Thermodynamics and kinetics of flavylium salts: Malvin revisited

Article abstract of DOI:10.1039/a802602e

The pH-dependent structural transformations in aqueous solutions of natural and synthetic flavylium salts are re-examined. The procedure uses Malvin as a reference compound and exploits the different timescales of the kinetic process that take place prior to the equilibration. For each process a kinetic expression was deduced allowing calculation of all the equilibrium constants and most of the rate constants of the system. The equilibrium constants were confirmed by comparison with the data obtained by ¹H NMR. Clear evidence for the formation of significant amounts of trans-chalcone in Malvin was obtained.

Full text of DOI:10.1039/a802602e

View Article Online / Journal Homepage / Table of Contents for this issue
Thermodynamics and kinetics of Ñavylium salts
Malvin revisited
Fernando Pina
Departamento de Qu•mica, Centro de Qu•mica Fina e Biotecnologia, Faculdade de Ciencias e
T ecnologia, Universidade Nova de L isboa, 2825 Monte de Caparica, Portugal
The pH-dependent structural transformations in aqueous solutions of natural and synthetic Ñavylium salts are re-examined. The
procedure uses Malvin as a reference compound and exploits the di†erent timescales of the kinetic process that take place prior
to the equilibration. For each process a kinetic expression was deduced allowing calculation of all the equilibrium constants and
most of the rate constants of the system. The equilibrium constants were conÐrmed by comparison with the data obtained by 1H
NMR. Clear evidence for the formation of signiÐcant amounts of trans-chalcone in Malvin was obtained.
The fact that anthocyanins are responsible for a variety of
beautiful colours in Ñowers and fruits has been known since
the early decades of this century.1,2 The Ðrst impression is
that these biological molecules possess a rather simple chemi-
cal structure which contrasts with the generality of the solu-
tions adopted by nature in other biological functions.
However, in spite of their simplicity, these molecules are
involved in a series of equilibria, giving rise to di†erent forms
with several colours, see Scheme 1 for Malvidin 3,5-digluco-
side (Malvin).
Regardless of the mechanism and structure through which
colour in plants is achieved, the knowledge of the structural
transformations reported in Scheme 1 is of crucial importance.
Since the pioneering work of Robinson,3 synthetic Ñavylium
salts have been associated with natural anthocyanins. This is
more than a coincidence, because the structural transform-
ations of synthetic Ñavylium salts follow the same general
pattern as natural anthocyanins, Scheme 1. Moreover, the
information acquired for the kinetic processes that occur in
synthetic Ñavylium salts4h6 have forced a correction of the
models and interpretations used for anthocyanins.7h9 This has
not been sufficiently emphasized and, as a consequence, equi-
librium and rate constants of anthocyanins appear in di†erent
works with di†erent interpretations. Moreover, although
Malvin is the most studied anthocyanin, a complete set of
equilibrium and rate constants obtained at the same tem-
perature (e.g. 25 ¡C) were not available prior to this work.
In order to illustrate the kinetic processes described in
Scheme 1 a hydraulic analogy can be made, as for example in
the case of 4@-hydroxyÑavylium,10 Scheme 2. The various
forms of this compound are related by interconverting pro-
cesses in a way that evokes a system of communicating
vessels. Using such a hydraulic analogy, the behaviour of
aqueous solution of Ñavylium ions upon a pH jump from 1.0
to e.g. 4.0 can be schematically represented as: (i) In I the
system is equilibrated at pH 1.0. (ii) In II the system has been
taken to pH 4.0, and this pH jump has an e†ect comparable
to raising the piston. The scheme represents the situation
immediately after the proton transfer process. (iii) In III, when
the cis ] trans isomerization is very slow, it is possible to
obtain an intermediate (pseudo-equilibrium) state involving
the species AH`, A, B and C . (iv) In IV the thermodynamic
c
equilibrium at pH 4.0 is Ðnally reached.
In this work it is shown that Malvidin 3,5-diglucoside
(Malvin) exhibits the same qualitative behaviour as described
in Scheme 2, conÐrming the importance of synthetic Ñavylium
salts as model compounds for natural anthocyanins. The
approaches used to calculate the rate and equilibrium con-
stants of the processes described in Scheme 1, are reviewed,
and a general procedure using Malvin as an example is pro-
Scheme 1
J. Chem. Soc., Faraday T rans., 1998, 94(15), 2109È2116
2109

View Article Online
izatation of the cis-chalcone, eqn. (1)È(4)
Ka
AH` ] H O A8B A ] H O`
(1)
(2)
(3)
(4)
2
3
Kh
AH` ] H O A8B B ] H O`
2
3
Kt
B A8B C
Ki
cis
C
A8B C
cis
trans
In this section we consider the system at its thermodynamic
equilibrium, a situation which, starting from AH`, is achieved
in a timescale ranging from a few minutes to days,4,5,7h10
depending on the substituents of the Ñavylium.
As previously shown12 the molar fraction distribution of
the acidic form can be obtained from
[AH`]
[H`]
\ a@ \
(I)
C
[H`] ] K@
0
a
where K@ is given by eqn. (II) and C \ [AH`] ] [A] ] [B]
a
0
] [C ] ] [C ].
cis trans
Scheme 2
K@ \ K ] K (1 ] K ) ] K K K
(II)
a
a
h
t
h t i
Inspection of eqn. (I) shows that its mathematical form is ana-
logous to the molar fraction of a single acidÈbase equilibrium
and, in consequence, the complex equilibria described by eqn.
(1)È(4) can be expressed by one single equation with acidity
posed. Some aspects of previous work published in the liter-
ature and not correctly interpreted are also discussed.
constant K@ :
Experimental
a
Ka{
Materials
AH` ] H O A8B CB ] H O`
(5)
2
3
Malvin was purchased from Extrasynthese, and synthetic
Ñavylium salts were prepared according to a published pro-
cedure.11 All other chemicals were of analytical grade.
The “conjugate baseÏ (CB) that is in equilibrium with AH`,
is the sum of the “basicÏ species [A] ] [B] ] [C ] ] [C ],
and its molar fraction distribution is given by
cis
trans
[A] ] [B] ] [C ] ] [C
]
K@
pH measurements
cis
trans
a
\ b@ \
\ 1 [ a@
C
[H`] ] K@
0
a
The pH was measured with a Metrohm 713 pH meter. The
Ñavylium solutions were generally stored at pH O1. pH
jumps were carried out by adding the necessary amount of
base to neutralize the stock solution of Ñavylium cation and
the amount of the desired bu†er in order to obtain a Ðnal
concentration of 0.05 M. The ionic strength was maintained at
(III)
Determination of Kº . The molar fraction a@ deÐned by eqn.
a
(I) and thus the important constant K@ , can be obtained by
a
spectrophotometric measurement12
0.1 M by addition of NaClO . At this ionic strength the e†ect
of ion-pair formation is very low. The concentration of bu†er
4
A
[ C
(Theorell Stenhagen universal bu†er) was maintained low in
order to avoid the bu†er e†ects which are only relevant at
high concentrations.9 Throughout all the text the notation H`
t
A
1 [ C
0
a@ \
(IV)
t
where A is the pH-dependent absorbance (at any wavelength,
but preferably at the absorption maximum of Ñavylium), A
the absorbance at the same wavelength, measured at a pH
value sufficiently low to obtain exclusively Ñavylium cation,
and H O` are used indiscriminantly.
3
0
Absorption spectroscopy
Spectra were recorded on a Perkin-Elmer Lambda 6 spectro-
photometer. A constant temperature of 25 ¡C in the quartz cell
(d \ 1 cm) was obtained by use of a Haake thermostatted
water bath.
and C the ratio A/A at a pH value high enough to have CB
t
0
as the sole species present in solution.
Fig. 1 shows the pH dependence of the absorption spectra
of Malvin, together with the representation of the Ðtting to
eqn. (IV), achieved for pK@ \ 1.70 ^ 0.05 (25 ¡C).13
a
Results and Discussion
Determination of the equilibrium constants. The individual
expressions of the molar fractions of each component of the
CB can be calculated using12
Thermodynamic equilibrium
As mentioned in the Introduction, the structural transform-
ations of natural and synthetic Ñavylium salts in acid and
slightly acidic aqueous solutions are described by Scheme
1.7h9 In general, it is possible to distinguish at the equilibrium
the Ðve species, shown in Scheme 1, i.e. (i) the Ñavylium cation,
AH`, (ii) the quinoidal base, A, obtained from the former by a
proton transfer, (iii) the hemiacetal formed from Ñavylium
[A]
K
[B]
K
K@
a
h
b@ ;
\
\
b@ ;
\
C
K@
C
0
a
0
a
[C
]
K K
[C
]
K K K
cis
h
t
trans
h t i
b@
b@ ;
\
(V)
C
K@
C
K@
0
a
0
a
cation by a hydration reaction, (iv) the cis-chalcone, C
,
According to eqn. (V), calculation of the several equilibrium
constants is thus reduced to the determination of the molar
fraction distributions of each component of CB (at any pH
cis
obtained from the hemiacetal through a tautomeric process,
and (v) the trans-chalcone, C resulting from the isomer-
trans
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
2110

View Article Online
Determination of K . As pointed out by Brouillard15 in the
a
case of natural anthocyanins and some synthetic Ñavylium
salts, more than one hydroxy substituent is available to form
the quinoidal bases. In this case eqn. (1) must be written in
more than one acidÈbase equilibrium. For example (without
loss of generality), considering two hydroxy substituents in
position 4@ and 7
Ka4{
AH` ] H O A8B A ] H O`
(1a)
(1b)
2
4{
3
Ka7
AH` ] H O A8B A ] H O`
2
7
3
This situation does not introduce any additional problem to
the approach proposed because as previously noted by Brouil-
lard,15 eqn. (1a) and (1b) can be written as the single eqn. (1)
in which K \ K ] K , (the relative amounts of each base
Fig. 1 Absorption spectra of Malvin, 1.25 ] 10~5 M, as a function of
a
a4{
a7
pH upon total equilibration. Inset: Fitting of the absorption data
are given by the ratios K /K and K /K ).
taken at 518 nm by means of eqn. (IV), pK@ \ 1.70 ^ 0.05.
a4{
a
a7
a
a
The “globalÏ acidity constant K can be calculated from
a
eqn. (V), in an alternative method as follows: pH jump from
value, but preferably when b@ \ 1) provided that K@ is already
pH \ 1 to a value where pH A pK . At this pH the Ñavylium
a
a
known from eqn. (IV).
cation is totally converted into quinoidal base and the hydra-
tion process is generally slow enough to be followed by a con-
ventional spectrophotometer. In addition, the absorption
spectrum of quinoidal base is red shifted in comparison with
those of the other species. This circumstance permits choice of
a wavelength for which quinoidal base is the sole absorbing
species and, therefore, the absorbance taken immediately after
Determination of the equilibrium constants by 1H NMR.
Calculation of the molar fractions of each component of CB
at the equilibrium can be conveniently obtained by 1H NMR.
A clear example of this strategy was reported for Malvin.14
The 1H NMR spectra enabled one to identify the Ñavylium
cation in fast equilibrium with quinoidal base, two R- and
S-hemiacetal isomers, as well as the cis- and trans-chalcones.
The value of the constants thus obtained are shown in Table
1. In this table the two hemiacetal isomers were considered as
a single species for the sake of simplicity.
the pH jump (i.e. after the proton transfer), A@ , corresponds to
0
the maximum of the concentration of this species. At the end
of the kinetic process (Ðnal equilibrium) the absorbance of the
quinoidal base indicates its Ðnal concentration A@ . The ratio
1
A@ /A@ is equal to the molar fraction distribution of the quin-
1
0
In ref. 14 a complete titration of Malvin was followed by 1H
NMR. However, the data reported in Table 1 can also be
obtained from a single 1H NMR spectrum taken at a pH
value sufficiently high to obtain the molar fraction distribu-
oidal base at the Ðnal equilibrium (when b@ \ 1). For Malvin
K /K@ \ 0.04 giving pK \ 3.1, in good agreement with the
a
a
a
value calculated by 1H NMR.
tion of the CB species, together with the measurement of K@
Kinetic processes
a
obtained through the a@ function by means of eqn. (IV). In
pH and temperature jumps. The systematic use of pH and
temperature jumps to study synthetic and natural Ñavylium
compounds was introduced by Brouillard and Dubois16,17
more than 20 years ago and even now is the simplest tech-
nique to elucidate the kinetics of transformation of these com-
pounds. In general, the compounds are stored at pH \1 and
pH jumps are carried out from this pH to higher values.
Otherwise the system can be equilibrated at pH [1 and con-
centrated acid added in order to obtain the back reaction that
forms Ñavylium cation.
general, a complete titration is necessary in order to identify
the peaks that correspond to each species.
Separation of the 1H NMR peaks of each species is possible
whenever the rate of interconversion between the several
species is slow in comparison with the 1H NMR timescale.
This is generally observed for all the processes except for the
proton transfer reaction. In this case Ñavylium cation is in
rapid exchange with quinoidal base and the peaks appear in a
single set. Nevertheless, when pH A pK@ this set is exclusively
a
due to the quinoidal base, and thus the molar fraction of
species A can be evaluated.
Proton transfer. The Ðrst process that occurs upon a pH
jump from pH \1 to higher values is the transfer of a proton
to water. This reaction is known to be very fast18 and for this
reason, conventional spectrophotometry, including stopped-
Ñow analysis, is useless. However, proton transfer in natural
and synthetic Ñavylium compounds can be studied by means
of temperature jumps, because the transfer of a proton from
Ñavylium cation to water is exothermic.16
Table 1 Equilibrium and rate constantsa of Malvin and 4@-
hydroxyÑavylium at 25 ¡C
1H NMRb
Malvinc
4@ OHd
pK@
1.8
3.2
1.1 ] 10~2
0.21
0.54
È
1.7
3.1
1.9
5.5
a
pK
a
K
1.4 ] 10~2
3.6 ] 10~6
h
K
t
0.37
È
Ka
K
i
È
0.25
18
ca. 10~3
8.9 ] 10~2
2.5 ] 104
\10~5
\10~8
AH` ] H O A8B A ] H O` ] D
(6)
2
3
k /dm3 mol~1 s~1
h
k
/dm3 mol~1 s~1
È
È
È
In eqn. (6) a temperature increase is accompanied by an
increase in the concentration of Ñavylium cation and corre-
sponding decrease in the amount of quinoidal base. The relax-
ation constant of this process is given by16,17
~h
k /s~1
3.6 ] 10~4
i
k
/s~1
6.6 ] 10~4
~i
a Equilibrium constants, including K are written without units. This
h
is a consequence of their deÐnition, see eqn. (1)È(4). This criterion was
k \ k ] k ([A] ] [H`]); (K \ k /k
)
(VI)
not used in previous work by other authors including ourselves. The
1
a
~a
eq
a
a ~a
same is true for k@ eqn. (II), which is a sum of terms all without units.
where [A] is the equilibrium concentration of the quinoidal
a
eq
b Equilibrium constants for the several processes involving Malvin at
base.19 Eqn. (VI) was veriÐed for natural and synthetic Ñavy-
25 ¡C, obtained by 1H NMR according to ref 14. c Equilibrium con-
stants for the several processes involving Malvin at 25 ¡C calculated
according to the procedure described in the text. d From ref. 5 and
10.
lium salts4,16,17 and allows one to calculate the value of the
proton transfer equilibrium constant, K , which can be com-
a
pared with the value obtained by 1H NMR and from the ratio
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
2111

View Article Online
A@ /A@ at 25 ¡C, see Table 1. For Malvin the value of pK \
1
0
a
3.9 at 6.5 ¡C16 was reported.
Hydration and tautomerization reaction. The Ðrst quantiÐca-
tion of the rate of the hydration reaction in Scheme 1 was
reported for Malvin, by Brouillard and Dubois in 1977.16 At
that time the existence of cis- and trans-chalcones had already
been noticed for synthetic Ñavylium salts,20 but not yet
described for natural anthocyanins, and no reference to tauto-
merization or cisÈtrans isomerization was made in that
work.16 In a following publication in the same year (but
regarding Oenin), Brouillard and Delaporte,17 claimed the
observation of a kinetic process that they improperly attrib-
uted to the tautomerization reaction to cis-chalcone from
hemiacetal. Only in 1990 did Brouillard and Lang9 clarify
deÐnitively the situation, assuming that the previously report-
ed kinetics of formation of cis-chalcone was in reality the
kinetics of formation of trans-chalcone. Moreover, by tem-
perature and pH jumps they were able to prove that the tau-
tomeric reaction is much more rapid than the hydration
reaction (unless the pH is lower than 1). In view of this last
conclusion the previous results obtained for Malvin were also
re-interpreted considering that the process studied as a hydra-
Fig. 2 Representation of eqn. (IV) for Malvin at a wavelength of 550
nm, immediately after conclusion of the hydration/tautomerization
processes
low, in agreement with the data previously obtained by 1H
NMR.14 According to these results, the value expected for
pK\ is 1.67, which is clearly outside the experimental accu-
a
racy.
tion reaction16 leads to a mixture of B and C in fast equi-
cis
Whenever the concentration of trans-chalcone at equi-
librium. However, this new interpretation has some
librium (when b@ \ 1) is larger, the di†erence between K@ and
implications on the precise meaning of the rate and equi-
librium constants, until now not completely clariÐed, see
below.
a
K\ allows us to calculate the product K K K . Several exam-
a
h t i
ples of this type of calculation are reported in the liter-
ature.4,5,21
Actually the qualitative kinetic pattern of Malvin and
Oenin (and probably other anthocyanins) is more similar to
that of many synthetic Ñavylium salts than originally thought.
Three main processes with very di†erent timescales can gener-
ally be observed for these natural compounds: (i) Proton
transfer is the fastest and occurs in the microsecond timescale.
(ii) Hydration (including tautomerization) takes place on a
timescale from seconds to several minutes (if pH is not much
Kinetic equations for the hydration reaction. On the basis of
the arguments presented above, the kinetic equations that
account for the second intermediate state (pseudo-equilibrium
attained prior to the cisÈtrans isomerization when the tauto-
merism is much more rapid than hydration) can be simpliÐed
to
`
K~a*H +
Kh
A ] H` E88F AH`E88F (C ] B) ] H` (7)
higher than pK , see below). (iii) Isomerization occurs in
cis
a
`
Ka
K~h*H +
hours.
Determination of K\. The fact that the three above-
mentioned processes can be separated by timescale is very
a
The processes shown in eqn. (7) are conveniently studied by
means of pH jumps, which can be viewed as a perturbation of
a previously equilibrated system and thus can be treated by
the relaxation method. Addition of bu†ers can give rise to
large changes in the rates of the reactions represented by eqn.
(7).9 However these e†ects are not ubiquitous to all bu†ers,
and are only important if the bu†ers are present in large con-
centrations. In this work we reduced the concentration of the
bu†er to a minimum value necessary to consider the pH con-
stant during the reaction. This is very advantageous because it
simpliÐes the resolution of the di†erential equations that
result from eqn. (7), to give eqn. (X) and (XI), see Appendix 1
convenient. For example, at the end of the hydration/
tautomerization reaction the system can be considered to be
at an intermediate (pseudo-equilibrium) state for which it is
possible to calculate the pseudo-equilibrium constants.12 In
other words the same treatment developed for the thermody-
namic equilibrium can again be used replacing K@ by the
a
pseudo-equilibrium constant K\.
a
K\ \ K ] K (1 ] K )
(VII)
a
a
h
t
The molar fraction distribution of the several species at the
end of the second process is given by the same set of pre-
viously discussed eqn. (V), replacing K@ by K\. In particular,
k \ k ] k [H`]
(X)
a
a
1
a
~a
for quinoidal base
[H`]
k \
k ] (1 ] K )k [H`]
(XI)
[A]
K
2
h
t ~h
a
[H`] ] K
\
b\
(VIII)
(IX)
a
C
K\
0
a
where k and k are, respectively, the relaxation constants for
1
2
K\
the proton transfer and hydration plus tautomerization pro-
cesses. The pH dependence of eqn. (XI) can be simpliÐed in
two extreme cases, both previously reported:16 (i) when
[H`] A K the observed relaxation constant k depends lin-
a
b\ \
[H`] ] K\
a
Determination of the pseudo equilibrium constant K\ is
useful because it allows one to determine the product
a
a
2
early on [H`]
K (1 ] K ) and in some cases, K K K .
h
t
h t i
In Fig. 2 eqn. (IV) is applied to the pseudo-equilibrium
state. This state is reached from a few seconds (at low pH
values) to 30 min (at high pH values) after the pH jump from
k \ k ] (1 ] K )k [H`]
t ~h
(XII)
2
h
(ii) when [H`] @ K the contribution of the back reaction is
a
pH \1 to 1 \ pH \ 5. The Ðtting was achieved for pK\ \
very low [k (1 ] K )[H`] @ aK ] and eqn. (XIII) is
a
~h
t
h
1.7 ^ 0.1, allowing one to calculate K (1 ] K ) \ 1.9 ] 10~2.
obtained
h
t
For Malvin the di†erence between K@ and K\ lies within
the experimental error, which means that the molar fraction
a
a
k
K
h
a
k \
[H`]
(XIII)
2
distribution of trans-chalcone at equilibrium (when b@ \ 1) is
2112
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
In Fig. 3 we report the data for Malvin at 25 ¡C. The Ðtting
was achieved for the values reported in Table 2. It must be
emphasized that from eqn. (XI) the ratio K /(1 ] K ) can be
h
t
calculated.
Determination of K and K . As mentioned above, the
h
t
hydration rate constants reported by Brouillard and Lang9
correspond to the formation of (B ] C
However, according to eqn. (XI) these constants are, in reality,
)
from AH`.
cis
k for the direct reaction and k (1 ] K ) for the reverse reac-
h
vh
t
tion. Moreover, the published equilibrium constant for the
hydration reaction of Malvin is an apparent constant that is
smaller then the real value by the factor (1 ] K ). From eqn.
t
(XI), the ratio K /(1 ] K ) is obtained, which means that both
h
t
Fig. 3 Representation of the Ðtting to eqn. (IV) for Malvin at 25 ¡C
K and K are available because the product K (1 ] K ) was
t
h
h
t
already calculated from the pseudo-equilibrium data. For
Malvin at 25 ¡C we obtained the values reported in Table 1, in
very good agreement with the data from 1H NMR.
Table 2 Rate and equilibrium constants of Malvin obtained from
the kinetics of the hydration reaction at 25 ¡C
Cis–trans isomerization. The analysis of the cisÈtrans isom-
erization can also be performed separately from the other pro-
cesses because, if the pH is not too high this reaction generally
occurs in a timescale much slower than all the other
events4,5,9
k /s~1
k
(1 ] K )/mol dm~3 s~1
K /(1 ] K )
pK
h
~h
t
h
t
a
0.25
25
0.01
3.3
Keq
B ] A ] AH` E8F C
Ki
(8)
(9)
cis
C
E8F C
cis
trans
K~1
As shown in Appendix 2, the relaxation constant for the
slowest process prior to reaching the Ðnal equilibration is
given by
K K
[H`] ] K\
h
t
k \
k ] k
(XIV)
3
i
~i
a
All the equilibrium constants that appear in this last equation
were already obtained from the analysis described in the pre-
vious sections and, therefore, if the equilibrium constant K is
known, both direct and reverse isomerization rate constants
are available.
In the case of Malvin, and in contrast with previous
results,9,16,17 we observe formation of non-negligible quan-
i
Fig. 4 Spectral variations upon a pH jump from pH \1 to 5.5 fol-
lowed at 330 nm as a function of time. The Ðrst decay can be attrib-
uted to the hydration reaction and the second kinetic process to the
isomerization.
Fig. 5 Schematic representation of the general procedure used to calculate rate and equilibration constants of Scheme 1
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
2113

View Article Online
Fig. 6 Energy diagram showing the thermodynamic levels of the Ðve species of Malvin, together with the three kinetic processes that occur prior
to the equilibrium at 25 ¡C. The diagram is valid only in the neutral and acidic region. (a) according to ref. 7.
tities of trans-chalcone. The results are shown in Fig. 4 from
which it is possible to detect the hydration reaction followed
by the slower isomerization process. The signal was obtained
at 330 nm because, at this wavelength, the molar absorption
coefficients of hemiacetal/cis-chalcone and trans-chalcone are
sufficiently di†erent. The kinetics was treated with eqn. (XIV)
distribution of 4@-hydroxyÑavylium at the three steps,10 as
well as the Ðrst and third steps.24
This work was supported by Centro de Qu•mica-Fina e Bio-
tecnologia da Universidade Nova de Lisboa, Programa Plu-
rianual, Portugal, and by a grant from Acordo Cultural
JNICT(Portugal) and FRAE-CNR (Bologna) Italy. The
and Ðtting was achieved for k \ 1.4 ] 10~3 s~1. Using the
3
isomerization equilibrium constant from Table 1 it is possible
to calculate the direct and the reverse rate constants for the
isomerization process. The only limitation of this method is
the fact that (as discussed previously) whenever K@ is not suffi-
a
ciently di†erent from K\, the isomerization equilibrium con-
a
stant can only be determined with accuracy by means of 1H
NMR.
The existence of non-negligible amounts of the trans-
chalcone form of Malvin has already been observed14 by 1H
NMR, ca. 8%. This amount is larger than that of the quinoi-
dal base, which is only ca. 5%.
In Fig. 5 we propose a general procedure to obtain the rate
and equilibrium constants of anthocyanins and some synthetic
Ñavylium salts.
In some other synthetic Ñavylium salts, e.g. 7-
hydroxyÑavylium and 4@,7-dihydroxyÑavylium the hydration
reaction (and not the cisÈtrans isomerization) is the control-
ling step prior to the system reaching the Ðnal equilibration.22
In those cases pH jumps can be complemented by Ñash pho-
tolysis measurements as reported elsewhere.22
Energy level and molar fraction distribution diagrams
Complete knowledge of the equilibrium constants of a natural
or synthetic Ñavylium salt allows the construction of an
energy level diagram for the several species appearing in
aqueous solutions.10,21,22 These diagrams are very useful to
visualize not only the thermodynamic equilibrium but also to
understand the complex processes that occur prior to equili-
bration. In Fig. 6 we represent the diagram for Malvin on the
basis of the data of Table 1.
Finally, the molar fraction distribution of the Ðve species at
the equilibrium can be obtained by means of eqn. (I), (II) and
(V). The same set of equations allows one to calculate the
molar fraction distribution at the pseudo-equilibrium (after
conclusion of the hydration/tautomerization processes), repla-
cing K@ by K\. The molar fraction distribution immediately
Fig. 7 Molar fraction distribution of Malvin (top) and 4@-
hydroxyÑavylium (bottom): thermodynamic equilibrium (ÈÈÈ);
immediately after the hydration/tautomerization processes (È È È È);
immediately after the proton transfer step (ÉÉÉÉÉÉÉ)
a
a
after the proton transfer is straightforwardly obtained from
knowledge of the pK . In Fig. 7 is shown the molar fraction
a
2114
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
author thanks Prof. V. Balzani, Prof. M. Maestri and Dr R.
Ballardini for ongoing collaboration and helpful suggestions.
The secular determinant is given by
K
a
[ k
a
K
11
12
\ 0
(AXVI)
a
a
[ k
21
22
Appendix 1
and the resolution
In contrast to the approach used by Brouillard and Dubois,16
in this treatment the pH is controlled by the minimum con-
centration of bu†er.
k ] k \ a ] a
(AXVII)
1
2
11 22
k ] k \ a
a
[ a
a
(AXVIII)
1
2
11 22
12 21
k~a
A simpliÐcation is possible because one of the processes is
A ] H` ÈÈÈ AH`
(A1)
(A2)
(A3)
(A4)
much faster than the other a A a . In addition k and k
11
22
.
a
~a
ka
are much higher than k and k
AH` ÈÈÈ A ] H`
h
~h
\ k ] k [H`]
a
(AXIX)
(AXX)
kh
11
a
~a
AH` ÈÈÈ B ] H`
a
\ [ k [H`]
12
~a
k~h
B ] H` ÈÈÈ AH`
a
\ k
(AXXI)
(AXXII)
(AXXIII)
21
h
Consider now the system when completely equilibrated. If a
pH jump is carried out, a new equilibrium will be reached,
a
\ k [H`]
22
~h
k \ k ] k [H`]
AH` , A
B
. Immediately after the pH jump (AH`, A, B)
1
a
~a
eq
eq eq
the system is out of this equilibrium as follows:
which is the kinetic expression for the proton transfer process
[AH`] \ [AH`] ] x
(AI)
(AII)
([k [H`])k
eq
~a
h
k \ k [H`] [
2
~h
~h
k
k ] k [H`]
~a
[B] \ [B] [ y
a
eq
k
[H`]k ] k [H`]k [H`] ] k [H`]k
[A] \ [A] [ z
(AIII)
a
~h
~a
~a
~a
h
\
\
eq
k ] k [H`]
a
dx
dt
[
\ (k ] k )([AH`] ] x)
eq
[H`]k
k
[H`](k ] k [H`])
a
h
~a
h
~h
a
~a
~a
]
k ] k [H`]
k ] k [H`]
a
~a
a
[ k [H`]([A] [ y) [ k [H`]([B] [ z) (AIV)
~a eq ~h eq
(AXXIV)
(AXXV)
(AXXVI)
dx
dt
[
\ (k [ k )[AH`]
eq
k
[H`]k
a
h
~a
k ] k [H`]
~a
h
k \
] k [H`]
2
~h
a
[k [H`][A] [ k [H`][B]
~a eq ~h
eq
k \ ak ] k [H`]
2
h
~h
] (k ] k )x ] k [H`]y ] k [H`]z
(AV)
a
h
~a ~h
with
According to the new equilibrium condition
(k ] k )[AH`] [ k [H`][A] [ k [H`][B] \ 0
[H`]
a \
(AXXVII)
[H`] ] K
a
h
eq
~a
eq
~h
eq
a
(AVI)
this being the solution for the second kinetic process.
Let us assume that, as in the case of Malvin, the species B is
dx
dt
in fast equilibrium with C . In this case a new equilibrium
[
[
\ (k ] k )x ] k [H`]y ] k [H`]z
~a ~h
(AVII)
cis
a
h
described by eqn. (A5) must be added to eqn. (A1)È(A4)
dx
dt
Kt
\ (k ] k )x ] k [H`](x [ z) ] k [H`]z
~a ~h
B E8F C
(A5)
a
h
cis
Inspection of this new set of equations shows that only eqn.
(A4) is a†ected by the new condition of equilibrium. Because
[B] ] [C ] is equal to [B](1 ] K ) the Ðnal solution is
\ (k ] k ] k [H`])x ] (k [H`] [ k [H`])z
a
h
~a ~h ~a
(AVII)
cis
t
obtained
d[B] dz
dt
\
\ k ([AH`] ] x) [ k [H`]([B] [ z)
eq ~h eq
dt
k \ ak ] (1 ] K )k [H`]
(AXXVIII)
h
2
h
t ~h
Appendix 2
\ k [AH`] [ k [H`][B] ] k ] x ] k [H`]z
eq ~h eq ~h
h
h
In this case we present the integration of the di†erential equa-
tions when isomerization is the slowest process. The relax-
ation treatment gives identical results.
\ k x ] k [H`]z
(AIX)
h
~h
at this point we can follow the usual resolution of the di†eren-
tial equations (or alternatively integrate).
Keq
dx
dt
B ] A ] AH` E8F C
Ki
(B1)
(B2)
[
\ a x ] a
z
(AX)
cis
11
12
C
E8F C
dz
dt
cis
trans
\ a x ] a
z
(AXI)
K~i
12
22
C \ [AH`] ] [A] ] [B] ] [C ] ] [C
]
0
cis
trans
a
\ k ] k ] k [H`]
(AXII)
(AXIII)
(AXIV)
(AXV)
(K\ ] [H`])
11
a
h
~a
a
\
[C ] ] [C
cis
]
(BI)
a
\ k [H`] [ k [H`]
trans
K K
12
~h ~a
h
t
a
\ k
with
21
h
a
\ k [H`]
K\ \ K ] K (1 ] K )
(BII)
22
~h
a
a
h
t
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
2115

View Article Online
6
7
8
9
R. A. McClelland, D. B. Devine and P. E. Sorensen, J. Am. Chem.
Soc., 1985, 107, 5459.
derivation of eqn. (BI)
d[C
R. Brouillard, B. D. Delaporet and J. E. Dubois, J. Am. Chem.
Soc., 1978, 100, 6202.
]
K K
K\ ] [H`]
d[C
]
cis
h
t
trans
dt
[
\
(BIII)
(BIV)
(BV)
dt
R. Brouillard, B. Delaporte, J. M. E. H. Chahine and J. E.
Dubois, J. Chim. Phys., 1979, 76, 273.
R. Brouillard and J. Lang, Can. J. Chem., 1990, 68, 755.
a
from eqn. (B2)
10 F. Pina, A. Roque, M. J. Melo, M. Maestri, L. Belladelli and V.
Balzani, Chem. Eur. J., in press.
d[C
]
trans
\ k [C ] [ k [C
cis ~i trans
]
i
dt
11 C. Michaelidis and R. Wizinger, Helv. Chim. Acta, 1951, 34, 1761.
12 F. Pina, L. Benedito, M. J. Melo, A. J. Parola and M. A. Ber-
nardo, J. Chem. Soc., Faraday T rans., 1996, 92, 1693.
13 The absorbance at very low pH values is always slightly larger
than the value predicted by eqn. (IV). This is probably due to the
formation of an ion pair between chloride and Ñavylium cation.23
14 H. Santos, D. L. Turner, J. C. Lima, P. Figueiredo, F. Pina and
A. L. Macanita, Phytochemistry, 1993, 33, 1227.
15 R. Brouillard, in Anthocyanins as Food Colors, ed. P. Markakis,
Academic Press, New York, 1982, p. 1.
16 R. Brouillard and J. E. Dubois, J. Am. Chem. Soc., 1977, 99, 1359.
17 R. Brouillard and B. Delaporte, J. Am. Chem. Soc., 1977, 99,
8461.
using eqn. (BI) in eqn. (BIV)
d[C
trans
]
G
K\ ] [H`]
H
a
\ k ] k
[C ] [ k
C
i
~i
cis
~i 0
dt
K K
h
t
by substitution of eqn. (BIII) into eqn. (BV)
d[C
]
G
K K
K\ ] [H`]
H
cis
h
t
[
\
k ] k [C ] [ k
C
(BVI)
i
~i
cis
~i 0
dt
a
This is again a typical reversible Ðrst-order reaction whose
integration gives
18 L. G. Arnaut and S. J. Formosinho, J. Photochem. Photobiol., A,
1993, 75, 21.
A
[C ]0 [ [C ]eB A K K
B
19 In their Ðrst work Brouillard and Dubois16 considered [A]
@
cis
cis
h t
eq
ln
\
k ] k
t
(BVI)
[H`] and found a linear relation between k and [H`]. In spite
of the low equilibrium value of quinoidal base, in the case of
i
~i
[C ] [ [C ]e
K\ ] [H`]
1
cis
cis
a
Malvin, this approximation is too drastic. In e†ect, for a total
and the rate constant for the slowest process is given by
concentration of Malvin 1.2 ] 10~3 M used by these authors
[A] is ca. 6 ] 10~5 M for pH 54. In a second study on Oenin,
K K
eq
h
t
k \
k ] k
(BVII)
Brouillard and Delaport17 report exactly eqn. (VI). However,
3
i
~i
K\ ] [H`]
these results were compared with those of Malvin which were
a
calculated neglecting [A]
.
eq
20 L. Jurd, T etrahedron, 1969, 25, 2367.
References
21 F. Pina, M. J. Melo, M. Maestri, R. Ballardini and V. Balzani, J.
Am. Chem. Soc., 1997, 119, 5556.
1
2
D. D. Pratt and R. Robinson, J. Chem. Soc., 1922, 1577.
22 F. Pina, M. J. Melo, R. Ballardini, L. Flamigni and M. Maestri,
New J. Chem., 1997, 21, 969.
R. Willstater and J. L. Everest, Justus L iebigs Ann. Chem., 1913,
401.
23 F. Pina and A. Roque, J. Photochem. Photobiol., 1998, 114, 59.
24 In Malvin the di†erence between the molar fraction distribution
of the second step and the Ðnal equilibration is small and thus
the second step was omitted in order to facilitate the perception
of the Ðgure.
3
(a) A. Robertson and R. Robinson, J. Chem. Soc., 1926, 1951; (b)
F. M. Irvine and R. Robinson, J. Chem. Soc., 1927, 2086; (c) G.
M. Robinson, J. Biochem., 1931, 25, 1687.
R. A. McClelland and S. Gedge, J. Am. Chem. Soc., 1980, 102,
5838.
R. A. McClelland and G. H. McGall, J. Org. Chem., 1982, 47,
3730.
4
5
Paper 8/02602E; Received 6th March, 1998
2116
J. Chem. Soc., Faraday T rans., 1998, V ol. 94