Markov growth model

Hulliger, J. Alaga-Bogdanovic, M. Bebie, H. Growth-induced effects of polarity in molecular crystals Comparison of Schottky-and Markov-type models with Monte Carlo simulations. J. Phys. Chem., B 2001. 36. 8504-8512. 

The active centers in this process are free radicals, whose reaction with double bonds of monomers leads to the growth of a polymer chain. In the framework of the ideal kinetic model, the reactivity of a macroradical is exclusively governed by the type of its terminal unit. According to this model, the sequence distribution in macromolecules formed at any moment is described by the Markov chain with elements controlled by the instantaneous composition of the monomer mixture in the reactor as... 

Two-phase polymerization is modeled here as a Markov process with random arrival of radicals, continuous polymer (radical) growth, and random termination of radicals by pair-wise combination. The basic equations give the joint probability density of the number and size of the growing polymers in a particle (or droplet). From these equations, suitably averaged, one can obtain the mean polymer size distribution. 

All the statistical characteristics of copolymer chain structure and composition inhomogeneity, (including the ones reported in the above papers) can be easily calculated by means of the Markov chain formalism for any of kinetic models presented in Sect. 2. Then it does not seem advisable for the solution of such problems to apply the Monte-Carlo method with which the simulation of the copolymer chain growth was carried out [83-93]. 

First-order Markov processes are therefore defined by two independent addition probabilities. Although the propagation steps shown above depict free radical polymerisation, the statistical models are equally applicable to other types of chain growth as found, for example, in ionic and Ziegler-Natta polymers (see section 2.3.4). 

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