Materials Science Forum Vols. 654-656 (2010) pp 1654-1657 © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.654-656.1654
Determination of Interphase Thickness and Mechanical Properties of Effective Nanofillers in Polymer Nanocomposites by Molecular Dynamic Simulation Wen Xu1, a, Qinghua Zeng1, 2, b, Aibing Yu1, c, and Donald R Paul3, d 1
School of Materials Science and Engineering, The University of New South Wales, Sydney 2052, Australia 2 School of Engineering, University of Western Sydney, Penrith South DC NSW 1797, Australia 3 Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712, U.S.A.
a
[email protected] [email protected] [email protected] [email protected]
Keywords: Molecular dynamics simulation, polymer nanocomposites, interphase thickness, effective nanoclay, mechanical properties
Abstract. The properties of interphase in polymer composites are often different from those of bulk polymer matrix, which may include chemical, physical, microstructural, and mechanical properties. The nature of interphase is critical to the overall properties and performance of polymer materials, in particular in nanofiller reinforced composites. Experimental efforts have been made to determine the effective interphase thickness and its properties, for example, by nanoindentation and nanoscratch techniques. Yet, it is very difficult to quantify the interphase and its properties because of its nanoscale nature and the unclear boundary. In this regard, computer simulation, e.g., molecular dynamics, provides an effective tool to characterize such interphase and the properties. In this work, molecular dynamics simulations are applied to quantify the interphase thickness in clay-based polymer nanocomposites. Then, the mechanical properties of the so-called effective nanofiller (i.e., the physical size of nanofiller plus the thickness of interphase) will be determined by a series of simulations. Introduction The interphase is a main structural feature of polymer nanocomposites. It plays an important role in understanding the size effect and enhancement mechanisms of nanocomposites. The interphase and thickness effects on the mechanical, structural, physical properties of polymer thin films and polymer nanocomposites have been investigated by many recent studies [1-3]. The properties of interphase in polymer composites are often different from those of bulk polymer matrix, which may include chemical, physical, microstructural, and mechanical properties depending on the filler and matrix used [4-5]. The properties of an interphase are mainly decided by the components properties, the environmental conditions and manufacturing processes. Since the components are different in each system, so the properties of an interphase are unique [6]. Experimental efforts have been made to determine the effective interphase thickness and its properties by means of various techniques including, for example, the nanoindentation and nanoscratch techniques. The first nanoindentation test has been made to characterize the carbon fibre-epoxy interphase [7]. Kim et al. [8] used nanoindentation and nanoscratch and thermal capacity jump measurement to determine the interphase thickness and properties of glass fibre-vinylester matrix composites with different silane coupling agents. However, it is still very difficult to quantify the interphase thickness and properties because of its nanoscale nature and unclear boundary. With the increase of computational power and the development of novel algorithms, computer simulation, e.g., Monte Carlo (MC), molecular dynamics (MD) simulation became useful tools. MC method is faster than MD simulation. However, it cannot obtain the dynamic properties of atoms which we need to analyse the interphase thickness. In this paper, MD simulation was carried out to determine the interphase thickness of clay-based polymer nanocomposites as well as mechanical properties of a single effective clay platelet. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 137.154.73.31-27/05/10,00:37:29)
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Simulation method MD simulations were carried out using MATERIALS STUDIO4.3 software package (Accelrys Co.) The clay structure consists of octahedral sheets of aluminum or magnesia with each sandwiched by two silica tetrahedral sheets [9]. The polymer is nylon 6, and the surfactant is octadecyltrimethyl ammonium (ODTMA), the overall dimension of the MD cell is a=25.959Å, b=27.0459Å, c=175Å in which there are ten ODTMA and ninety nylon 6 chains. The simulation method has been validated through the comparison of the calculated and experimental mechanical properties of a single clay platelet [10]. The force field employed is CVFF (Consistent Valence Force Field).The equations of motion were solved with the Verlet velocity algorithm [11]. The time step of integration was set to 0.001 ps. The van der Waals and Coulomb forces were calculated by Ewald summation method. Initial velocities were randomly assigned according to Boltzmann distribution. To achieve a maximum mixing of the different components, a NVT MD simulation was initially performed at elevated temperature of 513 K for 10 ps, followed by a few steps of NVT MD simulations down to 298 K. The equilibration state has been achieved at 298 K in the first 5 ps, judged from the stable potential energy and the data collection has been made to the last 45 ps. During the simulation, the temperature was controlled by Anderson method. To determine the compression modulus of a single effective clay platelet, NPT MD simulations of 100 ps were performed under different compressive stresses applied along z direction.
no14 it 12 art 10 ne 8 cn 6 oc 4 ev 2 tia le 0 R-2
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Distance from clay surface Fig.1 The snapshot of the final structure of a MD simulation.
Fig.2 Concentration profiles of surfactant, polymer and the whole structure.
Results and Discussion The dynamic behavior of the structure was described by tracking the movement of molecules during simulation. It is shown that the head groups (nitrogen atoms of ODTMA in large blue ball) move toward clay surface, this is mainly due to the strong electrostatic interaction energy between the positive head group and the negative clay surface. In the meantime, the polymer molecules are found to be mixed with the surfactant molecules, this may attribute to the exposed clay surface available to polymer chains as suggested by Fornes et al [12]. Fig. 1 is extracted from the snapshot of the final MD simulated structure, showing the clay platelet and the interphase. One of the main characteristics of interphase is its thickness which can be defined as the distance from which the atomic properties (atomic density profile, atomic mobility) is different from those in bulk systems. The atomic concentration profiles of surfactant and polymer (Fig. 2) shows that the surfactants locate within 30 Angstroms of clay surface, and the polymer matrix reach its uniform bulk density beyond 30 Angstroms of clay surface. Thus, we can estimate the interphase thickness as 3 nm. For a molecular system under equilibrium state, all atoms still move around their equilibrium locations. Such dynamic property can be expressed by the mean squared displacement (MSD) of the atoms or groups. Based on the Brownian motion the MSD is proportional to the time elapsed. ＜r2＞=6Dt+C.
(1)
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PRICM7
where D is the most important parameter which represents the self-diffusion of atoms. D value is equal to the initial slope in a MSD-time curve. Fig. 3 shows the MSD curves of atoms located in each 1 nm layer away from clay surface. It was found that the dynamic motion of the atoms increases with their distance from clay surface. Moreover, there is a significant change (Fig. 4) of atomic mobility starting at a distance between 3 and 4 nm away from clay surface, that is, the atoms move faster beyond 30 Angstroms away from the surface. The interphase is a mixture of surfactant and nylon 6 because nylon 6 can approach to the exposed clay surface, owing to the interaction between polar clay and polar nylon 6 as suggested by Fornes et al. [12]. In addition, as compared to those in bulk polymer matrix, a denser atomic packing within the interphase was observed. Such denser packing results in a lower atomic self-diffusion within the interphase.
Fig. 3 MSD plots of atoms located in each nanometer thickness from clay surface.
Fig. 4 The atom mobility versus distance from clay surface.
Based on the above calculated interphase thickness, we constructed an effective clay platelet which consists of a clay platelet sandwiched by two 3 nm interphase of surfactant and nylon 6 mixture. As is shown in Fig. 5, the strain increases with the applied compressive stress, and the estimated compression modulus is obtained through the initial slope of the stress-strain curve. Based on the fitted curve, the calculated modulus is 28.54 GPa for the effective clay platelet of a mass ratio of 0.33 between clay and organic. In addition, the stress-strain curves along x and y directions are almost the same, and the structure deformation along x and y directions is not so obvious compared with that along z direction. 30 longitude
Stress σ (Gpa)
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Fig. 5 Stress-strain curves of effective nanoclay along x, y (lateral) and z (longitude) directions. Conclusions MD simulation has been used to calculate the interphase thickness of clay-based polymer nanocomposites. The atomic density profile and atomic mobility are used to calculate the interphase thickness. Both methods indicate that the interphase thickness of clay-based nylon 6 nanocomposites is 3 nm. The effective clay platelet is constructed to calculate its compression
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modulus. The stress-strain curves indicate that the strain (structure deformation) increases with the applied external stress. Such structural deformation is limited and equivalent along x and y direction. The final compression modulus along z direction is estimated to be 28.54 GPa according to the stress-strain curve. Acknowledgment The authors are grateful to the ARC and the DIISR for the financial support through the Australia-India collaborative research program. References [1] [2] [3] [4] [5]
Lee, W.J., S.P. Ju, and C.H. Cheng: Langmuir, 2008. 24(23): p. 13440-13449. Sheng, N., et al: Polymer, 2004. 45(2): p. 487-506. Wang, H.Y., et al: Acta Mater., 2002. 50(17): p. 4369-4377. Drzal, L.T., M.J. Rich, and P.F. Lloyd: Journal of Adhesion, 1983. 16(1): p. 1-30. Kim, J.-K. and Y.W. Mai, Engineered Interfaces In Fiber Reinforced Composites. 1st ed. 1998, Amsterdam ; New York: Elsevier Sciences. xiii, 401 p. [6] Kim, J.K. and A. Hodzic: Journal of Adhesion, 2003. 79(4): p. 383-414. [7] Williams, J.G., et al: Mater. Sci. Eng. A,1990. 126: p. 305-312. [8] Kim, J.K., M.L. Sham, and J.S. Wu: Composites Part a-Applied Science and Manufacturing, 2001. 32(5): p. 607-618. [9] Zeng, Q.H., A.B. Yu, and G. Lu: in Advances in Composite Materials and Structures, Pts 1 and 2, J.K. Kim, et al., Editors. 2007, Trans Tech Publications Ltd: Stafa-Zurich. p. 753-756. [10] Luo, J.J. and I.M. Daniel: Composites Science and Technology, 2003. 63(11): p. 1607-1616. [11] Verlet, L.: Physical Review, 1967. 159(1): p. 98-103. [12] Fornes, T.D., D.L. Hunter, and D.R. Paul: Macromolecules, 2004. 37(5): p. 1793-1798.
