Multiphonon relaxation slows singlet fission in crystalline hexacene

Article abstract of DOI:10.1021/ja503980c

Singlet fission, the conversion of a singlet excitation into two triplet excitations, is a viable route to improved solar-cell efficiency. Despite active efforts to understand the singlet fission mechanism, which would aid in the rational design of new materials, a comprehensive understanding of mechanistic principles is still lacking. Here, we present the first study of singlet fission in crystalline hexacene which, together with tetracene and pentacene, enables the elucidation of mechanistic trends. We characterize the static and transient optical absorption and combine our findings with a theoretical analysis of the relevant electronic couplings and rates. We find a singlet fission time scale of 530 fs, which is orders of magnitude faster than tetracene (10-100 ps) but significantly slower than pentacene (80-110 fs). We interpret this increased time scale as a multiphonon relaxation effect originating from a large exothermicity and present a microscopic theory that quantitatively reproduces the rates in the acene family.

Full text of DOI:10.1021/ja503980c

Article
pubs.acs.org/JACS
Multiphonon Relaxation Slows Singlet Fission in Crystalline
Hexacene
†
,‡,∥
Timothy C. Berkelbach, Bharat Kumar,¶,∥ Alexey Chernikov, Yu Zhong,
¶,∥
§
¶
Erik Busby,
§
¶
§
‡
‡
¶
Htay Hlaing, X.-Y. Zhu, Tony F. Heinz, Mark S. Hybertsen, Matthew Y. Sfeir, David R. Reichman,
¶
,†,‡
Colin Nuckolls, and Omer Yaffe*
†
¶
§
Energy Frontier Research Center, Department of Chemistry, and Departments of Physics and Electrical Engineering, Columbia
University, New York, New York 10027, United States
‡
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973-5000, United States
S Supporting Information
*
ABSTRACT: Singlet fission, the conversion of a singlet excitation into two
triplet excitations, is a viable route to improved solar-cell efficiency. Despite
active efforts to understand the singlet fission mechanism, which would aid in
the rational design of new materials, a comprehensive understanding of
mechanistic principles is still lacking. Here, we present the first study of singlet
fission in crystalline hexacene which, together with tetracene and pentacene,
enables the elucidation of mechanistic trends. We characterize the static and
transient optical absorption and combine our findings with a theoretical
analysis of the relevant electronic couplings and rates. We find a singlet fission
time scale of 530 fs, which is orders of magnitude faster than tetracene (10−
1
00 ps) but significantly slower than pentacene (80−110 fs). We interpret this
increased time scale as a multiphonon relaxation effect originating from a large
exothermicity and present a microscopic theory that quantitatively reproduces the rates in the acene family.
INTRODUCTION
strong charge-transfer (CT) character exhibit strong coupling
between the low-lying excited singlet and triplet pair
states.
■
Singlet fission (SF) is a spin-allowed energy conversion process
that occurs in select organic molecules and aggregates where an
excited singlet state converts into two triplet states on adjacent
2
,5−10
The elucidation of generic mechanistic features of SF has
been hindered by the lack of materials which exhibit the
phenomenon. The linear acenes, especially tetracene and
pentacene, have received the most attention. These are perhaps
the best understood SF systems, and they have proven to be
some of the fastest and most efficient SF materials. With
respect to energetics and considerations of electronic coupling,
pentacene in particular satisfies the two key conditions for SF
1
,2
chromophores.
This form of carrier multiplication has
recently attracted much attention as a means of improving
upon the fundamental efficiency limitations of single junction
3,4
photovoltaic cells. While recent theoretical and experimental
work has led to significant progress in the field, a complete and
quantitative understanding of the variables that need to be
optimized in order to exploit SF for photovoltaic applications is
still far from complete.
discussed above: the process is slightly exothermic (−ΔE
≈
SF
1,11
1
10−170 meV)
and the electronic coupling is reasonably
The current understanding of SF suggests that the efficiency
i.e., singlet to triplet conversion ratio) and the rate of the SF
process is governed mainly by two parameters: the energy
difference between the excited singlet (S ) and the multiexciton
7
,10,12
large (V ≈ 10−50 meV).
The strong electronic coupling
SF
(
has been linked to the large CT character of the S state, which
1
manifests as a large Davydov splitting (130 meV) seen in
1
9,13−15
polarization-resolved absorption spectra.
These metrics
triplet pair (TT) states, ΔE = 2E(T ) − E(S ) (where 2E(T )
SF
1
1
1
have helped rationalize the extremely fast SF time scale in
≈
E(TT)), and the electronic coupling between these states,
= ⟨S |H|TT⟩ (H is the electronic Hamiltonian). It is
pentacene (k− ≈ 80−110 fs).
1
11,16−18
Such a short time scale
V
SF
SF
1
allows SF to out-compete other relaxation channels, leading to
a high thermodynamic yield for the overall SF process. These
properties of pentacene provide strong impetus for a systematic
study of the larger acenes such as hexacene, for which the
magnitudes of ΔESF and VSF are expected to be even larger, in
generally accepted that SF is most efficient in systems for which
the process is exothermic (ΔE < 0) and the electronic
SF
coupling is large. The magnitude of the electronic coupling is
strongly dependent on the intermolecular distance and
orientation as well as the microscopic mechanism by which
SF takes place. While there is an ongoing debate regarding the
relative importance of different mechanisms, it is currently
accepted that molecular systems with excited states that have
Received: April 21, 2014
Published: July 1, 2014
©
2014 American Chemical Society
10654
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Article
Figure 1. (a) Unpolarized transmission spectra of single crystal, polycrystalline, and solution-phase (single-molecule) hexacene (reproduced with
permission from ref 23). (b) Reflection spectra of the single crystal with polarization parallel to the a, a + b, and b crystallographic directions,
demonstrating the Davydov splitting of 160 meV. (c) Hexacene crystal structure and lattice vectors referenced in (b).
order to gain further insight into both fundamental and
potentially practical aspects of SF.
progression, the structure of the crystalline spectra is
significantly different, and quite similar to pentacene crystals,
suggesting that the higher lying peaks can be interpreted as
various mixtures of Frenkel and CT exciton compo-
Until recently, the photophysics of acenes larger than
pentacene have been unobtainable, due to a lack of synthesis
and preparation methods. In this work, we adopt a recently
developed synthetic technique for producing high-quality, pure
9
,13,15,24
nents.
We also note that E(S ) for pure hexacene is
1
about 200 meV less than previously reported values for a
19
25
hexacene films and crystals to experimentally study how
aspects of the electronic structure influence SF rates in acene
crystals. We report here the first experimental determination of
the SF dynamics in hexacene which, together with tetracene
and pentacene, allows for a systematic study of the influence of
electronic properties on the SF rate.
substituted hexacene derivative, which we interpret as the
result of greater intermolecular coupling in the absence of steric
effects from functional groups.
An experimental determination of ΔE in the crystal would
SF
also require measuring E(T ). However, while the energy of the
1
dipole-allowed singlet state for hexacene is readily determined
with absorption measurements, the energy of the dipole-
forbidden triplet state is much more difficult to measure
precisely. In the smaller acenes (anthracene, tetracene, and
pentacene), the crystal-phase triplet energy is rather uniformly
A unique feature of hexacene is that the measured E(S ) is
1
nearly three times the expected E(T ). Singlet fission in the
1
regime where there exists both large exothermicity and large
electronic coupling has not been previously explored. This
allows for the possibility of two competing relaxation processes:
2
6−28
3
0−50 meV below that of the single-molecule triplet.
In
2
3
SF into three triplets (S → 3 × T ) or SF into two triplets
1
1
hexacene, the single-molecule triplet energy is 540 meV,
accompanied by the emission of high energy phonons (S → 2
1
suggesting that the crystal phase triplet energy is very close to
500 meV. Taken together, this suggests that the energy needed
for the formation of two triplets is 1.0 eV and for three triplets
is 1.5 eV. When compared to the singlet energies measured
×
T1 + phonons). In order to understand the relative
contributions of these two mechanisms, we characterize the
static and dynamical optical absorption properties and combine
our findings with a detailed theoretical analysis of the relevant
electronic couplings and rates. Our analysis strongly suggests
that the (S1 → 2 × T1 + phonons) SF mechanism
predominates. We find a SF time scale of 530 fs, which is
here, we find that SF to generate two triplets is strongly
(2)
exothermic (ΔE ≈ −500 meV) and SF to generate three
SF
(3)
SF
triplets is slightly endothermic (ΔE ≈ 100 meV). Never-
theless, it is important to note that we have neglected entropic
contributions to the driving force as well as the possibility of a
large triplet−triplet binding energy. As an example, SF in
20−22
significantly faster than tetracene (10−100 ps)
than pentacene (80−110 fs).
but slower
1
1,16−18
2
1,22
tetracene is slightly endothermic yet it is still efficient,
albeit
RESULTS AND DISCUSSION
dramatically slower than in the exothermic case of pentacene.
Next, we investigate the intermolecular electronic coupling in
hexacene single crystals. Like the shorter members of the linear
acene family, hexacene molecules arrange in a triclinic crystal
■
We begin by investigating the linear optical transitions of
crystalline and polycrystalline hexacene, which will ultimately
determine the thermodynamic driving forces for SF. Clearly,
19
the energy difference between S and the multiexciton TT
structure with a herringbone motif (Figure 1c). The presence
of two translationally inequivalent molecules in the unit cell
1
states will depend sensitively on the molecular environment,
given that molecular interactions, screening, and polarization
effects can dramatically alter the electronic structure. In Figure
13
gives rise to a Davydov splitting (DS) of the exciton levels.
Importantly, a positive correlation between the magnitude of
the DS and the degree of CT character in the low-lying excited
states has recently been established in the family of acene
1
a, we compare the room-temperature transmission spectra of
single crystal hexacene, polycrystalline film, and the solution-
phase single molecule (reproduced from ref 23). As expected,
there is a strong solution-to-crystal redshift, yielding a decrease
1
3
crystals. The magnitude of the Davydov splitting can
frequently be inferred from the splitting of the first two peaks
in the unpolarized absorption, and the data presented in Figure
1a suggest a DS of about 160 meV. To more conclusively
identify these peaks as Davydov doublets, we have performed
in E(S ) from 1.82 eV in solution to 1.48 eV in polycrystalline
1
films and to 1.46 eV in the single crystal. While the molecular
spectrum in solution exhibits the typical acene vibronic
1
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Figure 2. (a) Transient absorption signal as a function of time and probe energy (probe beam at 45°), highlighting the photoinduced absorption
features of the singlet (S ) and triplet (T ). (b) Singlet and triplet photoinduced absorption spectra as extracted from global analysis. The strong
1
1
negative signal at energies between 1.4 and 2.0 eV is associated with the ground-state bleach; inverted ground-state absorption (GSA) is shown for
comparison. (c, top) Kinetic traces at S and T induced absorption maxima with exponential fits. (c, bottom) Singlet and triplet population kinetics
1
1
extracted from global analysis, demonstrating the 530 fs singlet fission time scale. Inset depicts the three-state kinetic model used in global analysis to
fit the TA data.
polarization-resolved reflection spectroscopy measurements.
Figure 1b presents measured spectra on a high-quality single
crystal of hexacene. The intensities of the first two peaks at 1.44
and 1.60 eV (slightly shifted in reflection when compared to
transmission) strongly depend on the angle of the linearly
polarized light. The effect of polarization angle is opposite for
the two peaks: along the a crystallographic direction (see
Figure 1c) the 1.44 eV peak reaches its maximum intensity
while the 1.60 eV peak is eliminated and vice versa along the b
crystallographic direction. This behavior confirms that the two
peaks are a Davydov doublet with a DS of 160 meV. This value
is indeed larger than the values reported for tetracene (∼80
consider the conventional mechanism to generate two triplets.
The very fast time scale that we observe (vide infra) confirms
this assumption, because it is roughly 2 orders of magnitude
faster than tetracene, the fastest known endothermic system.
However, it is interesting to note that for longer acenes (e.g.,
heptacene), the (S → 3 × T ) pathway may become more
1
1
competitive due to increased CT character and improved
energetic alignment.
We now turn to the investigation of the excited-state
dynamics to measure the rate of SF in hexacene. For that
purpose, we use broadband femtosecond transient absorption
(TA) spectroscopy on polycrystalline hexacene films (Figure
2). Hexacene films were excited at 1.49 eV, which corresponds
to the lowest-energy electronic transition (Figure 1a). Pump-
power dependence measurements were conducted to ensure
that the excitation density was sufficiently low, so as to avoid
singlet−singlet exciton annihilation and other nonlinear
processes (see Supporting Information). Following excitation
2
2,29
18,30
meV)
and pentacene (∼130 meV),
suggesting that the
degree of CT character in hexacene is very large. As discussed
above, the electronic coupling VSF which mediates conventional
2
,7,9,15
SF is therefore expected to be quite large.
Such large CT character also has interesting implications for
(3)
V
= ⟨S |H|TTT⟩, the electronic coupling which mediates the
SF
1
2
(
S → 3 × T ) process. Using a simple model consisting of six
(17.6 μJ/cm ), two distinct induced absorption species are
1
1
valence electrons on three neighboring molecules, one can
observed in Figure 2a: a short-lived, featureless absorption
centered at 2.13 eV and long-lived feature showing two peaks at
2.0 and 2.2 eV (Figure 2b). The first feature is assigned as the
consider Frenkel excitations, |S S S ⟩, and CT excitations, |
1
0 0
CAS ⟩, where C and A denote cationic and anionic
0
configurations on each molecule. One can show that ⟨S S S |
singlet exciton (S ), in qualitative agreement with other acene
1
0
0
1
1
7,25
H|TTT⟩ = 0, i.e., pure Frenkel excitons do not couple (to
lowest order) to a three-triplet multiexciton state (see
Supporting Information). However, when the low-lying
adiabatic states have CT character, i.e., |S ⟩ ∼ α|S S S ⟩ + β|
systems.
The second feature is assigned to the triplet
exciton (T ), in agreement with unsubstituted hexacene in
1
23
25
solution and substituted hexacene films. This T → T
1
n
absorption band features a progression of peaks with 180 meV
spacing that is characteristic of vibronic coupling to the ring-
breathing mode in acene systems. We also note that the
magnitude of the triplet induced absorption signal is dependent
on the probe-substrate angle of incidence, due to the combined
effects of molecular orientation nearly normal to the substrate
surface and a triplet transition dipole that is oriented along the
long axis of the molecule. As a result, the triplet TA signal is
maximized with a large angle of incidence, which is in
1
1 0 0
CAS ⟩, then the CT component provides a first-order two-
0
electron coupling and a second-order mediated coupling. This
result is analogous to the usual case where Frenkel excitons
couple to a two-triplet state via a two-electron integral, whereas
1
,2,6
CT excitons couple via a larger one-electron integral.
Therefore, we have the interesting result that strong CT
character in S increases the probability for SF to generate three
1
triplets, just as has been concluded for SF to generate two
2
,6,7,9
27
triplets.
Nevertheless, although nonzero, these couplings
agreement with previous observations in pentacene. All
can be inferred to be small due to the interplay of orbitals on
three distinct molecules. This small electronic coupling
combined with the likelihood of uphill, endothermic SF to
generate three triplets strongly suggests that the process does
not occur in crystalline hexacene, and we henceforth only
displayed TA data were acquired with the probe beam at 45°
incidence; data acquired at normal incidence are presented in
the Supporting Information.
To quantitatively validate the SF reaction scheme, obtain rate
constants, and decompose the TA data into time-independent
1
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Figure 3. (a) Comparison of theoretical and experimental singlet fission rates. Red circles denote the experimentally measured singlet fission rates
for tetracene, pentacene, and hexacene (left to right) with approximate error bars highlighting the spread of reported values (see text for references).
Experimental rates are compared to the 1-phonon and multiphonon rate theories, for which only the latter is capable of capturing the SF rate of
hexacene. (b) The spectral density employed in the calculations, which is representative of the high-frequency CC stretching modes in acenes.
spectral signatures, the data are analyzed within the framework
sion, note that if one only considers linear exciton−phonon
coupling (characterized by a weighted phonon density of states,
Γ(ω)) treated at lowest order in perturbation theory, then the
31,32
of global target analysis
(for details, see Supporting
Information). This was performed for the full set of data,
which includes absorption in the near IR and delay times up to
7
SF rate is given by
3
000 ps. The data are well reproduced with a three-state model
2
λω
ΔE
⎛
Γ⎜−
⎝
⎞
k (ΔE < 0, T) = 8
πV
ℏ
ph
2
SF
ΔESF
ℏ
SF
of SF depicted in the inset of Figure 2c, bottom: excitation from
the ground state creates a singlet exciton, the singlet then
undergoes SF to form triplets, and on a longer time scale the
triplets decay to repopulate the ground state (triplet decay
dynamics are included in the Supporting Information). This
model intentionally neglects the fast (∼ 100 fs), wavelength-
dependent dynamics that can be observed near the high energy
tail of the singlet absorption feature, since it (i) is uncorrelated
to the rise of the triplet absorption feature, (ii) does not result
in ground state repopulation, and (iii) is obscured at some
wavelengths by coherent artifacts. While they do not influence
the following analysis or conclusions, they are interesting to
point out and may result from relaxation of the photoexcited or
multiexciton transition state. The resultant model provides
good kinetic fits and completely deconvolves the singlet and
triplet into their respective time-independent, photoinduced
absorption spectra (Figure 2b) and time-dependent population
trajectories. In Figure 2c, we show the experimental kinetic
⎟[N(−ΔE ) + 1]
SF
SF
SF
⎠
(1a)
2
SF
λω
⎛
⎞
k (ΔE > 0, T) = 8
πV
ℏ
ph
2
SF
ΔESF
Γ⎜
⎟N(ΔE )
SF
SF
SF
ΔE ⎝ ℏ ⎠
(1b)
where λ is the vibrational reorganization energy, ωph is a
characteristic phonon frequency, and N(E) = [exp(E/k T) −
B
−1
1
]
is the phonon thermal occupancy. Because Γ(ω) peaks at a
−1
characteristic vibrational frequency (roughly 1450 cm for
CC stretching) and completely vanishes beyond a maximum
−1
frequency (roughly 3000 cm for C−H stretching), the above
expression predicts a rate which goes to zero for sufficiently
large exothermicity, such as found in hexacene (−ΔE ≈ 500
SF
−1
meV ≈ 4000 cm ). This phenomenon is sometimes referred
to as a phonon bottleneck and to capture the nonzero rate of
SF in hexacene requires the inclusion of (slower) multiphonon
traces and their fits (top) as well as the extracted population
34
relaxation effects. Assuming that nonlinear exciton−phonon
coupling terms treated to lowest order are dominant over linear
coupling terms treated to higher order, we can derive a rate
law (see Supporting Information) which captures multiphonon
kinetics (bottom). This analysis yields a SF time scale of k−
1
SF
≈
530 fs.
35
We note that singlet exciton deactivation via competing
photoluminescence or intersystem crossing is safely neglected
in our analysis. Like in solid-state pentacene, these processes
are essentially unobserved in crystalline hexacene due to the
processes:
∞
(n)
n
k (ΔE < 0, T) =
∑
k
(−ΔE , 0)[N(−ΔE /n) + 1]
1
,16,17
SF
SF
SF
SF
SF
rapid SF.
Similarly, as described above, we work at
n=1
1
8
−3
sufficiently low excitation density, ∼ 6.3 × 10 cm , to neglect
(2a)
2
0,33
singlet−singlet annihilation,
especially in light of the fast
∞
(
subpicosecond) SF rate. We conclude that effectively all
(
n)
n
k (ΔE > 0, T) =
∑
k
(ΔE , 0)[N(ΔE /n)]
SF
SF
SF
SF
SF
singlet excitons undergo SF, resulting in a triplet quantum yield
of nearly 200%. However, the SF time scale for hexacene (530
fs) is significantly slower than that for pentacene, despite the
increased CT character discussed above.
n=1
(2b)
where
In order to rationalize the decreased rate of SF in hexacene
and to more broadly place hexacene within the family of acenes
we have extended the theory developed in refs 6 and 7 to
systems with a large exothermicity (for full details, see
Supporting Information). To understand the required exten-
2
SF
λω
(ΔE , 0) = 8
πV
ℏ
ph
2
SF
n!α2n−2
(
n)
k
SF
SF
ΔE
∞
∞
1
2π
iΔESFt/ℏ
∫0 Γ(ω)e−iωtdω) dt
n
×
∫−∞
e
(
(3)
1
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Journal of the American Chemical Society
Article
In the above expressions, n is the number of phonons emitted
expression presented here should be preferred. It is worth
mentioning that there are other microscopic routes to
multiphonon behavior and energy gap laws, including higher-
order perturbation theory in the linear exciton−phonon
(
or absorbed) and a new parameter α quantifies the importance
of nonlinear exciton−phonon coupling terms (α = 0 recovers
the lowest-order expression, eq 1).
35
Employing the physically motivated model parameters VSF
0 meV, λ = 250 meV, and α = 0.55, we can accurately
=
coupling. Such a protocol is responsible for the Englman-
37
3
Jortner theories of radiationless transitions, of which the low-
reproduce the SF rate behavior seen experimentally in
tetracene, pentacene, and hexacene, as shown in Figure 3a.
These results were obtained using a spectral density relevant for
high-frequency optical phonons:
temperature strong coupling limit was employed in Singh’s
38
early theory of SF. Despite the apparent similarity with
respect to turnover behavior, one should be cautious applying
semiclassical Marcus-like theories which are only accurate for
low-frequency phonons or at high temperatures, i.e., ℏω /k T
⎧
3
ph
B
2
2
⎪
3 [Δ − (ω − ωph) ], ωph − Δ < ω < ωph + Δ
≪ 1, which does not seem to be the case for the crystalline
acene materials. For example, the latter will predict an
unphysically strong temperature dependence even for exother-
mic SF. A proper quantum mechanical treatment of high-
frequency phonons, as embodied in the present theory, predicts
essentially no temperature dependence for the exothermic case
⎨ Δ
4
Γ ω =
(
)
⎪
⎩
0
,
ω < ωph − Δ, ω > ωph + Δ
(4)
−
1
−1
with ω /2πc = 1450 cm
and Δ/2πc = 800 cm ,
ph
characteristic of the acenes which are dominated by intra-
36
11
molecular CC stretching modes. This spectral density is
plotted in Figure 1b. Low-frequency phonons are irrelevant due
to their weak coupling to electronic transitions and small
energy scales (∼10 meV) incapable of providing or accepting
comparatively large energy differences (≳100 meV). For
demonstrative purposes, we have assumed that the electronic
coupling VSF is the same for all materials, such that the
observed behavior is entirely due to changes in the
of pentacene, in agreement with experiment. Our theory does
predict a slight temperature dependence for hexacene,
providing an interesting−if not challenging−test of the
multiphonon behavior proposed here. Specifically, the SF rate
in hexacene is predicted to be temperature independent from 0
to 300 K, but to increase by roughly 15% at temperatures
approaching 600 K (the melting/sublimation temperature of
most acenes). The theory described here also predicts an
activated, temperature dependence to the SF of tetracene.
While early experiments found evidence of such activated
exothermicity ΔE . The electronic coupling is only expected
SF
to vary by a factor of 2 or so over the range considered and for
sufficiently large electronic couplings, the rate is expected to
undergo a nonadiabatic to adiabatic transition, becoming
3
9,40
behavior,
all recent experiments show temperature-
2
0−22,41
independent SF,
suggesting that earlier measurements
7
,10
independent of the coupling VSF.
should be reinterpreted. We consider this to be an important
topic for future study.
We emphasize that our measured SF rate in hexacene places
a much stricter requirement on competing theories than was
previously available. In particular, viable kinetic theories for SF
in acenes must explain the observed turnover in rate versus
exothermicity. Extrapolating, we can make a prediction that
crystalline heptacene should exhibit a still-smaller rate constant,
CONCLUSION
■
To summarize, we have elucidated important mechanistic
features of SF by studying the electronic structure and ultrafast
dynamics in crystalline hexacene. Combined with the wealth of
existing results on tetracene and pentacene, our findings enable
for the first time a systematic examination of trends in this
prototypical family of molecules. More specifically, we have
addressed (i) the dominant relaxation mechanism in hexacene
−1
with a time scale of of kSF ≈ 1−10 ps. Our experimental and
theoretical findings tighten the frequently quoted design
criterion ΔE < 0. For the largest SF rates, one should strive
SF
for −ΔE ≈ E , where E is an energy scale associated with
SF
ph
ph
the phonon degrees of freedom; crystalline pentacene almost
perfectly satisfies this criterion, in accord with its ultrafast SF
behavior.
crystals, i.e., (S → 2 × T + phonons) versus (S → 3 × T );
1
1
1
1
and (ii) the rate of SF in hexacene crystals and its interpretation
within a unified theoretical framework. Regarding the first
point, optical spectroscopy on polycrystalline and single crystals
of hexacene has been combined with simple quantum chemistry
2
5
A previously studied substituted hexacene derivative
provides an interesting, independent test of our theory. The
solid-state hexacene derivative has a large exothermicity, −ΔE
SF
2
5
arguments to conclude that (S → 2 × T + phonons) is the
=
650 meV, and can be expected to have vibrational
1
1
dominant relaxation pathway. In the context of photovoltaics,
this implies that hexacene is suboptimal due to the excess
energy wasted as heat. For the second point, we have
performed ultrafast TA measurements on polycrystalline films
to show that SF in hexacene is highly efficient but is
significantly slower than in pentacene. We explain this turnover
to a slower rate in hexacene by extending our previously
properties very similar to the unsubstituted acenes allowing a
direct application of the present multiphonon theory. For this
material, we can see from Figure 3a that the theory predicts a
SF time scale of about 2 ps, which compares favorably to the
experimentally measured time scale of 5.1 ps. The remaining
discrepancy can be attributed to the decreased electronic
coupling due to poor packing, i.e., a smaller VSF than used in
Figure 3a.
25
6
,7
developed theoretical model
to include multiphonon
A simplification of the above microscopic expression gives
rise to an approximate “energy gap law” for the downhill,
relaxation processes. Through this analysis, we conclude that
SF to generate two triplets in hexacene imposes an exothermic
driving force which is much larger than the energy of the
available phonons. In turn, the SF process necessitates
multiphonon relaxation processes that slow down the SF rate
in comparison to pentacene. Interestingly, this conclusion
implies that for longer acenes such as heptacene, the even-
larger exothermicity combined with further increased CT
2
exothermic process, kSF ∝ (V /ΔE ) exp(ΔE /E ), which is
SF
SF
SF
0
common in electron and energy transfer. This type of energy
gap law qualitatively captures the rate reduction with increasing
driving force and may be useful for simple interpretations of
experimental data. However, we emphasize that an energy gap
law is typically phenomenological and the microscopic rate
1
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dx.doi.org/10.1021/ja503980c | J. Am. Chem. Soc. 2014, 136, 10654−10660

Journal of the American Chemical Society
Article
character may result in favorable conditions for the (S → 3 ×
1
Office of Science Graduate Fellowship Program (DOE SCGF),
administered by ORISE-ORAU under contract no. DE-AC05-
1
T ) process.
0
6OR23100. A.C. gratefully acknowledges funding from the
EXPERIMENTAL SECTION
Alexander von Humboldt Foundation within the Feodor-Lynen
Fellowship program. Research was carried out in part at the
Center for Functional Nanomaterials, Brookhaven National
Laboratory, which is supported by the U.S. Department of
Energy, Office of Basic Energy Sciences, under contract no. DE-
AC02-98CH10886.
■
Sample Preparation and Characterization. Hexacene synthesis
and single crystal growth were as reported in ref 19. Polycrystalline
films were grown by a vapor-phase transport method. A source of
hexacene (ca. 1 mg) was placed in the sublimation zone at 200 °C
under vacuum (ca. 450 mTorr) with flowing high-purity argon
(
99.999%) as a carrier gas with a flow rate of 50 sccm. Fused silica
substrate, which was coated with a self-assembled monolayer of
octyltrichlorosilane was placed in the crystallization zone. Following
preparation, both single crystals and polycrystalline films were
transferred into a controlled-environment glovebox. Single crystal
characterization involved examination under an optical microscope.
Polycrystalline characterization involved grazing incidence wide-angle
X-ray scattering measurements and scanning electron microscope
imaging.
Reflectance Contrast Measurements. Broadband radiation from
a tungsten quartz halogen source was focused on the sample by a 40×
objective, yielding a spot of about 2 μm in diameter. The reflected
signal was collected and analyzed with a grating spectrometer and a
liquid nitrogen-cooled CCD with a spectral resolution of about 5 nm.
Polarization angle-dependent measurements were performed by using
a linear polarization filter. The reflectance was obtained by normalizing
the sample signal to that of the bare fused silica substrate for each
setting of the polarization angle.
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ASSOCIATED CONTENT
Supporting Information
■
(
*
S
Synthesis, sample preparation and characterization, transient
absorption, and theoretical formalism details. This material is
available free of charge via the Internet at http://pubs.acs.org.
2
(
(
AUTHOR INFORMATION
Corresponding Author
oy2118@columbia.edu
■
(
(
Author Contributions
Islam, M. M.; Yuan, C.-H.; Tao, Y.-T.; Shinmyozu, T.; Chow, T. J. Nat.
Chem. 2012, 4, 574.
∥
These authors contributed equally.
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Notes
The authors declare no competing financial interest.
́
ACKNOWLEDGMENTS
■
Clark, J.; Friend, R. H. J. Am. Chem. Soc. 2013, 135, 16680.
Overall project coordination, sample growth and optical
characterization were supported as part of the Center for Re-
Defining Photovoltaic Efficiency Through Molecular-Scale
Control, an Energy Frontier Research Center funded by the
US Department of Energy (DOE), Office of Science, Office of
Basic Energy Sciences under Award DE-SC0001085. O.Y. and
E.B. were supported by the EFRC as a research fellows. We
wish to thank Mikas Vengris (Vilnius University) for graciously
providing his global analysis software package for our use.
T.C.B. was partially supported by the Department of Energy
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