A series of experiments have been run to determine which mechanisms dominate carbon black reinforcement of rubber. A broad range of compounds using oil-extended and non-oil-extended rubbers and carbon blacks covering the spectrum of tread blacks have been tested. The results for measurements made in an all-SBR formulation are reported here. The primary experiment consisted of measurement of the dynamic modulus and hysteresis of the cured and uncured compounds over a broad range of frequencies, temperatures, and strains. Ternperatures ranged from −70°C to +90°C; frequencies varied from 0.01 to 10 Hz; double strain amplitudes varied from 0.5% to 35%. From a discussion of the literature and evaluation of the experimental results, two mechanisms have been found to control the primary effects of carbon black on rubber reinforcement, where reinforcement refers to a general enhancement of properties, such as modulus, as well as the tensile strength of the compound. Hydrodynamic interaction, which is the increase in properties caused by the modification of strain fields in the region of an aggregate, dominates the large-strain dynamic and tensile properties of the compound. The primary carbon black variable in this mechanism is the effective aggregate size, such as measured by tint, which controls the effective volume loading of the carbon black at a given weight loading of carbon black. At low strains, the modulus is even higher than that predicted from the hydrodynamic-interaction/effective-volume model. This additional reinforcement is caused by the entanglement network formed between the tightly absorbed bound rubber on the carbon black surface and the bulk rubber far removed from the surface. The main carbon black variables in this mechanism are surface area and surface chemistry. The strain dependence of modulus is caused by the breaking and reforming of effective crosslinks in the rubber forming a transition zone between the bound rubber and the bulk rubber. To a large extent, this mechanism is dominated by the rubber properties, such as molecular weight and molecular-weight distribution. However, the dynamics of the entanglement network may be modified by altering specific interactions between carbon black and rubber.

While lattice models are used extensively for macromolecules (synthetic polymers proteins, etc), calculation of the absolute entropy, S, and the free energy, F, from a given Monte Carlo (MC) trajectory is not straightforward. Recently we have developed the hypothetical scanning MC (HSMC) method for calculating S and F of fluids. Here we extend HSMC to self-avoiding walks on a square lattice and discuss its wide applicability to complex polymer lattice models. HSMC is independent of existing techniques and thus constitutes an independent research tool; it provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation.Lattice models have been utilized to study a wide range of phenomena in polymer physics [1][2][3][4][5] as well as in structural biology, mainly related to protein folding and stability [6-9] (Refs 1-9 constitute a very limited representation of hundreds of papers published in the last 15 years). Because of their simplicity these models have been invaluable tools for understanding global properties that do not depend strongly on molecular details. Such models vary in complexity, ranging from self-avoiding walks on a square lattice to chain models on enriched 3D lattices with a large effective coordination number.Commonly, these systems are simulated by variants of Metropolis Monte Carlo (MC) -a dynamical method that enables one to generate samples of chain configurations i distributed according to their Boltzmann probability, P i B , from which equilibrium information can be extracted [10]. Using MC it is straightforward to calculate properties that are measured directly from i, such as the potential energy E i . On the other hand, the value of P i B cannot be obtained in a straightforward manner, which makes it difficult to calculate the absolute entropy, S ~ -lnP i B directly, i.e., as a byproduct of the simulation (like E i ). There is a strong interest in S as a measure of order and as an essential ingredient of the free energy, F=E−TS, where T is the absolute temperature; F constitutes the criterion of stability, which is mandatory in structure determination of proteins, for example. Furthermore, because MC simulations constitute models for dynamical processes, one would seek to calculate changes in F and S during a relaxation process, by assuming local equilibrium in certain parts along the MC trajectory; a classic example is simulation of protein folding [11].S, and F are commonly calculated by thermodynamic integration (TI) techniques [12][13][14] that do not operate on a given MC sample but requires conducting a separate set of MC simulations. This is a robust approach that enables one to calculate differences, ΔS ab and ΔF ab , between two states a and b of a system; however, if the structural variance of such states is large (e.g., helical and hairpin states of a polypeptide) the integration from state a to b becomes difficult *Corresponding author

The thermogravimetry (TGA) in nitrogen was measured for poly(tetramethyl‐p‐silphenylene)‐siloxane (TMPS) fractions with narrow molecular weight distributions and for block copolymers of TMPS and dimethyl siloxane (DMS) with varying composition. The measurements were made with the Perkin‐Elmer DCS IB‐TGA attachment which consists of a Cahn electrobalance and a wire‐wound furnace with programmable temperature controls. The weight loss curves for heating rates of 10, 20, and 40°C/min were analyzed using the method of Flynn and Wall. The analysis indicates that thermal degradation proceeds primarily by scission of the siloxane bond with an activation energy of 44 ± 3 kcal/mole for the uncatalyzed reaction and 13 ± 2 kcal/mole for the reaction occurring in the presence of residual catalyst. The thermal stability of the TMPS–DMS copolymer is impaired through increasing the concentration of the DMS component. Cyclic DMS trimer and TMPS monomer and dimer were observed by mass spectrometry which gave results consistent with the proposed mechanism of degradation.

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