Determining the reduced ion mobility of ion species by trapped ion mobility spectrometry (TIMS)
View Patent ↗The invention provides methods and devices for determining the reduced ion mobility K o of an ion species by trapped ion mobility spectrometry wherein the reduced ion mobility K o is determined from a measured arrival time t m of the ion species and predetermined instrumental parameters by applying the inverse of a system function: K o =SYS −1 (t m ,p i ) or from multiple arrival times t m,i of the ion species measured for multiple values of an instrumental parameter.
1. A method for determining the reduced mobility K o of an ion species by trapped ion mobility spectrometry (TIMS) comprising:
providing ions of the ion species to a TIMS analyzer which comprises an electric DC field with a field gradient and a gas flow opposing a force of the electric DC field or a gas flow with a velocity gradient and an electric DC field opposing a drag force of the gas flow;
trapping the ions in the TIMS analyzer by setting the electric DC field and the gas flow;
adjusting a strength of the electric DC field and/or a velocity of the gas flow in time to release the trapped ions;
measuring an arrival time t m of the released ions at an ion detector;
determining instrumental parameters p i of the TIMS analyzer; and
determining the reduced mobility K o by inverse of a system function:
K o =SYS −1 (t m ,p i ),
wherein the instrumental parameters comprise a gas velocity v q at a plateau of the electric DC field, a gas pressure P at the plateau and a gas temperature T at the plateau,
wherein a gas pressure P in and a gas temperature T in at an entrance of the TIMS analyzer and a gas pressure P out at an exit of the TIMS analyzer are measured,
wherein the gas velocity at the plateau v g and the gas pressure P at the plateau are determined by parameter functions which depend on P in and P out , and
wherein the gas temperature T at the plateau is determined by a parameter function which depends on P in and the gas temperature T in .
2. The method according to claim 1 , wherein the inverse of the system function SYS is approximated by:
K
o
=
1
(
1
2
β
v
g
2
L
p
β
+
(
1
2
β
v
g
2
L
p
β
)
2
-
β
v
g
(
t
m
-
t
t
-
E
0
β
)
)
2
P
p
o
T
o
T
wherein t m is the measured arrival time at the ion detector, β is a scan speed, v g is the gas velocity at the plateau, L p is an effective length of the plateau, E o is a strength of the electric DC field at the plateau at a start of a scan, t t is a transfer time between an end of the plateau and the ion detector, P is the gas pressure at the plateau, T is the gas temperature at the plateau, T o is a standard temperature and P o is a standard pressure.
3. The method according to claim 1 , wherein the ion detector is one of a Faraday detector, a secondary electron multiplier, an image-current detector and a mass analyzer, said mass analyzer being one of time-of-flight with orthogonal ion injection, electrostatic ion trap, RF ion trap, ion cyclotron resonance analyzer and quadrupole mass filter.
4. The method according to claim 1 , wherein the plateau is located downstream of the field gradient and has a substantially constant electric DC field, and the gas flow has a substantially constant velocity at a beginning of the plateau.
5. The method according to claim 4 , wherein the gas flow is directed downstream towards the ion detector and the electric DC field comprises a rising electric DC field gradient opposing the drag force of the gas flow.
6. The method according to claim 5 , wherein the electric DC field strength of the plateau E p is linearly decreased in time: E p (t)=E 0 −βt, wherein E o is the electrical field strength of the plateau at the start of the scan E p (t=0) and β is the scan speed.
7. A method for determining the reduced mobility K o of an ion species by trapped ion mobility spectrometry (TIMS) comprising:
(a1) providing ions of the ion species to a TIMS analyzer which comprises an electric DC field with a field gradient and a gas flow opposing a force of the electric DC field or a gas flow with a velocity gradient and an electric DC field opposing a drag force of the gas flow;
(a2) trapping the ions in the TIMS analyzer by setting the electric DC field and the gas flow;
(a3) adjusting a strength of the electric DC field and/or a velocity of the gas flow in time to release the trapped ions;
(a4) measuring an arrival time t m of the released ions at an ion detector;
(b) repeating the steps (a1) to (a4) for at least two different values of an instrumental parameter x to obtain measured data (t m ,x) i=1 . . . n wherein n is the number of measurements; and
(c) determining the reduced mobility K o by one of:
fitting a system function t m =SYS(x,p i ,K o ) to the measured data (t m ,x) i=1 . . . n by varying the reduced mobility K o ; and
transforming measured data (t m ,x) i=1 . . . n , determining polynomial coefficients c j by fitting a polynomial function to the transformed data ( t m , x ) i=1 . . . n and determining the reduced mobility K o using the polynomial coefficients c j and inversed coefficient functions C j (K o ,p i ) of a transformed system function SYS:
t
_
m
=
S
Y
S
(
x
¯
,
p
i
,
K
o
)
=
∑
j
=
1
N
C
j
(
p
i
,
K
o
)
x
¯
j
K o =C j −1 (p i ,c j )
wherein p i are predetermined instrumental parameters which are not varied in the repeated measurements.
8. The method according to claim 7 , wherein the system function SYS is approximated by:
t
m
(
K
o
,
E
0
,
β
,
v
g
,
L
p
,
t
t
)
=
E
0
β
-
v
g
β
1
K
+
2
L
p
β
1
K
+
t
t
with
K
=
K
o
P
o
P
T
T
o
wherein t m is the arrival time at the ion detector, β is a scan speed, v g is a gas velocity at a plateau of the electric DC field, L p is an effective length of the plateau, E o is a strength of the electric DC field at the plateau at a start of a scan, t t is a transfer time between an end of the plateau and the ion detector, K is the mobility, K o is the reduced mobility, P is a gas pressure at the plateau, T is a gas temperature at the plateau, T o is a standard temperature and P o is a standard pressure.
9. The method according to claim 7 , wherein the instrumental parameter x is one of an effective length of a plateau L P of the electric DC field, a scan speed β and a gas velocity v g at the plateau.
10. The method according to claim 8 , wherein the varied instrumental parameter is one of the effective length of the plateau L P , the scan speed β and the gas velocity v g at the plateau.
11. The method according to claim 7 , wherein each one of the instrumental parameters p i is measured and/or determined from a parameter function p i =P i (q i ) wherein q i (i=1 . . . n, n≥1) is at least one measured instrumental parameter.
12. The method according to claim 7 , wherein a gas pressure P in at an entrance and/or a gas pressure P out at an exit of the TIMS analyzer are measured and at least one of the instrumental parameters is determined by a parameter function of P in , P out or both.
13. The method according to claim 12 , wherein the instrumental parameters comprise a gas velocity v g at a plateau of the electric DC field, a gas pressure P at the plateau, and a gas temperature at the plateau, and wherein the gas velocity at the plateau v g and the gas pressure P at the plateau are determined by parameter functions which depend on P in and P out and wherein a gas temperature T at the plateau is determined by a parameter function which depends on P in and a gas temperature T in measured at the entrance of the TIMS analyzer.
14. The method according to claim 7 , wherein the ion detector is one of a Faraday detector, a secondary electron multiplier, an image-current detector and a mass analyzer, said mass analyzer being one of time-of-flight with orthogonal ion injection, electrostatic ion trap, RF ion trap, ion cyclotron resonance analyzer and quadrupole mass filter.
15. The method according to claim 7 , wherein the electric DC field comprises a field gradient and a plateau, which is located downstream of the field gradient and has a substantially constant electric DC field, and the gas flow has a substantially constant velocity at the beginning of the plateau.
16. The method according to claim 15 , wherein the gas flow is directed downstream towards the ion detector and the electric DC field comprises a rising electric DC field gradient opposing the drag force of the gas flow.
17. The method according to claim 16 , wherein the electric DC field strength of the plateau E p is linearly decreased in time: E p (t)=E 0 βt, wherein E o is the electrical field strength of the plateau at the start of the scan E p (t=0) and β is the scan speed.