Local mechanical properties of polymeric nanocomposites

The inclusion of a nanoparticle into a polymer matrix is studied by efficient Monte Carlo simulations. The resulting structural changes in the melt and glass exhibit a strong dependence on the strength of the polymer attraction to the surface of the filler. The mechanical properties of the nanocomposite are analyzed in detail through a formalism that permits calculation of local elastic constants. The average shear and Young’s modulus of the nanocomposite are higher than those of the pure polymer for neutral or attractive nanoparticles. For repulsive particles, these moduli are lower. Simulation of local properties reveals that a glassy layer is formed in the vicinity of the attractive filler, contributing to the increased strength of the composite material. In contrast, a region of negative moduli emerges around repulsive fillers, which provides a mechanism for frustration relief and a lowering of the glass transition temperature.

Figure 1

Density of the polymer matrix (substracting the volume of the particle) over a wide temperature range for the unfilled and attractive filler case. For clarity, results for other type of interactions are not shown. The glass transition temperature is extracted from the change of the slope. In the inset, the same results are presented but magnified for the range of interest. The lines are linear regressions of the data (solid line, unfilled polymer; dashed line, attractive particle).

Figure 2

Young’s modulus $E$ as a function of temperature divided by the glass transition temperature of each system for all cases studied in this paper.

Figure 3

(a) Distribution of the local stress $\overline{\sigma }$ with respect to the distance $r$ from the center of the nanoparticle for the three types of interaction considered in this paper, at $T=0.5$. (b) Filler-monomer pair distribution function $g_{12}\left(r\right)$ for $T=0.5$ as a function of the distance $r$ from the center of the nanoparticle.

Figure 4

(a) Distribution of the local ${\overline{C}}_{44}$ with respect to the distance $r$ from the center of the nanoparticle for the three types of interaction considered at $T=0.5$. (b) Distribution of the local ${\overline{C}}_{44}$ with respect to the distance $r$ from the center of the nanoparticle for the attractive particle in the melt and glass regime.

Figure 5

(a) (Color online) Color map of the local shear modulus ${\overline{C}}_{44}$ around the attractive nanoparticle at $T=0.2$. (b) Distribution of the local ${\overline{C}}_{44}$ for different cube lengths at $T=0.2$. A Gaussian distribution is observed for all levels of resolution. The inset compares the distributions for the pure and the filled polymer at the highest level of resolution considered here, $l=1.9\sigma$.