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APPLIED PHYSICS LETTERS 86, 143105 共2005兲
Surface-charge-induced asymmetric electrokinetic transport in confined
silicon nanochannels
R. Qiao and N. R. Alurua兲
Department of Mechanical and Industrial Engineering, Beckman Institute for Advanced Science and
Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
共Received 1 December 2004; accepted 2 March 2005; published online 28 March 2005兲
Molecular dynamics simulations of a NaF solution transport in a confined silicon nanochannel
indicated that the water flux and the ionic conductivity through two oppositely charged silicon
channels, that are otherwise similar, differ by a factor of more than three, and the co-ion fluxes are
in the opposite direction. Such a behavior cannot be predicted by the classical electrokinetic
transport theory, and is found to originate from the asymmetric dependence of the transport
properties of water near the charged silicon surface. © 2005 American Institute of Physics.
关DOI: 10.1063/1.1897430兴
Electrokinetic transport, referring to the transport of water and ions induced by an external electric field, is widely
encountered in many biological and engineering systems,
e.g., ion channels, fuel cells, and chemical analysis
devices.1–4 Electrokinetic transport is widely used in
nanoscale fluidic systems due to its scalability and
ease-of-control.4 In the classical continuum modeling of
electrokinetic transport, the ion transport is modeled by using
the Poisson-Nernst-Planck equations and the fluid transport
共usually referred to as electro-osmotic transport兲 is modeled
by using the Navier–Stokes equations.3 In this letter, through
detailed molecular dynamics 共MD兲 simulations, we report on
the asymmetric effect of surface charge on the electrokinetic
transport of a NaF solution in silicon slit nanochannels. Classical electrokinetic theory predicts that the water flux and
ionic conductivity of an electrolyte in two oppositely charged
channels are the same if the magnitude of the external electric fields is identical. However, MD simulations indicate
that the water flux and the ionic conductivity through a negatively charged silicon nanochannel are more than three times
larger compared to those in a positively charged channel with
the magnitudes of the external electric field and the surface
charge density kept the same. We explain this unexpected
behavior by the asymmetric dependence of the transport
properties, e.g., viscosity, of the interfacial water on the surface charge.
The simulation system consists of a slab of water/ions
confined between two channel walls.5 Each wall is made up
of four layers of silicon atoms oriented in the 具111典 direction.
The channel width, defined as the distance between the two
innermost wall layers, is 3.49 nm. A total charge of 32e 共or
−32e兲 were distributed evenly among the atoms of the innermost layer of the channel wall, giving a surface charge density 共␴s兲 of 0.13 C / m2 共or −0.13 C / m2兲. Water was modeled
by using the SPC/E model,6 and ions were modeled as
charged Lennard-Jones 共LJ兲 particles. The number of ions in
the system were chosen to maintain the electroneutrality of
the system and the desired ion concentrations at the channel
center. The LJ parameters for the O–O, Si–O pairs were
a兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
taken from the Gromacs force field,7, and those for the ion–
ion and ion–O pairs were taken from Ref. 8.
Simulations were performed with a modified Gromacs
3.0.5.7 Periodic boundary conditions were used in the channel length directions 共x and y directions兲. Fluid temperature
was maintained at 300 K by a Nose thermostat.9 The electrostatic interactions were computed by using a particle mesh
Ewald method with a slab correction.10 The electrokinetic
transport is obtained by applying an external electric field
Eext,x in the x direction. Other simulation details can be found
in a prior paper.5 Starting from a random configuration, the
system was simulated for 2 ns to reach steady state, followed
by a production run of 10 ns.
We first consider the electrokinetic transport of NaF solution through two channels with surface charge densities of
0.13 C / m2 共case 1兲 and −0.13 C / m2 共case 2兲. The external
electric field, Eext,x, is −0.25 and 0.25 V / nm in case 1 and
case 2, respectively. Such strong fields are necessary to generate a velocity field that can be retrieved with reasonable
accuracy from MD simulations. Figure 1共a兲 compares the
counter-ion concentration profiles in case 1 共counter-ion: F−兲
and case 2 共counter-ion: Na+兲. As 兩␴s兩 is identical, and the
size of Na+ and F− ions is comparable, the counter-ion distributions are similar in both cases.11 The co-ion concentration profiles are also similar in both cases and are not shown
because of the small contribution of co-ions to the fluid flow.
Figure 1共b兲 compares the water velocity 共ueo兲 profiles for
case 1 and case 2 as obtained from continuum and MD simulations. The continuum simulation is based on the Stokes
equation:
d
关␮dueo共z兲/dz兴 +
dz
N
qici共z兲Eext,x = 0,
兺
i=1
共1兲
where z is the position across the channel width, ␮ is the
water viscosity, N is the number of ionic species, and qi and
ci共z兲 are the charge and the concentration of ion i. Here, ci共z兲
is taken from the MD simulation results. The continuum
theory predicts a similar velocity in both cases,12 while the
MD results predict that ueo in a negatively charged silicon
channel is much higher compared to that in a positively
charged silicon channel, and the difference in ueo between
the two cases is mainly due to the different velocity behavior
in the region of about 5 Å from the channel wall.
0003-6951/2005/86共14兲/143105/3/$22.50
86, 143105-1
© 2005 American Institute of Physics
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143105-2
Appl. Phys. Lett. 86, 143105 共2005兲
R. Qiao and N. R. Aluru
FIG. 2. Effective viscosity of water across the channel in the positively
charged channel 共a兲 and negatively charged channel 共b兲. The effective viscosity is scaled by the viscosity of water in the central portion of the channel
␮0 = 0.736 mPa s.
FIG. 1. 共a兲 Counter-ion concentration profiles across the channel 共channel
width is in the z direction兲 for case 1 and case 2; z = 0 corresponds to the
innermost layer of the lower channel wall; 共b兲 comparison of the water
velocity profile for case 1 and case 2, as obtained from the continuum theory
and the MD simulations. In the continuum simulation, a no-slip boundary
condition is applied at a position of 0.16 nm from the surface—this is consistent with the MD observation. A constant viscosity of ␮ = 0.736 mPa s is
used, which gave the best match of the velocity profile curvature in the
central portion of the channel with the MD results.
Table I shows the ionic fluxes and their electrical migration 共Jmig兲 and convective 共Jeo兲 components. The ionic fluxes
are dramatically different in the two cases. Specifically, 共a兲
the counter-ion flux density in case 2 is 3.88 times of that in
case 1, and 共b兲 the co-ion flux in the two cases is in the
opposite direction. Observation 共a兲 can be understood by noting that both the convection and the electrical migration
components of the counter-ion flux are stronger in case 2
than in case 1. Observation 共b兲 can be understood by noting
that though the electrical migration component of the co-ions
is comparable in both cases, the convection component of
the co-ions in case 2 is much stronger than that of case 1.
The strong convection component dominates the overall coion transport in case 2, and this leads to the opposite overall
TABLE I. Ionic flux density and conductivity in electrokinetic transport.a
Case 1
共␴s = 0.13 C / m2兲
Case 2
共␴s = −0.13 C / m2兲
counter-ion
flux
共kmol/ m2 / s兲
JFeo− = 2.511
JFmig
− = 1.919
JF− = 4.430
eo
JNa
+ = 11.788
mig
JNa
+ = 5.385
JNa+ = 17.173
co-ion
flux
共kmol/ m2 / s兲
eo
JNa
+ = 0.366
mig
JNa+ = −0.476
JNa+ = −0.110
JFeo− = 1.294
JFmig
− = −0.491
JF− = 0.803
conductivity
共S/m兲
␬1 = 1.750
␬2 = 6.308
a
transport of the co-ions. Table I also shows that the ionic
conductivity in case 2 is 3.61 times of that of case 1, even
though the number of ions and the magnitude of the surface
charge is identical in both cases.
Phenomenologically, the above results can be attributed
to the different transport properties of water and ions near the
charged silicon surfaces, i.e., the water viscosity ␮ 共counterion mobility兲 is much higher 共lower兲 near a positively
charged silicon surface compared to that near a negatively
charged silicon surface. To evaluate this quantitatively, we
computed the effective viscosity of water in the two channels. Specifically, we divided the channel into 5 bins 共0–0.46,
0.46–0.76, 0.76–2.73, 2.73–3.03, and 3.03– 3.49 nm兲, and
assumed that the viscosity in each bin is represented by an
effective viscosity ␮eff. ␮eff in each bin was computed by
solving Eq. 共1兲 and requiring that the solution match with the
MD velocity at the edge of each bin and at the channel center. Figure 2共b兲 shows the effective water viscosity in the two
channels. We observe that ␮eff in the bin adjacent to the
positively charged channel surface is 4.90 times of that in the
channel center 共␮0 = 0.736 mPa s兲, while the ␮eff in the bin
adjacent to the negatively charged channel surface is almost
the same as that in the channel center. Since in both
nanochannels, most of the driving force for the fluid flow
exists only within a thin layer near the surface, the different
viscosity of the interfacial water can lead to dramatically
different water flow in the entire channel. The dependence of
the water viscosity on the surface charge has been
reported.2,3 However, the asymmetric effect of surface
charge, to our knowledge, is not known. We also investigated
the diffusion coefficient of water in the direction parallel to
the surface, D储, by turning off the external electrical field in
case 1 and 2, and by performing equilibrium MD simulations. Figure 3 shows that D储 is much smaller near the positively charged surface compared to that near the negatively
charged silicon surface. This is consistent with the viscosity
variation results shown in Fig. 2 which indicate that the water near a positively charged silicon surface is less mobile
共more viscous兲 compared to that near a negatively charged
silicon surface.
In summary, we have observed that the electrokinetic
transport of water and ions through charged silicon
A flux is denoted positive if it is in the positive x-direction, and negative
otherwise.
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143105-3
Appl. Phys. Lett. 86, 143105 共2005兲
R. Qiao and N. R. Aluru
water and ions. Though such an asymmetric effect may not
significantly alter transport in macroscopic channels, in
nanofluidic channels, where the surface-to-volume ratio is
very high and a significant portion of the fluid is in contact
with the surface, the interfacial properties can govern the
overall transport in confined channels. As a result, to predict
the electrokinetic transport in nanofluidic systems accurately,
it is necessary to model the transport properties of the interfacial water and ions accurately.
This research was supported by the waterCAMPWS at
the University of Illinois at Urbana-Champaign.
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The two velocity profiles will be identical if the ion concentrations obtained by using the continuum theory are used in the Stokes equation.
1
FIG. 3. Diffusion coefficient of water in the direction parallels to the channel surface in the positively charged channel 共a兲 and negatively charged
channel 共b兲.
nanochannels has an asymmetric dependence on the surface
charge. Specifically, for the same magnitude of surface
charge, the water flux and ionic conductivity is much higher
in the negatively charged silicon channel compared to that in
the positively charged silicon channel. Such a behavior is
mainly caused by the transport properties of the interfacial
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