Transport of Ions, DNA Polymers, and Microtubules in the Nanofluidic Regime

DEREK STEIN, MARTIN VAN DEN HEUVEL, AND CEES DEKKER

1.1 INTRODUCTION

Lab-on-a-chip fluidic technology takes inspiration from electronic integrated circuits, from which its name is derived. Lab-on-a-chip systems aim to improve chemical and biological analysis by using chip-based micromachining techniques to shrink the size of fluid handling systems. In this way it borrows both the fabrication technology and the "smaller, cheaper, faster" paradigm from the integrated circuit industry. For silicon-based electronics, miniaturization eventually gave rise to qualitatively different transport phenomena because the device dimensions became comparable to important physical length scales, such as the de Broglie wavelength. Nanoelectronics has consequently become nearly synonymous with quantum mechanical effects. As fluidic devices are shrunk down to the nanoscale in the quest to manipulate and study samples as minute as a single molecule, it is natural to ask, "What physical phenomena should dominate in this new regime?"

As early as 1959, Richard Feynman recognized the challenges to controlling the motion of matter at the nanoscale in his famous speech, "There's plenty of room at the bottom". He drew attention to the friction, surface tension, and thermal forces that would become important at such small dimensions. In the earliest nanofluidics experiments, the pioneering groups of Austin and Craighead observed unusual transport properties of DNA. Channel dimensions comparable to the coil size of the polymers, called the radius of gyration, gave rise to strong entropic effects. Nanofluidics is in fact a regime where multiple physical length scales and phenomena become important, including the persistence length of a polymer, the Debye screening length for electrostatics, and the charge density along a channel surface.

In this chapter we review our studies of nanofluidic channels. These are the most fundamental structures in lab-on-a-chip devices, and represent the "wires" in the circuit analogy. It has therefore been natural to focus on the transport properties of nanofluidic channels, which we have investigated for small ions, DNA polymers that possess many internal degrees of freedom, and microtubules that undergo motion as part of their biological function. A recurring theme in our experiments has been the strong departure from bulk behaviour in sufficiently small channels. Different fluidic, statistical, or electrostatic effects can drive the crossover to a new regime in each case. This highlights the importance of understanding multiple interacting phenomena as new nanofluidic applications are sought.

1.2 IONIC TRANSPORT

Ions are ubiquitous in aqueous solution, and manifestations of their motion have been the subject of inquiry for centuries. In recent years the transport of ions in nanoscale systems has attracted increasing attention because of its importance to fundamental biological processes, e.g. ion channels in cellular and sub-cellular membranes, as well as man-made porous membranes for applications such as fuel cells, and solid-state nanopores for single molecule DNA analysis. The motion of ions is also coupled to the motion of the fluid by viscosity. This gives rise to electrokinetic effects such as electro-osmotic flow (EOF), which is widely applied in lab-on-a-chip technology.

In order to study the transport of ions in the nanofluidic regime in detail, we fabricated channels with highly controlled geometries that were straightforward to analyze using theoretical calculations. A typical slit-like channel is illustrated in Figure 1.1. The 4 mm long, 50 µm wide channel was lithographically patterned between two 1.5 mm x 2 mm reservoirs on a fused silica substrate. A reactive ion plasma then etched the fused silica at a rate of 30 nm/min and was timed to stop when the desired channel height, h, had been reached. The channels were sealed by bonding them to a second, flat, fused silica substrate. Bonding was achieved using either a sodium silicate adhesive layer, or by direct thermal bonding. Pre-drilled holes allowed access to the reservoirs for introducing fluids or electrical connections.

1.2.1 Electrically Driven Ion Transport

We have studied the electrically driven transport of ions in our nanofluidic channels. The ionic current was measured while a DC voltage, ΔV, was applied across a channel filled with aqueous solution of a given potassium chloride (KCl) salt concentration, n. The salt dependence of the conductance is shown in Figure 1.2 for 5 channels ranging in height from h = 70 nm to h = 1050 nm. At high salt concentrations, the channel conductances scaled with the salt concentration and the channel height, just as would be expected for a bulk KCl solution. For low salt concentrations, however, the conductance saturated at a minimum value independent of the channel height, and was orders of magnitude higher than would be expected from the bulk conductivity of the fluid.

The ionic conductance saturation results from the electrostatic influence of the charged channel walls on the ionic fluid. The silica surface is negative in solution at neutral pH, and therefore attracts positive counter-ions, while repelling negative co-ions. The thin region of fluid near the surface in which a net charge density is created is called the double layer. It is the transport of mobile counter-ions in the double layer that accounts for the extra conductance observed at low salt concentrations.

The conductance of nanofluidic channels can be understood quantitatively. It is necessary to account for all the ions, including the double layer, and properly couple their motion to that of the fluid. We have modelled the electrostatic potential in the double layer using the nonlinear Poisson-Boltzmann (PB) equation, which is the conventional mean field theory that describes the competition between electrostatic and entropic forces on the ions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)

Here kBTψ(x)/e is the electrostatic...