Crystalline and Amorphous Interface Simulations of Donor-Acceptor Blends.

In an organic solar cell, exciton dissociation and charge transport to generate current depend on interface and bulk morphology, respectively, and their rates dictate device performance. Blend miscibility and processing determine the final morphology. We investigate the blend miscibility of P3HT and O-IDTBR, employing our recently developed "push-pull" computational technique, and explore its effect on nanoscale morphology. The resulting Flory-Huggins χ parameter is primarily enthalpic, and the blend exhibits UCST behavior. To directly simulate an equilibrated morphology in such a blend requires large (30 nm) systems and long (10 µs) simulations, which we attain with our virtual site coarse graining technique. In the resulting amorphous phase-separated state, O-IDTBR swells P3HT by about 15%, but does not percolate within the P3HT-rich phase. The interfacial profile depends on crystallinity: the amorphous interface is several nanometers wide, whereas an acceptor crystal induces order in the adjacent donor polymer, forming a sharp interface quite similar to a crystal-crystal interface. The wide amorphous interface promotes more donor-acceptor contacts with a wide range of relative orientations; however, the acceptors do not form a percolating network, which will likely lead to charge recombination. A crystal interface exhibits fewer donor-acceptor contacts with primarily face-on orientation that are more likely to charge-separate because of instant access to the preferred domain.

Tight-binding model predicts exciton energetics and structure for photovoltaic molecules.

Conjugated molecules and polymers are being designed as acceptor and donor materials for organic photovoltaic (OPV) cells. OPV performance depends on generation of free charge carriers through dissociation of excitons, which are electron-hole pairs created when a photon is absorbed. Here, we develop a tight-binding model to describe excitons on homo-oligomers, alternating co-oligomers, and a non-fullerene acceptor - IDTBR. We parameterize our model using density functional theory (DFT) energies of neutral, anion, cation, and excited states of constituent moieties. A symmetric molecule like IDTBR has two ends where an exciton can sit; but the product wavefunction approximation for the exciton breaks symmetry. So, we introduce a tight-binding model with full correlation between electron and hole, which allows the exciton to coherently explore both ends of the molecule. Our approach predicts optical singlet excitation energies for oligomers of varying length as well as IDTBR in good agreement with time-dependent DFT and spectroscopic results.

Backbone and Side Group Interchain Correlations Govern Wide-Angle X-ray Scattering of Poly(3-hexylthiophene).

Identifying the origin of scattering from polymer materials is crucial to infer structural features that can relate to functional properties. Here, we use our recently developed virtual-site coarse graining to accelerate atomistic simulations and show how various molecular features govern wide-angle X-ray scattering from a conjugated polymer, poly(3-hexylthiophene) (P3HT). The efficient molecular dynamics simulations can represent the structure and capture the emergence of crystalline order from amorphous melts upon cooling while retaining atomistic details of chain configurations. The scattering extracted from simulations shows good agreement with wide-angle X-ray scattering experiments. Amorphous P3HT exhibits broad scattering peaks: a high-q peak from interchain side-group correlations and a low-q peak from interchain backbone-backbone correlations. During amorphous to crystalline phase transitions, the distance between backbones along the side-group direction increases because of lack of interdigitation in the crystalline phase. Scattering from π-π stacking emerges only after crystallization takes place. Intrachain correlations contribute negligibly to the scattering from the amorphous and crystalline phases.

Tuning polymer-backbone coplanarity and conformational order to achieve high-performance printed all-polymer solar cells.

All-polymer solar cells (all-PSCs) offer improved morphological and mechanical stability compared with those containing small-molecule-acceptors (SMAs). They can be processed with a broader range of conditions, making them desirable for printing techniques. In this study, we report a high-performance polymer acceptor design based on bithiazole linker (PY-BTz) that are on par with SMAs. We demonstrate that bithiazole induces a more coplanar and ordered conformation compared to bithiophene due to the synergistic effect of non-covalent backbone planarization and reduced steric encumbrances. As a result, PY-BTz shows a significantly higher efficiency of 16.4% in comparison to the polymer acceptors based on commonly used thiophene-based linkers (i.e., PY-2T, 9.8%). Detailed analyses reveal that this improvement is associated with enhanced conjugation along the backbone and closer interchain π-stacking, resulting in higher charge mobilities, suppressed charge recombination, and reduced energetic disorder. Remarkably, an efficiency of 14.7% is realized for all-PSCs that are solution-sheared in ambient conditions, which is among the highest for devices prepared under conditions relevant to scalable printing techniques. This work uncovers a strategy for promoting backbone conjugation and planarization in emerging polymer acceptors that can lead to superior all-PSCs.

Negative Dielectric Constant of Water at a Metal Interface.

Water polarizability at a metal interface plays an essential role in electrochemistry. We devise a classical molecular dynamics approach with an efficient description of metal polarization and a novel ac field method to measure the local dielectric response of interfacial water. Water adlayers next to the metal surface exhibit higher-than-bulk in-plane and negative out-of-plane dielectric constants, the latter corresponding physically to overscreening of the applied field. If we account for the gap region at the interface, the average out-of-plane dielectric constant is quite low (ε_{⊥}≈2), in agreement with reported measurements on confined thin films.

Pulling simulation predicts mixing free energy for binary mixtures.

Predicting the mixing free energy of mixing for binary mixtures using simulations is challenging. We present a novel molecular dynamics (MD) simulation method to extract the chemical potential µ(X) for mixtures of species A and B. Each molecule of species A and B is placed in equal and opposite harmonic potentials ±(1/2)Uex(x) centered at the middle of the simulation box, resulting in a nonuniform mole fraction profile X(z) in which A is concentrated at the center, and B at the periphery. Combining these, we obtain Uex(X), the exchange chemical potential required to induce a given deviation of the mole fraction from its average. Simulation results for Uex(X) can be fitted to simple free energy models to extract the interaction parameter χ for binary mixtures. To illustrate our method, we investigate benzene-pyridine mixtures, which provide a good example of regular solution behavior, using both TraPPE united-atom and OPLS all-atom potentials, both of which have been validated for pure fluid properties. χ values obtained with the new method are consistent with values from other recent simulation methods. However, the TraPPE-UA results differ substantially from the χ obtained from VLE experimental data, while the OPLS-AA results are in reasonable agreement with experiment, highlighting the importance of accurate potentials in correctly representing mixture behavior.

Fast, Faithful Simulations of Donor-Acceptor Interface Morphology.

The local structure of conjugated polymers governs key optoelectronic properties, such as charge conduction and photogeneration at donor-acceptor interfaces. Because conjugated polymers are large, stiff, and relax slowly, all-atom molecular dynamics simulations are computationally expensive. Here, we describe a coarse-graining method that exploits the stiffness of constituent aromatic moieties by representing each moiety as rigidly bonded clusters of atoms wherein virtual sites replace several atoms. This approach significantly reduces the degrees of freedom while faithfully representing the shape and interactions of the moieties, resulting in 10 times faster simulations than all-atom simulations. Simulation of a donor polymer (P3HT) and a non-fullerene acceptor (O-IDTBR) validates the coarse-graining method by comparing structural properties from experiments, such as the density and persistence length. The fast simulation produces equilibrated systems with realistic morphologies. The simulation results of an equimolar mixture of P3HT, with a molecular weight of 1332 g mol-1, and an O-IDTBR mixture suggest that the interface width must be larger than 7 nm. Also, we investigate the effect of slow cooling on morphologies, particularly the number of close contacts that facilitates carrier transport. Slow cooling increases close contacts, and the effect is more pronounced in crystal-forming P3HT than in O-IDTBR, where bulky side-groups hinder crystal formation.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach.

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H2O-···-H2O), the free energy to transform an H3O+ cation into an H5O2+ cation, and the hydrogen bond free energy of protonated water clusters (H3O+-···-H2O and H5O2+-···-H2O). The computed equilibrium hydrogen bond free energy of H2O-···-H2O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H3O+ by roughly 1-2 kBT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H+ cation and H2O in solution were found to be stronger than between two H2O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.

A simple simulation model for complex coacervates.

When oppositely charged polyelectrolytes mix in an aqueous solution, associative phase separation gives rise to coacervates. Experiments reveal the phase diagram for such coacervates, and determine the impact of charge density, chain length and added salt. Simulations often use hybrid MC-MD methods to produce such phase diagrams, in support of experimental observations. We propose an idealized model and a simple simulation technique to investigate coacervate phase behavior. We model coacervate systems by charged bead-spring chains and counterions with short-range repulsions, of size equal to the Bjerrum length. We determine phase behavior by equilibrating a slab of concentrated coacervate with respect to swelling into a dilute phase of counterions. At salt concentrations below the critical point, the counterion concentration in the coacervate and dilute phases are nearly the same. At high salt concentrations, we find a one-phase region. Along the phase boundary, the total concentration of beads in the coacervate phase is nearly constant, corresponding to a "Bjerrum liquid''. This result can be extended to experimental phase diagrams by assigning appropriate volumes to monomers and salts.

Using osmotic pressure simulations to test potentials for ions.

This paper presents a new method to simulate the osmotic pressure of an ionic solution. Previous simulation methods confine ions between walls, and the osmotic pressure is inferred from the force required to maintain this confinement. In this work, we impose a harmonic potential on the ions to form a nonuniform concentration profile in the solution. As this profile arises from the force balance of the harmonic potential with the osmotic pressure, it can be used to determine the osmotic pressure across the entire concentration profile. This method can be performed without specialized programming, making it accessible to the general user. Using our method, we find that standard potentials for Na+ and Cl- ions need adjustments to be consistent with experimental osmotic pressure at high concentrations.

Tight binding models accurately predict band structures for copolymer semiconductors.

Conjugated polymers possess a wide range of desirable properties including accessible band gaps, plasticity, tunability, mechanical flexibility and synthetic versatility, making them attractive for use as active materials in organic photovoltaics (OPVs). In particular, push-pull copolymers, consisting of alternating electron-rich and electron-deficient moieties, offer broad optical absorption, tunable band gaps, and increased charge transfer between monomer units. However, the large number of possible monomer combinations to explore means screening OPV copolymers by first-principles quantum calculations is computationally intensive. If copolymer band structures could be rapidly computed from homopolymer data, potential materials could be screened more efficiently. In this work, we construct tight binding models of copolymer band structures with parameters determined by density functional theory (DFT) calculations on homopolymers. We use these models to predict copolymer valence and conduction bands, which compare well to direct DFT calculations of copolymer band structures.

Polaron hopping barriers and rates in semiconducting polymers.

Conjugated polymers are potential next-generation materials for organic electronic devices. The ability of these materials to transport charges is a key factor limiting their performance. Charge carriers in conjugated polymers are localized by disorder and polaronic effects. Charge transport in these materials is often described by thermally activated hopping, with a rate given by Marcus theory. The polaron hopping activation energy determines the temperature dependence of the Marcus rate. This energy barrier is dictated by the transition state, in which the charge carrier is equally divided between the initial and final locations. The prefactor for the polaron hopping rate is set by the charge tunneling rate between the initial and final locations. We use a tight-binding polaron model, in which charge carriers are stabilized by both nuclear reorganization and polarization of the surrounding dielectric, to compute the activation energy, charge tunneling rate and overall rate constant for intrachain and interchain charge hopping processes in poly(3-hexylthiophene) (P3HT) crystalline lamellae and amorphous melts. Charge transport in these two environments is limited by interchain hopping processes. Both hopping barriers and rates predicted by the model are in good agreement with experiments on a variety of crystalline and amorphous P3HT materials. Qualitatively, the barriers largely depend on how well the transition state is stabilized by polarization effects, and on the hopping integral between the initial and final locations, both of which penalize hopping over longer distances.

Thermal Fluctuations Lead to Cumulative Disorder and Enhance Charge Transport in Conjugated Polymers.

All conjugated polymers examined to date exhibit significant cumulative lattice disorder, although the origin of this disorder remains unclear. Using atomistic molecular dynamics (MD) simulations, the detailed structures for single crystals of a commonly studied conjugated polymer, poly(3-hexylthiophene-2,5-diyl) (P3HT) are obtained. It is shown that thermal fluctuations of thiophene rings lead to cumulative disorder of the lattice with an effective paracrystallinity of about 0.05 in the π-π stacking direction. The thermal-fluctuation-induced lattice disorder can in turn limit the apparent coherence length that can be observed in diffraction experiments. Calculating mobilities from simulated crystal structures demonstrates that thermal-fluctuation-induced lattice disorder even enhances charge transport in P3HT. The mean inter-chain charge transfer integral is enhanced with increasing cumulative lattice disorder, which in turn leads to pathways for fast charge transport through crystals.

Energetics of exciton binding and dissociation in polythiophenes: a tight binding approach.

Organic photovoltaics offer a potential low-cost alternative to inorganic solar cells. Crucial to the performance of these devices is the generation of free charges, which occurs through the dissociation of excitons. Here we study excitons in polythiophenes, their stability and energetics of dissociation and separation into charge carriers. Excitons are excited electron and hole pairs bound by Coulomb interactions. To separate into unbound charges, the exciton binding energy must be overcome. We use a tight binding Hamiltonian to describe the exciton binding energy and its dissociation potential, for an exciton confined to a single polymer chain. Our model accounts for polaronic effects, arising from reorganization of nuclei and from polarization of the surrounding dielectric, which stabilize the separated carriers and thereby affect the exciton dissociation potential. We examine the effects of an applied electric field on the dissociation potential, and relate the field strength necessary to unbind the hole-electron pair to the maximum attractive Coulomb force between them. We apply our model to study the exciton at a donor-acceptor interface on a block-copolymer. Interfacial polarization alters the exciton binding potential, rendering the hole-electron pair easier to unbind.

Anisotropic Growth of Silver Nanoparticles Is Kinetically Controlled by Polyvinylpyrrolidone Binding.

Polyvinylpyrrolidone (PVP) is used in the synthesis of Ag nanoparticles (NPs) with controlled shape, most commonly producing cubes. The mechanism for shape control is unclear but believed by many to be caused by preferential binding of PVP to Ag(100) facets compared to Ag(111) facets and assumed by most to be the result of thermodynamic control, whereby facets with lower interfacial free energy predominate. To investigate this mechanism, we measured adsorption isotherms of PVP on different-shaped Ag NPs, to determine the thermodynamics of PVP adsorption to Ag(100) and Ag(111) facets. The equilibrium adsorption constant is independent of PVP molecular weight and depends only weakly on NP shape (and thus Ag facet). The equilibrium adsorption constant for PVP on Ag(111) (2.8 M-1) is about half that on Ag(100) (5 M-1). From a Wulff construction, this difference is not nearly enough to produce cubes via thermodynamic control. This result indicates the importance of kinetic control of the Ag nanoparticle shape by PVP, as has recently been proposed.

A geometrical criterion for glass transition in soft-sphere fluids.

As glass-forming fluids become colder and denser, structural rearrangements become slow and eventually cease. For hard-sphere fluids, percolation of particles unable to change neighbors (T1-inactive particles) signals the glass transition. To investigate this geometrical criterion for mobility in soft-sphere systems, we simulate monodisperse fluids interacting with a generalized Weeks-Chandler-Andersen (WCA) potential in metastable equilibrium, using our previously developed crystal-avoiding method. We find that the vanishing diffusivity as the glass transition is approached can be described by a power law below the onset temperature of super-Arrhenius behavior. By mapping the soft spheres to hard spheres based on mean collision energy, we find that the diffusivity versus effective volume fraction curves collapse onto the hard-sphere curve for all systems studied. We find that the onset of super-Arrhenius behavior and the MCT dynamic glass transition correlate well with temperature when the T1-inactive particles form clusters of two particles on average and when the T1-inactive clusters percolate the entire system, respectively. Our findings provide new insight into the structural origin of glassy dynamics.

Nematic Order Imposes Molecular Weight Effect on Charge Transport in Conjugated Polymers.

Nematic order, in the bulk or at interfaces, is ubiquitous for semiflexible conjugated polymers. Nevertheless, the effect of liquid crystalline order on charge transport remains unclear. Using an analytical model, we demonstrate that nematic order leads to an enhancement in charge mobilities when compared to isotropic chains. Furthermore, we predict a quadratic dependence of the charge mobility on molecular weight of the chains. Analysis of the probability of forming hairpin defects also shows how the persistence length affects charge transport in conjugated polymers. We speculate that the prevalence of nematic order in conjugated polymers explains the reported increase in charge mobilities with molecular weight.

Polaron formation mechanisms in conjugated polymers.

In semiconducting polymers, interactions with conformational degrees of freedom can localize charge carriers, and strongly affect charge transport. Polarons can form when charges induce deformations of the surrounding medium, including local vibrational modes or dielectric polarization. These deformations then interact attractively with the charge, tending to localize it. First we investigate vibrational polaron formation in poly(3-hexylthiophene) [P3HT], with a tight-binding model for charges hopping between adjacent rings, coupled to ring distortions. We use density functional theory (DFT) calculations to determine coupling constants, including the "spring constant" for ring distortions and the coupling to the charge carrier. On single chains, we find only broad, weakly bound polarons by this mechanism. In 2d crystalline layers of P3HT, even weak transverse hopping between chains destabilizes this polaron. Then, we consider polarons stabilized by dielectric polarization, described semiclassically with a polarizable continuum interacting with the carrier wavefunction. In contrast to vibrational polarons, we find dielectrically stabilized polarons in P3HT are narrower, more strongly bound, and stable in 2d crystalline layers.

Predicting Flory-Huggins χ from Simulations.

We introduce a method, based on a novel thermodynamic integration scheme, to extract the Flory-Huggins χ parameter as small as 10^{-3}kT for polymer blends from molecular dynamics (MD) simulations. We obtain χ for the archetypical coarse-grained model of nonpolar polymer blends: flexible bead-spring chains with different Lennard-Jones interactions between A and B monomers. Using these χ values and a lattice version of self-consistent field theory (SCFT), we predict the shape of planar interfaces for phase-separated binary blends. Our SCFT results agree with MD simulations, validating both the predicted χ values and our thermodynamic integration method. Combined with atomistic simulations, our method can be applied to predict χ for new polymers from their chemical structures.

Extended Ensemble Approach to Transferable Potentials for Low-Resolution Coarse-Grained Models of Ionomers.

We develop an extended ensemble method for constructing transferable, low-resolution coarse-grained (CG) models of polyethylene-oxide (PEO)-based ionomer chains with varying composition at multiple temperatures. In particular, we consider ionomer chains consisting of 4 isophthalate groups, which may be neutral or sulfonated, that are linked by 13 PEO repeat units. The CG models represent each isophthalate group with a single CG site and also explicitly represent the diffusing sodium counterions but do not explicitly represent the PEO backbone. We define the extended ensemble as a collection of equilibrium ensembles that are obtained from united atom (UA) simulations at 2 different temperatures for 7 chemically distinct ionomers with varying degrees of sulfonation. We employ a global force-matching method to determine the set of interaction potentials that, when appropriately combined, provide an optimal approximation to the many-body potential of mean force for each system in the extended ensemble. This optimized xn force field employs long-ranged Coulomb potentials with system-specific dielectric constants that systematically decrease with increasing sulfonation and temperature. An empirical exponential model reasonably describes the sensitivity of the dielectric to sulfonation, but we find it more challenging to model the temperature-dependence of the dielectrics. Nevertheless, given appropriate dielectric constants, the transferable xn force field reasonably describes the ion pairing that is observed in the UA simulations as a function of sulfonation and temperature. Remarkably, despite eliminating any explicit description of the PEO backbone, the CG model predicts string-like ion aggregates that appear qualitatively consistent with the ionomer peak observed in X-ray scattering experiments and, moreover, with the temperature dependence of this peak.