Photokinetics

Inhaltsverzeichnis

1. Frontmatter

2. Basics of Photokinetics

   1. Frontmatter

   2. Chapter 1. Kinetics: A Preview

      Mounir Maafi

      Abstract

      The concepts operating the evolution of reactions and the quantification of the changes occurring with reaction time make up the subject of kinetics. This general idea is valid for all reactions, including thermal and photochemical processes. By a detailed kinetic investigation, many specificities are revealed that help differentiate between the types of reactions. This overview seeks to shed light on some specificities of kinetics.

   3. Chapter 2. Some Technical Aspects of Photokinetics

      Mounir Maafi

      Abstract

      Conducting photokinetic measurements and analyses requires the general background knowledge needed for kinetics of thermal reactions, but not only that. Some specific conditions and features proper to the kinetics of photoreactions must be part of the kinetic toolkit. We will review here a few relevant aspects needed for photokinetic investigation.

   4. Chapter 3. A Mathematical Tool-Kit

      Mounir Maafi

      Abstract

      As kinetics is part of physical chemistry, it naturally involves mathematical treatments. The kinetic traces are modelled by equations and formulae that link the chemical phenomenon taking place in the reaction to observed outputs. A great deal of kinetics is based on analytical chemistry analyses, which equally requires the use of mathematical tools. A few examples of this principle have been discussed in Chap. 2. The purpose of the present chapter is to give a succinct overview of some methods, procedures and tools that might be considered as the minimum mathematical background necessary for a consistent kinetic investigation.

3. Unsettled Concepts

   1. Frontmatter

   2. Chapter 4. Kasha’s Rule and Photochemistry

      Mounir Maafi

      Abstract

      The dependence of photochemistry on excitation wavelength is not a recently observed phenomenon; nonetheless, it has, surprisingly enough, been largely ignored in the field. The reasons for this situation are not fully understood but might be related to a provisional extension of Kasha’s rule to photochemistry or perhaps to a difficulty in justifying the kind of short timescales implied in such photochemistry, which challenges the usually held view giving predominance to fast internal conversion and vibrational relaxation. Regardless of the reasons, it is still a matter of fact that a complete and satisfactory interpretation for experimentally proven wavelength-dependent photochemistry is not yet available, and the community endeavours to build a holistic understanding and a comprehensive view of the phenomenon. The present chapter compiles a non-exhaustive overview of the published data in the field, reporting on some of the most prominent features, issues and interpretations. Part of this chapter has been reused from Maafi [1] under an Open Access CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/.

   3. Chapter 5. The Photochemical Quantum Yield Formula

      Mounir Maafi

      Abstract

      The quantum yield definitions and formulae have been discussed succinctly in the previous chapters (e.g. Sect. 1.9). The importance of determining the correct value of the quantum yield of a reaction, or more precisely of a photoactive species (reactant or product), is essential in photokinetics not only as a means to evidence a possible excitation-wavelength effect (Chap. 4) but also to characterise the reactive species, to appropriately model photoreactivity and to predict the evolution of the reaction. We have seen, in the previous chapter, that several equations were proposed by a number of studies for the photochemical quantum yield. This sample is by no means exhaustive of similar formulae found in the related literature. A situation that raises a question about which equation is suitable for the purpose or whether a series of different equations can safely be used to determine the quantum yield of a species. These matters are looked into here with the aim to lift, at least partially, the confusion that might exist around the photochemical quantum yield equation.

   4. Chapter 6. Hidden Hurdles in Chemical Kinetics: Distinctability, Distinguishability, and Identifiability Concepts

      Mounir Maafi

      Abstract

      Distinguishability, identifiability, and distinctability concepts lie at the heart of kinetic analysis despite the fact that they have not been described in relation to photokinetic investigation. The three concepts represent the issue of degeneracy of the kinetic solution. This chapter gives their definitions and, more importantly, demonstrates that a kinetic analysis of any photoreaction cannot be considered complete until these three concepts are fully addressed and the issues they may pose are consistently resolved. They should naturally represent the tripod pillar of a full and consistent kinetic analysis. Not addressing any of them exposes the kinetic analysis, results, and conclusions to serious mistakes, misinterpretation, and/or invalidation.

   5. Chapter 7. The Debated Order of a Photoreaction

      Mounir Maafi

      Abstract

      Does a photoreaction have a kinetic order? Thus far, this basic question has no clear answer in the literature. Most often, photochemical reactions were treated by the classical thermal kinetic models set out for 0th-, first- or second-order kinetics. Even if a debate was shortly held about this issue to justify the relevance of thermal kinetic orders for photoreactions, the controversy was not definitely settled. Hence, today, whether a primary photoprocess has a particular kinetic order or whether it should simply obey a thermal order is not a fully resolved issue. This chapter will succinctly review the scarce literature around that opening basic question.

4. Photokinetics for Monochromatic Isosbestic Irradiation

   1. Frontmatter

   2. Chapter 8. The Reaction-Order Under Monochromatic and Isosbestic Irradiation

      Mounir Maafi

      Abstract

      The simplest light type from the viewpoint of a mathematical description of photoreactions is the monochromatic and isosbestic irradiation (at λ_isos, see Sect. 2.9). We start here from that relatively scarce irradiation condition since, if they occur, isosbestic points exist only in limited numbers for any given reaction. Isosbesticity also means that there should be more than one reactive species absorbing the incident light.

   3. Chapter 9. Degeneracy of the Kinetic Solution: Distinguishability and Identifiability in Relation to XY(mk, nΦ) Photothermal Reactions and Naphthopyran (NPY) Thermal Bleaching

      Mounir Maafi

      Abstract

      We will explore the occurrence of degeneracy in kinetics due to distinctability, distinguishability, and/or identifiability, in relation to the analyses of kinetic equations and analytical solutions that were proposed in the previous chapter. Some sub-mechanisms of the XY₂(mk, nΦ) reactions are studied hereafter for illustration of the kinetic solution degeneracy.

   4. Chapter 10. Kinetic Elucidation

      Mounir Maafi

      Abstract

      The occurrence of degeneracy of the kinetic solution, as seen in the previous chapter, imposes the development of an elucidation method by which the true kinetic solution is obtained. The elucidation method must provide a set of equations that uniquely define each of the unknown parameters of the reaction at hand. In these formulae, each parameter must be expressed as a function of experimentally accessible quantities or those previously made available by the elucidation procedure.

5. Analytical Description of Kinetics Under Non-isosbestic Irradiation

   1. Frontmatter

   2. Chapter 11. Defining the Φ-Order Kinetics

      Mounir Maafi

      Abstract

      The description of photokinetics under isosbestic irradiation (at λ_isos), detailed in Part III, has advanced our understanding of the photothermal reaction’s kinetic behaviour and characteristics but did not inform about the features of the reaction when the employed monochromatic light is non-isosbestic (at λ_n − isos). Our investigation of photokinetics under this type of irradiation light would naturally start from the basic photoreaction, the simplest that occurs in the realm of photochemical transformations, that is, the primary photoprocess, X → Y. This reaction is also considered because despite its simplicity, its kinetics has not been described in the literature at the required level of detail (i.e. when the monochromatic irradiation light is non-isosbestic). It turns out that unravelling and understanding the properties of this primary photoprocess under λ_n − isos-irradiation shapes a template that will allow setting up the fundamental bases for a larger photokinetics endeavour (as shall be seen in Chaps. 14 and 19).

   3. Chapter 12. The Hurdle

      Mounir Maafi

      Abstract

      The analytical solution achieved for the simplest photoreaction and the discovery of Φ-order kinetics, as described in the previous chapter, raise interest towards studying more photokinetic systems under non-isosbestic irradiation. The central question here is whether closed-form integrations can be achieved for other photoreversible and photothermal reactions. One can observe that, unlike what is found in thermal kinetics, answers to the latter question do not seem to have been explored in any detail within the literature of photochemistry. A way forwards to shed light on this aspect is to look at the integration of the rate-laws of reactions having a slight incrementation in complexity compared to that of the unimolecular reaction whose product is transparent.

6. Modelling Approaches for the Unsolvable Kinetics Under Monochromatic/Non-isosbestic Irradiation

   1. Frontmatter

   2. Chapter 13. The Power Series Expansion Approach

      Mounir Maafi

      Abstract

      In Chap. 12, three types of unsolvable integrals were identified for the most basic photo- and photothermal reactions. The insolvability of those integrals made the solutions of their respective rate-laws not possibly achievable by analytical means. We will attempt here to bring approximated solutions to these integrals by using the Maclaurin expansion series [1]. The approximation using first-order expansion to the primary photoreaction (with \( {\varepsilon}_Y^{\lambda_{n- isos}}=0 \)) has previously been reported in Sect. 11.6. Such a first-order expansion treatment is the only level of approximation reported in the literature [2]. The approximation in the present chapter will be performed with second-order expansion series. It will be applied to the series of unsolvable integrands laid out in the previous chapter. The second-order expansion is employed here because treatments based on third and higher expansion orders are not practically useful since they will ultimately lead to complicated integrands that do not have known antiderivatives.

   3. Chapter 14. A Semi-Empirical Method

      Mounir Maafi

      Abstract

      To palliate both the restricted absorbance range associated with using Maclaurin power series expansion and the lack of typical formulations of the integrated rate-law for the unsolved integrals, a new method based on a semi-empirical approach [1–3] is considered.

   4. Chapter 15. Established Semi-Emperical Model Equations (SEM)

      Mounir Maafi

      Abstract

      The semi-empirical method can, in principle, apply to any photo- or photothermal reaction. So far, it has produced equations for the kinetics of five photoreactions, namely, the unimolecular reaction, XY(1Φ) with \( {\varepsilon}_Y^{\lambda_{n- isos}}\ne 0 \); the reversible XY(2Φ), XY(1Φ, 1k), and XY(2Φ, 1k) reactions (where the thermal reaction-step is Y → X); and the multi-consecutive reaction involving four photoproducts and four photochemical reaction-steps, XY₄(4Φ). The order in which these reactions are listed follows, in fact, the chronology that should be adopted for such studies, adhering to a progressive incrementation of the complexity of the mechanism. This strategy is justified by the novelty of SEM, which imposes that each new reaction has to be individually checked, the details of which are presented hereafter.

   5. Chapter 16. Elucidation Methods Using SEM Equations

      Mounir Maafi

      Abstract

      The full set of information required for a complete kinetic analysis should include an elucidation method, as was reviewed for the kinetics performed under isosbestic irradiation (Chap. 10). The analysis of the reaction data by the SEM-model equations is followed by detailed elucidation methods for each individual reaction so that the cases where the identifiability issues can be solved will be identified and separated from those where they cannot. This process is discussed in this chapter.

7. Quantification by SEM Equations

   1. Frontmatter

   2. Chapter 17. Reaction Photostabilisation and Quantum Yield Variability with Wavelength

      Mounir Maafi

      Abstract

      Photokinetic investigation also expands to quantification of various effects induced on photo- and photothermal reactions by changes occurring on extrinsic experimental parameters and reaction conditions. The tools used for that purpose are available in the SEM-equations and the elucidation methods developed in Chaps. 15 and 16. These photokinetic tools are applied here to the experimental data of reactive systems. The quantification, in this chapter, aims at a dual objective: assessing extrinsic and intrinsic parameters, namely, on the one hand, the extrinsic factors causing photostabilisation and, on the other hand, the wavelength dependence of the intrinsic quantum yield parameter.

   3. Chapter 18. Development of Actinometers

      Mounir Maafi

      Abstract

      Actinometry is essential in photochemical studies because photoreactions depend on the amount of photons received by the considered reactive species. Around 70 chemical actinometers are listed in the IUPAC report [1] as standard actinometers. Most of these have known variable effective usage in experimental investigations. The most popular among these is the ferrioxalate actinometer. Limitations as well as the dynamic ranges of application of these actinometers were discussed. In general, the suitability of a photoactive chemical compound for actinometry has been linked to possessing a wavelength-invariant quantum yield. Almost none of the actinometric methodologies of the known actinometers used photokinetic data obtained through a kinetic analysis. In the present chapter, the foundations for kinactinometry are laid out for isosbestic and non-isosbestic monochromatic irradiations. The actinometric method is based on the photokinetic analyses developed in the previous chapters. The photosystems studied in Chap. 17 are experimentally tested here for kinactinometry. These represent the first examples of a series of common chemical compounds to be turned into efficient actinometers by using their respective kinetic data.

8. A General Photokinetic Model Equation for Photo-thermal Reactions Under Monochromatic and Polychromatic Lights

   1. Frontmatter

   2. Chapter 19. A General Model Equation for Photokinetics

      Mounir Maafi

      Abstract

      Our journey, so far, has led us to develop a better understanding of photokinetics through the development of various strategies. Nonetheless, the efficiency of solving photokinetics remains limited, mainly useful for relatively simple reaction mechanistic options. And among other matters, two important ideas have become self-evident. The first relates to a lack, in photokinetics, of integrated rate-laws, and the second, inferred from the first, stipulates that when the integrated rate-equations are available, they considerably simplify both data treatment and kinetic elucidation.

   3. Chapter 20. Standardisation of Photokinetic Elucidation for Photothermal Reactions

      Mounir Maafi

      Abstract

      One of the main objectives of a photokinetic investigation is to determine the absolute values of the reaction parameters. A general standard procedure for such a goal is still lacking in the literature, even though a few methods have been proposed for solving the kinetics of particular reactions, as those reviewed in Chaps. 10 and 16. In this chapter, a new method is introduced for the elucidation of the photokinetics of any photothermal reaction. It is based on the general model equations proposed in Chap. 19.

   4. Chapter 21. Revisiting Some Concepts

      Mounir Maafi

      Abstract

      A fresher look at previously discussed concepts might be useful in light of the new general equations of rates (Eq. 19.5) and concentrations (Eq. 19.10) established in Chap. 19. The target is to evaluate if these equations can help in characterising further or allow to establish general equations for the quantum yield and the photonic yield at low and high initial concentrations, irrespective of the nature (monochromatic or polychromatic) of the light used.

   5. Chapter 22. Quantification of Photothermal Reactions

      Mounir Maafi

      Abstract

      We will now explore a few ways to use the explicit general model equations (Eqs. 19.5, 19.10, and 19.13) for the quantification of some kinetic properties of photo- and photothermal reactions when exposed to either mono- or polychromatic light. In each case, an interpretation of the phenomenon is provided on the basis of the observed behaviour of the simulated data in relation to the fundamental kinetic equations.

   6. Chapter 23. Kinactinometry

      Mounir Maafi

      Abstract

      Actinometry is a measure of \( {P}_0^{\lambda_{irr}} \) (the incident light flux) at each λ_irr that enters the reactor (a slab-shaped reactor). A chemical actinometer is a standardised photothermal reactive system that is able to deliver \( {P}_0^{\lambda_{irr}} \).

9. Backmatter