Glass transition temperature of functionalized

Integrated Ferroelectrics An International Journal

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Glass transition temperature of functionalized graphene epoxy composites using molecular dynamics simulation Anurag Yadav, Amit Kumar, Pradeep K. Singh & Kamal Sharma To cite this article: Anurag Yadav, Amit Kumar, Pradeep K. Singh & Kamal Sharma (2018) Glass transition temperature of functionalized graphene epoxy composites using molecular dynamics simulation, Integrated Ferroelectrics, 186:1, 106-114, DOI: 10.1080/10584587.2017.1370331 To link to this article: https://doi.org/10.1080/10584587.2017.1370331

Published online: 04 Jan 2018.

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Date: 08 January 2018, At: 10:45

INTEGRATED FERROELECTRICS , VOL. , – https://doi.org/./..

Glass transition temperature of functionalized graphene epoxy composites using molecular dynamics simulation Anurag Yadav, Amit Kumar, Pradeep K. Singh, and Kamal Sharma

Downloaded by [45.127.226.81] at 10:45 08 January 2018

Department of Mechanical Engineering, GLA University, Mathura, India

ABSTRACT

ARTICLE HISTORY

Molecular Dynamics (MD) simulations were carried out to investigate the effect of functionalization of graphene on glass transition temperature (Tg ) of epoxy composites were built using LY556 epoxy resin cross-linked with DETDA. Three different formats of graphene including pristine, with amine (−NH2 ) groups and carboxyl (−COOH) groups respectively involved in the investigation. The simulation results indicated that Tg of the graphene epoxy composites are higher than that of pure epoxy. Furthermore, Tg of composites randomly embedded with functionalized graphene were lower than that with pristine graphene, and Tg of the composites embedded with COOH-graphene was much lower than that with NH2 -graphene. The simulation results of Tg were in good agreement with experimental results indicating that this computational method can be used to predict effectively the Tg of graphene epoxy composites.

Received  November  Accepted  April  KEYWORDS

Glass transition temperature; functionalized graphene; epoxy resins; molecular dynamics simulation

1. Introduction Graphene, a two dimensional (2D) and single layer nanosheet of sp2 -hybridized carbon atoms [1, 2], has been significantly increasing the mechanical and thermal properties of graphene/epoxy composites [3–5]. The detention of interfacial interactions between graphene and epoxy plays an important role in the designing of nanocomposites with excellent physical and mechanical properties. Many applications of graphene in the field of bioengineering [6], electronics [7], and energy storage [8] have been reported. Glass transition temperature (Tg ) is one of the significant perspectives to evaluate visco-elastic properties of epoxy and their composites. Xue et al. [9] predicted Tg of graphene-polymer composites and found that the functionalized graphene inside a polymer matrix can greatly enhance Tg values of the resulting composites and also higher thermal expansion coefficients compared to that of bulk PMMA. Li. et al. [10] estimated Tg of isomeric polyimide using MD simulation method. They

CONTACT Amit Kumar amit@gmail.com Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ginf. ©  Taylor & Francis Group, LLC


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observed that Tg of isomeric polyimide is higher than its corresponding symmetrical polyimide and also analyze the role of energy component in glass transition process. Jeyranpour et al. [11] investigated Tg of cross-linked epoxy polymer with different curing agents and conclude that Tg of DGEBA/DETDA in all crosslinking densities has a higher value than that of DGEBA/TETA epoxy system. Choi et al. [12] predicted coefficient of thermal expansion (CTE) and the elastic stiffness of cross-linked epoxy based nanocomposites using MD simulation. They conclude that the Tg and thermoelastic properties of pure epoxy improved by embedding the silicon carbide (SiC) nanoparticles to the epoxy. Gojny and Schulte [13] investigated the thermo-mechanical behavior of multi-wall carbon nanotube (MWNT)/epoxy composites by DMA. Epoxy based composites with different wt.% of MWNTs (with and without functionalization) were fabricated and increase in Tg was observed with increasing wt.% of MWNTs. It was seen that samples containing functionalized nanotubes showed a stronger influence on Tg in comparison to composites containing the same amount of non-functionalized nanotubes. DMA measures the visco-elastic properties of polymer materials under controlled temperature and frequency [14] but the experimental approach of material characterization is very expensive and imposes significant limitations on them. Thus, the molecular dynamic (MD) simulations are used to calculate the thermo-mechanical properties of different functionalized graphene, which may be a feasible solution to overcome the difficulties in conducting the experiments regularly. In this work, MD simulation method is used to find out the effects of functionalized graphene on Tg of graphene epoxy composites. Tg of pristine graphene, amine functionalized graphene (NH2 -graphene) and carboxyl functionalized graphene (COOH-graphene) reinforced with cross-linked LY556 epoxy composites and compared with the neat cross-linked LY556 epoxy resin. 2. Experimental section 2.1. Modeling of cross-linked LY556 epoxy resin

LY556 epoxy resins are thermosetting polymers containing more than one epoxide group per molecule with excellent adhesion properties, good thermal stability, high modulus and corrosion resistance. Because of these excellent features, epoxy resins are widely used as polymer matrix to form polymer nanocomposites. The general molecular model of the LY556 epoxy resin (a) is given in Fig. 1. The hydrogen atom in the amine (NH2 ) groups of the curing agent (di ethylene toluene di amine – DETDA) molecule reacts with the epoxide groups of epoxy resin (b) as shown in Fig. 1. The resulting cured resin molecule (c) further reacts with epoxy molecules at the site of HN and NH2 and one curing agent molecule reacts at the site of another epoxide group. Finally, a crosslink (d) between the epoxy resin and the curing agent is formed. As the reaction continues, the epoxy resin and curing agent molecules generate more crosslinks. These crosslinks motion in all directions and generate a mesh of macromolecules [15, 16].


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Figure . Molecular modeling of cross-linking between (a) LY epoxy resin, (b) DETDA curing agent, (c) model of cured epoxy resin and (d) model of cross-linked epoxy resin under minimum energy.

2.2. Modeling of representative unit cell systems

In this study, DGEBA cross-linked with DETDA is used as a polymer matrix. Single layer graphene sheet, which has 162 carbon atoms in total, was chosen as the nanofiller in the composites as shown in Fig. 2. Graphene sheet was end grafted by adding hydrogen atoms at the ends for avoiding their unsaturated boundary effects [17, 18]. Chemical functionalization may be a viable solution to achieve a good dispersion as well as a strong adhesive interface between the surrounding polymer chains and graphene. Chemical functionalization is based on the covalent linkage of functional groups onto carbon scaffold of graphene. There are numerous difficulties that need to be focused upon in order to use graphene as an effective reinforcement in polymer composites. The dispersion of graphene is one of the most widely considered difficulties. Some of the organic molecules, such as –NHn , –CHn , –OH, and –COOH can be formed by chemical covalent bonds between the polymer chains and the functionalized graphene in the composites. Different functional groups are discussed, out of which amine group has a high reactivity and can be directly incorporated into the epoxy resin, as reported by Shen et al. [19]. This may overcome the problem of dispersion and agglomeration of graphene in the epoxy matrix. Thus the chemical covalent bond mechanism of functional groups to the



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Figure . Molecular model of nanocomposite consists of cross-linked LY epoxy resin with graphene and modified graphene as filler.

surface of the graphene is very useful in maintaining the stable bonds between functionalized graphene and the epoxy. 2.3. Force field and simulation procedure

We used COMPASS force field, which is implanted in Material studio (MS) 6.0 [20]. The valence parameters were derived using COMPASS force field ab initio parameterization techniques and validated using condensed phase properties in addition to empirical data for molecules in isolation. The COMPASS force field consists of three categories of energy terms: the bonded energy terms, the cross-terms, the non-bonded energy terms, a Coulombic function for electrostatic interactions and a 6–9 Lennard-Jones potential for van der Walls interactions and are follows in Equation 1. Etotal = Eb + Eθ + Eφ + Eχ + Eb,b + Eb,θ + Eb,φ + Eθ,φ +Eθ,θ + Eθ,θ ,φ + Eq + EvdW

(1)

where, Eb = covalent bond-stretching energy, Eθ = bond-angle bending energy, Eφ = torsion-angle rotation energy, Eχ = out-of-plane energy, Eq = electrostatic energy, EvdW = van der Walls energy and, Eb,b , Eb,θ , Eb,φ , Eθ,φ , Eθ,θ , Eθ,θ ,φ = cross terms representing the energy due to the interaction between bond stretch-bond stretch, bond stretch-bond bend, bond stretch-bond torsion, bond bend-bond torsion, bond bend-bond bend and bond bend-bond bend-bond torsion, respectively.

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The size of the simulation cell is adjusted to set the density of LY556 epoxy resin as 1.20 g/cc. In order to obtain a relaxed configuration through energy minimization via discover tool in Material Studio, further we performed an ‘anneal cycle’ from 300 to 550 K at intervals of 50 K to remove averse interaction in the initial structure. For this system equilibration procedure involved the conjugate gradient minimization method with high convergence root mean square force (1 × 10−3 Kcal/mol ˚ After minimization the simulation cell is subjected to immediate cooling by A). using the forcite quench dynamics run. Further simulated annealing dynamics tool is used in a mid-circle temperature of 2073 K. The thermal annealing procedure involves heating the system from 300 to 2073 K in 25 K increments followed by cooling to 300 K using the Forcite tool of MS. The time interval and the simulation run were set at 1.0 ps and 17.8 ps, respectively. All the MD simulations were performed using NVT ensemble and a pressure of 0.1 MPa. 3. Results and discussion 3.1. Tg of functionalized graphene epoxy composites

The glass transition is mainly caused by the freezing of the motion of chain segments i.e. local chain movement [21]. Therefore there are two factors to be considered, (a) free volume and (b) the mobility of chain segments, which will directly affect a polymer when it is cooled down and slewed to its glassy state. Our simulated result shows that the epoxy matrix with functionalized graphene can enhance Tg . As shown in Fig. 3 the COOH-graphene and NH2 -graphene epoxy composite has a higher Tg of 456.8 K and 461.4 K, which was 40 K and 45 K higher than Tg of neat bulk epoxy resin respectively. The simulation results show that the epoxy matrix reinforced with functionalized graphene can increase Tg . The main reason for the large enhancement of Tg is the modified groups which provided a stronger interlocking between the graphene and epoxy molecules. Ramanathan et al. [22] performed a comparative study concerning the effect of nanofillers including expanded graphite (EG), single walled nanotubes (SWNTs) and, functionalized graphene sheet (FGS) on the Tg of the epoxy nanocomposites. In case of FGS epoxy nanocomposites the great shift of Tg nearly 30 K. Whereas, in SWNT epoxy nanocomposites no significant shift of Tg was observed. As seen from above computational results of Tg were in good agreement with the experimental data [22] indicating that the simulation method can be effective way to predict Tg of graphene based epoxy nanocomposites. 3.2 Radial distribution function

The radial distribution function (RDF), ga-b (r) which is obtained directly from the MD simulations using forcite analysis in MS software. It is an important parameter which gives a measure of probability and used to study the influence of several factors, such as filler, cross-linking density, and additives, on the local structure (both



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Figure . Density versus temperature graph for functionalized graphene reinforced epoxy system: (a) graphene modified by –COOH, (b) graphene modified by –NH .

solid and liquid packing) of the constructed epoxy nanocomposites system [23]. g(r) is also defined as the probability of findings an atom in a spherical shell at a distance r from an arbitrary atom [24]. The RDF is calculated by given Equation 2. rAi − rB j 4π r2 dr V δ r − i= j ga−b (r) = (2) NA NB − NAB where, i and j are the ith and jth atom of the group A of NA atoms and B of NB atoms respectively; NAB is the number of atoms common to both groups A and B. Figure 4 shows the RDF curve, which is estimated for all three simulated mod˚ and 2.32 A ˚ correspond to chemical bond distance els. The first peaks around 2.1 A ˚ and 2.5 A ˚ between hydrogen and other atoms. The second peaks at around 2.4 A


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Figure . Total radial distribution function for three different epoxy composites at room temperature.

corresponds to the distance between bonded and non bonded carbon atoms. The subsequent intra-molecular peaks results from distance between atoms, including ˚ and carbon atoms in hydrogen and carbon atoms in H−C−C sequences (r = 2.16 A) ˚ [25, 26]. As the content of graphene increases, the C−C−C sequences (r = 2.44 A) overall molecular RDFs decrease for the direct chemical bonds between hydrogen and other atoms. However, the RDFs behavior changes for other bonds.

Conclusions In this study, the effects of functionalized graphene as an addition of cross-linked epoxy resin LY 556 were studied using MD simulation. Three different types of cross-linked epoxy systems were used for analysis, of which one has pristine graphene and two have different functional groups (NH2 -graphene and COOHgraphene). The simulation results show that for modified graphene epoxy composites of the estimated Tg are found to be 461.4 K (for NH2 -graphene) and 456.8 K (for COOH-graphene) which are higher than that of neat bulk epoxy resin. Furthermore, the effects of graphene on the growth of the local structures were deliberated by analyzing their RDFs.

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