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

Article abstract of DOI:10.1016/j.saa.2017.06.067

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 (Φ_A?→?B^λ_irr) and reverse (Φ_B?→?A^λ_irr) reaction quantum yields were dependent on the monochromatic irradiation wavelength according to sigmoid patterns over the spectral ranges of their electronic absorption (260–360?nm). An 11.4- and 6.6-fold increases were recorded for Φ_B?→?A^λ_irr and Φ_A?→?B^λ_irr, respectively. The efficiencies of the former (Φ_B?→?A^λ_irr, ranging between 2.3?×?10^??2 and 26.3?×?10^??2) were 33 to 60% smaller than those of the respective Φ_A?→?B^λ_irr 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 295–360?nm. The usefulness of Φ-order kinetics for the investigation and quantification of phytoproducts’ photodegradation was discussed.

Full text of DOI:10.1016/j.saa.2017.06.067

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular
Spectroscopy
journal homepage: www.elsevier.com/locate/saa
Φ-order spectrophotokinetic characterisation and quantification of
trans-cis oxyresveratrol reactivity, photodegradation and actinometry
⁎
Mounir Maafi , Mohammed Ahmed Al-Qarni
Leicester School of Pharmacy, De Montfort University, The Gateway, Leicester LE1 9BH, UK
a r t i c l e i n f o
a b s t r a c t
Article history:
A new Φ-order kinetic method was proposed in this study for the investigation of trans-cis photoisomerization
Received 1 March 2017
Received in revised form 13 June 2017
Accepted 30 June 2017
reaction of Oxyresveratrol (ORVT) subjected to non-isosbestic irradiation. In ethanolic media, it has been proven
that forward (ΦAλ→B) and reverse (ΦBλ→A) reaction quantum yields were dependent on the monochromatic irradi-
ation wavelength according to sigmoid patterns over the spectral ranges of their electronic absorption (260–
irr
irr
Available online 02 July 2017
360 nm). An 11.4- and 6.6-fold increases were recorded for ΦλB→A and ΦAλ→B, respectively. The efficiencies of the
irr
irr
former (ΦλB→A, ranging between 2.3 × 10−2 and 26.3 × 10−2) were 33 to 60% smaller than those of the respective
irr
Keywords:
ΦλA→B measured at the irradiation wavelengths selected. Overall, between 57 and 97% degradation of the initial
irr
Oxyresveratrol
Photodegradation
Φ-order kinetic
Quantum yield
Actinometry
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 impor-
tant phytomolecule that possesses therapeutic value of interest to pharmaceutical applications. The Φ-order kinet-
ics also offered a simple way to develop a reliable actinometric method that proved ORVT to be an efficient
actinometer for the dynamic range 295–360 nm. The usefulness of Φ-order kinetics for the investigation and quan-
tification of phytoproducts' photodegradation was discussed.
© 2017 Elsevier B.V. All rights reserved.
1. Introduction
The description of ORVT's photokinetics has not yet been made avail-
able in the literature. It has however been quantitatively established that
Oxyresveratrol (ORVT) belongs to the stilbenoid group of
phytomolecules that is widely found in plants and fruits such as peanuts,
raspberries, blueberries, tea, and highly concentrated in grapes and wine
[1]. The anti-oxidative properties have long been known for
hydroxystilbenoids [2] as well as for ORVT [3]. The latter molecule has
been attributed a number of other biological effects including but not
limited to being antiviral [4], hepatoprotective [5], anti-tumor [6,7] and
anti-herpes [8]. In addition, ORVT has neuroprotective ability for trauma
cells and cerebral ischemia [9,10]. Such an action was evidenced by the
significant inhibition of neuronal death [9], which is thought to proceed
via a mechanism of action similar to a tyrosinase inhibition [10]. From
this point of view, ORVT possesses a medicinal potential and a therapeu-
tic value that might be exploited in medicine or as a food complement
[11,12].
The stilbenoid group is known to undergo trans/cis isomerization
which can be achieved by either heat or UV-light irradiation. Despite,
the t-isomeric form of stilbenoid is thermodynamically more stable
than the c-form, the thermal isomerization in both directions requires,
in general, relatively high temperatures as part of the properties of
stilbenoids documented in an earlier comprehensive review [13].
it undergoes a trans-cis photoisomerization in organic media [13]
(Scheme 1). The photochemical data available on close analogue mole-
cules, indicated that stilbenoids obeyed a relatively fast (28 ps) singlet-
state dominated trans-cis photoisomerization in organic solvents [13].
In terms of photoreactivity in solution, t-resveratrol (t-RVT) [14,15], for
instance, phototransforms faster into the c-form when the whole range
of UV-VIS is used compared to a UV-irradiation at 254 nm. Nonetheless,
t-RVT also reacts to irradiation with visible light (400–600 nm) yet in a
slower transformation despite the fact that its electronic absorption
spectrum does not exceed 360 nm [14].
In terms of kinetic data analysis, first-order kinetics was the basic tool
used to calculate photoreactions' rate-constants and quantum yields of
stilbenoids such as resveratrols [13,14]. Interestingly, it has been report-
ed that the t-RVT rate-constant increased with irradiation wavelength
[14].
It is however important to underline that the description of photore-
actions by thermal kinetics (such as first-order kinetics) is not adequate
since the latter models ignore the contribution of light to the mathemat-
ical equations [16–18]. In this respect, the Φ-order kinetics is a much
better tool to rationalise the behaviour and to reliably quantify photore-
actions' parameters such as quantum yields.
In this study we present, for the first time, a new method to analyse
the photokinetic data relative to trans-cis photoisomerization driven by
⁎
Corresponding author.
E-mail address: mmaafi@dmu.ac.uk (M. Maafi).
http://dx.doi.org/10.1016/j.saa.2017.06.067
1386-1425/© 2017 Elsevier B.V. All rights reserved.

M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
65
Scheme 1. Reversible photoisomerization of t-ORVT (A) and c-ORVT (B).
non-isosbestic UV or visible irradiation and its application to ORVT kinet-
ic analysis. The kinetic tool explores ORVT photodegradation percentages
and its actinometric usefulness.
3. Result and Discussion
3.1. The Mathematical Background
3.1.1. General Equations
2. Materials and Methods
Φ–Order main equation model for the photoreversible transforma-
tion of compound (A) and photoproduct (B), which are driven by differ-
ent forward (ΦλA→B) and reverse (ΦBλ→A) quantum yields (Scheme 1), is
irr
irr
2.1. Material
given by Eq. (1) for a non-isosbestic and continuous irradiation at wave-
λirr
length λirr where species A and B absorb differently (ελA ≠εB ) the inci-
irr
Oxyresveratrol, (E)-2,3′,4,5′-Stilbenetetrol, 2,3′,4,5′-Tetrahydroxy-
trans-stilbene,
4-[(1E)-2-(3,5-Dihydroxyphenyl)
ethenyl]-1,3-
dent light (Pλ ) [19].
irr
benzenediol (ORVT) was purchased from Sigma Aldrich. Spectrophoto-
metric grade ethanol was purchased from Fisher Scientific.
irr =λobs
irr =λobs
Aλtot
ð0Þ−Aλtot
ðpssÞ
irr =λirr
l
λobs
irr =λobs
Aλtot
irr =λobs
ðtÞ ¼ Aλtot
ðpssÞ þ
ꢀ
l
λirr
irr=λirr
Aλtot
ð0Þ−Aλtot
ðpssÞ
h
i
"
!
#
ꢀ
ꢁ
l
λ
=λ
λ
=λ
λ
irr irr
irr irr
irr
λ
Atot
ð0Þ−Atot
ðpssÞ ꢀlλ
2.2. Monochromatic Continuous Irradiation
irr
A⇋Bꢀt
obs
ꢀ log 1 þ 10
−1 ꢀ e−k
An Ushio1000 W xenon arc-lamp was used as a light source. The
lamp was connected to a monochromator model 101. The excitation
beam was guided by an optical fibre to impinge from the top of the
quartz cuvette holding the sample. In this configuration, the excitation
and the monitoring light beams were perpendicular to each other.
ð1Þ
In Eq. (1), lλ and lλ are independent (non-equal) quantities corre-
irr
obs
sponding respectively to the optical path lengths of the irradiation and
monitoring beams inside the sample. Aλtot obs is the measured total ab-
irr/λ
sorbance of the medium along lλ and at the observation wavelength
obs
(λobs), at the initial time (t = 0), at time t and at the photostationary
state, pss (t = ∞). Log is the base 10 logarithm.
2.3. The In Situ Monitoring Systems
The exponential factor, representing the overall rate-constant
kλAi⇋rr B that can be obtained by fitting the kinetic trace to Eq. (1),
has the following analytical expression (Eq. (2)),
A diode array spectrophotometer (Agilent 8453) was equipped with
a 1-cm cuvette sample holder and a Peltier system model Agilent 8453
for temperature control. The sample was kept at 22 °C, stirred continu-
ously during the irradiation, and completely sheltered from the ambient
light.
ꢂ
ꢃ
kλA⇋irrB
¼
ΦA→B ꢀ ελA þ ΦB→A ꢀ ελB
ꢀ lλ ꢀ Pλ ꢀ Fλ ðpssÞ
λirr
λirr
irr
irr
irr
irr
irr
¼ βλ ꢀ Pλ
ð2Þ
irr
irr
A radiant power/energy meter model 70260 was used to quantify the
radiant power of the monochromatic incident excitation beams.
with βλ represents the pseudo-rate constant and the factor
Fλ (pss)irirs the time-independent photokinetic factor, given by
irr
2.4. HPLC Measurements
λ
tot
=λ
irr irr
ðpssÞꢀlλirr =lλobs
1−10−ðA
Þ
Fλ ðpssÞ ¼
ð3Þ
irr
irr =λirr
Aλtot
ðpssÞ ꢀ lλ =lλ
The HPLC system consisted of reversed-phase Waters symmetry (C18
150 mm × 3.9 mm 5 μm) column equipped with a PerkinElmer Series
200 pump, UV/Vis detector, vacuum degasser and a Perkin Elmer type
Chromatography Interface 600 series Link linked to a computer system.
The operating conditions included a mobile phase consisting of 85%
water and 15% acetonitrile, a flow rate of 1.5 mL/min and a detection at
328 nm. The retention times of the species were 10.3 and 11.3 min, the
calibration equation was PA=5×109×C−59575 with r2 = 0.996, and
irr
obs
3.1.2. The Elucidation Method
In order to avoid degeneracy of the kinetic solution [17,20,21], an elu-
cidation method capable of delivering the true set of values for the reac-
tion unknowns which for a photoreversible reaction such as that
observed for ORVT photoisomerization, are the forward (ΦλA→B) and
irr
a linearity range within the limits 4.7 × 10−4–4.75 × 10−6
.
the reverse (ΦλB→A) quantum yields, in addition to the absorption coeffi-
irr
cient of the photoproduct (ελB of c-ORVT). We propose for the first time
irr
in this work a method exclusively based on non-isosbestic irradiation.
This elucidation method can be realised in three steps. (i) The first
step involves the determination of the concentration (CA(pss)) of the ini-
tial species (A or t-ORVT in Scheme 1) at the pss by monitoring its
photodegradation reaction performed under a non-isosbestic irradiation
at a given λirr, using HPLC. The concentration of photoproduct at the
photostationary state (CB(pss)) is worked out from the mass balance
equation as, CB(pss)=C(0)−CA(pss). (ii) The second step involves
2.5. Oxyresveratrol Solutions
A 4.09 × 10−3 M stock solution of ORVT in ethanol was diluted to pre-
pare fresh analytical solutions (ca. 2 × 10−5 M) for analysis. The flasks
were protected from light by aluminium foil wrapping and were kept
in the fridge.
All experiments were conducted at least in triplicates.

66
M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
reconstructing the photoproduct's absorption spectrum (ελB ) using Eq.
irr
(4).
irr =λobs
Aλtot
ðpssÞ−CAðpssÞ ꢀ ελirr ꢀ lλ
εBλ
¼
ð4Þ
obs
A
irr
ðCð0Þ−CAðpssÞÞ ꢀ lλ
obs
In the final step, (iii) the absolute values for ΦλA→B and ΦBλ→A at any
irr
irr
irradiation wavelength can be derived from Eqs. (5a) and (5b).
irr =λobs
υ0λ
ΦλA→irr B
¼
¼
ð5aÞ
ð5bÞ
ꢂ
ꢃ
ελB −εA ꢀ lλ ꢀεAλ ꢀ lλ ꢀ Pλ ꢀ Fλ ð0Þ ꢀ C0
λirr
irr
irr
obs
irr
irr
irr
"
#
kλA⇋irr B
1
εBλ
ΦλB→irr A
−ΦA→B ꢀ ελA
λirr
irr
irr
lλ ꢀ Pλ ꢀ Fλ ðpssÞ
irr
irr
irr
Fig. 2. Photokinetic traces of ORVT in ethanol solution (2 × 10−5 M) at λirr = 260, 280, 310,
328, 350 and 370 nm and λobs = 328 nm. The circles represent the experimental data
whereas the lines represent the fitting traces using Eq. (1).
Eq. (5a) is obtained by rearranging the equation (Eq. (6a)) of the re-
action initial velocity (υλ0 obs), whose numerical value can be worked
irr/λ
out from Eq. (6b) that has been derived by differentiation of Eq. (1).
3.1.3. The Degradation Percentage
The knowledge of the quantum yields and the absorption coeffi-
cients of both species at any irradiation wavelength, as determined in
the previous section, allows the determination of the thermodynamic
ꢂ
ꢃ
irr=λobs
υ0λ
¼
ελB −εA ꢀ lλ ꢀΦA→B ꢀ ελA ꢀ lλ ꢀ Pλ ꢀ Fλ ð0Þ
λirr
λirr
irr
irr
obs
irr
irr
irr
ꢀ CAð0Þ
ð6aÞ
λirr
equilibrium constant (K⇋ ) of the reaction for the selected irradiation
wavelength as given by Eq. (7).
with Fλ (0) calculated using Eq. (3) where Aλtot irr(t) was set to equal Atλoirtr
irr(0).
irr/λ
/
irr
λirr
ΦA→B ꢀ ελA
λ
irr
CBðpssÞ
CAðpssÞ
K⇋λ
¼
¼
ð7Þ
irr
λirr
ΦB→A ꢀ ελB
irr
!
dAλtot
dt
Aλtot
ð0Þ−Aλtot
ðpssÞ
ðpssÞ
irr =λobs
irr =λobs
irr =λobs
irr =λobs
υ0λ
¼
¼
irr =λirr
Aλtot
irr =λirr
ð0Þ−Aλtot
Therefore, using the mass balance, the concentration of the initial
compound (Eq. (8)) is calculated for any irradiation wavelength without
the need for further HPLC analyses.
0
ꢆ
ꢇ
ꢄꢀ
ꢁ
ꢅ
kλA⇋irr Bðmod:Þ
irr irr
irr irr
λ
=λ
λ
=λ
Atot
ðpssÞ−Atot
ð0Þ ꢀlλirr =lλobs
ꢀ
ꢀ
obs
10
−1
Lnð10Þ ꢀ lλ =lλ
irr
CAð0Þ
CAðpssÞ ¼
ð8Þ
ð6bÞ
Kλ⇋ þ 1
irr
This methodology, presented here for the first time, circumvent the
The degradation percentage of species A at a given irradiation wave-
exclusive requirement of an isosbestic irradiation offered by the previous
approach [19]. In this sense, the present method not only widens the ap-
plicability of the kinetic elucidation to the entire spectrum of the absorb-
ing photoreversible species (ORVT has only three isosbestic points in a
200-nm absorption span, Fig. 1) but also reduces the number of steps
to be performed.
length is then given by
CAðpssÞ
Degradation% ¼ 100−CAðpssÞ% ¼ 100 ꢁ
ꢀ 100
ð9Þ
CAð0Þ
3.2. ORVT Photodegradation and Φ-Order Reaction
The electronic spectra of ORVT isomers are characterised by two
major bands in the 200–250 and 250–400 nm with the main maximum
situated at 328 nm (logε = 4.45). These bands are attributed to π,π* tran-
sitions corresponding to the extended π system in ORVT which might
overlay a minor contribution of n,π* transitions due to the presence of
hydroxyl groups [13]. This spectral pattern was generally observed for
stilbenoids, where the electronic donor effects of the hydroxyls on both
benzenic groups of ORTV induced a bathochromic shift of the spectrum
(~48 nm) compared to t-stilbene [13].
Table 1
Overall photoreaction rate-constant, spectroscopic and kinetic parameter values of ORVT
for a set of monochromatic irradiations performed in ethanol at 22 °C.
irr/λ
λ
irr/nm
Aλtoirtr/328(0)
Aλtot irr(pss)
Pλ × 107/einstein s−1 dm−3
kλAi⇋rr B/s−1
irr
260
295
310
320
328
340
350
360
0.474
0.492
0.474
0.489
0.486
0.498
0.480
0.468
0.222
0.270
0.219
0.240
0.240
0.216
0.215
0.175
1.79
2.52
2.10
5.41
2.39
2.83
3.21
4.60
0.0004
0.0015
0.0025
0.0085
0.0047
0.0068
0.0080
0.0150
Fig. 1. Example of consecutive electronic absorption spectra of 2 × 10−5 M ORVT in ethanol
solution subjected to continuous and monochromatic irradiation at 328 nm (total
irradiation time of 2.6 × 103 s at radiant power of P328 = 2.64 × 10−7 einsteins−1 dm−3).
The arrows indicate the absorption change during photoreaction whereas the vertical line
corresponds to the isosbestic points.

M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
67
Table 2
Spectrophotometric and experimental parameters of ORVT reaction performed at λirr = λobs = 328 nm and 22 °C. The variation of the initial species concentration was monitored by HPLC
as presented in Fig. 3.
ΔC × 105/M
A3to2t8/328(0)
A3to2t8/328(pss)
ε3A28/M−1 cm−1
lobs /cm
lirr /cm
F328(0)
F328(pss)
P328×107/einstein s−1 dm−3
1.68
0.565
0.269
28,261.8
1
2.01
0.816
1.317
2.76
The temporal evolution of the spectrophotometric spectra obtained
under continuous monochromatic irradiation (Fig. 1) of the ethanolic so-
lutions of t-ORVT (Scheme 1) was characterised by two main features.
The appearance of a new peak at 205 nm, adjacent to the B-band at
220 nm [13] which itself was not significantly affected during the
phototransformation, and a significant decrease in absorbance of the
long wavelength band (280–400 nm). Three isosbestic points were ob-
served on the consecutive spectra at 240, 253 and 279 nm. These features
strongly suggest that the phototransformation occurs quantitatively
without by-products, in less than an hour. The variation of the spectra
was exclusively due to a photoreaction because in the dark (but other-
wise in the same experimental conditions) t-ORVT is found to be ther-
mally stable at 22 °C for long periods (N4 h). These results also suggest
that the isomerization is the only photoreaction taking place under our
experimental conditions. The possible photocyclisation of c-ORVT is
discarded because usually the electronic spectrum of the closed isomer
is much different from those of the c- and t-stilbenoids (the produced
dihydrophenanthrene absorbs in the visible region (N400 nm) of the
spectrum [22], a missing feature on ORVT spectra performed in our ex-
perimental conditions).
are variable between experiments. Hence, the numerical values of
Φ-order kλAi⇋rr B have a meaning only for the particular conditions of
the experiment at hand and the nature of the analysed compound.
Therefore, kλAi⇋rr B values are not useful for comparison between different
experiments performed on the same compound. This statement
includes the cases when only the irradiation wavelength is different
(Table 2), experiments involving different compounds, let alone exper-
iments employing polychromatic light for irradiation. It is important to
underline that the radiant power (Pλ ) represents the most difficult
irr
parameter to tune between different experiments. In this respect, it is
recommended to determine all the fundamental parameters prior to
proceeding with comparison.
The discussion above is even more acutely relevant when the kinetic
data treatments use classical/thermal order kinetics since in such a case,
the determined rate-constants lack any fundamental physical meaning
for photoreactions.
3.3. Example of Unidentifiability Issues
The identifiability issue is raised whenever a degeneracy of the kinet-
ic solution is observed as a direct consequence of a lack of information
[20,21,23,24]. The identifiability is an issue for reaction kinetics whenev-
er it is possible to propose different sets of plausible values (kinetic solu-
tions) for the set of the reaction's unknowns. This is the case when
Kinetic traces were recorded at selected irradiation wavelengths that
cover most of the absorption spectrum of ORVT (λirr = 260, 280, 310,
328, 350 and 360 nm). These traces were fitted with Eq. (1) for various
observation wavelengths; we present a sample of kinetic traces in Fig. 2
where a unique observation (λobs = 328 nm) was used for comparison
purposes.
As can be seen, good fittings with Eq. (1) were obtained for all traces
(Fig. 2). These results confirm that both ORVT obeys Φ-order kinetics and
Scheme 1 is reliable.
The trans-cis overall rate-constant values (kAλi⇋rr B
) of ORVT
photodegradation reaction were determined as the fitting parameter
(Table 2). The kλAi⇋rr B values increased steadily from 260 to 350 nm but de-
creased beyond. However, according to Eq. (2), the experimental values
of kλAi⇋rr B should be considered with care as the overall rate-constant de-
λirr
λirr
pends on both reaction attributes (ελA , εB , ΦA→B and ΦBλ→A) and exper-
irr
irr
imental conditions (lλ , Pλ and CA(0)). The former parameters
irr
irr
should be assumed wavelength-dependent, and the latter ones
Fig. 3. Evolution of t-ORVT concentration (CA(0) = 2 × 10−5 M, CA(pss) = 3.2 × 10−6 M)
monitored by HPLC when irradiated continuously with a monochromatic beam at 328 nm
(2.39 × 10−7 einstein s−1 dm−3, 22 °C) and fitted by Eq. (10a). The circles correspond to
experimental data whereas the line represents Eq. (10a) that has been fed with the data of
case # 1 in Table 3.
Fig. 4. Examples of good fitting of the experimental values of t-ORVT concentrations
(circles, as shown in Fig. 3) by Eq. (10a) using the data of Table 3 corresponding to cases
# 2 and 5 (lines).

68
M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
Table 3
Examples of fitting parameters and calculated unknowns for the reaction of ORVT in ethanol.
Case #→
1
2
3
4
5
6
7
Parametersa↓
Fitting
αb
35,391.74
0.005
10,653.97
0.23
2525
25,586
0.003
15,532.45
0.17
49,256
0.0031
3756.33
0.17
53,145
0.0033
1821.51
0.19
55,351
0.0037
723.99
0.21
57,124
0.0037
−158.09
0.21
b
kλAi⇋rr B
0.0023
27,005.58
0.13
εBλ
irr
Unknowns
ΦλABirr
ΦλBAirr
0.21
0.025
0.057
0.24
0.54
1.50
−6.89
a
ελB (in M−1 cm−1) was calculated using Eq. (10b) for cases # 2–7.
irr
b
α and kλAi⇋rr B expressed in M−1 and s−1, respectively.
considering a reactive system's kinetic data or even a single kinetic trace
of that reactive system. Each of the distinct solutions provides an excel-
lent fitting of the experimental data and therefore the knowledge of
the true solution (among the set of these plausible solutions) becomes
impossible. We show hereafter an illustration example of identifiability
for the case of ORVT.
Let's consider the data obtained by HPLC (Fig. 3) that correspond to
the progressive depletion of t-ORVT concentration in the reactive medium
through time, up to the pss. These data also provide the values for the ini-
tial and pss concentrations of ORVT (i.e. CA(0) and CA(pss), respectively).
The formula that describes this reaction kinetic can be obtained by
rearranging Eq. (1) and combining it with the mass balance.
here is whether there is a unique set of parameters (α and kλAi⇋rr B) that
can be extracted from the curve fitting.
The treatment of the data according to model Eq. (10a) yields a
great number (an infinity in theory) of very good fittings of the HPLC
data (Fig. 4) which yield significantly different values for the reaction's
λirr
basic unknowns (εBλ , ΦA→B and ΦBλ→A) due the fact that the worked
out fitting parameters (α and kλAi⇋rr B) for each case are substantially differ-
ent from case to case (Table 3).
irr
irr
This proves that using valid equations (Eqs. (10a)–(10d)) is not in it-
self sufficient to perform a complete kinetic analysis since here it is pos-
sible to obtain a series of plausible solutions. This degeneracy cannot also
be solved by only taking the “good fit” of the experimental data to an
equation as the unique criterion. Among the solutions proposed in
Table 3, some cases (# 6 and 7) fit well the experimental data however
h
ꢂ
ꢃ
i
λ
1
α
irr
CAðtÞ ¼ CAðpssÞ þ Log 1 þ 10αꢀΔC−1 ꢀ e−k
ð10aÞ
A⇋Bꢀt
they yield physically meaningless (negative or ΦλA→B N 1) values for the
irr
unknowns and hence have to be discarded. Others (cases # 2–5) gener-
ate plausible values for the unknowns. Because these values are different
but plausible, they represent a typical case of unidentifiability. It is im-
portant to underline that all these results found for the unknowns for
cases # 2–5, do not conform with the true solution (case # 1) that was
obtained by our elucidation method (vide infra Table 4).
This strongly indicates that despite the basic equations (Eqs.
(10a)–(10d)) are perfectly valid and a good fit was found for each case,
there is still confusion about what the true solution might be.
Eq. (10a) is written here as dependent on two parameters α and
kλAi⇋rr B (ΔC=CA(0)−CA(pss)), where the latter corresponds to Eq.
(2) whereas the former parameter is given by;
ꢂ
ꢃ
λirr
α ¼ ελA −εB
ꢀ lλ
ð10bÞ
irr
irr
The definition of these two parameters will allow the determination
λirr
of the three reaction unknowns, namely ελB , ΦA→B and ΦBλ→A derived
irr
irr
The degenerate solution (cases # 1–5) represents practically an acute
challenge for the identification of the true solution. The identifiability
problems exist, in its general terms, as well for thermal reaction kinetics.
It is important to stress here that the identifiability problem exists as well
when classical treatments based on 0th-, 1st- and 2nd-order kinetics are
applied to photodegradation reactions but in addition to the issue of
identifiability, there is the more important issue of the validity of the lat-
ter mathematical models (which are not suitable) for photoreactions.
Therefore, not only it is recommended to use Φ-order kinetics for such
studies but it is also mandatory to develop an elucidation method to
solve uniquely the kinetics. The above discussion is also pertinent if the
absorbance traces (such as those presented in Fig. 2) were used instead
of the concentration profiles (Fig. 3).
from Eqs. (10b), (10c) and (10d), respectively.
CBðpssÞ ꢀ kλ
irr
A⇋B
ΦλA→irr B
¼
¼
ð10cÞ
ð10dÞ
ελA ꢀ lλ ꢀ Pλ ꢀ Fλ ðpssÞ ꢀ C0
irr
irr
irr
irr
CAðpssÞ ꢀ kλ
irr
A⇋B
ΦλB→irr A
ελB ꢀ lλ ꢀ Pλ ꢀ Fλ ðpssÞ ꢀ C0
irr
irr
irr
irr
The experimental conditions and spectrophotometric parameters of
the reaction monitored by HPLC (Fig. 3) and subjected to non-isosbestic
irradiation, are given in Table 2.
For the purposes of illustration of the identifiability problem, we as-
sume that only Eqs. (10a)–(10d) are available (of course more equations
have been derived to achieve an elucidation method as proposed in ear-
lier sections). Hence, the above framework serves the fitting of the ex-
perimental HPLC data (Fig. 3) to Eq. (10a). The important question
3.4. Elucidation of ORVT Kinetics
The elucidation method proposed in Section 3.1.2 was used here to
evaluate the kinetic parameters of ORVT.
Table 4
Quantum yields, overall rate-constant, absorption coefficients and initial velocity values for ORVT photodegradation reactions under different monochromatic irradiations.
irr/nm Pλ ×107/einsteins−1 dm−3 Atot irr(pss) kA⇌B/s−1 υ0λ irr×104/s−1 ελA /M−1 cm−1 ελB /M−1 cm−1 Fλ (0) (ΦA→B SD) × 102 (ΦB→A SD) × 102
λ
irr/λ
λirr
irr/λ
λirr
λirr
irr
irr
λ
i
r
r
i
r
r
260
295
310
320
328
340
350
360
1.95
2.25
2.29
4.68
2.01
4.02
4.55
7.64
0.097
0.227
0.232
0.252
0.239
0.148
0.096
0.031
0.00028
0.0016
0.0026
0.009
0.005
0.015
0.13
3137.99
7239.39
2.03
1.18
1.21
0.99
0.92
1.01
1.16
1.61
6.90 0.86
10.50 0.17
15.40 1.32
21.34 0.14
23.30 1.57
35.01 1.32
43.80 1.60
45.38 0.67
2.30 1.02
4.30 0.42
9.10 1.72
13.97 0.11
21.91 3.21
26.34 5.77
26.26 1.4
6.87 1.6
−1.29
−1.84
−11.17
−7.35
−23.44
−21.94
−14.94
18,858.67
18,800.78
25,047.97
28,261.80
26,490.31
17,801.98
9783.39
11,834.99
12,053.62
12,150.87
10,654.78
7110.86
0.015
0.015
3912.45
1690.81

M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
69
Table 5
Concentrations of the species, thermodynamic equilibrium constants at pss and
photodegradation percentage of t-ORVT at various irradiation wavelengths.
irr/nm CA(0)×105/M CA(pss)×106/M CB(pss)×105/M K⇋
% degradation
λirr
λ
260
295
310
320
328
340
350
360
1.79
1.74
1.69
1.74
1.6
1.61
1.91
1.68
7.83
3.54
4.65
4.21
4.19
2.7
1.003
1.36
1.22
1.32
1.18
1.34
1.69
1.64
1.28
3.92
2.63
3.15
2.82
4.95
7.59
56.17
79.67
72.47
75.90
73.83
83.20
88.36
2.23
0.43
38.23 97.45
It is also interesting to notice that the evolution of the quantum
yields' values with λirr is well described by sigmoid functions (Fig. 6,
Eqs. (11a) and (11b)), and a linear correlation is found between the cal-
culated (Φcld.) and experimental (Φexp.) quantum yield values (inset of
Fig. 6).
Fig. 5. Native and reconstructed electronic absorption spectra (absorption coefficient
units) of t-ORVT and its cis-isomer photoproduct, respectively.
0:417
HPLC monitoring of the evolution of ORVT concentration during a se-
lected non-isosbestic irradiation at 328 nm (Fig. 3), allowed the determi-
nation of the initial and pss concentrations as 2 × 10−5 M and 3.2
× 10−6 M, respectively.
ΦλA→irr B ¼ 0:068 þ
ΦλB→irrA ¼ 0:025 þ
ð11aÞ
ð11bÞ
irr−254Þ
1 þ 440 ꢀ e−0:0826ðλ
0:28
The absorption spectrum of the photoproduct (ελB ) was then recon-
1 þ 135 ꢀ e−0:0925ðλ
irr−270Þ
irr
structed using both Eq. (4) and the absorption spectrum of the reaction
medium at pss (the reconstruction is carried out without physically sep-
arating c-ORVT from the reaction medium), Fig. 5.
The overall vibrational shape of c-ORVT spectrum is identical to that
recorded for its photoisomer with variable absorption values, in agree-
ment with the general pattern observed for stilbenoids [13]. These fea-
tures also support the occurrence of the photoisomerization without
any further degradation processes, as indicated in Scheme 1.
Once the absorption coefficients of the photoproduct are known, the
determination of the individual absolute values of the quantum yield at
any irradiation wavelength was achieved by using Eqs. (5a) and (5b) to-
gether with the numerical value of the reaction initial velocity (ν0) that
can be calculated by Eqs. (6a) and (6b).
One of the advantages of our method is offered by Eqs. (11a) and
(11b) that allow the determination of the quantum yield values for
both isomers at any irradiation wavelength, in the spectral section
260–350 nm, based on the knowledge of only a few experimental values.
The overall similarity between the sigmoid functions (Fig. 6) was also in-
dicated by a good linear correlation established between the two sets
quantum yield values (ΦλA→B = 0.922 × ΦBλ→A + 0.043, r = 0.97, be-
tween 260 and 340 nm).
irr
irr
The above findings suggest that the photodegradation of ORVT is
mainly driven by UVA light (N310 nm). The quantum yield values
(0.02–0.45 in ethanol) are within the range of values reported for stil-
benes (0.48–0.32, for stilbene in methanol at 313 nm [25]). The reverse
reaction (ΦλB→A) was relatively less photoreactive over irradiation than
irr
Both forward and reverse quantum yields have been found to depend
on the irradiation wavelength (Table 4). 6.6- and 11.4-fold increases
were recorded for ΦAλi→rr B and ΦBλi→rr A values, respectively, in the 260–
350 nm range (Table 4). The values of the reverse quantum yield were
always smaller than those observed for the forward reaction and the
ratio of quantum yield values, ranging between 1 and 3, correlated line-
arly in an inverse proportionality relationship with the irradiation wave-
its counterpart in agreement with the general trend observed for
stilbenoids and azobenzenes [13,26]. The variation of the quantum
yield ratio with irradiation proves that the photoisomers' exited-states
might be significantly different, which does not support the hypothesis
that the decay of both isomers originates from a common intermediate.
Indeed, it has been postulated that a twisted (θ = 90) intermediate oc-
curs, irrespective of irradiation wavelength, at the bottle neck region sit-
uated between excited-state and ground-state potential energy surfaces
[27]. In this interpretation, the quantum yields of the trans and cis
length (ΦλA→B/ΦBλ→A = −0.0246 × λirr + 9.44, r = 0.95, in the range
260–350 nm).
irr
irr
Fig. 6. Sigmoid patterns (Eqs. (11a) and (11b)) obeyed by the experimental quantum yield
(ΦA→B and ΦB→A ) values of both ORTV isomers as experimentally measured for various
irr
irr
irradiation wavelengths. Inset: linear relationship of the experimental and calculated (Eqs.
(11a) and (11b)) values of ΦA→B and ΦB→A
Fig. 7. Correlation between t-ORVT photodegradation % at pss and irradiation wavelength
(λirr).
.
irr
irr

70
M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
Fig. 8. Calculated βirr values (circles) using Eq. (2) and the values of kA⇌B and Pirr provided
Fig. 10. Linear correlation of experimental (Pexp.) with calculated (Pcld.) values of the
irr
in Table 1. The fitting of the experimental data was drawn by the sigmoid model Eq. (12)
radiant power for wavelengths between 310 and 350 nm.
(line).
a number of hypotheses have been proposed, which mainly relate to
the existence of various excited states that may be due to different con-
formers [35].
isomers are expected to be equal in the absence of major sterical hin-
drance, as they decay from the same species [25] and/or at least their ra-
tios should be constant with irradiation wavelength (as would be
stipulated by Kasha's rule [28]). Such a hypothesis has not been con-
firmed by a large number of quantum yield experimental data published
in the literature for a variety of stilbenoids. The determined values of
quantum yields for the isomers of each particular stilbene derivative
were, in general, not found to be equal or wavelength independent
[13]. For example, the most largely studied trans-stilbene has a quantum
yield of 0.48 and its isomers a value of 0.32 in the same experimental
conditions [27]. The situation is even more evidenced as, for instance,
the quantum yield of trans-stilbene has been reported to vary with irra-
diations (0.48 at 254 nm and 0.32 at 313 nm) [13,25]. However, at the
best of our knowledge there are no systematic studies of the effects of ir-
radiation on stilbenoids quantum yields available in the literature, even
though there are many examples of wavelength-dependent quantum
yields for a variety of molecules [25,26,29,30]. Similar sigmoid behaviour
was also observed for a number E/Z photoisomerizations [26,31–33].
The above literature results, which are corroborated by those laid out
in the present study, do not back the hypothesis relating to a common
excited-state intermediate that occurs independently of the irradiation
wavelength. From a more general viewpoint, the wavelength depen-
dence of the quantum yields corroborates the statement of Turro et al.
[34] stipulating the non-universal applicability of Kasha's rule to photo-
reactions. If there is still no rational interpretation of this phenomenon
The calculated percentage of photodegradation of t-ORVT in ethanol
was found to range between 56 and 97% within the 260–360 nm spectral
region (Table 5). Overall, the degradation percentage increases linearly
with irradiation wavelength (Fig. 7). These results prove that the photo-
reaction favours the phototransformation of t-ORVT where c-ORVT has a
major contribution to the pss species composition. This corroborates the
lower quantum yields and absorption coefficient values of c-ORVT com-
pared to those of the initial isomer. However, the high degradation per-
centages meant that exposure of ORVT to UVA and/or Visible light causes
almost its complete depletion and therefore it is strongly recommended
to shield it from light in all applications and manipulations. This would
also justify raising some questions about the photostability of t-ORVT
in vivo [36].
The method presented here would be useful for the study of
phytomolecules/drugs that obey photoisomerization reactions and will
contribute to fully characterise and rationalise their photokinetics and
photostability with the aim of improving their safety and durability.
3.5. ORVT Actinometer
The actinometric potential of ORVT can be evaluated by using the
data obtained on the photoreactivity of this species at different wave-
lengths. Using the data of Table 1, the values of the β factors can readily
be calculated on the basis of Eq. (2). This methodology has the advantage
to be much faster and simpler than the previously used approach [19].
When the β factors were graphically represented against the corre-
sponding wavelengths, a sigmoid shape is obtained (Fig. 8, Eq. (12)).
23900
1 þ 139 ꢀ e−0:089ꢀðλ
βλ ¼ 2220 þ
ð12Þ
irr
irr −260Þ
The advantage of Eq. (12) is both to allow obtaining the β values at
any wavelength in the range studied, and to facilitate the determination
of the radiant power (Pλ ) of an unknown source if its monochromatic
irr,x
beam wavelength (λirr,x) is situated between 310 and 350 nm, the most
useful part of photodegradation causative range of ORVT. This can be
achieved by simply taking the ratio Pλ =kλAi⇌rr,xB/βλ , with these param-
irr,x
eters correspond to the βλ value calculated usingiErr,xq. (12) for λirr,x, and
irr,x
kλAi⇌rr,xB is obtained by irradiating a 2 × 10−5 M ORVT ethanolic solution
(2.1 mL) by the considered beam (at λirr,x) and fitting its trace to Eq. (1).
In order to test the validity of this new procedure, the actinometric
properties of ORVT have been evaluated on freshly prepared solutions
that were subjected to irradiation (at λirr = 310, 328, 340 and 350 nm)
using beams of different radiant powers (the rest of the experimental
Fig. 9. Effect of increasing the radiant power of the monochromatic irradiation beam (at
340 nm) on the photokinetic traces of t-ORVT (2 × 10−5 M). The experimental data
(circles) were fitted by Eq. (1). Inset: Linear correlation of kA⇌B (in s−1) with Pirr (in
irr
einstein s−1 dm−3) for each wavelength.

M. Maafi, M.A. Al-Qarni / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 188 (2018) 64–71
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λ
irr, the experimental kinetic traces for the series of radiant power values
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For the purpose of this study, the various radiant power values of
these experiments were considered unknown and were determined as
stated above (using the determined Φ-order rate-constants for each irra-
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as its reliability make it a good alternative to the actinometric methods
provided in the literature [37]. More specifically for drugs, ORVT can
stand as an alternative for the ICH recommended procedure that uses
the controversial quinine hydrochloride actinometer [38–40]. ORVT acti-
nometry would be also very useful for the study of the photostability of
phytochromes absorbing in the range 310–350 nm. Finally, it is impor-
tant to notice that to implement the actinometric method presented in
this work, it is not required to know neither the absolute values of the
forward and reverse quantum yields nor the produced photoisomers'
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the recommendation that this compound should be shielded from light
at all stages whether in production, formulation or in use conditions (es-
pecially in solution).
It seems that the quantum yield of trans/cis photoreversible systems
should a priori be considered wavelength dependent, as indicated by the
results of ORVT, but also other studies [25,26,29,30]. Therefore, the quan-
tum yield values obtained using polychromatic irradiations, might be
deemed misleading, as the quantum yield might not be constant over a
spectral range covered by the polychromatic irradiation, and must be
considered with care, as only an average value is obtained that does
not hint to the possible fine tuning of the quantum yield values.
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