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Understanding bond rupture in polymer networks remains a fundamental challenge due to the interplay of network topology and condensed phase effects. In this work, we introduce a predictive approach for determining bond rupture in thermosets based on shortest paths (SPs) analysis of the network topology. This method enumerates SP sets in networks with periodic boundary conditions, with applications to both all-atom and coarse-grained simulations. We find that bond rupture is most likely to initiate on the first (shortest) SP in the thermoset network and the strain at which the first bond ruptures is linearly correlated with the topological path length. As a result, one can predict the first bond rupture by computing the first SP directly from the initial thermoset topology without resorting to MD simulations. Furthermore, the specific bond rupture location along the first SP follows a probability distribution associated with the SP-based betweenness centrality. Subsequent bond rupture events are dictated by the instantaneous SP of partially broken networks. Moreover, we quantify the length scale dependence of SP distributions, introducing a means of partially bridging the observed ductile rupture in molecular simulations and brittle rupture in experiments. 

Understanding the relationship between multiscale morphology and electronic structure is a grand challenge for semiconducting soft materials. Computational studies aimed at characterizing these multiscale relationships require the complex integration of quantum-chemical (QC) calculations, all-atom and coarse-grained (CG) molecular dynamics simulations, and back-mapping approaches. However, the integration and scalability of these methods pose substantial computational challenges that limit their application to the requisite length scales of soft material morphologies. Here, we demonstrate the bottom-up electronic coarse-graining (ECG) of morphology-dependent electronic structure in the liquid-crystal-forming semiconductor, 2-(4-methoxyphenyl)-7-octyl-benzothienobenzothiophene (BTBT). ECG is applied to construct density functional theory (DFT)-accurate valence band Hamiltonians of the isotropic and smectic liquid crystal (LC) phases using only the CG representation of BTBT. By bypassing the atomistic resolution and its prohibitive computational costs, ECG enables the first calculations of the morphology dependence of the electronic structure of charge carriers across LC phases at the ~20 nm length scale, with robust statistical sampling. kinetic Monte Carlo (kMC) simulations reveal a strong morphology dependence on zero-field charge mobility among different LC phases as well as the presence of two-molecule charge carriers that act as traps and hinder charge transport. We leverage these results to further evaluate the feasibility of developing truly mesoscopic, field-based ECG models in future works. The fully CG approach to electronic property predictions in LC semiconductors opens a new computational direction for designing electronic processes in soft materials at their characteristic length scales. 

Bottom-up methods for coarse-grained (CG) molecular modeling are critically needed to establish rigorous links between atomistic reference data and reduced molecular representations. For a target molecule, the ideal reduced CG representation is a function of both the conformational ensemble of the system and the target physical observable(s) to be reproduced at the CG resolution. However, there is an absence of algorithms for selecting CG representations of molecules from which complex properties, including molecular electronic structure, can be accurately modeled. We introduce continuously gated message passing (CGMP), a graph neural network (GNN) method for atomically decomposing molecular electronic structure sampled over conformational ensembles. CGMP integrates 3D-invariant GNNs and a novel gated message passing system to continuously reduce the atomic degrees of freedom accessible for electronic predictions, resulting in a one-shot importance ranking of atoms contributing to a target molecular property. Moreover, CGMP provides the first approach by which to quantify the degeneracy of “good” CG representations conditioned on specific prediction targets, facilitating the development of more transferable CG representations. We further show how CGMP can be used to highlight multiatom correlations, illuminating a path to developing CG electronic Hamiltonians in terms of interpretable collective variables for arbitrarily complex molecules. 

Despite growing interest in polymers under extreme conditions, most atomistic molecular dynamics simulations cannot describe the bond scission events underlying failure modes in polymer networks undergoing large strains. In this work, we propose a physics-based machine learning approach that can detect and perform bond breaking with near quantum-chemical accuracy on-the-fly in atomistic simulations. Particularly, we demonstrate that by coarse-graining highly correlated neighboring bonds, the prediction accuracy can be dramatically improved. By comparing with existing quantum mechanics/molecular mechanics methods, our approach is approximately two orders of magnitude more efficient and exhibits improved sensitivity toward rare bond breaking events at low strain. The proposed bond breaking molecular dynamics scheme enables fast and accurate modeling of strain hardening and material failure in polymer networks and can accelerate the design of polymeric materials under extreme conditions. 

Conjugated polyelectrolytes (CPEs) are a rising class of organic mixed ionic-electronic conductors, with applications in bio-interfacing electronics and energy harvesting and storage devices. Here, we employ a quantum mechanically informed coarse-grained model coupled with semiclassical rate theory to generate a first view of semidilute CPE morphologies and their corresponding ionic and electronic transport properties. We observe that the poor solvent quality of CPE backbones drives the formation of electrostatically repulsive fibers capable of forming percolating networks at semi-dilute concentrations. The thickness of the fibers and the degree of intrafiber connectivity are found to strongly influence electronic transport. Calculated structure factors reveal that fiber formation alters the position and scaling of the inter-chain PE peak relative to good solvent predictions and induces a narrower distribution of interchain spacings. We also observe that electrostatic interactions play a significant role in determining CPE morphology, but have only a small impact on the local site energetics. This work presents a significant step forward in the ability to predict CPE morphology and ion-electron transport properties, and provides insights into how morphology influences electronic and ionic transport in conjugated materials. 

We employ deep kernel learning electronic coarse-graining (DKL-ECG) with approximate Gaussian processes as a flexible and scalable framework for learning heteroscedastic electronic property distributions as a smooth function of coarse-grained (CG) configuration. The appropriateness of the Gaussian prior on predictive CG property distributions is justified as a function of CG model resolution by examining the statistics of target distributions. The certainties of predictive CG distributions are shown to be limited by CG model resolution with DKL-ECG predictive noise converging to the intrinsic physical noise induced by the CG mapping operator for multiple chemistries. Further analysis of the resolution dependence of learned CG property distributions allows for the identification of CG mapping operators that capture CG degrees of freedom with strong electron–phonon coupling. We further demonstrate the ability to construct the exact quantum chemical valence electronic density of states (EDOS), including behavior in the tails of the EDOS, from an entirely CG model by combining iterative Boltzmann inversion and DKL-ECG. DKL-ECG provides a means of learning CG distributions of all-atom properties that are traditionally “lost” in CG model development, introducing a promising methodological alternative to backmapping algorithms commonly employed to recover all-atom property distributions from CG simulations.