Systematic modification of functionality in disordered elastic networks through free energy surface tailoring.

A combined machine learning-physics-based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective variables, it becomes possible to identify critical molecular interactions in the considered system, the modulation of which enables a systematic tailoring of the system's free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity and points to its potential for design of complex molecular systems.

Relative effects of polymer composition and sample preparation on glass dynamics.

Modern design of common adhesives, composites and polymeric parts makes use of polymer glasses that are stiff enough to maintain their shape under a high stress while still having a ductile behavior after the yield point. Typically, material compositions are tuned with co-monomers, polymer blends, plasticizers, or other additives to arrive at a tradeoff between the elastic modulus and toughness. In contrast, strong changes to the mechanics of a glass are possible by changing only the molecular packing during vitrification or even deep in the glassy state. For example, physical aging or processing techniques such as physical vapor deposition increase the density, embrittle the material, and increase elastic modulus. Here, we use molecular simulations, validated by positron annihilation lifetime spectroscopy (PALS) and quasi-elastic neutron scattering, to understand the free volume distribution and the resulting dynamics of glassy co-polymers where the composition is systemically varied between polar 5-norbornene-2-methanol (NBOH) and non-polar ethylidene norbornene (ENB) monomers. In these polymer glasses, we analyze the structural features of the unoccupied volume using clustering analysis, where the clustering is parameterized to reproduce experimental measurements of the same features from PALS. Further, we analyze the dynamics, quantified by the Debye-Waller factor, and compare the results with softer, lower density states. Our findings indicate that faster structural relaxations and potentially improved ductility are possible through changes to the geometric structure and fraction of the free volume, and that the resulting changes to the glass dynamics are comparable to large changes in the monomer composition.

Predicting plasticity of amorphous solids from instantaneous normal modes.

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the VDOS of affinely strained configurations at varying strain values. The affine strain, found analytically on the static (undeformed) snapshot of the glass, leads to configurations that are rich with soft low-energy modes as well as unstable modes (negative eigenvalues) that are otherwise completely "washed out" and lost if one lets the system fully relax after strain. This procedure is consistent with the structure of NALD. The INM spectrum of deformed states allows for the analytical prediction of the stress-strain curve of a model glass. Good parameter-free quantitative agreement is shown between the prediction and simulations of athermal quasistatic shear of a coarse-grained polymer glass.

Plasticity in Amorphous Solids Is Mediated by Topological Defects in the Displacement Field.

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatiotemporal correlations in the undeformed glass that may trigger plastic instability. In contrast, in this Letter we show that the topological defects that correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) that are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular nonlocal peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between antiparallel DTDs; and (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45° for uniaxial deformations, as widely observed in experiments and simulations.

Vapor-Deposited Glasses Highlight the Role of Density in Photostability.

Photoresponsive molecules can be integrated into glassy materials to probe the local environment and invoke responsive changes in polymer behavior. For example, recent experiments and simulations have studied increased stability in vapor-deposited glasses by examining the photoisomerization rate of a probe molecule. At the theoretical level, past work relied on coarse-grained simulations to explain the role of photoisomerization on glass behavior. In order to effectively exploit these molecular probes, an ability to quantify how the local environment influences the photoisomerization rate is needed. In this work, we present all-atom molecular-dynamics (MD) simulations of molecular glasses of photoresponsive azobenzene (AB) molecules. The stability of these in-silico samples is probed using photoisomerization, where AB molecules can undergo trans → cis transition upon light exposure. Vapor-deposited and bulk-cooled glasses of AB are simulated using a classical dihedral-switching potential developed by Böckmann et al. (J. Phys. Chem. A 2010, 114, 745-754) to model the photoisomerization process. The MD simulations include thousands of molecules and run for tens of nanoseconds. These size and time scales allow us to explore the broad distribution of photoisomerization wait times, which yields two results. First, the wait-time distributions for both physical vapor deposition and bulk-cooled glasses depend strongly on sample and local density, showing that density or local packing is a primary factor in glass stability against photoisomerization and the experimentally measured photoresponse. Second, the distribution follows a power-law with exponent b ≈ 1.25-1.3 that extends to longer times with increasing density. The power-law distribution suggests a connection with previous experiments that related barriers to photoisomerization with an effective photoisomerization temperature.

Growth and arrest of topological cycles in small physical networks.

The chordless cycle sizes of spatially embedded networks are demonstrated to follow an exponential growth law similar to random graphs if the number of nodes [Formula: see text] is below a critical value [Formula: see text] For covalent polymer networks, increasing the network size, as measured by the number of cross-link nodes, beyond [Formula: see text] results in a crossover to a new regime in which the characteristic size of the chordless cycles [Formula: see text] no longer increases. From this result, the onset and intensity of finite-size effects can be predicted from measurement of [Formula: see text] in large networks. Although such information is largely inaccessible with experiments, the agreement of simulation results from molecular dynamics, Metropolis Monte Carlo, and kinetic Monte Carlo suggests the crossover is a fundamental physical feature which is insensitive to the details of the network generation. These results show random graphs as a promising model to capture structural differences in confined physical networks.

Monodisperse Polymer Melts Crystallize via Structurally Polydisperse Nanoscale Clusters: Insights from Polyethylene.

This study demonstrates that monodisperse entangled polymer melts crystallize via the formation of nanoscale nascent polymer crystals (i.e., nuclei) that exhibit substantial variability in terms of their constituent crystalline polymer chain segments (stems). More specifically, large-scale coarse-grain molecular simulations are used to quantify the evolution of stem length distributions and their properties during the formation of polymer nuclei in supercooled prototypical polyethylene melts. Stems can adopt a range of lengths within an individual nucleus (e.g., ∼1-10 nm) while two nuclei of comparable size can have markedly different stem distributions. As such, the attainment of chemically monodisperse polymer specimens is not sufficient to achieve physical uniformity and consistency. Furthermore, stem length distributions and their evolution indicate that polymer crystal nucleation (i.e., the initial emergence of a nascent crystal) is phenomenologically distinct from crystal growth. These results highlight that the tailoring of polymeric materials requires strategies for controlling polymer crystal nucleation and growth at the nanoscale.

Divining the shape of nascent polymer crystal nuclei.

We demonstrate that nascent polymer crystals (i.e., nuclei) are anisotropic entities with neither spherical nor cylindrical geometry, in contrast to previous assumptions. In fact, cylindrical, spherical, and other high symmetry geometries are thermodynamically unfavorable. Moreover, postcritical transitions are necessary to achieve the lamellae that ultimately arise during the crystallization of semicrystalline polymers. We also highlight how inaccurate treatments of polymer nucleation can lead to substantial errors (e.g., orders of magnitude discrepancies in predicted nucleation rates). These insights are based on quantitative analysis of over four million crystal clusters from the crystallization of prototypical entangled polyethylene melts. New comprehensive bottom-up models are needed to capture polymer nucleation.

A coarse-grain model for entangled polyethylene melts and polyethylene crystallization.

The Shinoda-DeVane-Klein (SDK) model is herein demonstrated to be a viable coarse-grain model for performing molecular simulations of polyethylene (PE), affording new opportunities to advance molecular-level, scientific understanding of PE materials and processes. Both structural and dynamical properties of entangled PE melts are captured by the SDK model, which also recovers important aspects of PE crystallization phenomenology. Importantly, the SDK model can be used to represent a variety of materials beyond PE and has a simple functional form, making it unique among coarse-grain PE models. This study expands the suite of tools for studying PE in silico and paves the way for future work probing PE and PE-based composites at the molecular level.

Identifying Nonaffine Softening Modes in Glassy Polymer Networks: A Pathway to Chemical Design.

Using molecular simulations and theory, we develop an explicit mapping of the contribution of molecular relaxation modes in glassy thermosets to the shear modulus, where the relaxations were tuned by altering the polarity of side groups. Specifically, motions at the domain, segmental, monomer, and atomic levels are taken from molecular dynamics snapshots and directly linked with the viscoelasticity through a framework based in the lattice dynamics of amorphous solids. This unique approach provides direct insight into the roles of chemical groups in the stress response, including the time scale and spatial extent of relaxations during mechanics. Two thermoset networks with differing concentrations of polar side groups were examined, dicyclopentadiene (DCPD) and 5-norbornene-2-methanol (NBOH). A machine learning method is found to be effective for quantifying large-scale correlated motions, while more local chemical relaxations are readily identified by direct inspection. The approach is broadly applicable and enables rapid predictions of the frequency-dependent modulus for any glass.

Mechanics and nanovoid nucleation dynamics: effects of polar functionality in glassy polymer networks.

We use molecular simulations and experiments to rationalize the properties of a class of networks based on dicyclopentadiene (DCPD), a polymer with excellent fracture toughness and a high glass transition temperature (Tg), copolymerized with 5-norbornene-2-methanol (NBOH). DCPD is a highly non-polar hydrocarbon, while NBOH contains a hydroxy group, introducing polar functionality and hydrogen bonds (H-bonds). NBOH thus represents a possible route to improve the chemical compatibility of DCPD-based networks with less-hydrophobic materials. We systematically vary the NBOH content (polar chemistry) in DCPD networks, while keeping other network parameters nearly constant, including the molecular weight between cross-links, chain rigidity, and Tg. Using molecular dynamics (MD) simulations, we quantify the thermovolumetric and mechanical properties, including Tg, cohesive energy density, stiffness, and yield strength. We compare these results with experiments on networks of similar composition, finding good agreement. The relation between these properties and polar chemistry are studied by examining a secondary network of physical cross-links, formed by hydrogen bonds between NBOH units. Further, we examine nanovoid formation, an energy dissipation mechanism hypothesized to contribute to the toughness of pDCPD. Using metadynamics to accelerate sampling, we quantify the nanovoid nucleation rate under hydrostatic tension, similar to the stress state in the plastic zone preceding a crack tip. Small additions of NBOH have minimal effect, but the rate drops steeply with larger amounts. Several properties are mapped at nanometer scales, including stiffness and mobility, and associated with void nucleation. Estimates of the length- and time-scale of the plastic zone near a crack tip are used in discussing nanovoid formation as a plausible toughening mechanism in these materials. Overall, the results suggest that pDCPD tolerates the addition of some polar chemistry without degrading its excellent mechanical properties.

Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics.

We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approach to the glass transition. These results provide evidence that the mechanical glass transition itself is continuous and thus represents a crossover rather than a true phase transition. The relatively sharp drop of the low-frequency storage modulus across the glass transition temperature can be explained mechanistically within the proposed theory: the proliferation of low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy excitations) is directly responsible for the rapid growth of a negative non-affine contribution to the storage modulus.

Influence of molecular weight between crosslinks on the mechanical properties of polymers formed via ring-opening metathesis.

The apparent molecular weight between crosslinks (Mc,a) in a polymer network plays a fundamental role in the network mechanical response. We systematically varied Mc,a independent of strong noncovalent bonding by using ring-opening metathesis polymerization (ROMP) to co-polymerize dicyclopentadiene (DCPD) with a chain extender that increases Mc,a or a di-functional crosslinker that decreases Mc,a. We compared the ROMP series quasi-static modulus (E), tensile yield stress (σy), and fracture toughness (KIC and GIC) in the glassy regime with literature data for more polar thermosets. ROMP resins showed high KIC (>1.5 MPa m0.5), high GIC (>1000 J m-2), and 4-5 times higher high rate impact resistance than typical polar thermosets with similar Tg values (100 °C to 178 °C). The overall E values were lower for ROMP systems. The σy dependence on Mc,a and T-Tg for ROMP resins was qualitatively similar to more polar thermosets, but the overall σy values were lower. In contrast to more polar thermosets, the KIC and GIC values of the ROMP resins showed strong Mc,a and T-Tg dependence. High rate impact (∼104-105 s-1) trends were similar to the KIC and GIC behavior, but were also correlated to σy. Overall, a ductile failure mode was observed for quasi-static and high rate results for a linear ROMP polymer (Mc,a = 1506 g mol-1 due to chain entanglement), and this gradually transitioned to a fully brittle failure mode for highly crosslinked ROMP polymers (Mc,a ≤ 270 g mol-1). Molecular dynamics (MD) simulations showed that low Mc,a ROMP resins were more likely to form molecular scale nanovoids. The higher chain stiffness in low Mc,a ROMP resins inhibited stress relaxation in the vicinity of these nanovoids, which correlated with brittle mechanical responses. Overall, these differences in mechanical properties were attributed to the weak non-covalent interactions in ROMP resins.

Topological structure and mechanics of glassy polymer networks.

The influence of chain-level network architecture (i.e., topology) on mechanics was explored for unentangled polymer networks using a blend of coarse-grained molecular simulations and graph-theoretic concepts. A simple extension of the Watts-Strogatz model is proposed to control the graph properties of the network such that the corresponding physical properties can be studied with simulations. The architecture of polymer networks assembled with a dynamic curing approach were compared with the extended Watts-Strogatz model, and found to agree surprisingly well. The final cured structures of the dynamically-assembled networks were nearly an intermediate between lattice and random connections due to restrictions imposed by the finite length of the chains. Further, the uni-axial stress response, character of the bond breaking, and non-affine displacements of fully-cured glassy networks were analyzed as a function of the degree of disorder in the network architecture. It is shown that the architecture strongly affects the network stability, flow stress, onset of bond breaking, and ultimate stress while leaving the modulus and yield point nearly unchanged. The results show that internal restrictions imposed by the network architecture alter the chain-level response through changes to the crosslink dynamics in the flow regime and through the degree of coordinated chain failure at the ultimate stress. The properties considered here are shown to be sensitive to even incremental changes to the architecture and, therefore, the overall network architecture, beyond simple defects, is predicted to be a meaningful physical parameter in the mechanics of glassy polymer networks.

Nanovoid formation and mechanics: a comparison of poly(dicyclopentadiene) and epoxy networks from molecular dynamics simulations.

Protective equipment in civilian and military applications requires the use of polymer materials that are both stiff and tough over a wide range of strain rates. However, typical structural materials, like tightly cross-linked epoxies, are very brittle. Recent experiments demonstrated that cross-linked poly(dicyclopentadiene) (pDCPD) networks can circumvent this trade-off by providing structural properties such as a high glass transition temperature and glassy modulus, while simultaneously exhibiting excellent toughness and high-rate impact resistance. The greater performance of pDCPD was attributed to more facile plastic deformation and nano-scale void formation, but the chemical and structural mechanisms underlying this response were not clear. Here, we use atomistic molecular dynamics to compare the molecular- and chain-level properties of pDCPD and epoxy networks undergoing high strain rate deformation. We quantify the tensile modulus and yield strength of the networks as well as the prevalence and characteristics of nanovoids that form during deformation. Networks of similar molecular weight between cross-links are compared. Two key molecular-level properties are identified - monomer flexibility and polar chemistry - that influence the behavior of the networks. Increasing monomer flexibility reduces the modulus and yield strength, while strong non-covalent interactions (e.g., hydrogen bonds) that accompany polar moieties provide higher modulus and yield strength. The lack of strong non-covalent interactions in pDCPD was found to account for its lower modulus and yield strength compared to the epoxies. We examine the molecular-level properties of nanovoids, such as shape, alignment, and local stress distribution, as well as the local chemical environment, finding that nanovoid formation and growth are increased by the monomer rigidity but decreased by polar chemistry. As a result, the pDCPD network, which has a stiff chain backbone with nonpolar alkane chemistry, exhibits more and larger nanovoids that grow more readily during deformation, which could account for the higher toughness and more ductile behavior observed in pDCPD.

Characteristics of thermal conductivity in classical water models.

The thermal conductivities of common water models are compared using equilibrium (EMD) and non-equilibrium molecular dynamics (NEMD) simulation. A complete accounting for electrostatic contributions to the heat flux was found to resolve the previously reported differing results of NEMD and EMD Green-Kubo measurements for the extended simple point-charge (SPC/E) model. Accordingly, we demonstrate the influence of long-range electrostatics on the thermal conductivity with a simple coulomb cutoff, Ewald summation, and by an extended particle-particle particle-mesh method. For each water model, the thermal conductivity is computed and decomposed in terms of frequency-dependent thermodynamic and topological contributions. The rigid, three-site SPC, SPC/E, and transferable intermolecular potential (TIP3P-Ew) water models are shown to have similar thermal conductivity values at standard conditions, whereas models that include bond stretching and angle bending have higher thermal conductivities.

Entangled triblock copolymer gel: morphological and mechanical properties.

The morphological and mechanical properties of entangled ABA triblock copolymer gels, where solvent were selective to the midblock, were studied as a function of polymer concentration using a novel dissipative particle dynamics model which includes a modified segmental repulsive potential that restricts chain crossing. Morphological properties, such as micelle size, distance between micelles, and the bridge fraction, were calculated as a function of concentration. Although the micelle size was shown to have a strong dependence on concentration, the bridge fraction and distance between micelles were shown to plateau at moderate concentrations. Deformation under uni-axial tension was also performed to extract the cross-link and entanglement contribution to the elastic modulus. Scaling results qualitatively agree with other theoretical predications.

Shock Hugoniot calculations of polymers using quantum mechanics and molecular dynamics.

Using quantum mechanics (QM) and classical force-field based molecular dynamics (FF), we have calculated the principle shock Hugoniot curves for numerous amorphous polymers including poly[methyl methacrylate] (PMMA), poly[styrene], polycarbonate, as well as both the amorphous and crystalline forms of poly[ethylene]. In the FF calculations, we considered a non-reactive force field (i.e., polymer consistent FF). The QM calculations were performed with density functional theory (DFT) using dispersion corrected atom centered pseudopotentials. Overall, results obtained by DFT show much better agreement with available experimental data than classical force fields. In particular, DFT calculated Hugoniot curves for PMMA up to 74 GPa are in very good agreement with experimental data, where a preliminary study of chain fracture and association was also performed. Structure analysis calculations of the radius of gyration and carbon-carbon radial distribution function were also carried out to elucidate contraction of the polymer chains with increasing pressure.

An enhanced entangled polymer model for dissipative particle dynamics.

We develop an alternative polymer model to capture entanglements within the dissipative particle dynamics (DPD) framework by using simplified bond-bond repulsive interactions to prevent bond crossings. We show that structural and thermodynamic properties can be improved by applying a segmental repulsive potential (SRP) that is a function of the distance between the midpoints of the segments, rather than the minimum distance between segments. The alternative approach, termed the modified segmental repulsive potential (mSRP), is shown to produce chain structures and thermodynamic properties that are similar to the softly repulsive, flexible chains of standard DPD. Parameters for the mSRP are determined from topological, structural, and thermodynamic considerations. The effectiveness of the mSRP in capturing entanglements is demonstrated by calculating the diffusion and mechanical properties of an entangled polymer melt.

Molecular binding of black tea theaflavins to biological membranes: relationship to bioactivities.

Molecular dynamics simulations were used to study the interactions of three theaflavin compounds with lipid bilayers. Experimental studies have linked theaflavins to beneficial health effects, some of which are related to interactions with the cell membrane. The molecular interaction of theaflavins with membranes was explored by simulating the interactions of three theaflavin molecules (theaflavin, theaflavin-3-gallate, and theaflavin-3,3'-digallate) with a mixed bilayer composed of 1-palmitoyl-2-oleoyl phosphatidylcholine (POPC) and 1-palmitoyl-2-oleoyl phosphatidylethanolamine (POPE). The simulations show that the theaflavins evaluated have an affinity for the lipid bilayer surface via hydrogen bonding. The molecular structure of theaflavins influenced their configuration when binding to the bilayer surface, as well as their ability to form hydrogen bonds with the lipid headgroups. The theaflavin-bilayer interactions studied here help to define structure-function relationships of the theaflavins and provide a better understanding of the role of theaflavins in biological processes. The significance of the results are discussed in the context of black tea composition and bioactivity.