A Focus on the Agglomerates of Nanodiamond Surrounded by Interphase Zone to Simulate the Tensile Modulus of Polymer Composites Publisher



Zare Y ; Naqvi M ; Arefian M ; Rhee K Y
Source: Composites Science and Technology Published:2026

Abstract

Despite the presence of nanodiamond (ND) agglomeration in composites, this critical factor has been unnoticed in prior models predicting the tensile modulus of ND-filled systems. In the present study, the properties of agglomerates and their surrounding interphase are incorporated to state a predictive expression for the Young's modulus in the ND-reinforced samples. The operative volume share of reinforcement ( ϕ eff ) is defined by agglomerate radius ( R agg ), ND size, and the interphase thickness ( t ). Notably, ϕ eff reaches a maximum value of 0.55 at ND radius of 5 nm (indicating no agglomeration), but significantly decreases to 0.015 at R agg = 50 nm, indicating that larger agglomerates cause the least reinforcement. The nanocomposite modulus exhibits a 420% enhancement at R agg = 10 nm; however, further increases in agglomerate size markedly reduce stiffness. Similarly, a 300% increase in modulus is attained at t = 20 nm, whereas thinner interphases lead to diminished reinforcement. A stiffer interphase also improves mechanical performance; 215% enhancement in the stiffness is seen at an interphase modulus of 30 GPa. In contrast, a lower interphase modulus of 5 GPa induces only a marginal 35% improvement of nanocomposite modulus. The proposed model substantially overestimates the modulus when assuming well-dispersed NDs, but accurately predicts the stiffness of real composites containing agglomerated NDs. © 2026 Elsevier Ltd.