Detection of charged macromolecules by means of fi eld-effect devices (FEDs): possibilities and limitations - Electrochemical Sensors, Biosensors and Their Biomedical Applications - page 199

a s

Cell radius

r ss R s

n ( r )

ssDNA

λ D

r

n 0

Interprobe
space

Ion-sensitive layer

FED

FIGURE 7.6 Cell model for the theoretical calculations of the DNA hybridization-induced ion-
concentration redistribution as well as the average concentration of cations and anions in the intermolecu-
lar spaces. Both the ssDNA and dsDNA have been modeled as negatively charged cylinders with a radius
r ss 0.5 nm and r ds 1 nm, respectively, which form a hexagonal lattice with a cell radius of R s ; the DNA
molecules are arranged normal to surface of the FED with a center-to-center average separation distance
of a s 2 R s ; n ( r ) is the ion concentration as a function of the coordinate r from the DNA axis and n 0 is the
bulk-ion concentration.

anions in the intermolecular spaces is sketched in Fig. 7.6. The ssDNA and dsDNA have
been modeled as uniformly negatively charged, infi nitely long cylinders with a radius
r ss 1 nm, respectively, which form a hexagonal lattice with a cell

radius of R s . The effect of DNA hybridization is modeled by doubling the linear charge
density of the cylinder and by increasing the cylinder radius from 0.5 nm to 1 nm. For
simplicity, the model does not take into account the charge state of the sensor surface.
For the above-described model, the average concentration of cations and anions in
the intermolecular spaces can be calculated using equations derived in [51]:

0.5 nm and r ds

( )

2

〈 nR ()

s

〉 n ζ ζ 1 (5)

0

with

1 θ

ζ

(6)

2 π bn ( R

2

a

2

)

0 s

Here, b is the distance between the nearest unit charges along the cylinder ( b

0.34 nm for the ssDNA and b 0.17 nm for the dsDNA), ( ) and ( ) are related to

cations and anions, respectively, and a r ds for the dsDNA.

The expressions (5) and (6) have been obtained using the equations for the electrostatic
potential derived in [64, 65], where a linearization of the Poisson-Boltzmann equation
near the Donnan potential in the hexagonal DNA cell was implemented.

r ss for the ssDNA and a