Gregory M. Odegard

2-D nano-scale finite element analysis of a polymer field

Abstract Two types of 2-D nano-scale finite elements, the chemical bond element and the Lennard–Jones element, are formulated based upon inter-atomic and inter-molecular force fields. A nano-scale finite element method is employed to simulate polymer field deformation. This numerical procedure includes three steps. First, a polymer field is created by an off-lattice random walk, followed by a force relaxation process. Then, a finite element mesh is generated for the polymer field. Chemical bonds are modeled by chemical bond elements. If the distance between two non-bonded atoms or monomers is shorter than the action range of the Lennard–Jones attraction (or repulsion), a Lennard–Jones element is inserted between them. Finally, external load and boundary conditions are applied and polymer chain deformation is simulated step by step. During polymer deformation, failed Lennard–Jones bond elements are removed and newly formed Lennard–Jones elements are inserted into the polymer field during each loading step. The process continues until failure occurs. Two examples are presented to demonstrate the process. Stress–strain curves of polymer fields under unidirectional tensile load are derived. Continuum mechanical properties, such as modulus and polymer strength, are determined based upon the stress strain curve. Further, throughout the deformation process one observes polymer chain migration, nano-scale void generation, void coalescence and crack development.

THE EFFECT OF CHEMICAL FUNCTIONALIZATION ON MECHANICAL PROPERTIES OF NANOTUBE/POLYMER COMPOSITES

The effects of the chemical functionalization of a carbon nanotube embedded in a nanotube/polyethylene composite on the bulk elastic properties are presented. Constitutive equations are established for both functionalized and nonfunctionalized nanotube composites systems by using an equivalent-continuum modeling technique. The elastic properties of both composites systems are predicted for various nanotube lengths, volume fractions, and orientations. The results indicate that for the specific composite material considered in this study, most of the elastic stiffness constants of the functionalized composite are either less than or equal to those of the non-functionalized composite.

Prediction of Mechanical Properties of Polymers With Various Force Fields

The effect of force field type on the predicted elastic properties of a polyimide is examined using a multiscale modeling technique. Molecular Dynamics simulations are used to predict the atomic structure and elastic properties of the polymer by subjecting a representative volume element of the material to bulk and shear finite deformations. The elastic properties of the polyimide are determined using three force fields: AMBER, OPLS-AA, and MM3. The predicted values of Young’s modulus and shear modulus of the polyimide are compared with experimental values. The results indicate that the mechanical properties of the polyimide predicted with the OPLS-AA force field most closely matched those from experiment. The results also indicate that while the complexity of the force field does not have a significant effect on the accuracy of predicted properties, small differences in the force constants and the functional form of individual terms in the force fields determine the accuracy of the force field in predicting the elastic properties of the polyimide.

Atomistic Modeling of Cross-linked Epoxy Polymer

Molecular Dynamics simulations are used to study cross-linking of an epoxy polymer. OPLS force field parameters are used for modeling a 2:1 stoichiometric mixture of epoxy resin and the cross-linking agent. The model has 17,928 united atoms and a static cross-linking method is used along with molecular minimization and molecular dynamics techniques to achieve two different cross-link densities. The crosslinked models can be used for understanding various phenomenon occurring in cross-linked epoxy resins at the atomic scale. Glass-transition temperature ranges of two differently cross-linked samples have been predicted using the models. These models will be used for studying aging behavior at the atomic level in epoxy materials and understanding the influence of aging on mechanical properties.

Predicting the Influence of Nano-scale Material Structure on the In-plane Buckling of Orthotropic Plates

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the nonfunctionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Temperature Effects in Multiscale Modeling of Polymer Materials

The effects of temperature on the predicted mechanical properties of an amorphous polyimide (LaRC-CP2) have been investigated. A multiscale constitutive modeling approach was used to evaluate the equivalent-continuum properties of the modeled polyimide over a series of temperatures ranging from 73K to experimentally measured glass transition temperature. The resulting mechanical properties have been compared to experimentally-obtained properties. The predicted moduli did not show the expected temperature dependence and the sudden change at the glass transition temperature. The lack of expected trends in the results is discussed in the context of the mechanism proposed by three widely accepted theories of glass transition phenomenon. I. Introduction Polymer-based materials have found innumerable engineering applications due to the wide range of physical and mechanical properties that can be achieved through manipulation of the nano- and microstructure. Specifically, polymer nanocomposites can provide considerable improvements to mechanical properties relative to traditional composite materials due to their extremely high surface-to-volume ratios for the same volume fraction of reinforcing phase. Polymer-based materials also exhibit superior strengthto-weight and stiffness-to-weight ratios making them ideal for applications with stringent weight restrictions. For aerospace applications, polymer-based materials must demonstrate mechanical reliability under service temperatures ranging from cryogenic to the glass transition temperature. To facilitate the development of polymer materials for this purpose, multiscale modeling techniques must be developed that provide efficient and accurate structure-property relationships which can also account for effects of temperature.

Molecular Modeling of the Influence of Crosslink Distribution on Epoxy Polymers

Experimental studies on epoxies report that the microstructure consists of highlycrosslinked localized regions connected with a dispersed phase of low-crosslink density epoxy. Because epoxies play a major role in many structural applications, the influence of the crosslink distribution on the thermo-mechanical properties must be determined. But as experiments cannot reliably report the exact number or distribution of crosslinked covalent bonds present in the molecular network, molecular modeling is a valuable tool that can predict the influence of crosslink distribution on thermo-mechanical properties. In this study, molecular dynamics are used to establish well-equilibrated molecular models of an EPON 862-DETDA epoxy system with a range of crosslink densities and distributions. Crosslink distributions are varied by forming highly crosslinked clusters within the epoxy network and then forming additional crosslinks that connect between clusters. Results of simulations on these molecular models indicate that the thermal expansion coefficient decreases with overall crosslink density, both above and below the glass transition temperature. It is also found that within the range of crosslink distributions investigated, there is no discernible influence of crosslink distribution on the linear thermal expansion coefficient of the epoxy.

Parametric Studies in Multiscale Modeling of High- Performance Polymers

A computational parametric study has been performed to establish the effect of Representative Volume Element (RVE) size, force field type, and simulation temperature on the predicted mechanical properties of polyimide and polycarbonate materials modeled atomisticially. The results of the simulations indicate no clear effect of RVE size and force field type on the predicted mechanical response of the polyimide and polycarbonate polymer systems. A multiscale modeling technique was utilized to determine the equivalentcontinuum Young’s moduli, density, and stress-strain behavior for the set of mentioned modeling parameters. Parametric studies also indicate no clear effect of the simulation temperature on the predicted material densities of LaRC-CP2 when the AMBER force field is used. However, the MM3 force field predicts a steady decrease in the density of LaRCCP2 as the temperature increases up to and beyond the glass transition temperature. These force fields vary slightly in form and with the associated parameters