Towards better understanding the stiffness of nanocomposites via parametric study of an analytical model modeling parameters and experiments.

The stiffness of polymeric materials can be improved dramatically with the addition of nanoparticles. In theory, as the nanoparticle loading in the polymer increases, the nanocomposite becomes stiffer; however, experiments suggest that little or no stiffness improvement is observed beyond an optimal nanoparticle loading. The mismatch between the theoretical and experimental findings, particularly at high particle loadings, needs to be understood for the effective use of nanoparticles. In this respect, we have recently developed an analytical model to close the gap in the literature and predict elastic modulus of nanocomposites. The model is based on a three-phase Mori-Tanaka model coupled with the Monte-Carlo method, and satisfactorily captures the experimental results, even at high nanoparticle loadings. The developed model can also be used to study the effects of agglomeration in nanocomposites. In this paper, we use this model to study the effects of agglomeration and related model parameters on the stiffness of nanocomposites. In particular, the effects of particle orientation, critical distance, dispersion state and agglomerate property, and particle aspect ratio are investigated to demonstrate capabilities of the model and to observe how optimal particle loading changes with respect these parameters. The study shows that the critical distance defining agglomerates and the properties of agglomerates are the key design parameters at high particle loadings. These two parameters rule the optimal elastic modulus with respect to particle loading. The findings will allow researchers to form design curves and successfully predict the elastic moduli of nanocomposites without the exhaustive experimental undertakings.

A predictive model towards understanding the effect of reinforcement agglomeration on the stiffness of nanocomposites.

Nanocomposite technologies can be significantly enhanced through a careful exploration of the effects of agglomerates on mechanical properties. Existing models are either overly simplified (e.g., neglect agglomeration effects) or often require a significant amount of computational resources. In this study, a novel continuum-based model with a statistical approach was developed. The model is based on a modified three-phase Mori-Tanaka model, which accounts for the filler, agglomerate, and matrix regions. Fillers are randomly dispersed in a defined space to predict agglomeration tendency. The proposed model demonstrates good agreement with the experimentally measured elastic moduli of spin-coated cellulose nanocrystal reinforced polyamide-6 films. The techniques and methodologies presented in the study are sufficiently general in that they can be extended to the analyses of various types of polymeric nanocomposite systems.