Online proceedings - EDA Publishing Association

11-13
May, 2011, Aix-en-Provence, France
Measurement of Diffusivity in Nanochannels
Yu-Tze Tsai 1 1, 2*
and Gou-Jen Wang 1 Department of Mechanical Engineering
2 Graduate Institute of Biomedical Engineering
National Chung-Hsing University, Taichung 40227, Taiwan
Tel:+886-4-22840725 x 320
Email: gjwang@dragon.nchu.edu.tw
Abstract- Diffusion is the ruling manner of the migration of ions
through a nanochannel. Fick’s law and its derivatives are used as
the basis for diffusion mathematical modeling. In this study, a
simple principle for the detection of the diffusivity of
nanoparticles in a nanochannel based on the Fick’s first law is
proposed. The diffusivity in a nanochannel can be estimated by
simply plotting the natural logarithmic value of the electrolyte
conductance difference across the nanochannel versus time and
calculating its slope. Experimental results demonstrate the
feasibility of the proposed nanochannel diffusivity measuring
scheme.
I. INTRODUCTION
Most of the physiological reactions in a cell are owing to
the small changes of the surrounding environment. The small
variations of the ambient environment are carried out in terms
of the migrations of ions through the ion channels of the cell
membrane, resulting in slight molecular variations inside the
cell. The migrations of calcium ions, potassium ions, and
sodium ions are the well-known examples. The slight
molecular variations hence induce syntheses of corresponding
macromolecules such as proteins to counter the variations. The
in-vivo detection of the physiological reaction induced
molecular variations can provide a very useful tool for better
understanding of the physiological reaction. Hence the trend of
nanopore research has been pushed forward by the recent
progress in nanobiotechnology. The applications of nanopore in
biotechnology include ion-pumping [1], ion-channel biosensors
[2], DNA sequencing [3-4], polymers moving counting [5],
biosensor [6], artificial cell membrane [7, 8], and nucleic acid
detection [9-12].
Diffusion is the ruling manner of the migration of ions
through a nanochannel. Diffusion due to concentration gradient
allows particles to travel from a higher concentration region to a
lower concentration region. Diffuser, mixer, reactor, and
doping of semiconductor are the commonly seen applications in
our daily life [13-15]. Fick’s law [16] and its derivatives are
used as the basis for diffusion mathematical modeling [17-19].
If effective methods for the on-line sensing of the diffusion
coefficient and concentration gradient can be developed, it will
provide a useful tool for the modeling and investigation of the
dynamic behavior of ions in a nanochannel. Resultantly the
physiological reactions of a cell due to small variations of the
ambient environment can be further explored.
For the measurement of diffusivity in microchannel
devices, many approaches such as the on-the-flyby
-electrophoresis [20], stopped flow [21], and the E-field method
[22] have been proposed. Culbertson et al. measured the
diffusion coefficient of microfluidic devices using a static
imaging method and three dynamic methods--stopped flow,
E-field method, and length method [23]. Wu et al. [24]
observed that the etching rate of oxide in a nanochannel is much
slow than that in a microchannel. It was presumed that the cause
is the low diffusivity of the etchant molecules in a nanochannel.
If the diffusivity in a microchannel was multiplied by 6.5×10 -2
as the nanochannel diffusivity, the resulting etching rate could
match the experimental results. However, the presumption for
the nanochannel diffusivity was not further verified by a real
measurement.
Besides the ion concentration gradient across the
nanochannel, the migration of charged nanoparticles in a
nanochannel was also influenced by the electric double-layer
and the Zeta potential on the channel wall [25-27]. A feasible
method for the measurement of the diffusivity in a nannochanel
is thus desired. In this study, a simple principle for the detection
of the diffusivity of nanoparticles in a nanochannel based on the
Fick’s first law is proposed. Anodic aluminum oxide (AAO)
membranes are used to replace membranes with single
nanochannel for the measurement of the diffusivity. A
home-made electrochemical bath that can hold an AAO
membrane to separate vessels with different ion concentrations
is built. The across channel ionic concentration difference is
estimated in terms of the conductance difference across the
AAO membrane using a Wheatstone bridge circuit.
II. MATERIALS AND METHODS
Assuming ideal diffusive behavior, for a sufficiently low
diffusivity membrane and sufficiently large vessels, the
concentration profile across the membrane should become
practically linear after some initial induction period. At this
point, the flux of iodide would be constant across the membrane,
and the corresponding concentration gradient would also be
constant. This behavior is known as the constant gradient
approximation (CGA) [28], and has been used elsewhere to
analyze diffusion data. The schematic shown in Figure 1
depicts a system in the constant gradient state. The thin line
depicts the concentration of iodide throughout the system;
382