Upgrading of a theoretical model for tensile strength of polymer - cellulose nanocrystals system to derive a new equation for interfacial shear strength

Abstract

Cellulose nanocrystals (CNCs) can be used as effective reinforcement for polymers, because of their large surface area and excellent tensile strength. Few models are available to determine the stiffness of CNC-reinforced polymer composites (PNCs). Due to the absence of interphase section and CNC dimensions, the accessible models cannot accurately estimate the properties of PNCs. By focusing on the interphase area, this work develops simple models to calculate the strength and interface shear strength (τ) for PNCs reinforced with CNCs. This study introduces a novel modeling approach that simultaneously predicts both the relative tensile strength (σ_R) and τ for polymer-CNC nanocomposites by incorporating interphase properties. This dual prediction capability represents a significant advancement over traditional models, offering a more comprehensive insight into the mechanical reinforcement mechanisms. The proposed equations consider the diameter (d), length (l) and concentration of CNCs with the interphase thickness (t) and strength (σ_i). The proposed models are examined using a variety of experimental data and parametric investigations. There is a good agreement between all predictions and experimental data of PNC strength at different CNC concentrations. The highest relative strength (ratio of PNC strength to strength of matrix) as 8 and maximum τ = 14 MPa are shown at d = 2 nm with l = 500 nm. Additionally, the supreme relative strength of 6 and the uppermost τ = 16 MPa are seen at t = 20 nm with σ_i = 90 MPa. CNC diameter adversely affects the PNC strength and τ, while longer CNCs with denser and stiffer interphase highly enhance the τ strengthening the PNCs.