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Modeling is the applications of methods to analyze complex, real-world problems in order to make predictions about what might happen with various actions. When it is too difficult, time consuming, costly or dangerous experiments, the modeler resort to computer simulations, or having a computer program imitate reality, in order to study situations and make decisions. Mathematical modeling is being used extensively in the field of polymer reaction engineering to ascertain various parameters. The use of mathematical modeling reduces the need for costly and time consuming experimentation. Mathematical models have been useful tools to enhance the understanding of polymerization processes and have been essential for process design, parameter estimation, sensitivity analysis, process simulation and optimization. Moreover, they are also useful for education and training purposes. [1-4] For example, several models have been proposed to simulate free-radical homopolymerization. The majority of these models predicting only averages molecular properties, but not complete distributions. Various modeling techniques have been used in the field of polymer engineering depending on the suitability and on the targeted parameters. The most commonly used techniques are namely: 1) Instantaneous distributions, 2) Population balances with the method of moments, and 3) Monte Carlo method. The three methods have their own advantages and disadvantages. For examples, the method of moments cannot predict the molecular weight distribution (MWD) while the instantaneous distribution and Monte Carlo method can easily predict the MWD. In the case of copolymerizations, Monte Carlo technique is capable of predicting both average results and the full distribution. The focal point of this chapter would be on the Monte Carlo method since this technique can give full understanding about the polymerization processes. The modeler of the Mote Carlo simulation have full understanding of the molecular behavior in the reactor and use its programming skills to translate this understanding into valuable results. Monte Carlo simulation is a probabilistic model involving an element of chance. Monte Carlo method provides approximate solutions to a variety of mathematical problems by

Applying Dynamic Monte Carlo Simulation for Living Free Radical Polymerization Processes: Emphasis on Atom Transfer Radical Polymerization (ATRP)