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Multiscale Modeling of Reinforced Epoxy Resins by Carbon Nanotubes and Graphene

Kelvin Suggs, Vernecia Person, Chantel Nicolas and Xiao­Qian Wang

MRS Proceedings / Volume 1312 / 2011DOI: 10.1557/opl.2011.263

Link to this article: http://journals.cambridge.org/abstract_S1946427411002636

How to cite this article:Kelvin Suggs, Vernecia Person, Chantel Nicolas and Xiao­Qian Wang (2011). Multiscale Modeling of Reinforced Epoxy Resins by Carbon Nanotubes and Graphene. MRS Proceedings,1312, mrsf10­1312­ii02­07 doi:10.1557/opl.2011.263

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Mater. Res. Soc. Symp. Proc. Vol. 1312 © 2011 Materials Research SocietyDOI: 10.1557/opl.2011.263

Multiscale Modeling of Reinforced Epoxy Resins by Carbon Nanotubes and Graphene

Kelvin Suggs,1,2 Vernecia Person,1 Chantel Nicolas,1 and Xiao-Qian Wang2

1Department of Chemistry, 2Department of Physics, Center for Functional Nanoscale Materials, Clark Atlanta University, Atlanta, Georgia 30314, U.S.A. ABSTRACT

Nanocomposites are of increasing interest due to their unique structural, electronic, and thermal properties. Simultaneously, multiscale molecular modeling is becoming more robust. Therefore computational models are able to be examined with increased accuracy, complexity, and dimension. Graphene based molecules are lauded for their conductive properties as well as their architecture-like geometry which may allow bottom up nanoscale fabrication of nanoscopic structures. Furthermore, these macrocycled molecules allow high interactivity with other molecules including highly tensiled polymers that yield other novel supramolecular structures when interacted. These supramolecular structures are being investigated in lieu of a variety of potential applications. Nanocomposites of cured epoxy resin reinforced by single-walled carbon nanotubes exhibit a plethora of interesting behavior at the molecular level. A fundamental issue is how the self-organized dynamic structure of functional molecular systems affects the interactions of the nano-reinforced composites. A combination of force-field based molecular dynamics and local density-functional calculations shows that the stacking between the aromatic macrocycle and the surface of the SWNTs manifests itself via increased interfacial binding. First-principles calculations on the electronic structures further reveal that there exists distinct level hybridization behavior for metallic and semiconducting nanotubes. In addition there is a monatomic increase in binding energy with an increase in the nanotube diameter. The simulation studies suggest that graphene nanoplatelets are potentially the best fillers of epoxy matrices. The implications of these results for understanding dispersion mechanism and future nanocomposite developments are discussed. INTRODUCTION

Lightweight and high strength composite materials provide an appealing combination that propels composites to new perspective in advanced aerospace vehicles and propulsion systems.1,2 Epoxy resins are leading candidates for these types of applications due to their excellent combination of physical and mechanical properties.3 Nanocomposites of cured epoxy resin reinforced by single-walled carbon nanotubes exhibit a plethora of interesting behaviors at the molecular level.4,5 We have employed a combination of force-field-based molecular mechanics and first-principles calculations to study the corresponding binding and charge-transfer behavior.

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The simulation study of various nanotube species and curing agent configurations provides insight into the optimal structures in lieu of interfacial stability.6,7 An analysis of charge distributions of the epoxy functionalized semiconducting and metallic tubes reveals distinct level hybridizations. These results are important for understanding dispersion mechanism and future nano reinforced composite developments.

Epoxy resins serve as key elements in the field of high-performance materials, coatings, and composites. These materials have demonstrated high cured glass transition temperature and a satisfactory combination of low and stable melt viscosity, thermal and mechanical performance, cost, as well as free of toxic monomers.8,9 The availability of a wide variety of epoxy systems, along with different physical performances associated with various cross-linking degrees, makes these thermosetting polymers extremely suitable for applications such as structural, medical, or aerospatial.10 Although epoxy resins are inherently brittle, curing processing in the manufacture of high-performance composites offers high modulus, stiffness and thermal stability. In this regard, remarkable progress has been made in the curing of epoxy resins, and several studies have been performed to investigate the curing mechanism and the influence of various parameters on processing and material properties.11,12 On the other hand, carbon nanotubes have been employed as reinforcers, which are connected to their unique properties and outstanding performance. While recent demonstration of the potential of these types of resins offers an unprecedented combination of high temperature laminate performance13,14 with superior processing characteristics, there is a striking lack of theoretical prescriptions for developing nano-reinforced epoxy resins. To gain the understanding necessary to develop such prescriptions, it is desirable to consider realistic models for nano-reinforced composites.

Epoxy-based polymer materials have diverse applications such as metal coatings, automotive primer, printed circuit boards, semiconductor encapsulants, adhesives, and aerospace composite materials.15,16 The current trial-and-error formulation approach faces many challenges to satisfy an ever increasing demand for a “designer” range of properties of epoxy resin end-products, a greater economic pressure for efficiency, and a larger focus on the environmental impact requirements. Lightweight multifunctional composites with enhanced properties can potentially be produced by effectively incorporating individual carbon nanotubes (CNTs) into polymer matrices. Composites produced by conventional methods, such as solution mixing and melt blending, usually fail to yield significant improvements of bulk mechanical and electrical properties, when compared to individual nanotubes.10-12 A controlled nanostructure of CNT/epoxy thin sheet can be achieved through impregnating CNT networks with epoxy solution, and the simulation study will be crucial for understanding the effects of composition, aspect ratio, diameter, chirality and functionalization. By changing various parameters, such as concentration of epoxy solution, oxidation state of CNT material and impregnation protocol, it is possible to tune the mechanical/ electrical properties of the prepared composites. The enhancement of Young’s modulus and a tensile strength will be beneficial for a variety of applications such as conductive composite films for electromagnetic shielding, as well as for components in the lightweight multifunctional composites.10-17

The goal of our multiscale modeling work is to provide fundamental understanding of the mechanisms at the molecular level of the curing reaction and the effects of catalysts and accelerators using multiscale modeling methods. Such information will significantly aid the formulation process to meet its demands. The multiscale modeling approach is based on a combination of force-field-based molecular dynamics and local density-functional calculations. Force-field-based molecular dynamics can be used to pre-select molecular geometries, and first-

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principles calculations can be employed to determine the electronic structure of the nano-reinforced composites. A fundamental issue is how the self-organized dynamic structure of functional molecular systems affects the interactions of the nano-reinforced composites. The proposed multiscale approach will provide a systematic investigation of the π–π stacking between the aromatic macrocycle and the surface of the SWNTs that manifests itself via increased interfacial binding. First-principles calculations on the electronic structures can further characterize level hybridization behavior for metallic and semiconducting nanotubes. COMPUTATIONAL METHODS

In this section, we summarize the simulation methods that will be used in this study of nanoreinforced composites. All of them are state-of-the-art multiscale modeling methods. We will use the density functional theory23 to study the system’s energetics in order to address the size-dependent and shape-dependent stability and atomic arrangements of these nanocomposites. The atomic motions are investigated using molecular dynamics with forces obtained from the density functional theory. Density functional theory

To properly handle a many-electron system so that one can derive its various properties from fundamental quantum mechanics is a constant challenge in theoretical physics and chemistry. Although the interaction between electrons is well known, the facts that electrons, with a spin quantum number of ½, have to obey specific statistical rules and that one normally has to deal with quite a few of them at the same time make this problem immensely formidable. One approach that has become the standard one for large-scale electronic simulations is the density functional theory23 in the so-called Kohn-Sham framework.24 It is based on a theorem stating that the ground-state energy of a many-electron system can be represented as a functional of the electron density only. Thus one can hope to obtain the electronic energy without dealing with the many-body wave functions that are highly multidimensional with the notorious property of being antisymmetric with respect to particle exchange. Being a scalar in the real space, the electron density is a much simpler quantity to manage, making it possible to investigate more complex systems. By minimizing the energy functional with respect to possible density distributions one can then determine the ground-state electronic energy for a given atomic arrangement. The energy minimization procedure is most conveniently carried out by a mapping of the truly interacting system to an auxiliary system of noninteracting particles with the same density distribution.24

The fact that the effective potential is a simple local function makes a tremendous difference in practical calculations. Other quantum-chemistry schemes such as the Hartree-Fock method commonly involves nonlocal operators which require much more computational resources. It is not surprising that the density-functional theory has become the prevailing approach in modern electronic-structure calculations with wide applications in quantum chemistry and materials physics. In practical calculations, approximations to the energy functional are required. Commonly used ones include the local-density approximation (LDA)23, in which the density is assumed to be locally uniform and the result for a homogeneous electron gas is used point by point based on the local density, and the generalized gradient approximation

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(GGA), in which the gradient correction to the LDA is added. These are also the approximations we will use in our studies.

In order to study systems of hundreds of atoms, we will focus on the properties of the valence electrons and employ norm-conserving pseudopotentials to model the effects of core electrons. The one-particle orbital will be expanded in terms of plane waves to eliminate any bias in the basis functions. Evaluating relevant quantities in either the real space or momentum space will carry out the self-consistent solution of the corresponding Kohn-Sham orbitals. Molecular dynamics with ab initio forces

In first-principles (ab initio) molecular-dynamics simulations (FPMD), the forces underlying the atomic motion (Helmann-Feynman forces) originate from the electronic distributions that are evaluated in the course of the simulations, concurrent with the instantaneous spatial configuration of the atoms. This is the source of the name ab initio, namely, free of a priori assumptions. The FPMD simulation method that have gained a primary position in theoretical investigation if materials are those based on the Kohn-Sham density functional with the LDA20,23, LSDA, or GGA approximations for exchange and correlation functional. Since the forces are calculated completely based on density-functional theory, they provide a more accurate description of interatomic interactions than simpler methods such as model interatomic potentials, We plan to use FPMD in a large part of our planned investigations, employing mostly the Bohn Oppenheimer method, formulated and implemented for simulations of dynamics at finite temperature, in addition to electronic structure and geometrical optimization. It is worth noting that our FPMD codes have been rewritten and optimized by us for massive parallel computations, allowing treatment of rather complex and large systems.

Force-field-based molecular-dynamics simulations

Proteins undergo large conformational changes in connection with their function. The conformational changes are associated with ligand binding thereby allowing proper positioning of the substrate for catalysis, or allowing function within a receptor-signaling pathway. Molecular dynamics simulations are very useful in characterizing the energetics and dynamics of the relationships of the various conformations.18 The time scales of these conformational changes are typically too long for conventional molecular dynamics simulations. This presents a challenge both to computational resources and theoretical methods. It is important to study energetic relationships between two known conformations and the prediction of how the ligand-enzyme structure changes as a result of mutations. We have been employing the force-field-based molecular dynamics package, Nanoscale Molecular Dynamics (NAMD), to study a selected number of biomolecule systems. NAMD25 is a parallel, object-oriented molecular dynamics code designed for high-performance simulation of large biomolecular systems. Based on CHARMM++ parallel objects, NAMD scales to hundreds of processors on high-end parallel platforms. Single-walled carbon nanotubes

SWNTs are rolled graphene sheets along a certain chiral vector. The structure of a SWNT is uniquely characterized by (n, m) chiral indices. Among chiral vectors, there are two distinctive

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high-symmetry directions, corresponding to (n, 0) “zig-zag” and (n, n) “armchair.” From the rolling graphene model, the chiral angle and diameter d0 of a (n, m) SWNT (0 m n) are19-21

2 20dd n m nm= + +

π (1)

1 32

mtann m

θ −=+

(2)

respectively, where d0 is the bond length of graphene. A SWNT is considered to be metallic if n

m is divisible by 3, and semiconducting otherwise. However, the electronic structure of metallic SWNTs is very sensitive to radial deformations because of the presence of degenerate low energy electronic states in these systems. The effect of breaking symmetry due to non-covalent functionalization remains a paucity of classification from first principles calculations.

The SWNTs involved in the present study were constructed based on a sp2 hybridization model. The initial value of b = 1.42 Å was used. The geometric structures of the SWNTs were fully relaxed in the molecular dynamics through intensive simulated annealing. A systematic evaluation of the available empirical force fields showed that the MM+ and CHARMM force fields provide consistent results for both the carbon nanotubes and epoxy resins. Epoxy resins

The molecular and chemical structures of the EPON resin 862 are shown in Fig. 1, along with two prototype curing agents, diethyltoluenediamine (DETDA) and diethyltoluenamine (DETA). The consensus is that DETDA represents characteristic features of the curing agent W.

Figure 1. Molecular and chemical structures of (a) diethyltoluenediamine (DETDA), (b) EPON resin 862, respectively. Colored with blue, red, cyan, and white are nitrogen, oxygen, carbon, and hydrogen atoms respectively.

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The terminal groups of the EPON resin 862 can open up and connect to curing agents.

The formation of a chain-like or crosslinked structure15 is reminiscent of the cured state of the nano-reinforced composites. In order to explore the nature at the molecular level of nanotube composites, we have performed intensive geometry optimization studies of conformations via force-field-based molecular dynamics. Whereas our molecular dynamics simulation confirms that the EPON resin 862 self-assembles onto the surface of the SWNTs, the cured state of the EPON resin 862 adopts energetically favorable configurations by wrapping around the tube helically. Illustrated in Figure 2 is the optimized structure of a SWNT wrapped with chain-like cured EPON 862. A careful examination of the dynamical structural and energetic changes reveals that electrostatic interactions within the EPON backbone are primarily responsible for the wrapping into a helical structure. The aromatic rings in the EPON resins 862 are planar to the surface of the SWNT, and the structural changes proceed through a rearrangement of the torsional angles.

Figure 2. Top and side views of armchair (6, 6) helically wrapped with EPON resin 862. The carbon, oxygen, nitrogen, and hydrogen atoms are colored with grey, red, blue, and white, respectively.

RESULTS AND DISCUSSION

The binding of the epoxy resin to the SWNT is a combination of electrostatic and van der Waals (vdW) interactions. As a consequence, the electrostatic interactions are stronger than vdW binding for non-conjugated molecules, which may explain why the nanotubes are generally dispersed better with conjugated molecules. In general, the adsorption energy can be estimated from the difference between the potential energy of the composite system and the potential energies of the epoxy resin and corresponding SWNTs as follows:

E = ESWNT + EEpon Etotal, (3)

where Etotal is the total potential energy of the nanohybrid, ESWNT is the energy of the nanotube without the porphyrin and EPpon is the energy of the epoxy resin without the nanotube.

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Figure 3. Calculated binding energy of nano-reinforced epoxy resin of carious diameters on the basis of fore-field-based molecular dynamics. We illustrate in Figure 3 the calculated adsorption energies using force field-based MD. As seen from Figure 3, the adsorption energy increases with increasing diameter of the tube. This is attributed to an improved geometric match between the epoxy resin conformation and the carbon nanotube, as well as a reduction in -orbital misalignment.

Another important aspect of the nanotube reinforced epoxy resin is the charge transfer behavior. It is well known that classical molecular dynamics cannot properly describe charge transfers. To this end, we plan to carry out intensive first-principles calculations based on density functional theory. For large systems, a semi-empirical density-functional molecular dynamics will be employed, which is capable of handling a few thousands of atoms. The proposed project will provide insight to the charge transfer behavior of carbon nanotube and graphene-reinforced epoxy resins. In lieu of the rapid progress in this field, the combination of computational simulation and experimental characterization will be very fruitful in the future development of nano-reinforced composite materials.

In addition to the helical wrapping conformations, the cured epoxy network can be formed through cross-linking of the EPON 862 resin with curing agents. During the curing reaction, the amine groups of curing agents react with the epoxide groups of epoxy resins. While for the chain-like conformation the curing reaction is limited at the –NH2 site of the curing agents, the cross-linking activity can happen at the NH site as well. As a result, the cross-link expands in all directions and forms a network of macromolecules. It is worth noting that DETA-cured EPON resin 862 can assume either chain-like or cross-linked conformations. Although the helically wrapped chain configuration is energetically preferred, the availability of additional reaction sites at NH for the cross-linked structure may lead to increased density for the nano-reinforced composite. As the curing reaction is a dynamic process, the interplay between the energy and molecular density can be studied on the basis of quantum calculations.

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Figure 4. Molecular dynamics simulation of EPON 862 and curing agent W chain interacts noncovalently with a graphene nanoplatelet. Electronic structure characteristic of nanohybrid is investigated.

CONCLUSIONS

In summary, we have shown in this paper that multiscale modeling is complementing experimental studies in providing useful information of nano-reinforcement of composites. Our results show that the stacking between the aromatic macrocycle and the surface of the SWNTs manifests itself via increased interfacial binding. First-principles calculations on the electronic structures further reveal that there exists distinct level hybridization behavior for metallic and semiconducting nanotubes.22 In addition, there is a monotonic increase in binding energy with an increase in the nanotube diameter. Our simulation studies suggest that graphene nanoplatelets are potentially the best fillers of epoxy matrices.

ACKNOWLEDGMENTS

The authors thank E. Mintz, I. M. Khan, and M. W. Shute for stimulating discussions. This work was supported in part by the National Science Foundation (Grant Nos. DMR-0934142 and HRD-0630456), NASA (Grant No. NCC3-1044), and Air Force Minority Leaders Program (Grant No. CL-ATL-10-5567-0016-02-C2)

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