Biomedical Engineering Reference
In-Depth Information
å
c M
i
i
å
i
I
( )
θ
=
K c M Kc
=
=
KcM
(8.13)
i
i
w
å
c
i
i
i
where
M
w
is the weight averaged molecular weight.
This is an ideal formula and, particularly for polymers, the classical analysis
of these experiments proceeds by plotting
I
for various concentrations and various
angles (Zimm plot).
For larger objects whose size becomes comparable with
λ
, the light can scatter
from different places of the same object. This effect decreases the scattered light
even more so for large angles and one has to take into account a structure factor
that can be analytically expressed only for a few simple geometries.
8.3.2.2 Dynamic Light Scattering (DLS) [34, 35]
Also known as photon correlation spectroscopy, DLS consists in measuring the
scattered light
dynamically
at a fixed angle. As the molecules diffuse within the
observation volume, the emitted light resulting from the scattering interferes.
The analyses of these time fluctuations are then used to deduce a diffusion coeffi-
cient. This technique is well suited to particles in the range 10 nm-1
m
m.
This analysis is performed by computing the correlation function
G
(
τ
). For
simple diffusive processes,
G
(
τ
) can be accurately modeled and is found to be ex-
ponential:
G
( )
τ
=
I t
( )
×
I t
(
+
τ
)
=
A
[1
+
B
exp( 2
- G
τ
)]
(8.14)
where G =
Dq
²,
q
= (4
π n
/
λ
) sin(
θ
/2),
n
being the refractive index of the sample and
D
the diffusion coefficient.
When several different particles characterized by different diffusion coefficients
are present, a multiexponential is used to fit the function
G
(
τ
) and access these dif-
ferent diffusion constants. From these measurements, one gets the hydrodynamic
radius
R
h
by inverting the Stockes-Einstein relationship:
kT
R
=
(8.15)
h
6
πη
D
thus the dimension measured with this technique is actually the radius of the equiva-
lent sphere that would diffuse similarly. This is a simplification that can have severe
consequences in the case of nonspherical particles: an increase in the length or in
the diameter of a rod for instance contributes very differently to its hydrodynamic
radius.
8.3.3 Biochemical Characterization
8.3.3.1 Surface Plasmon Resonance [36]
The surface plasmon resonance (SPR) technique is used to quantify the amount of
material on a surface. In biotechnology, this technique is used to detect and measure
