution P(E) immediately after IR excitation; P(E) is dcternl~ed by tbc distribu~on at room terr~perature but sbiftcd by the cncrgy of the IR excitation. (b) Occupation probability N(ui) of fundamental vibrational modes of cner~y Ilvi for two temperatures, 300 and 470 K. V~IUCSof A+[) cdculJted for tbc distribution curve 2 arc indicated for wveral modes by the full points. Note the close correlation with the line for 470 K. This distribution 2 differs from the equilibrium distribution 3 calculated for anthracene at 470 K. At

equilibrium there exist numerous molecules with a total energy smaller and larger than indicated by rhe shifted distribution 2. The energy redist~but~on and the internal temper-

Volunlc 11 I. number 4.5

CHEMICAL PHYSICS LET’IXIIS

ature after excitation are more readily discussed with the help of fig. 4b. Hcrc, the population probability N(Vi) of a vibrational state with energy /‘vi is plotted as a function of Vi for a number of fundamental vibrational modes of anthracene. At room temperature, i.e. at equilibrium, the N(Vi) values of all modes are located on curve 4, which rcprescnts the Boltzmann factor N(vi) = exp(-hvi/kT) with T= 300 K. The IR excitation populates very briefly the CH-stretching modes, which is indicated by the arrow at ‘3;-= 3050 Cl11 -I. This energy is rapidly redistributed over a very large number of isoenergetic combination modes. The new population probability of the fundamental modes of the excited molecules is calculated as follows: WC take slices of the distribution curve 2 at an energy E and of width AE = 2 cm-1 _ For each slice with total energy E, all possible combinationsofvibrationalstates arc calculated and the population probability NI;-(vi) of the individual modes is deduced. The population probability An for tile entire distribution of curve 2 is calculated according to

The points in fig. 4b represent calculated N(vJ values for a few selected vibrational modes vi_ The full line 5 - which fits our points very well - corresponds to a temperature T of 470 K. The system behaves as if it had a higher temperature. We call this temperature the internal temperature of the excited molecules. We point to the limitation of the temperature concept. The AU&) values of the higher vibrational data are not fully accounted for by our internal temperature of 470 K. Fig. 4b shows quite clearly the increase of the population probability N(Vi) of the vibrational modes around 1400 cm-l _Going from the room-temperature population to the value for the internal temperature of 470 K, one finds an enhancement by a factor of ten. This agrees quite well with the experimental increase of the extinction coefficient of the hot bands around 1400 cm-l as discussed in connection with fig. 1.

6. Intermolecular

energy dissipation

After intramolecular

energy redistribution,

the vi-

9 November I984

brationalty excited anthracene molecules transfer their cxccss energy to the solvent molecules and return to thermal equilibrium. The transfer of energy from lowlying vibrational states to the translational degrees of freedom of the system represents an efficient dissipation mechanism. In this case, the reverse process has to be included [9] _To a good approximation, the energy transfer rate is proportional to the excess energy Kc,, i.e. we obtain &(‘I

= &\(O) exp(-U~)

((3

-

Neglecting the temperature dependcncc of the specific heat, we find for the internal temperature T,(r), T,(t) - To = [TI (0) - To1 cxp(-r/~)

>

(7)

where 7 is a relaxation time and To = 300 K. Introducing T,(t) into eq. (4) allows the calculation of the time dependence of A&. The near-exponential decay of Aol/cu with time is found to be consistent with our observations of fig. 3. More quantitatively, with T = 25 ps one calculates decay constants of 10 and 17 ps for the two probe frequencies F = 23530 and Y”= 24760 respectively_ The agreement with the expericm-l, mentally observed decay of A&Y is satisfactory. We note that the apparent decay constants are shorter when higher vibrational states are monitored_ A certain temperature decrease affects more strongly the population of higher vibrational modes and leads to a faster decay of excess absorption at smaller probing frequencies_ The time dependence of the absorbance change 31 and around the O-O transition is affected by the small shift of the absorption peak. An analysis of these data will be published elsewhere_

7. Summary The vibrational dynamics of anthracene in solution has been studied following the excitation of CH-stretching modes. The excess population of vibrational modes in the electronic ground state was observed by investigating the change of the electronic absorption’tail after IR excitation. Our data suggest an intromolecular redistribution of the excess vibrational energy in less than 2 ps. Most - if not all -vibrational modes of the molecule participate in this distribution process. The observed popu331

Volume 111, number 4.5

CHEMICAL PHYSICS LETTERS

lation of the vibrational modes is consistent with the concept of a transient internal temperature. The intermolecular energy dissipation is considerably slower. The time constant for energy flow from the excited molecule to the solvent is found to be 25 ps. Acknowledgement The authors are grateful to Professor S. Fischer for valuable discussions.

References [ 1] IV. Zinth, C. Kohneder, B. Benna, A. Igens-Defregger,

[2j

S.F. Fischer and \V. Kaiser, J. Chem. Phys. 78 (1983) 3916. R. Naaman, D.M. Lubman and R.N. Zare, J. Chem. Phys. 71 (1979) 4192;

332

9 November 1984

J.C. Black, P. Kolodner. M.J. Shultz. E. Yablonovitch and N. Bloembergen. Phys. Rev. 19 (1979) 704; J.W. Perry, N-F_ Scherer and A.H. ZewaiJ. Chem. Phys. Letters 103 (1983) 1; H. Hippler, J. Troe and H.J. Wendelken, J. Chem. Phys. 78 (1983) 5351. 131 N.H. Cottfried and W. Kaiser, Chrm. Phys. Letters 101 (1983) 331. I41 F. Wondrazek, A. Seilmeier and W. Kaiser, Chem. Phys. Letters 104 (1984) 121; A. Seilmeier, P.O.J. Scherer and W. Kaiser, Chem. Pbys Letters 105 (1984) 140. A. SeiJmeier and W. Kaiser, Appl. Phys. 23 (1980) 113. LB. Berlman, Fluorescence spectra of aromatic molecules (Academic Press, New York, 1971). K. Ohno, Chem. Phys. Letters 53 (1978) 571. S.E. Stein and B.S. Rabinovitch, J. Chem. Phys. 58 (1973) 2438. 191 K.F. Herzfeld and Th.A. Litowitz, eds , Absorption and dispersion of ultrasonic waves (Academic Press, New York, 1959).