Journal of the American Chemical Society
Article
DBF
The chemical structure of BTDF is shown in Figure 1c. The
two triphenylsilyl groups are attached to a dibenzofuran core,
which lowers its electron-transport level below that of the
emitter. The details of the synthesis are described in the
Supporting Information.
energy (the dibenzofuran core has λ
increases electron-hopping rates.
= 0.27 eV) and hence
e(h)
The distributions of conformational energy differences,
ΔEcef(h), are of Gaussian type with a moderate variance of σ
cf
e(h)
= 0.04 (0.05) eV and are uncorrelated in space, which allows us
to draw them from such a distribution in the larger box of 4096
molecules. Simulations are then additionally averaged over two
realizations of this disorder.
2. RESULTS
2.1. Computer Simulations. To relate charge carrier
mobility to the chemical structure, atomistic molecular
dynamics (MD) is used to simulate material morphologies.
Then the high-temperature limit of Marcus theory15,16 is
employed to evaluate charge-transfer rates between molecules i
and j according to
Electrostatic contributions to site energy differences are
calculated using partial charges for charged and neutral
molecules in the ground state obtained from DFT. Polarization
contributions are taken into account self-consistently using the
Thole model33,34 with a cutoff of 3.5 nm between molecular
centers of mass. This results in polarized electrostatic site
J2
(ΔEij − λij)2
4λijkBT
⎡
⎤
⎥
el
energy differences, ΔE , that are Gaussian distributed with a
ij
π
e(h)
⎢
ω =
exp −
el
e(h)
ij
variance of σ
= 0.12 (0.11) eV when computed from the
ℏ
λijkBT
⎢
⎥
⎦
⎣
(1)
neighbor list. Rather small energetic disorder and weak spatial
correlations are due to small variations of atomic partial charges
(local dipole moments) as well as the total dipole moment of
BTDF of less than 1 D. Note that the attachment of the
substituents does not affect the molecular dipole moment. All
distributions are shown in Figure 2a.
where T is the temperature, Jij is the electronic coupling
element, or transfer integral, and ΔEij is the site energy
difference which has contributions due to an applied electric
field, electrostatics including polarization, ΔEel, and internal
energy differences due to molecular conformations, ΔEcf.
Finally, λij is the reorganization energy which is dominated by
intramolecular contributions due to a small Pekar factor.17
More information about the transport parameters can be found
in the Supporting Information.
The rates and molecular centers of mass are used in kinetic
Monte Carlo simulations to solve the master equation for a
charge drift-diffusing in a box with periodic boundary
conditions in an applied electric field F. The charge carrier
mobility is then determined as μ = ⟨v⟩/F, where ⟨v⟩ is the
averaged projection of the carrier velocity on the direction of
the field.
Simulated mobilities are averaged over two MD snapshots,
ten injection points, and six different spatial directions of the
field. More details are given in the Supporting Information.
Simulations are performed using the VOTCA package.17,18
This approach has been used to calculate mobility in columnar
discotic mesophases,19−24 amorphous systems,25−28 self-
assembled monoloayers,29 and conjugated polymers.30,31
An amorphous morphology of 4096 BTDF molecules is
obtained by first annealing the system at 700 K, well above the
glass transition temperature, Tg = 380 K, followed by fast
quenching to room temperature. The final length of the cubic
box is L = 16 nm. To determine intermolecular charge-hopping
rates in this morphology, a neighbor list based on the closest
approach of centers of mass between phenyl rings or
dibenzofuran cores is constructed using a cutoff of 0.7 nm.
The parameters entering the rate expression eq 1 are then
calculated for each molecular pair from the neighbor list.
Since BTDF has soft degrees of freedom, such as dihedrals δ
in Figure 1c, molecules in the amorphous phase have different
conformations. The distribution of this dihedral angle is shown
in the inset of Figure 2a. These conformations are frozen on the
time scale of charge transport (see the Supporting Information
The remaining ingredient entering the rate expression, eq 1,
is the transfer integral J, which relies on the definition of
diabatic states of a pair of molecules. The latter are usually
constructed from representative orbitals of the π-conjugated
parts, since the effect of attached substituents on the diabatic
states is rather small (e.g., in case of alkyl or glycol side
chains20,24,26). Following this approach, the diabatic states are
evaluated by substituting triphenylsilyl by a hydrogen (without
modifying the rest of the morphology). Reorganization energies
of the dibenzofuran core are used, and transfer integrals are
then calculated on DFT level with the PBE functional and a
TZVP basis set using the dimer projection method.35,36 The
distribution of the logarithm of transfer integrals J (see Figure
2b) for pairs of the neighbor list is very broad. This can be
rationalized in terms of morphology, as the transfer integral
depends exponentially on the intermolecular separation. The
distance between the dibenzofuran cores is large due to the
attached bulky substituents, as illustrated by the radial
distribution function for centers of mass of dibenzofuran
cores, shown in the inset of Figure 2b. The onset of this
function is at ca. 0.5 nm and has a peak g(r) > 1 at a separation
larger than 1 nm, which eventually leads to the broad
distribution of J. The small number of high transfer integrals
due to a few close-lying cores is apparently not sufficient for
charge percolation. As a consequence, simulations predict low
mobilities at experimentally relevant electric fields, μe(h) < 4 ×
10−7 (3 × 10−8) cm2/V·s, which would lead to ohmic losses and
poor device performance.
The above assumptions on the nature of the diabatic states
seem logical but are ultimately invalid. Indeed, if the diabatic
states are constructed using the frontier orbitals of the entire
BTDF molecule, the distributions of transfer integrals become
significantly less broad and peak at much larger values, as
shown in Figure 2b. As a result, predicted mobilities are much
higher, μe(h) ≈ 5 × 10−4 (10−5) cm2/V·s, which is in agreement
with experiments performed by admittance spectroscopy (AS).
2.2. Admittance Spectroscopy. AS allows to extract
mobilities in an organic film sandwiched between two
electrodes by applying dc and ac voltages and finding the
transit time of the carriers in the film from a maximum in the
negative differential susceptance −ΔB = ω(C − C0), where C
for details). Reorganization energies λij and internal energy
cf
ij
differences ΔE are therefore computed from potential energy
surfaces of 512 molecules in neutral and charged states making
use of density functional theory (DFT). We find a small
variance in reorganization energies which does not affect the
mobility. Hence, the mean values of λe(h) = 0.19 (0.27) eV for
electrons (holes) are used. Due to delocalization effects,32
attaching the triphenylsilyl groups decreases the reorganization
13820
dx.doi.org/10.1021/ja305310r | J. Am. Chem. Soc. 2012, 134, 13818−13822