Systematic Coarse-Graining of the Dynamics of Self-Attractive Semiflexible Polymers

Competing single-chain folding and multi-chain aggregation pathways control solution-phase aggregate morphology of organic semiconducting polymers

Understanding the solution-phase behaviour of organic semiconducting polymers is important for systematically improving the performance of devices based on solution-processed thin films of these molecules. Conventional polymer theory predicts that polymer conformations become more compact as solvent quality decreases, but recent experiments have shown the high-performance organic-semiconducting polymer P(NDI2OD-T2) to form extended rod-like aggregates much larger than a single chain in poor solvents, with the formation of these extended aggregates correlated with enhanced electron mobility in films deposited from these solutions. We explain the unexpected formation of extended aggregates using a novel coarse-grained simulation model of P(NDI2OD-T2) that we have developed to study the effect of solvent quality on its solution-phase behaviour. In poor solvents, we find that aggregation through only a few monomers gives effectively inseparable chains, leading to the formation of extended structures of partially overlapping chains via non-equilibrium assembly. This behaviour requires that multi-chain aggregation occurs faster than chain folding, which we show is the case for the chain lengths and concentrations shown experimentally to form rod-like aggregates. This kinetically controlled process introduces a dependence of aggregate structure on concentration, chain length, and chain flexibility, which we show is able to reconcile experimental findings and is generalisable to the solution-phase assembly of other semiflexible polymers.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.

Photovoltaic Blend Microstructure for High Efficiency Post-Fullerene Solar Cells. To Tilt or Not To Tilt?

Achieving efficient polymer solar cells (PSCs) requires a structurally optimal donor-acceptor heterojunction morphology. Here we report the combined experimental and theoretical characterization of a benzodithiophene-benzothiadiazole donor polymer series (PBTZF4-R; R = alkyl substituent) blended with the non-fullerene acceptor ITIC-Th and analyze the effects of substituent dimensions on blend morphology, charge transport, carrier dynamics, and PSC metrics. Varying substituent dimensions has a pronounced effect on the blend morphology with a direct link between domain purity, to some extent domain dimensions, and charge generation and collection. The polymer with the smallest alkyl substituent yields the highest PSC power conversion efficiency (PCE, 11%), reflecting relatively small, high-purity domains and possibly benefiting from "matched" donor polymer-small molecule acceptor orientations. The distinctive morphologies arising from the substituents are investigated using molecular dynamics (MD) simulations which reveal that substituent dimensions dictate a well-defined set of polymer conformations, in turn driving chain aggregation and, ultimately, the various film morphologies and mixing with acceptor small molecules. A straightforward energetic parameter explains the experimental polymer domain morphological trends, hence PCE, and suggests strategies for substituent selection to optimize PSC materials morphologies.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Gelation, Phase Separation, and Fibril Formation in Aqueous Hydroxypropylmethylcellulose Solutions

The thermoresponsive behavior of a hydroxypropylmethylcellulose (HPMC) sample in aqueous solutions has been studied by a powerful combination of characterization tools, including rheology, turbidimetry, cryogenic transmission electron microscopy (cryoTEM), light scattering, small-angle neutron scattering (SANS), and small-angle X-ray scattering (SAXS). Consistent with prior literature, solutions with concentrations ranging from 0.3 to 3 wt % exhibit a sharp drop in the dynamic viscoelastic moduli G' and G″ upon heating near 57 °C. The drop in moduli is accompanied by an abrupt increase in turbidity. All the evidence is consistent with this corresponding to liquid-liquid phase separation, leading to polymer-rich droplets in a polymer-depleted matrix. Upon further heating, the moduli increase, and G' exceeds G″, corresponding to gelation. CryoTEM in dilute solutions reveals that HPMC forms fibrils at the same temperature range where the moduli increase. SANS and SAXS confirm the appearance of fibrils over a range of concentration, and that their average diameter is ca. 18 nm; thus gelation is attributable to formation of a sample-spanning network of fibrils. These results are compared in detail with the closely related and well-studied methylcellulose (MC). The HPMC fibrils are generally shorter, more flexible, and contain more water than with MC, and the resulting gel at high temperatures has a much lower modulus. In addition to the differences in fibril structure, the key distinction between HPMC and MC is that the former undergoes liquid-liquid phase separation prior to forming fibrils and associated gelation, whereas the latter forms fibrils first. These results and their interpretation are compared with the prior literature, in light of the relatively recent discovery of the propensity of MC and HPMC to self-assemble into fibrils on heating.

A Simple Analytical Model for Predicting the Collapsed State of Self-Attractive Semiflexible Polymers

We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy ( γ s ), energy of bundle end folds ( γ e ), and bending energy per unit length in a torus ( γ b ). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain.

Decreasing Polymer Flexibility Improves Wetting and Dispersion of Polymer-Grafted Particles in a Chemically Identical Polymer Matrix

We present a molecular dynamics simulation study of nanocomposites containing homopolymer-grafted particles in a homopolymer matrix, where the graft and matrix chemistries are identical, to elucidate the effect of polymer flexibility on the wetting of the grafted layer by the matrix and the nanocomposite morphology. Decreasing flexibility of the graft and matrix causes increased wetting of the grafted layer by the matrix. This increased wetting of the grafted layer with decreasing flexibility is more significantly driven by decreasing the graft flexibility than by decreasing the matrix flexibility. This is due to a large increase in mixing entropy of the graft and matrix upon wetting rather than the reduction in conformational entropy loss of matrix upon wetting. Due to this improved wetting with decreasing flexibility of the graft and matrix, we observe increased particle dispersion in the polymer matrix.