Interphase effect on the elastic and thermal conductivity response of polymer nanocomposite materials: 3D finite element study

Abstract

In this study, we developed 3-dimensional (3D) finite element modeling for the investigation of interphase effects on the elastic modulus and thermal conductivity of polymer nanocomposite materials filled with randomly oriented as well as unidirectional particles. We studied the effects of fillers geometry (long cylinders to sphere and thin discs), volume fraction and properties contrast and particularly the effect of interphase thickness and properties contrast on the effective thermal conductivity and elastic modulus of nanocomposite structures. Our results show that while the interphase effect is significant for the spherical fillers, it turns to be less effective as the fillers’ geometry deviates more from spherical shape. The obtained results could be useful to guide design of nanocomposite materials with superior elastic and thermal conductivity properties.

Introduction

Recent advances in the fabrication of nanoscale materials with extraordinary high thermal and mechanical properties such as graphene [1], [2], graphite nanosheets, carbon nanotubes [3], nanoclays [4] and metal oxide nanoparticles, has motivated an ongoing demand for the reinforcement of electrical, thermal and mechanical properties of polymer based materials. In comparison with microscale fillers, nanoscale fillers present considerably higher surface to volume ratio which significantly improve their reactivity [5]. In term of reinforcement in thermal conductivity and elastic stiffness of polymeric materials, from theoretical point of view, the two-phase nanocomposites materials would not have any priority in comparison with two-phase microcomposites, if one considers similar fillers shape ratios and volume fraction. However, in the case of formation of an interphase between the fillers and matrix with superior material properties than matrix, it would be expected that the nanocomposite materials present higher thermal and stiffness response. This is due to the existence of higher contacting surface of fillers with matrix and consequently higher interphase volume in the nanocomposite structures in comparison with microcomposites at the same fillers volume fraction. We should note that the interphase has a thickness in the order of 1–2 nm [6], i.e. several interatomic spacing. Thus, the interphase effect would be convincingly negligible in the microscopic polymer composites. The interphase thickness can be approximately assumed to be constant and can be viewed as intrinsic characteristics of the fillers and polymer matrix materials. Although this scale is at the limit of reliability of continuum mechanics assumptions, as far as the effective properties are concerned, the continuum mechanics approach can still be used [7].

It is already well known that the efficiency of the reinforcement in nanocomposite properties strongly depends on the fillers concentrations, geometry and properties as well. Although it is obvious that the interphase also plays an important role in the nanocomposite materials, no adequate information exist about the intensity of interphase effect on the final reinforcement in thermal conductivity and elastic stiffness of nanocomposites. From the experimental viewpoint, it is considerably difficult to obtain comprehensive knowledge on the interphase effect on the final composite effective properties. The experimental characterizations for the evaluation of interphase effect are time consuming and the results are dependent on the availability of nanoparticles with controlled shape and size. Moreover, the quality of experimental results depends on the ability in making homogeneous nanocomposites with controlled dispersion of fillers [5]. On the other hand, characterizations of such nanocomposites are difficult due to complexity and uncertainties [8] of experimental characterizations techniques at the nanoscale. In this frame, the use of theoretical and numerical approaches sounds promising. For the evaluation of two-phase composite materials, the analytical micromechanics theories such as Mori–Tanaka [9], [10] and the Halpin–Tsai [11] have been widely used [12], [13], [14]. These micromechanics methods have been modified to include the effects of interphase on the effective composite properties [7], [15], [16], [17], [18]. These methods could predict the effective properties of composite materials with reasonable accuracy. However, they cannot accurately consider the interactions between adjacent inclusions and they have limitation in the evaluation of the micro-stresses involved with individual inclusions [19]. The numerical methods, such as finite element (FE) have been also widely used for the modeling of thermal conductivity and elastic properties of composite structures [13], [14], [15], [16], [17], [19], [20], [21], [22], [23], [24]. By the use of finite element method it is possible to evaluate the micro-stresses and also more elaborately take into account the adjacent inclusions effects on the effective properties. In our recent study [19], we elaborately compared Mori–Tanaka, 3D finite element and statistical continuum theory of strong-contrast and we concluded that despite of modeling complexities and computational difficulties, the finite element estimations are more reliable and promising as well.

The objective of this paper is to investigate the interphase effects on the effective thermal conductivity and elastic stiffness of nanocomposite materials using 3D finite element approach. We should note that 2D finite element models could not accurately describe the fillers geometries in the fabricated nanocomposite samples [19]. In order to provide a better viewpoint in comparison with existing studies in the literature, 3D finite elements models were developed for unidirectional and randomly oriented fillers with different geometries varying from long cylinders to sphere and thin discs. In this work, the interphase is considered as the third phase which is introduced as the homogenous and isotropic covering layer of the outer surface of fillers within a distinct thickness. Then, we studied the effects of fillers geometry, volume fraction and properties contrast and more elaborately the effect of interphase thickness and properties contrast on the effective thermal conductivity and elastic response of the nanocomposite structures. We should note that in all the studied cases, the filler, interphase and matrix materials properties are assumed to be homogeneous and isotropic as well. Moreover, the perfect bonding conditions are applied between fillers, interphase and matrix. The herein reported results could be useful to guide the modeling and design of a wide range of nanocomposite materials reinforced by metal oxide particles, nanoclays, carbon nanotubes, graphene or graphite.