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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