Inverse rule of mixtures at the nanoscale: prediction of elastic properties of cellulose nanofibrils

A way to model properties of nanomaterials consists of applying well-established approaches based on a macroscopic view of matter, therefore ignoring any peculiar features due to the smallness of these materials. In this work, we inspect the capability of a simple micromechanical model, the inverse rule of mixtures, to predict the elastic modulus of multi-component composites, e.g. cellulose nano fibrils, when load is perpendicular to the stratified structure, by implementing molecular dynamics simulations. The results show that the inverse rule of mixtures can predict the tensile modulus of the modelled cellulose nano fibrils in the fibril direction. These findings could be further generalized in computing the mechanical properties of multi-phase nanocomposites, in case the constituents are loaded in series, as well as, to approximate the degree of crystallinity of single cellulose nano fibrils.