Advanced protein features
Chapter 6
Zetasizer Nano accessories guide
Page 6-17
Once the
molecular weight
- either measured or estimated - and the
specific
volume
are known, the
particle shape
information can be estimated by using the
Protein utilities
tool. The Shape estimate calculator takes the entered data and
then applies two equations - the
Stokes-Einstein
and the
Perrin
factor.
Stokes-Einstein equation
The measured data in a DLS experiment is the correlation curve. Embodied within
this curve is all of the information regarding the diffusion of particles within the
sample that has been measured.
By fitting the correlation curve to an exponential function, the diffusion coefficient
(
D
) can be calculated (
D
is proportional to the lifetime of the exponential decay).
With the diffusion coefficient (
D
) now known, the
Hydrodynamic diameter
can
be calculated by using a variation of the Stokes-Einstein equation.
D
H
: Hydrodynamic diameter.
k
: Boltzmann constant.
f
: Particle frictional coefficient.
: Solvent viscosity.
T
: Absolute temperature.
D
: Diffusion coefficient.
The Stokes-Einstein equation was developed using the assumption of hypothetical
hard spheres.
Perrin factor
For non-spherical particles, the
Perrin
or shape factor (
F
) can be used to estimate
particle shape.
The Perrin factor is used to calculate the prolate and oblate axial ratios for ellipsoids
with the same Perrin factor value.
The Perrin factor is defined as the ratio of the frictional coefficient for a sphere
with the same volume as the particle being measured, to the frictional coefficient
for a sphere with the same mass as the particle being measured.
The
Stokes-Einstein
equation for
the Hydrodynamic diameter is :
The
Perrin
factor (
F
) is :
D
H
kT
f
------
kT
3
D
---------------
=
=
F
f
Vol
f
Mass
-----------
6
D
Vol
6
D
Mass
-------------------------
D
Vol
D
Mass
--------------
D
H
D
Mass
--------------
=
=
=
=
Summary of Contents for Zetasizer Nano Series
Page 2: ......
Page 3: ...Zetasizer Nano accessories guide MAN0487 Issue 1 1 April 2013...
Page 12: ...Chapter 1 Introduction and accessory range Page 1 6 MAN 0487...
Page 42: ...Chapter 2 General cells and cuvettes Page 2 30 MAN 0487...
Page 98: ...Chapter 5 Microrheology Page 5 20 MAN 0487...
Page 125: ......