Module 6 : Sampling and Metropolis Monte Carlo

Lecture 27 : Markov process and its applications - 1

Example: Application of Markov process in Free radical copolymerization (Random Copolymer)

In a Random copolymerization system, let us assume, there are two types of repeat units (1) & (2)

The chain propagation step will have the following possibilities

M1& M2 are two types of repeat units and M1* & M2* are the respective free radicals.

Rate of propagation of each step can be written as

(1)

The rate of consumption of M1 & M2 can be given by

(2)


(3)

Dividing (2) by (3), we get,

(4)

From (1),

(5)

Using (1) & (5) into (4),

(6)