Solid-State Nanopores: Methods of Fabrication and Integration, and Feasibility Issues in DNA Sequencing - Nanopores: Sensing and Fundamental Biological Interactions - page 181

Fig. 8.3 SEM images. ( Left ) A mechanically punched hole, ~200 m in diameter, in a membrane

made of Apiezon-W wax. The dashed lines here indicate the direction of Laplace pressure when
the material is fluidized. ( Right ) After exposing to a laser beam (514 nm in wavelength), the hole
shrinks to a pore of 200 nm in diameter while the hole (pore) size being monitored optically. Below
200 nm, a feedback mechanism using ionic current is needed [ 11 ]. Used with permission.
Copyright Nano Letters 2006

m

Figure 8.3 shows SEM images of a 200 m plastic hole being shrunk to a 200 nm

pore. The nearly perfect circular geometry at the inner rim of the 200 nm pore is a
clear indication the driving mechanism here is surface tension. In contrast to SiO 2 in
TEM, the plastic material is expected to be uniform under laser heating.
It was noticed that the linear time-dependence of the pore diameter (or radius)
shown in Fig. 8.1 was also seen by Wu et al. [ 8 ] in their laser-induced shrinking of
plastic pores, suggesting that the linear time dependence is a universal behavior of
pore closing. Wu et al. [ 8 ] extended the surface-tension model to account for the
time dependence.
As shown in Fig. 8.3 , at any given point on the innermost surface of the pore, the
Laplace pressure is given by the Laplace-Young equation

m

1
r þ

1
r d

P ¼ g (8.2)

is the surface tension, r the radius of the pore and r d the radius of the
curvature along the pore channel direction. For clarity, the signs of the radii of
opposing curvatures are given explicitly. During pore shrinking, the thickness of the
membrane is large compared with the pore radius, so the first term in Eq. (8.2)
dominates.
To derive an equation of motion to describe pore shrinking, Wu et al. [ 8 ] showed
that, assuming the membrane is made of an incompressible fluid and it thins
uniformly as the pore closes, by balancing the viscous drag with surface tension,
one arrives at:

g

where

r ¼ 4

r
r d

1 þ : (8.3)

where is the viscosity of the fluidized material.