The chemistry of accelerated sulfur vulcanization is reviewed and a fundamental kinetic model for the vulcanization process is developed. The vulcanization of natural rubber by the benzothiazolesulfenamide class of accelerators is studied, where 2-(morpholinothio) benzothiazole (MBS) has been chosen as the representative accelerator. The reaction mechanisms that have been proposed for the different steps in vulcanization chemistry are critically evaluated with the objective of developing a holistic description of the governing chemistry, where the mechanisms are consistent for all reaction steps in the vulcanization process. A fundamental kinetic model has been developed for accelerated sulfur vulcanization, using population balance methods that explicitly acknowledge the polysulfidic nature of the crosslinks and various reactive intermediates. The kinetic model can accurately describe the complete cure response including the scorch delay, curing and the reversion for a wide range of compositions, using a single set of rate constants. In addition, the concentration profiles of all the reaction intermediates as a function of polysulfidic lengths are predicted. This detailed information obtained from the population balance model is used to critically examine various mechanisms that have been proposed to describe accelerated sulfur vulcanization. The population balance model provides a quantitative framework for explicitly incorporating mechanistically reasonable chemistry of the vulcanization process.

An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Such networks are found in a variety of applications such as in supply chain networks, computer and communication networks, metabolic networks, foodwebs etc. Here we present a theory of self-organization by evolutionary adaptation in which we show how the structure and organization of a network is related to the survival, or in general the performance, objectives of the system. We propose that a complex system optimizes its network structure in order to maximize its overall survival fitness which is composed of short-term and long-term survival components. These in turn depend on three critical measures of the network, namely, efficiency, robustness and cost, and the environmental selection pressure. Fitness maximization by adaptation leads to the spontaneous emergence of optimal network structures, both power law and non-power law, of various topologies depending on the selection pressure. Using a graph theoretical case study, we show that when efficiency is paramount the "Star" topology emerges and when robustness is important the "Circle" topology is found. When efficiency and robustness requirements are both important to varying degrees, other classes of networks such as the "Hub" emerge. This theory provides a general conceptual framework for integrating survival or performance objectives, environmental or selection pressure, evolutionary adaptation, optimization of performance measures and topological features in a single coherent formalism. Our assumptions and results are consistent with observations across a wide variety of applications. This framework lays the ground work for a novel approach to model, design and analyze complex networks, both natural and artificial, such as metabolic pathways, supply chains and communication networks.In press, Computers and Chemical Engineering, 2004

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The first step in accelerated vulcanization is the formation of the active sulfurating species via the incorporation of sulfur by an accelerator like benzothiazole. Several mechanisms for the pick-up of sulfur by the accelerator have been proposed, including lumped pick-up of the full S8 species, sequential pick-up of individual sulfur atoms in S8 and numerous proposals where the stoichiometry is not clearly specified. For the reaction of MBTS with S8 Gradwell, et al. observed that benzothiazole terminated sulfurating species with lower sulfur rank form in greater concentrations than the sulfurating species with higher sulfur rank, where a sequential sulfur pick-up mechanism was then postulated. A detailed kinetic model will be developed to describe the Gradwell, et al. data. Density functional theory (DFT) simulations were used to provide information on the thermochemistry of the various reaction intermediates. The DFT simulations indicated that both sequential and lumped S8 pick-up are thermodynamically feasible. Population balance models have been developed that explicitly account for all polysulfidic species that are present in the MBTS+S8 reaction system. The chemically consistent population balance model includes the following reactions: (i) dissociation of polysulfides, including the opening of S8 rings, to form radical pairs, (ii) combination of a pair of persulfenyl radicals, (iii) reaction of a persulfenyl radical with a polysulfide. The effect of chain length on the kinetic constants for these reactions was determined from the DFT simulations, where the bonds that are close to the benzothiazole groups have significantly different rates of reaction. It is shown that (i) lumped sulfur pick-up alone is not thermodynamically consistent, and (ii) sequential sulfur pickup alone can not adequately describe the experimental data of Gradwell, et al.; however, a chemically consistent model with both sequential and lumped sulfur pick-up can explain the data. The identification of the above mechanism and the associated distribution of sulfurating species of different sulfur rank provide the starting point for a quantitative kinetic description of the accelerated vulcanization.

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