Mechanical Percolation in Nanocellulose-Filled Composites: A Model for the Modulus of Composites Containing Nanocellulose/Interphase Network Publisher



Ghasemi S ; Espahbodi A ; Naqvi M ; Zare Y ; Rhee KY
Source: Cellulose Published:2026

Abstract

This study presents a model for predicting the tensile modulus of cellulose nanomaterial (CNM)-reinforced composites by accounting for the contributions of both the filler and the interphase network beyond the mechanical percolation onset (ϕp). The model links the nanocomposite modulus to the moduli and volume fractions of CNM, the percolated network, and the surrounding interphase network. To test the model, experimentally measured moduli from various nanocomposite systems are compared with predictions from parametric analyses. The results show a strong agreement between experimental and calculated values, which supports the validity of the model. Composites with a higher CNM content and a lower percolation threshold yield significantly stronger materials. For example, no reinforcement occurs when the filler volume fraction is below 0.02 and ϕp = 0.08; however, raising the CNM volume fraction to 0.06 and lowering ϕp to 0.01 increases the modulus by 300%. An interphase network modulus (EiN) below 2 GPa does not improve stiffness, while interphase depth of 22 nm and EiN = 12 GPa lead to a 600% increase in modulus. Therefore, a deeper and stiffer interphase network produces stronger composites. Similarly, no reinforcement is observed for CNM radii greater than 15 nm, but the modulus increases by 700% at R = 5 nm and a CNM length of 3 μm. These results indicate that thinner and longer CNMs produce stiffer nanocomposites. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.