Mechanical Properties of Polymeric Nanocomposites with Liquid Inclusions

We study mechanical properties of polymeric nanocomposites of liquid inclusions in network matrix using molecular dynamics simulations and analytical calculations. The shear modulus of nanocomposite is shown to be a non-monotonic function of the elastocapillary number $\gamma _{\mathrm{SL}}$/($G_{\mathrm{N}}R)$, where $\gamma_{\mathrm{SL}}$is the interfacial energy network/liquid interface, $G_{\mathrm{N}}$is the shear modulus of network and $R$is the initial size of liquid inclusion. First, in the range of elastocapillary numbers, $\gamma _{\mathrm{SL}}$/($G_{\mathrm{N}}R)$ \textless \textless 1, the composite shear modulus increases with increasing this parameter value. In this interval of elastocapillary numbers, a liquid inclusion softens the network such that the composite modulus $G_{\mathrm{comp}}$is smaller than $G_{N}.$This is in agreement with the classical Eshelby theory. However, for elastocapillary numbers $\gamma_{\mathrm{SL}}$/($G_{\mathrm{N}}R) \quad \approx $ 1, the liquid inclusions reinforces the network, $G_{\mathrm{comp}}$\textgreater $G_{N}$. In this range of parameters the surface energy of the deformed liquid inclusions strengthens the composite. When the elastocapillary number increases further, $\gamma _{\mathrm{SL}}$/($G_{\mathrm{N}}R)$ \textgreater \textgreater 1, the interfacial energy of network/liquid interface dominates the mechanical response of the composite resulting in composite weakening. Analysis of the elongation ratio of the liquid inclusion shows that it decreases with increasing elastocapillary number $\gamma _{\mathrm{SL}}$/($G_{\mathrm{N}}R)$. The classical Eshelby's theory of inclusions fails to explain this phenomenon. We develop a new linear elasticity model of this class of nanocomposite materials capable to explain this unusual mechanical response of nanocomposite materials.