Electrophoretic Mobility of Polyelectrolytes within a Confining Well

Abstract

We present a numerical study of polyelectrolytes electrophoresing in free solution while squeezed by an axisymmetric confinement force transverse to their net displacement. Hybrid multi-particle collision dynamics and molecular dynamics simulations with mean-field finite Debye layers show that even though the polyelectrolyte chains remain "free-draining", their electrophoretic mobility increases with confinement in nanoconfining potential wells. The primary mechanism leading to the increase in mobility above the free-solution value, despite long-range hydrodynamic screening by counterion layers, is the orientation of polymer segments within Debye layers. The observed lengthdependence of the electrophoretic mobility arises due to secondary effects of counterion condensation related to confinement compactification.Understanding the electrophoresis of confined polyelectrolytes is crucial to the advancement of many separation techniques [1]. Methods such as translocation through nanopores [2][3][4] and sieving through arrays of microscopic posts [5][6][7][8][9] belong to a family of techniques that depend on nanoengineered geometrical constraints. In particular, the motion of polyelectrolytes (such as DNA) in narrow nanochannels raises a number of fundamental questions that are not yet fully understood in spite of practical interest [10,11].It is well-known that long, electrophoresing polyelectrolyte chains are "free-draining": their behavior is described by local effective properties, with long-ranged hydrodynamic coupling mostly screened [12]. When an electric field E applies a force to a chain segment, it also applies an equal and opposite force to the diffuse layer of counterions over the characteristic Debye length λ D . Thus, the viscous forces on the surrounding fluid are effectively cancelled with only a rapidly decaying residual hydrodynamic field beyond λ D [13]. This causes the effective friction coefficient ξ eff to increase linearly with degree of polymerization N , just like the charge Q eff ; the freesolution electrophoretic mobility µ 0 = Q eff /ξ eff is thus independent of chain length [14].One way to subvert this size independence is to apply a parallel mechanical force f simultaneously with the electric field. If the mechanical force acts only on the monomers and not on the counterions then the net force on the fluid does not cancel, long-ranged flows are possible and the chain is no longer free-draining [15]. This concept has been applied to many situations [12] including tethered polyelectrolytes [16] and end-labeled freesolution electrophoresis [17]. One oft-given example is the electrophoretic motion of a deformed polyelectrolyte through a nanofluidic channel [18][19][20] A negatively charged polyelectrolyte chain undergoing electrophoretic motion under the action of an electric field E. Point-like MPCD fluid particles are assigned a charge specified by the Debye-Hückel approximation and feel an electric force in the opposite direction to the monomer. A cylindrical harmonic potential radially ...

Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels

“…To simulate colloids in a flowing and thermally fluctuating nematic liquid crystal confined within a complex channel, a multi-particle collision dynamics (MPCD) algorithm is used. [39][40][41][42] MPCD has been employed to simulate reactiondiffusion dynamics, 43,44 electrophoresis, 45,46 thermophoresis, 47 swimmers, [48][49][50] polymers, [51][52][53][54] colloidal suspensions, 55,56 binary mixtures, 57 viscoelastic fluids, 58 ferrofluids, 59,60 and dense stellar systems. [61][62][63] Most relevantly, MPCD has been used to simulate nematic liquid crystals.…”