##manager.scheduler.building##: Edificio Santa Maria

##manager.scheduler.room##: Auditorio San Agustin

Date: 2019-07-08 11:45 AM – 03:30 PM

Last modified: 2019-06-15

#### Abstract

To design an artifact to separate polymers must consider issues such as its length, its mass, its interaction with the environment of the polymers, etc, without modifying them. Some known methods are dielectrophoresis and electrophoresis, but there are also separation mechanisms using ratchets. Two types of ratchets mechanisms can be distinguished: thermal (in which the Brownian motion plays an important role and usually ratchets of the on / off type are used) and steric (typically using an asymmetrical 2D geometric structure to separate the particles). In this study we propose to use a thermal ratchet mechanism in which the ratchet is on all the time but is externally forced.

For this, we studied the transport phenomena of a string of N+1 spherical monomers equal mass coupled N massless springs harmonics. The chain is immersed in a periodic potential with an externally forced left-right asymmetry periodically both spatially and temporally. It is considered that the monomers do not overlap and, in addition, there are hydrodynamic interactions (Rotne-Prager-Yamakawa Tensor).

The periodic potential and external forcing parameters are varied, as well as the length of the chain and the intensity of the coupling. We also analyze the case in which the monomers are coupled by springs of the Rouse type whose constant k = 3k<sub>B</sub>T ⁄ l^2 where l<sup>2</sup> = ⟨ R<sub>j</sub><sup>2</sup> ⟩ (R<sub>i</sub>, i = 1,…, N are the connection vectors).

The dynamics is described by the generalized Langevin Equation: dr<sub>i</sub> ⁄dt = ∑<sub>j=0</sub><sup>N</sup> μ<sub>ij</sub> (V<sub>j</sub>+ ξ<sub>j</sub> )

where r<sub>i</sub>, i=0,…, N are the position vectors, μ<sub>ij</sub> is the Rotne-Prager-Yamakawa diffusion tensor, V<sub>j</sub> represents the conservative forces that affect the monomer and ξ<sub>j</sub> is a stochastic variable.

The characteristic quantities that are analyzed are the end-to-end distance, the radius of rotation (the avarage of the second moment of the mass distribution relative to the center of mass) and the velocity of the center of mass.