Molecular insight into the Mullins effect: irreversible disentanglement of polymer chains revealed by molecular dynamics simulations.

The debate regarding the possible molecular origins of the Mullins effect has been ongoing since its discovery. Molecular dynamics (MD) simulations were carried out to elucidate the underlying mechanism of the Mullins effect. For the first time, the key characteristics associated with the Mullins effect, including (a) the majority of stress softening occurring in the first stretch, (b) continuous softening with stress increase, (c) a permanent set, and (d) recovery with heat treatment, are captured by molecular modeling. It is discovered that the irreversible disentanglement of polymer chains is physically sufficient to interpret these key characteristics, providing molecular evidence for this long-controversial issue. Our results also reveal that filled polymers exhibit three distinct regimes, i.e., the polymer matrix, the interface, and the filler. When subjected to external strain, the polymer matrix suffers from excess deformation, indicating strong heterogeneity within the filled polymer, which offers molecular insight for the formulation of physics-based constitutive relations for filled polymers.

Nature of Carbon Black Reinforcement of Rubber: Perspective on the Original Polymer Nanocomposite.

Adding carbon black (CB) particles to elastomeric polymers is essential to the successful industrial use of rubber in many applications, and the mechanical reinforcing effect of CB in rubber has been studied for nearly 100 years. Despite these many decades of investigations, the origin of stiffness enhancement of elastomers from incorporating nanometer-scale CB particles is still debated. It is not universally accepted whether the interactions between polymer chains and CB surfaces are purely physical adsorption or whether some polymer-particle chemical bonds are also introduced in the process of mixing and curing the CB-filled rubber compounds. We review key experimental observations of rubber reinforced with CB, including the finding that heat treatment of CB can greatly reduce the filler reinforcement effect in rubber. The details of the particle morphology and surface chemistry are described to give insights into the nature of the CB-elastomer interfaces. This is followed by a discussion of rubber processing effects, the influence of CB on crosslinking, and various chemical modification approaches that have been employed to improve polymer-filler interactions and reinforcement. Finally, we contrast various models that have been proposed for rationalizing the CB reinforcement of elastomers.

A Nonequilibrium Model for Particle Networking/Jamming and Time-Dependent Dynamic Rheology of Filled Polymers.

We describe an approach for modeling the filler network formation kinetics of particle-reinforced rubbery polymers-commonly called filler flocculation-that was developed by employing parallels between deformation effects in jammed particle systems and the influence of temperature on glass-forming materials. Experimental dynamic viscosity results were obtained concerning the strain-induced particle network breakdown and subsequent time-dependent reformation behavior for uncross-linked elastomers reinforced with carbon black and silica nanoparticles. Using a relaxation time function that depends on both actual dynamic strain amplitude and fictive (structural) strain, the model effectively represented the experimental data for three different levels of dynamic strain down-jump with a single set of parameters. This fictive strain model for filler networking is analogous to the established Tool-Narayanaswamy-Moynihan model for structural relaxation (physical aging) of nonequilibrium glasses. Compared to carbon black, precipitated silica particles without silane surface modification exhibited a greater overall extent of filler networking and showed more self-limiting behavior in terms of network formation kinetics in filled ethylene-propylene-diene rubber (EPDM). The EPDM compounds with silica or carbon black filler were stable during the dynamic shearing and recovery experiments at 160 °C, whereas irreversible dynamic modulus increases were noted when the polymer matrix was styrene-butadiene rubber (SBR), presumably due to branching/cross-linking of SBR in the rheometer. Care must be taken when measuring and interpreting the time-dependent filler networking in unsaturated elastomers at high temperatures.

Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber.

Undispersed filler agglomerates or other substantial inclusions/contaminants in rubber can act as large crack precursors that reduce the strength and fatigue lifetime of the material. To demonstrate this, we use tensile strength (stress at break, σb) data from 50 specimens to characterize the failure distribution behavior of carbon black (CB) reinforced styrene-butadiene rubber (SBR) compounds. Poor mixing was simulated by adding a portion of the CB late in the mixing process, and glass beads (microspheres) with 517 µm average diameter were introduced during milling to reproduce the effects of large inclusions. The σb distribution was well described with a simple unimodal Weibull distribution for the control compound, but the tensile strengths of the poor CB dispersion material and the compounds with the glass beads required bimodal Weibull distributions. For the material with the lowest level of glass beads-corresponding to less than one microsphere per test specimen-the bimodal failure distribution spanned a very large range of σb from 13.7 to 22.7 MPa in contrast to the relatively narrow σb distribution for the control from 18.4 to 23.8 MPa. Crack precursor size (c0) distributions were also inferred from the data, and the glass beads introduced c0 values in the 400 µm range compared to about 180 µm for the control. In contrast to σb, critical tearing energy (tear strength) was unaffected by the presence of the CB agglomerates and glass beads, because the strain energy focuses on the pre-cut macroscopic crack in the sample during tear testing rather than on the microscopic crack precursors within the rubber. The glass beads were not detected by conventional filler dispersion measurements using interferometric microscopy, indicating that tensile strength distribution characterization is an important complementary approach for identifying the presence of minor amounts of large inclusions in rubber.

Strain-induced nonlinearity of filled rubbers.

Dynamic strain-induced nonlinearity in the modulus of filled rubbers shows a striking similarity to what is known about the glass transition of solid materials and the jamming transition of granular materials. This analogy stems from the reality that shear strain in dynamic mechanical measurements introduces fluctuations in a filler network by forcing the system to explore different configurations. Such fluctuations can be described by an "effective temperature" that has many attributes of a true temperature, and particularly is proportional to the strain amplitude. Thus, filled rubbers with respect to strain will display many unusual phenomena that are usually observed in glass-forming materials, but now demonstrated in filled rubbers, including asymmetric kinetics, crossover effects, and glasslike kinetic transitions. The nonlinearity in the modulus of filled rubbers simply reflects a dejamming transition of fillers in rubber matrices. The agglomeration of filler in an elastomeric matrix shares a common ground of physics with the jamming process and glass formation.

Isoenergetic jamming transition in particle-filled systems.

A full understanding of the jamming transition remains elusive, but recent advances which draw upon the common features of frustrated systems are encouraging. Herein, we show that, for mixtures of oil and silica particles, the dependence of the dejamming stress on filler volume fraction, phi is consistent with the shape of a reported jamming phase diagram [Trappe, Nature (London) 411, 772 (2001)]. We discover for the first time, however, that the role of phi disappears when mechanical energy input, defined as stress multiplied by strain, is used instead of stress as the critical parameter. We also examine literature results for aqueous suspensions of boehmite alumina powders, latex dispersions of polystyrene particles, and carbon black-filled elastomers in order to illustrate the universality of our finding. This study provides evidence for a thermodynamic interpretation of the jamming transition.