Nanodiamond agglomeration in polymer composites: A practical model predicting the tensile modulus

This study investigates the agglomeration of nanodiamonds (NDs) and its influence on the modulus of polymer nanocomposites through a simplified simulation approach. The proposed model incorporates the size and concentration of agglomerated NDs, as well as the interphase thickness ( t ) and modulus ( E i ). The predicted moduli of nanocomposites containing both well-dispersed and agglomerated NDs are compared with experimentally measured values. The effects of agglomerate radius ( R agg ), ND content, interphase characteristics, and ND modulus on the composite modulus are assessed and justified using the developed model. Smaller agglomerates positively influence their effective volume fraction and interphase contribution within the composite. While the calculations based on well-dispersed NDs tend to overestimate the composite modulus, the predictions considering agglomerated NDs exhibit strong agreement with the experimental results. For instance, R agg = 10 nm can enhance the nanocomposite modulus by up to 205%; however, an increase in agglomerate size diminishes stiffness, resulting in only a 40% improvement by R agg = 60 nm. Additionally, an interphase thickness of t = 20 nm and modulus of E i = 40 GPa can enhance the composite modulus by 145%, whereas a thinner interphase ( t < 5 nm) leads to only a 50% improvement. Therefore, the nanocomposite modulus increases proportionally with a denser and tougher interphase.