Malvern Mastersizer 3000 User Manual

Chapter 5 Viewing measurement results
Page 5-14 MAN 0474
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 .
 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  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
b–
=

1–
b
------
Ln T=
a
i
Q
i
r
i
2
n
i
=

Malvern Mastersizer 3000 Specifications

General

Measurement principle	Laser diffraction
Blue laser wavelength	470 nm
Sample dispersion options	Wet and dry dispersion
Data acquisition rate	10 kHz
Particle size range	0.01 to 3500 microns
Laser type	He-Ne and solid state
Accuracy	Better than 1%
Repeatability	Better than 0.5%
Technology	Mie and Fraunhofer theories
Sample dispersion units	Hydro MV, Hydro LV, Aero S
Optical model	Mie theory
Power requirements	100-240 V, 50/60 Hz
Detector arrangement	Log-spaced array