 |
|
|
| |
Adobe Reader 6.0 or higher is required to view our PDF documents.
|
| |
Electroosmotic Force and Flow (EOF)
EOF is the result of electroneutrality constraints, which cause the formation of a charge double layer at the walls of most microchannels and capillaries. The walls of the capillaries contain fixed charges resulting either from the materials of construction or the adsorption of charged analytes to the surface, except at very specific conditions, like low pH. These fixed charges attract a layer of counterions creating an electric double-layer at the wall (shown in animation above). When an electric field is applied across the flow channel, the soluble counterions are free to move, but the fixed wall charges are not. The viscous drag caused by movement of the counter-ions localized along the capillary wall transfers momentum to the rest of the bulk fluid inside the capillary. Since there is no other fixed surface inside the capillary against which the bulk fluid can dissipate this momentum, the bulk fluid begins to move with the same velocity as the ions at the wall. This induced bulk flow is called electroosmotic flow (EOF). According to the Helmholtz-Smoluchovski Equation (1), the contribution of EOF to the apparent mobility of the ions (mEOF or μEOF) is proportional to zeta-potential of the wall (ζw), and permitivity of solvent (ε) and inversely proportional to viscosity of the solution (η). The actual induced bulk fluid velocity (vEOF) is proportional to the applied field strength (E).
(1)
Why is EOF control important?
In the early days of capillary electrophoresis EOF was welcomed since the possibility it brought of simultaneous analysis of cations and entrained anions was considered a benefit.[1,2] The velocity profile of EOF is much narrower than that of hydrodynamic flow which makes EOF a useful tool for capillary electrochromatography applications.[3-11] While EOF has some obvious advantages, in general terms, the negative impact of EOF on separation was quickly recognized.[12]
It is well established from both empirical studies[13, 14] and first principles analysis[15] that EOF, even in coated capillaries reduces the separation capacity of CE methods by causing the capillary contents to drain during the separation process. The migration of an analyte in an electrical field can be described by its mobility (m or μ). This value is empirically derived (Equation 2) from the inverse of the elution time (telution) adjusted for field strength (E) and distance traveled (d). Since the migration of any charged species is the sum of its electrophoretic (or intrinsic) mobility (μelectrophoretic) and EOF mobility (μEOF),
(2)
this leads to poor reproducibility of elution times (telution) if EOF varies from run to run. From Equation 2 it is obvious that when the intrinsic mobility of the analyte is small compared to the EOF mobility (e.g., large molecules with low net charge, like proteins, or zwitterionic species near their isoelectric point) the apparent mobility of the analyte approaches the EOF mobility and no separation can be attained. In protein separations based on isoelectric points by CIEF (capillary isoelectric focusing), EOF has to be eliminated to achieve the highest resolution for this equilibrium method.[16]
It is also readily shown that when there are small differences in the electrophoretic mobility of the analytes being separated (e.g., para-, meta-, and ortho-hydroxybenzoic acid) EOF can drain the capillary before the desired separation is attained. If we define resolution of analytes 1 and 2 as the difference in their elution times being equal to the average peak width (twidth),
(3)
in the absence of isotachophoretic focusing, the length of the sample plug and axial diffusion ultimately determine the width of the peak.
From Equation 2 the mobility of each analyte is the sum of its electrophoretic and EOF mobilities and on substitution and rearrangement yields:
(4)
which can be approximated by:
(5)
when μEOF dominates the mobility term. Clearly, since (E·twidth/d) is effectively a constant, μEOF must approach zero as Δμelectrophoretic approaches zero for resolution to be maintained.
EOF Mismatches Cause Resolution Loss
It wasn't until recently, however, that the effect of minor variations in EOF on peak resolution have been fully appreciated. Ross et al.[17] showed that the resulting CE flow front is rapidly distorted by the EOF-induced pressure-driven flow caused by discontinuities in the coatings of CE microchannels. This effect is even more pronounced in capillaries with more significant regions of EOF mismatch. This is shown in the movies below created from caged fluorophor studies in electrophoretic microchannels partially coated with poly(ethylene oxide).[14] The counter-intuitive result is that, despite lower overall EOF, more peak distortion occurs as a result of the EOF mismatch.
|
|
|
|
