Stochastic modelling of polymer conformation in external fields

Soundararajan Krishnaswami, Purdue University

Abstract

The Gaussian chain model, which is a good approximation of flexible chains, resembles the trajectory of a particle executing Brownian motion. In the absence of an external field, the problem is trivial. But in the presence of an external potential the process becomes non-Markovian and is difficult to solve. By augmenting the system with a variable that depends on the conformational energy, the dimensions of the system is augmented by one, and the augmented system becomes Markovian. This facilitates the treatment, because stochastic differential equations can be written to model the Gaussian chain in an external field. To this system, the idea of a constrained stochastic process or 'bridge' process was used to evolve only conformations within a certain range of energy that is most useful for property computation. This was achieved by constructing a 'bridge' type process for the energy dependent augmented variable. Simulations were done for the Gaussian chain by solving this vector stochastic bridge process, and conformations generated. The configurations were generated both by the regular unconstrained Brownian motion process and the constrained bridge process. The conformations clearly showed a trend towards the low energy regions for the Bridge process simulations. Size related properties like the end-to-end distance and the radius of gyration were computed. The average configurational energy was also calculated. Corresponding computations were done for the case when there is no constraint on the energy of the conformations. The constrained process showed a much lower error bound. The convergence of these properties was also studied. As expected the convergence of these properties was found to be faster when the bridge simulations were performed. Formulations were also done for the case of a Gaussian chain in an arbitrary potential. The method of solution for this case is successive approximation using the method of characteristics. Using this solution any type of potential could be dealt with ease. Potentials of an absorptive kind with a negative well close to the walls and positive or zero far away would be of interest from a practical point of view.

Degree

Ph.D.

Advisors

Ramkrishna, Purdue University.

Subject Area

Chemical engineering

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