Detection of Gases on Biosensor Surfaces - Biosensors and Biosensor Kinetics - page 255

prepared by the spray pyrolysis method onto a glass substrate ( Shinde et al., 2007 ), (b) the
binding and dissociation of different NH 3 concentrations in air to a sol-gel derived thin film
biosensor ( Roy et al., 2005 ), (c) binding of NH 3 in air to an optical fiber-based evanescent
sensor ( Cao and Duan, 2005 ), (d) binding to a nc-Fe 3 O 4 /Si-NPA (nanocrystal magnetite/sili-
con nanoporous pillar array) humidity sensor ( Wang and Li, 2005 ), and (e) the binding and
dissociation of different methanol concentrations in ppm) to a polyimide thin layer biosensor
( Manera et al., 2006 ).

As discussed elsewhere in the different chapters in the topic, fractal analysis is just one pos-
sible method to analyze the binding and dissociation kinetics of the different analytes (gases
in this case) to the different biosensor surfaces. The distinct advantage of the method is that it
provides binding and dissociation (if applicable) rate coefficient values, and the fractal
dimension, D f or the degree of heterogeneity present on the biosensor surface. Furthermore,
the analysis attempts to relate these binding and dissociation rate coefficients to the degree of
heterogeneity present on the biosensor surface.

10.2 Theory

Havlin (1987) has reviewed and analyzed the diffusion of reactants towards fractal surfaces.
The details of the theory and the equations involved for the binding and the dissociation
phases for analyte-receptor binding are available ( Sadana, 2001 ) in the literature. The details
are not repeated here except that the equations are given to permit an easier reading. These
equations have been applied to other biosensor systems ( Ramakrishnan and Sadana, 2001;
Sadana, 2001, 2005 ). For most applications, a single- or a dual-fractal analysis is often
adequate to describe the binding and the dissociation kinetics. Peculiarities in the values of
the binding and the dissociation rate coefficients, as well as in the values of the fractal
dimensions with regard to the dilute analyte systems being analyzed will be carefully noted,
if applicable.

10.2.1 Single-Fractal Analysis

Binding Rate Coefficient

Havlin (1989) points out that the diffusion of a particle (analyte [Ag]) from a homogeneous
solution to a solid surface (e.g., receptor [Ab]-coated surface) on which it reacts to form a
product (analyte-receptor complex; Ab Ag) is given by:

t ð 3 D f , bind Þ= 2 t p ,

¼ t < t c

ð Ab Ag Þ : ð 10 : 1 Þ

t 1 = 2 , t > t c

Here D f,bind or D f (used later on in the chapter) is the fractal dimension of the surface during
the binding step. t c is the cross-over value. Havlin (1989) points out that the cross-over value