On photokinetics under polychromatic light.

Since the dawn of photochemistry 150 years ago, photoreactions have been conducted under polychromatic light. However, despite the pivotal role that photokinetics should naturally play for such reactive photosystems, the literature lacks a comprehensive description of that area. Indeed, one fails to identify explicit model integrated rate laws for these reactions, a characteristic type for their kinetic behavior, or their kinetic order. In addition, there is no consensus in the community on standardized investigative tools to evaluate the reactivity of these photosystems, nor are there venues for the discussion of such photokinetic issues. The present work is a contribution addressing some of these knowledge gaps. It proposes an unprecedented general formula capable of mapping out the kinetic traces of photoreactions under polychromatic light irradiation. This article quantitatively discusses several reaction situations, including the effects of initial reactant concentration and the presence of spectator molecules. It also develops a methodology for standardizing actinometers and defines and describes both the spectral range of highest reactivity and the photonic yield. The validity of the model equation has been proven by comparing its results to both theoretical counterparts and those generated by fourth-order Runge-Kutta numerical calculations. For the first time, a confirmation of the Φ-order character of the kinetics under polychromatic light was established.

On photokinetics under monochromatic light.

The properties of photokinetics under monochromatic light have not yet been fully described in the literature. In addition, for the last 120 years or so, explicit, handy model equations that can map out the kinetic behaviour of photoreactions have been lacking. These gaps in the knowledge are addressed in the present paper. Several general features of such photokinetics were investigated, including the effects of initial reactant concentration, the presence of spectator molecules, and radiation intensity. A unique equation, standing for a pseudo-integrated rate law, capable of outlining the kinetic behaviour of any photoreaction is proposed. In addition, a method that solves for quantum yields and absorption coefficients of all species of a given photoreaction is detailed. A metric (the initial velocity) has been adopted, and its reliability for the quantification of several effects was proven by theoretical derivation, Runge-Kutta numerical integration calculations and through the model equation proposed. Overall, this study shows that, under monochromatic light, photoreaction kinetics is well described by Φ-order kinetics, which is embodied by a unifying model equation. This paper is aimed at contributing to rationalising photokinetics via reliable, easy-to-use mathematical tools.

Photokinetics of Dacarbazine and Nifedipine under polychromatic light irradiation and their application as new reliable actinometers for the ultraviolet range.

The photokinetic behaviour of drugs driven by polychromatic light is an area of pharmaceutics that has not received a lot of attention. Most often, such photokinetic data is treated by thermal kinetic models (i.e., the classical 0th-, 1st- or 2nd-order equations). Such models were not analytically derived from the rate-laws of the photodegradation reactions. Polychromatic light kinetic modelling is hence of importance, as a means to providing adequate toolkits and metrics. This paper aims at proposing two reliable drug-actinometers useful for polychromatic UVA range. The general actinometric methodology offered here is also useful for any drugs/materials obeying a primary photoprocess where both reactant and photoproduct absorb the incident light, of the [Formula: see text] type. The present method has been consolidated by the η-order kinetics. This framework further demonstrated the lamp-specificity of actinometers. Overall, Dacarbazine and Nifedipine photodegradations obeyed η-order kinetics, and stand as effective actinometers that can be recommended for the ICH Q1b photostability testing.

Φ-order spectrophotokinetic characterisation and quantification of trans-cis oxyresveratrol reactivity, photodegradation and actinometry.

A new Φ-order kinetic method was proposed in this study for the investigation of trans-cis photoisomerization reaction of Oxyresveratrol (ORVT) subjected to non-isosbestic irradiation. In ethanolic media, it has been proven that forward (ΦA→Bλirr) and reverse (ΦB→Aλirr) reaction quantum yields were dependent on the monochromatic irradiation wavelength according to sigmoid patterns over the spectral ranges of their electronic absorption (260-360nm). An 11.4- and 6.6-fold increases were recorded for ΦB→Aλirr and ΦA→Bλirr, respectively. The efficiencies of the former (ΦB→Aλirr, ranging between 2.3×10-2 and 26.3×10-2) were 33 to 60% smaller than those of the respective ΦA→Bλirr measured at the irradiation wavelengths selected. Overall, between 57 and 97% degradation of the initial trans-ORVT was observed under relatively weak light intensities, with the highest values recorded at the longest wavelengths. These findings strongly recommend protection from light in all situations of this biologically important phytomolecule that possesses therapeutic value of interest to pharmaceutical applications. The Φ-order kinetics also offered a simple way to develop a reliable actinometric method that proved ORVT to be an efficient actinometer for the dynamic range 295-360nm. The usefulness of Φ-order kinetics for the investigation and quantification of phytoproducts' photodegradation was discussed.

Modeling and Elucidation of the Kinetics of Multiple Consecutive Photoreactions AB4(4Φ) With Φ-order Kinetics. Application to the Photodegradation of Riboflavin.

New semi-empirical rate-law system of equations is proposed for the first time for consecutive photoreactions that involve up to 4 photoreaction steps, AB4(4Φ). The equation system was developed, tested, and validated against synthetic kinetic traces generated by fifth-order Runge-Kutta calculations. The model accurately fitted the kinetic traces of Riboflavin photodegradation in ethanol which decomposes via the AB2(2Φ) mechanism involving 2 consecutive photoreaction steps. A kinetic elucidation methodology useful for consecutive photoreactions was also proposed to determine all the kinetic parameters and reaction attributes defining AB2(2Φ) reactions. The quantum yields of photodegradation, determined for wavelengths in the visible region 400-480 nm, ranged from 0.005 to 0.00756 and 0.0012 to 8 10-5 for the first and second photoreaction steps, respectively. They were found to increase with wavelength in defined sigmoid functions. For this monochromatic irradiation range, riboflavin proved to be a useful actinometer. Finally, a photodegradation scale based on pseudo-rate-constant values was also proposed for drugs. This scale (including 4 groups) is thought to contribute to rationalizing photodegradation testing and might prove useful in categorizing drugs' photodegradation reactivity.

Determination of Dacarbazine Φ-Order Photokinetics, Quantum Yields, and Potential for Actinometry.

The characterization of drugs' photodegradation kinetics is more accurately achieved by means of the recently developed Φ-order kinetics than by the zero-, first-, and/or second-order classical treatments. The photodegradation of anti-cancer dacarbazine (DBZ) in ethanol has been investigated and found to obey Φ-order kinetics when subjected to continuous and monochromatic irradiation of various wavelengths. Its photochemical efficiency was proven to be wavelength dependent in the 220-350 nm range, undergoing a 50-fold increase. Albeit this variation was well defined by a sigmoid pattern, the overall photoreactivity of DBZ was proven to depend also on the contributions of reactants and experimental attributes. The usefulness of DBZ to serve as a drug-actinometer has been investigated using the mathematical framework of Φ-order kinetics. It has been shown that DBZ in ethanol can represent a good candidate for reliable actinometry in the range 270-350 nm. A detailed and easy-to-implement procedure has been proposed for DBZ actinometry. This procedure could advantageously be implemented prior to the determination of the photodegradation quantum yields. This approach might be found useful for the development of many drug actinometers as alternatives to quinine hydrochloride.

Actinometric and Φ-order photodegradation properties of anti-cancer Sunitinib.

The photodegradation reaction of Sunitinib (SUT), occurring via Z-E photoisomerisation, has been evaluated in this study using the recently developed Φ-order kinetics. In ethanol, the forward (Z → E) photoreaction of SUT was invariant with irradiation (its quantum yield, Φ(E-->Z)(λ)(irr) ≈ 0.019) in contrast to the E → Z isomerisation whose Φ(E-->Z)(λ)(irr) undergoes a 30-fold, sigmoid-shaped, increase with increasing irradiation wavelength. This situation limited usefully the extent of Z-SUT photodegradation at the photostationary state to a maximum of c.a. 30% of the initial concentration. Nevertheless, these results support a strong recommendation for a complete protection of SUT from light at all stages. Furthermore, a SUT-actinometer was developed and was proven to be useful for the 320-480 nm spectral range. The latter wavelength interval defined as well SUT photodegradation causative range. The formalism of Φ-order kinetics proves to be a useful investigative tool for drugs' photodegradation studies.

Quantitative assessment of photostability and photostabilisation of Fluvoxamine and its design for actinometry.

Despite the numerous concerns that have been raised in relation to considering 0(th), 1(st) and 2(nd)-order kinetic treatments for photodegradation characterisation and assessment of drugs, they still are employed, as they are the only tools available for these types of studies. The recently developed Φ-order kinetic models have opened new perspectives in the treatment of photoreaction kinetics and stand as the best known alternative to the classical approach. The Φ-order kinetics have been applied here to Fluvoxamine (Fluvo) with the aim of setting out a detailed and comprehensive procedure capable of rationalising photodegradation/photostability of drugs and proposing a platform for photosafety studies. Our results prove that quantum yields of drugs (0.0016 < Φ(λirr)(Fluvo) < 0.43) should a priori be considered wavelength-dependent; their photostabilisation (up to 75% for Fluvo) by means of absorption competitors can explicitly be related to a decrease of the photokinetic factor, and photoreversible drugs can be developed into efficient actinometers (as Fluvoxamine in the 260-290 nm range). A pseudo-rate-constant factor was proposed as a descriptive parameter, circumventing the limitations of overall rate-constants and allowing a comparison between kinetic data of drugs obtained under different conditions.

Ф-order kinetics of photoreversible-drug reactions.

BACKGROUND: Drug photodegradation data are usually treated by zero-, first- or second-order kinetic equations. Such treatments would lack reliability since the aforementioned equations have been originally developed for pure thermal reactions. In this respect, it has recently been shown that unimolecular photodegradations obey Ф-order kinetics (Maafi and Maafi, 2013). However, no similar information is, thus far, available for other reactions including photoreversible AB(2Ф) systems. This paper aims at filling this gap for AB(2Ф) kinetics. METHODS: Runge-Kutta numerical integration data for photoreversible reactions traces were combined with a template equation in order to derive an optimized (semi-empirical) integrated rate-law equation for AB(2Ф) reactions. The proposed model equation was test by examining its ability to fit synthetic Runge-Kutta data that have not been used for the optimization. The obtained fitting parameters are then compared to their theoretical counterparts. RESULTS: Both an integrated rate-law and an analytical equation for the overall reaction rate-constant were set for photoreversible drug reactions. The values of overall reaction rate-constant and initial velocity obtained theoretically correlated well with those obtained by fitting the kinetic traces of reactions with the derived integrated rate-law. AB(2Ф) photodegradation reactions have been proven to obey Ф-order kinetics. The equation proposed describes faithfully their kinetic behaviour in solution. The formula of the overall rate-constant involves both reagents' characteristics and experimental parameters. These equations facilitated the rationalisation and prediction of the individual effects of each reaction parameter. Specially, our results proved a self-photostabilisation with increasing initial drug-concentration and demonstrated the potential for actinometry of drugs obeying AB(2Ф) mechanism.

Montelukast photodegradation: elucidation of Ф-order kinetics, determination of quantum yields and application to actinometry.

A recently developed Ф-order semi-emperical integrated rate-law for photoreversible AB(2Ф) reactions has been successfully applied to investigate Montelukast sodium (Monte) photodegradation kinetics in ethanol. The model equations also served to propose a new stepwise kinetic elucidation method valid for any AB(2Ф) system and its application to the determination of Monte's forward (Ф(λ(irr))(A-->B)) and reverse (Ф(λ(irr))(B-->A)) quantum yields at various irradiation wavelengths. It has been found that Ф(λ(irr))(A-->B) undergoes a 15-fold increase with wavelength between 220 and 360 nm, with the spectral section 250-360 nm representing Monte effective photodegradation causative range. The reverse quantum yield values were generally between 12 and 54% lower than those recorded for Ф(λ(irr))(A-->B), with the trans-isomer (Monte) converting almost completely to its cis-counterpart at high irradiation wavelengths. Furthermore, the potential use of Monte as an actinometer has been investigated, and an actinometric method was proposed. This study demonstrated the usefulness of Monte for monochromatic light actinometry for the dynamic range 258-380 nm.

Modelling nifedipine photodegradation, photostability and actinometric properties.

BACKGROUND: The photodegradation of drugs obeying unimolecular mechanisms such as that of nifedipine (NIF) were usually characterised in the literature by zero-, first- and second-order kinetics. This approach has been met with varying success. This paper addresses this issue and proposes a novel approach for unimolecular photodegradation kinetics. The photodegradation of the cardiovascular drug nifedipine is investigated within this framework. METHODS: Experimental kinetic data of nifedipine photodegradation were obtained by continuous monochromatic irradiation and DAD analysis. Fourth-order Runge-Kutta calculated kinetic data served for the validation of the new semi-empirical integrated rate-law model proposed in this study. RESULTS: A new model equation has been developed and proposed which faithfully describes the kinetic behaviour of NIF in solution for non-isosbestic irradiations at wavelengths where both NIF and its photoproduct absorb. NIF absolute quantum yield values were determined and found to increase with irradiation wavelength according to a defined sigmoid relationship. The effects of increasing NIF or excipients' concentrations on NIF kinetics were successfully modelled and found to improve NIF photostability. The potential of NIF for actinometry has been explored and evaluated. A new reaction order (the so-called Φ-order) has been identified and specifically proposed for unimolecular photodegradation reactions. CONCLUSION: The semi-empirical and integrated rate-law models facilitated reliable kinetic studies of NIF photodegradation as an example of AB(1Φ) unimolecular reactions. It allowed filling a gap in kinetic studies of drugs since, thus far, thermal first-order or a combination of first- and zero- order kinetic equations were generally applied for drug photoreactions in the literature. Also, a new reaction order, the "Φ-order", has been evidenced and proposed as a specific alternative for photodegradation kinetics.

The potential of AB(1Φ) systems for direct actinometry. Diarylethenes as successful actinometers for the visible range.

A new actinometric procedure based on the analysis of kinetic traces of the actinometer is proposed in this study. It is suitable for thermally-stable photochromes, such as diaryethenes, which may be useful candidates for visible-range actinometry. The treatment of the traces employs a rate law which was achieved via the closed-form integration of the differential equation describing the kinetics of unimolecular photoreactions (i.e. an initial species A converted into a photoproduct B, AB(1Φ)), subjected to monochromatic irradiation. The advantage of the present method is that it may allow the development of reliable actinometers without the need for prior knowledge of some important reaction attributes, namely, the absolute values of the photoreaction quantum yield, the concentration and the molar absorption coefficient of the actinometric species at the irradiation wavelength or their variation with irradiation. This method has been tested against both kinetic data obtained from Runge-Kutta calculations and experimental traces of a diarylethene derivative. The usefulness of this derivative for actinometry has been studied in the visible (405-570 nm) spectral range. It has also been shown that the procedure can be applied to individual measurements from steady-state experiments and it is able to identify and overcome quantum yield variability with irradiation wavelength. This method is expected to help recruit AB(1Φ) photochromes for actinometry with the aim of extending their operative range over the entire visible region.

Kinetic analysis and elucidation options for AB(1k,2phi) systems. New spectrokinetic methods for photochromes.

Two new spectrokinetic methods aimed at solving the identifiability problem and leading to the true solutions of AB(1k,2phi) and AB(2phi) kinetics are proposed in this paper. The methods consider the systems under two respective assumption conditions relating to the variability of the quantum yields with irradiation wavelengths. It is shown through a detailed mathematical analysis that a set of only two traces, obtained under isosbestic and non-isosbestic irradiations of the reactive system are sufficient to reach a solution. Evaluation tests of the validity of these assumptions, and hence the usefulness of the methods, are provided and discussed. Also, the analytical expression for a coefficient (alpha) is proposed, whose value can be calculated using available experimental data, and used for the determination of whether the forward quantum yield is wavelength dependent. The kinetics of a photochromic diarylethene derivative is used as an illustration for the application of the elucidation methods.

Useful spectrokinetic methods for the investigation of photochromic and thermo-photochromic spiropyrans.

This review reports on the main results of a set of kinetic elucidation methods developed by our team over the last few years. Formalisms, procedures and examples to solve all possible AB photochromic and thermophotochromic kinetics are presented. Also, discussions of the operating conditions, the continuous irradiation experiment, the spectrokinetic methods testing with numerical integration methods, and the identifiability/distinguishability problems, are included.