Investigation of interphase effects in silica-polystyrene nanocomposites based on a hybrid molecular-dynamics–finite-element simulation framework

A recently developed hybrid method is employed to study the mechanical behavior of silica-polystyrene nanocomposites (NCs) under uniaxial elongation. The hybrid method couples a particle domain to a continuum domain. The region of physical interest, i.e., the interphase around a nanoparticle (NP), is treated at molecular resolution, while the surrounding elastic continuum is handled with a finite-element approach. In the present paper we analyze the polymer behavior in the neighborhood of one or two nanoparticle(s) at molecular resolution. The coarse-grained hybrid method allows us to simulate a large polymer matrix region surrounding the nanoparticles. We consider NCs with dilute concentration of NPs embedded in an atactic polystyrene matrix formed by 300 chains with 200 monomer beads. The overall orientation of polymer segments relative to the deformation direction is determined in the neighborhood of the nanoparticle to investigate the polymer response to this perturbation. Calculations of strainlike quantities give insight into the deformation behavior of a system with two NPs and show that the applied strain and the nanoparticle distance have significant influence on the deformation behavior. Finally, we investigate to what extent a continuum-based description may account for the specific effects occurring in the interphase between the polymer matrix and the NPs.

Figure 1

Simulated hybrid systems in the undeformed configurations; only the bottom halves are displayed: (a) one single silica nanoparticle (yellow), (b) two silica nanoparticles (yellow) embedded in a polystyrene matrix and simulated using the hybrid scheme (finite elements: green; anchor points: blue; polystyrene superatoms: red); geometric quantities such as nanoparticle diameter and domain extensions are introduced in Sec. 3c.

Figure 2

Spatial setup of the coupled system: MD particles are given as small spheres, anchor points as large spheres; the overall coupling is given by the coupling between the anchor points and the continuum (via the Arlequin method) and the coupling between the anchor points and the polymer beads; the weighting factor $\alpha$ is used for energy blending.

Figure 3

Departing from the undeformed configuration, the staggered coupling scheme iterates between a static FE simulation (coupling between anchor points and the continuum) and an equilibration of the MD system (coupling between anchor points and the particle domain) until equilibrium of the deformed system is obtained.

Figure 4

(a) Mean FE stress ${\overline{\sigma }}_{PS}^{FE}$ (pure PS) and ${\overline{\sigma }}_{NC}^{FE}$ (NC with a single NP) evaluated after 100 MD-FE iteration steps in each load step; (b) relative difference $\delta {\overline{\sigma }}^{FE}$ at each load step; a strain of ${\varepsilon }_{}^{FE}=1\%$ is applied in every load step. Both figures have been published previously [46].

Figure 5

Order parameter $P_2$ of chain segments consisting of five monomers, displayed as a function of the distance from the NP surface in case of the undeformed sample and for strains of $3\%$ and $7\%$.

Figure 6

Hybrid simulation: normalized strain ${\tilde{\varepsilon }}^{\mathit{NP}}$ between NP centers as a function of global strain ${\varepsilon }_{}^{\mathit{MD}}$ for different initial interparticle distances $L_{}^{\mathit{NP}}$.

Figure 7

Pure FE simulation: normalized interparticle strain ${\tilde{\varepsilon }}^{\mathit{NP}}$ as a function of the global strain ${\varepsilon }_{}^{\mathit{MD}}$ for various initial interparticle distances $L_{}^{\mathit{NP}}$.

Figure 8

Normalized strain between NP centers ${\tilde{\varepsilon }}^{\mathit{NP}}$ obtained from hybrid and pure FE simulations, (a) for the closest center-to-center distance of NPs ($L_{}^{\mathit{NP}}=5.93\mathrm{nm}$) and (b) for the largest NP distance ($L_{}^{\mathit{NP}}=9.47\mathrm{nm}$).

Figure 9

FE-simulated distribution of the local tensile strain ${\varepsilon }_{}$ in the center plane at an overall strain ${\varepsilon }_{}^{\mathit{MD}}=7.75\%$, (a) for minimum ($5.93\mathrm{nm}$) and (b) maximum ($9.47\mathrm{nm}$) initial particle center-to-center distances.