Charles University in Prague Faculty of Mathematics and Physics
Formation and loss of
complex ions in the gas-phase
by
Kseniya Dryahina
Thesis supervisor: RNDr. Patrik Španěl, Dr.
Doctoral thesis in branch F-2, Physics of Plasma and Ionised Media
Department of Electronics and Vacuum Physics
Prague 2007
Acknowledgements
There are many people to whom I wish to express my gratitude for making this thesis and the research described in it possible.
I would like to thank Mathematics and Physics Faculty of Charles University in Prague where I have started my postgraduate studies after moving to Prague from Sumy. I am especially grateful to my first supervisor Prof. Juraj Glosík for introducing me into the interesting world of laboratory research of ion processes. I also wish to thank Prof. Jana Šafránková for all her support during my graduate studies.
My thanks also go to the J. Heyrovsky Institute of Physical Chemistry. Namely, I thank my supervisor, Dr. Patrik Španěl, who more than anyone else has been responsible for making my graduate studies a positive experience. I was fortunate to be his student, he has always been available to talk to me and has provided support and guidance. I would also like to thank to the colleagues at the department of Chemical Physics: Prof. Zdeněk Herman, Dr. Ondřej Votava, Dr. Ján Žabka, Dr. Andriy Pysanenko, Ing. Jiří Kubišta, Dr. Viktoria Poterya and Dr. Michal Fárník for the various ways in which they helped me during my work at the institute. Last but not least, I would like to thank Prof. David Smith who several times visited our laboratory and gave me a chance to visit Keele University for providing the stimulation and for useful discussions.
This work was in part supported by the Grant Agency of Czech republic (project number 202/03/0827 and 203/02/0737) and by the Academy of Sciences of the Czech Republic (project number K4040110).
Finally, I would like to thank all my family members for all of their kind support, encouragement and unconditional love.
Contents
Acknowledgements ... 2
Contents ... 3
Summary... 6
1. Introduction ... 7
1.1. Aims of this work ... 7
1.2. Background... 7
1.3. Interactions between ions and molecules ... 12
1.3.1. Elastic and inelastic collisions... 12
1.3.2. Theory of collision kinetics ... 14
1.3.3. Chemical kinetics of ion molecule reactions ... 16
1.3.4. Classification of ion-molecule reactions ... 17
1.3.5. Ionisation ... 20
1.3.6. Recombination... 20
1.4. The history of flow tube experiments... 22
1.4.1. Stationary afterglow ... 22
1.4.2. Flow tubes ... 23
1.4.3. Selected Ion Flow Tube... 24
1.4.4. Recent developments ... 27
1.5. Selected Ion Flow Tube Mass Spectrometry (SIFT-MS)... 28
1.5.1. Principle of the SIFT-MS technique... 30
1.5.2. SIFT-MS Instrumentation ... 32
1.5.3. Gas chromatography / Selected Ion Flow Tube Mass Spectrometry ... 33
2. Formation of complex ions... 34
2.1. Experimental: Selected Ion Flow Tube (SIFT) instrument ... 34
2.1.1. Ion source and selected ion region ... 36
2.1.2. Precursor ions ... 36
2.1.3. Practical quadrupole theory ... 37
2.1.4. Reaction flow tube region... 40
2.1.5. Detection region ... 41
2.1.6. Channel electron multiplier ... 41
2.1.7. The SIFT instrument operated modes ... 42
2.2. Kinetic Model ... 45
2.3. Formation of complex ions involving nitroalkanes reactions ... 51
2.3.1. Water clusters/hydrates... 51
2.3.2. Proton and nitrosonium bound dimers ... 52
2.3.3. Secondary complex ions with organic ligands ... 53
2.4. SIFT-MS of an explosives marker DMNB... 55
2.4.1. Background... 55
2.4.2. Our SIFT-MS experiments ... 56
3. Disappearance of complex ions. Diffusion... 59
3.1. Introduction ... 59
3.1.1. Concepts and theory of diffusion in flow tubes... 59
3.1.2. Influence of diffusion on SIFT-MS quantification... 61
3.1.3. Previous experimental and theoretical work on mobility and diffusion of ions in gases ... 63
3.2. Theory of calculation of Ionic Diffusion Coefficients ... 65
3.2.1. Determination of ion geometries and calculation of hard-sphere collision cross section ... 65
3.2.2. Interaction potential and approximated interaction integrals ... 66
3.2.3. Calculation of reduced zero field mobilities and diffusion coefficients... 71
3.2.4. The DiffusionCalc program... 72
3.2.5. Calculation results ... 74
3.3. Experimental studies of free ionic diffusion... 76
4. Conclusions ... 79
4.1. Outcomes ... 79
4.2. Ideas and plans for further work... 80
References ... 81
Papers included in the thesis:
A1. Dryahina K., Polášek M., Španěl P. A selected ion flow tube, SIFT, study of the ion chemistry of H3O+, NO+ and O2+•
ions with several nitroalkanes in the presence of water vapour.
International Journal of Mass Spectrometry 239 (2004) 57-65.
A2. Dryahina K., Španěl P. A convenient method for calculation of ionic diffusion coefficients for accurate selected ion flow tube mass spectrometry, SIFT-MS. International Journal of Mass Spectrometry 244 (2005) 148–154.
A3. Španěl P., Dryahina K., Smith D. A general method for the calculation of absolute trace gas concentrations in air and breath from selected ion flow tube mass spectrometry data.
International Journal of Mass Spectrometry 249/250 (2006) 230-239.
A4. Kubišta J., Španěl P., Dryahina K., Workman C., Smith D. Combined use of gas chromatography and selected ion flow tube mass spectrometry for absolute trace gas quantification. Rapid Commun. Mass Spectrom. 20 (2006) 563–567.
Summary
This thesis describes the processes of formation and loss of complex ions in the Selected Ion Flow Tube (SIFT) used for the study of positive ion-molecule reactions in the gas phase and which forms a basis of the analytical method called Selected Ion Flow Tube Mass Spectrometry (SIFT-MS). SIFT allows experimental investigation of ion chemistry including kinetics and reaction mechanisms, product ion distributions and diffusion processes. SIFT-MS on the other hand can be used for accurate quantification of trace gases and vapours present namely in human breath and in other types of samples.
The first part of this thesis reviews the history of flow tube experiments and the current status of understanding of various elementary collisional processes of ions in the gas phase.
The second part of this work discusses the results of Selected Ion Flow Tube studies of the reactions of H3O+, NO+ and O2+• precursor ions with six nitroalkane compounds and with 2,3-dimethyl-2,3-dinotrobutane. The measured rate coefficients and the identified distributions of primary products together with the secondary products of their reactions with H2O are presented. Thus the kinetic data for formation of complex ions, containing up to three H2O molecules, were characterised.
The final third part of this work discusses the loss of ions, including the complex ions, from the volume of the flow tube. Theoretical and experimental studies of diffusion coefficients of ions are presented that are important for the accuracy of the Selected Ion Flow Tube Mass Spectrometry, SIFT-MS, analytical method. The theoretical calculations of diffusion coefficients are based on the (12, 4) model potential for interaction between the ions and the helium atoms, with the repulsive part approximated by the mean hard-sphere cross section and the attractive part describing the ion-induced dipole interactions. The reduced zero-field mobilities at 300K are calculated using the Viehland and Mason theory, parameterised by a simple formula as a function of the mean hard-sphere cross section, and converted to diffusion coefficients using the Einstein relation. The ions for which this method is demonstrated, include the SIFT-MS precursors H3O+, NO+, O2•+
and their hydrates, the product ions relevant to analysis of breath trace metabolites ammonia, acetaldehyde, acetone, ethanol and isoprene. The method is tested on a set of SIFT experimental data for simple ions and cluster ions.
1.1. Aims of this work 7
1. INTRODUCTION
1.1. Aims of this work
This thesis outlines the experimental research carried out in the years 2001 – 2006 by the author in the field of the elementary processes occurring in ionised gases. The main objective was to quantitatively describe the kinetics of formation and loss of the complex ions present in weakly ionised gases at low pressures and ambient temperature. Motivation for this comes mostly from the need to precisely characterise formation and loss of the ions involved in absolute quantification of concentrations of trace gases in air using the Selected Ion Flow Tube Mass Spectrometry, SIFT-MS, analytical method. Before outlining the details of this laboratory research and its results it is useful to briefly introduce the background to this work.
1.2. Background
A nice definition of the term complex ion is: “a single ion surrounded by one or more neutral molecules” [1]. Ions and molecules contained within such complex ions can be bound by chemical (covalent) or weaker (Van der Waals) bonding. In the terms of their elemental composition the complex ions can either be composed of a single type of atom or they can be composed of two or more different types of atoms or molecules. The molecules surrounding the central ion are called ligands. The number of bonds connecting the ligands to the central atom or ion is sometimes, especially when the central atom is metal, called coordination number or ligancy. The bonding holding the ligands to the central atom or ion is similar to covalent bonding between atoms but is more complex. All the ligands surrounding the central ion do not need to be the same, and some positions can be occupied by solvent molecules [2]. Because ligands remain in a fixed position around a central atom or ion, in many complexes different isomers or arrangements of the ligand groups are possible. When there are four or more ligands around a central atom then different stereoisomers, or spatial configurations, are possible.
Complex ions in the condensed phase have been studied for several reasons, including their colour. The specific colour of a complex depends on both the central atom or ion and the ligands. For example, when cobaltous chloride is dissolved in water, a pale pink solution, sometimes called invisible ink, results because of the presence of the hydrated cobaltous ion, Co(H2O)62+ [2]; this solution does not show up well on paper, but if the paper is heated to drive the water off, visibility improves because of the formation of a blue tetrachlorocobalt (II)-2 complex. Some well known examples of the biochemically important complex ions are vitamin
1.2. Background 8
B12, chlorophyll, and the heme group of hemoglobin, in which the central metal ions are cobalt, magnesium, and iron, respectively, and the ligands are complex organic molecules [2]. Also many enzymes contain a metal ion around which parts of the protein are coordinated.
However, in this work I will be exclusively concerned with the gas phase complex ions.
The most common form of the complex ions that are present in the gas phase are ionic clusters or cluster ions, as they are commonly called. The ion and neutral ligands within the clusters retain their individuality and are tied together by weak bonds. Cluster ions are typically formed when the ionised gas is cooled down or more precisely when the internal and kinetic energies of the particles are thermalised to sufficiently low temperature. Molecules and ions in the gaseous state are relatively widely separated and continually move. As the temperature in the gas drops, molecular motion slows down and the collisions between the molecules and the ions are becoming more important. When the thermal energy of the ions and molecules is low enough, the intermolecular forces of attraction bind the molecules together thus forming the cluster ions [1]. One important form of the simplest possible cluster ions are proton bound dimers where two identical neutral molecules share a proton forming a symmetrical ion [3]. The complex ions, or cluster ions, which are formed by water molecules attached as ligands to a central ion, are named hydrates. It is the research of the formation and loss of these hydrates that represents the major part of this thesis.
Just about the only natural environment where gas phase ionic complexes are present are the planetary atmospheres. From these, it is for obvious reasons the terrestrial atmosphere (ionosphere) where the composition of the complex ions is best understood. Primary ions are formed in the terrestrial atmosphere by the action of solar ultraviolet and cosmic rays and by radioactive emanations on the ambient neutral atmospheric components [4].
The photoionisation of the tenuous upper atmosphere results in the creation of the ionosphere. Because different wavelength of the ionising ultraviolet radiation are absorbed at different altitudes at varying efficiencies by gas of varying composition, “ledges” occur in the ionisation number density. These “ledges” (often called “Chapman layers” [5]) divide the ionosphere where free electrons occur into regions that are called the D-region (between about 60 and 80 km), E-region (between about 80 and 120 km), and F-regions (above about 120 km) as illustrated in Figure 1.1 a) the positive ion composition of the atmosphere as a function of altitude (km). The profiles of the total positive ion number density, ni+ (thick red curve), and of the total negative ion number density, ni– (thick blue dashed curve) are shown together with typical profiles of the number densities of the various positive ion types [5, 6]. The electron number density, ne, is equal to ni+ in the absence of negative ions (above 90 km, in electron-ion plasma). In the lower atmosphere, where negative ions do exist, ne = ni+ - ni–, the ledge
1.2. Background 9
designated as the lowest of these regions, D-region is largely due to the selective ionisation of NO by solar Lyman-α radiation [6], the photon energy being closely equal to the ionisation energy of NO molecules. Note that there are no free electrons in the stratosphere and the troposphere (where ni+ = ni– in an ion–ion plasma). Below the D-region, the electrons are almost entirely attached to form negative ions [5, 6].
The primary positive ions and the negative ions formed by electron attachment undergo a sequence of ion molecule reactions with the molecules present in the atmospheric gas forming more the more complex ions. This is called atmospheric ion chemistry and it is now well understood after decades of in situ measurements and laboratory research [6].
From the chemical kinetics viewpoint, the atmospheric ion chemistry is rather well divided into simply low-pressure (high-altitude) and high-pressure (low-altitude) regimes, the boundary being roughly 80 km. The low-pressure, high-altitude ion chemistry of the F- and E- regions is dominated by a relatively small number of bimolecular positive ion reactions occurring at temperatures between about 300 and 1500 K. Here, in the upper terrestrial atmosphere, only bimolecular ion chemistry occurs and the ion types remain simple, O+, O2+, and NO+ being dominant [6]. The high-pressure, low-altitude ion chemistry of the D-region, stratosphere, and troposphere involves both positive and negative ion reactions, as well as termolecular and bimolecular reactions. In D-region of the ionosphere, for example, the most abundant ions are H3O+, NO+ and O2+
, which are unreactive in binary collisions with the main components of air and will be used a precursor ions in all our experiments. As the pressure increases with the decreasing altitude complex ions such as H3O+·nH2O and NO+·nH2O are formed, a process which will be discussed in this work later (see Figure 1.1 b).
Hydrated hydronium ions, as the H3O+.(H2O)n are called, are inevitably present in any ionised gas containing water, and under favourable conditions, especially low temperatures and high pressure, the number of clustered water molecules, n, can be very large. The binding energy of the H2O molecule decreases with increasing n, and it is largely this that limits n to 3 or 4 in ionised gases at 300 K. The discovery some thirty years ago of the hydronium hydrates in the upper terrestrial atmosphere stimulated a great deal of interest in their formation mechanisms and their reactivity with other gases.
At the high pressures of the lower atmosphere the ions are formed by above sea by cosmic rays [4] (rate of ionisation is 2 ions/cm3/s). Above the land the additional sources of ionisation are the radioactive emanations of earth (3.5 ions/cm3s) and air (2 ions/cm3s).
Consequently, the total number of primary positive ions and electrons that are formed in 1 cm3 volume each second is typically 7.5 near the earth surface [4].
F-region
n+
1 2 3
N+
H3O+.(H2O)n
NO+ O+ H+
He+
n-
higher order clusters km
50 60 70 80 90 100 200 300 400
cm-3 106
105 104
103 102
101
H3O+
O2+
E-region
D-region O+
N+
N2+
NO+ electron-ion plasma
ion-ion plasma
O2(1Dg) N2
O2
O2+
Cosmic Rays, EUV, X-Rays
O4+
H2O O2
O hu
O2+.H2O
H3O+.H2O H2O
H2O H2O
H3O+ H2O
H3O+.OH
H2O
H3O+.2H2O H3O+.3H2O
H2O
NO+
NO
Ly a NO
N
NO+.H2O H2O NO+.2H2O H2O NO+.3H2O H2O
H2O
NO+.CO2 NO+.H2O.CO2 NO+.H2O.CO2
NO+.N2 NO+.H2O.N2 NO+.H2O.N2 CO2
H2O
CO2
CO2
H2O
CO2
H2O
CO2 CO2
N2 N2
N2
Figure 1.1 a) - The positive ion composition of the atmosphere as a function of altitude (km) [51, 6]. The profiles of the total positive ion number density, n+ (thick curve), and
of the total negative number ion density, n- (thick dashed curve) are shown together with typical profiles of the number densities of the various positive ion types. All number densities are given in cm-3.
b) - The positive ion chemistry of the lower atmosphere (the mesosphere, the stratosphere and the troposphere).
1.2. Background 11
Termolecular association reactions are then important, and these primary ions are quickly converted to very complex cluster ions of the type H+(H2O)n(bases)m with bases including NH3
and CH3CH, and a parallel negative ion chemistry develops from the primary negative ions O– and O2–
producing ions like NO3–
(H2O)n(acid)m with acids HNO3 and H2SO4 [6]. Thus the air surrounding us at this very moment is full of thousands of various complex ions.
The other naturally occurring low temperature ionised gas medium is found in the giant interstellar clouds of gas and dust. Within these so-called dense interstellar clouds [6]
association takes place forming polyatomic ions. Whilst there is so far no direct observational evidence for the presence of larger cluster ions in these media, it is possible that they may in part be responsible for so called diffuse absorption bands. However this is only a speculation and at this stage this was not seriously considered in the astrochemical literature.
In the laboratory conditions, the cluster ions are always formed when gas at pressures of the order of few tens of Pa containing vapour of water or volatile liquids is ionised at temperatures around or below 300 K. Thus formation of these cluster ions can influence plasma chemical processing of surfaces, if the residual humidity in the process gases interferes with the desired process. However, currently the most important reason to study the processes of formation and loss of the cluster ions is the need to fully understand their kinetics in order to be able to quantitatively analysed concentrations of trace gases and vapours present in air and liquid vapour samples using the Selected Ion Flow Tube Mass Spectrometry (SIFT-MS) [7, 8]
chemical ionisation mass spectrometry technique.
1.3. Interactions between ions and molecules 12
1.3. Interactions between ions and molecules
1.3.1. Elastic and inelastic collisions
Interactions or collisions between ions and molecules can be broadly divided into two classes: elastic and inelastic.
An elastic collision is one in which the total kinetic energy of a pair of colliding particles is the same before and after a collision, no energy is transferred to any form of their internal energy. But the directions and velocities of the particles change. Multiple elastic collisions lead to random motion of the particles within the gas medium. Elastic collisions are the elementary process governing the transport phenomena in gases or weakly ionised plasmas. One of the transport processes directly controlled by elastic collisions is diffusion. Free diffusion of ions in laboratory experiments is always a volume loss process. The understanding of this process is very important in experimental studies of kinetics of ionic processes in gases and plasmas. In its physical meaning diffusion represents transfer of matter in inhomogeneous gas mixture caused by thermal movement, ions diffuse down a concentration gradient until they loose their charge at the wall of an experimental vessel. The Section 3 deals in detail with ionic diffusion in flow tube experiments. The other processes mediated by elastic collisions are, for completeness sake, thermal transfer and viscosity of gases, but they are not manifested in the weakly ionised gases that are subject of these thesis.
The second class of collisions are the inelastic collisions, in which the energetic states of the colliding particles are changed and accordingly their full kinetic energy is not conserved.
Some fraction of this lost kinetic energy may be converted into the vibrational and rotational energy of the molecules. The examples of inelastic collisions are processes such as excitation, ionisation, chemical reactions, dissociation and others.
A special case are reactive collisions, in which the chemical composition or electrical charge of the colliding particles are changed. Sometimes even the number of particles after an elementary reactive collision could be different then the number of colliding particles. In any ionised gas, a variety of reactive species can be present including electrons, positive and negative ions, and neutral radicals. Several types of gas phase ionic reactions can be observed in discharge plasmas, including ion-molecule reactions, electron attachment, electron-ion recombination and ion-ion recombination. Via those reactions, new ionic and neutral species are generated.
Interest in the reactions between charged and neutral species in plasma has a long history.
Great stimulus has been brought to the subject by astrophysicists and astrochemists, because of a desire to understand the processes which result in the generation of ions and molecules in
1.3. Interactions between ions and molecules 13
planetary atmospheres and interstellar gas clouds [5, 6]. In our case the ion-neutral elementary processes take place in the flow tube experiment.
Figure 1.2 is a generalised block diagram of the major reaction types involving only charged particles which can occur in discharge plasma. Positive ions are generated by the primary process of collisional ionisation and negative ions are generated largely by non-thermal and thermal dissociative electron attachment reactions [9]. Reactions of the primary positive and negative ions with the abundant neutrals generate positive ions with smaller recombination energies and negative ions with larger electron detachment energies. Subsequent ion-neutral reactions can generate complex ions. Detachment reactions of negative ions can regenerate free electrons and a variety of neutral species. Some of these individual reaction types will be briefly discussed in this paragraph.
Gas mixture
Ionisation
Ionisation
Electron attachment
Electrons
Primary positive ions
Complex positive ions, dimers, clusters
Primary negative ions
Secondary negative ions
Complex negative ions,
clusters Negative ion - neutral reactions
Positive ion - electron recombination
Neutrals, radicals
Positive ion - negative ion recombination Positive ion - neutral reactions
Secondary positive ions
Figure 1.2 – Block diagram of the major reaction types involving only charged particles which can occur in discharge plasma
Essential parameters in establishing the production and loss rates due to individual reactions are their rate constants (in the field of gas phase ion chemistry commonly called rate coefficients) which are determined by the collision frequency, the number of collisions that an ion suffers per unit of time, and by the concentration of the target molecules. The collisional frequency can be related to a cross section and a concentration of the colliding particles and their relative velocity.
1.3. Interactions between ions and molecules 14
It is important to mention here that the cross sections for the collisions of ions with neutral gas are typically much larger than the corresponding cross sections for the mutual collisions of neutral molecules. The reasons for these large cross sections found for ion-molecule collisions were first given detailed quantitative treatment by Langevin (1905) who was interested in the mobility of ions in gaseous media. The original Langevin theory [10, 11] assumes the attractive potential between ions and non polar neutrals only originates from ion-induced dipole moment.
1.3.2. Theory of collision kinetics
It is useful to briefly highlight the main features of the classical theory, as it helps in understanding of the phenomena that will be discussed in detail later. The ion-molecule collision can be regarded as a one-dimensional motion of a particle of mass mi with initial speed v0 toward a remote particle of mass mn which is at rest. If the particles were not interacting and the movement would remain straight, the closest distance between mi and mn would be b, the impact parameter.
The long-range potential between an ion and a neutral spherical polarisable molecule changes with the fourth power of the distance, that is
(
0)
42
4 ) 2
( r
r q
V πε
− α
= , (1.1)
where q is the charge of the ion and α is the electric polarisability of the molecule,
1 1 2 12
0 =8.854⋅10− C J− m−
ε is the permittivity of vacuum. At close-range there must be a repulsive (hard core) potential that could be approximated by the twelfth power of the distance, giving a possible complete model potential for the interaction as
(
0)
42
12 2 4
)
( r
q r
r B
V πε
− α
= . (1.2)
where B is a constant.
The orbits of particles moving within such a potential are shown in Figure 1.3. Two types of orbit are possible in this potential field. A shape of the orbit is determined by two parameters, the relative initial velocity, v0, and the impact parameter, b. Now considering a situation when the impact velocity is fixed a given v0, if the impact parameter b is large enough, the orbit is hyperbolic but when b is smaller than a certain critical value b0 an inward spiralling motion takes place until some repulsive force reversed the trend. When the repulsive interaction is neglected, b0, the limiting value of b can be expressed as:
1.3. Interactions between ions and molecules 15
4 / 1
2 0 2 0
4
= Mv
b q α
, (1.3)
where M is the reduced mass of the system. Orbits for which b<b0 would pass through the origin if no repulsive core is present, whereas those orbits for which b≥b0 come no closer than r0 =b0/ 2.
Figure 1.3 – A typical family of trajectories for the inverse-fourth-power polarization potential as a function of the impact parameter b for a given relative velocity v0. The dotted trajectory is the critical one for b = b0 and the radius of the corresponding critical orbit radius is b0/ 2. In this figure only the incoming branch of each spiralling trajectory is shown. Represented from ref. [12]
In order to use this model to predict the probability of the interaction between the colliding particles it can be considered that only the spiraling orbits lead to interaction whilst the hyperbolic do not bring the particles close enough for any non-elastic interaction to occur [11].
This model is represented graphically in Figure 1.4. The critical parameter of the theory b0 is a good approximation of the collision radius.
We may therefore assume that the cross section for the reaction depends on v0 as [10]
( )
2 1/20 0 0
2
=
= M
q b v
v π π α
σ . (1.4)
The approach described here has been used initially in 1957 by Gioumousis and Stevenson [12] to calculate the so-called collisional rates of ion-molecule reactions for non-polar
1.3. Interactions between ions and molecules 16
molecules, later it was several times extended to account for molecular permanent dipole moments, and finally in 1982, Su and Chesnavich formulated very accurate and satisfactory equations for ion-polar molecule interactions [13]. This was the method that was used to determine collisional reaction rate coefficient in our experiment (Section 3.3).
Impact parameter Probability of reaction
Figure 1.4 – Notional sketch of probability of reaction versus impact parameter. Represented from ref. [11].
It is also instructive to plot the probability of reaction as a function of the impact parameter b, for several constant initial velocity values. The plot of probability may not be symmetrical about the centre of mass of the target particle [11] if the interaction of an orbiting ion with a rotating molecule depends on the sense of rotation. This is in principle the case for all particles other then spherical symmetry. The significance of such plots to our problems will be considered in section 3.2.1.
1.3.3. Chemical kinetics of ion molecule reactions
The macroscopic change of composition of ionised gas comprising a large number of individual particles can be described in the terms of chemical kinetics by a rate constant, as the rate of disappearance of a reactant (primary ion) or of appearance of product (secondary ion).
The meaning and also significantly the units of the reaction rate constant depend on so-called molecularity of reaction, defined as the number of species that must collide to produce the reaction indicated by that step. A reaction involving one molecule is called a unimolecular reaction. Reactions involving the collision of two and three species are termed bimolecular and termolecular, respectively [14].
1.3. Interactions between ions and molecules 17
The schematic mechanism of elementary reactions with different number of reactant is shown in the Figure 1.5. The general kinetic differential equations describing the rate of change of concentrations of the reactants are:
unimolecular (one-body): A→ products (reactions caused by thermal decomposition) ]
] [ [
1 A dt k
A
d =
− (1.5)
bimolecular (two-body): A+B→ products, (any two chemically-active species that collide) ]
][
] [ [ ]
[
2 A B
dt k B d dt A
d =− =
− (1.6)
termolecular (three-body): A+B+C → products (fairly rare reactions) ] ][
][
] [ [ ]
[ ]
[
3 A B C
dt k C d dt B d dt A
d =− =− =
− (1.7)
where k1, k2, k3 are reaction rate coefficient. The rate coefficient is a constant for a given temperature, pressure, and set of reactants, and relates the gas concentrations to the rate of reaction. Such rate coefficients are determined experimentally.
Units of reaction rate coefficients depend on type of reaction: for unimolecular reaction is in [s-1]; for bimolecular reaction, when concentrations are expressed in the traditional units of cm-3 k2 is in [cm3 s-1]; for termolecular reaction k3 is in [cm6 s-1].
1.3.4. Classification of ion-molecule reactions
There are many types of reactions which may occur in encounters of an ion and a molecule. They may be subjected to some degree of classification on the following lines.
Transfer of an electron. The positive ion may abstract an electron to give simple charge transfer. For example,
2
2 NO NO O
O + + → ++ (1.8)
The amount of excess energy in (1.8) is partitioned between kinetic energy of both NO+ and O2 and internal excitation of the NO+.
Cross section of charge exchange usually decrease towards low energies, except for the case represented as
+ ++AB→AB+AB
AB (1.9)
1.3. Interactions between ions and molecules 18
Which is termed “resonant charge transfer”, and usually shows the contrary behaviour, with quite large cross sections (approximately 10-100·10-16 cm2) at low energies [11].
Charge transfer may be followed by dissociation.
He N N N
He++ 2 → ++ + (1.10)
The small amount of excess energy in (1.10) appears as a kinetic energy in the product fragments.
Transfer of heavy ions. Positive ions with small proton affinities (PA) may donate a proton to species with larger PA. Species with large PA include H2O, NH3 and most organic acids, alcohols, cyanides etc, and these will therefore usually appear in their protonated forms in ionised gases [9]. Thus, the ions H3O+, HN4+
, etc. are invariably present in plasma containing H2O, NH3, etc., especially for example when the bulk gas is hydrogen since H3+
rapidly forms (via the reaction H2++H2 →H3++H) which is very effective proton donor e.g.
2 3
2
3 H O H O H
H++ → ++ . (1.11)
Such proton transfer processes are quite common and usually of high cross section (10-14 cm2) while the hydride ion transfer shows somewhat lower values. Examples of such reaction are
B A+
AB*
temporary bond
D C+ D C AB B
A++ → * → ++ (a) Illustration of a binary, two- body, reaction between reactant particles A+ and B yielding the product C and D.
AB* is an intermediate activated complex
B A+
AB*
M AB M
B
A+ + + → ++
M M
AB+
chemical bond
(b) Illustration of a ternary, three- body, reaction between reactants A+ and B forming AB* a three-way collision with another molecule, M
Figure 1.5 – The fundamental mechanisms of elementary reactions.
1.3. Interactions between ions and molecules 19
O H COH ) (CH CO
) (CH O
H3 ++ 3 2 → 3 2 ++ 2 (1.12)
The proton or hydride ion transfer may be followed by dissociation of the new ion AB
D CH CD
ABH++ → ++ + (1.13a)
ABH D
C CDH
AB++ → ++ + (1.13b)
This variation of proton transfer is called dissociative proton transfer and is one of the processes that complicate use of proton transfer in “chemical ionisation” for mass spectrometry.
Transfer of neutral groupings. The transfer of a chemical group or atom X can in principle be either from or to the ion, though cases of the former seem rare
CDX AB
CD
ABX+ + → ++ (rarely) (1.14a)
CD ABX
CDX
AB++ → ++ (1.14b)
Cross sections of this class cover the whole range of values. For examples one may mention
3 5
4
4 CH CH CH
CH++ → ++ (1.15a)
H H H
H2++ 2 → 3++ (1.15b)
Ligand switching. The cluster ions are stripped of their ligands in dissociative collisions in which the ligand group is switched out. It is now postulated that the mechanism that best explains observed tropospheric positive ion composition begins with a cosmic ray- or radioactive decay-initiated production of H+(H2O)n ions. These ions subsequently react by ligand-switching with less abundant trace neutral species to form progressively more stable atmospheric ions [15].
Complex ions can undergo ligand-switching reactions with trace compounds which have a higher gas phase basicity than complex ion core, such as reaction of H3O+(H2O)n with acetonitrile or acetone [16]:
O H O) CN(H CH
H CN CH O)
(H O
H3 + 2 n + 3 → + 3 2 n + 2 (1.16)
O H O) CO(H )
(CH H CO ) (CH O)
(H O
H3 + 2 n + 3 2 → + 3 2 2 n + 2 (1.17)
Three-body association. Positive ions which have small recombination energies and negative ions which have large detachment energies do not generally undergo binary reactions but are candidates for ternary association reactions, for example:
O H O H O
H O
H3 ++ 2 →M 3 +⋅ 2 (1.18)
1.3. Interactions between ions and molecules 20
(
2)
23 M 2 2
3O H O H O H O H O
H +⋅ + → +⋅ (1.19)
These reactions proceed via the formation of an excited intermediate complex. This complex can decompose back to the reactants or suffer a collision with a third body, M, which removes sufficient energy to stabilise the product ion [9].
1.3.5. Ionisation
Ionising collision is a primary elementary process of formation of charged atoms and molecule, the ions. Generally this term is used to describe collisions of some type of ionising particles with neutral atoms or molecules.
The mechanisms of ionisation of neutral gas can be classified into the following types:
photoionisation, electron ionisation, chemical ionisation. Photoionisation is the process where a molecule or atom, A, interacts with a photon, hν , and loses one or more electrons as a consequence.
− ++
→
+ A e
A hν (1.20)
Earlier an example was given of the upper terrestrial atmosphere where ions form largely due to the solar radiation. In the laboratories, ionised gases are often created by collisions with electrons, this is called electron ionisation, EI.
B A e
AB+ −→ ++ (1.21)
Electrons can either be prepared in a form of a beam with defined energy or can be created in the bulk of the gas by some form of electrical gaseous discharge. This is the method we used to create the precursor ions also in our experiment, where a microwave glow discharge is established in air/water vapour mixture at a pressure of about 50 Pa creating a mixture of ions including H3O+, NO+ and O2+ (see later the detailed description in Section 2.1).
The negative ions form due to the electron attachment, which can be represented by B
A AB
e
AB+ − → −*→ − + (1.22)
where a general molecule, AB, combines with a free electron, e–, to give a superexcited anion AB–* which dissociates to give molecular fragments, A– and B.
1.3.6. Recombination
Recombination is the main elementary process for the loss of charge particles.
Recombination of positive ions can occur on the walls of the experimental vessel: when most ions (>99%) colliding with a metal surface are reflected as neutral atoms, as long as their recombination energy is larger than the work function of the metal surface [10]. However,
1.3. Interactions between ions and molecules 21
recombination as an elementary process in the gas phase occurs within its volume and can be divided into two types. In an electron-ion plasma (devoid of negative ions), the major de- ionisation processes occurring within the gas volume is electron-positive ion recombination (usually dissociative):
B A e
AB+ + − → + . (1.23)
If the carriers are both ionic, when negative ions are involves, the process is called ion- ion recombination
B A B
A++ −→ + ; (1.24)
The kinetics of recombination of two oppositely charged carriers is described by their recombination coefficient, α, which is basically a rate coefficient for a binary reaction (see equation 1.6) and thus has units of cm3/s.
For a simple two-component system the recombination rate equals the loss rate of each of the two charge carriers
−
− +
+ = =− n n
dt dn dt dn
i
i α (1.25)
If we suppose that the ionised gas is quasineutral: ni+ =n− =n and that n=n0 at t =0, the simple analytical solution gives:
n t n
1 1
0
α +
= . (1.26)
In the atmosphere, most ions generated by galactic cosmic rays will be lost because of ion-ion recombination. This is the main process of loss of complex ions in the natural atmosphere.
Both experimental and theoretical studies of recombination have a long history.
However, Biondi and his colleagues using their pulsed afterglow technique have made the major contribution [17]. Now other groups have studied the recombination of different simple and complex ions using various techniques [18, 19].
1.4. The history of flow tube experiments 22
1.4. The history of flow tube experiments
The research of elementary processes occurring in plasmas and other ionised gases has a long history reaching back to the first experiment with gaseous discharge [20]. In the second half of 20th century the concerted research effort was made in this field using multiple related and continuously evolving methods. Experimental methods for study of elementary processes in plasma (ionisation, diffusion and recombination) are divided to two different groups according to the mode of movement of the plasma medium. The first group of methods is in stationary afterglow plasma and the second one is in flow tube plasma.
1.4.1. Stationary afterglow
The first low-pressure experiments on recombination were carried out by M.A. Biondi and S.C. Brown in 1949 using the stationary afterglow (SA) technique mentioned above [17].
The afterglow plasma was created in a microwave cavity resonator in order to study the decrease in mean number density of free electrons ne [21]. Later, D. Smith and colleagues [22] combined the SA technique with a movable Langmuir probe, which allowed spatially localized measurements of ne (see Figure 1.6). This led to studies of a variety of plasma phenomena including ambipolar space charge fields, diffusion cooling and, most importantly, electron-ion recombination. Currently, a similar arrangement called Advanced Integrated Stationary Afterglow (AISA) using the advanced vacuum and microwave technology and using much larger chamber dimensions in order to minimise the diffusion effects is used by J. Glosik and co- workers for studies of slow electron-ion recombination reactions [18].
Microwave power
QMS Gas Flow In
Langmuir probe
Figure 1.6 – Schematic view of the stationary afterglow instrument. For more details see ref. [18].
1.4. The history of flow tube experiments 23
The main part of the SA instrument is the discharge chamber — see Figure 1.6. This chamber has a few ports. The gas entry ports are mounted on a single flange so that there is good mixing of gases prior to entering the chamber. The largest port of the chamber is a quartz window for passing the microwave power into the chamber. Pulses of microwave power ignite the discharge. On the opposite side of the vessel there is a smaller flange that carries the quadrupole mass spectrometer. The mass spectrometer chamber must be differentially pumped.
The mass spectrometer is used for the determination of the types of ions which are presented in discharge plasma. A cylindrical Langmuir probe is mounted from the same side as the quadrupole sticks into the discharge chamber. The electron number densities and their time evolutions are obtained from the probe characteristics. Actually the current to the probe is measured as a function of the decay time at a constant probe potential. The probe potential is measured against the potential of the discharge vessel, which is grounded.
1.4.2. Flow tubes
The first application of flow tubes to the study of gas phase ion-molecule reactions was made in 1962 at the National Bureau of Standards in Boulder, Colorado by E.E. Ferguson and co-workers who developed the flowing afterglow (FA) technique [23]. The motivation was primarily to obtain a quantitative understanding of the ion chemistry of the terrestrial ionosphere, a program that was substantially achieved. The thermal energy measurements were extended in temperature from 300 K to a range of 80 K-900 K and subsequently to a centre-of-mass kinetic energy range up to approximately 2 eV with the introduction of a drift tube into the FA. This technique has been very successful in providing data required to meet the demands of detailed models of ion processes occurring in the Earth’s ionosphere [5].
Reactant
movable Langmuir probe Carrier
gas
Microwave
resonator QMS
Figure 1.7 – Simplified schematic diagram of a typical flowing afterglow Langmuir probe (FALP) instrument. For more detailes see ref. [102].
1.4. The history of flow tube experiments 24
Following the SA technique D. Smith and colleagues included the Langmuir probe into the FA, thus creating the flowing afterglow/Langmuir probe (FALP), which represented a major step forward in the study of ionic reactions at thermal energies. The inclusion of the probe for the determination of electron ne and ion ni number densities and electron temperatures Te
measurements has permitted the study of positive ion–electron recombination [18, 19], electron attachment [24, 25] and positive ion–negative ion recombination [26] in one apparatus. Hence the FALP is arguably the most versatile apparatus yet devised for the study of ionic reactions at thermal energies. Currently FALP is used by J. Glosik at Charles University in Prague for studies of the recombination of H3+ and H5+ ions [27], by J.M. Van Doren at Holy Cros and by T.M. Miller at Ionospheric Physics Division, Hanscom Air Force Base, USA [28] for studies of electron attachment and detachment.
Schematic diagram of the flowing afterglow Langmuir probe is shown in the Figure 1.7.
The main part of the FALP instrument is a cylindrical flow tube. A microwave discharge in the carrier gas, for example helium, is used to generate helium metastable atoms, He*. A few reactant gas inlets are downstream the discharge. This configuration allows to produce a desired gas mixture. The metastable atoms further downstream ionise reactant gas atoms. The quadrupole mass spectrometer at the downstream end of the tube was used to monitor the ion composition of the plasma and to ascertain that no significant impurity ions are present. The movable Langmuir probe measures the electron density as a function of distance.
A serious disadvantage involving the FA technique is that polyatomic molecules when exposed to an ionising electron beam produce a multiplicity of primary ions in the afterglow plasma. The ensuing reactions of these ions with the neutral reactant gas (and with electrons under some circumstances) make it practically impossible to identify the product ions resulting from the primary reaction. The selected ion flow tube (SIFT) developed in 1976 by N.G. Adams and D. Smith in University of Birmingham (Great Britain) [29, 5] has avoided the complication of multiple ion production by mass selecting the ion under study prior to its injection into the neutral carrier gas.
1.4.3. Selected Ion Flow Tube
The main difference of the SIFT instrument from the FALP is using the quadrupole mass filter after the ion source. Ions are produced in an external ion source from an appropriate source gas. From the mixture of ions extracted from the source the desired single type of a primary ion is selected by a quadrupole mass filter. After the selection the primary ions are injected into the flow tube. Helium is usually used as the carrier gas in flow tube studies of ion-neutral reaction rate coefficients. Therefore understanding the transport coefficients of cluster ions in helium is of
1.4. The history of flow tube experiments 25
considerable importance. Thus SIFT allows to derive the ions of interest in a remote ion source and inject mass selected ions into a flowing carrier gas in the absence of the source gas. This instrument is most suitable for determination of ion-molecule reaction rate coefficients and product ion distributions. The procedure to calculate the reaction rate coefficients from the decay of the primary ion count rate as a function of reactant gas flow rate will be described in Section 2.3.
Using the SIFT, the rate coefficients and product ions for a large number of positive and negative ion-neutral reactions have been studied. They include the bimolecular reactions of doubly-charged ions, electronically and vibrationally-excited ions, cluster ions, and termolecular reactions, some over a wide range of temperature. This has led to not only a greater understanding of the mechanisms, kinetics and energetics of these reactions, but also a clearer understanding of the chemistry of planetary atmospheres, interstellar gas clouds and laboratory plasmas such as gas lasers and technological plasmas.
A schematic diagram of the first SIFT apparatus is shown in Figure 1.8 [29]. Ion had been produced in an ion source which was remote from the flow tube, by a microwave discharge through an appropriate gas contained in a quartz tube, S1. Ions effusing from the source through the orifice, O1 (diameter 0.5 mm), were accelerated and focused into a quadrupole mass filter, QMF, by an electrostatic lens, L1. After selection in this mass filter, the ion species of interest was focused through a second orifice, O2 (diameter 0.5 mm), by a second electrostatic lens, L2, and thence into the stainless-steel flow tube. The ion current through the orifice, O2, were monitored by movable collector, C.
After injection into the flow tube (7.3 cm diameter, ca. 100 cm long) the ions were
Optical viewing port
Flow Tube T2
Reactant gas entry ports
Optical viewing port S2
Diffusion pump S1
O1 L1
QMF
L2 T1
C
O3
pico- ammeter
Diffusion pump
QMS CM
L3 Roots pump
O2
Figure 1.8 – The first Selected Ion Flow Tube, SIFT, instrument constructed in 1976 in Birmingham.
The schematic drawing is redrawn following figures from [5, 28].
1.4. The history of flow tube experiments 26
transported in the carrier gas (introduced through port T1) where they were rapidly collisionally thermalized and at a position some 20–30 cm downstream were expected to establish a radial density distribution close to a fundamental-mode Bessel-function. On their passage along the flow tube the ions pass entry ports through which neutral reactant gas can be introduced.
Reactant gas concentrations were obtained by measuring their flow rates into the flow tube using calibrated capillary tubes. The availability of entry ports at more than one axial position along the flow tube facilitates the determination of so called “end correction” to the reaction- length used in determination of the reaction time (see equation (7) in the included paper [A3]).
Multiple inlet ports also provide the opportunity for the study of consecutive reactions with different reactant gases.
At the end of the reaction zone the ions were sampled through an orifice, O3, and then focused by lens L3, mass-selected by quadrupole mass spectrometer, QMS, and detected using a channel multiplier, CM, in association with conventional pulse counting equipment.
In 1979 the inlet orifice O2 after the quadrupole mass filter (Figure 1.8) was changed into a Venturi based SIFT injector [5]. A diagram of such injector is shown in Figure 1.9. The carrier gas is introduced into an annular space around the ion inlet orifice and enters the flow tube through twelve 1-mm diameter apertures arranged in a circle with the ion beam passing through its centre. These holes direct the gas at high velocity (approaching the speed of sound) parallel to the incoming ion beam and then down the flow tube. The effect of the Venturi is to minimize backstreaming from the flow tube into the source chamber.
A modified version of the SIFT was developed by D.K. Bohme and co-workers in 1980 in York University (Canada) [30]. The apparatus has four regions, ion source, mass filter, flow tube (8.9 cm diameter, 85 cm long) and a mass analysis region located sequentially in straight line. The distinctive feature of this SIFT modification is in the injector region. In their Venturi inlet the helium carrier gas enters the flow tube through a nozzle incorporating a narrow annular gap. In 1987 the design of a tandem flowing afterglow-SIFT-drift Carrier gas
Selected
ions Carrier gas
flow
Figure 1.9 – An illustration of a cross section through a Venturi SIFT injector.
1.4. The history of flow tube experiments 27
instrument which provides high sensitivity, resolution, and chemical versatility was developed by C.H. Depuy and V.M. Bierbaum (The University of Colorado, Boulder, USA) [31]. This technique can be used to study a wide variety of ions, including isotopically labelled species, highly reactive ions, cluster ions, as well as novel species which must be synthesized by a series of gas-phase reactions.
SIFT apparatuses were also used at University College of Wales, Aberystwyth, UK (J. Glosik, late N.D. Twiddy) [32] and at The Hebrew University of Jerusalem (late C. Lifshitz) [33]. There are currently several SIFT apparatuses used in active research around the world, to list just the most well known few:
• University of Canterbury, Christchurch, New Zeland (M.J. McEwan) [34],
• University of Colorado, Boulder, USA (V.M. Bierbaum) [31],
• Ionospheric Physics Division, Hanscom Air Force Base, USA (A.A. Viggiano, J.M. Van Doren and J.F. Paulson) [35],
• University of Georgia, Athens, USA (N.G. Adams and L.M. Babcock) [36],
• York University, Toronto, Canada (D. Bohme) [37],
• Belgian Institute for Space Aeronomy, Brussels, Belgium (N. Schoon, C. Amelynck, late E. Arijs) [38],
• Keele University, Stoke-on-Trent, UK (D. Smith) [39],
• Technical University, Berlin, Germany (H. Schwarz) [40],
• J. Heyrovsky Institute, Prague, Czech Republic (K. Dryahina, P. Španěl [A1])
1.4.4. Recent developments
Traditionally the SIFT instruments have been built as large systems filling whole laboratory, sometimes with a separate adjacent pump room. They all had flow tube about 1 m in length and in order to suppress diffusion along this flow tube they had to use heavy Roots blowers (several hundred kilograms or over a tonne) with very large pumping speeds (several hundred L/s). In the year 1997 Transportable Selected Ion Flow Tube (TSIFT) instrument was constructed at Keele university with 40 cm flow tube and smaller Roots pump (100 L/s) [41] and in year 1998 a smaller laboratory SIFT has been constructed in Prague (60 cm and pumping speed 230 L/s) [42], this is the SIFT on which most of the measurements discussed in the subsequent sections were done. Currently almost all new SIFT instruments are based on the TSIFT concept and use flow tubes of about 40 cm length. It may be possible in future to reduce the size even further. Most recently in the year 2006 a new generation of compact SIFT instruments intended primarily for SIFT-MS but also usable for ion chemistry research was made available with flow tubes only 5 cm long.
