LSM 880
Left Tool Area and Hardware Control Tools
ZEISS
10/2014 V_01
000000-2071-464
207
D. Diffusion terms
Diffusion is driven by Brownian motion. We can distinguish translational, rotational and flow diffusion.
D.1 Rotational diffusion
In the most general form, rotation can be described as the sum of 5 exponential terms
∑
=
⋅
−
⋅
⋅
+
−
=
5
1
/
,
1
)
(
m
r
m
a
a
r
m
r
m
e
c
R
R
g
t
t
t
(8a)
with R
a
being the amplitude, c
m
the relative amplitude, r
m
the frequency factor and
t
r,m
the rotational
diffusion time.
However, there are special cases that are of more use.
In symmetric rotation, the general formula reduces to:
r
e
R
R
G
a
a
r
t
t
t
−
⋅
+
−
=
1
)
(
not normalized
(8b)
a
a
r
R
e
R
G
r
−
⋅
+
=
−
1
1
)
(
t
t
t
normalized
(8c)
with R
a
being the rotational amplitude and
t
r
the rotational diffusion time.
R
a
and
t
r
are both fit parameters.
If rotation occurs dependent from other processes, the formula used as an additive term is defined as:
r
e
R
G
a
r
t
t
t
−
⋅
=
)
(
(8d)
R
a
in this case is either a fit parameter or a fixed value and often takes the value 4/5.
In case of asymmetric rotation, the term is as follows:
)
(
1
)
(
2
,
2
1
,
1
2
1
r
r
r
r
a
a
r
e
c
e
c
R
R
G
t
t
t
t
t
⋅
−
⋅
−
⋅
+
⋅
⋅
+
−
=
not normalized
(8e)
Summary of Contents for LSM 880
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