Phase separation in bulk heterojunctions of semiconducting polymers and fullerenes for photovoltaics.

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Phase Separation in Bulk Heterojunctions of Semiconducting Polymers and Fullerenes for Photovoltaics Neil D. Treat1 and Michael L. Chabinyc2 1 Department of Materials and Centre for Plastic Electronics, Imperial College London, London SW7 2AZ, United Kingdom 2 Materials Department and Materials Research Laboratory, University of California, Santa Barbara, California 93106; email: [email protected]

Annu. Rev. Phys. Chem. 2014. 65:59–81

Keyword

The Annual Review of Physical Chemistry is online at physchem.annualreviews.org

organic electronics

This article’s doi: 10.1146/annurev-physchem-040513-103712

Abstract

c 2014 by Annual Reviews. Copyright All rights reserved

Thin-film solar cells are an important source of renewable energy. The most efficient thin-film solar cells made with organic materials are blends of semiconducting polymers and fullerenes called the bulk heterojunction (BHJ). Efficient BHJs have a nanoscale phase-separated morphology that is formed during solution casting. This article reviews recent work to understand the nature of the phase-separation process resulting in the formation of the domains in polymer-fullerene BHJs. The BHJ is now viewed as a mixture of polymer-rich, fullerene-rich, and mixed polymer-fullerene domains. The formation of this structure can be understood through fundamental knowledge of polymer physics. The implications of this structure for charge transport and charge generation are given.

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1. INTRODUCTION Over the past decade, there has been a resurgence of interest in solar energy conversion (1). Fossil fuels are a relatively inexpensive source of energy, but their use has a significant influence on atmospheric levels of CO2 , thereby impacting the climate of the Earth (2). If we are to use alternative sources of energy to address this problem, they must be competitive in cost. In contrast to single-crystal silicon solar cells, thin-film solar cells comprise a layer of active semiconductors on an insulating substrate, which reduces the material and manufacturing costs and energy input for production (3). For high power conversion efficiency (PCE) using thin films, the semiconductor(s) must have a strong optical absorbance that overlaps with the solar spectrum for the generation of charge. Organic semiconductors have large optical extinction coefficients and are relatively inexpensive to synthesize and process, making them particularly attractive for thin-film solar cells (4). Organic bulk heterojunctions (BHJs) are a class of photovoltaic active layers comprising a blend of organic electron-donating and electron-accepting materials, either polymeric or molecular (5) in nature, in which two (or more) materials meet within a complex phase-separated structure. The blend of the donor and acceptor is required for efficient charge generation owing to the relatively high binding energy (>0.3 eV) of the electron and hole in an organic material, the exciton binding energy, necessitating a heterojunction for charge generation. These heterojunctions can be fabricated using a variety of different techniques, ranging from solid-state (6) to solution processing (7). This review focuses on polymer:fullerene BHJs deposited from solution, which are currently the most efficient type of organic solar cell (7) and possibly the most economical deposition method (Figure 1). Solution-processed molecular materials are rapidly showing improvements in PCE but are not discussed here (5). In the formation of a polymer:fullerene BHJ, a polymeric donor and fullerene acceptor are mixed in a solvent and then cast from solution, leading to spontaneous phase separation upon solidification in a thin (∼100–200 nm) film; thus, although the BHJs have complex morphology, they are simple to fabricate. Transmission electron microscopy (TEM) of BHJs with high internal quantum efficiency (i.e., the ratio of charges generated to the number of incident photons) shows domains with apparent length scales of 10–30 nm (8). The high surface area allows charge generation by the excitation of molecules at molecular interfaces and also by exciton diffusion from molecules away from these interfaces. A built-in electrical potential is provided by the electrodes, leading to the extraction of photogenerated carriers by drift through the phase-separated blend. The best BHJ solar cells currently have efficiencies near 10%, but there

PCE: power conversion efficiency BHJ: bulk heterojunction


TEM: transmission electron microscopy

1 mm

1 µm

1 nm Light

Electrode

e– Substrate

Polymer Fullerene

Figure 1 Schematic representation of the multiple length scales within a polymer:fullerene bulk heterojunction solar cell. (Moving from left to right) Length scales range from the area of a solar cell (larger than millimeters), to the device thickness (in hundreds of nanometers), to the aggregate and crystallite size of the polymer and fullerene (in tens of nanometers), and finally to the interaction of light with the polymer and fullerene (less than 10 nm). 60

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Donor

OCH3 S

Acceptor

O S

n

LUMO

P3HT (donor)

PCBM (acceptor)

Energy

b D* + A Exciton

(D+ + A– ) CT state

Free energy


LUMO

D+ : A–

CT transition

Proximal carriers

D+ + A– HOMO

~ [LUMO(A)-HOMO(D)]-0.6 eV HOMO

D+A Ground state

log (DOS) (cm–3/eV) Distance

Figure 2 (a) Chemical structures of P3HT and PCBM, the most widely studied materials for bulk heterojunctions. (b) State diagram showing the processes that lead to free charge carriers. The energies of the states depend on the electric field and charge density. (c) Schematic illustration of the electronic density of states of the valence (HOMO) and conduction (LUMO) of a donor polymer and acceptor fullerene. The tail of states into the gap is caused by structural disorder. Abbreviations: CT, charge transfer; DOS, density of states.

are still significant questions about their detailed operation, with debate regarding the dominant mechanisms of charge generation and losses (9). The phase-separated structure of BHJs is known to be critical for both the generation and extraction of charge. In the simplest form, the BHJ can be thought of as an effective semiconductor in which the electrons move in the lowest unoccupied molecular orbital (LUMO) states of the acceptor (conduction level) and the holes move in the highest occupied molecular orbital (HOMO) states of the donor (valence level) (Figure 2) (9). The transport states must be offset to prevent trapping of charges and to provide a driving force for splitting excitons. Both the donor and acceptor are semicrystalline or glassy, leading to a band tail of localized electronic states extending into the transport gap. Photoinduced charges may be generated by excitation of the donor or acceptor, or by direct excitation of a charge transfer state of two neighboring molecules. Importantly, because of the excitonic nature of BHJs, the optical states (two-particle states) cannot be represented simply on the same diagram as the electronic levels (one-particle states), and Jablonski-type diagrams are preferable when analyzing excitonic and charged states together (10). The charges may then separate and subsequently travel through energetically accessible states www.annualreviews.org • Phase Separation in Organic Solar Cells

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P3HT: poly(3hexylthiophene)


PCBM: [6,6]-phenylC61 -butyric acid methyl ester

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in the donor and acceptor. This model is clearly overly simplistic because it ignores transport through the three-dimensional (3D) structure of the BHJ, and multiscale models are now being developed to provide more realistic models for charge transport (11). We discuss here recent progress toward understanding how the phase-separated structure forms in polymer:fullerene BHJs. Given the complexity of the micro/nanostructure of polymer:fullerene BHJs, we discuss the interplay between ordering of each component and their blends and address the role that each phase can play during the formation of a BHJ. For example, many schematic illustrations of BHJs suggest sharp interfaces between the donor and acceptor, but this picture has recently been overturned by various measurements demonstrating that fullerenes are partially miscible in most semiconducting polymers (12–20). BHJs are therefore better thought of as multiphase blends in which regions of pure donor, pure acceptor, and mixed polymer and fullerene exist. There are significant questions as to whether this structure is beneficial for charge generation and extraction. We focus here on the features of the most studied BHJ of P3HT [poly(3-hexylthiophene)] and PCBM ([6,6]-phenyl-C61 -butyric acid methyl ester) and also discuss relevant results with other polymeric donors for comparison. For other aspects of BHJs not covered here, there are many excellent reviews on synthetic design (21, 22), photophysics (23, 24), and charge transport (25).

2. MICROSTRUCTURE AND ORDERING OF SEMICONDUCTING POLYMERS: FROM SOLUTION TO SOLID STATE The semiconducting polymer plays an essential role in the phase-separation process of BHJs and in both light absorption and transport of holes, positively charged carriers, within BHJs. To allow processing from solution, one needs to synthesize polymers with conjugated backbones with nonconjugated side chains (Figure 3, top). Because there is negligible hybridization of the molecular orbitals of the aliphatic side chains and the conjugated backbone, the molecular architecture of the π-conjugated backbone dictates the electronic transport gap (difference between the HOMO and LUMO) and the optical gap (10). The number of attached side chains per repeat unit and structure modifies the solubility of polymers in organic solvents and their crystallization kinetics (discussed in more detail below). We note that the electronic levels and optical properties of polymers are also affected more subtly by molecular ordering of the polymer (i.e., the conformation of the backbone and intermolecular interactions) and can be influenced by the processing conditions used to form thin films. Importantly, the structure of the polymer backbone and side chains will also dictate the noncovalent interactions of the polymer with other species (e.g., solvent and fullerene) and thus phase separation in BHJs.

2.1. Structural Characteristics of Semiconducting Polymers in Solution Polymer:fullerene BHJs are formed by solidification from relatively dilute solutions (e.g., 2% w/w); therefore, the conformation of the polymer in solution is essential to the kinetics of polymer crystallization during solvent evaporation (Figure 3, bottom) (see the sidebar Rigidity of Polymer Backbones). Semiconducting polymers can have less conformational freedom relative to many nonconjugated polymers, but their rigidity depends on their molecular structure (26). Early studies of P3HT demonstrated that it adopts a random-coil conformation in solution with a persistence length (lp ) of 2.4 nm (i.e., approximately six repeat units) (27), which agrees well with a recent study of regioregular and regiorandom samples of P3HT, yielding 2.9 nm and ∼1 nm, respectively (28). The bond angles between the thiophene rings in P3HT are not perfectly colinear [121.1◦ (29)], and the barrier to rotation between rings in isolated molecules is relatively low 62

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Side chains


ckbone ated ba Conjug

Increasing persistence length

Figure 3 (Top) Representation of a typical conjugated polymer with a π-conjugated backbone and aliphatic side chains. (Bottom) A representation showing that increasing the persistence length decreases the flexibility of the polymer chain in solution (see the sidebar Rigidity of Polymer Backbones).

[∼15.3 ± 3.0 kcal/mol (30)], helping to rationalize this result. The coiled nature of poly(3alkylthiophenes) (P3ATs) in solution represents a unique property of this polymer family, likely leading to some of their behavior in polymer:fullerene BHJs (i.e., cold crystallization). Polymers with (nearly) linear couplings in the backbone, such as poly(9,9-dioctylfluorene) and poly(phenylene ethylenes), are more rod-like, with lp of approximately 8.5 nm (31) and 15 nm in solution, respectively (32). There are also examples of very stiff semiconducting polymers,

RIGIDITY OF POLYMER BACKBONES The statistical treatment of the conformation of polymers in solution was developed by Flory and others (87, 118). The worm-like chain model applicable to semiconducting polymers provides a so-called persistence length, which is the length at which correlations in the direction of the tangents of the backbone monomers are lost. An alternative model is that of a freely jointed chain in which the correlation of the backbone is given by a Kuhn length, which is equal to twice the persistence length (87). Qualitatively, polymer chains with longer persistence lengths have more rod-like character, and chains with shorter persistence lengths are better described as random coils. The persistence length can be experimentally quantified by light or neutron scattering and inferred by gel permeation chromatography by the determination of the radius of gyration and molecular length (using molecular weight and assuming the monomer repeat length, respectively). To put this into perspective, polyethylene and polystyrene are random coils that have a persistence length of 1.92 nm and 3.34 nm (119), respectively, whereas the classic rod-like double-helical polymer DNA has a persistence length of 60–90 nm in solution (120).

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Donor-acceptor polymer: a copolymer in which the backbone comprises two monomers with differing electronic levels that lower the optical gap Entanglement: describes how polymer chains cannot spatially coexist, leading to the limitation of their rotational and translational degrees of freedom

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such as the electron-conducting ladder-type polymers (i.e., monomers are linked by two bonds) poly(benzimidazo-benzoisoquinoline) (BBL), for which lp is 154 nm in solution (33). Donoracceptor-type polymers used in highly efficient BHJs (7) will most likely have intermediate lp between those reported for P3HT and BBL, but these properties have yet to be reported. The idea of the lp , and how it relates to molecular length, is important because it describes the conformation of the polymer in solution (or melt) and therefore its ability to reptate and crystallize during solvent evaporation. The thermodynamic equilibrium temperature at which a polymer will melt, T m◦ , is equal to the ratio of the enthalpy and entropy of melt, H m◦ /Sm◦ . Assuming similar molecular lengths, polymer-solvent interactions, and H m◦ , polymers with larger lp will have lower conformational entropy in solution and favor the formation of crystalline material at higher temperatures or concentrations (26). Alternatively, assuming no change in the persistence length and solidification conditions, polymers with larger molecular lengths have a greater thermodynamic driving force for crystallization, as indicated by an increase in Tm (34, 35), but also have a greater probability of forming entanglements, hindering the rate of crystallization during solidification. Therefore, a combination of the semiconducting polymer’s lp and molecular length (weight) will dictate the thermodynamics and kinetics of crystallization during solvent evaporation and thus influence their optoelectronic performance. Therefore, it is likely that the differences between the lp of P3AT and stiffer donor-acceptor-type polymers affect their crystallization during casting and thus the fabrication conditions that are required to achieve efficient photoconversion in BHJs.

2.2. Polymer Solidification: Crystallite Nucleation, Growth, and Microstructure During typical processing conditions, the polymer:fullerene blend solidifies such that the chains have restricted motion, which results in incomplete crystallization of the polymer and the formation of crystalline and disordered polymer domains. In almost all examples, the domains of semiconducting polymers that do crystallize are pure despite the presence of the fullerene. Evidence for the formation of single-component polymer crystallites is found in X-ray and electron diffraction from polymer:fullerene blends in comparison to neat polymer films (36, 37). The diffraction patterns are relatively insensitive to blending with the fullerene, with only small changes in d-spacing, suggesting that no fullerene is incorporated into crystalline polymer domains for many systems (38). There are some examples of polymer-fullerene bimolecular crystals (39), however, so it is important to study how polymer crystallization occurs in BHJs to understand the mechanisms of phase separation. We note that these polymer crystallites are still relatively disordered compared to molecular crystals and contribute to the tail of electronic states observed by transport experiments (40). The first step of polymer crystallization is primary nucleation (41) in which a stable nucleus of critical size must be formed by passing through a barrier (i.e., a thermodynamically unstable process with a positive G). The temperature-dependent rate of primary nucleation is proportional to the bulk free energy of crystallization as well as the surface free energy of the growing nuclei, G∗ , and the energy required to transport material across a phase boundary, Gη . The combination of the latter two factors produces a nucleation rate (I ∗ ) that is temperature dependent (i.e., G∗ decreases with decreasing temperature and Gη increases with decreasing temperature) with a bell shape; the global maximum of the nucleation rate represents the minimization of G∗ and Gη and, for polymers, typically occurs at supercoolings (T = Tm – T ) of 30◦ C to 100◦ C (42). At larger supercoolings, the primary nucleation rate decreases owing to the increase in Gη (i.e., the increase in viscosity). After the formation of a stable nucleus, repeat units begin to add to the growing crystallite, the rate of which is called the linear crystallite growth rate. For polymers, the rate-limiting step of the linear growth rate is the secondary nucleation of the 64

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CRYSTALLINE STRUCTURE OF POLYMERS


The crystal structure of conjugated polymers can be determined by X-ray or electron-scattering experiments. The intensity and position of the diffracted photons (or electrons) in reciprocal space are determined by the electron density in real space (i.e., the arrangement of molecules). In many cases, one observes only a limited number of diffraction peaks, making the determination of the molecular packing structure of polymers less detailed than what is possible for molecular compounds. Information about the deviations from crystalline order can be determined by detailed analysis of scattering data; for more information on this subject, readers are referred to thorough reviews on X-ray techniques (40, 121).

polymer chains on the growing crystallite. Classically, the linear growth rate of a polymer crystallite from solution is constant with time until it becomes limited by the concentration of remaining crystallizable material (43). Because the linear growth rate is dependent on secondary nucleation, its temperature dependence will follow a bell-shaped curve similar to that describing primary nucleation; the bell-shaped nature of the linear growth rate has been measured in a recent study of oligo(3-hexylthiophene)s (35). Combining both the primary nucleation and linear crystallite growth rates, one yields the overall crystallization rate within a given polymer system, which links the microscopic models of polymer crystal growth to their solid-state microstructure. After the nucleation and growth of crystalline domains, the microstructure of semicrystalline polymer in the polymer:fullerene BHJ forms an intricate mixture of disordered and crystalline domains (see the sidebar Crystalline Structure of Polymers). The fringed micelle model is a relevant description of polymers with molecular lengths above the entanglement limit [e.g., 50–100 repeat units or ∼20 kDa for P3HT (44)] (Figure 4). The microstructure of such a system results from a complex free energy landscape owing to variations in chain mobility (e.g., entanglements limiting reptation) and molecular structure (e.g., persistence length) (42). Polymers crystallize into two main forms: chain-folded or chain-extended crystallites. Chain-extended polymer crystallites are the most thermodynamically stable crystallite form (i.e., the equilibrium crystallite form). Chainextended crystallites have been directly visualized using low-dose high-resolutionTEM in BHJs of P3HS and PCBM (13) and have also been seen in neat films of conjugated polymers with a variety of chemical structures and persistence lengths (45, 46). Chain-folded crystallites have a metastable crystallite form and, because of the decrease in H m◦ resulting from the folds, typically exhibit a lower Tm relative to chain-extended crystallites (34, 42). Chain-folded crystallites (i.e., 60◦ and 120◦ folds) have been observed in scanning tunneling microscopy images of P3AT crystallized on highly oriented pyrolytic graphite surfaces (47, 48). Evidence of chain folding has also been observed in solution-grown P3HT fibrils, in which the long axis of the polymer is perpendicular to the long axis of the fibril; above a critical Mn (i.e., 10 kDa), the fibril diameter was independent of the molecular length, revealing that P3HT has the ability to form chain-folded crystallites (49, 50). Both these examples indicate that the crystalline regions can be composed of either folded or extended chains. However, the propensity to form chain-folded crystallites likely is limited to flexible semiconducting polymers (e.g., P3AT), which is indicated by the absence of small-radius chain folds in the more rigid polymers [e.g., poly(dioctylbithiophene-alt-fluorenone)] (51). The competition between extended-chain and chain-folded crystallites is dictated by the chain mobility (i.e., the persistence length and molecular length of the polymer) and solidification rate (i.e., processing conditions). For instance, in the case of crystallization from the melt (or theta solvent), a flexible polymer (e.g., P3HT) with limited chain mobility will generate a higher fraction of chain-folded crystallites, whereas decreasing the solidification rate will encourage the formation www.annualreviews.org • Phase Separation in Organic Solar Cells

Reptation: the motion of polymer chains in concentrated solution or melt analogous to a pile of snakes slithering through one another

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Figure 4 Solid-state microstructure of a conjugated polymer: (left) chain-folded crystallite, (top) extended-chain crystallite, (right) disordered polymer, and (middle) the combination of all three microstructures in the fringed micelle model. Figure adapted from Reference 42.

of the thermodynamically most stable crystallite form (i.e., the chain-extended crystallite). As the lp increases, the molecular length at which chain folding can occur increases (i.e., an increase in the chain-folding radius), and this transition occurs at molecular lengths that are larger than those commonly reported for donor-acceptor polymers. Therefore, it is anticipated that the increased stiffness of donor-acceptor polymers compared to P3ATs will result in the formation of predominantly chain-extended crystallites and represents a clear difference between these two classes of materials. A combination of the nucleation and growth mechanisms (i.e., the overall crystallite growth rate) of semiconducting polymers will ultimately control the solid-state microstructure of the semiconducting polymer. The overall growth rate can be modeled, using the impingement of propagating waves in a given volume (52), by the Avrami equation (53–55), 1 −v c (t) = exp(−Ktn ), with v c describing the volume fraction of the crystalline material as a function of time, t. In the ideal case, the exponent, n, is a whole number and describes both the nucleation type (i.e., heterogeneous versus homogeneous) and crystallite growth geometry (i.e., spatial dimensionality). However, it is more common to observe fractional exponents that vary with crystallization time. For isothermally crystallized oligomers of 3-hexylthiophene, the Avrami exponent was determined to be ∼2, revealing homogeneous nucleation and subsequent 1D linear growth (35), typically yielding a fibril-like microstructure in the solid state (56). This fiber-like microstructure (i.e., homogeneous nucleation with 1D linear growth) has been observed in systems ranging from single-crystal semiconducting polymers grown from dilute solutions (49, 57–61) to high-performance polymer:fullerene blends (62–64). From these observations, it is plausible that homogeneous nucleation and fibrillar growth are characteristics of semiconducting polymers. One possible explanation relies on favorable faceto-face packing of the π-conjugated polymer backbones. Even though a detailed understanding 66

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of the mechanism of crystallite nucleation and growth in semiconducting polymers is still incomplete, these principles are operative and thus control the optoelectronic performance in a polymer:fullerene blend film.


3. MICROSTRUCTURE OF FULLERENES

GIWAXS: grazing incidence wide-angle X-ray scattering

Whereas much attention has been paid to the microstructure of the polymeric donor, it is widely known that fullerenes make efficient power conversion in BHJs possible. There are relatively few examples of efficient BHJs with nonfullerene acceptors, despite many materials having similar electronic levels. One suggestion is that fullerenes are roughly spherical, allowing efficient, relatively isotropic electronic coupling between molecules, leading to efficient transport of electrons through the BHJs (65, 66). This feature does not, however, explain their role in nanoscale phase separation, and if these properties could be translated to other materials, it could open the range of possible acceptors.

3.1. Fullerene Solidification: Microstructure Fullerenes in BHJs have disordered molecular packing, although they can crystallize readily in neat films. The majority of fullerene derivatives are initially molecularly dissolved in solvents, and after solvent evaporation, typical processing conditions at room temperature produce disordered thin films that lack long-range order. Like many organic materials, upon nucleation, fullerene derivatives crystallize rapidly and can have many polymorphic forms. Selected-area electron diffraction (67–70) and grazing incidence wide-angle X-ray scattering (GIWAXS) (14, 37, 38) data of neat and BHJ films reveal a highly textured crystalline microstructure that varies with a number of parameters (e.g., processing conditions). Until recently, the single-crystal structure of PCBM had been determined only with cocrystalized solvent (71, 72). The thin-film structure of PCBM has not been fully modeled to determine if it adopts the structure observed in solvent-free bulk crystals. This tendency of fullerenes to vitrify persists in efficient BHJs. GIWAXS of both neat and polymer:fullerene BHJ films shows two broad isotropic scattering rings centered at 0.7 A˚ −1 and 1.36 A˚ −1 with peak widths at half maximum of ∼0.22 A˚ −1 , indicating a correlation length between molecules of only ∼3 nm, or about three molecules (73). This disordered microstructure is mostly independent of the chemical structure of the fullerene derivative in efficient cells and is observed in blends of both polymer and molecular donors. The nucleation and growth of PCBM crystallites have most commonly been observed during thermal annealing at temperatures greater than 110◦ C after casting the BHJ (4, 74). We note that there is large variability in the size and number of PCBM crystallites, which is likely a result of residual solvent (75) and material purity (N.D. Treat & M.L. Chabinyc, unpublished results). PCBM forms very large lateral domains (on the micrometer scale) that can protrude hundreds of nanometers from the surface of a BHJ (70). The observation of these large fullerene crystallites is widely linked to degradation in the PCE and represents a pathway that limits long-term stability (76). Therefore, the ability of a fullerene to remain disordered when processed with a variety of conditions and donor materials is one of the morphological factors that has resulted in its widespread success relative to other acceptors.

3.2. Soluble Fullerenes: Crystallite Nucleation and Growth To explain this persistence to vitrify, we again address the conversion of amorphous material to crystalline material (or, in this case, the lack thereof ), which is predicated on the rate of primary nucleation. There are few studies of the bulk crystallization of fullerenes; most focus on the www.annualreviews.org • Phase Separation in Organic Solar Cells

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crystallization of PCBM within P3HT and do not distinguish between the primary nucleation rate and linear growth rate, as well as the combination of these rates in the overall crystallization rate (38, 77, 78). As discussed in Section 2.2, the nucleation rate is proportional to both the free energy of crystallization of a nucleus of critical size, G∗ (proportional to the bulk free energy of crystallization and both the surface energy and surface area of the nuclei), and the free energy of activation governing the transport of material across a phase boundary, Gη (proportional to the temperature-dependent viscosity of the disordered material). Intuitively, one should anticipate that the persistence of the fullerene to vitrify during solvent evaporation results from a low rate of primary nucleation at the processing temperature and concentration due to a thermodynamically and/or kinetically unfavorable combination of G∗ and Gη . This explanation has recently been experimentally verified in a study of the nucleation and growth of PCBM crystallites within a low-band-gap polymer, poly[2,3-bis-(3-octyloxyphenyl)quinoxaline-5,8-diyl-alt-thiophene-2,5diyl] (TQ1) (74). PCBM heterogeneously nucleated from the substrate, and there was a broad maximum in the nucleation rate between 150◦ C and 170◦ C; the investigators concluded that nucleation was limited by diffusivity below 150◦ C (i.e., Gη ) and by the formation of a nucleus of critical size above 170◦ C (i.e., G∗ ). The key finding in this study was that PCBM has a low rate of nucleation, which explains the propensity of fullerene to remain disordered in neat and blended thin films. The linear growth rate varied over two orders of magnitude between 110◦ C and 230◦ C and was diffusion limited by the movement of PCBM within TQ1. Importantly, the nucleation and linear growth rate of PCBM crystallites was severely limited at temperatures below the Tg of the blend (i.e., for TQ1:PCBM, Tg = 110◦ C), thus signifying a critical design rule for achieving thermally stable polymer:fullerene BHJs. Therefore, the low density of large PCBM crystallites observed in most polymer:fullerene BHJs likely results from a limited primary nucleation rate and relatively fast linear crystallite growth rate. Recent results suggest that dimers of fullerene may form during deposition, which can also limit the growth of the size of PCBM crystallites (79). Although the mechanism is still not fully understood, it will be important to evaluate prior results with this new information.


Tg : glass transition temperature

4. MIXED POLYMER AND FULLERENE DOMAINS Until recently, many studies assumed that the components of the polymer:fullerene BHJ were not miscible. Because polymers and fullerenes were believed to have limited miscibility, phase separation from the initially mixed state was thought to arise from mass diffusion of the fullerene (enhanced by thermal annealing) during crystallization of the polymer. This concept of immiscibility led many to believe that the BHJ microstructure comprised well-defined, nanoscale interfaces between pure bicontinuous domains of the polymer and fullerene, which facilitated both exciton dissociation and free charge carrier transport. Recently, several studies found that semiconducting polymers and fullerene are partially miscible, revealing the presence of mixed polymer and fullerene domains in BHJs. Importantly, these studies demonstrate that efficient power conversion does not necessarily depend on the formation of only phase-pure domains of polymers and fullerenes. In this section, we first introduce the findings demonstrating the miscibility of the polymer and fullerene and then focus on the properties influencing their partial miscibility.

4.1. Evidence for the Partial Miscibility of Polymers and Fullerenes The diffusion coefficient of PCBM in semiconducting polymers, such as P3HT, was not quantified until recently, and these studies revealed the important result that PCBM was partially miscible in disordered domains of polymers. Investigators used scanning transmission X-ray microscopy 68

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to study the demixing of P3HT:PCBM blended films after annealing at elevated temperature (17, 18), which helped to quantify the concentration and Fickian diffusion coefficient of PCBM in P3HT during the growth of PCBM crystallites. The key information revealing partial miscibility was the presence of residual 19% v/v PCBM in P3HT near a growing crystallite, which increased as a function of temperature. An alternate study used depth profiling of the composition of an initially pure bilayer of deuterated PCBM and P3HT as a function of annealing temperature using dynamic secondary ion mass spectrometry (DSIMS), revealing interdiffusion and partial miscibility of the polymer and fullerene (14). The measured concentration of the deuterated PCBM in P3HT relates to the temperature-dependent miscibility of the fullerene in the semicrystalline polymer in the absence of fullerene crystallites, mimicking the microstructure of efficient BHJs. The exact values for the miscibility of the fullerene in semicrystalline polymers such as P3HT depend on the volume fraction of the disordered polymer (i.e., the polymer degree of crystallinity), which is difficult to quantify in spin-cast thin films. This structure can be observed from GIWAXS during the interdiffusion of PCBM into P3HT. The isotropic scattering corresponding to disordered PCBM and the d-spacing of the P3HT crystallites remained unchanged during and after complete intermixing. This finding reveals that PCBM not only is miscible within the disordered phase of P3HT, but also rapidly diffuses without disrupting the P3HT crystallites. Additionally, the diffusion coefficient of deuterated PCBM in disordered P3HT is strongly temperature dependent, varying from 2.2 × 10−11 cm2 /s at 50◦ C to 1.0 × 10−9 cm2 /s at 110◦ C at PCBM volume fractions of 0.01, with an activation energy of 15.6 kcal/mol, which is surprisingly close to that reported for thiophene-thiophene bond rotation (i.e., 15.3 ± 3 kcal/mol) (12). In the polymer:fullerene BHJs, the mixed phase comprises molecularly dissolved or small clusters of the fullerene in the disordered polymer (12–19, 80–85). Overwhelming evidence from studies of P3HT:PCBM and BHJs with low-band-gap donor-acceptor polymers using techniques such as scanning transmission X-ray microscopy (17, 18), DSIMS (13, 14, 16), GIWAXS (64), small-angle X-ray scattering (64), neutron scattering (19, 86), neutron reflectivity, scanning electron microscopy (14), and energy-filtered TEM (64) strongly supports the idea of the miscibility of the disordered polymer and fullerene phases in systems. This feature therefore cannot be ignored in mechanistic studies of charge generation and extraction in BHJs.

DSIMS: dynamic secondary ion mass spectrometry

4.2. Thermodynamic Considerations for Partial Miscibility Because the polymer-fullerene mixed phases comprise two disordered components, it is reasonable to discuss the phase-separation process beginning with the miscibility of two amorphous components (i.e., the partial miscibility of two liquid components framed by Flory-Huggins solution theory) (87). Criteria for mixing in any two-component polymer-fullerene blend can be expressed by a Gibbs free energy of mixing (Gmix ) comprising both entropy and enthalpy as a function of temperature. Beginning from an initially homogeneous solid solution at elevated temperature, as the temperature decreases, a point is reached at which the polymer and fullerene are no longer miscible in all proportions (i.e., the upper critical solution temperature; less than T3 in Figure 5). Below this critical temperature, the polymer and fullerene will phase separate into two phases: a polymer-rich phase and a fullerene-rich phase. This partial miscibility can be described by a temperature-composition diagram consisting of a boundary curve (i.e., a binodal curve; Figure 5) that distinguishes between the homogeneous (outside) and phase-separated (inside) regions. Blends falling within this binodal curve will phase separate into two phases with compositions resting on the binodal curve, and the fraction of phases can be defined by a tie line. There is evidence to support the idea that the equilibrium miscibility of PCBM and disordered P3HT can be described as a temperature-composition diagram with a binodal curve. The key www.annualreviews.org • Phase Separation in Organic Solar Cells

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Figure 5 (a) Representation of a temperature-composition diagram featuring binodal (solid ) and spinodal (dashed ) curves with (b) microstructures of the disordered polymer and fullerene from three different temperatures. T1 (orange) is at low temperature with the lowest partial miscibility and highest volume fraction of single-component phases, T2 (blue) is an intermediate temperature and microstructure, and T3 ( green) is the temperature above the upper critical solution temperature and represents a homogeneous solid solution.

piece of evidence observed in both demixing (17) and intermixing (14) experiments is that the miscibility of disordered P3HT and PCBM increases with increasing temperature; this general finding is the classic behavior of a partially miscible amorphous polymer-liquid binary system that can be described with a binodal curve. The increase in partial miscibility with temperature has also been revealed in other polymer:fullerene blends, indicating this is likely a general trend in high-performance polymer:fullerene blend films. The temperature and composition dependence of the partial miscibility (i.e., the shape of the binodal curve) is a function of the enthalpic chemical interactions between the polymer and fullerene, described by the Flory-Huggins interaction parameter, χ (87). This parameter takes into account the energy of dispersing polymers with a solvent (i.e., the fullerene). Qualitatively, χ can be either positive or negative; for instance, more positive values lead to a less compatible system, an increase in the area of the two-phase region, and a shift in the upper critical solution temperature to higher temperatures. Therefore, χ is one of the key parameters that can be used to describe temperature- and composition-dependent partial miscibility within the polymer and fullerene binary system. Because χ depends on chemical interactions, it varies with the chemical structure of the polymer and fullerene (13, 88, 89). For P3HT:PCBM blends, the χ parameter has been determined from the melting-point depression of P3HT in P3HT:PCBM blends using differential scanning calorimetry (64). From these fits, χ was determined to be 0.86 ± 0.09. Importantly, this value further supports the idea of the partial miscibility of the polymer and fullerene and binodal phase separation at higher fullerene concentrations. Unfortunately, there has been limited investigation of the composition dependence of χ , but it is anticipated that thermodynamically stable polymer:fullerene BHJs would have similar or more negative values for it. Therefore, developing an understanding of χ across material systems is essential for understanding the factors that control the phase separation from solution within polymer:fullerene blends. 70

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One should use caution when framing the discussion of phase separation within a polymer:fullerene blend using the idea of partial miscibility of two amorphous components. An obvious point is that this approach assumes an equilibrium partial miscibility of the disordered polymer and fullerene. There are examples indicating that the BHJ microstructure after solvent evaporation is metastable (i.e., the initially disordered fullerene phase will crystallize at elevated temperature). However, the majority of efficient polymer:fullerene BHJs comprise disordered fullerene, suggesting that the approach is a reasonable start. A more subtle point is that the previous explanation treats the polymer as a single component with uniform molecular length and end groups. In practice, the polymer will have a distribution of molecular lengths that will influence its miscibility with the fullerene (e.g., chains with shorter and larger molecular lengths will have different miscibilities with the fullerene). Despite these precautions, understanding the partial miscibility of two amorphous components is essential to understanding the phase separation of polymer-fullerene mixed domains.

5. PHASE-SEPARATION MECHANISM IN POLYMER: FULLERENE BULK HETEROJUNCTIONS The polymer and fullerene of a BHJ are initially codissolved in a single or mixture of solvents; therefore, any phase separation will occur during solidification. The simplest model allows for two possible routes toward phase separation during solvent evaporation: crystallization (i.e., solidliquid phase separation) or demixing of the amorphous components (i.e., liquid-liquid phase separation). Importantly, the event that initiates phase separation will control the microstructure of the resulting active layer. Even though there are few examples studying phase separation during solvent evaporation, an emerging picture is that the production of BHJs with efficient power conversion is dependent on phase separation caused by polymer crystallization. While binary phase diagrams (90) of the polymer and fullerene provide useful insight into their long-term stability, ternary phase diagrams that include the solvent are essential to understand phase separation during solvent evaporation. The solvent concentration at which phase separation occurs is dictated by the noncovalent interaction of the polymer, fullerene, and solvent, which is described by χ for each interacting pair. Given that the fullerene most commonly vitrifies during solidification (as discussed in Section 3), the phase separation must result from either polymer crystallization or liquid-liquid demixing from the polymer:fullerene:solvent mixture before the crystallization of the polymer. Solidification via either of these two routes will result in strikingly different microstructures and thus PCEs. One can imagine a case in which the crystallization of the polymer is thermodynamically hindered, meaning that liquid-liquid demixing will occur before polymer crystallization, resulting in droplets, with compositions determined by intercepts with the binodal or spinodal curve. Interestingly, there are numerous reports of polymer:fullerene:solvent combinations that produce a microstructure with droplets of the fullerene within a polymer layer resulting in BHJs with poor PCEs. These conclusions are in excellent agreement with a recent publication, which modeled the phase separation mechanism in blends comprising donor-acceptor diketopyrrolepyrrole-quinquethiophene polymer and PCBM (91). Initial evidence to support the requirement of solid-liquid phase separation is found in solid-state films of P3HT:PCBM; these findings reveal that the phase separation is not limited by the mass diffusion of the fullerene in the polymer [i.e., 10× greater diffusion distance relative to phase separation (12)] or the partial miscibility of the disordered polymer and fullerene [a small value for χ indicates miscibility up to 42% v/v PCBM in P3HT (64)]. This evidence strongly suggests that phase separation in efficient polymer:fullerene BHJs is not initiated by liquid-liquid demixing until the later stages of solvent evaporation. www.annualreviews.org • Phase Separation in Organic Solar Cells

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This picture also appears to be true when observing phase separation during solvent evaporation. Recently, the time-dependent phase separation within P3HT:PCBM blends was thoroughly investigated during spin coating with a combination of in situ GIWAXS (i.e., monitoring diffraction from P3HT crystallites) and grazing incidence small-angle X-ray spectroscopy (i.e., monitoring phase separation of P3HT and PCBM) (92). Importantly, the crystallization of P3HT was found to initiate phase separation during solvent evaporation, which seems to be a common finding in other high-performance polymer:fullerene:solvent systems (93, 94). Thus, it is plausible that the formation of efficient BHJs occurs in systems in which the nucleation and growth of polymer crystallites (or aggregates) initiate phase separation. Intuitively, because polymer crystallites are phase pure, their crystallization during solvent evaporation not only controls the formation of single-component, fibrillar polymer crystallites, but also induces the formation of saturated disordered fullerene phases into disordered polymer phases. Then liquid-liquid demixing likely dominates the phase separation of disordered fullerenerich domains from saturated polymer-fullerene mixed domains. Thus, a key driving force for the formation of bicontinuous domains of the polymer and fullerene likely is the nucleation and growth of polymer crystallites during solvent evaporation.

6. ROLE OF SINGLE-COMPONENT POLYMER AND FULLERENE DOMAINS IN POWER CONVERSION Efficient charge collection from a polymer:fullerene BHJ relies on the formation of continuous charge transport pathways to the electrodes (see the sidebar Solar Cells). Intuitively, this process should rely on the formation of interconnected polymer-rich and fullerene-rich domains. Additionally, the volume fractions of the ordered single-component semiconducting polymer phases and fullerene-rich phases are directly linked to the fraction of mixed disordered polymer:fullerene phases and thus the proximity of the donor and acceptor, which is important for exciton dissociation. Therefore, there must be an intermediate volume fraction of polymer crystallites and fullerene-rich domains that balances the amount of polymer-fullerene mixed domains with interconnectivity, maximizing charge generation and transport (Figure 6). Most observations indicate that a high PCE of BHJs depends on the formation of a sufficient volume fraction of pure polymer (36, 37, 95–97). For many materials (e.g., P3HT), the pure polymer is readily recognized as semicrystalline by X-ray scattering, but in donor-acceptor-type polymers, the aggregation of polymer chains may be relatively defective and only observable by TEM (13, 62, 63). Thus, the idea of increasing the volume fraction of polymer crystallites has motivated the development of methods for processing efficient BHJs. For P3HT:PCBM, it is common to utilize post-processing treatments [e.g., thermal (37, 96) or solvent (36, 98) annealing] to improve the relative degree of crystallinity of P3HT, which results in an improvement in

SOLAR CELLS The ability of solar cells to convert light to electricity is given by its PCE, which is the ratio of power generation to incident irradiation. The PCE can be determined from a current-voltage (J-V) characteristic (see Figure 6) under illumination by the short-circuit current, Jsc , the open circuit voltage, Voc , and the fill factor (FF), which is the ratio of the maximum power divided by the product of Jsc and Voc : V OC FF . η = JSC p incident

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Figure 6 (a) Schematic illustration of predicted current-voltage (J-V) curves under illumination for a solar cell, with low, medium, and high polymer crystallinity. Shown are (orange) a highly mixed polymer:fullerene blend with a low degree of polymer crystallinity resulting in the lowest power conversion efficiency (PCE), (blue) a highly mixed polymer:fullerene blend with intermediate polymer crystallinity and fullerene aggregation with the highest PCE, and ( green) a highly phase-separated microstructure with a high degree of polymer crystallinity and fullerene aggregation and lower PCE. This representation demonstrates how increasing the polymer crystallinity will increase phase separation, which in turn affects the optoelectronic characteristics of solar cells. (b) The associated microstructures of the disordered polymer and fullerene. Abbreviation: MPP, maximum power point.

both the short-circuit current density and the fill factor (i.e., the PCE) (Figure 6). There is strong evidence correlating the increase in the degree of crystallinity of P3HT to PCE using temperature-dependent current-voltage characteristics with temperature-dependent GIWAXS data, revealing that both changes occur within the same timescale and annealing temperature. Improving the crystallinity of P3HT increases its absorption coefficient, thereby increasing the number of photons absorbed by the polymer, and also increasing the fill factor by improving charge collection (37, 81, 95, 99). To achieve efficient power conversion, BHJs of high-performance donor-acceptor-type polymers commonly require large weight fractions of the fullerene (i.e., as much as 80% w/w), the presence of which can result in the vitrification of the polymer. To overcome such effects, investigators have used high-boiling-point cosolvent additives, which result in an increase in the polymer degree of crystallinity (97, 100) and improves the PCE (101). An alternate and promising method to improve the crystallization rate is to use nucleating agents (i.e., nonvolatile additives that form surfaces from which crystallites may nucleate). This approach can be used to control the nucleation in a variety of materials and processing conditions without adversely influencing their ability to transport charge (73). Therefore, there is strong evidence to support the idea that increasing the volume fraction of polymer crystallites is directly linked to improving their PCE. The extraction of holes from the active layer requires the formation of a continuous pathway, allowing holes to move between polymer chains, which is aided by the interconnectedness between polymer crystallites (102, 103). Polymers with longer molecular lengths will have a higher probability of entanglements in the amorphous regions and tie chains that go between polymer crystallites. The molecular length at which these entanglements begin to form (i.e., entanglement www.annualreviews.org • Phase Separation in Organic Solar Cells

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molecular weight) has recently been determined to be 50–100 repeat units for P3HT, corresponding to an average molecular weight of 10–20 kDa (44). Even though lower–molecular weight samples of P3HT have higher crystallinity than do high–molecular weight samples in thin films, it has been shown that the mobility of carriers in thin-film transistors formed from them increases with molecular weight until the entanglement molecular weight is reached (higher interconnectivity), above which the values remain constant. Similarly, in polymer:fullerene BHJ solar cells, the PCE increases with increasing polymer molecular length (104–108) due to increases in both the short-circuit current density and the fill factor (i.e., the efficiency of charge carrier extraction). It is not anticipated that these improvements result from an increase in the degree of crystallinity of the polymer because the molecular length is usually inversely proportional to the rate of crystallization. There is still limited understanding of the molecular length at which tie chains begin to occur within stiffer high-performance semiconducting polymers, but the data still suggest that increasing molecular lengths increase the charge extraction efficiency. An increase in the polymer degree of crystallinity likely improves interconnectivity and transport within pure fullerene domains. Taking into account the partial miscibility of disordered polymers and fullerenes, by increasing the volume fraction of single-component polymer domains, one finds that there are less disordered polymers for the fullerene to mix with, leading to an increase in fullerene-rich domains. This picture agrees with the hypothesis that efficient charge generation and collection require the formation of interconnected polymer-rich and fullerenerich domains. There must be an upper limit to the volume fraction of these single-component domains, however. For P3HT:PCBM, it is commonly observed that the fraction of excited states that are quenched (i.e., from photoluminescence quenching studies) is inversely proportional to the relative degree of crystallinity (99). Because the dissociation of excitons within the polymer relies on proximity to a fullerene, charge generation can be limited at high volume fractions of polymer crystallites depending on their domain size. Thus, an intermediate volume fraction of polymer crystallites in the polymer:fullerene BHJ provides the surface area between the donor and acceptor, enabling the dissociation of excitons, as well as allowing the formation of a bicontinuous microstructure that efficiently collects generated charges.


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7. ROLE OF MIXED POLYMER-FULLERENE DOMAINS IN POWER CONVERSION Finally, we discuss in this section the implications of the role that these mixed polymer-fullerene domains play in photoinduced charge generation. In organic solar cells, charge generation occurs at an interface of a donor and acceptor. One therefore needs to understand the molecular interfacial area, essentially the number of donor-acceptor pairs, and how far an exciton might need to diffuse to reach such an interface to understand where charge can be generated. Let us consider a BHJ of P3HT:PCBM and its known morphology. The size of an exciton on a conjugated homopolymer is approximately 20 repeat units (109). The optical absorption plateaus at this value for many oligomers, including very rigid ladder materials, indicating that the wave function delocalizes over at least this many repeat units. This value is also similar to the number of repeat units between chain bends in P3HT, but this is likely coincidental because of similar predicted exciton sizes by theoretical calculations for polymer chains without defects. Using the density of P3HT (1.1 g/ml) and PCBM (1.6 g/ml), one can estimate the volume of the exciton and find that 19% v/v of PCBM would be required to fully dissociate every excited state generated in P3HT. We note that this simple estimation neglects the contributions of exciton diffusion and long-distance electron transfer, which would reduce the volume fraction of PCBM needed to dissociate these excited states. PCBM has been found to be partially miscible in disordered P3HT from 16% to 74

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22% v/v, suggesting that there is little to no exciton diffusion in the mixed regions. This estimate agrees with photoluminescence quenching in amorphous, regiorandom P3HT:PCBM blends. It has been found that 10% w/w (or 7% v/v) of PCBM in regiorandom P3HT led to 99% photoluminescence quenching; in other words, essentially all charges generated within the disordered regions are quenched (supporting the information in Reference 110). There are also other examples of high-performance polymer:fullerene blends that exhibit photoluminescence quenching of >98% (111). From photoluminescence quenching data, one can estimate that the distance an excited state on the polymer may diffuse before reaching a quenching site is approximately less than 1 nm (i.e., the diameter of a fullerene); this observation leads to the conclusion that excited-state dissociation can occur readily without the need for exciton diffusion. In BHJs without significant amounts of mixed regions, excitons must still migrate, and this information is of great value for interpreting experiments on charge generation. Determining the fractions of mixed and phaseseparation fullerenes can also aid in the understanding of the nature of charge transfer states in the band tails of BHJs (112, 113). The three-phase structure has also been determined to be critical for charge extraction. Researchers have proposed that the electronic levels of fullerenes in disordered regions are shifted such that electrons are pushed to more favorable states in the pure fullerene domains (111). Similar effects are expected for holes in the polymer as well. If such a mechanism is a dominant factor in aiding charge extraction, the three-phase structure may be highly beneficial relative to a structure with only pure polymer and fullerene domains. Alternative explanations, such as favorable molecular orientation of the donor and acceptor and dipolar interactions, have also been proposed (114, 115). Further control of the nanoscale morphology of BHJs is needed to validate these hypotheses through studies of model systems.

8. CONCLUSION There have been rapid advances in the PCE of polymer:fullerene BHJs in the past several years. The information gained about the phase-separation process and domain purity has provided key insights into the future design of materials and processing of efficient BHJs. Advances in synthetic chemistry leading to highly purified polymers and novel backbones are providing more reliable structure-property relationships. These advances, however, have progressed more rapidly than has our understanding of the details of the morphology, charge transport, and photophysics of BHJs. Emerging methods for physical characterization [e.g., polarized soft X-ray scattering (116) and pump-push spectroscopy (117)] and existing methods (e.g., TEM, DSIMS, and transient photocurrent) are providing new insights into the fundamental processes in BHJs. It is our hope that these new techniques will enable the community to solve the grand challenge of linking the polymer and fullerene molecular structures to the kinetic and thermodynamic factors that control the phase separation of polymers and fullerenes during solvent evaporation.

DISCLOSURE STATEMENT The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS The authors would like to thank the NSF for support of experimental work related to BHJs through the NSF SOLAR program (CHE-1035292) and the NSF ICC program (CHE-1026664). N.D.T. www.annualreviews.org • Phase Separation in Organic Solar Cells

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thanks the NSF for support from the ConvEne IGERT Program (NSF-DGE 0801627) and an NSF Graduate Research Fellowship. The authors also acknowledge stimulating discussions on the polymer science of BHJs with Prof. Ed Kramer, Prof. Glenn Fredrickson, Prof. Craig Hawker, Dr. Natalie Stingelin, Dr. Christian Muller, and Prof. Paul Smith. ¨ LITERATURE CITED


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48. Keg P, Lohani A, Fichou D, Lam YM, Wu Y, et al. 2008. Direct observation of alkyl chain interdigitation in conjugated polyquarterthiophene self-organized on graphite surfaces. Macromol. Rapid Commun. 29:1197–202 49. Liu J, Arif M, Zou J, Khondaker SI, Zhai L. 2009. Controlling poly(3-hexylthiophene) crystal dimension: nanowhiskers and nanoribbons. Macromolecules 42:9390–93 50. Zhang R, Li B, Iovu MC, Jeffries-EL M, Sauve G, et al. 2006. Nanostructure dependence of fieldeffect mobility in regioregular poly(3-hexylthiophene) thin film field effect transistors. J. Am. Chem. Soc. 128:3480–81 51. Brun M, Demadrille R, Rannou P, Pron A, Travers JP, Grevin B. 2004. Multiscale scanning tunneling microscopy study of self-assembly phenomena in two-dimensional polycrystals of π-conjugated polymers: the case of regioregular poly(dioctylbithiophene-alt-fluorenone). Adv. Mater. 16:2087–92 52. Poisson SD, Schnuse CH. 1841. Recherches sur la probabilité des jugements en matière criminelle et en matière civile. Paris: Meyer 53. Avrami M. 1941. Granulation, phase change, and microstructure kinetics of phase change. III. J. Chem. Phys. 9:177–84 54. Avrami M. 1940. Kinetics of phase change. II Transformation-time relations for random distribution of nuclei. J. Chem. Phys. 8:212–24 55. Avrami M. 1939. Kinetics of phase change. I General theory. J. Chem. Phys. 7:1103–12 56. Malik S, Nandi AK. 2002. Crystallization mechanism of regioregular poly(3-alkyl thiophene)s. J. Polym. Sci. B 40:2073–85 57. Kiriy N, Jahne E, Adler HJ, Schneider M, Kiriy A, et al. 2003. One-dimensional aggregation of regioregular polyalkylthiophenes. Nano Lett. 3:707–12 58. Ihn KJ, Moulton J, Smith P. 1993. Whiskers of poly(3-alkylthiophene)s. J. Polym. Sci. B 31:735–42 59. Rahimi K, Botiz I, Stingelin N, Kayunkid N, Sommer M, et al. 2012. Controllable processes for generating large single crystals of poly(3-hexylthiophene). Angew. Chem. Int. Ed. Engl. 51:11131–35 60. O’Carroll D, Iacopino D, O’Riordan A, Lovera P, O’Connor E, et al. 2008. Poly(9,9-dioctylfluorene) nanowires with pronounced β-phase morphology: synthesis, characterization, and optical properties. Adv. Mater. 20:42–48 61. Briseno AL, Mannsfeld SCB, Shamberger PJ, Ohuchi FS, Bao Z, et al. 2008. Self-assembly, molecular packing, and electron transport in n-type polymer semiconductor nanobelts. Chem. Mater. 20:4712–19 62. Li W, Hendriks KH, Roelofs WSC, Kim Y, Wienk MM, Janssen RAJ. 2013. Efficient small bandgap polymer solar cells with high fill factors for 300 nm thick films. Adv. Mater. 25:3182–86 63. Moon JS, Takacs CJ, Cho S, Coffin RC, Kim H, et al. 2010. Effect of processing additive on the nanomorphology of a bulk heterojunction material. Nano Lett. 10:4005–8 64. Kozub DR, Vakhshouri K, Orme LM, Wang C, Hexemer A, Gomez ED. 2011. Polymer crystallization of partially miscible polythiophene/fullerene mixtures controls morphology. Macromolecules 44:5722–26 65. Cheung DL, Troisi A. 2010. Theoretical study of the organic photovoltaic electron acceptor PCBM: morphology, electronic structure, and charge localization. J. Phys. Chem. C 114:20479–88 66. Tummala NR, Mehraeen S, Fu Y-T, Risko C, Brédas J-L. 2013. Materials-scale implications of solvent and temperature on [6,6]-phenyl-C61 -butyric acid methyl ester (PCBM): a theoretical perspective. Adv. Funct. Mater. 23:5800–13 67. Savenije TJ, Kroeze JE, Yang XN, Loos J. 2005. The effect of thermal treatment on the morphology and charge carrier dynamics in a polythiophene-fullerene bulk heterojunction. Adv. Funct. Mater. 15:1260–66 68. Bertho S, Janssen G, Cleij TJ, Conings B, Moons W, et al. 2008. Effect of temperature on the morphological and photovoltaic stability of bulk heterojunction polymer:fullerene solar cells. Sol. Energy Mater. Sol. Cells 92:753–60 69. Li L, Lu G, Li S, Tang H, Yang X. 2008. Epitaxy-assisted creation of PCBM nanocrystals and its application in constructing optimized morphology for bulk-heterojunction polymer solar cells. J. Phys. Chem. B 112:15651–58 70. Yang XN, Alexeev A, Michels MAJ, Loos J. 2005. Effect of spatial confinement on the morphology evolution of thin poly( p-phenylenevinylene)/methanofullerene composite films. Macromolecules 38: 4289–95


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Contents

Annual Review of Physical Chemistry Volume 65, 2014


A Journey Through Chemical Dynamics William H. Miller p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 1 Chemistry of Atmospheric Nucleation: On the Recent Advances on Precursor Characterization and Atmospheric Cluster Composition in Connection with Atmospheric New Particle Formation M. Kulmala, T. Petäjä, M. Ehn, J. Thornton, M. Sipilä, D.R. Worsnop, and V.-M. Kerminen p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p21 Multidimensional Time-Resolved Spectroscopy of Vibrational Coherence in Biopolyenes Tiago Buckup and Marcus Motzkus p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p39 Phase Separation in Bulk Heterojunctions of Semiconducting Polymers and Fullerenes for Photovoltaics Neil D. Treat and Michael L. Chabinyc p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p59 Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology Romana Schirhagl, Kevin Chang, Michael Loretz, and Christian L. Degen p p p p p p p p p p p p p83 Superresolution Localization Methods Alexander R. Small and Raghuveer Parthasarathy p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 107 The Structure and Dynamics of Molecular Excitons Christopher J. Bardeen p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 127 Advanced Potential Energy Surfaces for Condensed Phase Simulation Omar Demerdash, Eng-Hui Yap, and Teresa Head-Gordon p p p p p p p p p p p p p p p p p p p p p p p p p p p p 149 Ion Mobility Analysis of Molecular Dynamics Thomas Wyttenbach, Nicholas A. Pierson, David E. Clemmer, and Michael T. Bowers p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 175 State-to-State Spectroscopy and Dynamics of Ions and Neutrals by Photoionization and Photoelectron Methods Cheuk-Yiu Ng p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 197 Imaging Fluorescence Fluctuation Spectroscopy: New Tools for Quantitative Bioimaging Nirmalya Bag and Thorsten Wohland p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 225 v

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Elucidation of Intermediates and Mechanisms in Heterogeneous Catalysis Using Infrared Spectroscopy Aditya Savara and Eric Weitz p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 249 Physicochemical Mechanism of Light-Driven DNA Repair by (6-4) Photolyases Shirin Faraji and Andreas Dreuw p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 275 Advances in the Determination of Nucleic Acid Conformational Ensembles Lo¨ıc Salmon, Shan Yang, and Hashim M. Al-Hashimi p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 293


The Role of Ligands in Determining the Exciton Relaxation Dynamics in Semiconductor Quantum Dots Mark D. Peterson, Laura C. Cass, Rachel D. Harris, Kedy Edme, Kimberly Sung, and Emily A. Weiss p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 317 Laboratory-Frame Photoelectron Angular Distributions in Anion Photodetachment: Insight into Electronic Structure and Intermolecular Interactions Andrei Sanov p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 341 Quantum Heat Engines and Refrigerators: Continuous Devices Ronnie Kosloff and Amikam Levy p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 365 Approaches to Single-Nanoparticle Catalysis Justin B. Sambur and Peng Chen p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 395 Ultrafast Carrier Dynamics in Nanostructures for Solar Fuels Jason B. Baxter, Christiaan Richter, and Charles A. Schmuttenmaer p p p p p p p p p p p p p p p p p p 423 Nucleation in Polymers and Soft Matter Xiaofei Xu, Christina L. Ting, Isamu Kusaka, and Zhen-Gang Wang p p p p p p p p p p p p p p p p 449 H- and J-Aggregate Behavior in Polymeric Semiconductors Frank C. Spano and Carlos Silva p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 477 Cold State-Selected Molecular Collisions and Reactions Benjamin K. Stuhl, Matthew T. Hummon, and Jun Ye p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 501 Band Excitation in Scanning Probe Microscopy: Recognition and Functional Imaging S. Jesse, R.K. Vasudevan, L. Collins, E. Strelcov, M.B. Okatan, A. Belianinov, A.P. Baddorf, R. Proksch, and S.V. Kalinin p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 519 Dynamical Outcomes of Quenching: Reflections on a Conical Intersection Julia H. Lehman and Marsha I. Lester p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 537 Bimolecular Recombination in Organic Photovoltaics Girish Lakhwani, Akshay Rao, and Richard H. Friend p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 557 vi

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Mapping Atomic Motions with Ultrabright Electrons: The Chemists’ Gedanken Experiment Enters the Lab Frame R.J. Dwayne Miller p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 583 Optical Spectroscopy Using Gas-Phase Femtosecond Laser Filamentation Johanan Odhner and Robert Levis p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 605 Indexes


Cumulative Index of Contributing Authors, Volumes 61–65 p p p p p p p p p p p p p p p p p p p p p p p p p p p 629 Cumulative Index of Article Titles, Volumes 61–65 p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 632 Errata An online log of corrections to Annual Review of Physical Chemistry articles may be found at http://www.annualreviews.org/errata/physchem

Contents

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Annual Reviews It’s about time. Your time. It’s time well spent.

New From Annual Reviews:

Annual Review of Statistics and Its Application Volume 1 • Online January 2014 • http://statistics.annualreviews.org

Editor: Stephen E. Fienberg, Carnegie Mellon University


Associate Editors: Nancy Reid, University of Toronto Stephen M. Stigler, University of Chicago The Annual Review of Statistics and Its Application aims to inform statisticians and quantitative methodologists, as well as all scientists and users of statistics about major methodological advances and the computational tools that allow for their implementation. It will include developments in the field of statistics, including theoretical statistical underpinnings of new methodology, as well as developments in specific application domains such as biostatistics and bioinformatics, economics, machine learning, psychology, sociology, and aspects of the physical sciences.

Complimentary online access to the first volume will be available until January 2015. table of contents:

• What Is Statistics? Stephen E. Fienberg • A Systematic Statistical Approach to Evaluating Evidence from Observational Studies, David Madigan, Paul E. Stang, Jesse A. Berlin, Martijn Schuemie, J. Marc Overhage, Marc A. Suchard, Bill Dumouchel, Abraham G. Hartzema, Patrick B. Ryan

• High-Dimensional Statistics with a View Toward Applications in Biology, Peter Bühlmann, Markus Kalisch, Lukas Meier • Next-Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data, Kenneth Lange, Jeanette C. Papp, Janet S. Sinsheimer, Eric M. Sobel

• The Role of Statistics in the Discovery of a Higgs Boson, David A. van Dyk

• Breaking Bad: Two Decades of Life-Course Data Analysis in Criminology, Developmental Psychology, and Beyond, Elena A. Erosheva, Ross L. Matsueda, Donatello Telesca

• Brain Imaging Analysis, F. DuBois Bowman

• Event History Analysis, Niels Keiding

• Statistics and Climate, Peter Guttorp

• Statistical Evaluation of Forensic DNA Profile Evidence, Christopher D. Steele, David J. Balding

• Climate Simulators and Climate Projections, Jonathan Rougier, Michael Goldstein • Probabilistic Forecasting, Tilmann Gneiting, Matthias Katzfuss • Bayesian Computational Tools, Christian P. Robert • Bayesian Computation Via Markov Chain Monte Carlo, Radu V. Craiu, Jeffrey S. Rosenthal • Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models, David M. Blei • Structured Regularizers for High-Dimensional Problems: Statistical and Computational Issues, Martin J. Wainwright

• Using League Table Rankings in Public Policy Formation: Statistical Issues, Harvey Goldstein • Statistical Ecology, Ruth King • Estimating the Number of Species in Microbial Diversity Studies, John Bunge, Amy Willis, Fiona Walsh • Dynamic Treatment Regimes, Bibhas Chakraborty, Susan A. Murphy • Statistics and Related Topics in Single-Molecule Biophysics, Hong Qian, S.C. Kou • Statistics and Quantitative Risk Management for Banking and Insurance, Paul Embrechts, Marius Hofert

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Beyond fullerenes: design of nonfullerene acceptors for efficient organic photovoltaics.

Photoinduced Dynamics of Charge Separation: From Photosynthesis to Polymer-Fullerene Bulk Heterojunctions.

Deuterated polymers for probing phase separation using infrared microspectroscopy.

Free carrier generation in organic photovoltaic bulk heterojunctions of conjugated polymers with molecular acceptors: planar versus spherical acceptors.

Understanding charge transfer in carbon nanotube-fullerene bulk heterojunctions.

Steric Pressure among Membrane-Bound Polymers Opposes Lipid Phase Separation.

Compact bis-adduct fullerenes and additive-assisted morphological optimization for efficient organic photovoltaics.

Semiconducting polymers are light nanotransducers in eyeless animals.

Efficient organic photovoltaic cells with vertically ordered bulk heterojunctions.

Blending conjugated polymers without phase separation for fluorescent colour tuning of polymeric materials through FRET.

Vertical phase separation in bulk heterojunction solar cells formed by in situ polymerization of fulleride.

Universal formation of compositionally graded bulk heterojunction for efficiency enhancement in organic photovoltaics.

fullerene bilayer.

Semiconducting carbon nanotube aerogel bulk heterojunction solar cells.

Design of new Mott multiferroics via complete charge transfer: promising candidates for bulk photovoltaics.

Small-bandgap semiconducting polymers with high near-infrared photoresponse.

Semiconducting polymers with nanocrystallites interconnected via boron-doped carbon nanotubes.

Near infrared organic semiconducting materials for bulk heterojunction and dye-sensitized solar cells.

Fine tuning of the PCDTBT-OR:PC71BM blend nanoscale phase separation via selective solvent annealing toward high-performance polymer photovoltaics.

Molecular Design of Semiconducting Polymers for High-Performance Organic Electrochemical Transistors.

General strategy for self-assembly of highly oriented nanocrystalline semiconducting polymers with high mobility.

Temperature-responsive hyperbranched amine-based polymers for solid-liquid separation.

Tunable Semiconducting Polymer Nanoparticles with INDT-Based Conjugated Polymers for Photoacoustic Molecular Imaging.

Nanoparticles of conjugated polymers prepared from phase-separated films of phospholipids and polymers for biomedical applications.