Modeling Brittle Fractures in Epoxy Nanocomposites Using Extended Finite Element and Cohesive Zone Surface Methods.

Linear elastic fracture modeling coupled with empirical material tensile data result in good quantitative agreement with the experimental determination of mode I fracture for both brittle and toughened epoxy nanocomposites. The nanocomposites are comprised of diglycidyl ether of bisphenol A cured with Jeffamine D-230 and some were filled with core-shell rubber nanoparticles of varying concentrations. The quasi-static single-edge notched bending (SENB) test is modeled using both the surface-based cohesive zone (CZS) and extended finite element methods (XFEM) implemented in the Abaqus software. For each material considered, the critical load predicted by the simulated SENB test is used to calculate the mode I fracture toughness. Damage initiates in these models when nodes at the simulated crack tip attain the experimentally measured yield stress. Prediction of fracture processes using a generalized truncated linear traction-separation law (TSL) was significantly improved by considering the case of a linear softening function. There are no adjustable parameters in the XFEM model. The CZS model requires only optimization of the element displacement at the fracture parameter. Thus, these continuum methods describe these materials in mode I fracture with a minimum number of independent parameters.

Calculations of free energy of surface interactions in crystalline polyethylene.

The surface free energy of the crystalline polyethylene (PE) is an important property related with wettability, adhesion, and crystal growth. We investigated the profiles of free energy of surface interactions in the fully thermalized crystalline PE during debonding and shearing with atomistic molecular dynamics simulations using steered molecular dynamics and umbrella sampling techniques. The stress profiles during debonding and shearing processes were also estimated and compared with those obtained from analogous deformation simulations. We estimated the vacuum surface free energies of two different crystallographic surfaces (100) and (010) of the crystalline PE from the free energy changes during the debonding process. The estimated surface free energies were insensitive to the choice of simulation protocols after combining estimates from both forward and backward processes and were in excellent agreement with those obtained from an experiment on PE single crystal aggregates, which underscores the importance of the inclusion of the entropic contribution in the free energy calculated with the fully flexible interface adopted in this study.

High strength films from oriented, hydrogen-bonded "graphamid" 2D polymer molecular ensembles.

The linear polymer poly(p-phenylene terephthalamide), better known by its tradename Kevlar, is an icon of modern materials science due to its remarkable strength, stiffness, and environmental resistance. Here, we propose a new two-dimensional (2D) polymer, "graphamid", that closely resembles Kevlar in chemical structure, but is mechanically advantaged by virtue of its 2D structure. Using atomistic calculations, we show that graphamid comprises covalently-bonded sheets bridged by a high population of strong intermolecular hydrogen bonds. Molecular and micromechanical calculations predict that these strong intermolecular interactions allow stiff, high strength (6-8 GPa), and tough films from ensembles of finite graphamid molecules. In contrast, traditional 2D materials like graphene have weak intermolecular interactions, leading to ensembles of low strength (0.1-0.5 GPa) and brittle fracture behavior. These results suggest that hydrogen-bonded 2D polymers like graphamid would be transformative in enabling scalable, lightweight, high performance polymer films of unprecedented mechanical performance.

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.

AIREBO-M: a reactive model for hydrocarbons at extreme pressures.

The Adaptive Intermolecular Reactive Empirical Bond Order potential (AIREBO) for hydrocarbons has been widely used to study dynamic bonding processes under ambient conditions. However, its intermolecular interactions are modeled by a Lennard-Jones (LJ) potential whose unphysically divergent power-law repulsion causes AIREBO to fail when applied to systems at high pressure. We present a modified potential, AIREBO-M, where we have replaced the singular Lennard-Jones potential with a Morse potential. We optimize the new functional form to improve intermolecular steric repulsions, while preserving the ambient thermodynamics of the original potentials as much as possible. The potential is fit to experimental measurements of the layer spacing of graphite up to 14 GPa and first principles calculations of steric interactions between small alkanes. To validate AIREBO-M's accuracy and transferability, we apply it to a graphite bilayer and orthorhombic polyethylene. AIREBO-M gives bilayer compression consistent with quantum calculations, and it accurately reproduces the quasistatic and shock compression of orthorhombic polyethlyene up to at least 40 GPa.

Nonlinear mechanics of thermoreversibly associating dendrimer glasses.

We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work to fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, "strong, slow" SBs optimize strength, while "weak, fast" SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.

Cation-induced hydrogels of cellulose nanofibrils with tunable moduli.

Cellulose nanofibrils are biocompatible nanomaterials derived from sustainable natural sources. We report hydrogelation of carboxylated cellulose nanofibrils with divalent or trivalent cations (Ca(2+), Zn(2+), Cu(2+), Al(3+), and Fe(3+)) and subsequent formation of interconnected porous nanofibril networks. The gels were investigated by dynamic viscoelastic measurements. The storage moduli of the gels are strongly related to valency of the metal cations and their binding strength with carboxylate groups on the nanofibrils. Hydrogel moduli may be tuned by appropriate choice of cation. Cation-carboxylate interactions are proposed to initiate gelation by screening of the repulsive charges on the nanofibrils and to dominate gel properties through ionic cross-linking. Binding energies of cations with carboxylate groups were calculated from molecular models developed for nanofibril surfaces to validate the correlation and provide further insight into the cross-linked structures. The cellulose nanofibril-based hydrogels may have a variety of biomedical and other applications, taking advantage of their biocompatibility, high porosity, high surface area, and durability in water and organic solvents.

Exploring the ability of a multiscale coarse-grained potential to describe the stress-strain response of glassy polystyrene.

A new particle-based bottom-up method to develop coarse-grained models of polymers is presented and applied to polystyrene. The multiscale coarse-graining (MS-CG) technique of Izvekov et al. [J. Chem. Phys. 120, 10896 (2004)] is applied to a polymer system to calculate nonbonded interactions. The inverse Boltzmann inversion method was used to parametrize the bonded and bond-angle bending interactions. Molecular dynamics simulations were performed, and the CG model exhibited a significantly lower modulus compared to the atomistic model at low temperature and high strain rate. In an attempt to improve the CG model performance, several other parametrization schemes were used to build other models from this base model. The first of these models included standard frictional forces through use of the constant-temperature dissipative particle dynamics method that improved the modulus, yet was not transferrable to higher temperatures and lower strain rates. Other models were built by increasing the attraction between CG beads through direct manipulation of the nonbonded potential, where an improvement of the stress response was found. For these models, two parametrization protocols that shifted the force to more attractive values were explored. The first protocol involved a uniform shift, while the other protocol shifted the force in a more localized region. The uniformly shifted potential greatly affected the structure of the equilibrium model as compared to the locally shifted potential, yet was more transferrable to different temperatures and strain rates. Further improvements in the coarse-graining protocol to generate models that more satisfactorily capture mechanical properties are suggested.

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.

Surface orientation of polystyrene based polymers: steric effects from pendant groups on the phenyl ring.

Near edge X-ray absorption fine structure (NEXAFS) coupled with molecular dynamics simulations were utilized to probe the orientation at the exposed surface of the polymer film for polystyrene type polymers with various pendant functional groups off the phenyl ring. For all the polymers, the surface was oriented so that the rings are nominally normal to the film surface and pointing outward from the surface. The magnitude of this orientation was small and dependent on the size of the pendant functional group. Bulky functional groups hindered the surface orientation, leading to nearly unoriented surfaces. Depth dependent NEXAFS measurements demonstrated that the surface orientation was localized near the interface. Molecular dynamics simulations showed that the phenyl rings were not oriented strongly around a particular "average tilt angle". In contrast, simulations demonstrate that the phenyl rings exhibit a broad distribution of tilt angles, and that changes in the tilt angle distribution with pendant functionality give rise to the observed NEXAFS response. The more oriented samples exhibit a higher probability of phenyl ring orientation at angles greater than 60 degrees relative to the plane of the films surface.

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.

Determination of binding energy and solubility parameters for functionalized gold nanoparticles by molecular dynamics simulation.

The binding energy, density, and solubility of functionalized gold nanoparticles in a vacuum are computed using molecular dynamics simulations. Numerous parameters including surface coverage fraction, functional group (-CH(3), -OH, -NH(2)), and nanoparticle orientation are considered. The analysis includes computation of minimum interparticle binding distances and energies and an analysis of mechanisms that may contribute to changes in system potential energy. A number of interesting trends and results are observed, such as increasing binding distance with higher terminal group electronegativity and a minimum particle-particle binding energy (solubility parameter) based upon surface coverage. These results provide a fundamental understanding of ligand-coated nanoparticle interactions required for the design and processing of high-density polymer composites. The computational model and results are presented as support for these conclusions.

Discrete Optimization of Electronic Hyperpolarizabilities in a Chemical Subspace.

We introduce a general optimization algorithm based on an interpolation of property values on a hypercube. Each vertex of the hypercube represents a molecule, while the interior of the interpolation represents a virtual superposition ("alchemical" mutation) of molecules. The resultant algorithm is similar to branch-and-bound/tree-search methods. We apply the algorithm to the optimization of the first electronic hyperpolarizability for several tolane libraries. The search includes structural and conformational information. Geometries were optimized using the AM1 Hamiltonian, and first hyperpolarizabilities were computed using the INDO/S method. Even for small libraries, a significant improvement of the hyperpolarizability, up to a factor of ca. 4, was achieved. The algorithm was validated for efficiency and reproduced known experimental results. The algorithm converges to a local optimum at a computational cost on the order of the logarithm of the library size, making large libraries accessible. For larger libraries, the improvement was accomplished by performing electronic structure calculations on less than 0.01% of the compounds in the larger libraries. Alternation of electron donating and accepting groups in the tolane scaffold was found to produce candidates with large hyperpolarizabilities consistently.

Performance of DFT Methods in the Calculation of Optical Spectra of TCF-Chromophores.

We present electronic structure calculations of the ultraviolet/visible (UV-vis) spectra of highly active push-pull chromophores containing the tricyanofuran (TCF) acceptor group. In particular, we have applied the recently developed long-range corrected Baer-Neuhauser-Livshits (BNL) exchange-correlation functional. The performance of this functional compares favorably with other density functional theory (DFT) approaches, including the CAM-B3LYP functional. The accuracy of UV-vis results for these molecules is best at low values of attenuation parameters (γ) for both BNL and CAM-B3LYP functionals. The optimal value of γ is different for the charge-transfer (CT) and π-π* excitations. The BNL and PBE0 exchange correlation functionals capture the CT states particularly well, while the π-π* excitations are less accurate and system dependent. Chromophore conformations, which considerably affect the molecular hyperpolarizability, do not significantly influence the UV-vis spectra on average. As expected, the color of chromophores is a sensitive function of modifications to its conjugated framework and is not significantly affected by increasing aliphatic chain length linking a chromophore to a polymer. For selected push-pull aryl-chromophores, we find a significant dependence of absorption spectra on the strength of diphenylaminophenyl donors.

Optical Properties of Phthalocyanine and Naphthalocyanine Compounds.

Phthalocyanines, naphthalocyanins, and their derivatives are frequently used as light modulating materials. These compounds, with their stable planar square structure and highly delocalized π-electron system, are being used in numerous technological applications, such as pigments in chemical sensors, and more recently as photosensitizers for photodynamic therapy. The nonlinear optical properties (NLO) of these compounds are of particular importance. Using density functional method (DFT), we calculated the optical properties of phthalocyanine and naphthalocyanine complexes with Si as a central atom. We examined the effect of hydrophilic axial substituents and the size of polycyclic aromatic hydrocarbons surrounding the porphyrazine-Si kernel on the optical properties of title molecules. Both UV-vis and RSA spectra are calculated and are compared with available experimental results. The time-dependent DFT (TDDFT) with the B3LYP functional predicts that the characteristic UV-vis absorption maxima are blue-shifted; however, the relative error is almost constant for phthalocyanine and naphthalocyanine compounds. The TDDFT triplet-triplet absorption spectra of Si-phthalocyanine and Si-naphthalocyanine complexes reproduce experimental data well.