New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

3.2. INTRODUCTION TO MALDI TOF MS 27
ta =
=
v − v0
a
v − v0
m ·
E · q
=
=
v − v0
m ·
E · e · z
m v − v0
·
z E · e
(3.2.1)
The travelled distance (s) during this time, which is the distance to a zero s: Distance
position, measured from the initial position (s0) of the ion is calculated by: s0: Initial position of ion, relative to
zero position
s − s0 =
�
vdt
= v0 · t +
E · q
· t2
2 · m
After the acceleration through potential V and before the ions eventually hit
the detector ((5) in Figure 3.2.2) they travel through the drift region (with
length D, (4) in Figure 3.2.2) with kinetic energy UD and drift velocity vD
and with
we get
Ekin = 1
· m · v2
2
UD = q · V = q(E · sa) = 1
2 · m · (vD − v0) 2
This allows for the calculation of the drift velocity (vD):
vD = v0 +
� 2 · q · E · sa
and therefore we can compute the time the ions travel through the drift region:
tD = D
vD
m
�
m
= D · (
+
2 · q · E · sa
1
)
v0
�
m 1
= D · ( + )
2 · q · V v0
�
m
= D · (
z ·
�
1 1
+ ) (3.2.2)
2 · e · V v0
D: Length of drift region
U D: Energy of ion in drift region
v D: Drift velocity
Summarized, the total time-of-flight (TOF) is T OF : Time-of-flight
T OF = ta + tD
Of course, this is the assumption for a perfect world. In practice there are
(at least) two more variables: the time between the start of timing and the
acceleration of the ions (t0) and the detector response time (td). Including t0: Time of ion formation
t d: Detector response time