Structural Changes of Aggregated Filler Particles in Elongated Rubbers through Two-Dimensional Pattern Reverse Monte Carlo Modeling

To investigate the three-dimensional (3D) structure ofnanoparticle(NP) aggregates in rubber tire treads with a large system size, aparticle-mesh-based two-dimensional (2D) pattern reverse Monte Carlo(PM-2DpRMC) method was applied to a series of 2D scattering patterns(2DSPs) of NPs during stretching and unloading. To characterize thestructures of aggregated NPs, a high-connectivity cluster analysisbased on the number of NPs within a specific cutoff distance was introduced.Similar to the reverse Monte Carlo (RMC) analysis of a one-dimensionalscattering spectrum, PM-2DpRMC analysis for the case before stretchingclarified that the characteristic cluster sizes of silica NPs in end-modifiedstyrene-butadiene rubber (M-SBR) treads were smaller than thosein nonmodified SBR (n-SBR) treads. Changes in the 3D configurationsof NPs during stretching were modeled from a series of 2DSPs of NPsby repeating the stepwise deformation of the box of the periodic boundarycondition, and this method was termed the "on-the-fly PM-2DpRMC"method. The high-connectivity cluster analysis elucidated that theNPs in the M-SBR treads aggregated more at higher elongation ratios(& epsilon;); however, the characteristic sizes of the NP aggregatesin the n-SBR treads were slightly small at higher & epsilon; values.At a high & epsilon; of >140%, although the number of clusters intheM-SBR treads became close to those in the n-SBR treads, the differencebetween the characteristic sizes of NP aggregates was retained. Furthermore,the high-connectivity cluster analysis was mathematically more sensitivefor the characterization of NP morphologies than a previously reportedanalysis based on the Voronoi cell volume. The high-connectivity clusteranalysis helps clarify the justification of the on-the-fly PM-2DpRMCmethod and its numerical comparison with the PM-2DpRMC analysis startingfrom random NP configurations. Moreover, the results of this studyelucidate the importance of a lower scattering wavenumber, q, limit in the modeling of NP aggregation.