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Interaction of Coupled Particles Based on Lennard-Jones and Spring Forces in Brownian Ratchet Devices

R. Retkute and J.P. Gleeson
University College Cork, IE

electrophores, Brownian ratchet, coupled

Electrophoresis is a technique used to separate polyelectrolyte strands of different lengths. One of its fields of application in nanotechnology is in the separation of DNA. Chains of particles can undergo net transport on a potential energy that is externally driven to fluctuate between several states in Brownian ratchet device. We employ numerical solutions of Langevin equations to compare the classical elastically-coupled model of such motion with a more realistic model where particles interact through Lennard-Jones forces. Numerical simulations agree with analytical formulas for the limiting cases where the coupling is very weak or very strong. For two particles with elastic coupling a non-zero current in the absence of fluctuations is observed (as in Ajdari 1994), but is found to be absent in the equivalent Lennard-Jones model. In the presence of noise the current in the Lennard-Jones model is markedly different to the equivalent (i.e. linearized) spring model in various parameter regimes. A simple criterion for locating these parameter regimes is presented. Rigorous results on general models like this could indicate parameter sets for effective scenarios of DNA separation.

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