Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Article abstract of DOI:10.1021/ja011038u

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C₃)- or four (T_d, tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by Foerster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.

Full text of DOI:10.1021/ja011038u

Published on Web 01/26/2002
Coherent Effects in Energy Transport in Model Dendritic
Structures Investigated by Ultrafast Fluorescence Anisotropy
Spectroscopy
†
‡
§
§
Oleg P. Varnavski, Jacek C. Ostrowski, Ludmila Sukhomlinova, Robert J. Twieg,
‡
,†
Guillermo C. Bazan, and Theodore Goodson III*
Contribution from the Department of Chemistry, Wayne State UniVersity,
Detroit, Michigan 48202, Department of Chemistry, UniVersity of California,
Santa Barbara, California 93106, and Department of Chemistry, Kent State UniVersity,
Kent, Ohio 44242
Received April 25, 2001. Revised Manuscript Received September 26, 2001
Abstract: Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules
of different symmetry are reported. These molecules contain the fundamental branching center units of
larger dendrimer macromolecules with either three (C )- or four (T , tetrahedral)-fold symmetry. The
3 d
anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay
can be qualitatively explained by F o¨ rster-type incoherent energy migration between chromophores.
Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found
to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping
mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered.
The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of
a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent
and coherent interactions.
Introduction
interacting chromophores has led investigators to revisit past
5
work in the area of excitation of molecular crystals and the
The nature of excitations in large molecular aggregates has
been investigated in a large number of structural architectures.
6
excitonic character of photophysical processes. The character-
1
ization of the Hamiltonian by a Frenkel exciton (excited electron
and hole pair) has been applied to relatively new macromo-
Many of these investigations have involved aggregates of
important organic chromophores. The characterization of the
optical excitations in the aggregates often suggests that the
excitations may be localized on specific sites of the aggregate
or segments. The localization of the excitations is often directed
through dipole-dipole interactions.2 The formation of the
excitation of dyads (or triads) and excimers can be explained
under this context fairly well. More complicated macromo-
lecular systems such as pigments in light-harvesting photosyn-
thetic systems have also been investigated with close attention
7
lecular architectures such as organic dendrimers. Presently, the
investigation of energy transfer in organic dendrimers has
attracted recent attention that is motivated by the prospect of
8
creating artificial light-harvesting and -emitting systems. One
of the attractive features of this approach is the controlled
synthesis of dendrimers that results in a regular and well-defined
3
9
architecture. At the same time, the unique architecture of
dendrimers allows one to bring into close proximity a number
1
b,2b,4
to the nature of interactions between the pigment groups.
Much of the current interest in the nature of excitations in
(4) (a) Nagarajan, V.; Johnson, E. T.; Williams, J. C.; Parson, W. W. J. Phys.
Chem. B 1999, 103, 2297. (b) Jimenez, R.; Dikshit, S. N.; Bradforth, S.
E.; Fleming, G. R. J. Phys. Chem. B 1996, 100, 6825. (c) Bradforth, S. E.;
Jimenez, R.; van Mourik, F.; van Grondelle, R.; Fleming, G. R. J. Phys.
Chem. 1995, 99, 16179. (d) Savikhin, S.; Buck, D. R.; Struve, W. S. J.
Phys. Chem. B 1998, 102, 5556. (e) Walker, L. A., II; Shiang, J. J.;
Anderson, N. A.; Pullen, S. H.; Sension, R. J. J. Am. Chem. Soc. 1998,
*
To whom correspondence should be addressed. E-mail: tgoodson@
chem.wayne.edu.
†
Wayne State University.
University of California, Santa Barbara.
Kent State University.
1
20, 7286.
‡
§
(
5) Pope, M.; Swenberg, C. E. Electronic Processes in Organic Crystals;
Clarendon Press: New York, 1982.
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(
1) (a) Kobayashi, T., Ed. J-Aggregates; World Scientific: Singapore, 1996.
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03, 2327. (c) Lecuiller, R.; Berrehar, J.; Lapersome-Meyer, C.; Schott,
(
1
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1999, 110, 8161. (b) Minami, T.; Tretiak, S.; Chernyak, V.; Mukamel, S.
J. Lumin. 2000, 87-89, 115. (c) Kirkwood, J. C.; Scheurer, C.; Chernyak,
V.; Mukamel, S. J. Chem. Phys. 2001, 114, 2419.
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J. S.; BarHaim, A.; Klafter, J. Phys. ReV. Lett. 1997, 78, 1239. (b) Bar-
Haim, A.; Klafter, J. J. Lumin. 1998, 76, 197. (c) Halim, M.; Pillow, J. N.
G.; Samuel, I. D. W.; Burn, P. L. Synth. Met. 1999, 102, 922. (d) Lupton,
J. M.; Samuel, I. D. W.; Beavington, R.; Burn, P. L.; Bassler, H. Synth.
Met. 2001, 116, 357. (e) Varnavski, O.; Liu, L.; Takacs, J.; Goodson, T.,
III. J. Phys. Chem. 2000, 104, 179.
M. Phys. ReV. Lett. 1998, 80, 4068. (d) Tilgner, A.; Trommsdorf, H. P.;
Zeigler, J. M.; Hochstrasser, R. M. J. Chem. Phys. 1992, 96, 781. (e) Min,
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(
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2
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(
1
1
736 VOL. 124, NO. 8, 2002 J. AM. CHEM. SOC.
9
10.1021/ja011038u CCC: $22.00 © 2002 American Chemical Society

Energy Transport in Model Dendritic Structures
A R T I C L E S
of optically active subunits. These two features are also very
promising for creating molecular electronic devices.
nature of these interactions can be investigated by use of
fluorescence anisotropy, which is a powerful method in
characterizing the energy migration in particular multichro-
The fundamental challenge in dendrimer macromolecular
photophysics is the understanding of the photoexcitation energy
transfer between subunits and the degree of the excitation
delocalization. In most cases, the branching center in dendrimers
disrupts the conjugation, thus suggesting the dendrimer molecule
to be an ensemble of linear chromophores with no (or weak)
charge transfer between them. If such a charge transfer is
completely eliminated, and consequently the linear-segment
chromophores are well separated, then their interactions are
purely Coulombic. This explains the characterization of interac-
tions in the dendrimer molecule by a Frenkel exciton Hamil-
4
,11,12
mophore systems.
By using fluorescence depolarization,
it is possible to observe this intramolecular excitation transfer
because the latter process is accompanied by the reorientation
of the transition dipole resulting in depolarization of the
emission. Theoretical treatments of time-resolved polarized
emission from coherently excited chromophore pairs (and single
molecules with degenerate electronic transitions) showed that
the initial anisotropy can exceed the normally observed value
for a single chromophore of 0.4, before dephasing is initiated.11
Oscillations in optical anisotropy can be observed as a result
7
11,13
tonian. Recent theoretical studies on phenyl-acetylene den-
of the beating between excitonic levels.
However, in most
drimers showed that the charge coherence between linear
segments is negligibly small and that the Frenkel exciton
approximation is applicable for this system. There have been
experiments, the observed oscillations were assigned to the
vibrational wave packets formed by vibrationally impulsive
excitations. To actually observe the beatings between excitonic
levels for any particular system, the splitting parameter (interac-
tion strength) should fall in a narrow window of opportunity
between the limited experimental time resolution and the fast
dephasing. This condition, while theoretically viable, may not
be easily satisfied for many aggregated systems for which the
excitonic splitting is not exactly known.
7
no other reports regarding the effect of extended conjugation
on the energy migration process for other types of conjugated
dendrimers (branching centers). Furthermore, even if the charge
coherence between linear conjugated segments is negligible,
many important questions regarding the excited-state dynamics
and excitation energy transfer mechanisms in many important
synthetic dendrimer systems remain unanswered. Resonance
interactions between conjugated segments favor delocalized
Frenkel Hamiltonian eigenstates. This leads to coherent mech-
anisms of excitation energy transfer, which are maintained over
the duration of time during which well-defined phase relation-
ships between segments are preserved. Interactions with the
surrounding environment and with molecular nuclear motion,
however, destroy this phase coherence and stabilize localized
excitations. In the last case, the energy transfer between
dephased fragments may then occur in a random stochastic
However, there is also very important information in the
decay time and shape of the optical anisotropy. The anisotropy
decay time combined with isotropic dynamics and steady-state
spectroscopic information can be correlated with the excitation
energy migration (or redistribution) time in the aggregates
1
b,4
organized about a rotational axis.
In the limit of incoherent
interactions the anisotropy decay time is directly related to the
hopping time (interaction strength) between adjacent chromo-
4b,11a,14
phores.
In the excitonic limit this decay is associated with
the transition between the excitonic states possessing different
1
0
1e,11,13
fashion (hopping mechanism or weak interaction limit ). Both
interactions can be significant in dendrimers, and their relative
magnitudes will determine the contributions of coherent and
incoherent mechanisms to the dynamics of energy transfer. This
is an important issue concerning numerous promising applica-
directions of transition dipoles.
It is worth noting that for
the aggregated systems with axial symmetry (if it is not broken
after excitation) the excitonic levels with strong enough oscil-
lator strength remain doubly degenerated with different orienta-
2
a,4b
tion of the dipoles for each state.
The optical anisotropy
8a,b
8c,d
tions of dendrimers (artificial light antennas,
LEDs,
decay associated with mutual dephasing and population ex-
change between these two states which is driven by interactions
with random electric fields of the solvent molecules or dynami-
8
e
nonlinear optics ). Also, the question of coherence in dendri-
mers is an important fundamental problem. For example, it is
suggested that the photophysical processes are strongly affected
by geometrical confinement in dendrimers. However, neither
the dephasing rate nor the resonance interaction strength has
been experimentally measured for real conjugated dendritic
systems. For diphenylacetylene segments connected at meta-
positions, the interaction strength was theoretically estimated
1
e,11,15,16
cal breaking of the symmetry can be very fast.
The
anisotropy dynamics in a transition area between these two limits
4
c,13
can be modeled either numerically
or, with some restrictions,
1
7
analytically. Many parameters about the molecule itself and
solute-bath interactions are required to perform such modeling.
For natural photosynthetic systems, many of them have been
to be about 69 cm- (347 cm for longer segments), but this
1
-1
established in the course of many years of investigations.
1b,4
7
value was not independently estimated experimentally.
For new synthetic macromolecular systems (such as dendrimers),
most of the important physical quantities associated with a fast
depolarization process are still to be discovered.
To address the complicated problem of the excitation energy
transfer dynamics in dendritic systems in a meaningful way, a
simple dendritic model system (one branching center) may be
investigated. In this case, each component of the branching
center (each conjugated linear segment) either can be excited
by another segment or can transfer the excitation energy to the
other segments of the branching center. The interactions between
the chromophores at a branching center are strongly influenced
by the electronic and structural connectivity at the branch. The
(
11) (a) Knox, R.; Gulen, D. Photochem. Photobiol. 1993, 57, 40. (b) Wynne,
K.; Hochstrasser, R. M. Chem. Phys. 1993, 171, 2897.
(
12) Varnavski, O.; Menkir, G.; Beavington, R.; Samuel, I. D. W.; Lupton, J.;
Burn, P.; Goodson, T., III. Appl. Phys. Lett. 2000, 78, 1120. Varnavsky,
O.; Samuel, I. D. W.; Palsson, L. O.; Burn, P.; Goodson, T., III. J. Chem.
Phys., submitted.
(
13) Savikhin, S.; Buck, D. R.; Struve, W. S. Chem. Phys. 1997, 223, 303.
14) Latterini, L.; De Belder, G.; Schweitzer, G.; Van der Auweraer, M.; De
Schryver, F. C. Chem. Phys. Lett. 1998, 295, 11.
(
(15) (a) Yeh, A. T.; Shank, C. V.; McCusker, J. K. Science 2000, 289, 935. (b)
Schoenlein, R. W.; Bigot, J.-Y.; Portella, M. T.; Shank, C. V. Appl. Phys.
Lett. 1991, 58, 801.
(16) Ferro, A. A.; Jonas, D. M. J. Chem. Phys., submitted.
(17) Leegwater, J. A. J. Phys. Chem. 1996, 100, 14403.
(
9) (a) Tomalia, D. A.; Naylor, A. N.; Goddard, W. A., III. Angew. Chem.,
Int. Ed. Engl. 1990, 29, 138. (b) Frechet, J. M. J. Science 1994, 263, 1710.
(
10) Simpson, W. T.; Peterson, D. L. J. Chem. Phys. 1957, 26, 588.
J. AM. CHEM. SOC.
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VOL. 124, NO. 8, 2002 1737

A R T I C L E S
Varnavski et al.
Figure 2. Absorption (solid lines) and fluorescence (dash lines) spectra of
the carbon-cored distrylbenzene tetramer (tetrakis(3,5-di-tert-t-butylstyryl-
t
stilbene)methane, C( BuSSB)4) (thin lines), and adamantane-cored distryl-
Figure 1. Absorption and fluorescence spectra of the nitrogen-cored tris-
benzene tetramer (tetrakis(3,5-di-tert-t-butylstyrylstilbene)methane, Ad-
BuSSB)4) (bold lines), in chloroform. Fluorescence excitation wavelength
is 350 nm. Molecular structures are shown in the insets.
4,4′,4′′-(4-nitrophenylethynyl)triphenylamine. Fluorescence excitation wave-
t
(
length is 410 nm. The right inset shows the absorption spectrum of the
19
linear model compound dimethylnitrotolane (DMNAT). Molecular struc-
ture of the tris-4,4′,4′′-(4-nitrophenylethynyl)triphenylamine is shown in
the left inset.
Scheme 1
In this paper, we report a femtosecond time-resolved fluo-
rescence anisotropy study of the interchromophore energy
transfer processes in model branched dendritic molecules of C3-
symmetry with a nitrogen core and Td (tetrahedral) symmetry
with a carbon and adamantane core. From the fast fluorescence
anisotropy decay data, the interchromophore interaction strength
and energy transfer regime have been estimated. We showed
that the F o¨ rster energy transfer model can describe qualitatively
the interchromophore energy migration process in adamantine-
cored tetramers. However, for the triarylamine trimers, the
hopping dynamics are not appropriate, and exciton (coherent)
dynamics should be considered.
PPh3 (0.031 g, 0.012 mmol), CuI (0.012 g, 0.06 mmol), 4-nitro-
phenylacetylene (2.06 g, 12.8 mmol), and (i-Pr)2NH (1.8 mL,
12.8 mmol). After stirring for 3 days at room temperature, the
reaction mixture was diluted with toluene, the organic solution
was filtered, and the solvent was removed. The residue was
purified by column chromatography (ethyl acetate-petroleum
Results and Discussion
Synthesis and Characterization. The structure of the
nitrogen-cored tris-4,4′,4′′-(4-nitrophenylethynyl)triphenylamine
system is shown in the inset of Figure 1. In the inset in Figure
1
ether, 1:9) to give 2 g (92%) of 3, mp 244 °C. H NMR (300
MHz, CDCl3): 7.13 (d, 6H, J ) 8,1 Hz), 7.49 (d, 6H, J ) 8,4
Hz), 7.65 (d, 6H, J ) 8,7 Hz), 8.23 (d, 6H, J ) 8,4 Hz). The
synthesis and structural characteristics of the tetramer systems
with four distyrylbenzene chromophores grouped around the
tetrahedral adamantane or carbon core have been described
2
, the structures of the carbon-cored distrylbenzene tetramer
t
(tetrakis(3,5-di-tert-t-butylstyrylstilbene)methane, C( BuSSB)4),
and adamantane-cored dystrylbenzene tetramer (tetrakis(3,5-di-
t
tert-t-butylstyrylstilbene)methane, Ad( BuSSB)4), are both shown.
1
8
previously.
These model systems represent the fundamental branching units
of conjugated dendrimer molecules with coordination numbers
three and four. The triarylamine system is a new molecule and
is easily prepared by palladium-mediated C-C bond formation.
The synthesis procedure is sketched in Scheme 1. Tris-(4-
iodophenyl)amine (1): A mixture of triphenylamine (3.0 g, 12
mmol), HgO (12.18 g, 56 mmol), and I2 (15.24 g, 60 mmol) in
EtOH (150 mL) was stirred overnight at room temperature. The
solvent was removed, and the product was separated from
mercuric salts with boiling toluene. The solution was filtered
through the short column of Al2O3, and product was precipitated
Continuous wave fluorescence and absorption spectra of the
nitrogen-cored tris-4,4′,4′′-(4-nitrophenylethynyl)triphenylamine
system dissolved in chloroform are shown in Figure 1. The first
absorption band peaks are at 422 nm, and two other peaks are
found at 374 and 318 nm. It is important to note that the
absorption spectrum of the parent molecule dimethylnitroami-
notolane (DMNAT) representing the linear building block of
the tris-4,4′,4′′-(4-nitrophenylethynyl)triphenylamine system is
similar to the spectrum of trimer (shown in the inset of Figure
1
). The low-energy transition peak of the DMNAT (which has
1
from hot toluene with MeOH. Yield: 6.5 g (86%). H NMR
(
18) (a) Wang, S.; Oldham, W. J.; Hudack, R. A.; Bazan, G. C. J. Am. Chem.
Soc. 2000, 122, 5695. (b) Oldham, W. J., Jr.; Lachicotte, R. J.; Bazan, G.
C. J. Am. Chem. Soc. 1998, 120, 2987. (c) Oldham, W. J.; Miao, Y.-J.;
Lachicotte, R. J.; Bazan, G. C. J. Am. Chem. Soc. 1998, 120, 419. (d)
Robinson, M. R.; Wang, S.; Bazan, G. C.; Yong, C. AdV. Mater. 2000, 12,
1701.
(300 MHz, CDCl3): 7.53 (d, 6H, J ) 8,4 Hz), 6.80 (d, 6H,
J ) 8,4 Hz). Tris-[p-(4-nitrophenylethynyl)phenyl]amine (3):
To a solution of tris-(4-iodophenyl)amine (2.0 g, 3.3 mmol) in
THF (30 mL) were added PdCl2(PPh3)2 (0.022 g, 0.03 mmol),
1738 J. AM. CHEM. SOC.
9
VOL. 124, NO. 8, 2002

Energy Transport in Model Dendritic Structures
A R T I C L E S
Figure 4. Time-resolved fluorescence anisotropy of tris-4,4′,4′′-(4-nitro-
phenylethynyl)triphenylamine. Best fit curves are also shown (solid line).
Dash line shows modeling of the raw anisotropy with the 100 fs single-
exponential decay function. Dotted line represents instrument response
function. Excitation and detection wavelengths are 410 and 550 nm,
respectively. A semilogarithmic plot of the time-dependent part of the
fluorescence anisotropy [r(t) - rres] is shown in the right inset. The left
inset shows the fluorescence components of tris-4,4′,4′′-(4-nitrophenyleth-
ynyl)triphenylamine polarized perpendicular and parallel with respect to
the excitation.
Figure 3. Time-resolved fluorescence anisotropy of tetrahedral molecules
t
t
Ad( BuSSB)4 and C( BuSSB)4. Best fit curves are also shown (solid lines).
Excitation and detection wavelengths are 385 and 480 nm, respectively.
Dotted line represents the instrument response function. The perpendicular
t
and parallel fluorescence components of the Ad( BuSSB)4 are shown in
the inset.
19
charge-transfer character ) is slightly shifted in the absorption
spectrum from the trimer, and a small additional peak (shoulder)
appears at 374 nm as well. The shift and splitting in the trimer’s
spectrum reflect the interaction between monomers. A relatively
large Stokes shift and unresolved vibronic structure of fluores-
cence spectrum are correlated with the charge-transfer character
of the excited state of the tris-4,4′,4′′-(4-nitrophenylethynyl)-
triphenylamine. The linear absorption and fluorescence spectra
for both adamantane- and carbon-centered tetramer systems are
shown in Figure 2. The absorption spectrum of both samples
peaks at about 466-468 nm and shows weak vibronic structure.
The vibrational structure is more pronounced in the fluorescence
spectra revealing two distinct peaks and a red-shifted shoulder.
The spectral data for tetramers are similar to those for the parent
distyrylbenzene (DSB) chromophores. There are no substantial
differences in optical spectra, which might suggest that interac-
tions within the tetramer molecule are relatively weak. It is also
seen from Figure 2 that both absorption and fluorescence lines
excitation energy migration processes in branched systems.4,11
However, there have been only a few reports concerning fast
excited-state anisotropy dynamics in small symmetrical mol-
ecules. For example, pump-probe anisotropy measurements on
the Q-band of magnesium tetraphenylporphyrin (MgTPP)
revealed an initial anisotropy of 0.65 and a two-exponential
anisotropy decay with two time constants 210 fs and 1.6 ps.20
Very recently Jonas and co-workers performed pump-probe
anisotropy measurements for the Q-band of silicon 2,3 naph-
thalocyanine bis(trihexylsiloxide) and observed an initial ani-
sotropy of 0.4 that decayed to the residual value over 200 fs.16
High anisotropy values and fast anisotropy decay results have
1
5b
also been obtained from pump-probe anisotropy experiments
2+
15a
with an [Ru(bpy)3] molecule. The anisotropy decayed from
the initial value of ∼0.55 to ∼0.4 with a decay time of about
15a
1
00 fs. There have been even less fluorescence time-resolved
t
experiments which have shown these particular characteristics
of C( BuSSB)4 are somewhat shifted to the red as compared to
2
1,22
t
for symmetric molecular systems.
One experiment on the
those of Ad( BuSSB)4. This may be an indication of stronger
Soret band of ZnTPP showed the fluorescence anisotropy decay
interchromophore interaction in the carbon-centered system as
compared to that for the adamantane-centered system which has
a larger separation between branched DSB-chromophores.
The anisotropy decay result for tetramer systems is shown
in Figure 3, while Figure 4 shows the fluorescence anisotropy
dynamics (r(t)) of the triphenylamine system. The insets in both
figures show the parallel and perpendicular polarized fluores-
cence decay profiles measured at the same wavelengths. It is
clearly seen that the anisotropy decay is much faster for the
nitrogen-cored trimer as compared to those of both carbon- and
adamantane-centered tetramers. The best fit result for the
nitrogen-core trimer system showed an anisotropy decay time
of approximately 35 fs. The anisotropy dynamics contain
important information about interchromophore interactions and
21
time of 200 fs with high initial value g0.7. The time-dependent
fluorescence anisotropy was also measured for aluminum(III)
tris(8-hydroxyquinoline) (Alq3) and was found to decay with a
2
2
time constant of 2.0 ps.
The process of incoherent energy transport in a C3-symmetry
system (amino-substituted phenylbenzene derivative p-EFTB)
14
was reported by Latterini et al. utilizing pump-probe experi-
1
4
ments with time resolution of about 140 fs. The anisotropy
was found to decay in a picosecond time range (8 ps).14 The
authors attributed this slow anisotropy decay result to the
incoherent hopping of the excitation between initially localized
14
single branches. It is worth noting that pump-probe anisotropy
(
20) Galli, C.; Wynne, K.; LeCours, S. M.; Therien, M. J.; Hochstrasser, R. M.
Chem. Phys. Lett. 1993, 206, 493.
(
19) (a) Stiegman, A. E.; Miskovski, V. M.; Perry, J. W.; Coulter, D. R. J. Am.
Chem. Soc. 1987, 109, 5884. (b) Stiegman, A. E.; Graham, E.; Perry, K.
J.; Khundkar, L. R.; Cheng, L.-T.; Perry, J. W. J. Am. Chem. Soc. 1991,
(21) Gurzadyan, G. G.; Tran-Thi, T.-H.; Gustavsson, T. J. Chem. Phys. 1998,
108, 385.
(22) van Velhoven, E.; Zhang, H.; Glasbeek, M. J. Phys. Chem. A. 2001, 105,
1
13, 7658.
1687.
J. AM. CHEM. SOC.
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VOL. 124, NO. 8, 2002 1739

A R T I C L E S
Varnavski et al.
Figure 6. Time-resolved fluorescence anisotropy of the model system p-bis-
(o-methylstyryl)-benzene (bis-MSB). Excitation and detection wavelengths
are 395 and 450 nm, respectively. The molecular structure of bis-MSB is
shown in the inset.
Figure 5. Simulations for the raw fluorescence anisotropy of the
C( BuSSB)4 using a single-exponential decay model for the anisotropy decay.
t
a single-exponential function. However, as can be seen in Figure
t
3
, the anisotropy decay of the C( BuSSB)4 fits well to a two-
results are complicated by a collection of contributions from
ground-state bleaching, stimulated emission, excited-state ab-
sorption, and possibly pump-probe coherence coupling and
exponential decay function. The best fit of the decay profile
gives two relaxation times, one that is 45 ( 20 fs, which is
followed by another of 610 ( 50 fs.
perturbed free induction decay.4a In some cases it is difficult to
account accurately for all these contributions. Fluorescence time-
resolved measurements give direct information about the decay
of the excited state. However, the fluorescence upconversion
technique usually operates with Stokes-shifted (already relaxed)
states. It complicates recovering the true early stage of the
excited-state dynamics. As a result, many contradictions in time-
resolved pump-probe and upconversion experimental results
and interpretations of the dynamics of the optical anisotropy of
symmetrical molecules still persist. For example, it has been
shown theoretically that the quantum mechanical and stochastic-
kinetic description of a square symmetric chromophore system
To gain further insight into the physics behind the fast
depolarization process, it is important to compare the anisotropy
dynamics of the tetramers with that for a single chromophore
(monomer). We measured the fluorescence anisotropy for the
model system of p-bis(o-methylstyryl)-benzene (bis-MSB)
representing the linear building block of the tetramers. The result
is shown in Figure 6. It is clearly seen that fluorescence
anisotropy dynamics of the model system of bis-MSB strongly
differ from those of tetramers. Starting at the initial value close
to 0.4, the fluorescence anisotropy decays with the time constant
of about 100 ps, which agrees with the rotational diffusion time
of the bis-MSB molecule. Comparing the anisotropy decay
results for tetramers with those for the model system bis-MSB
suggests that the initial ultrafast transition dipole reorientation
is due to intersegment interactions in the tetramers. The residual
anisotropy slowly decays to zero over 1.2 ns due to rotational
diffusion of the molecule. The result of the slow decay of the
residual anisotropy in tetramers is shown in Figure 7. A single-
exponential best fit gave the rotational diffusion time estimate
of the carbon-centered tetramer in chloroform of ∼550 ps.
(
D4h) requires degeneracy between two relaxation rates that may
23
not be distinguished from each other. However, experiments
on square porphyrin-type molecules showed two- or even
multiphase anisotropy decay with well-distinguished decay
2
0
times. Indeed, more experimental and theoretical efforts such
as those reported here are necessary to resolve the problems
with an accurate characterization of the energy transfer in
multichromophore symmetrical and branched molecules.
The decay of the anisotropy for both adamantane- and carbon-
centered tetramer systems (shown in Figure 3) was measured
at an emission wavelength of 480 nm and excited at 385 nm.
The inset shows the parallel and perpendicular polarized
fluorescence decay profiles measured at the same wavelengths.
The fluorescence anisotropy decays from an initial value just
below 0.4 to the residual anisotropy of approximately 0.06-
The anisotropy (r(t)) decay result for the triphenylamine
anisotropy decay measured at the emission wavelength of 450
nm and excited at 410 nm is shown in Figure 4. For the case of
the triphenylamine anisotropy decay, it was possible to fit the
measured profile with a single exponential as seen in Figure 4.
The best fit result showed the anisotropy of the triphenylamine
system decays rapidly to a residual value with a time constant
of ∼35 fs. The raw initial anisotropy was below 0.4 (Figure 4);
however, the best fit to the monoexponential decay gave the
initial value r(0)) 0.47 ( 0.10. The depolarization time is
shorter than the duration of the instrument response function
0.12, for the carbon and adamantane systems, respectively. The
presence of a decay component in the range of ∼1 ps is clearly
observed for both systems. The fluorescence anisotropy decay
of adamantane-centered tetramers can be fit well with a one-
exponential decay function with a lifetime of ∼880 fs and an
initial value of 0.36. The carbon-centered tetramer showed a
more complex decay pattern as compared to those for the
adamantane-centered system and the trimers. Figure 5 shows
the attempt to fit the anisotropy decay of the carbon-centered
tetramer to a number of different possibilities of parameters with
(IRF, also shown in Figure 4). Nevertheless, even if a single-
exponential depolarization process occurs on a shorter time scale
then the width of IRF, most of the information about the
depolarization process can be recovered. However, for a more
complex anisotropy decay law, the uncertainty in determining
initial anisotropy as well as the fast decay time can be
substantial. The success of the fitting procedure critically
(
23) Raghavan, S.; Knox, R. S.; Eberly, J. H. Chem. Phys. Lett. 2000, 326,
2
07.
1740 J. AM. CHEM. SOC.
9
VOL. 124, NO. 8, 2002

Energy Transport in Model Dendritic Structures
A R T I C L E S
during the relaxation process.11b For equilibrated systems, these
values are easy to calculate just using the law of summation
2
5a,b
(additivity) of anisotropies.
For triarylamine trimer, we
observed the residual anisotropy to be 0.120 ( 0.005 which is
slightly above the expected value of 0.1 for a planar molecule.
The triphenylamine molecule has been reported to have a
propeller-like geometry with the N-C bonds lying almost in
2
5b
one plane. Twisting of the phenyl rings may lead to a small
inclination angle of the transition dipoles of the nitrophenyl-
acetylene branches relative to the NC-bond plane. The inclina-
tion angle of about 9.5° could lead to the residual anisotropy
of tryarylanime trimer observed in our experiments.2 The
reasons for the nonzero (and different) residual anisotropies of
carbon- and adamantine-cored tetramers are less clear. It can
be suggested that there is a small amount of distorted molecules
possessing high anisotropy. This could lead to a different
nonzero residual anisotropy for the carbon- and adamantane-
cored tetramers.
5c
Figure 7. Time-resolved fluorescence anisotropy of the tetrahedral molecule
t
C( BuSSB)4 on the long time scale (rotational diffusion). Best fit curve is
t
also shown (solid line). The fluorescence components of the C( BuSSB)4
In comparing the ultafast anisotropy decays for the tetramers
with that for the trimer it can be suggested that the relatively
slow decay result for the tetramers corresponds to the weaker
interaction (hopping) limit of the interchromophore interaction.
Alternatively, the fast decay time in the case of the nitrogen-
polarized perpendicular and parallel with respect to the excitation are shown
in the inset.
depends on the signal-to-noise ratio in the experimental decay
curves in the vicinity of the IRF. In the case of analysis of the
raw fluorescence anisotropy, this ratio drops down very quickly
as we go toward the negative delays as the experimental
anisotropy is associated with the ratio of two experimental values
1
2
cored DSB-trimer may result from a stronger interaction
among the same distyrylbenzene branching chromophore groups.
In a weak coupling limit (hopping regime), the energy transfer
26a
can be described by the F o¨ rster theory. To evaluate the ability
of the F o¨ rster theory to describe the energy transfer between
DSB-chromophores in tetramers, we compare the theoretical
and measured energy transfer rates. For the case of a very weak
interaction between chromophores in the macromolecule, the
chromophores should behave as individual isolated molecules,
and the fluorescence anisotropy decay can be described by the
(parallel and perpendicular polarized fluorescence) which both
tend to zero. This may be the cause for the many contradictory
data in the literature about the raw and calculated initial
1
e,15,16,20,21
anisotropies.
However, the modeling of the experi-
mental anisotropy decay showed that it could not be satisfac-
torily fit with an IRF-convoluted exponential with the decay
times longer then 60 fs independently on the initial anisotropy
r(0). The result of such modeling with a 100 fs exponential
decay law is shown in Figure 4. It is seen that actual decay is
shorter then 100 fs. This result is similar to what was found for
a distyrylbenzene trimer dendrimer, where the anisotropy also
decayed to a residual value within the instrument response
function of the upconversion unit (190 fs).12 This fast depolar-
ization may be due to the strong interactions of the three
nitrotolane chromophore groups (or the three distyrylbenzene
groups for the case of ref 12) around nitrogen.
4
b
expression
1
-t/τD
τhopping
r(t) ) [1 + 3e
], τ )
(1)
D
2
1
0
4(1 - cos θ)
Here τhopping is the excitation hopping time (in the absence of
rotational diffusion), and θ is the angle between the transition
dipoles of chromophores in a planar-symmetrical system.4b
Similar to eq 1 for the depolarization time (rate) in planar
systems, the expression for the depolarization rate in a tetra-
hedral molecular system can be derived:
It is important to note that for the isotropic (magic angle)
fluorescence dynamics of the tetramers and trimers, we did not
observe the same fast decay components as we observed for
the anisotropy decay. This is an indication that in our case the
fast dipole moment reorientation is not directly related to the
processes that are responsible for isotropic fluorescence decay.
A dynamic Stokes shift associated with the solvation processes
2
τhopping
2
τhopping
τD )
)
(2)
4
9
(1 - cos θ)
where θ ) 109.47° is the tetrahedral angle between transition
24
is usually reflected in the isotropic fluorescence decay pattern.
dipoles. The F o¨ rster rate of energy transfer between donor and
2
6a
Hence the main time scale of the solvation dynamics is different
from that for the anisotropy decay, and solvation effects do not
contribute substantially to the anisotropy dynamics. The residual
value of the fluorescence anisotropy (before molecular rotation)
contains geometrical and structural information. For a planar
acceptor separated by a distance RDA is given by
6
RF
1
kt(r) )
(3)
(
)
T R
D
DA
molecule with the rotational symmetry higher than C2, the
(
25) (a) Hall, R. D.; Valeur, B.; Weber, G. Chem. Phys. Lett. 1985, 116, 202.
(b) Sobolev, A. N.; Belsky, V. K.; Romm, I. P.; Chernikova, N. Yu.;
Guryanova, E. N. Acta Crystallogr. 1985, C41, 961. (c) Demidov, A. A.;
Andrews, D. L. Photochem. Photobiol. 1996, 63, 39.
residual anisotropy should be 0.1.1
1a,25a
In the case of the point
3
-D symmetry molecule, the anisotropy should decay to zero
(
26) (a) F o¨ rster, Th. Ann. Phys. 1948, 2, 55. (b) Dexter, D. L. J. Chem. Phys.
1953, 21, 836. (c) Harcourt, R. D.; Scholes, G. D.; Ghiggino, K. P. J. Chem.
Phys. 1994, 101, 10521.
(
24) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. J. Phys. Chem.
1
995, 99, 17311.
J. AM. CHEM. SOC.
9
VOL. 124, NO. 8, 2002 1741

A R T I C L E S
Varnavski et al.
exponential anisotropy decay. Fast equilibration within a cluster
(for example, a strongly exchange-coupled dimer) leads to an
initial 45 fs drop in anisotropy, while the remainder of the
depolarization decays due to intercluster energy transfer.4c The
anisotropy decay results in tetramers which are different from
the dynamics of the nitrogen-centered trimers investigated in
this work as well as for what was reported previously.12 For
both nitrogen-cored trimer systems, the experimental depolar-
ization times were found to be too short (<100 fs) to be
described by a F o¨ rster transfer model. The F o¨ rster transfer time
for the nitrogen-cored DSB-system was calculated to be ∼4
ps. This is not in agreement with the experimental anisotropy
decay times.
To analyze the case of strong interactions in the triphenyl-
amine (Figure 4), we have utilized a phenomenological model
1
7
to describe the system. A modest distortion of the absorption
spectrum of the triphenylamine as compared to that of linear
chromophore DMNAT (monomer) mentioned above suggests
that the role of electron delocalization is not significant and
the excitonic model can be used at least for qualitative analysis.
In this particular case, the discussion of coherence of the
excitations is led by using a model in which the limiting cases
of F o¨ rster transfer (weak interaction) and completely delocalized
excitonic states (strong interaction) are continuously connected
to each other. This analysis uses the infinite temperature
Figure 8. Spectral overlap between emission and absorption spectra of
the Ad( BuSSB)4. F o¨ rster energy transfer parameters are also shown.
t
where TD is the fluorescence lifetime of the donor in the absence
of acceptor, and RF is the F o¨ rster radius, which is the critical
distance between the donor and acceptor such that the energy
transfer probability equals the emission probability. The spectral
overlap between the absorption and emission spectrum of the
t
26a
Ad( BuSSB)4, which is critical for the F o¨ rster radius calculation,
is shown in Figure 8. The F o¨ rster radius calculation gave us
the value of 38.1 Å. We estimated the distance between the
centers of adjacent DSB-chromophores to be about 18 Å. Using
this distance, an energy transfer time of τhopping )1/kt ) 12.1
ps was obtained. In accordance with eq 2, this should lead to a
depolarization time τD of 3 ps. This is in qualitative agreement
17
approximation for the extremely small phonon correlation time.
The interesting conclusions of this approach are that for certain
limiting symmetry examples it is possible to relate the depo-
larization time to the ratio J/Γ of the interaction (J) and
homogeneous line width (Γ). For the case of N-fold symmetry
planar), they are related by
17
with our experimental anisotropy measurements with Ad-
17
(
t
(
BuSSB)4. The difference between calculated and experimental
times could be due to the fact that the distance between DSB
chromophores is comparable with the chromophore’s size, and
the point dipole model is not accurate in this case. Nevertheless,
the order of magnitude of the F o¨ rster transfer rate is comparable
with experimental results, and this is in qualitative agreement
with our suggestions of a predominately hopping character of
energy migration in tetramers. This result is also in qualitative
agreement with the calculation performed for DSB-dimers by
Mukamel et al. By using a collective electronic oscillator
approach (CEO), it was shown that in the case of DSB-dimers
with a paracyclophane bridge, the lowest electronic excitation
is localized mostly on the DSB-unit (monomer). In the case of
adamantane-cored tetramers, the distance between DSB units
is larger than that in paracyclophane-based dimers, and the
interaction should be even smaller. It was shown above (Figures
1
tdep
)
(4)
Γ(1 - A)
where
N
2
1
Γ
A )
∑
2
2
2
2
N
k)1 Γ + 16J sin (2π/N) sin (2πk/N)
2
7a
Here N is the number of chromophores contributing to the
energy migration process. In the weak interaction limit, it can
1
7
be shown that eq 4 reduces to eq 1. We have calculated the
profile of eq 4 against realistic values of the homogeneous line
width for the case of the trimer. The calculated curves for eq 4
versus the interaction parameter J are shown in Figure 9. From
our result with the triphenylamine system, we obtained a
depolarization time of approximately 35 fs. To estimate the
interaction strength J and energy transfer regime, we need to
know the homogeneous line width Γ. Selective excitation at a
different wavelength over the absorption spectrum showed no
dependence of the fluorescence spectrum on excitation wave-
length. However, this steady-state result does not necessarily
imply that the line is homogeneously broadened on the time
scale of our experiment. Using the full line width instead of
homogeneous line width would be an overestimation of Γ. A
set of curves describing eq 4 for different values of homoge-
neous broadening Γ taken similar to the full low-energy
3
and 4) that the anisotropy decay for carbon-centered tetramers
is two-exponential, opposite to single-exponential decay for
adamantine-centered tetramers. Apparently, a relatively small
decrease of the interchromophore separation (2.9 Å, 16% of
t
the distance between DSB-centers) in C( BuSSB)4 with respect
t
to Ad( BuSSB)4 leads to a substantial change of the anisotropy
dynamics associated with interchromophore interaction. This
critical distance dependence may suggest the presence of a short-
2
6b.c
range interaction of exchange (Dexter)-type
to come into
effect. Intramolecular chromophore clustering4 associated with
small distortions can be suggested as the reason for two-
c
-
1
absorption peak line width (2840 cm , estimated by multi-
Gaussian best fit analysis) is shown in Figure 9. Fortunately,
several important inferences can be drawn from Figure 9 without
(
27) (a) Bazan, G. C.; Oldham, W. J.; Lachicotte, R. J.; Tretiak, S.; Chernyak,
V.; Mukamel, S. J. Am. Chem. Soc. 1998, 120, 9188. (b) Bartolomew, G.
P.; Bazan, G. C. Acc. Chem. Res. 2001, 34, 30.
1742 J. AM. CHEM. SOC.
9
VOL. 124, NO. 8, 2002

Energy Transport in Model Dendritic Structures
A R T I C L E S
trimers), this would result in an ultrafast energy transfer time
in organic dendrimers based on these branching units.
Experimental Section
Steady-State Spectra. Steady-state absorption spectra were recorded
with a Hewlett-Packard 8452A diode array spectrometer. Fluorescence
spectra were taken with Shimadzu RF-1501 or SPEX spectrofluorom-
eters.
Time-Resolved Fluorescence Anisotropy Measurements. Femto-
second upconversion spectroscopy was employed to resolve temporally
the polarized fluorescence. The optical arrangement for our upconver-
sion experiments has been described previously.1
2a,28
The sample
solution was excited with a frequency-doubled light from a mode-locked
Ti-sapphire laser (Tsunami, Spectra Physics). This produces pulses of
approximately 100 fs duration in a wavelength range of 385-430 nm.
The polarization of the excitation beam for the anisotropy measurements
was controlled with a Berek compensator. The sample cuvette was 1
mm thick and was held in a rotating holder to avoid possible
photodegradation and other accumulative effects. The horizontally
polarized fluorescence emitted from the sample was upconverted in a
nonlinear crystal of â-barium borate using a pump beam at about 800
nm that was first passed through a variable delay line. This system
acts as an optical gate and enables the fluorescence to be resolved
temporally with a time resolution of about 200 fs (pump-excitation
Figure 9. Theoretical dependence of depolarization time τr on the
interchromophore interaction J for a C3-three-chromophore molecular
system. The arrow shows the depolarization time obtained from experiment
for the trimer system.
exact knowledge of Γ. First, it is clearly seen that within the
frame of this model it is impossible to have a anisotropy decay
time of 35 fs and to reside in the F o¨ rster regime (small
interaction) for any homogeneous broadening smaller than the
full line width. Here, coherence must be taken into account.
Actually, the experimental anisotropy decay time falls at the
curvature of the plot of eq 4 and may be interpreted as a
crossover region between incoherent (hopping) dynamics and
the existence of excitonic interactions. Extrapolation of the
7
90/395 nm cross correlation function had a fwhm of 190 fs). Spectral
resolution was achieved by dispersing the upconverted light in a
monochromator and detecting it by using a photomultiplier tube
(Hamamatsu R1527P). The excitation average power was kept at a level
below 0.5 mW. In this excitation intensity regime, the fluorescence
dynamics were found to be independent of the excitation intensity for
all investigated solutions.
Fitting Procedures for Fluorescence Anisotropy. Raw fluorescence
anisotropy R(t) was calculated from the decay curves for the intensities
of fluorescence polarized parallel Ipar(t) and perpendicular Iper(t) to the
polarization of the excitation light according to the expression R(t) )
-
1
2
000-3000 cm curves to find the estimated interaction
-
1
strength corresponds to a magnitude close to 1000 cm . It is
worth noting that the appearance of a small peak (shoulder) at
(Ipar - GIper)/(Ipar + 2GIper). The factor G accounts for the difference
374 nm in the trimer’s absorption spectrum (see Figure 1) could
in sensitivities for the detection of emission in the perpendicular and
parallel polarized configurations. It was measured using perylene in
methanol as a reference. In the real experiment, the G-factor has been
found to be essentially in unity (1.02 ( 0.02). The initial dynamics of
fluorescence anisotropy for the triarylamine system were found to be
very fast, completing within the duration of the instrument response
function. To make a reasonable estimation of the fluorescence anisot-
ropy decay time, we performed Impulse Reconvolution29 assuming for
triarylamine the one-exponential decay law for anisotropy decay with
also be an indication of excitonic coupling in the trimer. These
results strongly suggest that coherent interactions are essential
in describing the energy migration in the trimer branched
chromophore system.
In this paper, we have characterized the interactions between
branch chromophore units in model dendritic systems. The three-
and four-fold symmetry model branching centers showed
different excitation dynamics probed by time-resolved fluores-
cence anisotropy. The fluorescence anisotropy of the triaryl-
amine system decayed to a residual value with a time constant
of 35 fs, while the tetramer systems showed a more complex
decay with at least two decay components for the carbon-
centered tetramer. The slower components of the anisotropy
decay for the tetramer system may be inferred as the result of
weaker chromophore interactions and can qualitatively be
described by a F o¨ rster model. For the triarylamine system,
theoretical modeling showed the energy migration to be at the
crossover region between coherent and incoherent type as
estimated by a phenomenological model. These results give
stronger evidence for the significance of coherence in energy
transport by strong interchromophore interactions in branched
fluorescent macromolecules of various symmetries. The nature
and magnitude of the interaction strengths in these branched
structures are very important for applications in light emission
and light harvesting. If the migration time around a single
branching center is very fast (for the case of nitrogen-cored
time constant τ
a
and the residual value of τ . Difference (Ipar - GIper)
r
and isotropic (Ipar + 2GIper) decay curves were fitted to the result of
the convolution of the instrument response function with an exponential
2
30
model to minimize the reduced ø value. The minimum value was
obtained by the Marquardt nonlinear least-squares method. The quality
2
of the fit was monitored by values of the reduced ø as well as by
inspection of the residuals and autocorrelation function. Numerical
modeling of the raw fluorescence anisotropy for different sets of
isotropic and anisotropic parameters was also performed and compared
with the experiment.
Acknowledgment. At KSU, the work was supported by NSF
ALCOM grant 89-DMR20147. T.G. III acknowledges NSF and
Air Force AFSOR for support.
JA011038U
(
28) (a) Varnavski, O.; Leanov, A.; Liu, L.; Takacs, J.; Goodson, T., III. Phys.
ReV. B 2000, 61, 12732. (b) Varnavski, O.; Ispasoiu, R. G.; Balogh, L.;
Tomalia, D. A.; Goodson, T. G. J. Chem. Phys. 2001, 114, 1962.
29) Soutar, I.; Swanson, L.; Christensen, R. L.; Drake, R.; Phillips, D.
Macromolecules 1996, 29, 4931.
(
(30) Grinvald, A.; Steinberg, I. Anal. Biochem. 1974, 59, 583.
J. AM. CHEM. SOC.
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VOL. 124, NO. 8, 2002 1743