Graphene Double-Layer Coating

Subscriber access provided by Kaohsiung Medical University

Letter

Thermal Analysis of Montmorillonite/Graphene Doublelayer Coating as a Potential Lightning Strike Protective Layer for Crosslinked Epoxy by Molecular Dynamics Simulation Farzin Rahmani, and Sasan Nouranian ACS Appl. Nano Mater., Just Accepted Manuscript • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Nano Materials

Thermal Analysis of Montmorillonite/Graphene Double-layer Coating as a Potential Lightning Strike Protective Layer for Crosslinked Epoxy by Molecular Dynamics Simulation Farzin Rahmani,† Sasan Nouranian*,†

†

Department of Chemical Engineering, University of Mississippi, MS, 38677, United States

ABSTRACT: Non-reactive molecular dynamics simulations were performed to determine the thermal conductivities and through-thickness temperature profiles of unprotected crosslinked epoxy, as well as protected epoxy with graphene (Gr) and montmorillonite (MMT)/Gr surface coatings against lightning strike damage. Three representative hot surface temperatures of 500 K, 1,000 K, and 10,000 K were used for the thermal analysis. The MMT/Gr double-layer coating provided the most efficient thermal shielding of the epoxy sublayer and the epoxy/MMT/Gr system exhibited a 55% lower thermal conductivity than that of the neat epoxy. The results imply that the MMT/Gr double-layer coating may be used for lightning strike protection.

KEYWORDS: graphene, montmorillonite, epoxy, thermal analysis, lightning strike damage, molecular dynamics simulation

Lightning strike damage protection is a critical aspect of the design of modern aircraft composite structures. Near the lightning strike site on a composite part, a peak current of about 200 kA and a lightning arc plasma temperature of about 20,000°C may be observed in a fraction of a second.1 As composite materials gradually replace aluminum in critical aircraft parts, such as fuselage and

1 ACS Paragon Plus Environment

ACS Applied Nano Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 17

wings, the lightning strike hazard increases to alarming levels because of a generally lower electrical and thermal conductivities of the composite materials compared to aluminum. Therefore, it is imperative to protect the new-generation composite-heavy aircraft, such as Boeing 787 Dreamliner, against catastrophic failure due to lightning strike damage. During the strike event, the polymer matrix, which is generally epoxy, decomposes through ignition and pyrolysis followed by a catastrophic fiber delamination in the composite. To mitigate the localized damage, the electric charge needs to be swiftly distributed over a large surface area. Moreover, the transverse heat conduction should be minimized by employing a suitable thermal shielding mechanism. While the use of metal meshes and ply-integrated interwoven wires2 have proven to be effective in the lightning strike protection of fiber-reinforced composites, these meshes and wires significantly increase the weight of the structures. Herein, the efficacy of a novel lightweight montmorillonite (MMT)/graphene (Gr) double-layer protective top coating in mitigating the lightning strike damage extent in the crosslinked epoxy sublayer is investigated using molecular dynamics (MD) simulation. Gr is known to possess excellent electrical and thermal conductivities,3 while montmorillonite is known for its superior thermal shielding characteristics.4–7 In an interesting work by Kim et al.,7 supersonically sprayed clay microparticles onto flexible substrates provided excellent thermal insulating properties. Though lightning is an electrothermal phenomenon, the current work only focuses on the thermal aspects of the strike event, thereby providing molecular insights into the thermal shielding behavior of the MMT/Gr coating and its implications for lightning strike damage mitigation. While the thermal properties of Gr8 and Graphene oxide,9 Gr/epoxy10–14 and MMT/epoxy15,16 systems have been studied before, to the best of our knowledge, the thermal behavior of an epoxy/MMT/Gr


Page 3 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


multilayer system has not been investigated yet. In what follows, the MD simulation details and thermal analysis data are presented. All initial chemical structures were created in BIOVIA Materials Studio (V8.0). Initially, a 2:1 ratio17,18 of epoxy monomers (bisphenol A diglycidyl ether (DGEBA) with the chemical formula C21H24O4) to hardener molecules (1,3-phenylenediamine) were packed in a 3D-periodic simulation box (target density: 1.2 g/cm3) at 298 K in the Amorphous Cell module of Materials Studio. All simulations in this work were performed using the Consistent Valence Forcefield (CVFF).19 This forcefield has previously been used for the MD simulation of similar systems, such as Gr-polymer20 and polymer-MMT21 and is deemed appropriate for this work. However, it is non-reactive and, therefore, does not allow for chemical bond breaking or formation in a material degradation event at high temperatures. Next, a geometry minimization was performed on the epoxy/hardener system using the Conjugate Gradient method22 followed by equilibration of the system at 298 K using the NPT ensemble for 1 ns. In all simulations, a time step of 1 fs was used. The cut-off distance for long-range intermolecular interactions was fixed at 12 Å. The system temperature and pressure were controlled by Andersen thermostat and barostat,23 respectively. Once the system density was equilibrated at around 1.18 g/cm3, a crosslinking algorithm in Materials Studio24 was employed with an initial target of 100% curing agent conversion. After the conclusion of the crosslinking procedure, an actual conversion of about 85% was achieved for the hardener. Next, MMT crystal structure (a = 5.171 Å, b = 8.956 Å, and c = 9.740 Å; α = 90º, β = 96.1º, γ = 90º)25 was imported from the American Mineralogist Crystal Structure Database (Figure 1). Three stacked MMT layers were constructed from this unit crystal in the size of 40×40×17 Å. Finally, six layers of pristine graphene (Gr) (size: 40×40 Å2) were separately stacked at an



Page 4 of 17

equilibrium interlayer distance of 4 Å. In this work, the number of Gr and MMT layers were fixed at six and three, respectively, and the effects of the number of Gr and MMT layers on the thermal properties of the composite systems were not investigated. Altogether, three systems were constructed from the above base layers in Materials Studio: 1) neat crosslinked epoxy, 2) crosslinked epoxy/Gr, and 3) crosslinked epoxy/MMT/Gr (Figure 1). Structural details of these systems are summarized in Table 1.

TABLE 1 Structural details of the different systems Material System Neat epoxy Epoxy/Gr Epoxy/MMT/Gr

Number of Monomer/Hardener Molecules 358/179 270/135 166/83

Layer Thickness (Å)a,b Epoxy MMT 135 115 95 17

Gr 18 18

a

Simulation box size for all systems: 40×40×135 Å3 b The interfacial distance between the layers is about 2-5 Å in the different systems

Next, these systems were imported to the LAMMPS software package26 and equilibrated at 298 K using the NPT ensemble for 10 ns. Then, a 2D simulation was run (periodicity in the x and y-directions) on the equilibrated structures using the NVE ensemble for 1 ns, where the top surface was subjected to temperatures of 500 K, 1,000 K, and 10,000 K (hot surface in Figure 1).


Page 5 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Initial snapshot of the epoxy/MMT/Gr triple-layer system. The unit crystal structure of MMT is shown in the zoomed-in view. Once the systems reached thermal equilibrium, a through-thickness temperature profile was generated as a function of normalized thickness for each material system. For this purpose, the simulation box was divided into N slabs and the temperature was calculated for each slab. To investigate the effect of the slab size on the temperature and number of atoms in each slab, three different slab sizes of 1, 2, and 4 Å were used. In Figure 2, the effect of slab size on the temperature profile evolution of the triple-layer epoxy/MMT/Gr system exposed to the hot surface temperature of 1,000 K and the corresponding number of atoms per slab as a function of the normalized thickness are given. As seen in this figure, increasing the slab size smooths the temperature profiles, which is more evident for the MMT layers (Figure 2a). It should be noted



Page 6 of 17

herein that, in the MD simulation, only the configurational or kinetic energy based temperature is calculated. Therefore, the observed effect of temperature drop between the MMT layers (Figure 2a) is not unphysical, but has to do with smaller number of atoms present in between these layers at any slab size (Figure 2b). At the extreme case (slab size of 1 Å), there is essentially vacuum in between the MMT layers at the molecular scale. This point is revisited later.

(a)

(b)

Figure 2. a) Through-thickness temperature profile of the epoxy/MMT/Gr system exposed to a hot surface temperature of 1,000 K as a function of normalized thickness and slab size; b) Number of atoms/slab as a function of normalized thickness and slab size for the material system given in a). The simulation time is 10 ns.

In Figure 3, an example of the temperature profile evolution and equilibration with increasing simulation time is given for the neat crosslinked epoxy system (hot surface temperature of 1,000 K). In this figure, the temperature profiles at 5 ns and 10 ns overlap, signifying the achievement of thermal equilibrium for this system. The temperature profiles for all systems were compared after 10 ns of simulation.


Page 7 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Evolution of the through-thickness temperature profile in the neat crosslinked epoxy system towards equilibration as a function of simulation time. The hot surface temperature is 1,000 K.

Müller-Plathe’s algorithm27 was employed to calculate the thermal conductivity of the various systems. For this purpose, a slab size of 1 Å was used. Thermal conductivity was then calculated using the following formula:27 m 2 2 ( vh − vc ) transfers 2 λ= , ∂T 2tLx Ly ∂z

∑

(1)

where t is the simulation time, m is the particle mass, Lx and Ly are the simulation box lengths in x- and y-directions, respectively, T is the temperature, and v is the atomic velocity. Subscripts h and c refer to hot and cold atom, respectively. The sum is over all kinetic energy transfers between the particles and the temperature gradient in the z-direction is ensemble-averaged. More details about the algorithm are given in Müller-Plathe’s work.27 The through-thickness temperature distributions are given for the two protected epoxy systems, i.e., epoxy/Gr and epoxy/MMT/Gr, as well as the control epoxy system for each of the 7 ACS Paragon Plus Environment


Page 8 of 17

three surface temperatures (500 K, 1,000 K, and 10,000 K) are given in Figure 4. In this figure, the temperature data are given for a slab size of 1 Å. The unprotected epoxy system shows a flat temperature profile for all three cases of the surface temperatures. The thermal degradation onset temperature for the neat crosslinked epoxy is around 680 K,28 and, hence, it is implied that the system should undergo complete thermal degradation during the lightning strike event. In this work, the thermal degradation of epoxy and the other systems are only inferred from the thermal distribution observation after 10 ns. This analysis is just suggestive and not based on the actual complex physics and chemistry of thermal degradation that may be responsible for the degradation phenomenon. When a Gr protective layer is applied to the surface of epoxy (epoxy/Gr system), a significant drop is observed for the local temperatures in the epoxy layer at all hot surface temperatures (a 30-50% relative temperature drop compared to the neat epoxy system) (Figure 4). In addition, a decrease in the local temperature is observed when transitioning between the Gr sheets in the protective Gr layer. This phenomenon is attributed to the lower transverse thermal conductivity of Gr compared to its longitudinal thermal conductivity.29 At the epoxy/Gr interface, another drop in the local temperature is observed, which is most noticeable at 10,000 K (Figure 4c). This temperature drop is due to a strong phonon scattering at the epoxy/Gr interface as a result of a weak bonding and phonon mismatch between the epoxy and Gr layers.30 The data in Figure 4 imply that a relatively strong thermal protection is observed when the crosslinked epoxy is coated with a thin Gr layer.


Page 9 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b)

(a)

(c) Figure 4. Through-thickness temperature profiles in the epoxy, epoxy/Gr, and epoxy/MMT/Gr systems exposed to a hot surface temperature of (a) 500 K, (b) 1,000 K, and (c) 10,000 K. The simulation time is 10 ns. The temperature of the onset of degradation for neat epoxy is about 680 K.28

A still stronger thermal protection is observed when a thin MMT/Gr double-layer coating is applied to the epoxy surface (epoxy/MMT/Gr system). Similar to the epoxy/Gr system, no degradation of epoxy is observed at the lower surface temperature of 1,000 K (Figure 4b). In this case, the thermal barrier effect of MMT is more noticeable at high temperatures. At lower temperatures, MMT and Gr exhibit a similar thermal protection behavior (Figures 4a and 4b).



Page 10 of 17

Transitioning between each MMT layer, a sharp drop of local temperature is observed, which is attributed to the existence of local atomic-scale “vacuum” in the interlayer spacing. This successive layer-by-layer thermal shielding is clearly seen in Figure 4. While at the smallest slab size for the calculation of the local temperature, there is “vacuum” between the MMT layers, the conduction heat transport through the interface is still taking place, since the interfacial atoms are interacting with one another across the interface due to long-range interactions. Therefore, the interfacial effect on heat conduction is not necessary neglected. The interlayer distance between the MMT layers is in the order of Ångströms, well within the range of surface atom interactions. So, the presence of “vacuum” in the atomic scale, as discussed in this work, does not mean a vacuum at the macroscale. Moreover, the absence of interlayer vacuum at the macroscale does not necessary translate to a significant degradation in the thermal shielding of the MMT layer. Essentially, at any slab size for the temperature calculation (1, 2, and 4 Å in this work), the thermal shielding effect of both MMT and Gr layers is observed. However, the apparent sudden drop in the local temperature vanishes with larger slab sizes (Figure 2a). Decreasing clay bulk density or increasing its porosity have been shown to cause a drop in the effective thermal conductivity of the material.31 The MMT interlayer “vacuum” herein is loosely corresponding to porosity. Thermal conductivities (λ) of the neat crosslinked epoxy, epoxy/Gr, and epoxy/MMT/Gr systems are given in Table 2. By applying a top Gr coating to the neat crosslinked epoxy, a 27% reduction in the thermal conductivity of the composite is observed. However, a top coating of MMT/Gr brings about a nearly 55% reduction in the thermal conductivity of the system. This observation signifies a better thermal shielding of the epoxy sublayer when the MMT/Gr system is used as the top coating.


Page 11 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE 2 Thermal conductivities (λ) of the various systems System Epoxy Epoxy/Gr Epoxy/MMT/Gr a

Calculated λ (W/m K) 0.11±0.09 0.08±0.01 0.05±0.007

Experimental λ (W/m K) 0.15-0.25a -

From the work of Chung and Lin32

In summary, by computationally investigating the through-thickness temperature profiles and thermal conductivities of unprotected neat crosslinked epoxy, and protected epoxy/Gr, and epoxy/MMT/Gr systems against lightning strike damage, it is implied that the MMT/Gr top coating has a great potential to be used as a lightning strike damage protection measure for epoxy-based composite systems. A more thorough multi-physics (electrothermal) analysis of the epoxy/MMT/Gr system may further reveal its lightning strike damage mitigation efficacy. Because of the higher thermal and electrical conductivity of Gr, it is anticipated that the lightning strike energy is dispersed in the Gr layer, but it will eventually degrade as the temperature rises during the strike event, well below the upper limit of hot surface temperature in this work. The same may hold true for the MMT layer.

AUTHOR INFORMATION Corresponding Author: * Email: [email protected] ORCID ID: Sasan Nouranian: 0000-0002-8319-2786 Notes



Page 12 of 17

The authors declare no competing ﬁnancial interest. ACKNOWLEDGEMENTS This work was sponsored by a re-grant from the National Aeronautics and Space Administration (NASA) through the Mississippi Space Grant Consortium under the award number NNX15AH78H. The authors also wish to acknowledge Dr. Nathan E. Murray for his support.

REFERENCES (1)

Klomp-de Boer, R.; Smeets, M. Lightning Strike Behaviour of Thick Walled Composite Parts; Nationaal Lucht- en Ruimtevaartlaboratorium (National Aerospace Laboratory, NLR), Report No. NLR-TP-2013-401, 2013.

(2)

Gagné, M.; Therriault, D. Lightning Strike Protection of Composites. Prog. Aerosp. Sci. 2014, 64, 1–16.

(3)

Shahil, K. M. F.; Balandin, A. A. Thermal Properties of Graphene and Multilayer Graphene: Applications in Thermal Interface Materials. Solid State Commun. 2012, 152 (15), 1331–1340.

(4)

Uddin, F. Clays, Nanoclays, and Montmorillonite Minerals. Metall. Mater. Trans. A 2008, 39 (12), 2804–2814.

(5)

Allie, L.; Thorn, J.; Aglan, H. Evaluation of Nanosilicate Filled Poly (Vinyl Chloride-CoVinyl Acetate) and Epoxy Coatings. Corros. Sci. 2008, 50 (8), 2189–2196.

(6)

Luangtriratana, P.; Kandola, B. K.; Myler, P. Ceramic Particulate Thermal Barrier Surface Coatings for Glass Fibre-Reinforced Epoxy Composites. Mater. Des. 2015, 68, 232–244. 12 ACS Paragon Plus Environment

Page 13 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(7)

Kim, D.-Y.; Lee, J.-G.; Joshi, B.; Lee, J.-H.; Al-Deyab, S. S.; Yoon, H. G.; Yang, D. R.; Yarin, A.; Yoon, S. S. Supersonically Sprayed Thermal Barrier Layers Using Clay MicroParticles. Appl. Clay Sci. 2016, 120, 142–146.

(8)

Alamusi; Li, H.; Ning, Y.; Gu, B.; Hu, N.; Yuan, W.; Jia, F.; Liu, H.; Li, Y.; Liu, Y. Molecular Dynamics Simulations of Thermal Expansion Properties of Single Layer Graphene Sheets. Mol. Simul. 2018, 44 (1), 34–39.

(9)

Sun, Y.; Chen, L.; Cui, L.; Zhang, Y.; Du, X. Molecular Dynamics Simulation of the Effect of Oxygen-Containing Functional Groups on the Thermal Conductivity of Reduced Graphene Oxide. Comput. Mater. Sci. 2018, 148, 176–183.

(10)

Teng, C.-C.; Ma, C.-C. M.; Lu, C.-H.; Yang, S.-Y.; Lee, S.-H.; Hsiao, M.-C.; Yen, M.-Y.; Chiou, K.-C.; Lee, T.-M. Thermal Conductivity and Structure of Non-Covalent Functionalized Graphene/epoxy Composites. Carbon N. Y. 2011, 49 (15), 5107–5116.

(11)

Li, Q.; Guo, Y.; Li, W.; Qiu, S.; Zhu, C.; Wei, X.; Chen, M.; Liu, C.; Liao, S.; Gong, Y. Ultrahigh Thermal Conductivity of Assembled Aligned Multilayer Graphene/epoxy Composite. Chem. Mater. 2014, 26 (15), 4459–4465.

(12)

Lian, G.; Tuan, C.-C.; Li, L.; Jiao, S.; Wang, Q.; Moon, K.-S.; Cui, D.; Wong, C.-P. Vertically Aligned and Interconnected Graphene Networks for High Thermal Conductivity of Epoxy Composites with Ultralow Loading. Chem. Mater. 2016, 28 (17), 6096–6104.

(13)

Zhang, P.; Zeng, J.; Zhai, S.; Xian, Y.; Yang, D.; Li, Q. Thermal Properties of Graphene Filled Polymer Composite Thermal Interface Materials. Macromol. Mater. Eng. 2017. 13 ACS Paragon Plus Environment


(14)

Page 14 of 17

Loeblein, M.; Tsang, S. H.; Pawlik, M.; Phua, E. J. R.; Yong, H.; Zhang, X. W.; Gan, C. L.; Teo, E. H. T. High-Density 3D-Boron Nitride and 3D-Graphene for High-Performance Nano–thermal Interface Material. ACS Nano 2017, 11 (2), 2033–2044.

(15)

Bozkurt, E.; Kaya, E.; Tanoğlu, M. Mechanical and Thermal Behavior of Non-Crimp Glass Fiber Reinforced Layered Clay/epoxy Nanocomposites. Compos. Sci. Technol. 2007, 67 (15–16), 3394–3403.

(16)

Lakshmi, M. S.; Narmadha, B.; Reddy, B. S. R. Enhanced Thermal Stability and Structural Characteristics of Different MMT-Clay/epoxy-Nanocomposite Materials. Polym. Degrad. Stab. 2008, 93 (1), 201–213.

(17)

Fan, H. B.; Yuen, M. M. F. Material Properties of the Cross-Linked Epoxy Resin Compound Predicted by Molecular Dynamics Simulation. Polymer (Guildf). 2007, 48 (7), 2174–2178.

(18)

Varshney, V.; Patnaik, S. S.; Roy, A. K.; Farmer, B. L. A Molecular Dynamics Study of Epoxy-Based Networks: Cross-Linking Procedure and Prediction of Molecular and Material Properties. Macromolecules 2008, 41 (18), 6837–6842.

(19)

Dauber‐Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Hagler, A. T. Structure and Energetics of Ligand Binding to Proteins: Escherichia Coli Dihydrofolate Reductase‐trimethoprim, a Drug‐receptor System. Proteins Struct. Funct. Bioinforma. 1988, 4 (1), 31–47.

(20)

Awasthi, A. P.; Lagoudas, D. C.; Hammerand, D. C. Modeling of Graphene–polymer Interfacial Mechanical Behavior Using Molecular Dynamics. Model. Simul. Mater. Sci. 14 ACS Paragon Plus Environment

Page 15 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Eng. 2008, 17 (1), 15002. (21)

Karataş, D.; Tekin, A.; Bahadori, F.; Çelik, M. S. Interaction of Curcumin in a Drug Delivery System Including a Composite with Poly (Lactic-Co-Glycolic Acid) and Montmorillonite: A Density Functional Theory and Molecular Dynamics Study. J. Mater. Chem. B 2017, 5 (40), 8070–8082.

(22)

Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Iterative Minimization Techniques for Ab Initio Total-Energy Calculations: Molecular Dynamics and Conjugate Gradients. Rev. Mod. Phys. 1992, 64 (4), 1045.

(23)

Andersen, H. C. Molecular Dynamics Simulations at Constant Pressure And/or Temperature. J. Chem. Phys. 1980, 72 (4), 2384–2393.

(24)

DeJoannis, J.; Todd, S.; Wescott, J. Materials Studio Script: Cross-Link between an Oligomer and Crosslinker Using Atomistic Models. 2017.

(25)

Gournis, D.; Lappas, A.; Karakassides, M. A.; Többens, D.; Moukarika, A. A Neutron Diffraction Study of Alkali Cation Migration in Montmorillonites. Phys. Chem. Miner. 2008, 35 (1), 49–58.

(26)

Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117 (1), 1–19.

(27)

Müller-Plathe, F. A Simple Nonequilibrium Molecular Dynamics Method for Calculating the Thermal Conductivity. J. Chem. Phys. 1997, 106 (14), 6082–6085.

(28)

Gu, A.; Liang, G. Thermal Degradation Behaviour and Kinetic Analysis of 15 ACS Paragon Plus Environment


Page 16 of 17

Epoxy/montmorillonite Nanocomposites. Polym. Degrad. Stab. 2003, 80 (2), 383–391. (29)

Pop, E.; Varshney, V.; Roy, A. K. Thermal Properties of Graphene: Fundamentals and Applications. MRS Bull. 2012, 37 (12), 1273–1281.

(30)

Du, F.; Yang, W.; Zhang, F.; Tang, C.-Y.; Liu, S.; Yin, L.; Law, W.-C. Enhancing the Heat Transfer Efficiency in Graphene–epoxy Nanocomposites Using a Magnesium Oxide–graphene Hybrid Structure. ACS Appl. Mater. Interfaces 2015, 7 (26), 14397– 14403.

(31)

Gualtieri, M. L.; Gualtieri, A. F.; Gagliardi, S.; Ruffini, P.; Ferrari, R.; Hanuskova, M. Thermal Conductivity of Fired Clays: Effects of Mineralogical and Physical Properties of the Raw Materials. Appl. Clay Sci. 2010, 49 (3), 269–275.

(32)

Chung, S.-L.; Lin, J.-S. Thermal Conductivity of Epoxy Resin Composites Filled with Combustion Synthesized H-BN Particles. Molecules 2016, 21 (5), 670.


Page 17 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Contents Graphic


Graphene Double-Layer Coating

Recommend Documents