Dinâmica de polímeros lineares em armadilhas tipo delta

Abstract

The polymer micromanipulation have become more viable every day (by optical or magnetic means, or by applying electric fields on charged polymer units). One of the most important tecnique from this field is electrophoresis. This technique involves the separation of polyelectrolytes by size, by making usse of an external electric field. The toy model used in this work was proposed by a careful observation of the electrophoresis tecnique.

Theoretical studies and computational models become increasingly relevant in order to understand the polymer dynamics, pointing out possible new techniques, applications and to reduce the costs. Thus, in the present work the dynamics of linear polymers was studied through computer simulations.

We propose a mathematical construction for a linear polymer through a random walk of $N$ monomers, which are linked together, forming a periodic structure. Using the Bond-Fluctuation Model (BFM) as a basis, we created a program to simulate the movement of a polymer under the influence of traps. In order to fit the simulation's results we use the analytical results obtained from a normal modes analyse of the polymer, in other words the paths in which the structure can walk in time.

For this purpose we use the Rouse model, which is one of the simplest theoretical model and it can be solved analytically. The dynamics of the polymer within Rouse model can be described by the Langevin equation, which can be solved analytically by making use of the generalized Gaussian structures model.

In this way we analyze the dynamical behavior of linear polymers in periodic delta potentials. We use our simulation results to check the polymer displacement in different traps' configurations and by fitting our computational results with the analytical results.