Non-affine deformation of polystyrene nanocomposites leads to significant increase of local elastic properties

This paper presents an investigation of local elastic properties of polystyrene doped with a SiO2 nanoparticle. The local elasticity is analyzed using the local density fluctuations at various length scales. A significant enhancement of local elastic properties of polystyrene was observed around the nanoparticle, and it was revealed that the additional stiffness has an exponential behavior with a typical length scale R0 ≈ 1.4 nm. At the same time, it was shown that the density and other structural properties of polystyrene at this distance from the nanoparticle surface are identical to those for the bulk polystyrene. The enhancement of the local elastic properties was attributed to the effect of non-affine deformations caused by the strong spatial fluctuations of polystyrene stiffness at the length scale below 1 nm. The effect was confirmed using the random matrix model with variable strength of disorder. ∗ ilia.solovyov@uni-oldenburg.de 1 ar X iv :2 10 5. 04 53 7v 1 [ co nd -m at . d is -n n] 1 0 M ay 2 02 1 Polymer nanocomposites have attracted significant attention due to their unique properties and enormous potential as future materials [1]. Experimental investigations have demonstrated that due to the nanometer-size inclusions, polymer nanocomposites could possess tailored mechanical, electrical, and thermal properties, as compared to the pure polymers [2–4]. Among many characteristics, the elastic properties of pure polymers and associated nanocomposites have historically attracted considerable attention [5–7]. It was established that polymer doping with nanoparticles even in small concentrations could lead to significant changes in the elasticity of the host material [8–11]. For example, it was shown that doping of polymethylmethacrylate with just 3 wt. % of SiO2 nanoparticles may increase the storage modulus of the nanocomposite by 50 % [12]. It is well known that for a homogeneous elastic medium the classical elasticity theory defines the relation between local strain and local stress [13]. Applied to doped polymers, the Eshelby theory can then be used to determine the deformation of the nanoparticles and the surrounding medium caused by the macroscopic external stress [14], and the resulting overall stiffness of nanocomposites can be calculated using the Mori-Tanaka approach [15, 16]. However, this theory becomes inaccurate for small nanoparticles. Elastic properties of nanocomposites can be described by the so-called three-phase model [17]. The model assumes that the structure of a polymer is perturbed around the nanoparticle, which results in an effective interface layer around the nanoparticle with intermediate elastic properties. Due to the large total surface area of a nanoparticle, the interfacial layer has a strong influence on the overall stiffness of the nanocomposite. However, the properties and the thickness of the interfacial layer are usually unknown and so far the three-phase model was used as a phenomenological model [18–22]. The present investigation considers an example of polystyrene doped with an amorphous SiO2 nanoparticle and presents a study of local elastic properties around the nanoparticle. The results demonstrate a significant increase of polystyrene local elastic properties in a thick shell around the nanoparticle, where the internal structure of the polystyrene is not perturbed by the nanoparticle. The specific case study illuminates a general and versatile approach that can easily be adapted to study elastic properties of arbitrary nanocomposites. To elucidate the role of disorder in the studied system, we further utilize the random matrix model with variable strength of disorder [23]. The important property of a nanocomposite is the inhomogeneity of its constituents at a