Atomistic simulation of KCl transport in charged silicon nanochannels: Interfacial effects

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Abstract

Electroosmotic flow is an important fluid transport mechanism in nanofluidic systems. In this paper, we investigate the ion distribution and velocity profiles of KCl solution in two oppositely charged silicon nanochannels by using molecular dynamics simulations. The continuum theories, based on the Poisson–Boltzmann equation and the Navier–Stokes equations, predict that the distribution of the counter-ions, water flux and ionic conductivity in the two oppositely charged channels are the same. However, molecular dynamics simulations show very different results. First, the counter-ion distributions are substantially different in the two channels. Second, the water flux and ionic conductivity in the two channels differ by a factor of more than three. Third, the co-ion fluxes are in the opposite direction. The different counter-ion distributions in the two channels are attributed to the different size of the K+ and Cl ions and the discreteness of the water molecules, and the asymmetric dependence of the water and ion transport is attributed to the asymmetric dependence of the hydrogen bonding of water near the charged silicon surface, which influences the dynamic behavior of interfacial water significantly.

Introduction

Electroosmotic flow is widely encountered in many biological and engineering systems [1], [2]. The basic concept of electroosmotic flow can be summarized as follows: when an ionic solution is in contact with a charged surface, an electrical double layer (EDL) with a net positive or negative charge develops near the surface. If an external electrical field is applied in the direction tangential to the surface, the fluid will be dragged by the moving ions in the EDL and an electroosmotic transport is generated. The most important observables in electroosmotic flow are the ion distribution and the velocity profile in the channel. Because of its scalability and ease-of-control, electroosmotic transport is widely used in many microfluidic systems, and its application in nanofluidic systems is gaining increasing attention in the recent years [3], [4], [5], [6]. For example, Bohn and co-workers studied the effect of surface charge and ionic strength on the electroosmotic transport through nuclear-track-etched nanopore membrane [5], in which the pore diameter is on the order of 10–100 nm. More recently, nanopores as narrow as one nanometer have been fabricated by using focused ion beam drilling, and electrokinetic transport in these nanopores has been studied experimentally [7], [8].

Modeling and simulation of electroosmotic flow in nanometer wide channels can address many of the fundamental issues currently facing the design of nanofluidic systems [6]. At present, the simulation of electroosmotic flow is primarily based on the classical continuum theories, i.e., the Poisson–Boltzmann equation for the ion distribution and Navier–Stokes equations for the fluid transport [9], [10], [11]. In the Poisson–Boltzmann equation, the ions are modeled as point charges and the water is modeled as a dielectric continuum. Therefore, the molecular nature of the ion and the discreteness of the water molecules are not accounted for in the Poisson–Boltzmann equation. Likewise, in the Navier–Stokes equations, water is modeled as a continuum medium with a constant viscosity, and the effect of the surface–water interactions is accounted for as a velocity boundary condition. Therefore, the physics at the atomistic length scales, such as density oscillations near the surface, and the effect of confinement are not accounted for. Though these atomistic details may be neglected in microscale channels, they can become dominant in nanofluidic systems, where the surface-to-volume ratio is very high and the critical dimension is comparable to the size of the fluid molecules.

Atomistic simulation, and in particular Molecular Dynamics (MD) simulation, is an important tool to study fluid flow in nanometer wide channels. In an MD simulation, ion–ion, ion–wall and ion–water interactions are calculated explicitly, the trajectory of the system is integrated by using classical mechanics and various measurables, e.g., ion concentration and bulk velocity, are obtained from statistical averaging. By using proper interaction potentials between the atoms in the system, an MD simulation can provide a quantitative understanding of the various physical processes involved without relying on the many assumptions built into the continuum theory. However, MD simulations are usually computationally very expensive, and compared to the continuum simulations, they are relatively less widely employed at present. The few studies on electroosmotic flow in nanochannels using MD indicated that to describe the ion distributions accurately, one needs to account for the molecular nature of the water/ions in detail, and to model the velocity profile accurately, one needs to account for the fluid–surface interactions on the transport properties of interfacial fluids [12], [13], [14], [15], [16], [17], [18]. Though the finite size effect of ions has been accounted for in many theoretical studies on the ion distribution in the electrical double layer [19], [20], [21], [22], [23], the influence of the molecular nature of water on the ion distribution is beginning to draw a significant attention only recently [24], [25]. Similarly, even though the effect of surface–fluid interactions on the transport properties of fluid has already been realized [1], [2], a molecular level understanding of the mechanism is currently missing.

In this paper, we present a study of the electroosmotic transport and ionic conductivity of a KCl solution in two silicon nanochannels with opposite surface charge densities. Specifically, we investigated how the ion distribution is influenced by the finite size of the ion and the water molecules, and how the electroosmotic transport is influenced by the surface–fluid interactions. The rest of the paper is organized as follows: in Section 2 we present the MD simulation details; in Section 3, we discuss ion distributions in nanochannels; and in Section 4, we discuss how the dynamic properties of interfacial water, and thus the electroosmotic flow, are influenced by the surface charge. Finally, Section 5 presents the conclusions.

Section snippets

Simulation methods

Fig. 1 shows the schematic diagram of the channel system. The system consists of a slab of KCl solution (or water) sandwiched between two channel walls. Each wall is made up of four layers of silicon atoms oriented in the 111 direction. The lateral dimensions of the channel wall are 4.66 nm × 4.22 nm. The channel width, defined as the distance between the two innermost wall layers, is 3.49 nm. The silicon atoms in the innermost layer of the channel wall (layer I of the lower channel wall and

Ion distribution in nanochannels

Fig. 2 shows the concentration profiles of Cl ion and water across the channel for case 1, where the surface charge density is 0.13 C/m2. The co-ion (K+ ion) concentration is not shown as its magnitude is small and thus its contribution to the electroosmotic flow is also small. The Cl ion concentration obtained from the Poisson–Boltzmann (PB) equation (see [14] for details on the PB equation and its numerical solution) is also shown for comparison. In solving the PB equation, the dielectric

Water and ion transport

Fig. 5 compares the water velocity profiles for cases 1 and 2 as obtained from continuum and MD simulations. In the continuum simulation, we used the ion distribution obtained from the MD simulation as input to the Stokes equation:ddzμdueo(z)dz+i=1Nez˜ici(z)Eext=0where ueo(z) and ci(z) are the electroosmotic velocity and ion concentration across the channel, respectively, μ is the dynamic viscosity of the fluid, N is the number of ion species in the channel (here N=2), e is the electron charge

Conclusions

In this paper, we have presented a molecular dynamics study of the electroosmotic transport and ionic conductivity of a KCl solution in two silicon nanochannels with opposite surface charge densities. Though the classical continuum theories predict that the ion distribution and the water/ion transport are the same in both channels, MD simulations show a very different picture. The counter-ion distributions are substantially different near the channel wall, and the water flux and ionic

Acknowledgement

This research was supported by the waterCAMPWS at the University of Illinois at Urbana-Champaign.

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