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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 Downloaded 09 Apr 2005 to 130.126.121.152. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp 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. Downloaded 09 Apr 2005 to 130.126.121.152. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp 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. M. H. Friedman, Principles and Models of Biological Transport 共Springer, Berlin, 1986兲. 2 R. J. Hunter, Zeta Potential in Colloid Science 共Academic, New York, 1981兲. 3 J. Lyklema, Fundamentals of Interface and Colloid Science 共Academic, San Diego, CA, 1995兲. 4 T. C. Kuo, L. A. Sloan, J. V. Sweedler, and P. W. Bohn, Langmuir 17, 6298 共2001兲. 5 R. Qiao and N. R. Aluru, Phys. Rev. Lett. 92, 198301 共2004兲. 6 H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 共1987兲. 7 E. Lindahl, B. Hess, and D. van der Spoel, J. Mol. Model. 7, 306 共2001兲. 8 S. Koneshan, J. C. Rasaiah, R. M. Lynden-Bell, and S. H. Lee, J. Phys. Chem. B 102, 4193 共1998兲. 9 S. Nose, Mol. Phys. 52, 255 共1984兲. 10 I. Yeh and M. Berkowitz, J. Chem. Phys. 111, 3155 共1999兲. 11 R. Qiao and N. R. Aluru, J. Chem. Phys. 118, 4692 共2003兲. 12 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 Downloaded 09 Apr 2005 to 130.126.121.152. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp