Annular Coated Inclusion model and applications for polymer nanocomposites – Part I: Spherical inclusions

• An Annular Coated Inclusion (ACI) model for spherical inclusion problem is proposed.
• ACI model provides the analytical solution of the dilute strain concentration tensor.
• Interphase properties can strongly influence the effective nanocomposite behavior.
• “Stress-shielding” is accurately captured by the model when the interphase is soft.
• Model can be used to interpret experimental data presented in the literature.

There is considerable interest in using various nanoparticles to create multifunctional polymer nanocomposite materials with enhanced properties. Due to the large amount of surface area available within the nanocomposite, the effects of non-bulk polymer in the vicinity of the nanoinclusion, with different properties than the bulk polymer, can complicate micromechanical predictions of effective properties. Several micromechanical approaches require one to calculate the dilute strain concentration tensor, for which elegant solutions are available for separate, physically distinct ellipsoidal inclusion geometries using the well-known Eshelby tensor. Here the general coated inclusion problem is formulated for the case of a spherical inclusion, such that the components of the dilute strain concentration tensors for both the inclusion and the interphase/coating region are analytically determined, from which they can then be directly implemented within standard micromechanical models. Model predictions indicate that the proposed approach is able to accurately capture the effects of the interphase coating. Moreover, several published experimental data sets for soft interphase systems have been examined to illustrate the utility of the proposed model. An advantage of the proposed method is that the solution of the auxiliary problems allows determination of the stress and strain fields which can be extended in a straightforward manner to enable a wide range of composite studies. It is anticipated that the proposed model will be particularly useful in evaluating the impact of chemical functionalization techniques and other strategies that seek to tailor the properties of the interphase region in these materials.

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