Table Of ContentApparent phonon side band modes in π-conjugated systems: polymers, oligomers and
crystals
E. Ehrenfreund1, C.C. Wu2, Z.V. Vardeny2
1Department of Physics, Technion–Israel Institute of Technology, Haifa 32000, Israel
2Department of Physics, University of Utah, Salt Lake City, UT 84112
6
0 The emission spectra of many π-conjugated polymers and oligomers contain side-band replicas
0 with apparent frequencies that do not match the Raman active mode frequencies. Using a time
2 dependent model we show that in such many mode systems, the increased damping of the time
n dependent transition dipole moment correlation function results in an effective elimination of the
a vibrational modes from theemission spectrum; subsequently causing the appearance of a regularly
J spaced progression at a new apparent frequency. We use this damping dependent vibrational re-
1 shapingtoquantitativelyaccountforthevibronicstructureintheemission spectraofπ-conjugated
1 systemsintheformoffilms,dilutesolutionsandsinglecrystals. Inparticular,weshowthatbyusing
theexperimentallymeasuredRamanspectrumwecanaccountindetailfortheapparentprogression
] frequencies and theirrelative intensities in theemission spectrum.
r
e
h Keywords: Optical absorption and emission spectroscopy, Photoluminescence, Raman spec-
t
o troscopy, Conjugated and/or conductingpolymers
.
t
a 1. Introduction form [3]:
m
∞
- Thetypicalphotoluminescence(PL)spectrumofmany iEt
nd π-conjugatedsystemsiscomposedofvibronicprogression F(E)=Z−∞f(t)exp(cid:18) ¯h (cid:19)dt . (1)
series (e.g., Fig. 1a, [1]). One key feature of the vibronic
o
progressionisthatitcontainsside-bandreplicaswithap- where the dipole correlationfunction, f(t), is given by:
c
[ parent frequencies that do not match the measured Ra-
1 mthaenriachctiRveammaondsepse(cet.rgu.m, Fiisg.red1ubc,ed[1]t)o. oInnlymoanneyorcatsweos f(t)=|P|2exp(cid:20)−i¯hE0t −S+S+(t)+S−(t)−Γ|t|(cid:21) .
v
vibronic progression in the emission spectrum, not nec- (2)
8
1 essarily having the same frequencies as the most intense In Eq. (2), P is the dipole matrix element and E0 is the
2 Raman modes. In this work we account for the appar- bare energy for the relevant optical transition. S and
1 entmodesthatappearinthePLspectraofπ-conjugated S±(t) are given by the following sums over the vibration
0 systems,such aspolymers, oligomersand single crystals. modes:
6
We use the measured pre-resonance Raman spectra in
0
/ order to quantify the relativeconfigurationdisplacement S+(t)= Sj(nj +1)exp(−iωjt) ;
t (or, equivalently, the Huang-Rhys factor) for each of the Xj
a
m modes. We then utilize these relative Huang-Rhys (HR) S−(t)= Sjnjexp(iωjt) ; (3)
factors in a damped time dependent model for the PL
- Xj
d emission. We show that the apparent vibronic frequen-
n cies in the PL spectrum are the result of a ”weighted S = Sj(2nj +1) ,
o beating”ofallRamanfrequencies. Thesefrequenciesare Xj
c not,ingeneral,thesimpleaverageoftheRamanfrequen-
: where ω are the Raman mode frequencies, n are the
v cies,andthuscannotbepredictedapriori. Furthermore, j j
i the relativeintensities ofthe apparentvibronicstructure equilibrium mode populations according to the Bose-
X Einstein distribution, S = ω ∆2/2h¯ (∆ is the mode
areuniquelydeterminedbytheirstrengthsintheRaman j j j j
r equilibrium displacement in the optically excited elec-
a spectrum.
tronic state relative to the ground state) are identified
as the mode HR factors, whereas S=S(T) is the total
2. Time dependent multi-vibrational analysis of temperature dependent HR factor. We emphasize here
photoluminescence that it is the ”electron temperature”, Te, which deter-
mines the mode occupation, n . T is determined by the
j e
In order to account for the PL spectrum of a multi- photon excitation energy and the electron excess energy
vibrational system in relation to its Raman spectrum, it relaxationrate and may be considerably higher than the
is useful to employ time dependent analysis rather than lattice temperature, T. The time dependent term S+(t)
the often used sum-over-states Franck-Condon approach is responsible for the red shifted vibronic side bands in
[2]. We write the PL spectrum, F(E), as a Fouriertrans- the PL spectrum, while the S−(t) term gives rise to blue
1
shifted(duetoa”hotluminescence”process)sidebands, The HR factors that determine the vibronic structure
which may appear for low frequency modes at relatively are closely related to the measured Raman spectrum,
high temperatures. In Eq. (2) we introduced a simple sincetheRamanprocessisenabledbythesameelectron-
mode independent phenomenological damping parame- phonon interaction. The T=0 K intensity, I0, of each
j
ter Γ; it represents losses due to natural line broadening Raman line measures its excited state displacement ∆
j
and/or other degrees of freedom [4]. [2]: I0 ∝ ω2; we then have: S ∝ I0/ω2. We note the
j j j j j
proportionality of S to ω−2, which emphasizes the con-
j j
tributionoflowerfrequencyRamanmodestothevibronic
(a) ~0.17 eV ~1370cm-1 structure in the PL emission.
Asanexamplefortheaboveanalysis,weconsiderfilms
PL
ofpoly(dimethoxyphenylenevinylene)[PDMeOPV].Us-
ing the Raman data published previously [1] (Fig. 1b),
we have calculated the expected PL vibronic structure.
This is shown in Fig. 1c. As seen, the calculated spec-
trum is in agreement with the experimental spectrum:
(a) Both spectra are composed of a single vibronic pro-
gression; (b) The calculated progression frequency of ≈
0.16 eV in the PL spectrum (Fig. 1c) is very close to
the measured one (Fig. 1a). A choice of total HR factor
of S(0)=0.75 and damping of Γ=66 ps−1 yields relative
intensities and line broadening similar to that measured
at T=80 K.
(b) 1582
Raman 3. The case of distyryl-benzene
Theexcitedstatepropertiesofdistyryl-benzene(DSB),
1306
which is the three phenyl group oligomer of p-phenylene
vinylene (Fig. 2a, inset), have been the subject of re-
1110 cent experimental [5,6] and theoretical [7] spectroscopic
studies, because of potential opto-electronic applications
600
964 [8]. DSB PL spectroscopy has been the subject of nu-
merous research studies, since it is strongly dependent
upon the packing order. The first excited state of iso-
lated DSB molecules is optically allowed, making them
stronglyluminescentanduseableasactivemediainlight
emitting devices [8]. The room temperature PL spec-
trumofisolatedDSBmoleculesconsistsofthefundamen-
1.0 (c) 0-0 tal (”0-0”) optical transition and a single apparent fre-
quencyphononsidebandreplicaseries. InDSBfilmsthe
PDMeOPV
nits)0.8 80 K minogltehcuelPesLfeomrmissHionagqguraengtautems,ytiheuldsrseulabtsitvaenttoiatllhyewiseoalakteend-
arb. u0.6 S=0.7 5c,a Γlc=u6l6a tpeds-1 0-1 oDlSigBomsienrgsliencdriylusttaelss:olduutieontos[t9h].eThherisriinsgesbpoenceiasllyymtmrueetriny
sity (0.4 the fundamental optical transition is either totally ab-
n 0-2 sent or significantly reduced [9]. Typical PL spectra of
e
nt DSB chromophores contain vibronic progression series,
I0.2
L ofwhichthe relativeintensity andfrequenciesdependon
P
the packing and temperature. The PL emission spectra
0.0
ofcrystalline DSB are discussedelsewhere [10]. Here, we
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 discuss only ourresults for dilute solutions,whichreflect
E-E (eV) the single molecule PL spectrum.
0
FIG. 1. (a) PL spectrum of PDMeOPV; showing a sin-
gle vibronic frequency at ≈1370 cm−1. (b) Raman spectrum
3.1. DSB solution
of PDMeOPV. The Raman frequencies are marked. Inset:
chemical structure. (Data from: Woo et. al., Ref. [1]). (c) In Table I we list the most intense Raman modes ob-
Calculated PL spectrum using the data of Fig. 1b and Eqs. served for DSB. The Raman spectra for the solution or
1-3. Theresultingvibronicseparationis≈1350cm−1. Energy crystalline forms are similar. Here we present the crys-
is measured relative to the 0-0 transition energy (E0). talline data since its signal to noise ratio is much better.
2
Alongwiththefrequenciesandrelativeintensities,welist curve), there appears a dominant ”high frequency” vi-
foreachmodethe deducedrelativeHRfactor,calculated bronic progression of ≈0.17 eV (≈1370 cm−1), which,
using the model discussed in Section 2 and the Raman however does not match any of the Raman frequencies
data presented in Fig. 2. It is important to recognize (Fig. 2b); it is not even in the close vicinity of the
that the lowest frequency mode has the largest HR fac- strongly coupled modes (Table I). The highest energy
tor, although its intensity is only ≈1% of the strongest PL peak (marked ”0”) is interpreted as the fundamental
line! optical transition (1A → 1B ), whereas the lower en-
g u
ergy peaks (marked”1,2,3”)are the vibronic side bands.
) At low temperatures, the high frequency progression is
s
t (a) modulated by a different ”low frequency” progression of
i
n 0,n ≈17-19 meV (Fig. 1a, T=20 K). We denote this modu-
u lated vibronic structure by k, n (k=0,1,2,3, n=0,1,2,...),
. wherek(n)istheorderofthehigh(low)frequencymod-
b
1,n ulation.
r
a UsingthedataofTableIweshowinFig. 3athedipole
( auto-correlationfunction,f(t),generatedforlowandhigh
2,n
y 3,n damping. It is visually striking that the 11 mode system
t
i 20K is dominated by only two apparent modes: a short pe-
s
n riod mode modulated by a long period mode. Moreover,
e the frequencies associated with these two modes do not
nt 2 1 0 coincide with any DSB normal mode. The data given in
3
i Table I is used also to generate the PL spectra shown in
L 200K
Fig. 3b. Here,thevaluesoftheelectrontemperature,T ,
e
P 2.4 2.6 2.8 3.0 3.2 HR factorSanddamping Γ wereadjustedto best fit the
frozensolutionexperimentaldata atlowandhighlattice
Photon energy (eV) temperatures, T (Fig. 2a).
)4 DSB
s (b) j 1 2 3 4 5 6
t T=10 K
ni ν (cm−1) 131 261 640 873 1000 1181
u λ =514 nm
b. exc I/I10(%) 1.2 0.45 0.71 0.77 6.7 50
r S 0.88 0.098 0.025 0.025 0.088 0.48
a
( j 7 8 9 10 11
ty 2 ν (cm−1) 1330 1452 1561 1591 1635
i
ns I/I10(%) 19 2.7 13 100 42
e
t S 0.15 0.018 0.068 0.50 0.20
n X50
i
n
a Table I. The most intense Raman lines of DSB at T=10
m
K. ν, I and S are the frequency, relative intensity and HR
a
R0 factor, respectively, for each mode.
400 800 1200 1600
-1
Raman shift (cm ) Thehigherdampingspectrumthatpresumablyoccurs
at T=200 K (Γ=42 ps−1, Fig. 3b) shows a vibronic pro-
FIG.2. (a) PL spectroscopy of DSB in solution at 20 and
gression dominated by a single frequency of 173 meV
200 K.Theindices0and1,2,3 in the200 Kspectrumdenote (≈1400 cm−1). These progression peaks are marked as
thefundamentalandvibronicreplicatransitions,respectively.
”1,2,3”. This is in excellent agreement with the experi-
The pairs of indices k, n (k=0,1,2,3) in the 20 K spectrum
mental data at T=200 K (Fig. 2a, bottom curve). For
denote the complex modulated vibronic structure (see text).
this case we chose T = T, since the relevant modes are
Inset: Chemical structure of DSB molecule. (b) High sensi- e
at high frequencies. At lower lattice temperatures we
tivity preresonant Raman spectrum of DSB crystal at 10 K.
expect the damping to decrease. Consequently, the low
The Raman frequencies and intensities are listed in Table 1.
frequency apparent mode is less suppressed, making the
PL spectrum sensitive to the actual value of T . For
e
In Fig. 2a we show the PL spectra of DSB in di- low Γ values, there appears a low frequency modulation
lute frozen solution of tetradecane [11] at low and high (≈17 meV) of the high frequency vibronic series, as seen
temperatures. The measured PL spectrum at T=200 K in Fig. 3b (top curve). The combined progression peaks
has the typical vibronic progression shape as other π- are denoted as (k,n), where k=0,1,2,3 denotes the high
conjugated systems, but notable changes occur with de- frequency apparent progression and n=0,1,2... denotes
creasing temperature. At T=200 K (Fig. 2a, bottom the low frequency modulation. The PL spectrum in Fig.
3
3b (top curve) was calculated using T =150 K; it shows Insummary,wehaveshownthatincreaseddampingin
e
two blue shifted peaks, in very good agreement with the multi-vibrational π-conjugated systems results in effec-
experimental data at T=20 K (Fig. 2a, top curve). We tive elimination of vibrational modes from the emission
thusconcludethatduetothenon-resonantPLexcitation and absorption spectra and the eventual appearance of
the electron temperature is much higher than the lattice a nearly regularlyspacedprogressionatan apparentfre-
temperature: T >T. quency. We have presented a method by which measur-
e
ing the full Raman spectrum, the emission spectrum of
100
π-conjugatedsystemscanbeaccountforindetail. Inpar-
(a)
ticular, we interpret the blue shifted small peaks above
the 0-0 transition, in the frozen DSB solution spectrum,
d) 10-2 as due to a ”hot luminescence” process. In such a pro-
e
aliz Γ=6ps-1 cess,duetoahighelectrontemperature,thefirstexcited
rm 10-4 Γ=36ps-1 vibrational level is significantly populated.
o
(t) (n FGA-0c4knEoRw4l6e1d0g9maenndtsb–ySutphpeoIrstreadelinSpcaierntcbeyFDoOunEdgartaionnt
f
735/04.
10-6
10-8
0.0 0.2 0.4 0.6
Time (ps)
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ing the 11 mode system of Table I. (a) Normalized dipole 9D. Oelkrug , H.-J. Egelhaaf, J. Gierschner, A. Tompert,
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scale. (b) PL spectra obtained by the Fourier transform of Z.V. Vardeny, Phys. Rev. B (Rapid Commun.), 71 (2005)
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4
