Malvern Mastersizer 2000, User Manual

Page: 79 / 154

Understanding the views Chapter 6
Mastersizer 2000 Page 6-7
Fundamental concepts
To understand the meaning of the results from the Mastersizer, a number of fun-
damental concepts require explanation. These are:
„
How the concentration is calculated.
„
The results are volume-based.
„
The result is expressed in terms of equivalent spheres.
„
How the distribution parameters are derived.
Calculating the Concentration (Cv)
Beer-Lambert law
The software uses the Beer-Lambert law to calculate the concentration of the sam-
ple. This may be expressed as:
Where:
„
I is the intensity of light at a distance b in the particle field of absorbance α .
„
I
0
is the intensity of the light beam as it enters the particle field.
„
I / I
0
is the relative transmission T of the beam (measured directly by the
instrument). I
0
is the intensity of the laser beam measured at the receiver when
no sample is present and I is the intensity with sample in the beam.
Expressing the Beer-Lambert law in terms of relative transmission and re-arranging
to solve for absorbance gives:
(1)
Volume concentration
The term α contains information about the concentration and size of the particles.
From scattering theory the light attenuated by a particle i may be described by:
Where:
„
Q
i
is the efficiency of light extinction (by scattering and absorption), calculated
from Mie theory for a particle of radius r
i
.
I
I
0
---- e
α b –
=
α
1 –
b
------
Ln T
〈 〉
=
a
i
Q
i
π
r
i
2
n
i
=
MAN0384-1.0 Mastersizer 2000.book Page 7 Tuesday, March 20, 2007 8:56 AM