Malvern Mastersizer 2000, User Manual

Page: 80 / 154

Chapter 6 Understanding the views
Page 6-8 MAN 0384
„
The second term is the cross-sectional area of the particle and the final term n
i
is the number of particles of radius r
i
.
In terms of the volume of particles , the equation above becomes, for
an ensemble of particles:
The size of the particles is expressed by the diameter d and the volume terms can be
separated into a relative volume distribution v and a total concentration Cv (total
volume of particles in a unit volume of dispersant). The equation then becomes:
Substituting the above into equation (1) and solving for the concentration gives:
If d is measured in µ m and b in mm, and v is the relative concentration of the size
distribution (such that ) then:
This equation provides the concentration in parts per million (ppm). To calculate
the value as a percentage volume concentration, the final value is divided by 10,000.
In the above equation:
„
The Transmission ( T ) is a value between 0 and 1 and is measured directly by
the instrument.
„
The particle size distribution v
i
is the relative volume in size-class i with mean
diameter d
i
.
„
Q
i
- the mean extinction term for size-class i - is calculated from scattering the-
ory and is a function of the optical properties of the particle and dispersant
media.
V
i
4
3
---
π r
i
3
n
i
=
α
i
3
4
---
Q
i
V
i
r
i
-----------
∑
=
α
i
3
2
---
C
v
Q
i
V
i
d
i
-----------
∑
=
C
v
2 Ln T
( )
–
3 b
Q
i
v
i
d
i
----------
∑
------------------------ =
v
i
∑
1 =
C
v
ppm
( )
2000 Ln T
( )
–
3 b
Q
i
v
i
d
i
----------
∑
------------------------------ =
MAN0384-1.0 Mastersizer 2000.book Page 8 Tuesday, March 20, 2007 8:56 AM