Radiative Cooling of Gas-Phase Ions A Tutorial Robert C. Dunbar Case Western Reserve University...
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Transcript of Radiative Cooling of Gas-Phase Ions A Tutorial Robert C. Dunbar Case Western Reserve University...
Radiative Cooling of Gas-Phase Ions
A Tutorial
Robert C. Dunbar
Case Western Reserve University
Innsbruck Cluster MeetingMarch 18, 2003
Outline
Plan:
I. Overview of molecular cooling
II. Diatomics -- A single mode
III. Polyatomics
IV. Tools for measurement, and examples
AdvertisementI wrote a review covering many of these basic principles:
R. C. Dunbar, Mass Spectrom. Rev. 1992, 11, 309
1. Cooling through thresholds: Monitor reactions2. Cooling through a threshold: Two-pulse experiment3. TRPD thermometry
4. kEmit from radiative association kinetics5. Deceptive cooling curves from various techniques
Introduction
Consider an ion, (or a population of ions,) having internal energy higher than that of the surroundings.
It may lose energy, and thus cool its internal degrees of freedom, by two means:
1. Collisions with neutrals
2. Radiative energy loss
We will focus on the theory and measurement of the second of these two possibilities.
I. Overview of cooling: Hot ion preparation
Initial preparation of hot ions can involve initial electronic excitation.
Most ions rapidly convert this electronic energy to vibrational internal energy by internal conversion.
ElectronicExcitation
Vibrationally ExcitedGround State
I. Overview -- Cooling
Radiative Cooling and Equilibration with Walls
Spontaneous Emission
Photons/sec = A1-0 = 1.25 x 10-7 v2 I1-0
I1-0 = Integrated Infrared Intensity
Induced Emission
Absorption
Equal rate constants
Photons/sec = B1-0 = B0-1
A1-0 = 3
3c
h8
~B1-0
Relations for an individual vibrational mode:
Exchange of radiation with walls is governed by three processes, with their Einstein coefficients.
Overview – Background Radiation
Black-body radiation field
1ec
h8kTh
3
3
Cooling rate constants
Many “cooling rate constants” are reported in literature. Their quantitative meaning is often obscure!
We should be careful about definitions. Two clearcut quantities can be defined:
kEmit Rate of IR photon emission
kCool Rate of relative energy loss = dt
Ed
dt
dE
E
1 intint
int
ln
In the special case of exponential cooling kCool is constant. Then
tko
CooleEE int
If the cooling is purely radiative call it kRCool
If the cooling is purely collisional, call it kCCool
Cooling example: N2H+ a
Mode Freq. (cm-1) I1-0 Calc.
(km/mol)
kEmit(1-0)
Calc. (s-1)
kEmit
Expt. (s-1)
1 3600 600 1000 670
2 800 115 9
3 2600 7 6
a P. Botschwina, Chem. Phys. Lett. 1984, 107, 535;
W. P. Kraemer, A. Kormornicki, D. A. Dixon, Chem. Phys. 1986, 105, 87.
II. Diatomics
Radiative cascade down vibrational ladder
Harmonic approximation:
Avv-1 = vA10
Exponential cooling of diatomics
For a harmonic diatomic oscillator, the rate constants work out to give exactly exponential cooling (kRCool = constant)
Uniform cooling of diatomics
Thermal energy
Arbitrary initial distribution
Uniform cooling of diatomics
The preceding picture does not take thermal spreading into account. Actually the final population distribution is a Boltzmann distribution.
Arbitrary initial distribution
III. Polyatomics
A polyatomic molecule looks like a collection of 3N-6 (or 3N-5) vibrational normal modes, each having a frequency i and each having a value of its vibrational quantum number vi
In the harmonic approximation, the normal modes are independent of each other. Absorption and emission of radiation is treated individually for each mode.
In the weakly coupled harmonic picture, they are still essentially independent, but they are coupled together sufficiently strongly so that excitation energy flows from one normal mode to another somewhat rapidly (IVR).
Polyatomics: Cooling is much slower
• Many modes are excited no higher than to v=1Remember that radiation v
• Much of the energy is stored in excitation of dark “reservoir” modes
• Much of the energy is stored in weak low-frequency modesRemember that radiation 2
Three factors combine to make the cooling of a polyatomic much slower than for a diatomic, even if the oscillator strengths of some normal mode vibrations are comparable to the oscillator strength of the diatomic.
Energy storage in polyatomics
500 cm-1
10001500
% of Energy 44% 32% 24%
A simple model molecule:
6 vibrational modes2 x 500 cm-12 x 1000 2 x 1500
Total Eint = 4000 cm-1
Tm = 1800 K
Polyatomics:Vibrational distributions
Two approaches:
1. Direct statistical count
The task is to find the probability of finding a molecule in quantum number v of mode n given that the molecule contains Eint of energy.
Pn,v =
Number of states of molecule excluding mode n and excluding energy contained in mode n
Number of states of entire molecule with full energy
2. Microcanonical temperatureDefine effective (microcanonical) internal temperature Tm
Boltzmann: Pn,v = mkTvh
ne
q
1
Polyatomic emission calculations
vn
01vnvn
1vvvnEmit vAPAPk,
,,
,
n01vn
vnRCool hvAPk ,
,
Frequencies and IR intensities can be calculated ab initio, so the cooling properties can be predicted theoretically.
Polyatomic experimental examples
kRCool Values
Ion Energy range (eV) kRCool (s-1)
C6H5Cl+ 2.5-1.2 4.0
C6H5Cl+ 0.5-0.2 0.4
C6H6+ 2.7-1.5 15
C6F6+ 2.7-2.3 25
Fe(C5H5)+ 0.7-0.24 0.28
Polyatomic experimental examples
Ion Energy range (eV) kEmit (s-1)
C3H5– 0.3 50
(CH3CN)2H+ 1.3 40
SF6– 0.5 2500
kEmit Values
IV. Techniques for measurement
A cooling experiment will usually involve
• Initial preparation of hot ions
• A variable delay time t for cooling
• An experimental probe of the amount of internal energy remaining in the ion after time t (thermometry).
Hot ion preparation
Some approaches to making hot ions
Monoenergetic Known Energy
Complexes
Electron impact ionization
No No No
PEPICO Yes Yes No Photoionization No Maybe No Photoexcitation Yes Yes Yes Charge transfer ~ Yes Yes No Exothermic ion-
molecule reaction Maybe Maybe Maybe
Probe methods
Thermometry by time-resolved photodissociation (TRPD)
TRPD branching ratio
Cooling through TRPD threshold
Cooling through ion-molecule reaction threshold(s) (Monitor reactions)
Ion-molecule reaction branching ratio
Radiative association kinetics
Calculation from IR absorption intensities (experimental or theoretical)
1. Cooling through thresholds: Monitor reactions
Monitor reactions: Reaction is endothermic unless reactant has at least v quanta of vibrational excitation.
This provides a thermometer function to observe the radiative cooling of reactant ions.
Transition kEmit (s-1)
10 110
21 204
32 330
43 400
NO+ Cooling
Beggs, Kuo, Wyttenbach, Kemper, Bowers, Int. J. Mass Spectrom. Ion Proc. 1990, 100, 397
Feinstein, Heninger, Marx, Mauclaire, Yang, Chem. Phys. Lett., 1990, 172, 89.
2. Cooling through a TRPD threshold
Two-pulse pump-probe technique
1. Excitation laser pulse at t = 0
Raises ions above the one-photon threshold
2. Delay time t
A fraction of the ions cool below the one-photon threshold
3. Probe laser pulse after time t
Dissociates ions still lying above one-photon threshold
Thermal ions
Dissociation threshold
h1
h2
h2
Inte
rnal
Ene
rgy
One-photon threshold
Two-pulse example: Cr(CO)5-
B. T. Cooper, S. W. Buckner, JASMS 1999, 10, 950.
Thermal ions
30 kJ/mol
Dissociation threshold
142 kJ/mol
h1
112 kJ/mol
h2
h2
Inte
rnal
Ene
rgy
One-photon threshold
67 kJ/mol
Two-pulse example: Cr(CO)5-
Modeling of the cascade relaxation kinetics gives a kRCool value of 15 s-1 at an internal energy level of ~ 110 kJ/mol.
Kemit is modeled to be 115 s-1.
3. TRPD thermometry: TTBB
h
2
CH
++
+ 3
Calibration Reaction
J. D. Faulk, R. C. Dunbar, J. Phys. Chem., 1991, 95, 6932.
TTBB – Cooling curve
kRCool = 1.1 s-1
Y.-P. Ho, R. C. Dunbar, J. Phys. Chem., 1993, 97, 11474.
TTBB – Pressure effect
As pressure is raised, collisional cooling competes with radiative cooling, and can also be measured.
kColl = 4 x 10-10 cm3 molec-1 s-1
Y.-P. Ho, R. C. Dunbar, J. Phys. Chem., 1993, 97, 11474.
4. kEmit from radiative association kinetics
At low pressure, the association of an ion with a neutral molecule proceeds with emission of an infrared photon according to the following kinetic scheme:
In the McMahon analysis a plot of association rate constant against pressure gives a slope and intercept which yield kr, which is the same as kEmit.
P. Kofel, T. B. McMahon, J. Phys. Chem. 1988, 92, 6174
5. Deceptive cooling curves
This cooling curve for Cr(CO)5- was made by plotting a reaction branching ratio as
a function of time. It looks like a simple exponential with kRCool = 3.3 s-1. But other measurements and modeling show that the true cooling curve is severely non-exponential, and kRCool varies from 15 s-1 at t=0 to ~3 s-1 at t=0.4. This branching ratio thermometer is severely non-linear, and was not calibrated.
B. T. Cooper, S. W. Buckner, JASMS 1999, 10, 950.