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