Malvern Mastersizer 2000, User Manual

Page: 86 / 154

Chapter 6 Understanding the views
Page 6-14 MAN 0384
In the above formulae K and X depend on the distribution being calculated as
shown in this table:
The various derived diameters are related by:
For “mono-size” distributions such as latex, the distribution mean is reported as
the geometric mean of the size class and
standard deviation , skewness and kur-
tosis are reported as zero.
The procedure used for other parameters of the distribution is to create a spline fit
to the fundamental result. Intermediate values are then read from this curve allow-
ing interpolation of percentile points which do not coincide with the measurement
size band boundaries.
Optical models
This section contrasts the Fraunhofer approximation used in some instruments
with the Mie theory which underpins Mastersizer 2000 operation.
Fraunhofer approximation
Older instruments and some existing instruments rely on the Fraunhofer approxi-
mation only. This assumes that:
„
The particle is much larger than the wavelength of light employed. ISO 13320
defines this as being greater than 40x wavelength (25µm when a He-Ne laser is
used).
„
All sizes of particle scatter with equal efficiencies.
„
The particle is opaque and transmits no light.
These assumptions are incorrect for many materials and for small particles they can
give rise to errors approaching 30%, especially when the relative refractive index of
the material and medium is close to unity, or when the particles are transparent.
Distribution K
X
i
Volume 3 V
i
Surface 2 V
i
/d
i
Length 1
V
i
/d
i
2
Number 0
V
i
/d
i
3
D m n
, [ ]
m n –
D m 0
, [ ]
m
D n 0
, [ ]
n
----------------------- =
MAN0384-1.0 Mastersizer 2000.book Page 14 Tuesday, March 20, 2007 8:56 AM