Charged Species Transport, Separation, and Dispersion in Nanoscale Channels:  Autogenous Electric Field-Flow Fractionation

Abstract

Numerical methods are employed to examine the transport of charged species in pressure-driven and electroosmotic flow along nanoscale channels having an electric double-layer thickness comparable to the channel size. In such channels, the electric field inherent to the double layer produces transverse species distributions that depend on species charge. Flow along the channel thus yields mean axial species speeds that also depend on the species charge, enabling species separation and identification. Here we characterize field-flow separations of this type via the retention and plate height. For pressure-driven flows, we demonstrate that mean species speeds along the channel are uniquely associated with a single species charge, allowing species separation based on charge alone. In contrast, electroosmotic flows generally yield identical speeds for several values of the charge, and these speeds generally depend on both the species charge and electrophoretic mobility. Coefficients of dispersion for charged species in both planar and cylindrical geometries are presented as part of this analysis.

Transport phenomena in nanofluidics

“…This effect is illustrated as follows. Two like-charged objects repel each other due to Coulombic interactions, resulting in a segregation of negatively charged molecules toward the center of the likecharged nanochannel ͑Garcia et Griffiths and Nilson, 2006͒. On the contrary, positively charged analyte molecules equilibrate close to the negatively charged walls.…”

Transport of charged samples in fluidic channels with large zeta potentials

“…We would like to point out that the parameter Pe t used here is equal to the units of electronic charge carried by an analyte species (z) for a spherical molecule [3,4,11,12]. This is because the electrophoretic mobility of a sphere of radius a may be expressed as (ze)/(6pZa) while its molecular diffusivity may be estimated by the Stokes-Einstein value D = (k B T)/(6pZa) yielding Pe t = (mk B T)/(eD) = z.…”

“…2a for a pressure-driven flow system. Under strong Debye layer overlap conditions (l * .. 1), it has been shown by other researchers [11,12] that an increase in l reduces the magnitude of the lateral electric field in nanochannels thereby diminishing the effects of transverse electromigration on analyte transport. In this limit, the mean velocity of charged samples in the conduit approaches that of the fluid (or neutral solutes) yielding a very weak dependence on the value of z * .…”

“…As the extent of the Debye layer overlap increases however, the strength of the lateral electric field between the parallel plates decays off as 1/l *2 diminishing the nonuniformity in the solute concentration profile described above [22][23][24]. In the limit of l * .. 1, the Taylor-Aris dispersion for all charged species therefore approach that for a neutral molecule (Pe t = 0) and hence does not depend on thewww.electrophoresis-journal.com Electrophoresis 2007, 28, 4552-4560 Miniaturization 4557 values of Pe t or z * in both pressure-driven and electrokinetic flow systems [11,12]. Moreover, because the electric potential induced the surface charges under these conditions approaches the zeta potential at the channel walls, the electrical charge density in the liquid phase becomes uniform with an increase in the extent of the Debye layer overlap.…”

“…? [11,12,22]. While the non-uniformity in the solute concentration may be ignored in the limit of l * .. 1, it tends to modify the dispersion of sample slugs as the thickness of the Debye layer relative to d is reduced.…”