Ideal isotropic auxetic networks from random networks.

Auxetic materials are characterized by a negative Poisson's ratio, ν. As the Poisson's ratio approaches the lower isotropic mechanical limit of ν = -1, materials show enhanced resistance to impact and shear, making them suitable for applications ranging from robotics to impact mitigation. Past experimental efforts aimed at reaching the ν = -1 limit have resulted in highly anisotropic materials, which show a negative Poisson's ratio only when subjected to deformations along specific directions. Isotropic designs have only attained moderately auxetic behavior or have led to solutions that cannot be manufactured in 3D. Here, we present a design strategy to create isotropic structures from disordered networks, which result in Poisson's ratios as low as ν = -0.98. The materials conceived through this approach are successfully fabricated in the laboratory and behave as predicted. ν depends on network structure and bond strengths; this sheds light on the motifs which lead to auxetic behavior. The ideas introduced here can be generalized to 3D, a wide range of materials, and a spectrum of length scales, thereby providing a general platform that could impact technology.

Electronic structure at coarse-grained resolutions from supervised machine learning.

Computational studies aimed at understanding conformationally dependent electronic structure in soft materials require a combination of classical and quantum-mechanical simulations, for which the sampling of conformational space can be particularly demanding. Coarse-grained (CG) models provide a means of accessing relevant time scales, but CG configurations must be back-mapped into atomistic representations to perform quantum-chemical calculations, which is computationally intensive and inconsistent with the spatial resolution of the CG models. A machine learning approach, denoted as artificial neural network electronic coarse graining (ANN-ECG), is presented here in which the conformationally dependent electronic structure of a molecule is mapped directly to CG pseudo-atom configurations. By averaging over decimated degrees of freedom, ANN-ECG accelerates simulations by eliminating backmapping and repeated quantum-chemical calculations. The approach is accurate, consistent with the CG spatial resolution, and can be used to identify computationally optimal CG resolutions.

Structural Correlations and Percolation in Twisted Perylene Diimides Using a Simple Anisotropic Coarse-Grained Model.

Large, twisted, and fused conjugated molecular architectures have begun to appear more prominently in the organic semiconductor literature. From a modeling perspective, such structures present a challenge to conventional simulation techniques; atomistic resolutions are computationally inefficient, while traditional isotropic coarse-grained models do not capture the inherent anisotropies of the molecules. In this work, we develop a simple coarse-grained model that explicitly incorporates the anisotropy of these molecular architectures, thereby providing a route toward analyzing π-stacking, and thus qualitative electronic structure, at a computationally efficient coarse-grained resolution. Our simple coarse-grained model maintains relative orientations of conjugated rings, as well as inter-ring dihedrals, that are critical for understanding electronic and excitonic transport in bulk systems. We apply this model to understand structural correlations in several recently synthesized perylene diimide (PDI)-based organic semiconductors. Twisted and nonplanar molecular architectures are found to promote amorphous morphologies while maintaining local π-stacking. A graph theoretical network analysis demonstrates that these twisted molecules are more likely to form percolating three-dimensional pathways for charge motion than strictly planar molecules, which show connectivity in only one dimension.

Optimizing self-consistent field theory block copolymer models with X-ray metrology.

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

Quantitative Three-Dimensional Characterization of Block Copolymer Directed Self-Assembly on Combined Chemical and Topographical Prepatterned Templates.

Characterization of the three-dimensional (3D) structure in directed self-assembly (DSA) of block copolymers is crucial for understanding the complex relationships between the guiding template and the resulting polymer structure so DSA could be successfully implemented for advanced lithography applications. Here, we combined scanning transmission electron microscopy (STEM) tomography and coarse-grain simulations to probe the 3D structure of P2VP-b-PS-b-P2VP assembled on prepatterned templates using solvent vapor annealing. The templates consisted of nonpreferential background and raised guiding stripes that had PS-preferential top surfaces and P2VP-preferential sidewalls. The full 3D characterization allowed us to quantify the shape of the polymer domains and the interface between domains as a function of depth in the film and template geometry and offered important insights that were not accessible with 2D metrology. Sidewall guiding was advantageous in promoting the alignment and lowering the roughness of the P2VP domains over the sidewalls, but incommensurate confinement from the increased topography could cause roughness and intermittent dislocations in domains over the background region at the bottom of the film. The 3D characterization of bridge structures between domains over the background and breaks within domains on guiding lines sheds light on possible origins of common DSA defects. The positional fluctuations of the PS/P2VP interface between domains showed a depth-dependent behavior, with high levels of fluctuations near both the free surface of the film and the substrate and lower fluctuation levels in the middle of the film. This research demonstrates how 3D characterization offers a better understanding of DSA processes, leading to better design and fabrication of directing templates.