Monte-Carlo Simulation of Polymers With Configurational-Bias Algorithm

By Yeng-Long Chen and Tzu-Chieh Wei
 
The process of making a polymer and measuring its physical properties is very resource-consuming, thus it is of importance to be able to predict the properties of a polymer before committing the resources.  Simulation of polymers is of interest because of the ability to predict the physical properties and phase behavior before resources are committed.  In recent years, configurational-bias Monte Carlo method has been used to simulate polymers in a grand canonical ensemble1,6.  These simulations have predicted phase behavior of long-chain alkanes and adsorption of polymers on zeolites.
The Configuration-Bias Monte Carlo (CBMC) algorithm was first developed in the 1950s by Rosenbluth and Rosenbluth2 in a study of polymer conformations on a lattice.   The method essentially considers possible trial configurations of the polymers and chooses a configuration using its weight, which is determined from its interaction with other polymers.  This method is preferred over conventional Monte Carlo because random walks with polymers are generally difficult, and by weighting possible moves CBMC allows easier random walks.
In this project, this method is applied to simulate Lennord-Jones polymers in order to study physical properties such as the polymers radius of gyration, the density distribution function, and the scattering function.  We are also interested in studying the phase transition and the equation of state of the polymeric system.  Finally, since CBMC uses weighting-bias in MC trial displacement, it is expected to be more efficient than the reptation algorithm.  We will attempt to confirm this hypothesis in this study.
Configurational-Bias Algothrithm
Simulation Results

Conclusion and Future Improvements

References

Simulation Source Codes