A Concave Fluorescent Sensor for Anions Based on 6-Methoxy-1-methylquinolinium

Article abstract of DOI:10.1002/chem.200305338

The ligand 2, in which three fluorogenic 6-methoxy-1-methylquinolinium fragments are appended to a mesityl platform, in MeCN forms 1:1 adducts with halides and other inorganic anions. ¹H NMR studies and molecular modelling indicate that 2 provides a cavity for anion inclusion and establishes electrostatic interactions with the guest. Anion inclusion induces quenching of the fluorogenic fragments with an efficiency decreasing along the series Br ^- ? I^- > NCS^- ? Cl^- > NO₃^- > > HSO₄^-. The fluorimetric response of 2 to anions is orders of magnitude more sensitive than that of just 6-methoxy-1-methylquinolinium, ligand 1.

Full text of DOI:10.1002/chem.200305338

FULL PAPER
A Concave Fluorescent Sensor for Anions Based on 6-Methoxy-1-
methylquinolinium
Valeria Amendola, Luigi Fabbrizzi,* and Enrico Monzani[a]
Abstract: The ligand 2, in which three
fluorogenic 6-methoxy-1-methylquino-
linium fragments are appended to a
mesityl platform, in MeCN forms 1:1
adducts with halides and other inorgan-
ic anions. H NMR studies and molecu-
lar modelling indicate that 2 provides a
cavity for anion inclusion and estab-
lishes electrostatic interactions with the
guest. Anion inclusion induces quench-
ing of the fluorogenic fragments with
an efficiency decreasing along the
À
series BrÀ @IÀ >NCSÀ @ClÀ >NO3
>
HSO4À. The fluorimetric response of 2
to anions is orders of magnitude more
sensitive than that of just 6-methoxy-1-
methylquinolinium, ligand 1.
Keywords:
fluorescence
anions
spectroscopy
¥
¥
1
molecular recognition ¥ receptors ¥
sensors
Introduction
sion band develops at 440 nm. This band is quenched more
or less completely on addition of anions, depending upon
the pertinent KSV value.
A variety of fluorophores exist that do not interact firmly
with the desired substrate, but give rise to occasional colli-
sions, which may lead to the quenching of the fluorophore
emission. This behaviour is typically regulated by the Stern
Volmer equation: Io/I=1 + kqto[A]=1 + KSV[A], whose
plot makes it possible to determine quantitatively, over a
wide range, the concentration of analyte A from the mea-
sured fluorescence intensity I.[1]
A classical fluorophore typically used in Stern Volmer
titrations is 6-methoxy-1-methylquinolinium (1), which,
being positively charged, is suitable for interaction with
anions, and is currently employed for the detection of ha-
lides (in particular chloride) in various media.[2,3] On excita-
tion of a solution of 1 at l=330 nm, a rather intense emis-
Systems operating with a Stern Volmer behaviour, even if
useful in particular circumstances, have to be considered
rather primitive sensing devices for analytes, whether charg-
ed or not. For several years, interest has developed for the
design of more sophisticated molecular systems (receptors,
R) capable of strongly interacting with the envisaged ana-
lyte (A), giving rise to an adduct with 1:1 stoichiometry,
characterised by a definite association constant Kass (related
to the equilibrium:R + AÐ[R¥A]). Such receptors must
contain multiple interaction sites for the analyte, symmetri-
cally positioned within their framework.[4,5] If the analyte is
an anion, these sites could be positively charged groups. Fol-
lowing this, we synthesised system 2, in which three 6-meth-
oxy-1-methylquinolinium fragments have been implanted on
a mesityl platform. The 1,3,5-functionalised benzene scaffold
has been frequently used in order to build up a variety of re-
ceptors.[6,7] In particular, system 2 possesses three symmetri-
cally placed positive charges and, as suggested by molecular
modelling, may generate a cavity suitable for anion inclu-
sion.
It will be shown that 2 behaves as an efficient receptor for
anions, giving rise to 1:1 adducts, whose logKass values, de-
termined through spectrophotometric and 1H NMR titra-
tions in MeCN, vary from 4.55 (for ClÀ) to 3.40 (for NCSÀ).
Most interestingly, the spectrofluorimetric response of 2 is
remarkably enhanced relative to that of 6-methoxy-1-meth-
ylquinolinium alone. In particular, I0/I versus [anion] plots
of a much higher slope (and sensitivity) are produced, which
fit Stern Volmer type equations containing both KSV and
Kass parameters.
[a] Dr. V. Amendola, Prof. L. Fabbrizzi, Dr. E. Monzani
Dipartimento di Chimica Generale
Universit‡ di Pavia
via Taramelli 12, 27100 Pavia (Italy)
Fax :( +39)0382-528544
E-mail:luigi.fabbrizzi@unipv.it
76
¹ 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
DOI: 10.1002/chem.200305338
Chem. Eur. J. 2004, 10, 76 82

76 82
at 344 nm on progressive addition of BrÀ (as equivalents).
This titration profile clearly indicates the formation of an
adduct of 1:1 stoichiometry. Nonlinear least-squares treat-
ment of spectral data (using the HYPERQUAD program)[8]
gave an association constant Kass of 4.42Æ0.04 log units for
the equilibrium given in Equation (1):
2þ
3þ þ BrÀ Ð ½2 Á BrŠ
ð1Þ
2
Spectral changes and titration profiles indicating the for-
mation of 1:1 adducts were obtained for a variety of anions:
corresponding values of logKass are reported in Table 1. Ti-
tration with perchlorate and triflate anions did not induce
any spectral changes indicating no or extremely weak inter-
action with 23+
.
Table 1 indicates that the investigated receptor displays
the highest affinity towards chloride. Looking at the three
studied spherical anions (halides), the affinity decreases
Table 1. Association constants Kass between 2 and anions in MeCN.
Results and Discussion
[a]
[b]
Anion
2/logKass
2/logKass
ClÀ
BrÀ
IÀ
4.55Æ0.03
4.42Æ0.04
3.48Æ0.01
3.91Æ0.03
3.79Æ0.02
3.40Æ0.02
<2
4.64Æ0.06
4.28Æ0.05
Spectrophotometric determination of the association con-
stants with anions:Reversible binding of a given anion X
À
À
with the receptor 2 was investigated in MeCN , at 258C, by
means of spectrophotometric titration experiments. The 6-
methoxy-1-methylquinolinium fragment possesses push-pull
features that give rise to a charge-transfer transition in the
UV region. It is expected that the electrostatic interaction
of an anion with the positively charged nitrogen atoms
alters the dipole, thus modifying the absorption spectrum.
Indeed, this is observed with most of the investigated
anions. As an example, Figure 1 illustrates the family of
spectra obtained when a solution of 2 in MeCN (4î10À4 m)
is titrated with a standard solution of benzyltributylammoni-
um bromide. The presence of two distinct isosbestic points
indicates that only two species are present at equilibrium.
The inset in Figure 1 shows the increase of the absorbance
NO3
À
HSO4
NCSÀ
À
ClO4
CF3SO3
À
<2
[a] Constants were calculated by nonlinear least-squares treatment of
spectrophotometric data at 258C in MeCN. [b] Constants were calculated
by nonlinear least-squares treatment of 1H NMR titration data at 258C
in CD3CN.
along the series ClÀ >BrÀ >IÀ, that is, with the charge densi-
ty on the substrate, a trend that demonstrates the dominat-
ing role of the electrostatic interaction. Among polyatomic
anions, NO3 and HSO4À, which display similar Kass values,
À
offer three oxygen atoms with partially negative charges
that may fit with the array of the three positive charges of
the quinolinium groups of the receptor. The lowest affinity
is observed with the rodlike triatomic anion NCSÀ.
It has to be noted that titration of 6-methoxy-1-methylqui-
nolinium (1) with the same family of anions did not induce
any spectral modification, even after the addition of a large
excess of anion, indicating no formation of an adduct or ion-
pair. Thus, it appears that the presence of three pre-posi-
tioned quinolinium groups is essential for the formation of a
solution stable complex.
1H NMR titration experiments:For chloride and bromide
anions, titration experiments were carried out in CD3CN at
1
258C and followed by H NMR analysis. A standard solu-
tion of the benzyltributylammonium salt (chloride or bro-
mide) in CD3CN was progressively added to a solution of 2
in CD3CN.
Some representative spectra collected during the titration
with chloride are reported in Figure 2. The most remarkable
shifts are assigned to the H3 and H4 atoms. In particular, on
Figure 1. UV/Vis titration of 2 (4î10À4 m) with a standard solution of
BrÀ, in MeCN; the addition of the anion makes the absorption of the
bands of the receptor increase (in particular at 340 nm). Inset:titration
profile (molar absorbance of 2 at 340 nm vs equivalents of bromide).
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L. Fabbrizzi et al.
FULL PAPER
Figure 3. Molecular model of the [2¥Cl]2+ adduct obtained by the
AMBER program.
Figure 2. 1H NMR spectra of the solution containing 2 and a) 0, b) 0.3,
c) 0.6, d) 0.9 and e) 2.5 equivalents of chloride (258C, CD3CN).
Figure 4. Titration profile of 2 with a standard solution of chloride (varia-
tion of the chemical shift of H3 vs equivalents of ClÀ).
addition of ClÀ, the H3 signal undergoes a downfield shift
of about 1.5 ppm (Dd), reaching a limiting value of d=
10.15 ppm. The downfield shift of H4 is a more moderate
value of 0.2 ppm. These features can be accounted for by
considering that, on titration, 2 folds its 6-methoxy-1-meth-
ylquinolinium arms to give a cavity for anion inclusion. In
these circumstances, each H3 atom feels an electrostatic
field of increased positive charge, which induces the down-
field shift. Such an effect is lower for H4 atoms, which are
farther from the positive electrical charges. These results
point towards a stereochemical arrangement in which 2 has
adopted the shape of a bowl, containing the chloride ion.
Such a hypothesis is supported by molecular modelling. In
particular, molecular mechanics calculations, using the
AMBER package,[9] produced the model structure shown in
Figure 3:in the model, the receptor is arranged in such a
way to generate a well-defined cavity and the chloride ion
stays inside the bowl, close to the positively charged nitro-
gen atoms.
Figure 4 reports the variation of the chemical shift of H3
versus the equivalents of ClÀ. The titration profile confirms
the formation of a 1:1 adduct, whose Kass, calculated through
least-squares nonlinear fitting, is 4.64Æ0.06 log units. This is
in excellent agreement with the value calculated from the
spectrophotometric titration.
Similar behaviour was observed on titration of 2 with a
benzyltributylammonium bromide standard solution. The
distinct downfield shift of the H3 signal was also observed,
but its limiting value was lower than that found for chloride:
d=9.91 ppm. This may be due to the fact that the larger
bromide ion induces the formation of a more open cavity, in
which the quinolinium centres are farther from each other.
Again, the H3 chemical shift versus equivalents of bromide
profile indicates the formation of a complex of 1:1 stoichi-
ometry, with logKass =4.28Æ0.05, in good agreement with
the value obtained from spectrophotometric titrations. It has
to be noted that trifurcated receptors based on the mesityl
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Chem. Eur. J. 2004, 10, 76 82

A Fluorescent Sensor for Anions
76 82
core, whose side-chains contain the pyridinium fragment
and a variety of appendages, have been investigated by H
rophore, the sequence parallels the reducing tendencies of
the halide ion. In this context, it has to be noted that a rela-
tively high value of KSV is observed also for the NCSÀ ion,
which displays distinct reducing tendencies ((NCS/NCSÀ)
potential: À1.50 V vs NHE).[12]
1
NMR titrations and a similar sequence of association con-
stants was found with halide ions.[11]
Spectrofluorimetric studies:As far as the fluorimetric re-
sponse is concerned, it seemed initially convenient to inves-
tigate the quenching of 1 when titrated by inorganic anions
in MeCN.
Figure 5 reports the I0/I values versus the concentration of
the added anion (I0:fluorescence intensity before anion ad-
dition; I:fluorescence intensity during the addition). The
Stern Volmer [Eq. (2)] equation fits the data well:
In the case of 2, I0/I versus [anion] plots do not fit the
simple Stern Volmer equation [Eq. (2)]. Because the fluoro-
phore (receptor) and quencher (anion) form stable 1:1 ad-
ducts, more than just occasional collisions must be occurring.
Under these circumstances, we can consider two different
cases.
First we will consider the case in which the the 1:1 adduct
is not fluorescent at all (i.e., the emission of the receptor
fluorophore has been completely quenched by the included
anion). In this case, we can make use of Equation (3):[13]
I0=I ¼ 1 þ kqt0½QŠ ¼ 1 þ KSV½QŠ
ð2Þ
I0=I ¼ ð1 þ KSV½QŠÞð1 þ Kass½QŠÞ
ð3Þ
This parabolic behaviour is shown by the anions IÀ, NCSÀ
and BrÀ (see Figure 6).
Figure 5. Stern Volmer profiles obtained from the spectrofluorimetric
titrations of 1 with different anions.
as indicated by the least-squares straight lines in the figure.
Values of the Stern Volmer constants KSV obtained from the
fitting are reported in Table 2.
Figure 6. I0/I profiles for the titrations of 2 with BrÀ, IÀ and NCSÀ.
It is observed that among halides KSV decreases along the
series IÀ >BrÀ >ClÀ. This behaviour may be generically as-
cribed to the ™heavy atom effect∫.[10] However, if the fluo-
rescence-quenching is associated with the occurrence of an
electron-transfer process from the anion to the excited fluo-
Pertinent KSV and Kass values, obtained through nonlinear
fitting on Equation (3), are reported in Table 2. Kass values
obtained from spectrofluorimetric data are in good agree-
ment with those obtained through spectrophotometric titra-
tion experiments and reported in Table 1. Quite surprisingly,
the BrÀ ion shows a linear,
rather than a parabolic curve:
this is due to the fact that, at
the investigated concentration
of quencher, 1 + KSV[Q]ꢀ1.
As a consequence, the slope of
the linear plot should corre-
spond to the association con-
stant Kass. The agreement is not
perfect, but satisfactory:log Kass
fluorimetric:4.55 Æ0.05, spec-
Table 2. For compound 1 the Stern Volmer constants KSV are calculated with different anions, by the fitting of
the I0/I versus [anion] data with the Stern Volmer Equation (2).
[a]
[a]
[b]
[b]
Anion
ClÀ
1/logKSV
2/logKSV
2/logKass
2/logKSV
2/logKass
1
2.99Æ0.03
2.86Æ0.02
1.27Æ0.02
3.04Æ0.04
3.16Æ0.04
3.16Æ0.03
3.16Æ0.02
2.26Æ0.06
2.83Æ0.06
4.60Æ0.04
3.87Æ0.01
3.78Æ0.06[c]
0.71Æ0.01
0.31Æ0.01
0.98Æ0.04
À
NO3
À
HSO4
BrÀ
4.55Æ0.05
IÀ
4.09Æ0.03
3.91Æ0.05
3.48Æ0.01[c]
NCSÀ
3.40Æ0.02[c]
[a] Equation (3) was applied. [b] Equation (4) was applied; Equation (4) also contains the parameter 1, whose
refined values are obtained from the fitting. [c] In some cases, the spectrophotometrically determined Kass
values were employed in the fitting as fixed parameters.
trophotometric:4.42
Æ0.04;
NMR:4.28 Æ0.05). Therefore,
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L. Fabbrizzi et al.
FULL PAPER
we are not able to determine the KSV value for the BrÀ/2 in-
teraction.
The second case we consider is that the 1:1 adduct itself is
fluorescent (i.e., the emission of the receptor fluorophore
has not been completely quenched by the included anion).
If we define 1 as the residual fluorescence of the 1:1 adduct,
we can write Equation (4) (see Appendix for its derivation):
I0=I ¼ ð1 þ Kass½QŠÞð1 þ KSV½QŠÞ=ð1 þ 1Kass½QŠÞ
ð4Þ
This situation is observed in the case of ClÀ.
Figure 7 displays the I0/I versus [ClÀ] data, which fit Equa-
tion (4) very satisfactorily. Corresponding values of KSV and
Kass are reported in Table 2. The Kass values are in good
Figure 8. Profiles of I0/I versus [anion] for both 1 (open symbols) and 2
(filled symbols) are reported. The same symbol shape is used to indicate
the titration profile of 1 and 2 with the same anion (circles:Br À; squares:
IÀ; triangles up:Cl À; triangles down:HSO À; diamonds:NO À).
4
3
Conclusion
Quenching of simple fluorophores can be used for the deter-
mination of a variety of analytes, in particular anions, by
benefitting from the Stern Volmer equation, which corre-
lates the fluorescence intensity to the concentration of the
quenching analyte. We have demonstrated that organisation
of the fluorogenic fragments in an appropriate geometrical
array may generate a receptor capable of firmly interacting
with the anionic subtrate, giving rise to an inclusion com-
plex. This new situation astonishingly enhances the fluori-
metric response, increasing the sensitivity by several orders
of magnitude. Hence, in principle, selective or specific fluo-
rophores can be designed for any desired anionic guest by
choosing appropriate combinations of Kass and KSV. High
values of Kass can be obtained by synthesising receptors that
display selective interaction with the envisaged anion, possi-
bly introducing some rigidity in the molecular framework
and modulating shape and size of the cavity. On the other
hand, suitable values of KSV can derive from the choice of
fluorogenic fragments to be incorporated in the receptor. In
this context, tens of fluorophores are waiting on the shelf
(or in the chemical catalogues) to be chosen. In the very
end, the design of a fluorescent receptor, characterised by
convenient values of Kass and KSV, will lead to the achieve-
ment of analytically useful and especially sensitive I0/I
versus [anion] plots of the type illustrated in this work.
Figure 7. I0/I versus [ClÀ] profile for the spectrofluorimetric titration of 2
with chloride. The curve was fitted by Equation (4) and the pertinent pa-
rameters are reported in Table 2.
agreement with those reported in Table 1. Notice that the
calculated residual fluorescence 1 is 0.7. This means that the
ClÀ ion included in the cavity is able to quench only 30% of
the overall fluorescence of 2.
À
A similar behaviour is displayed by NO3 and HSO4À; for
both the anions, the formation of the adduct with 2 causes
just partial quenching of the emission intensity. The fitting
of the titration data by Equation (4) leads to the calculation
of the residual fluorescence intensity 1 and both KSV and
Kass. The calculated results are reported in Table 2.
The general behaviour is summarised in Figure 8, where
I0/I values versus [anion] are reported for both 1 and 2 and
for all the investigated anions. The following features have
to be remarked:1) compound 2 is much more anion sensi-
tive than 1; this is a result of the combination of KSV, gener-
ally higher for 2 than for 1, and of Kass, which allows a per-
manent contact between fluorophore and quencher; 2) com-
pound 2 displays the highest response to BrÀ, as a conse-
quence of the especially high value of Kass. The ClÀ ion
shows an even higher association constant, but inside the in-
clusion complex it quenches only 30% of the fluorescence
of 2. Besides, chloride presents a relatively low value of KSV,
not far from the one observed for 1.
Experimental Section
General procedures and materials:All reagents were purchased from Al-
drich/Fluka and used without further purification. Spectrophotometric
and spetrofluorimetric grade solvents were used for spectroscopic meas-
urements.
UV/Vis spectra were recorded on a Varian CARY 100 spectrophotome-
ter, with a quartz cuvette (path length:0.1 cm); spectrofluorimetric meas-
urements were carried out on a Perkin Elmer LS-50 luminescence spec-
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Chem. Eur. J. 2004, 10, 76 82

A Fluorescent Sensor for Anions
76 82
trometer, using quartz sample tubes (path length:1 cm). NMR spectra
were recorded on a Bruker Avance 400 spectrometer, operating at 9.37 T.
Spectrophotometric titrations were performed at 258C on 5î10À4 m solu-
tions of the ligand (1 or 2) in MeCN. Aliquotes of a fresh R4NX (R=
alkyl) standard solution were added and the UV/Vis spectra of the
sample were recorded. All spectrophotometric titration curves were
fitted with the HYPERQUAD program.[8] Spectrofluorimetric titrations
were carried out by adding a standard solution of the anion to a 2î
10À6 m solution of the ligand (the experiments were also repeated at
higher concentration, 10À5 m). In each spectrofluorimetric titration, the
excitation of the sample was performed at the wavelength value at which
only negligible variations of absorbance occurred.
1H NMR titrations were carried out as described before, but using
CD3CN as the solvent and working with high concentrations of the recep-
tor (>7î10À4 m).
Synthesis of 1:MeI (0.12 mL, 1.9 mmol) was added to a solution of 6-
methoxyquinoline (0.3 g, 1.88 mmol) in dry CHCl3 (5 mL). The mixture
was then heated at reflux for 1 h, under a dinitrogen atmosphere. A
yellow solid (1¥IÀ) was collected by filtration and washed with several
portions of Et2O. The crude product was dissolved in hot water and treat-
Scheme 1.
al to their observed lifetime in the presence of quencher [Eqs. (3a) and
(4a)]:
À
ed with an aqueous saturated solution of NH4PF6. 1¥PF6 precipitated as
1
a white solid (0.41 g, 77%). H NMR (400 MHz, CD3OD, TMS): d=9.15
t0
(d, 1H, arom.), 9.08 (d, 1H, arom.), 8.42 (d, 1H, arom.), 8.01 (dd, 1H,
arom.), 7.90 (dd, 1H, arom.), 7.80 (d, 1H, arom.), 4.68 (s, 3H, N+ÀCH3),
4.10 ppm (s, 3H, OÀCH3); elemental analysis calcd (%) for C11H12NOPF6
(319.1):C 41.40, H 3.79, N 4.38; found:C 41.05, H 3.90, N 4.23.
IfðMÞ
/
½MŠ
ð3aÞ
ð4aÞ
1 þ KSV½QŠ
t00
IfðMQÞ
/
½MQŠ
1 þ K0SV½QŠ
Synthesis of 2:A solution of 6-methoxyquinoline (0.3 g, 1.9 mmol) in ace-
tonitrile (20 mL) was added dropwise to a refluxing solution of 2,4,6-tris-
(bromomethyl)mesitylene (0.2 g, 0.5 mmol) in acetonitrile (40 mL). The
reaction was followed by TLC (silica gel, CH2Cl2/MeOH 8:0.5; Rf =0.1).
After 24 hrs at reflux, the solvent was removed by rotary evaporation
[MT] is the total concentration of the fluorescent receptor 2 (i.e., [MT]=
[M] + [MQ]). From this, I0, the steady-state fluorescence in the absence
of Q, can be obtained from Equation (3a) considering that [M]=[MT]
[Eq. (5a)]:
and the crude product was washed with CH3CN, then with Et2O and pu-
IfðMÞ / t0½MTŠ
ð5 aÞ
À
rified by recrystallisation. Anion exchange yielded 0.35 g (65%) 2¥3PF6
.
1H NMR (400 MHz, CD3OD, TMS): d=9.11 (d, 1H, arom.), 8.77 (d, 1H,
arom.), 8.75 (d, 1H, arom.), 8.08 (dd, 1H, arom.), 8.01 (dd, 1H, arom.),
7.88 (d, 1H, arom.), 6.40 (s, 2H, N+ÀCH2), 4.10 (s, 3H, OÀCH3),
2.28 ppm (s, 3H, ArÀCH3); elemental analysis calcd (%) for
C42H42N3O3P3F18 (1071.4):C 47.08, H 3.95, N 3.92; found:C 46.80, H
4.15, N 3.73.
In the presence of Q the global fluorescence intensity (If) is the sum of
that of species and MQ; thus, from Equations (3a) (5a), Equa-
tion (6a) can be obtained:
M
I
fðMÞ þ IfðMQÞ
If
1
½MŠ
t00=t0
½MQŠ
¼
¼
þ
ð6 aÞ
1 þ KSV½QŠ ½MTŠ 1 þ K0SV½QŠ ½MTŠ
I0
I0
The ratio t00/t0 can be indicated as the relative fluorescence intensity of
species MQ and M, namely 1. If M and MQ are at equilibrium, their con-
centration is ruled by the equilibrium constant (Kass), [Q] and [MT]. The
total Q concentration ([QT]) is:[Q T]=[Q] + [MQ]. Treating the fraction
of Q bound to M as negligible with respect to free Q ([MQ]![Q]), that
is, considering a low affinity equilibrium, the mass balance gives rise to
Equations (6b) and (6c):
Appendix
Derivation of the equations for the fluorescence intensity in the presence
of dynamic quenchingand partial static quenching :The here reported
approach considers the possibility for the molecule M to form, at the
ground state, a 1:1 complex (MQ) with the non-fluorescent species Q.
Both M and MQ are fluorescent and both excited states (M* and MQ*)
undergo dynamic quenching by species Q, according to Scheme 1, in
which (M*¥¥¥Q) and (MQ*¥¥¥¥Q) are the pair between Q and M* and
MQ* responsible for the dynamic quenching.
½MŠ
1
ð6 bÞ
ð6 cÞ
¼
½MTŠ 1 þ Kass½QŠ
½MQŠ
½MTŠ
Kass½QŠ
The decay of species M* and MQ* are described by the Equations (1a)
and (2a):
¼
1 þ Kass½QŠ
ꢀ
ꢁ
These can be substituted into Equation (6a) to give Equation (7a):
*
d½M Š
1
t0
1 þ kQt0½QŠ
1 þ KSV½QŠ
*
*
*
¼ À
þ kQ½QŠ ½M Š ¼ À
½M Š ¼ À
½M Š
dt
t0
t0
ꢀ
ꢁ
If
I0
1
1
1Kass½QŠ
ð1 aÞ
¼
þ
ð7 aÞ
1 þ Kass½QŠ 1 þ KSV½QŠ 1 þ K0SV½QŠ
ꢀ
ꢁ
1 þ k0Qt00½QŠ
1 þ K0SV½QŠ
*
d½MQ Š
1
þ k0Q½QŠ ½MQ Š ¼ À
½MQ Š ¼ À
½MQ Š
*
*
*
¼ À
t00
t00
t00
Taking the I0/If ratio, as in the Stern Volmer relation, and assuming that
the Stern Volmer constants for M and for MQ do not differ significantly
(KSV ꢀK0SV) Equation (7a) can be reduced to Equation (8a):
dt
ð2 aÞ
in which t0 and t00, kQ and kQ0 , KSV (=kQ ît0) and KS0 V (=k0Q ît00 ) are the
excited state lifetimes, the dynamic quenching rate constants and the
Stern Volmer constants for the species M and MQ, respectively. Both
equations were formulated by applying the Stern Volmer approach[1] and
considering the quenching rate constants as time-independent. The
I0 ð1 þ Kass½QŠÞð1 þ KSV½QŠÞ
¼
ð8 aÞ
If
1 þ 1Kass½QŠ
Within the approximation indicated (i.e., [MQ]![Q]), Equation (8a) re-
produces the fluorescence pattern reported in Scheme 1. It must be
noted that when species MQ is not fluorescent (1=0), Equation (8a) re-
steady-state fluorescence intensity of species M (If(M)) and MQ (If(MQ)
are directly proportional to their concentration and inversely proportion-
)
81
Chem. Eur. J. 2004, 10, 76 82
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¹ 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

L. Fabbrizzi et al.
FULL PAPER
duces to the simpler equation valid for the coupled static and dynamic
quenching.[1]
Acknowledgement
The financial support of the European Union (RTN Contract HPRN-CT-
2000-00029) and the Italian Ministry of University and Research (PRIN -
Dispositivi Supramolecolari) is gratefully acknowledged.
This approach can be extended to the case in which the equilibrium con-
stant (Kass) is so high (high affinity limit) that the fraction of Q bound to
M cannot be neglected in the mass balance. In this situation the relation
[Q]=[QT]À[MQ] must be explicitly considered in both dynamic quench-
ing and ground state equilibrium. Applying the mass balance to M and
on Q and considering the equilibrium constant Kass, the concentrations at
equilibrium are given by the Equations (9a) (12a):
[1] B. Valeur, Molecular Fluorescence, Principles andApplications
Wiley-VCH, Weinheim, 2002.
,
Kassð½MTŠ þ ½QTŠÞ þ 1ÀR
[2] S. Jayaraman, A. S. Verkman, Biophys. Chem. 2000, 85, 49.
[3] C. D. Geddes, K. Apperson, J. Karolin, D. S. Birch, Anal. Biochem.
2001, 293, 60.
ð9 aÞ
½MQŠ ¼
2Kass
Kassð½MTŠÀ½QTŠÞÀ1 þ R
2Kass
[4] F. P. Schmidtchen, M. Berger, Chem. Rev. 1997, 97, 1609.
[5] A. Bianchi, K. Bowman-James, E. GarcÌa-EspaÊa, Supramolecular
Chemistry of Anions, Wiley-VCH, New-York, 1997.
[6] S. L. Wiskur, H. Ait-Haddou, J. J. Lavigne, E. V. Anslyn, Acc. Chem.
Res. 2001, 34, 963.
[7] L. O. Abouderbala, W. J. Belcher, M. G. Boutelle, P. J. Cragg, J.
Dhaliwal, M. Fabre, J. W. Steed, D. R. Turner, K. J. Wallace, Chem.
Commun. 2002, 358.
[8] P. Gans, A. Sabatini, A. Vacca, Talanta 1996, 43, 1739.
[9] Hyperchem 6.0. Molecular Modeling System. Hypercube Inc.
[10] K. J. Wallace, W. J. Becher, D. R. Turner, K. F. Syed, J. W. Steed, J.
Am. Chem. Soc. 2003, 125, 9699.
[11] B. Valeur, Molecular Fluorescence, Principles andApplications
Wiley-VCH, Weinheim 2002, p. 73.
ð10 aÞ
½MŠ ¼
Kassð½MTŠ þ ½QTŠÞ þ 1ÀR
2Kass
ð11 aÞ
ð12 aÞ
½QŠ ¼ ½QTŠÀ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R ¼ K2assð½MTŠÀ½QTŠÞ þ 2Kassð½MTŠ þ ½QTŠÞ þ 1
2
The ratio I0/If can be obtained upon substitution of Equations (9a) (11a)
into Equation (6a) and assuming again that KSV ꢀK0SV [Eq. (13a)]:
I0
If
2Kass þ KSV½Kassð½QTŠÀ½MTŠÞÀ1 þ RŠ
ð13aÞ
¼ ½MTŠ
2Kass½MTŠ þ ð1À1Þ½Kassð½QTŠ þ ½MTŠÞ þ 1ÀRŠ
,
[12] H. Shizuka, M. Nakamura, and T. Morita, J. Phys. Chem. 1980, 84,
Equation (13a) differs from Equation (8a), because the shape of the I0/If
versus [QT] curve depends on the initial M concentration. However, it
should be noted that for Kass!0 or [MT]!0 Equation (13a) can be re-
duced to Equation (8a). Equation (13a) can also be applied when MQ is
not fluorescent, by simply using 1=0.
989.
[13] B. Valeur, Molecular Fluorescence, Principles andApplications
Wiley-VCH, Weinheim, 2002, p. 86.
,
Received:July 15, 2003 [F5338]
82
¹ 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Chem. Eur. J. 2004, 10, 76 82