Electrokinetic Transport in Nanochannels. 2.
Experiments
Sumita Pennathur* and Juan G. Santiago
Department of Mechanical Engineering, Stanford University, Stanford, California 94305
We present an experimental study of nanoscale electro-
kinetic transport in custom-fabricated quartz nanochan-
nels using quantitative epifluorescence imaging and cur-
rent monitoring techniques. One aim is to yield insight
into electrical double layer physics and study the ap-
plicability of continuum theory to nanoscale electrokinetic
systems. A second aim is to explore a new separation
modality offered by nanoscale electrophoretic separations.
We perform parametric variations of applied electric field,
channel depth, background buffer concentration, and
species valence to impose variations on ú potential,
effective mobility, and Debye length among other param-
eters. These measurements were used to validate a
continuum theory-based analytical model presented in the
first of this two-paper series. Our results confirm the
usefulness of continuum theory in predicting electroki-
netic transport and electrophoretic separations in nano-
channels. Our model leverages independent measure-
ments of ú potential performed in a microchannel system
at electrolyte concentrations of interest. These data yield
a ú potential versus concentration relation that is used as
a boundary condition for the nanochannel electrokinetic
transport model. The data and model comparisons to-
gether show that the effective mobility governing electro-
phoretic transport of charged species in nanochannels
depends not only on ion mobility values but also on the
shape of the electric double layer and analyte ion valence.
We demonstrate a method we term electrokinetic separa-
tion by ion valence, whereby both ion valence and mobility
may be determined independently from a comparison of
micro- and nanoscale transport measurements.
In nanometer-scale electrokinetic channels, electric double
layer (EDL) thicknesses are comparable to characteristic channel
dimensions. The velocity profile is highly nonuniform, resulting
in a decreased net flow rate per unit cross-sectional area relative
to the thin EDL case.
1-16
In the first of this two-paper series, we
presented a review of theoretical and experimental studies of
electrokinetic transport in nanometer-scale fluidic channels.
16
We
also presented analytical and numerical models for net streamwise
transport of both neutral and charged analyte species within long,
thin electrokinetic channels. We used a simple numerical integra-
tion technique to solve for the transverse potential, Ψ(y), in
conditions of both low and high ú potential. We considered the
addition of a dilute analyte sample species S whose concentration
is much lower than that of background electrolyte ions. We
demonstrated that transverse electromigration is in quasi-equi-
librium with transverse diffusion flux. This quasi-steady transverse
concentration distribution couples with the nonuniform velocity
profile of nanochannel electrokinetic transport to yield an ob-
served, area-averaged species velocity, 〈u
S
〉, of the form
where F is Faraday’s constant, ν
S
is the (typical) species mobility,
and the operator 〈〉represents a transverse (y-direction) depth-
averaged quantity of the form 〈〉 ) 1/(2h)∫
-h
h
()dy. The
channels used in our experiments have 20:1 width-to-depth aspect
ratios and so velocity and potential fields can be approximated as
functions of only the transverse dimension, y.
16
The operator 〈〉
can therefore also be interpreted as an area-averaging operation.
The term (1 - ψ(y)ú) in eq 1 describes the shape of the velocity
profile, and the product of this term and the exponential within
the area operator describes the coupling between the velocity
profile and the transverse concentration of the analyte of valence
z
S
. The resulting unsteady, two-dimensional species concentration
field can then be expressed as
where t is time, x is the streamwise coordinate, and D is the
(isotropic) molecular diffusion coefficient.
* To whom correspondence should be addressed. E-mail: sumita@stanford.edu.
Fax: (650)-723-7657.
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〈u
S
〉 )
Eú
µ
〈
exp
(
-z
S
e(ψ(y) - ψ
c
)
kT
)(
1 -
ψ(y)
ú
)〉
+ ν
S
z
S
FE
(1)
c
c
(x, y, t) ) cˆ
0
exp(-(x - 〈u
S
(x)〉 t)
2
/4Dt)
x4piDt
×
exp
(
-z
S
e(ψ(y) - ψ
c
)
kT
)
(2)
Anal. Chem. 2005, 77, 6782-6789
6782 Analytical Chemistry, Vol. 77, No. 21, November 1, 2005 10.1021/ac0508346 CCC: $30.25 2005 American Chemical Society
Published on Web 09/28/2005

The following relation highlights the effect of transverse
electromigration and valence number on net streamwise electro-
phoretic transport in a nanochannel:
16
where 〈ν
S,nano
〉 and ν
S
are the effective electrophoretic mobility of
a charged species in a nanochannel and a (thin EDL) microchan-
nel, respectively. ν
S
is the usual ion mobility of a species defined
as u
d
/EFz
S
, where u
d
is the net drift velocity (i.e., relative to the
local liquid velocity) for an ion of valence z
s
subject to an electric
field E.
15
〈ν
S,nano
〉 is an effective mobility parameter associated with
a net drift velocity that is measured relative to the background
area-averaged liquid velocity. 〈ν
S,nano
〉 is defined as (〈u
S
〉 - 〈u〉)/
(EFz
S
), where 〈u
S
〉 is the observed, area-averaged velocity of the
species and 〈u〉 is the area-averaged velocity of the liquid in the
channel. 〈ν
S,nano
〉 is distinct from the common definition of
electrophoretic mobility of an analyte in that it depends on both
transverse ion electromigration and its coupling with a nonuniform
electroosmotic velocity profile. The parameter â in eq 3 is the
ratio of the electrophoretic velocity to the Helmholtz-Smolu-
chowski velocity for electroosmotic flow, µz
S
ν
S
F/ú. The ratio
〈ν
S,nano
〉/ν
S
can be interpreted as the factor by which electro-
phoretic mobility is apparently changed from the standard ion
mobility value when the charged species is observed migrating
through a nanochannel (where its net axial motion couples with
the nonuniform velocity profile of the EDL). This ratio helps
quantify the net change in streamwise electrophoretic flux due
solely to nanochannel transport effects.
In this paper, we present an experimental investigation of
electrokinetic transport in nanometer-scale channels with finite
double layers. We investigate the accuracy and extent of applica-
tion of Gouy-Chapman-Stern continuum theory
17
by making
detailed comparisons between experiments and continuum theory.
We experimentally validate the analytical model of our previous
paper.
16
We also demonstrate a technique we term electrokinetic
separation by ion valence (EKSIV), which can be used to
determine both ion valence and mobility of analyte species from
a comparison of micro- and nanoscale transport measurements.
EXPERIMENTAL METHODS AND SETUP
Channel Design and Fabrication. We designed and fabri-
cated a variety of both nanochannel and microchannel devices
such as that shown in Figure 1. We fabricated various configura-
tions including straight channels, simple crosses, and so-called
double-T channel geometries. Straight channels had typical
lengths of 36 mm and simple cross and double-T channel
geometries channels all had a separation column length of 30 mm.
Both the nanometer- and micrometer-scale fluidic channels
were fabricated using conventional optical photolithography, dry
chemical etching, and bonding techniques.
18
Figure 1 shows
images from an atomic force microscope (AFM) and scanning
electron microscopy (SEM) for a typical nanochannel system prior
to bonding the cover plate. Channel depths of 2052, 102, and 38.5
nm were fabricated using this method and characterized by both
AFM and SEM measurements. These channel depths will be
referred to in this paper by the nominal values of 2 µm, 100 nm,
and 40 nm. Rms surface roughness as measured by AFM was
(0.2 nm for all channel depths.
To seal the channel and provide fluidic interconnects, 1.5-mm-
diameter through holes were created in a second fused-silica wafer
using CO
2
laser machining. Both wafers were hydrolyzed in H
2
-
SO
4
/H
2
O
2
at 80 °C, rinsed in deionized water, and mated, before
a 5-h anneal at 1200 °C. Cylindrical plastic reservoirs were potted
onto the substrate using epoxy. The channels are filled with
deionized water by capillary action and stored wet for future use.
Chemicals and Reagents. Our aqueous, buffered solutions
consisted of nine concentrations of sodium tetraborate buffer
(Sigma Aldrich, St. Louis, MO), ranging from 0.1 to 10 mM and
prepared using filtered deionized water (Fisher Scientific W2-20,
Fairlawn, NJ). The pH of the buffered solutions varied between
7.9 and 9.2 depending on concentration as measured using a pH
meter (Corning, Corning, NY), although the great majority of
conditions resulted in pH values between 8.8 and 9.2. We filtered
electrolyte solutions prior to experiments with 200-nm pore syringe
filters (Nalgene Labware, Rochester, NY). We measured species
velocities of three fluorescent analytes: rhodamine B (Acros
Organics, Geel, Belgium), bodipy (Molecular Probes, Inc.), and
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Sons: New York, 1994.
(16) Pennathur, S.; Santiago, J. Anal. Chem. 2005, 77, 6772-6781. ac050835y
(17) Lyklema, J. Fundamentals of Ineterdace and Colloid Science, 2; Academic
Press: New York, 1995.
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2063.
Figure 1. SEM (a) and AFM scan (b) of the inlet region of a
nanometer-scale fluidic channel. The spots in the SEM image are an
artifact of the metallization preprocessing of the sample. The vertical
scale of the AFM (z-direction in the plot) is exaggerated by a factor
of 20 for clarity of presentation (channel is 102 nm deep). The images
show 1-mm-diameter posts near the inlet of the nanochannel which
serve as an integrated filtering structure. (c) Schematic of nanochan-
nel device with 125 µmby75µm detection area centered 7 mm from
the injection point. Tick marks are etched below the nanochannel test
section to aid in registration and quantitation.
〈ν
S,nano
〉
ν
S
) 1 -
1
â
〈(
1 -
ψ(y)
ú
)(
exp
(
-z
S
e(ψ(y) - ψ
c
)
kT
)
- 1
)〉
(3)
Analytical Chemistry, Vol. 77, No. 21, November 1, 2005 6783