Simulations of Free-Solution Electrophoresis of Polyelectrolytes with a Finite Debye Length Using the Debye-Hückel Approximation

We introduce a mesoscale simulation method based on multiparticle collision dynamics (MPCD) for the electrohydrodynamics of polyelectrolytes with finite Debye lengths. By applying the Debye-Hückel approximation to assign an effective charge to MPCD particles near charged monomers, our simulations are able to reproduce the rapid rise in the electrophoretic mobility with respect to the degree of polymerization for the shortest polymer lengths followed by a small decrease for longer polymers due to charge condensation. Moreover, these simulations demonstrate the importance of a finite Debye length in accurately determining the mobility of uniformly charged polyelectrolytes and net neutral polyampholytes.

Figure 1

The mobility of short polyelectrolytes as a function of the degree of polymerization $N$ normalized by the free draining value ${\mu }_{\mathrm{FD}}$. The results of our hybrid simulations with and without counterion condensation (open circles and open diamonds, respectively), experimental results (filled symbols) and simulations using explicit ions (open squares). The open triangles are simulations using a thin Debye layer approximation. The experimental data and explicit ion simulation results are reproduced with permission from Ref. 7.

Figure 2

Effective friction ${\Gamma }_{\mathrm{eff}}$ (circles) and effective charge $Q_{\mathrm{eff}}$ (squares) per monomer as a function of the degree of polymerization $N$. Filled symbols are our hybrid simulation results while open symbols are simulations using explicit ions reproduced with permission from Ref. 7. The diamonds show the effective friction when there is no charge condensation. Inset: Effective charge of a monomer as a function of monomer position normalized by the average effective charge on all monomers.

Figure 3

Mobility of a uniformly charged polymer, ${\mu }_0$, as a function of the ${\lambda }_{\mathrm{D}}$, along with mobility of a net neutral block copolymer, ${\mu }^{*}$, rescaled by a constant factor. The inset shows the mobility of a net neutral block copolymer ($N=20$) as a function of cutting position $x$ for two values of ${\lambda }_{\mathrm{D}}$.