In this research work, we provide a detailed investigation of the structural and viscoelastic properties of crosslinked styrene butadiene rubber (SBR) networks that are studied using atomistic molecular dynamics simulations. The composition of the system ratio is (styrene/trans/vinyl/cis): (15/33/26/26) by weight and a 4-atom sulfur chain was used as a hardener for the crosslinking process. The main goal of our work is to characterize a fully percolated SBR network, with a crosslinking density of 8%, at the molecular level, structurally, mechanically and topologically and compare its properties with a system with a lower crosslinking density (3%) and the non crosslinked SBR melt. SBR crosslinked systems are generated via a recently proposed crosslinking algorithm. The shear stress relaxation modulus and the mean square displacement (MSD) were calculated for all systems along with structural properties, such as the pair distribution function, angles and dihedral distributions, and statistical distributions of the atoms between the crosslinks, and finally the topology of these networks was investigated according to the number of clusters that are created during the different crosslink densities, the molecular weight fraction of the largest cluster in these networks, and finally the percolation threshold. The results indicate that the higher we crosslink the SBR, the stiffer our final rubber becomes according to the results of the dynamics and rheology. We further probe the dependence of the structural and viscoelastic properties of the SBS rubber on crosslinking density by comparing a fully percolated system with one having lower crosslinking density (3%) and the non crosslinked SBR melt.
Chain relaxation in melts of moderately entangled macromolecules presents the first signs of topological constraints that are commonly manifested in the rheology of long commercial-grade polymers. In this study, we employ multiscale molecular dynamics simulations to examine the relaxation characteristics of model polyisoprene (PI) melts through the transition from the Rouse regime to entangled systems. We probed the impact of molecular weight and stereochemistry and evaluated the accuracy of theory in modeling the end-to-end relaxation. Our results support that trans-PI dynamics is distinct, with entanglements forming at a lower degree of polymerization than other compositions due to differences in the characteristic ratio and packing of this polymer. For all moderately entangled systems, modeling the end-to-end relaxation with the original Likhtman-McLeish theory with contour-length fluctuations presents deviations from recorded data in both the early time and terminal regime. We propose numerical modifications that significantly improve the model for all of the systems studied without introducing additional parameters. Our approach allows accurate predictions for long macromolecules based on data from detailed simulations with moderately entangled polyisoprene systems.
Crosslinking macromolecules is an important process that aims to modulate mechanical properties of elastomers and meet desired specifications based on the application sought. The impact of crosslinking density on rubber moduli has been well established by theory, experiments and computational studies. However, several reports imply a role for the length of the sulfide bond and the attachment location. In this study, we construct all-atom models of polyisoprene (PI) networks using equilibrated precursor melts and sulfide crosslinks of a specific chemical architecture. We first examine network characteristics which follow expectations based on our random crosslinking approach. We report the presence of a substantial number of intramolecular connections formed. Thermodynamics and microscopic dynamics of the resulting networks are also probed. Comparing systems with the same number of crosslinks, we find that local mobility is most decelerated in the presence of long quaternary connections. To resolve any impact on mechanical properties we resorted to extensive characterization of moduli via equilibrium (stress-stress fluctuations) and non-equilibrium processes (constant-rate and oscillatory deformations). Both equilibrium and non-equilibrium simulations (at times/frequencies accessible to our all-atom models) confirm that quaternary linkages provide for the highest moduli with linker length holding a secondary role during moderate deformations.
Through the analysis of the spatial correlations of local stress, we detect the propagation of long-ranged liquid-elasticity-mediated shear stress waves in polymeric and low-molecular weight liquids. The propagation of shear waves is effectively planar; i.e., sigma(alpha beta) propagates in the alpha beta plane. The autocorrelation functions of the local stress of a region are affected by both the relaxation of stress in that region and the propagation of stress from the region to the rest of the sample. However, due to the planar propagation of shear waves, the transfer of sigma alpha beta from those slices of the simulation box that are periodic in the alpha beta plane is negligible. This allows direct probing of the position-dependent local stress relaxation modulus of liquid in the vicinity of a confining surface.
ABSTRACT Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.
