C ONCEPT OF THIS W ORK

In preparation to the present work a number of mechanistic studies of IO and OIO formation were performed focussing on the different behaviour of the system under varying conditions of overall pressure, mixing ratios and different bath gases. Both full kinetic models (trying to model IO/OIO formation and consumption in detail) as well as approximate reduced models were extensively tested. A general result of these studies was the inconsistency of results, be it cross sections or rate coefficients or general behaviour of concentrations in time. Also the dependence on different reference data proved to be problematic, in line with the expectation mentioned above.

Therefore efforts were made to develop a method which enables a more independent determination of cross sections. If possible, usage of rate coefficients and assumptions on the chemical mechanism should be avoided as far as possible and cross sections of iodine oxides should be determined in an independent experiment.

for the actual study. Such a dependence is undesirable and might even impede a solution.

Another simplification could be to modify the mixing ratios and pressures in the experiment trying to favour some reactions over others. Then a simplified mechanism could be tested to explain a reduced set of observations. Continuing iteratively it might be possible to include other absorbers and reactions trying to explain more and more of the observations. But the approximations within such a procedure must not be underestimated, especially not in a complex system.

But given the incomplete understanding of the IO/OIO chemistry as summarised before, such limited approaches, which use part of this available data are not desirable, because they lead to unclear dependencies on the used reference data rather than to independent new results. In conclusion the following requirements were postulated for the present study:

1. Notwithstanding the reliability and validity of the previously determined parameters the objective of the present study was to enable an independent determination of sought cross sections for IO, OIO and further higher oxides.

2. Modelling of chemical kinetics was to be avoided. Thereby neither previous determinations of chemical rate coefficients nor mechanistic assumptions would be needed.

3. Estimates for the complete set of cross sections – i.e. of all iodine species formed in the experiment - should be obtained simultaneously to ensure their general validity.

This would at the same time avoid usage of any previous determinations of any cross sections.

These objectives can be satisfied by a method which in the following is referred to as the method of iodine conservation.

3.4.1 Conservation of iodine atoms

Given a system of n linearly independent equations in n unknowns, it is possible to solve this system for the n unknowns. No further information about the origin of the equations or the parameters in the individual equations is needed. If the number of linearly independent

equations is larger than the number of unknowns, over-determination enables optimisation techniques to determine optimal estimates for the sought unknowns.

This concept can be transferred to the present problem, where for a certain number of absorbers the unknown absorption cross sections are to be determined. This requires a set of observations, from which a set of equations can be deduced. Now consider a flash photolysis experiment, in which the different absorbers are formed and consumed with different rates of formation and consumption. By the flash a certain number of iodine atoms is released via photolysis of I2. The released iodine atoms are subsequently distributed in varying proportions over

1. free iodine atoms,

2. I2 molecules, which are possibly formed during the course of reaction, and

3. the different reaction products, i.e. the different iodine oxides formed and consumed during the experiment.

If the number of free iodine atoms and of I2 molecules is known by measurement as a function of time, the number of iodine atoms as a whole, which are contained in the remaining set of (even unknown) iodine oxides, can be determined. This is a reasonable assumption, because cross sections for both can be determined with high accuracy and reliability in separate static experiments. No complications due to complex chemical mechanisms interfere.

If furthermore the temporal behaviour of optical density of all iodine oxides formed is known, it will be possible to state for each point in time ti a linear equation, which contains

- the optical densities of individual iodine oxides measured at time ti as coefficients, - their reciprocal cross section as unknowns and

- the number of iodine atoms contained in all iodine oxides as a whole at time ti as the constant term.

The different equations describe how iodine is distributed across the different species as a function of time. The number of available data points ti in time defines the number of equations. The requirement that equations have to be linearly independent limits the number of equations, as especially for later times the curves of decay of different absorbers tend to

become very similar. But during a large part of the experiment containing the largest variations of different absorbers it will be possible to obtain a number of linearly independent equations considerably larger than the number of unknown cross sections. Solution of the over-determined system of equations by ordinary least squares techniques produces optimal estimates for the unknown cross sections simultaneously and consistently. Conservation of the number of available iodine atoms in time being the key to the system of equations explains the name, which we choose for the method.

Important conclusions:

• The coefficients in the system of equations are the optical densities of individual iodine oxides.

Their origin does not enter into the algorithm. Even their order in time is unimportant. The only purpose of time resolved measurement in this context is to provide a sufficient number of linearly independent equations. Therefore no knowledge of the chemical system nor any chemical kinetics reference data is needed for the solution. This satisfies the second requirement to the method stated above.

• Cross sections of iodine oxides are all treated the same and are determined simultaneously and consistently. No a priori determinations are used. This satisfies requirement three.

Together these two satisfy the first requirement for an independent determination of absorption cross sections. As a clear advantage even absorbers, whose stoichiometry is not yet known, can be included in the system, if their absorption is measured.

The only crucial assumption to the method is that all relevant absorbers are covered by measurement and are included in the system of equations with their corresponding optical density and their unknown cross section. This assumption can be tested by checking the residuals obtained from the least squares solution for systematic behaviour. If any systematic behaviour were present, this would indicate that a relevant absorber is not accounted for in the approach. The method will be presented in more detail in Chapter 10.

3.4.2 Experimental Requirements

Given the desired method, the experiment had to be tailored to it. The technique used in the experiments of this laboratory study was fast time resolved molecular and resonance

absorption spectroscopy of flash photolysis experiments. The flash photolysis technique was developed by Norrish and Porter [Norrish and Porter 1949] and successfully applied in many studies of shortlived radicals and their reactions [Norrish 1967, Porter and Wright 1953]. It is well suited to produce large numbers of radicals whose decay is observed subsequent to the flash. In our experiments we photolysed mixtures of I2 and O3 in bath gases N2 and O2 with broad band Xenon flash tubes. The flash photolysis of such mixtures produces iodine atoms and oxygen atoms in the presence of I2 and O3. These components then quickly react on time scales of some hundreds of microseconds to some tens of milliseconds depending on the mixing ratios to form the highly reactive radicals IO and OIO. These in turn were equally quickly consumed by further reactions that under certain conditions finally lead to strong formation of solid deposits indicating the existence of higher iodine oxides as final products.

The method of iodine conservation firstly requires a large and simultaneous coverage of as many absorbers as possible. Secondly the short life times of transient iodine radicals requires sufficiently fast time resolved optical detection systems with suitable vibration control systems for the whole optical set-up. For time resolved recording of intensity spectra a spectrometer and a CCD camera (charge coupled device: two-dimensional silicon semiconductor) were combined. The CCD camera was modified to enable time resolved operation. It enables simultaneous multichannel recording of full spectra per time step.

Optical throughput of the system was optimised to enable the necessary short exposure times.

By applying the Beer-Lambert law directly to the two-dimensional CCD recordings obtained with and without absorbers, optical density was calculated. The result is a matrix, whose entries are optical density as a function of wavelength and time.

The resonance absorption set-up consisted of an electrodeless iodine resonance lamp, a VUV-monochromator and a photomultiplier tube. Set to 183.038 nm it can be used to measure the concentration of ground state I(²P_3/2) given a knowledge of the oscillator strength of the 183.038 nm transition. The same holds for metastable I(²P1/2). But his proved to be irrelevant under the chosen conditions of our experiments. Both optical systems were combined in a reaction vessel with two crossed optical axes. Both were synchronised to each other and to the photolysis system.

Because the resonance absorption set-up can be empirically calibrated relative to the I2 -absorption, the necessary a priori data could in principle be reduced to solely the cross section σ_I2 of I₂. For this a number of published estimates exist. Being the keystone to the chosen

approach, it was to be determined within this work. Nevertheless also the oscillator strength for iodine atoms I(²P_3/2) was determined. But at the same time empirical calibration had to be performed to account for characteristics of the set-up.

From the time resolved multichannel optical absorption measurements performed with the CCD the temporal behaviour of optical density of - at best all relevant - iodine containing species I2, IO, OIO, vibrationally excited IO, and other yet unidentified absorbers had to be extracted. A good overview of the absorptions, which were to be expected, had been obtained from the preparatory studies to this work. Likewise for iodine atoms I(²P3/2) (ground state) the time dependent concentration was to be determined using resonance absorption.

3.4.3 Data Analysis Requirements

In the same way as the experimental set-up also the methods for data analysis had to be tailored to allow an optimal analysis of the time resolved molecular absorption data. A traditional method in chemical kinetics and spectroscopy is to calculate "intelligent differences" of spectra in order to isolate contributions dominantly caused by one absorber.

Similarly traces of temporal behaviour of individual absorbers can be determined, e.g. by "on-peak minus off-"on-peak" differences, which assumes approximately constant background absorption. This method finds its analogy in linear algebra, where a system of linear equations (corresponding to a set of mixed spectra observed at different times or to a set of observed variation of absorbance in time at different wavelengths) is solved by using the subtraction method for "manually" eliminating unknowns. But as the number and the relative magnitude of unknowns in the case of spectroscopy and chemical kinetics is itself not known and background absorptions of traces of other absorbers can not be excluded, this method is always an approximate one. Also it uses only a small fraction of the available data neglecting the major remainder of information contained in the data recording.

Here the introduction of multivariate analysis techniques like Principal Components Analysis and Independent Component Analysis (PCA and ICA) as well as different least squares techniques proved to be most important improvements. Their combination allowed for the first time to extract from overlapping measurements the practically pure curves of optical density versus time of the transient short-lived absorbers IO and OIO, the precursor I₂ plus a number of unidentified products. Vibrationally excited IO was also found to behave

curves are to a high degree free of technical drift effects and of mixing with absorbances of other overlapping absorbers [Gómez Martín et al. 2004]. This is a prerequisite to the application of the method of iodine conservation. The separation method enabled extraction of pure spectra of absorbers as well. They too are to a similar degree free of drift effects and overlapping absorbances. This is a clear and important improvement with respect to the formerly published spectra, refer to the discussion above.

Having determined pure curves of optical density versus time the last step before applying the method of iodine conservation is consideration of possible effects of limited resolution on the observed curves. A time resolved detection system with broad spectral coverage allows simultaneous measurement of multiple absorbers. This enables more accurate determination of absorption spectra and absolute cross sections in terms of coverage of relevant absorbers.

The same holds for subsequent studies of chemical kinetics. But as a trade-off to broad spectral coverage, banded spectral features can sometimes be recorded with insufficient spectral resolution and/or insufficiently fine detector binning. This renders the true physical spectrum of recorded intensities changed by instrumental and spectrum specific artefacts. This effect proved to be critical for the IO(4←0) absorption band with respect to apparent magnitude of absorption as well as to linearity between observed optical density and concentration. But other absorptions are affected too. To overcome this problem, an integral approach for the treatment of intensity recordings was developed. Thereby the apparent magnitude of absorption was corrected and the linearity between optical density and absorber concentration was re-established.

Having thus assured that the curves of optical density versus time are free of drift, overlap and resolution dependent effects, the method of iodine conservation could finally be applied to them. Following the concept described in the following chapters time resolved flash photolysis recordings obtained under different chemical conditions and with different spectral coverage were analysed and for the first time produced separated spectra of the different species and a self-consistent set of absolute absorption cross sections.

The separation of overlapped spectra also enabled analysis of band strength of the IO spectrum, its continuum absorption and of vibrationally excited states. This is also presented.