Applications Based on Monte Carlo Methods

Various approaches using MC techniques to model the amorphous polymer bulk have been proposed. We refer to the work of Corradini et al. as a very 

Long-range interactions were modeled with the Mason-Kreevoy potential function  

The MC procedure employed by Corradini was as follows. A chain end was randomly selected, and a new bond added to it with bond angle and length kept constant and the rotational angle chosen randomly from the distribution 

The nonbonded interaction energy was calculated for the new atom by summation over all nonbonded atoms within the set cutoff distance. The probability of acceptance was 

Meirovitch developed the scanning method to study a system of many chains with excluded volume contained in a box on a square lattice.With this method, an initially empty box is filled with the chain monomers step by step, with help of transition probabilities. The probability of construction of the whole system is the product of the transition probabilities selected, and therefore, the entropy of the system is known. Consequently standard thermodynamic relations can be used to make highly accurate calculations of pressure and chemical potential, directly from the entropy. In principle, all these quantities can be obtained from a single sample without the need to carry out any thermodynamic integration. 

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