Molecular Understanding of Fullerene – Electron Donor Interactions in Organic Solar Cells

Abstract

Organic solar cells hold promise of providing low-cost, renewable power generation, with current devices providing up to 13% power conversion efficiency. The rational design of more performant systems requires an in-depth understanding of the interactions between the electron donating and electron accepting materials within the active layers of these devices. Here, we explore works that give insight into the intermolecular interactions between electron donors and electron acceptors, and the impact of molecular orientations and environment on these interactions. We highlight, from a theoretical standpoint, the effects of intermolecular interactions on the stability of charge carriers at the donor/acceptor interface and in the bulk and how these interactions influence the nature of the charge transfer states as wells as the charge separation and charge transport processes.

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Molecular Understanding of Fullerene – Electron Donor
Interactions in Organic Solar Cells
Sean M. Ryno, Mahesh Kumar Ravva, Xiankai Chen, Haoyuan Li, and Jean-Luc Brédas*
Dr. S. M. Ryno, Dr. M. K. Ravva, Dr. X.-K. Chen,
Dr. H. Y. Li, Prof. J.-L. Brédas
Laboratory for Computational and Theoretical
Chemistry of Advanced Materials
KAUST Solar Center
Physical Science and Engineering Division
King Abdullah University of Science and Technology
Thuwal 23599–6900, Kingdom of Saudi Arabia
E-mail: jean-luc.bredas@kaust.edu.sa
DOI: 10.1002/aenm.201601370
recently gained substantial interest; non-
fullerene OSCs to date lead to PCEs up
to 9.5%,[4] which remains lower that the
best fullerene-based devices. The donor
materials, both small molecule and poly-
mers, have also seen significant research
efforts directed at developing increas-
ingly better performing materials; small-
molecule based devices now reach 9.0%[5]
while polymer-fullerene devices hold the
current record for single-junction devices
at 11.7%.[1]
In order to realize increased PCEs, a
detailed understanding of the energetic
landscape and intermolecular interactions
at the interface between the electron donor
and the electron acceptor is crucial. Also,
the morphology within the active layers, whether in a bilayer
structure or a blend (termed a bulk heterojunction (BHJ)), plays
a crucial role in the determining the efficiencies of the various
electronic and optical processes involved in OSC operation.[6–8]
Thus, by better understanding how intermolecular interactions
impact these processes and how advantageous characteristics
may be obtained by tuning the processing conditions, addi-
tional insight can be gained into the rational design of improved
organic electronic materials for photovoltaics applications.
In addition, one of the processes central to the operation
of OSCs as wells as organic light-emitting diodes and organic
thin-film transistors, and often a limiting factor in their perfor-
mance, is the efficiency with which the active layer can trans-
port generated or injected charges, either holes or electrons.
The charge-carrier mobility, the rate at which charges move
through a material, is dependent on a number of parameters
including the chemical and molecular structure of the material
constituents,[9] impurities and defects within the active layer
that can act as charge trapping sites that reduce the carrier
mobility,[10,11] and the solid-state molecular packing.[12–15]
In this Review, we focus, from a theoretical point of view,
on understanding the interactions between fullerene acceptors
and small-molecule or polymer donors, how these interactions
influence the site energies and charge transfer state energies of
the donor and acceptor components at their interfaces in OSCs,
what is the effect of delocalization on the site energies and
charge transfer states, and, finally, how do these interactions
impact the charge separation and charge transport processes.
Throughout this Review, we try to highlight how molecular
Organic solar cells hold promise of providing low-cost, renewable power
generation, with current devices providing up to 13% power conversion
efficiency. The rational design of more performant systems requires an
in-depth understanding of the interactions between the electron donating
and electron accepting materials within the active layers of these devices.
Here, we explore works that give insight into the intermolecular interactions
between electron donors and electron acceptors, and the impact of molecular
orientations and environment on these interactions. We highlight, from
a theoretical standpoint, the effects of intermolecular interactions on the
stability of charge carriers at the donor/acceptor interface and in the bulk and
how these interactions influence the nature of the charge transfer states as
wells as the charge separation and charge transport processes.
This Review is dedicated to Professor Nazario Martín, an outstanding scientist, wonderful friend,
and great fan of Atlético Madrid, at the occasion of his 60th birthday.
1. Introduction
Organic solar cells (OSC) are promising candidates for low-cost
renewable energy production due to their ability to be printed,
via high throughput methods, on large-area, flexible substrates.
Through years of research involving fullerenes and numerous
donor materials as well as engineering of device fabrication
techniques, the performance of fullerene-based OSCs have now
reached nearly 12% power conversion efficiency (PCE) in single-
junction devices,[1] while PCEs of greater than 13% have been
reported in proprietary multi-junction devices.[2,3] Despite these
efficiencies actually doubling over the past decade, still better
performance is necessary for many commercial applications.
Fullerenes, both substituted (e.g., PC61BM) and unsubsti-
tuted (e.g., C60), are ubiquitous as electron-accepting mate-
rials in the active layers of OSCs, with either a small mol-
ecule or polymer acting as the electron-donating material. We
note, however, that non-fullerene acceptor materials have also
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structure or intermolecular configurations impact the various
processes in OSCs to provide some general guidance for mate-
rials engineering efforts.
We note that, over the past 15 years, there has been a steady
increase in the number of publications discussing OSCs (Figure 1),
with over 13 000 publications in 2015 alone. As it is thus very
challenging to provide a complete overview of the field, we try
and select works that specifically relate to an increased under-
standing of the processes that occur in OSCs as they pertain to
intermolecular interactions. In particular, we focus on the fac-
tors that impact the site energies at the donor-acceptor inter-
face, on the interactions that dictate the charge transfer state
energies and the energetics of charge separation and on charge
transport in OSC materials. While our primary focus here is on
fullerene systems, it is important to note that these same princi-
ples should also apply to non-fullerene moieties. This Review is
organized as follows: Section 2 provides a brief reminder of the
key processes taking place in OSCs; Section 3 reviews common
OSC materials and the interactions within pure donors and
acceptors and between donors and acceptors; Section 4 consti-
tutes the primary focus of this Review and discusses the effects
of intermolecular interactions and molecular packing on the site
energies and charge transfer state energies, the effects of charge
carrier delocalization, and how the charge separation and charge
transport processes are impacted by molecular interactions;
lastly, Section 5 provides outlook and concluding remarks.
2. Brief Reminder of OSC Operation
Over the past couple of decades, there has been contin-
uous work to better understand the processes that occur in
OSCs,[7,16–20] which include: optical absorption, exciton forma-
tion, exciton migration, exciton dissociation, charge transport,
and charge collection. Importantly, charge recombination,
which negatively impacts performance through annihilation of
Mahesh Kumar Ravva
received his Master of
Science degree in Chemical
Sciences from Pondicherry
University, Puducherry,
in 2008 and his Ph.D.
degree in Chemistry from
the University of Madras,
Chennai, in 2013 from
the group of Venkatesan
Subramanian. After a post-
doctoral appointment at
the Georgia Institute of Technology, he is now working
as a postdoctoral fellow at King Abdullah University of
Science and Technology in the Solar and Photovoltaics
Engineering Research Center in the group of Jean-Luc
Brédas. His current research work mainly focuses on
understanding the nature of various non-covalent interac-
tions in functional materials using modern computational
chemistry methodologies.
Sean M. Ryno received his
Bachelor of Science degree
in Chemistry from the
University of North Georgia,
Dahlonega, Georgia in
2010. He then joined the
group of Jean-Luc Brédas
at the Georgia Institute
of Technology where he
received his Ph.D. in
Computational Chemistry in
2015. Currently, he is a post-
doctoral fellow at King Abdullah University of Science and
Technology in the Solar and Photovoltaics Engineering
Research Center in the group of Jean-Luc Brédas. His
current research interests are focused on understanding
the energetics at donor-acceptor interfaces in organic
photovoltaics.
Haoyuan Li received a dual
BSc degree in chemistry
and biotechnology from
Jilin University in 2010. He
then joined the group of
Yong Qiu in the Department
of Chemistry at Tsinghua
University, where he received
his Ph.D. in Chemistry
in 2015. He is currently
a postdoctoral fellow at
King Abdullah University of
Science and Technology in the group of Jean-Luc Brédas.
His research interests focus on understanding the physics
of organic electronics devices.
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Figure 1. Approximate number of publications relating to organic solar
cells and fullerenes. Citation report for “organic solar cells & fullerenes”
or “organic photovoltaics & fullerenes” in the publication title or topic.
Retrieved from Web of Science on June, 8, 2016.

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an electron-hole pair, may also occur after exciton formation or
dissociation. To provide a framework for later discussion, and
to familiarize readers with terminology, we now briefly describe
each of these processes.
The first process to occur in the
π
-conjugated materials that
composes the OSC active layer is the photogeneration of a Cou-
lombically bound electron-hole pair, referred to as an exciton.
In order to absorb photons over a significant portion of the
solar spectrum, low optical-gap materials have been developed
that efficiently absorb photons in the near-IR and often over
more than a 1 eV range.[8] Once an electron has been excited,
it vibrationally relaxes down to the bottom of the lowest excited-
state potential energy surface and an exciton is formed; the
energy associated with this excitation (most generally from a
singlet electronic ground state, S0, to the first singlet excited
state, S1) corresponds to the optical gap, Eopt (Figure 2); due to
this vibrational relaxation of the excited electron, excess energy
from high-energy incident photons is lost, which acts to reduce
the open-circuit voltage, VOC, of OSC devices.[21,22]
In the case of bilayer architectures, the exciton, a neutral spe-
cies, then randomly diffuses through the active layer, via a series
of energy transfer processes, until it reaches the electron donor-
electron acceptor interface.[23] During the time of this migration
process, excitons may decay back to the ground state before they are
able to reach the electron donor-electron acceptor interface where
they can dissociate. This is the main reason for the introduction
of the BHJ architecture, the excitons being then formed near an
interface.[17,24–30] Exciton dissociation leads to the formation of
a charge-transfer (CT) state related to an electron transfer from
the electron donor component to the electron acceptor compo-
nent. As will be discussed in Section 4.3, the energy associated
with this CT state is intimately dependent on the local molecular
configurations (packing) at the donor-acceptor interface. The
CT state can then dissociate into a charge separated (CS) state,
where the hole and electron move away from one another after
having overcome their Coulombic attraction.[31] The charge car-
riers migrate within the active layer of the devices to their respec-
tive electrodes for collection. The rate at which holes and elec-
tron migrate through their respective medium is determined by
the electronic couplings between relevant molecular orbitals on
adjacent molecular sites within the donor and acceptor phases
(the highest-occupied molecular orbital (HOMO) for holes and
lowest-occupied molecular orbital (LUMO) for electrons).[9]
During their migration to the electrodes, a hole and an electron
may find one another and reform a CT state at a donor-acceptor
interface; from there, they can either again separate into charge
carriers or recombine via non-geminate charge recombination.
3. Electron Donor and Electron Acceptor Materials
3.1. Small-Molecule and Polymer Electron Donor Materials
Small molecules, oligomers, and polymers are all used as elec-
tron donating materials in OSCs. Although these materials
belong to different classes and cover various length scales, the
basic electrical and optical properties are similar. An optimal
electron donating material should possess strong, broad absorp-
tion across the solar spectrum, large hole mobility for efficient
and fast charge transport, energy levels that align well and
couple strongly with the energy levels of the electron acceptor
for efficient charge transfer, and appropriate miscibility with
the electron acceptor to form the desired nanoscale morpholo-
gies. Various design principles, such as tuning of the energy
levels via chemical modification (for instance, via fluorine sub-
stitution) and incorporation of alternating electron-rich and
electron-poor moieties, have been established to develop new
donors with good performance in OSC devices (Figure 3).[32–34]
Poly-3-hexylthiophene (P3HT) and other homopolymers have
received considerable attention, in particular in the early stages
of development. In the case of P3HT, specific synthetic proce-
dures can lead the 3-hexylthiophene monomers to polymerize
in a regioregular fashion (only head-to-tail linkages, RR-P3HT)
rather than in a regiorandom fashion (head-to-tail, head-to-
head, and tail-to-tail linkages, RRa-P3HT).[35,36] The regularity
in RR-P3HT acts to reduce the steric interactions among alkyl
side-chains and induces better planarity of the backbone and a
lower optical gap than in RRa-P3HT.
Incorporating alternating electron-rich (“donor”) and electron-
poor (“acceptor”) moieties is currently one of the prominent
strategies to develop low optical-gap polymers and small mole-
cules.[37–40] Using such an approach, a myriad of low optical-gap
donor-acceptor co-polymers have been synthesized over the past
three decades. Examples of such materials include copolymers
based on benzothiadiazole (BT), pyrrolo[3,4-c]pyrrole-1,4-dione
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Figure 2. Illustration of the electronic states relevant in the opera-
tion of organic solar cells. S0 is the singlet electronic ground state of
the absorbing material (ususally the electron-donor component in the
case of fullerene-based OSCs); S1 is the first singlet excited state of the
absorbing material; and CT1 is the lowest energy charge-transfer state
at the donor-acceptor interface. IE and EA denote the ionization energy
and electron affinity, respectively. Eopt is the optical gap, considering the
S1-S0 energy difference; Efund is the fundamental gap, defined as
IE-EA. The exciton binding energy, EB, is defined as the energy difference
between S1 and Efund.

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(DPP), or benzo[1,2-b;4,5-b′]dithiophene (BDT), to name just a
few. The backbone along the copolymer chains is often twisted to
various extents due to steric interactions between adjacent rings
or side-chains. Since such twists can limit electronic delocaliza-
tion and widen the optical gap, strategies have also been devel-
oped to planarize the backbone, which include: (i) introducing
aromatic or vinylene spacers between the donor and acceptor
subunits;[41–43] (ii) choosing donor and acceptor units without
ortho-hydrogen atoms to prevent C-H···H-C steric interactions;
(iii) fusing donor and acceptor units to increase the rigidity of
the backbone (e.g., ladder polymers);[44] or (iv) fluorination of the
polymer backbone. Each of these strategies allows control of some
of the (intermolecular) interactions along the polymer chains.
To improve solubility, the
π
-conjugated polymer chains are
often functionalized with alkyl (or alkoxy) side-chains, either
linear or branched.[45] Such functionalization strongly impacts the
manner in which the polymer chains pack, often limiting their
crystallinity. For instance, in the case of PBDTTPD, composed
of alternating thieno[3,4-b]thiophene-pyrrole-4,6-dione and ben-
zodithiophene units, crystallite formation and relative backbone
orientations very much depend on the pattern of the alkyl side-
chains along the backbone.[46] Thus, choosing alkyl side-chains of
appropriate nature and length (side-chain engineering) is crucial
to the design of efficient electron donor materials. The current
champion polymer donor material, poly[(5,6-difluoro-2,1,3-benzo-
thiadiazol-4,7-diyl)] (PffBT4T), leads to devices with nearly 12%
efficiency when functionalized with suitable side-chains.[1,47]
While our discussion has focused so far on polymer donor
materials used in solution-processable polymer:fullerene BHJ
solar cells, small-molecule systems are emerging as a competi-
tive alternative to their polymer counterparts, as highlighted
in the Introduction. Compared to polymers, small molecules
have several potential advantages that make them attractive
materials, such as more versatile molecular structure, simpler
strategies for controlling energy levels, and more reproducible
synthetic procedures leading to materials of higher purity.
3.2. Electron Acceptor Materials
3.2.1. Fullerenes
The discovery and characterization of fullerene-C60 by Kroto
et al. has had a major impact on the chemistry and physics
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Figure 3. Chemical structures of representative electron donor polymers and small molecules. Structures: poly(3-hexyl-thiophene) (P3HT), Ref. [35];
poly(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene (MEH-PPV), Ref. [252]; poly[[2,6′-4,8-di(5-ethylhexylthienyl)benzo[1,2-b;3,3-b] dithiophene]
[3-fluoro-2[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl]] (PTB7-Th), Ref. [88]; poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3
′′′
-di(2-
nonyltridecyl)-2,2
′
;5
′
,2
′′
;5
′′
,2
′′′
-quaterthiophen-5,5
′′′
-diyl)] (PffBT4T-C9C13), Ref. [1]; 5,5′-bis {(4-(7-hexylthiophen-2-yl)thiophen-2-yl)-[1,2,5]thiadiazolo[3,4-c]
pyridine}-3,3′-di-2-ethylhexylsilylene-2,2′-bithiophene (DTS(PTTh2)2), Ref. [5]; poly(di(2-ethylhexyloxy)benzo[1,2-b:4,5-b′]dithiophene-co-octylthieno[3,4-
c]pyrrole-4,6-dione) (PBDTTPD), Ref. [46]; 2,2′-((5Z,5′Z)-5,5′-((3,3′′′′,3′′′′′,3′′′′′′,4′,4′′-hexa-octyl-[2,2′:5′,2′′:5′′,2′′′:5′′′,2′′′′:5′′′′,2′′′′′:5′′′′′,2′′′′′′-
sepithiophene]-5,5′′′′′′-diyl)bis(methanylylidene))bis(3-ethyl-4-oxothiazolidine-5,2-diylidene))dimalononitrile (DRCN7T), Ref. [253].

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of electron transport materials.[48,49] Following this discovery,
Heeger and co-workers demonstrated photo-induced electron
transfer from the excited state of poly-paraphenylene vinylene
to fullerene,[16] highlighting the electron accepting capabili-
ties of fullerene and their potential for exploitation in organic
photo voltaics devices. Among the fullerene family, C60 and
C70 and their derivatives have been extensively studied and
widely used as electron accepting materials in OSCs (Figure 4).
By blending C60 or the phenyl-C61-butyric acid methyl ester
(PC61BM) derivative with a conjugated polymer, Heeger and co-
workers and Friend and co-workers showed that efficient power
conversion and charge collection were possible in OSCs.[28,29]
The high electron affinity of fullerenes, which assists in effi-
cient photo-generation, and their three-dimensional structure,
which ensures packing[50–52] that allows for multiple pathways
and entropic gain for exciton dissociation[19,53,54] and charge
transport,[55] are among their attractive properties for OSCs.
The best performing devices currently incorporate a fullerene
as the electron acceptor.[1]
The low solubility of C60 has limited its application in BHJ
solar cells. The chemical functionalization of the fullerene cage
has been extensively used to improve solubility in many organic
solvents.[56] Since the functionalization destabilizes the LUMO
levels (due to partial loss of conjugation), higher open-circuit
voltages can be achieved than with bare C60; also, functionaliza-
tion alters the electron density in the fullerene cage and lowers
the molecular symmetry, which induces a dipole moment in the
molecule and enhances optical absorption.[57,58] Understanding
the impact functionalization has on the interactions among
fullerenes and with other molecules, their solubility, and their
aggregation properties, is key to determining the factors that
influence packing and morphology and to achieving higher
power conversion efficiencies.[59]
Of the several fullerene derivatives that have been synthe-
sized and evaluated,[48,56,60–67] PC61BM has been the most widely
exploited as an electron accepting material in OSCs.[56,60] C70
and its derivatives such as PC71BM, in spite of their high cost,
have also been used in order to benefit from their higher optical
absorption characteristics.[65] However, the elliptical structure of
the C70 cage leads to the formation of several regioisomers in
PC71BM, which increases disorder. A series of fullerene mono-
and multi-adducts have also been synthesized with the goal
of decreasing the electron affinity (and improving VOC).[68–70]
Among these, the indene-C60 monoadduct (ICMA) and indene-
C60 bisadduct (ICBA) have received considerable attention, with
the electron affinity evolving from 3.91 eV in PC61BM to 3.86 eV
and 3.74 eV in ICMA and ICBA, respectively.[68] As with C70, C60
bisadduct synthesis often results in several regioisomers whose
electronic properties can vary strongly from one isomer to the
next. For example, Zhang et al.[71] have shown that the electron
affinities estimated via cyclic voltammetry for different regioi-
somers of N-methyl-phenyl-C61-propyl-2-fullero-pyrrolidine, can
differ by over 0.1 eV. Xiao et al.[72] have also shown that OSC
performance can improve by more than one percentage point
by use of select regioisomers. As such, efforts are underway
to devise regioselective synthetic pathways.[71–76] Martín and
co-workers have developed a number of fullerene-functionalized
polymers and small molecules that have resulted in VOC greater
than 0.6 V when blended with P3HT, which is larger than the
0.5 V in PC61BM systems with the same donor.[77] Increasing
the level of functionalization causes additional reductions in
electron affinity, but also disruption of electron delocalization
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Figure 4. Chemical structures of C60, C70, and representative derivatives. Structures: C60, C70, Ref. [49]; phenyl-C61-butyric acid methyl ester (PC61BM),
Ref. [254]; diphenylmethanofullerene (DPM12), Ref. [77]; indene-C60 monoadduct (ICMA), indene-C60 bisadduct (ICBA), Ref. [68]; phenyl-C71-butyric
acid methyl ester (PC71BM), Ref. [65].

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and packing in the solid state, which can result in poor electron
transport.[78–80] Recently, the static disorder (time-independent
variations in molecular positions) and dynamic disorder (time-
dependent variations due to electron-vibration coupling) were
investigated in C60, C70, PC61BM, and PC71BM, using a com-
bined quantum mechanics and molecular dynamics approach.[81]
Tummala et al. found that, in the amorphous phase, the static
disorder increases by some 40% in going from C60 to C70 or
PC61BM to PC71BM and is more than doubled for the PCBM
derivatives vs the unsubstituted structures; the dynamic disorder
also adds a significant contribution in all instances. The resulting
distribution in electron affinities has negative impact as it leads
to charge carrier relaxation, energy loss, and reduced VOC.
3.2.2. Non-Fullerene Acceptors
Since fullerene acceptors generally suffer from weak absorp-
tion in the visible, limited opportunity of optical gap tuning,
aggregation during post-fabrication, increased disorder upon
functionalization of the fullerene cage, and, in the case of
C70 and its derivatives, cost prohibitive implementation,
non-fullerene n-type materials are garnering increased atten-
tion (Figure 5).[82,83] Both small-molecule and polymer non-
fullerene acceptors have been reported, with the choice of
appropriate material depending on the optical gap of the elec-
tron donor material.[82] For example, a weaker electron acceptor,
compared to a fullerene, can perform well when paired with a
wide optical gap polymer such as P3HT due to reduced electron
affinity offset. The opposite also holds true, wherein a low gap
donor must be paired with a very strong electron acceptor to
promote electron transfer. Several types of non-fullerene accep-
tors have been synthesized and studied, among which perylene
diimide (PDI) and naphthalene diimide (NDI) oligomers and
polymers have received the most attention.[84–87] PDI-based
monomers have been shown to exhibit wide absorption bands,
electron mobilities up to 1 cm2 V−1 s−1, and electron affinities
around 4 eV, all appropriate materials properties.[84] The large
planar
π
-conjugated core has the ability to form strong
π
–
π
interactions and leads to micrometer-sized crystallites in the
solid state. While these large crystallites allow for efficient
charge transport, the drawback is that they limit the donor-
acceptor interfacial area and act as trapping sites, limiting
exciton diffusion and long-range charge transport.
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Figure 5. Chemical structures of NDI and PDI small molecules and polymers and representative small-molecule non-fullerene acceptors. (Inset)
Substitution positions on PDI. Structures: naphthalene diimide (NDI), perylene diimide (PDI), Ref. [96]; poly([naphthalene-1,4,5,8-bis(dicarboximide)-
2,6-diyl]-alt-5,5′-(2,2′-bithiophene)) (PNDI-T2), poly([3,4,9,10-perylenedicarboximide-(1,7&1,6)-diyl]-alt-5,5′-(2,2′-bithiophene)) (PPDI-T2), Ref. [87];
poly([naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5′-(2-selenophene)) (PNDIS), Ref. [255]; indacenodithiophene-benzothiadiazole-3-ethyl-
rhodanine (IDTBR), Ref. [108]; perfluoropentacene (PFP), Ref. [94].

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There have been several strategies to minimize PDI aggre-
gation without compromising electron transport efficiency,
including the introduction of specific alkyl chains on the nitro-
gens (imide functionalization), functionalization at the ortho
and bay positions, linking two PDI units through NN bonds,
and the development of PDI oligomers. Via functionalization at
the bay position, Nuckolls and co-workers have demonstrated
BHJ OSCs with PCEs of 8.3% using poly[4,8-bis(5-(2-ethyl-
hexyl)thiophen-2-yl)benzo[1,2-b;4,5-b’]dithiophene-2,6-diyl-alt-
(4-(2-ethylhexyl)-3-fluorothieno[3,4-b]thiophene)-2-carboxylate-
2,6-diyl] (PTB7-Th) as the electron donor;[88] in this instance,
functionalization results in a twisted conformation that reduces
crystallinity and increases processability of the PDI oligomers.
Excitons generated in both donor and acceptor are found to
contribute to the photocurrent through efficient electron and
hole transfer at the donor-acceptor interface, mediated by
strong interactions between PDI and the electron donor due
to the twisted PDI conformation. Another way of introducing
twists along the PDI oligomer relies on inserting aromatic
rings between the PDIs.[89] For example, incorporating a thie-
nylene ring between two PDI units has been shown to produce
domain sizes of ≈30 nm while the PDI monomer yields crystal-
line domains on the order of 100 nm.
Apart from PDI-based oligomers, several other non-fullerene
acceptors have been developed.[90–93] Examples include: fluori-
nated pentacene derivatives,[94] arylene diimide small mol-
ecules,[95,96] arylene diimide polymers,[87,97] benzothiadiazole-
based small-molecules and copolymers,[98–106] rhodanine small
molecules,[82,107,108] and electron-poor fused aromatic ring spe-
cies.[109–114] Polyera have developed Polyera ActivInk N2200,[87]
a NDI-based polymer, that has resulted in all-polymer devices
with PCEs up to 8.3% using the J51 donor, a benzodithiophene
fluorinated-benzotriazole copolymer.[115,116] The indacenodith-
iophene-benzothiadiazole-3-ethyl-rhodanine (IDTBR) acceptors
of McCulloch and co-workers have achieved PCEs up to 6.4%
using P3HT as an electron donor;[108] here, the performance of
this system has been attributed to the complementary absorp-
tion profiles of IDTBR and P3HT that allow for photogenerated
charge carriers in either acceptor or donor. Using P3HT as a
donor and either a triphenylamine-based small molecule or
benzothiadiazole copolymer, Lin et al.[117] and Mori et al.,[103]
respectively, have demonstrated VOC values up to 1.26 V by
engineering materials with low electron affinity.
3.3. Molecular Interactions Between Fullerenes and Small
Molecules/Polymers
In this Section, we provide a first discussion of the nature of
the molecular interactions between fullerenes and electron
donors. The active layer of solution-processed OSCs is formed
by dissolving the electron donor and acceptor components and
casting the mixture into a film. As the solvent evaporates, the
electron acceptor and donor materials form a blend with par-
tial phase separation distributed throughout the film. The per-
formance of OSCs largely depends on the resulting nano-scale
morphology since the morphology directly impacts the electron
transfer rates,[118] charge separation,[119,120] charge recombina-
tion,[118,121] and charge transport pathways. While outside the
scope of the current Review, it is important to note that the mes-
oscale morphological details also play a key role in determining
the charge transport properties and performance of OSC
devices.[122,123] Aspects of mesoscale order such as the impor-
tance of domain size,[124–126] percolation pathways,[127–129] and
donor-acceptor phase segregation[130–132] have been discussed
elsewhere and we direct interested readers to these works.
Exploration and characterization of the purity and size of
the phase-separated domains have received significant atten-
tion.[1,127,132–138] Recent experimental investigations have
attempted to determine the energy landscape in the mixed and
pure phases. For instance, McGehee and co-workers have dem-
onstrated energy-level shifts in the polymer donor due to struc-
tural disorder and intermolecular interactions between polymer
chains and fullerenes using a combination of cyclic voltam-
metry and ultraviolet photoelectron spectroscopy; these authors
have underlined the implications of these shifts on OSC effi-
ciency.[139] Since it has been found that there is little to no
charge transfer between polymer and fullerene in the ground
state, the energy level shifts observed when mixing the two
components can be attributed primarily to intermolecular van
der Waals interactions.[140] On the other hand, the efficiency of
photo-induced charge transfer between polymer and fullerene
depends not only on the overall bulk morphology, but also on
whether the polymer can accommodate the fullerene in close
proximity to its backbone.[141,142]
As mentioned earlier, the solubility and processibility of
the conjugated polymers from organic solvents is generally
improved by attaching alkyl side-chains. It must be borne in
mind that these side-chains can significantly alter the optical
gaps,
π
–
π
stacking interactions, miscibility with fullerenes, and
thin-film order. For instance, in the case of poly-benzodithio-
phene-thienothiophene (PTB)-based polymers (alternating ben-
zodithiophene (BDT) and thienothiophene (TT) units), shorter
π
–
π
stacking distances have been observed when the BDT
units are functionalized by two linear chains rather than two
branched side-chains. Branched side-chains are also found to
impact the thin-film structural ordering and the preferential
orientation of the polymer backbones relative to the substrate,
for example, in the case of poly-benzo[1,2-b:4,5-b’]dithiophene–
thieno[3,4-c]pyrrole-4,6-dione (PBDTTDP).[47]
A recent study by Graham et al. has highlighted that a priori
minor changes in the structure and position of the alkyl side-
chains of PBDTTPD can significantly affect the efficiency of
the solar cells based on these polymers. For instance, when the
thieno[3,4-c]pyrrole-4,6-dione (TPD) moieties carry (sterically
accessible) linear alkyl side-chains and the benzodithiophene
(BDT) moieties (more sterically hindered) branched side-chains,
which implies that the PC61BM molecules are expected to locate
preferentially around the TPD units of the polymer chain, the
resulting system yields power conversion efficiencies up to ca.
8% and open-circuit voltages up to 1 V. On the other hand, for
the same conjugated polymer backbone, much lower power
efficiencies are observed if it is TPD that carries branched side-
chains and BDT linear side-chains.[143] That it is better for the
fullerenes to bind preferentially around the electron-rich moiety
of the polymer backbone has been observed in a number of
other instances. This trend is consistent with the transient spec-
troscopy data of Laquai and co-workers, which indicate that a
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PBDTTPD polymer with branched side-chains on the electron-
rich moieties and linear side-chain on the electron-poor moie-
ties exhibits lower geminate and non-geminate charge-carrier
recombination losses compared to the corresponding polymer
with only linear side-chains.[144] In contrast, McCulloch and
co-workers[145] have found that a copolymer consisting of thio-
phene flanked by an electron-poor 2,1,3-benzothiadiazole-
5,6-dicarboxylic imide (BTI) segment carrying branched alkyl
chains and an electron-rich benzo[1,2-b:3,4-b:5,6-d]trithiophene
(BTT) segment leads to high power conversion efficiencies, up
to 8.3%. In this case, it can be expected, however, that the elec-
tron-poor moiety, due to its larger size, is still able to interact
with PCBM even when it carries branched side-chains. While
more work is clearly desirable to better understand the relation-
ship between the polymer-fullerene interactions, morphology,
and PCE, probing such weak interactions and intermolecular
arrangements between the polymer chains and the fullerenes
in BHJs at the molecular scale remains a very challenging
experimental proposition. Thus, the insights provided by com-
putational studies could be extremely useful.
In this context, Ravva et al. have recently used long-range
corrected density functional theory calculations to evaluate the
binding between a long PBDTTPD oligomer and C60. In the
absence of any side-chains along the backbone, the C60 mol-
ecules prefer to bind through face-on configurations, which
maximizes
π
–
π
interactions, and importantly, with little prefer-
ence as to a specific position along the backbone.[146] The calcu-
lated binding energies per C60 are substantial, on the order of
12–15 kcal/mol. Thus, an interesting implication of these results
in that eventually it is the polymer side-chains and the fullerene
functional groups that dictate the preferential locations of the
fullerene cages on top of the backbone. This conclusion is con-
firmed by the molecular dynamics simulations of Wang et al.[147]
These authors have provided a detailed description of the impact
that the nature and location of side-chains and functional groups
have on the polymer-fullerene packing. They find that in general
linear side-chains tend to extend away from the polymer back-
bone, while the bulkier branched side-chains tend to remain
closer to the backbone. Thus, moieties carrying linear chains will
have more room to accommodate fullerene molecules than those
with branched side-chains. Their simulations on PBDTTPD-
PC61BM confirm that the probability of finding PC61BM close to
the TPD [BDT] moiety increases [decreases] when the TPD units
carry branched side-chains compared to all linear side-chains.
4. Intermolecular Interactions and Processes
in OSCs
4.1. Polarization Energy
The fact that organic electronic materials consist of a collection
of non-bonded molecules or chain segments that interact via
weak intermolecular interactions, inherently leads to significant
structural disorder at room temperature; as a result, charge car-
riers are either strongly localized or weakly delocalized over just
a few molecules or chain repeat units.[57,148–152] Intermolecular
interactions also act to stabilize (photogenerated or injected)
charges in the bulk material as compared to the gas phase, with
the amount of stabilization directly related to the nature of the
environment. In common organic electronic materials, this sta-
bilization causes a reduction of the ionization energy (IE) and
an increase of the electron affinity (EA) (Figure 6) on the order
of an eV (Table 1);[153,154] it corresponds to the electronic polari-
zation energy, defined by Lyons[150,155] as:
PI
EI
E
=−
+− −solidstate gasphase (1)
PE
AE
A
=−
−− −solidstate gasphase (2)
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Figure 6. Energy level diagram in organic materials as the system evolves from the gas phase to the solid state. IE and EA represent the ionization
energy and electron affinity, respectively. P± is the electronic polarization energy, w is the contribution from band dispersion, and d is the surface dipole
that accounts for the orientation dependence of the IE and EA. Adapted with permission.[156] Copyright 2015, American Physical Society.

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Here, the polarization energy due to a positive [negative]
charge, P+[P−], is the difference between the solid-state and gas-
phase ionization energies [electron affinities]. Note that the IE
[EA] of a specific donor [acceptor] site is referred to, in physics
terminology, as the site energy. In what follows, we use the
absolute value of the polarization energy as it is always stabi-
lizing. As highlighted by Yoshida et al.,[156] effects from band
dispersion and surface dipole must also be accounted for to
accurately describe the polarization energy in organic electronic
materials. Lattice and nuclear relaxations that occur at longer
time scales than the electronic polarization also contribute
some amount to the electronic polarization energy, generally
estimated to be on the order of 0.1 eV.[150]
Polarization energy impacts a number of processes in
organic electronic devices. Of focus here is the role of polariza-
tion on the charge separation and charge transport processes in
OSCs. In the following discussion, we illustrate that even small
changes to the electrostatic environment in the bulk donor and
acceptor materials and at the donor-acceptor interface can cause
changes in the polarization energy of several tenths of an eV.
4.1.1. Methods to Calculate Polarization Energy
Several methodologies have been developed for the calculation
of the electronic polarization energy in organic molecular crys-
tals. The methods range from simple isotropic functions that
rely on experimentally obtainable data, to electrostatic models
where each atom in the crystal is represented by multipole
and polarizability matrices, and to hybrid quantum-mechan-
ical/molecular-mechanical models that combine a quantum
mechanical treatment with simple electrostatic interactions.
In the Sections to follow, we briefly cover the most common
models, taking molecular crystals as representative examples
(we point the readers interested in more thorough discussions
to the recent review by Beljonne and co-workers).[157]
Cavity in a dielectric medium: The simplest model to deter-
mine the polarization energy of a material is based on clas-
sical electrostatic theory, i.e., the Born model,[158] where the
polarization energy relates to the stabilization of a point charge
in a spherical cavity embedded in an isotropic polarizable
medium:
/2 11/
2
Pe
ρε
()
()
=−
(3)
Here,
ρ
denotes the radius of the cavity and
ε
, the dielectric
constant. This model was highlighted by Sato et al.,[153] who
also proposed a modified version since
ρ
is generally difficult
to determine:
8.25 /
24/3
PeZV
α
()
= (4)
Here, in the context of a molecular crystal,
α
represents the
average molecular polarizability; Z, the number of molecules
per unit cell; and V, the volume of the unit cell. Note that
this model assumes an isotropic polarizability of the molec-
ular systems. However, this is often not the case in organic
π
-conjugated systems as they are often significantly more
polarizable along one axis due to their conjugated, elongated
nature.[159] The unsubstituted fullerenes represent a notable
exception since they have isotropic or nearly isotropic linear
polarizability due to symmetry.[160,161]
Electrostatic models: Of the models that explicitly include
terms for static (i.e., permanent multipole) and dynamic (i.e.,
induced dipole) electrostatic interactions, microelectrostatic
models offer the flexibility to be as simple or complex as is
desirable. For these models, the polarization energy is calcu-
lated by determining the static and dynamic intermolecular
interactions in the presence and absence of an excess charge
(i.e., the response of the system to an electric field) and rep-
resents the difference in energy between these two pictures.
Here, the permanent multipole and linear polarizability tensors
are distributed across an arbitrary number of points representa-
tive of the molecular system.
Early models[162] treated the molecules in a system as single
polarizable points and calculated the interaction energy between
an ion and the dipoles that it induces; the induced dipoles were
not considered to interact with each other, resulting in, some-
times, poor agreement with experimental results. As micro-
electrostatic models became more complex, the induced-dipole
interactions were treated self-consistently,[150,163] and molecules
were represented by more than one point,[164] increasing agree-
ment with experiment as the three-dimensional shape of the
molecules is better reproduced.
More recently, two electrostatics models have been increas-
ingly exploited in the literature: (i) the microelectrostatic model
of Heremans and co-workers[10,165–167] and (ii) the AMOEBA
force field-based model of Brédas and co-workers.[168] These
models, while conceptually similar, differ in how they describe
the molecular multipoles and the molecular polarizabilities.
The Heremans microelectrostatic model divides the molecular
quadrupole across a number of submolecular points such that
each point is equivalent and recreates the molecular quadru-
pole in an additive fashion; the linear polarizability tensor is
similarly divided across submolecular points and treated in
an additive fashion. The AMOEBA-based model uses an atom-
centered approach where each atom has charge, dipole, and
quadrupole tensors from a distributed multipole analysis that
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Table 1. Experimental polarization energies due to a positive (P+) or
negative (P−) charge and polarization asymmetry for common organic
electronic materials. All units in eV.
(eV) |P+| |P−| |P+ − P−|
Benzenea1.6 – –
Naphthaleneb1.72 1.10 0.62
Anthraceneb1.65 1.09 0.56
Tetracenec,d 1.63 0.92 0.71
Pentaceneb1.63 1.12 0.55
Fullerene (C60)e,f 1.1–1.4 1.4–1.6 0.0–0.5
Perylenea1.7 – –
Rubrenea1.1 – –
Tetracyanoquinodimethane (TCNQ)a2.1 – –
Tetracyanonaphthoquinodimethane (TNAP)a2.5 – –
aRef. [153], bRef. [154], cRef. [256], dRef. [257], eRef. [258], fRef. [259].

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recreates the molecular electrostatic potential; the Thole model
is used for the polarizability with atom-centered isotropic polar-
izabilities recreating the anisotropic molecular polarizability.
Typically, these differing treatments result in only quantitative
differences, although these actually depend on how the molec-
ular multipoles and polarizabilities are partitioned.
Charge redistribution models: The charge redistribution
models are based on a methodology originally proposed by
Stone,[169,170] wherein molecules are divided into sub-regions
that are individually polarizable. This model extends beyond the
microelectrostatic models by allowing charges to redistribute in
response to the electric field. Thus, while the overall charge of
a given molecule remains unchanged, the net partial charges
and multipoles at the various sites within a molecule evolve in
response to the environment. Here, the charge flow is in the
direction of the bonds; thus, polarization of the systems per-
pendicular to the bonds is not represented well.
There are two prominent charge redistribution models:
(i) the model of Tsiper and Soos;[171,172] and (ii) the charge
response kernel of Morita and Kato.[173–176] While very similar,
these two models differ in how they treat polarization perpen-
dicular to the direction of the bonds, which is poorly accounted
for by the charge flow. In the former model, this is accom-
plished through assigning atomic polarizabilities, while in the
latter polarizable auxiliary sites are used to capture this effect.
Quantum mechanical models: There have been a number of
quantum mechanical approaches proposed for the evaluation of
polarization energy.[11,177–183] These methodologies range from
hybrid quantum-mechanical/molecular-mechanical (QM/MM)
treatments that represent the bulk of the system as a polar-
izable field of point charges and the area of interest (the
molecular ion) quantum mechanically, to constrained density
functional theory (CDFT) methodologies that restrict a charge
to a predefined region.
Given the wide range of models, we briefly focus here on
just two: on one hand, the hybrid QM/MM model of Norton
et al.[177] and, on the other hand, the fully quantum-mechan-
ical treatment of Castet et al.[182] that restricts charges to indi-
vidual molecules and calculates, self-consistently, the response
of each molecular system in the bulk to the presence of an
excess charge. These two approaches provide good examples
of the different approaches to solving the electronic polariza-
tion problem. The hybrid QM/MM model has the advantage
of being computationally inexpensive as only the charged spe-
cies is treated at the QM level (typically this is done at the DFT
level) while the bulk is treated at the MM level via force fields
(e.g., UFF).[184] Within this model, the bulk is explicitly treated
as a field of polarizable point charges that react to the presence
of the QM region and that in turn influence the MM region;
thus, this requires a self-consistent treatment. The downside
to such an approach is that the electrostatic potentials of non-
polar molecules is not accurately reproduced, leading to qualita-
tive errors in higher-order multipole (i.e., greater than dipole)
interactions with the charged QM region. The fully quantum
mechanical valence bond Hartree-Fock (VBHF) model of Castet
et al.[182] surmounts this deficiency by treating every molecule
in the system quantum mechanically. To overcome the compu-
tational cost that comes with such a treatment, each molecule is
treated at the semiempirical level (using the neglect of diatomic
differential overlap, NDDO, Hamiltonian) and the charge of
each molecule is predefined. In this manner, the energy of
the system is solved in a self-consistent fashion where each
molecule feels the electric field generated by all surrounding
molecules. Similar methodologies that utilize constrained
density functional theory to provide a better description of the
molecular polarizability have also been used to great success.[183]
4.1.2. Influence of Intermolecular Interactions on
Polarization Energy
Since the seminal experimental work of Sato et al.,[153] the polar-
ization energies of bulk organic
π
-conjugated molecular mate-
rials had largely assumed to be similar, approximately 1.7 eV.
However, as work continued to better describe this phenom-
enon, it became increasingly clear that this is not necessarily
the case. The work of Koch and co-workers[185–187] has clearly
demonstrated that: (i) the molecular orientation has a pro-
found impact on the ionization energy, with the IE of penta-
cene varying by some 0.55 eV (Figure 7); (ii) by changing the
sign of molecular quadrupole components, e.g., via perfluori-
nation, the IE of a material such as pentacene can be shifted
by nearly 2 eV.[186] Indeed, different molecular orientations or
the sign of molecular quadrupoles impacts the molecular inter-
actions significantly. To better understand how the local elec-
trostatic environment determines the ionization energies of
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Figure 7. Experimental ultraviolet photoemission spectra of a monolayer
of pentacene lying face-on to a Au(111) surface (red) and a thin film of
pentacene standing edge-on to a silicon oxide surface (green). The energy
reference is the vacuum level directly above the sample. The Fermi level,
EF, is noted for the Au substrate. Reproduced with permission.[187] Copy-
right 2010, American Chemical Society.

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organic electronic materials, and thus the polarization energy,
we first discuss bulk materials before moving on to organic-
vacuum interfaces and organic-organic interfaces.
As stated above, electronic polarization in many organic
π
-conjugated molecular crystals is approximately 1.7 eV.
However, even in materials that are structurally similar the
electrostatic environment can be substantially different, due
to packing variations[188] or the amount of structural disorder
in the material.[57] Ryno et al. have investigated a series of
oligoacenes and their 6,13-bis(2-(tri-isopropylsilyl)ethynyl
(TIPS) substituted derivatives. Although pentacene and TIPS-
pentacene are electronically similar (i.e., the molecular quad-
rupoles and linear polarizabilities are similar), the manner
in which they pack is significantly different. Pentacene packs
in a herringbone motif and TIPS-pentacene in a brickwork
motif, which results in markedly different intermolecular
interactions; specifically, the quadrupole-quadrupole interac-
tions are stabilizing in pentacene, while they are destabilizing
in TIPS-pentacene. As a result, there occurs a large reduc-
tion in the calculated polarization energy of TIPS-pentacene
(P+, 0.59 eV; P−, 0.69 eV) compared to pentacene (P+, 1.02 eV;
P−, 0.79 eV). Additionally, the polarization asymmetry (i.e.,
the difference between P+ and P−) decreases from 0.23 eV
in pentacene to 0.10 eV in TIPS-pentacene. In a subsequent
study, Ryno et al. investigated the effect of packing density
for a given packing motif (herringbone), comparing tetracene
and rubrene; they observed strong dependence of P+ on the
intralayer (a/b-plane) packing density and an order-of-magni-
tude smaller impact on polarization energy for the interlayer
(c-axis) density.[189]
Even in the case of crystalline materials, defects can be pre-
sent in the form of grain boundaries between crystallites, which
act to impede charge transport. Verlaak and Heremans,[10]
through modeling four idealized types of grain boundaries in
pentacene showed that sites next to the boundaries can act as
either intrinsic barriers or trapping sites, depending on whether
the space between grains is filled or not, and inhibit efficient
charge transport. These authors showed that for both voids
and filled grain boundaries, charge-quadrupole interactions are
responsible for the resulting traps or barriers, with both span-
ning the range from 0.1 eV to 0.4 eV. We note that this investi-
gation used rigid crystals for the modeling of the grains; thus,
energetic disorder due to molecular motions comes as an addi-
tional contribution.
In a recent investigation on a series of fullerenes,
D’Avino et al.[57] find that although the polarization energies
of these systems are similar, each possesses differing amounts
of energetic disorder resulting in various polarization energy
distributions (Figure 8). For the fullerene derivatives investi-
gated, the polarization energy distributions centered around
0.9–1.0 eV; however, due to the different electrostatic inter-
actions present in C60 (rank 6) versus PC61BM or PC71BM
(dipolar), the standard deviations covered a large range: Crystal-
line C60 has a narrow distribution with
σ
= 0.005 eV; crystalline
PC61BM is more disordered due to the dipolar interactions with
σ
= 0.085 eV; and amorphous PC71BM is the most disordered
with
σ
= 0.160 eV. Thus, the variations in intermolecular inter-
actions cause the standard deviations of the polarization energy
distributions to change by a factor of ca. 30.
We now move our attention away from the bulk materials
to consider interfaces. Salaneck[190] reported that the ionization
energy at an anthracene surface was some 0.3 eV larger than in
the bulk. There have been numerous investigations that have
probed the organic-vacuum interface to determine the origin
of this reduced polarization energy at the surface compared
to the bulk. Tsiper and Soos[191] and Ryno et al.[189] discussed
the pentacene and tetracene surfaces, respectively. They report
that, for a hole, the polarization energy at the surface is reduced
by approximately 0.1 eV with respect to the bulk; interestingly,
this net P+ reduction at the surface is the result of two com-
peting contributions, a (larger) reduction in stabilization related
to induced interactions and an increased stabilization related
to static interactions. We note that, Gorczak et al.[192] have
reported that there is no change in the magnitude of the polari-
zation energy between the pentacene(001) surface and the bulk,
but describe similar trends for the induced and static interac-
tions as Ryno et al. Thus, while there is general consensus that
the intermolecular interactions at the surface differ from the
bulk, the net effect on the surface polarization is still a matter
of debate.
In OSCs, the processes of exciton dissociation and formation
of charge transfer states occur at organic-organic interfaces. As
has been underscored by a number of authors, the electrostatic
environment at these heterojunctions is clearly very different
from that of the surface.[119,123,165,166,192–197] In a recent investi-
gation, Ryno et al.[196] have shown that, in the case of the pen-
tacene(001)/C60 interface, each donor and acceptor site has in
fact a unique electrostatic environment. Polarization energies
vary not only from site-to-site but also change significantly as
a function of time, due to molecular vibrations and motions.
The polarization energies for pentacene molecules along the
interface range from about 0.9 eV to 1.1 eV, while the polariza-
tion energies for the interfacial C60 molecules range from less
than 0.75 eV to 0.85 eV. The reason for these distributions in
polarization is found in the variations in charge-quadrupole and
induced-dipole interactions amongst molecular sites (Figure 9).
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Figure 8. Probability distribution of polarization energies due to a nega-
tive charge carrier, P−. C60x has a maximum probability of 25 eV−1. Repro-
duced with permission.[57] Copyright 2016, Royal Society of Chemistry.

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This feature has also been highlighted by Linares et al.[166] for
the pentacene(01-1)/C60 interface; these authors pointed out that
not only does the magnitude of the induced dipoles change from
C60 to C60 molecule along the interface, but its directionality as
well. As will be discussed later, the nature of the intermolecular
interactions among organic molecules at the heterojunction
interface can be tuned to promote charge separation in OSCs.
Theoretical investigations focusing on polarization in poly-
meric materials are much more infrequent than for small
molecules. This limitation is primarily due to the difficulty of
describing such extended systems in a computationally fea-
sible manner. The recent works of Beljonne and co-workers
have attempted to tackle this problem using the poly(3-hexyl)-
thiophene (P3HT) and PC61BM or C60 model systems.[198]
They note overall smaller polarization energies but broader
distributions at the P3HT/PC61BM interface than in a P3HT/
C60 system. Similar to the investigation of D’Avino et al.,[57]
the authors highlight increased energetic disorder at PC61BM
interfaces than at C60 interfaces, due to the permanent dipole
present in PC61BM; such disorder will come into play when dis-
cussing charge separation. Each of the works discussed above
underlines that a proper account of the intermolecular inter-
actions is necessary to accurately account for the effects of the
electrostatic environment.
4.2. Delocalization
It is important to note that the majority of the works we have
discussed so far have been conducted in context of charge car-
riers being localized. This approximation allows for the use of
computationally inexpensive methodologies such as microelec-
trostatics, valence-bond/Hartree-Fock, or constrained-DFT to
describe molecular clusters. However, it has been pointed out
that delocalization effects can be of importance to describing
charge separation and the nature of the charge transfer
states.[121,199–204] Until recently, theoretical work devoted to
understanding delocalization in organic electronic mate-
rials had been limited. In the realm of small molecules, Yang
et al.[148] have used long-range corrected DFT to study the impact
of delocalization on the charge transfer (CT) state energy. Upon
increasing the number of pentacene molecules in a model pen-
tacene/C60 interface, there occurs a 0.3 eV reduction in the CT
state energy for face-on configurations, and a 0.8 eV reduction
for the edge-on configurations. These authors thus draw atten-
tion to the importance of delocalization while at the same time
highlighting the limited size of systems that can be investigated
using common electronic structure methodologies.
Beljonne and co-workers have proposed, in a number of
works,[57,121,195,198,202] electron and hole delocalization to be a
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Figure 9. Top: Induced-dipole moment vectors of C60 molecules at a pentacene/C60 heterojunction. Adapted with permission.[166] Copyright 2010,
American Chemical Society. Bottom: The z-component of the induced dipole on pentacene (left) and C60 (right) molecules at a pentacene(001)/C60
heterojunction. Adapted with permission.[196] Copyright 2016, American Chemical Society.

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key factor in the dissociation of the exciton at donor-acceptor
interfaces. In crystalline C60, they estimate electrons to delo-
calize over about 26 molecular sites, in agreement with some
experimental observations;[205] however, the delocalization of
an electron in functionalized PCBM is much more limited due
to energetic disorder related to the permanent dipole moment
(Figure 10). This comes in contrast to Cheung and Troisi[206]
who suggested delocalization of the electron across 40 mol-
ecules in PC61BM, although this result is probably affected
by the neglect of site energy differences among the fullerene
molecules. Moreover, both D’Avino[57] and Street[207] and their
co-workers point to decreasing delocalization with increasing
fullerene size, which suggests that reduced delocalization is
due to increasing energetic disorder in the larger fullerenes.
Savoie et al.[204] have taken a different approach and investi-
gated the effects of fullerene cluster size and dimensionality on
the delocalization of states within fullerene acceptor materials.
They obtain that efficient free charge carrier generation results
from good overlap of charge-separated states in the fullerene
acceptor and excited states in a polymer donor. Moreover, they
suggest that the ability of fullerenes to form extended three-
dimensional networks aids in the formation of such delocal-
ized states and eventually charge separation; on the other hand,
polymer non-fullerene acceptors, due to their bulky side-chains,
might inhibit the formation of these delocalized states.
Turning to delocalization in polymer donor materials,
Beljonne,[198] Burghardt,[199,200,208] and Thompson[207] and
their co-workers have investigated charge carrier delocaliza-
tion in derivatives of polythiophene mixed with PCBMs of
various sizes. For crystalline polymer domains, they each sug-
gest delocalization on the order of ten molecular units, with
delocalization being beneficial to charge separation. Tamura
and Burghardt[200] note a decreased delocalization of the hole
electronic states at the donor-acceptor interface than in the
pure donor material because of increased energetic disorder.
Additionally, Castet et al. have shown in the P3HT/PC61BM
system that high-lying CT states, wherein the hole is delocal-
ized over several polymer repeat units, become accessible due
to the polarization effects of the local environment;[195] these
authors suggest that these delocalized states may not only assist
in charge separation, but also act to reduce charge recombina-
tion.[121] Thus, these works highlight that the intermolecular
interactions dictate the amount of delocalization in these com-
plex systems, an effect that needs to be considered even though
its description is computationally challenging.
4.3. Charge Transfer States
When an exciton appears at the donor-fullerene interface, an
excited electron can jump from the electron donor to the fullerene
and form a charge transfer (CT) state, from which separation of
electron and hole generates free charge carriers. The discussion
in the previous Sections has illustrated that intermolecular inter-
actions greatly impact the ionization energies and electron affini-
ties of donors and acceptors, and that the interactions between
adjacent donors and acceptors can be modified by the orientation
of the respective moieties or their environment. The energy of
the lowest-lying CT state (CT1) can be approximated as:[209]
:
1DACoul
ECTIEEAE
DA
() ()
=− +
(5)
Here, IED is the ionization energy of the electron donor, EAA
is the electron affinity of the electron acceptor, and ECoul(D:A)
is the Coulombic attraction between the hole on the donor and
the electron on the acceptor (we recall that the first two terms
are positive quantities while the third one is negative). Thus,
the CT state energy is expected to be extremely sensitive to the
molecular-scale interactions between donor and acceptor.
Because of its strong dependence on molecular interactions,
the CT state energy can span a broad range by varying molecular
structure, packing, and degree of aggregation. Making again ref-
erence to the work of Yang et al. on model pentacene/C60 com-
plexes using long-range corrected density functional theory, it
was shown that there occurs an enhancement of hole delocaliza-
tion as a function of increasing the number of pentacene mol-
ecules in the complex, which acts to decrease the energy of the
CT state; this results from an increase in the distance between
the centers of the electron and hole distributions.[148] Further-
more, by rotating the pentacenes from a face-on orientation to an
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Figure 10. a) Distribution of the inverse participation ratio (IPR), which quantifies the number of molecules over which eigenstates are delocalized.
b) Thermal averages of the IPR at 300 K as a function of the charge carrier density, as calculated with Fermi-Dirac statistics. Straight lines are the
density-independent Boltzmann thermal averages. Dots represent the average values and error bars represent the standard deviations. C60x is crystal-
line C60, C61x is crystalline PC61BM, C61a is amorphous PC61BM, and C71a is amorphous PC71BM. Reproduced with permission.[57] Copyright 2016,
Royal Society of Chemistry.

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edge-on orientation, thereby changing the sign of the interacting
quadrupoles and increasing the distance between hole and elec-
tron, there is a nearly 0.5 eV increase in the CT state energy.[148]
The influence of intermolecular interactions extends past
simply determining the CT state energy, as they play a key role
in assessing the open-circuit voltage (VOC) and determining to
which sites the CT state moves along the donor-acceptor inter-
face during CT state energy transfer.[21,210] In the case of the
4,4’,4’’-tris(phenyl(m-tolyl)amino)triphenylamine:tris(2,4,6-tri-
methyl-3-(pyridine-3-yl)phenyl)borane system, Deotare et al.[211]
have experimentally observed CT states to migrate along the
donor-acceptor interface for distances between 5–10 nm, and
have corroborated these findings with Kinetic Monte Carlo
simulations. Their simulations point to the movement of the
electron-hole pair as proceeding in stretch-pull fashion along
the interface, whereby one charge carrier first moves and the
other follows. The interfacial energetic disorder, estimated to be
on the order of 100 meV or more, has also a negative impact on
VOC.[21,212] Using a numerical model, McGehee and co-workers
have demonstrated that decreasing the energetic disorder from
100 meV to 50 meV can increase VOC by up to 120 mV.[21] Fur-
thermore, Coropceanu and co-workers have separated this dis-
order into static and dynamic components, allowing for these
contributions to be independently considered.[81,213]
4.3.1. Theoretical Determination of the CT-State
Energies and Characteristics
The exact determination of the nature of the CT states, be them
more delocalized higher-energy states or more localized lower-
energy states, has proven to be difficult and is currently the focus
of many investigations in the theoretical community.[209,214–217]
Linear-response TD-DFT has been a popular choice for the
determination of excited-state properties due to its reasonable
computational cost.[218] Due to their tendency to promote exces-
sive delocalization, common hybrid functionals (e.g., B3LYP and
PBE0) strongly underestimate the CT excitation energies.[219]
The use of non-empirically tuned long-range corrected func-
tionals (that significantly reduce the electron self-interaction
error), such as BNL,[209]
ω
B97X,[220] and LC-
ω
PBE,[221] sup-
presses this overdelocalization and provides reliable estimates of
the low-lying CT state energies. However, describing the higher-
lying CT excitations remains more difficult.[216,218] To address
this issue, recent studies from the groups of Blasé[217,222,223] and
Rohlfing[214,224,225] have employed many-body Green’s function
theory by combining the GW approximation and the Bethe-
Salpeter equation (BSE) to investigate the optical excitations
in two donor-acceptor model complexes, anthracene-tetracya-
noethylene[226] and fullerene -oligomer donors systems.[214,215,225]
While such GW-BSE calculations give good agreement with
high-level ab initio methods (e.g., CASPT2),[222] their computa-
tional cost still limits their implementation.[215]
4.4. Charge Separation
Several models have been proposed as possible pathways to
overcome the barrier to charge separation once an exciton
appears at the donor-acceptor interface. It has been suggested
early on that hot CT states, that form after the initial photoex-
citation and prior to relaxation to the lowest-energy CT state,
might play a role in charge separation, by providing enough
energy for the charges to separate prior to relaxation to the
bottom of the CT state distribution. However, the work of
Baldo and co-workers and, in particular, of Vandewal and co-
workers, has demonstrated that the lower CT states are key
intermediates to the separation process.[211,227] McGehee and
co-workers[21] have recently proposed that the lower CT states
are in fact in equilibrium with the charge separated (free car-
rier) states. Thus, it is of interest to examine the complex ener-
getic landscape that occurs at the donor-acceptor interface and
its impact on the terms appearing in Equation. (5).
We first discuss the work of Verlaak et al.[165] who used a
model pentacene/C60 interface (wherein a slab of crystalline
C60 was deposited onto a crystalline slab of pentacene) to deter-
mine how molecular orientations and local electrostatic envi-
ronments influence the energy required for charge separation.
Focusing on the pentacene(001) (edge-on) and pentacene(01–1)
(face-on) surfaces, these authors showed that a hole-electron
pair at the edge-on interface is 0.6 eV more stabilized than at
the face-on interface. This increased stabilization translates to
a 0.44 eV charge separation barrier for a hole and an electron
at the edge-on interface and a 0.04 eV barrier at the face-on
interface. The origin of this difference is related to the different
orientations of the pentacene molecules, which changes the
sign of the quadrupole interacting with C60, and thus, the sign
of the induced dipoles in C60. While the face-on pentacenes are
closer to the C60 molecules, and the charges have a larger Cou-
lombic interaction (–1.11 eV for edge-on; –1.73 eV for face-on),
the closer the hole and electron get, the more they appear as a
neutral species. This results in a drastic reduction in the stabili-
zation due to induced dipoles, which cuts the –1.19 eV induced-
dipole stabilization for the edge-on system in half to –0.59 eV
(Table 2).
In a follow-up investigation, Linares et al.,[166] and later Idé
et al.,[119] demonstrated interfacial band bending as a function
of pentacene orientation; moving away from face-on pentacene
by rotating the pentacenes in 10° increments until an edge-on
configuration is obtained, can result in HOMO/LUMO shifts of
about 0.2 eV (Figure 11). In the face-on orientation, there is a
large induced dipole on both pentacene and C60 that is oriented
towards the C60; as the angle of the pentacene plane increases,
the induced dipole becomes smaller and eventually changes
sign. This has the effect of destabilizing the hole and electron
in the face-on orientation and stabilizing them in the edge-on
orientation, which induces a larger charge separation barrier
for edge-on pentacene.
Building upon the works of Idé et al.[119] and Verlaak et al.,[165]
Yost and Van Voorhis showed how electrostatic interactions
and dielectric differences at the interface influence the interfa-
cial energy levels to create environments that can be more, or
less favorable to charge separation (Figure 12).[228] Using QM/
MM simulations that account for either a single hole or elec-
tron, they show how the HOMO and LUMO levels in donor
and acceptor materials shift in response to the electrostatic
environment. Taking rubrene and C60 as a model system, with
dielectric values of 2.7 and 3.8, respectively, these authors find
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that the dielectric mismatch results in the HOMO/LUMO gap
of rubrene becoming smaller near the interface (Figure 12a);
this results from increased stabilization of both hole and elec-
tron. On the other hand, the HOMO and LUMO of C60 are
destabilized, which results from overall reduced polarization
energy. Thus, the 1.1 dielectric constant difference results in
shifts of over 0.1 eV for each of the energy levels. To model the
effects of changing multipole interactions, these authors use
two model interfaces of 4-(dicyanomethylene)-1-methyl-6-(4-
dimethylaminostyryl)-4H-pyran (DMC) with C60 (one with zero
interface dipole and one with interface dipole pointed towards
the C60 layer). In the system with no interfacial dipole, there
occurs relatively little modification to the energy levels at the
interface; however, in the presence of a strong interface dipole,
there are marked shifts of up to 1.0 eV in the HOMO and
LUMO levels of DMC and C60 (Figure 12c). In this case, the
interface dipole creates a situation where both hole and elec-
tron preferentially move away from the interface; here, the
HOMO [LUMO] level in DCM is destabilized
[stabilized] at the interface while the HOMO
[LUMO] level in C60 is stabilized [destabi-
lized]. However, it should be borne in mind
that the stabilization/destabilization of the
HOMO/LUMO levels is dependent on the
direction of the interface dipole.
Looking more closely at how molecular
motions influence intermolecular inter-
actions, Ryno et al.[196] and Poelking and
Andrienko[197] have investigated the effect
of disorder at the small-molecule donor-
acceptor interface. Using a model penta-
cene(001)/C60 bi-layer interface, Ryno et al.
employed molecular dynamics to observe
how the charge separation barrier changed
as a function of both time and position along
the interface. These authors show that, in
general, the IE of pentacene and EA of C60
are stabilized at the interface; however, the
disorder results in distributions with widths
of nearly 0.2 eV, and leads to charge separation barriers with
widths of about 0.2 eV centered at about 0.75 eV (Figure 12).
They note three primary pentacene/C60 configurations, two
with pentacene directly beneath a C60 and one where pentacene
is positioned between three C60 molecules. While the charge
separation barrier shows little change over time for the first two
configurations (up to 0.09eV), the third site shows much more
drastic change, e.g., the charge separation barrier for a single
site can change by 0.17 eV over a timespan of less than 10 ps.
This large change in charge separation barrier leads to the sug-
gestion that some mixing or disorder at the interface can be
beneficial for charge separation, if specific configurations can
be realized.
Poelking and Andrienko[197] and Fu et al.[229] have found
that even at a bi-layer interface there are protrusions of donor
into the acceptor and acceptor into the donor. Using mole-
cular dynamics snapshots of a bilayer based on a dicyanovinyl-
substituted thiophene derivative (D5M) and C60, Poelking and
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Table 2 . Interaction energies for an electron-hole pair near the interface and separated far
from the interface for both the pentacene(001)/C60 and pentacene(01–1)/C60 interfaces. Hole
(h) is on an interfacial pentacene and electron (e) is on an interfacial C60 for the bound pair.
QID is the quadrupole-induced-dipole interaction energy. All units in eV. Reproduced with per-
mission.[165] Copyright 2009, John Wiley and Sons.
Electron-hole
pair
Separated electron
and hole
Pentacene(001)/C60 Coulomb energy −1.114 0
Induced-dipole interaction −1.188 −1.058(h) − 0.791(e)
Quadrupole interaction −0.415(h) − 0.119(e) −0.310(h) + 0.004(e)
QID interaction +0.132(h) + 0.019(e) −0.053(h) − 0.039(e)
Total −2.685 −2.247
Pentacene(01-1)/C60 Coulomb energy −1.732 0
Induced-dipole interaction −0.593 −1.052(h) − 0.792(e)
Quadrupole interaction +0.025(h) + 0.284(e) -0.302(h) + 0.004(e)
QID interaction +0.053(h) − 0.128(e) +0.043(h) + 0.044(e)
Total −2.091 −2.055
Figure 11. Left: Induced dipole of the interfacial pentacene and C60 in a 1-dimensional stack as a function of the rotation angle. 0º is face-on and 90º is
edge-on. Negative values indicate an induced dipole oriented towards C60. Right: Band bending of the interfacial pentacene and C60 in a 1-dimensional
stack as a function of the rotation angle. Larger values for C60 indicate decreasing electron affinity, and larger values for pentacene indicate increasing
ionization energy. Adapted with permission.[119] Copyright 2010, John Wiley and Sons.

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Andrienko find that as the orientations of the donor molecules
change, and thus, as well the signs of the electrostatic interac-
tions, hole and electron pairs may either be bound or separate:
For face-on donor molecules in the protrusion at the interface,
the intermolecular interactions favor charge separation as holes
and electrons are destabilized, while the opposite occurs for the
edge-on systems. Additionally, charge separation occurs pref-
erentially when donor-acceptor pairs lie on either side of the
plane of the interface, rather than along the direction of the
interface; in some cases, the energetics at the interface can lead
to unbound electron-hole pairs.
For polymer donor/fullerene acceptor systems, the concept
of a localized charge carrier becomes more difficult to define
since even when a hole is localized to a single polymer chain it
may be delocalized over several repeat units. D’Avino et al. have
attempted to tackle this issue in the limit of a charge localized
to a single chain[198] and by allowing the hole and electron to
delocalize across multiple molecules.[121] In the limit of local-
ization along a single polymer chain, in this case P3HT in a
bi-layer configuration with C60, the charge separation barrier
distribution from MD simulations is centered around approxi-
mately 0.25 eV with only 3% of electron-hole pairs likely to
dissociate. However, when a P3HT/PC61BM bi-layer is con-
sidered, approximately 30% of electron-hole pairs are likely to
dissociate, the reason being the energetic disorder coming from
the dipole of PC61BM. As discussed in Section 4.2, allowing
holes and electrons to delocalize within the donor and acceptor
materials, respectively, is expected to increase the possibility of
hole-electron dissociation.
From Verlaak et al.’s[10] model using crystalline slabs of
pentacene and C60 brought into close contact, to the investiga-
tion of Yost and Van Voorhis[228] into the effect of electrostatics
on band bending, to the polymer:fullerene investigations of
D’Avino et al.,[198] each of these works explores how intermolec-
ular interactions impacts the charge separation process in OSC
active layers. By controlling the multipole interactions among
molecules, the polarizability of donor and acceptor moieties,
and the disorder at the donor-acceptor interface, we can begin
to apprehend how the energy required for charge separation
can be tailored.
4.5. Charge Transport
Regardless of whether OSCs, organic light-emitting diodes, or
organic field-effect transistors are being considered, the per-
formance of these devices is limited by the efficiency by which
charge carriers can be transported within the active layers.
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Figure 12. Top: Schematic representation of environmental effects on the band structure at the donor (blue) and acceptor (red) interfaces, including:
a) a difference in dielectric constant, b) poor molecular packing (represented as the insertion of a vacuum layer), c) static multipole moments cre-
ating an electric field, and d) the effect of disorder at the interface. e) The polarization energy due to a hole or electron on the donor (layer < 0) or
acceptor (layer ≥ 0) side of a pentacene(001)/C60 interface. f) Distribution of charge separation energies at a disordered pentacene(001)/C60 interface.
Figures (a–d) are adapted with permission.[228] Copyright 2013, American Chemical Society. Figures (e–f) are adapted with permission.[196] Copyright
2016, American Chemical Society.

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There have been numerous exhaustive reviews on charge trans-
port and the effects of molecular interactions on transport. As
such, we direct interested readers to the reviews of Coropceanu
et al.[9] and Gershenson et al.,[230] the books of Pope and Swen-
berg[152] and Silinsh and Capek,[231] and the book chapter of Li
et al.[232] Here, we restrict ourselves to a discussion of Kinetic
Monte Carlo (KMC) simulations, one of the methodologies
used to model charge transport in OSC devices on the device
scale while including information on the microscopic interac-
tions; our objective is to illustrate how morphology influences
transport, in particular in the case of fullerenes.
4.5.1. Brief Description of Kinetic Monte Carlo Simulations to
Model Processes in OSCs
KMC simulations have proven to be a very useful tool for mod-
eling OSC devices.[233–243] Simply put, KMC simulations allow
for the description of the dynamic evolution of a given system
composed of microscopic processes, i, that occur at some rate,
ki, over a given period of time. Thus, KMC simulations can be
thought of as a theoretical experiment conducted under perfect,
predefined conditions. Since the major microscopic processes
in an OSC happen after photon absorption – exciton migra-
tion, exciton dissociation, charge transport, recombination, and
charge collection at the electrodes – each has well-defined or
parameterizable rates; these rates can be used as input for KMC
simulations to understand the physics in OSC devices.[233] From
these simulations, device properties such as current density,
charge transport mobility, internal quantum efficiency (IQE), or
external quantum efficiency (EQE) can be extracted.
Depending on the strength of the interactions between
fullerene and electron-donor materials, varying degrees of
phase separation can occur. Strong interactions result in
well-mixed morphologies, while weaker interactions lead to
increased phase separation. Such structural differences sig-
nificantly impact the performance of the microscopic processes
in OSCs. One of the primary advantages of KMC simulations
over numerical modeling techniques, such as one-dimensional
drift-diffusion simulations, is that specific characteristics of the
morphology can be considered, which allows the investigation
of relationships between the morphology and device perfor-
mance.[244] Numerous KMC investigations have confirmed that
morphology influences the fundamental processes taking place
in OSCs. One early finding by Watkins et al.[233] is that excessive
phase separation reduces the internal quantum efficiency, as it
prevents excitons from reaching the donor-acceptor interface
and increases the probability of excitons decaying before dis-
sociation. However, in blended structures with large interfacial
areas, excitons have increased probability of reaching the inter-
face and dissociating. Thus, upon reaching the interface, the
exciton may dissociate into free holes and electrons, recombine
before separation (geminate recombination), or recombine after
separation (nongeminate recombination), with morphology
and intermolecular interactions determining the probability of
each occurring. In their work, Marsh et al.,[234] using various
system morphologies, have found that geminate recombina-
tion is generally more common than nongeminate recombina-
tion, because of the energy they consider as needed to initially
separate the hole and electron. However, altering the electro-
static interactions at the interface, by changing molecular ori-
entation as highlighted by Idé et al.,[119] or by changing the ori-
entation of the interface relative to the direction of the electric
field, can result in electric fields favorable to charge separation,
while improving charge transport.[234,235]
Increased interfacial area has been calculated to lead to
increased probability of charge recombination thereby, reducing
performance.[233] Groves et al.[236] have shown, with the aid of
drift-diffusion modeling, that changes in local carrier mobili-
ties can result in significant differences in currents and overall
device performance, due to increased bimolecular recombina-
tion rates. From such simulations that have focused on specific
aspects of the whole OSC device, optimal performance has
been suggested to be at an intermediate degree of phase separa-
tion, regardless of the actual blend morphology.[233,235,238]
4.5.2. KMC modeling of Charge Transport in Fullerenes
In combination with other techniques, KMC simulations can
be used to investigate some of the microscopic processes in
more detail. Here, we discuss KMC investigations of the charge
transport properties of fullerenes and their derivatives.
Nelson and co-workers[245,246] have used molecular configu-
rations from MD simulations as input into KMC modeling.
Based on evaluated parameters such as the charge transfer
integral and reorganization energy, KMC simulations can
provide estimates of charge mobilities, which are found to be
comparable to the experimental values. For disordered/amor-
phous C60, the field-effect mobilities calculated by Kwiatkowski
et al.[247] range from 2.4 to 4.4 cm2 V−1 s−1, which is only one
order of magnitude higher than the experimental values of
0.3 to 0.5 cm2 V−1 s−1.[248] Here, crystallinity is found not to be
very important since mobilities in crystalline and the most dis-
ordered C60 are evaluated to differ only by a factor of 2; this
result has been attributed to the efficient packing of C60 because
of its spherical shape.[247]
MacKenzie et al.[249] have used MD simulations to investi-
gate the molecular packing structure in solution-cast films of
fullerene derivatives with different chain lengths; the addition
of a side chain is seen to disrupt the packing of C60 molecules
and introduces energetic disorder. The side chains push apart
the C60 molecules, reducing the number of closely packed mol-
ecules and thus the number of molecules that can most elec-
tronically interact; as a result, the calculated electron mobilities
are strongly decreased. The authors find an inverse dependence
of mobility on electric field as well as a dependence on hydro-
carbon chain length, i.e., the reduction in mobility is larger at
high electric fields for a longer chain than for a shorter chain;
in such a situation, charge carriers are increasingly forced to
move exclusively along the direction of the electric field and
more efficient pathways cannot contribute to carrier transport.
In their work, Tummala et al.[250] focused on the properties
of various PC61BM aggregation structures using MD simula-
tions. The authors derived molecular packing structures and
charge transfer integrals, which then served as input into KMC
simulations of the electron mobilities. They find that the inter-
molecular interactions in crystalline structures are influenced
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by the inclusion of solvent molecules, which impacts the ori-
entations of neighboring PC61BM molecules and the overall
packing structure. As a result, the calculated electron mobilities
are different; for the triclinic co-crystal of PC61BM with chloro-
benzene, the largest electronmobility is about 0.2 cm2 V−1 s−1,
while for the monoclinic co-crystal with o-dichlorobenzene, the
largest mobility is about twice smaller. The electron mobilities
in amorphous PC61BMs are evaluated to be ca. one order of
magnitude lower than those in the crystalline structures, which
is consistent with the effects of increasing disorder described
by Nelson et al.[245] A reason for this reduction is that adjacent
PC61BMs that have strong intermolecular electronic couplings
are not oriented along a specific path; also, the Coulombic
repulsion among charge carriers, which limits charge carrier
motion, is seen to have a much larger impact in amorphous
systems, where there exist fewer efficient charge transport path-
ways. These results have been confirmed by Idé et al.[55] in their
KMC simulations of the charge transport properties of PC61BM
and ThC61BM (where the phenyl ring of the butyric acid methyl
ester is replaced with a thienyl ring) in different crystal mor-
phologies. Depending on the distribution of inter-fullerene
distances, charge transport can vary from one- to two- to three-
dimensional as a function of the crystal structure.
Moving towards the device scale, Steiner et al.[251] have used
a multiscale modeling approach where coarse-grained MD
simulations of fullerene derivatives (which enables the mod-
eling of 100 000 molecules in a given system) are combined
with quantum chemical estimates of the site energies, and
KMC simulations to calculate the charge-carrier mobilities
in PC61BM, bis-PC61BM and tris-PC61BM. The objective was
to better understand the reasons for reduced mobility as the
number of adducts increases. They find that the energetic dis-
order introduced as the number of phenyl-butyric acid methyl
ester groups increases, is the main contributor to the reduction
in carrier mobilities rather than packing disorder, which they
attribute to the spherical symmetry of the C60 cage. However, it
should be noted that Tummala et al.[250] have demonstrated that
the electronic couplings between adjacent fullerenes can span
from 0 meV to several hundred meV as one fullerene is rotated
around its neighbor; this result calls into question the assump-
tion that the spherical symmetry of the fullerenes necessarily
results in isotropic interactions among neighbors.
5. Outlook
With single-junction OSCs now reaching nearly 12% efficiency,
a comprehensive theoretical understanding of the electronic
processes that occur within the active layer of these devices is
necessary if we are to continue making significant progress
towards higher power conversion efficiencies. As this review
amply illustrates, the simple consideration of one acceptor
molecule and one donor molecule is not sufficient to provide
adequate insight into the complex interactions that occur at the
interfaces between the donor and acceptor materials. Recent
theoretical works demonstrate that the specific interactions
among the molecular (or polymer) species and the overall effect
of the molecular environment can result in qualitative changes
in the description of a given system with respect to its analog
in vacuum. Importantly, the energetics associated with specific
sites do evolve substantially as a function of time, which under-
lines the impact of the system dynamics. Thus, a feedback
approach is necessary wherein experimental investigations, that
are able to sample time scales not easily accessible via theo-
retical methods and that can provide accurate measures of the
properties of real systems, and theoretical investigations, that
can provide molecular level insight into the system order and
processes, complement and build upon each other.
From the computational and theoretical understanding that
has been reached of OSC devices, a clear message arises. To
accurately model these complex systems, a truly multiscale
approach is needed, which combines the ability to accurately
describe the interactions among molecular species, the effects
of the molecular environment well beyond just a few neigh-
boring molecules, the evolution of the system in time, and
the ability to explicitly consider enough sites that relevant sta-
tistics may be obtained. While a single unifying model that is
able to meet each of these requirements for all of the processes
taking place in OSCs has yet to be realized, efforts are currently
underway to investigate at least the individual processes on the
basis of such methodologies.
Acknowledgements
This work has been supported by competitive research funding at
King Abdullah University of Science and Technology (KAUST) and by
ONR Global (Award N62909-15-1-2003). We thank KAUST IT Research
Computing and the KAUST Supercomputing Laboratory for providing
continuous assistance as well as ample computational and storage
resources. S.R. thanks Dr. Tonghui Wang for providing structures for the
Table of Contents graphic.
Received: June 23, 2016
Revised: July 25, 2016
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