Free Solution Electrophoresis of Polyelectrolytes with Finite Debye Length Using the Debye-Huckel Approximation
Polyelectrolytes are bizarre objects. They are very long chains of charged monomers (repeating chemical blocks). Each of these macromolecules has a vast number of degrees of freedom but the connectivity and, even more importantly, the long-range electrostatic and hydrodynamic interactions between monomers make them hard to treat. Statistical approaches can only offer so much insight and fail to reproduce more than just the most fundamental characteristics of polyelectrolytes. On the other hand, simulations grind to a halt under the heft of the electrostatic and hydrodynamic calculations.
In order to computationally investigate such systems, we designed a mesoscale simulation technique that uses the Multi-Particle Collisions Dynamics (MPCD) algorithm to simulate the surrounding solvent molecules (and so capture hydrodynamic interactions) and the statistical Debye-Huckel approximation to assign effective charge to the MPCD particles. Our hybrid method can capture the electohydrodynamics without having to explicitly include counter-ions or make costly electrostatic calculations. Because it can capture the sharp rise in mobility at small lengths, eventual plateau at long lengths and even the small non-monotonic maximum at moderate lengths, our mean-field MPCD-MD Debye-Huckel method shows great potential for simulating electrophoretic behavior of polyelectrolytes in novel microfluidic devices.