Dual particle size carbon black filled natural rubber: how frequency dominates energy dissipation in the Payne effect

Research background and core findings: Carbon black is one of the most commonly used reinforcing fillers in tires and rubber products, and its particle size distribution and network structure directly affect the dynamic mechanical properties of vulcanized rubber. A recent study published in the Journal of Applied Polymer Science systematically investigated the frequency dependent viscoelasticity of natural rubber nanocomposites filled with dual particle size carbon black using coarse-grained molecular dynamics methods. Research has found that as the shear frequency increases, the dominant pair of carbon black particles in the system will transition from a pair of particles of the same size to a pair of particles of different sizes, while the storage modulus G ‘increases at a fixed strain amplitude. This frequency dependent behavior forms the basis of the energy dissipation mechanism behind the Payne effect.

The influence of frequency and strain amplitude on the Payne effect

Research has shown that the Payne effect becomes more significant with increasing frequency and strain amplitude.

. Under high-frequency conditions, the nanoparticle network undergoes extensive damage, resulting in a decrease in loss modulus; Under low frequency conditions, the network can be reformed, the friction between segments is enhanced, and the loss modulus increases under high strain. The variation of non bond interaction energy is mainly dominated by the carbon black carbon black interaction, and the contributions of natural rubber natural rubber and carbon black natural rubber can be ignored at each normalized scale. This result emphasizes the central role of the reinforcement filler network itself in dynamic response.

The key role of particles of different sizes

Research has identified a frequency driven transition: carbon black particles of the same size dominate at low frequencies, while particles of different sizes dominate at high frequencies.

. The frequency of 2.5 × 10 ⁻⁵ fs ⁻¹ is marked as a feature point, at which point the constraint of the nanoparticle network on the chain segment mobility reaches its maximum. The author believes that the Payne effect is mainly controlled by the dynamics of nanoparticle networks, and carbon black particles of different sizes play a key role in regulating frequency dependent energy dissipation. For tire and rubber formula design, this means that the particle size combination of reinforcing fillers not only affects the static reinforcement effect, but also changes the hysteresis heat generation and damping behavior under dynamic conditions.

Implications for the polymer additive industry

Although this study did not directly involve anti-aging agents, antioxidants, or vulcanization systems, its conclusions on the dynamics of reinforcing filler networks have reference value for the application of rubber additives.

. In dynamic load scenarios such as tire tread rubber, the particle size distribution design of reinforcing fillers such as white carbon black and carbon black needs to be considered in conjunction with the crosslinking density of the vulcanization system, anti-aging agents, and the aging resistance provided by antioxidants. The frequency dependent reconstruction behavior of packing networks affects the energy dissipation of materials under repeated deformation, which in turn relates to rolling resistance and heat generation. This work provides a simulation basis for understanding the behavior of reinforcing fillers from the perspective of microscopic particle pairs, but the relevant conclusions are based on coarse-grained molecular dynamics models, and the extrapolation to actual rubber and vulcanized rubber formulations still needs experimental verification.

Information source:Frequency‐Dependent Viscoelasticity in Bidisperse Carbon Black‐Filled Natural Rubber Nanocomposites: The Critical Role of Heterosized Filler Pairs， Organized by Herun Chemical.