On the Application of the Pseudophase Model to Excited State Processes: Quenching of Pyrene by the...

On the Application of thePseudophase Model toExcited State Processes:Quenching of Pyrene by theIodide Ion in β-Cyclodextrinand Micellar (SDS)SolutionsJOSE MARIA CARNERERO, FRANCISCO SANCHEZ, PILAR PEREZ-TEJEDA

Departamento de Quımica Fısica, Facultad de Quımica, Universidad de Sevilla, 41012 Sevilla, Spain

Received 27 February 2014; revised 18 June 2014; accepted 20 June 2014

DOI 10.1002/kin.20872Published online 27 August 2014 in Wiley Online Library (wileyonlinelibrary.com).

ABSTRACT: The pseudophase model, a two-state model, is based on the assumption of theexistence of an equilibrium between these two states (free and bound), which is not perturbed inthe case of a reactive event. This implies that the processes in which these two states participatemust be slow, in relation to the exchange processes between these states. This conditiondoes not hold in the case of very rapid photochemical quenching processes. However, forthese processes the pseudophase model is formally applicable. In this paper, a treatment thatquantitatively explains this formal applicability is presented. This treatment is checked throughthe study of the quenching of pyrene fluorescence by the iodide ion in solutions containingβ-cyclodextrin and sodium dodecyl sulfate (SDS) micelles. C© 2014 Wiley Periodicals, Inc. Int JChem Kinet 46: 597–605, 2014

Correspondence to: Pilar Perez-Tejeda; e-mail: [email protected] grant sponsor: Consejerıa de Educacion y Ciencia de la

Junta de Andalucıa.Contract grant number: FQM-03623.Supporting Information is available in the online issue at

www.wileyonlinelibrary.com.C© 2014 Wiley Periodicals, Inc.

INTRODUCTION

The pseudophase model of Menger and Portnoy [1]is a powerful tool for the rationalization of reactiv-ity under restricted geometry conditions, that is, un-der conditions in which one, at least, of the partici-pants is bound to some receptor. Although originallyproposed for unimolecular reactions in micellar solu-tions, the pseudophase model can be easily extended to

598 CARNERERO, SANCHEZ, AND PEREZ-TEJEDA

Rf M Rb

kf

P

kb

P

K

Scheme 1

bimolecular reactions and to the case of receptors dif-ferent from micelles, through simple modifications ofthe equations of the model that incorporate the pecu-liarities of each case [2,3]. In this way, the pseudophasemodel has been employed in the rationalization of ki-netic data both in the case of micellar solutions as in thecase of solutions containing cyclodextrins, polymers,dendrimers, etc. [2].

The success of the pseudophase model is due, atleast in part, to the simplicity of the ideas in which thismodel is based: A given reactant R, in the presence ofa receptor, M, is distributed in two states, free (Rf) andbound (Rb), which are at equilibrium (Scheme 1). Thisequilibrium is characterized by an equilibrium constantK.

If Rf and Rb participate in a reactive process (seeScheme 1), the equilibrium will be perturbed. How-ever, if the reaction is slow in relation to the exchangeprocesses between the two states of the reactants, theseexchange processes will restore the equilibrium. Underthese circumstances, the concentrations of Rf and Rb,referred to the total volume of the solution containingthem (and the receptor, M), are given by

[Rf] = 1

1 + K [M][R]; [Rb] = K [M]

1 + K [M][R] (1)

with [R] = [Rf]+[Rb], in such a way that the observedrate constant will be given by the following equation:

kobs ≡ −d[R]/dt[R]

= kf + kbK [M]

1 + K [M](2)

This equation (or some of its variants), as mentionedabove, holds in the presence of different kinds of re-ceptors for thermal processes [2].

For the case of photochemical reactions under re-stricted geometry conditions, many authors have beeninterested in these studies for several decades (see,e.g., [4–13]). In these studies, the authors addressedthe question of competition (coupling) between theexchange (free ↔ bound) of fluorophore and the pho-tophysical (or photochemical) processes in which the

fluorophore participates. However, to the best of ourknowledge, these authors have not addressed the atten-tion about the question dealt with here. That is, to checkwhether the pseudophase model is met or not when ex-cited states are involved in reactions under restrictedgeometry conditions. Accordingly, here is presenteda study of the quenching of pyrene fluorescence bythe iodide ion in solutions containing β-cyclodextrin(β-CD) and sodium dodecyl sulfate (SDS) micelles.This quenching process has been selected because itis free of kinetic complications arising from diffusionprocesses, which is essential for Eq. (2) holds.

As a matter of fact, some authors have testedthat the equations of the pseudophase model holdfor excited state (quenching) processes [14–16]. Inthese works, the kinetics of the oxidation of the ex-cited state of the [Ru(bpy)3]2+complex by S2O8

2−

is studied in several micellar media, such us sodiumbis-2-ethylhexylsulfosuccinate [14], and polyoxyethy-lene(23) lauryl ether (Brij-35) [15], or in DNA andstarburst dendrimer (SB4.5G) [16]. In these studies, thevalues of the quenching rate constants were obtainedfrom the Stern–Volmer plots [17], and the binding con-stants (K in Scheme 1) were found through Eq. (2) withmodifications that incorporated the singularity of eachreceptor. However, in the present case the values ofthe binding constants obtained from the fitting of theStern–Volmer constants to an equation similar to Eq.(2) (see Eq. (16) ) depends on the quencher concentra-tion. To clarify this dependence, we present in thispaper a treatment [18] that quantitatively explainsthe formal applicability of the pseudophase model toquenching processes, and, in particular, the depen-dence of the binding constant on the quencher con-centrations for the pyrene excited state—the iodide ionreaction in solutions containing β-CD and SDS mi-celles as before was indicated.

It is important to realize that in the previous pa-per [18] a homogeneous concentration of the quencherwas supposed. Here, we have extended and applied(SDS micelles) the treatment for the case of an in-homogeneous quencher distribution, which supposesa novelty in relation to the previous work [18].Moreover, in this paper, the relationship between theapparent and true binding constants through the quan-tum yields of the free and bound states of the reac-tant is quantitatively checked (see the section Discus-sion). Finally, here, we also applied the treatment forthe case of a quencher that binds to the receptor, and,thus, it competes with the fluorophore in this binding(β-CD).

Prior to proceeding to consider the application ofthe pseudophase model to the results of this study, nev-ertheless, it is desirable to establish the relationships

International Journal of Chemical Kinetics DOI 10.1002/kin.20872

APPLICATION OF THE PSEUDOPHASE MODEL TO EXCITED STATE PROCESSES 599

between Stern–Volmer and pseudophase model equa-tions, which will be done in the subsequent section.

THEORY

In this section, an expression for the observed Stern-Volmer constant in the presence of a receptor will beobtained. This constant is defined from Eq. (3) [17]:

I0

I= 1 + (KSV)obs [Q] (3)

that is,

(KSV)obs ≡ (I0/I ) − 1

[Q](4)

In this equation I0 and I are the emission intensities ofthe fluorophore in the solution containing the receptorin the absence and presence of the quencher, Q, whichis present at concentration [Q], and refers to the totalvolume of the solution.

We will consider only the slow exchange limit thatcorresponds to the situation in which the exchangeprocesses between free and bound emitters are slow inrelation to the decay processes. This, of course, impliesthat free and bound excited species decay in the samestate in which they are formed by light absorption.This is the usual situation in most studies of quenchingprocesses under restricted geometry conditions. Thus,for an excited species with a lifetime of 100 ns, thedecay rate constant kd is of the order of 107 s−1, whichis much higher than the rate constant for the exchangeprocesses in Scheme 1. These exchange rate constants,for similar receptors and reactants to those studied here,are of the order of 4 × 104 mol−1 dm3 and 102 s−1

for the entry and escape processes, respectively [19].Consequently, the slow exchange limit holds. In thislimit, under stationary conditions one can write

d[R∗i ]

dt= (Iabs)i − (kd)i

[R∗

i

] = 0 (i = f, b) (5)

where (Iabs)i represents the rate of light absorption instate i and (kd)i the decay rate constant of this state:

(kd)i = (kr)i + (knr)i + (kq)i [Q] (6)

where (kr)i, (knr)i, and (kq)i are the rate constantsfor radiative, nonradiative, and quenching processes,respectively.

According to Eq. (5), one can write

[R∗

i

] = (Iabs)i

(kd)i(7)

The emission intensities for the fluorophore in thestates i (f, b) are given by

Ii = (kr)i

[R∗

i

] = (kr)i(Iabs)i

(kd)i= (Iabs)i ϕi

ϕi = (kr)i

(kr)i + (knr)i + (kq

)i [Q]

(8)

which shows the dependence of ϕi = (kr)i/(kd)i, thequantum yield of the i state, on the quencher concen-tration, which is relevant for our purpose (see below).

Under the usual conditions, that is, low absorptionof light, Iabs is proportional to the light intensity thatreaches the solution and to the concentration of theabsorbing species. Thus,

(Iabs)i = i0εil [Ri] (9)

In this equation, [Ri] represents the concentration of Ri

in the ground state, εi the molar absorption coefficientof this species, l is the path length, and i0 the intensityof the light reaching the solution.

Assuming that the excitation (in conditions of lowabsorption) does not perturb the equilibrium betweenfree and bound species, in the ground state, and takinginto account Eqs. (1), one can write

(Iabs)f = [R]

1 + K [M]i0εf l

(Iabs)b = [R] K [M]

1 + K [M]i0εbl (10)

On the other hand,

(I0)f

If= 1 + (KSV)f[Q]

(I0)b

Ib= 1 + (KSV)b[Q] (11)

In writing Eq. (11), a uniform distribution for thequencher through the solution is assumed. This as-sumption does not hold in all cases. This question willbe considered later.



According to the definition of (KSV)obs (Eq. (3)),

I0

I= (I0)f + (I0)b

If + Ib= 1 + (KSV)obs[Q] (12)

Introducing (I0)f and (I0)b into this equation fromEq. (11), one obtains

I0

I= If + If(KSV)f [Q] + Ib + Ib(KSV)b [Q]

If + Ib

= 1 +(

If

If + Ib(KSV)f + Ib

If + Ib(KSV)b

)[Q]

(13)

Taking into account Eqs. (8) and (10),

If = (Iabs)fϕf = [R]

1 + K [M]ϕfi0εf l

Ib = (Iabs)bϕb = [R] K [M]

1 + K [M]ϕbi0εbl (14)

Introducing these equations into Eq. (13) one can write

I0

I= 1

+(

[R]1+K[M]ϕf i0εf l(KSV)f + [R]K[M]

1+K[M] ϕbi0εbl(KSV)b

[R]1+K[M]ϕf i0εf l + [R]K[M]

1+K[M] ϕbi0εbl

)

[Q] = 1 +(

ϕfεf (KSV)f + ϕbεbK(KSV)b[M]

ϕfεf + ϕbεbK[M]

)[Q]

(15)

According to this

(KSV)obs = (KSV)f + (KSV)bKapp[M]

1 + Kapp[M](16)

with

Kapp = ab

afK (17)

and

ai = ϕiεi; (i = f, b) (18)

Equation (16) deserves some comments. First, Kapp

and the observed Stern–Volmer constant depend on the

quencher concentration (through the quantum yields).So, as expected, curved Stern–Volmer plots will resultin the presence of receptors. Consequently, althoughformally (KSV)obs will follow the equation correspond-ing to the pseudophase model, the binding constant willbe different for each quencher concentration. Finally,Eq. (16) has been deduced assuming that receptors con-tain a unique class of union sites and that the bindingprocess is noncooperative. These assumptions can failin the case of biological receptors, such as DNA, withdifferent kinds of binding sites and/or when coopera-tive phenomena are present [20].

Before closing this section, it is of interest to con-sider the case of a nonuniform distribution of thequencher in the solution. This case is relevant in re-lation to the study that will be presented later: thequenching of the pyrene by iodide in SDS micellar so-lutions. Taking into account the negative charges of thequencher and receptor, it is expected that the concen-tration of the quencher in the regions of the solutionclose to the micelles will be lower than in the bulk ofthese solutions. In this case, it can be easily shown thatEq. (16) becomes

(KSV)obs[Q] = (K ′SV)f[Q]f + (K ′

SV)bKapp [M] [Q]b

1 + Kapp[M]

(19)

Notice that [Q]i has a different meaning to [Qi]. Thisdifference arises from the fact that [Qi] refers to thetotal volume of the solution and [Q]i refers to the localvolume.

But volume of the solvent, where Qf is located, is, ingeneral, close to the total volume of the solution. In thisway, [Q]f � [Qf]. Moreover, the amount of a quencherclose to the receptors will be small, in cases such asthose considered in this work (micellar solutions) inwhich the quencher and the receptor bear charges ofthe same sign. In this way,

[Qf] � [Q]f � [Q] (20)

On the other hand, one can define a partition coefficientas

ϕ = [Q]b

[Q]f� [Qb]

[Q](21)

And consequently, Eq. (19) becomes

(KSV)obs = (K ′SV)f + (K ′

SV)bϕKapp [M]

1 + Kapp[M](22)



That is, Eq. (16) is still applicable but now (KSV)b

is the product of the true Stern–Volmer con-stant (K′

SV)b by the partition coefficient, �, and(KSV)f � (K′

SV)f.

EXPERIMENTAL

Materials

Pyrene and β-CD meeting USP testing specificationswere obtained from Sigma-Aldrich Quimica (Madrid,Spain). Ethanol, NaI, NaCl, and SDS were obtainedfrom Merck (Madrid, Spain).

Materials were used as received because prelimi-nary experiments with purified material showed thatpurification does not produce changes in the experi-mental results.

Purified water used in the preparation of solutionswas obtained from a Millipore (Molsheim, France)Milli-Q water system. Its conductivity was less than10−6 Sm−1.

Stock solutions of pyrene were prepared by dis-solving weighted amounts of the solid in ethanol andkeeping them in the dark. Working solutions were ob-tained by dilution with water of the stock solution, toreach the desired concentration of pyrene, 2 × 10−6

mol dm−3. These working solutions always containedethanol at 10% v/v. Quencher concentrations rangedfrom 0 to 0.1 mol dm−3, and the ionic strength wasfixed at 0.1 mol dm−3 with NaCl, after checking thatthis salt does not produce any effect on the emission ofpyrene.

Steady-State Fluorescence Measurements

Fluorescence measurements were carried out in a spec-trofluorimeter (Hitachi F-2500) interfaced to a PC forreading and handling of the emission spectra. The spec-tral slits for both, emission, and excitation were 5 nm,and the PMT voltage was 400–700 V. The excitationwavelength was established as 332 nm. No magic an-gle polarizer conditions were employed. All the spectrawere obtained in the range of 350–500 nm. Under ex-perimental conditions, the characteristic band of thepyrene excimer emission at �470 nm is not observed.Figure 1 shows an emission spectrum as a representa-tive example. All the emission spectra were integratedin the range 350–500 nm. In the following, the emis-sion intensities will always be the integrated emissionintensities. All the measurements were carried out at298.2 ± 0.1 K.

Flu

ore

scen

ce e

mis

sio

n (

au)

0

1000

2000

3000

4000

λ /nm

360 400 440 480

Figure 1 Characteristic spectrum of pyrene in the pres-ence of a SDS micellar solution ([SDS]m = 2.78 ×10−3 mol dm−3).

RESULTS

Determination of the Critical MicellarConcentration

The determination of the critical micellar concentration(cmc) of SDS in our working conditions (ionic strength0.1 mol dm−3 and 10% ethanol (v/v)) was carried outusing the method of Zana et al [21]. The value of thecmc obtained in this way was 8.2 × 10−4 mol dm−3

(see the Supporting Information).

Binding Constants

It is known that the changes in fluorescence of pyreneare due to the sensitivity of this fluorophore to thepolarity of its surrounding media [22–24]. This fea-ture allowed us to get the equilibrium constant, K, inScheme 1 (see the section Introduction), for the bind-ing of pyrene to the receptors (SDS and β-CD). Thatis, from the changes in the intensity of emission ofthe fluorophore in the presence of different concentra-tions of receptors by applying Eq. (23), the equilibriumconstant was obtained:

I = If + IbK [M]

1 + K [M](23)

In this equation, K represents the true binding constantof pyrene (in its ground state) to the receptors and If

and Ib represent the emission intensities of pyrene freeand bound to the receptor, respectively. In the caseof micellar solutions, If corresponds to the emissionintensity at the cmc.

Figure 2 gives typical plots of the relative emis-sion intensities (the ratios of the integrated emission



[M] / mol dm−3

0.000 0.005 0.010 0.015 0.020

I

0.8

1.0

1.2

1.4

(a) -CDβ(b) SDS micelles

Figure 2 Relative emission intensities of pyrene in theabsence of the quencher in (a) β-CD solutions and(b) SDS micellar solutions. Points represent experimentaldata, and the lines correspond to the best fit obtained by usingEq. (23).

intensities in the presence of the receptor to thatin the absence of the receptor) when the concen-tration of the receptor changes. As can be seen,Eq. (23) fits the data well for both SDS micellesand β-CD solutions.∗ Therefore, the values of K forSDS micelles and β-CD were obtained. These val-ues were 2300 ± 300 and 1600 ± 400 mol−1 dm3,respectively (in the case of β-CD solutions, the givenvalue is the average value corresponding to 10 inde-pendent experiments).

As to the values of K (Eq. (23)) obtained in thiswork, it is important to realize that the values of thisparameter depend strongly on the working conditions.Thus, Bhoi et al. [25] have obtained a value of K =600 mol−1 dm3 for the binding of pyrene to β-CD inethanol/water mixtures 16% v/v. According to this, ourvalue seems reasonable because of the lower contentof ethanol of our solutions. In fact, the value of K de-pends on the solubility of the ligand (K decreases whenthe solubility increases) and the solubility of pyreneincreases strongly with the alcohol content of the so-lution [26]. For this reason, the binding constant ofpyrene to SDS micelles obtained here is lower than thevalue of this constant in water (K = 8620 mol−1dm3),without alcohol [27].

Stern–Volmer Constants

The Stern–Volmer constant, at each quencher concen-tration, was obtained through Eq. (4). These values, fora given (fixed) concentration of quencher and different

∗ K1 and K2 represent the equilibrium constants for 1:1 and 1:2complexes, respectively.

[ -CD] / mol dmββ −3

0.000 0.001 0.002 0.003

KS

V /

mo

l−1d

m3

0

40

80

120

Figure 3 Experimental KSV for the quenching of pyreneby the iodide ion at different β-CD concentrations ([I−] =0.02 mol dm−3). Points represent experimental data, andthe line corresponds to the best fit obtained by usingEq. (16).

[SDS] / mol dm−3

0.000 0.005 0.010 0.015 0.020

0

30

60

90

KS

V /

mo

l−1d

m3

Figure 4 Experimental KSV for the quenching of pyreneby the iodide ion at different SDS micelles concentrations([I−] = 0.02 mol dm−3). Points represent experimental data,and the line corresponds to the best fit obtained by usingEq. (16).

receptor concentrations, can be fitted to Eq. (16), asshown in Figs. 3 and 4, which are representative exam-ples. The values of Kapp obtained in this way are givenin Table I. This table also gives the values of (KSV)f

and (KSV)b. These values, of course, are independentof the quencher concentration.

No traces of coexistence of static and dynamicquenching were detected, that is, the plots of I0/I versus[Q] did not show the upward characteristic curvatureof this situation [17]. Instead, a downward curvature(see Fig. 5) was observed in the presence of receptorsin agreement with our treatment (see also [28]).



Table I Apparent Binding Constants of Pyrene to β-CDand SDS Micellar Solutions for Several [I−]

[I–] (mol dm–3) Kapp (× 10–3 mol−1dm3)

β-CD0.02 2.800.04 2.900.06 3.300.08 3.600.10 3.60

(KSV)f = 97 mol–1dm3 (KSV)b � 0 mol–1dm3

SDS0.02 3.700.04 6.700.06 9.100.08 11.50.10 14.9

(KSV)f = 74 mol–1dm3 (KSV)b � 0 mol–1dm3

[I- ] / mol dm−3

0.000 0.025 0.050 0.075 0.100

I 0/I

0.90

1.05

1.20

1.35

Figure 5 Plot of I0/I versus the quencher concentrations inthe presence of [SDS]m = 10−3 mol dm−3.

DISCUSSION

As shown in Table I, Kapp depends on the quencherconcentration, as expected, according to the results ob-tained in the section Theory of the paper. However, tocheck the results quantitatively, the values of ab/af toeach quencher concentration must be obtained. Theobtention of these ab/af values can be performed di-rectly from the data of the emission intensities, in thepresence of the quencher. Thus, if one uses a standardfor the obtention of the quantum yields of a probe, it ispossible to write [29]

ai = εiϕi = ϕsAsIin2

s

AiIsn2i

εi (i = f, b) (24)

Table II Values of ab/af (see the text) for theQuenching of Pyrene by I− in β-CD and SDS MicellarSolutions

[I–] (mol dm–3) ab/af

β-CD0.02 3.90.04 6.50.06 9.10.08 11.70.10 14.3

SDS0.02 2.10.04 3.20.06 4.40.08 5.60.10 6.7

In this equation, Ii and Is represent the integrated emis-sion intensities of the fluorophore in state i and that ofthe standard species, respectively. Ai and As are the op-tical density of the solutions containing the fluorophore(only) in state i and the standard species, respectively,and ni and ns are the refractive index of the solutionscontaining the i state of the fluorophore and the stan-dard species, respectively. εi has the same meaning asin Eq. (9). According to Eq. (24), it is clear that

ab

af= εbϕb

εfϕf= AfIbεb

AbIfεf(25)

because nf � nb (in the cases studied here).Taking into account that if (Af/εf) = (Ab/εb), it fol-

lows that

ab

af= Ib

If(26)

ab/af can be determined from the intensities of emis-sion of fluorophore in the free and bound states. In thisway, the values of this quotient appearing in Table IIhave been obtained. It is interesting to note that ab/af

varies linearly when the concentration of the quencherchanges (see Fig. 6). This gives consistency to our data.In fact,

ab

af= εb

εf

ϕb

ϕf= εb

εf· (kr)b((kr)f + (knr)f + (kq)f [Q])

(kr)f((kr)b + (knr)b + (kq)b [Q])

(27)

but (KSV)b � 0 (see Table I), and therefore (kq)b � 0;so that, according to Eq. (27), a linear dependence ofab/af on the quencher concentration is expected.



0.03 0.06 0.09 0.12

a b/af

4

8

12

16

-CD(b) SDS micelles

β

[I-] / mol dm−3

Figure 6 Plots of ab/af versus [I−] for (a) β-CD solutionsand (b) SDS micellar solutions.

Table III Calculated Values of the Apparent BindingConstant, (Kapp)calc, Obtained from Eq. (17) and theValues of ab/af Appearing in Table II

[I–] (mol dm–3) (Kapp)calc (×10–3 mol–1dm3)

β-CD0.02 6.200.04 10.40.06 14.60.08 18.70.10 22.9

SDS0.02 4.800.04 7.400.06 10.10.08 12.90.10 15.4

For β-CD solutions, it is clear that the (Kapp)calc

values obtained from Eq. (17) (see Table III) are dif-ferent from the values of Kapp given in Table I. Weconsidered that this fact is a consequence of the inter-action of the quencher with the receptor, in such a waythat the latter results blocked for the interaction withthe fluorophore. In others words, the concentration offree β-CD to be used to obtain Kapp should be lowerthan the stoichiometry concentration. So, the values ofKapp appearing in Table I must be corrected. The rela-tion between the corrected (true) values of the apparentbinding constant, (Kapp)corr and the Kapp appearing inTable I is [30]

(Kapp)corr

Kapp= 1 + KI−[I−] (28)

0.025 0.050 0.075 0.100

(Kap

p) calc/K

app

2

3

4

5

6

7

[I-] / mol dm−3

Figure 7 Plot of (Kapp)calc/Kapp versus [I−] for the quench-ing of pyrene in β-CD solutions (see the text, Eq. (29)).

where KI− is the binding constant of the iodide ionto β-CD. Assuming, for the moment, that (Kapp)calc =(Kapp)corr, one can write [29]

(Kapp)calc

Kapp= 1 + KI− [I−] (29)

Figure 7 gives a plot of the left-hand side of Eq. (29)versus [I−]. The slope of this plot provides KI− =49 mol−1 dm3. This value is close to the value ob-tained for α-CD solutions by others authors throughpotentiometric titrations [31].

Once the value of KI− has been obtained, one cancalculate the concentrations of free β-CD, at each I−

concentration. From these calculated concentrations,the (true) corrected values of Kapp, (Kapp)corr appear-ing in Table IV can be obtained. As can be seen, theagreement between these values and those of (Kapp)calc

(Table III) is good.To check that this result is not the consequence of

a simple calculation artifact, we studied the quenchingof pyrene in micellar (SDS) solutions. In this case, due

Table IV Corrected Values of the Apparent BindingConstant, (Kapp)corr, of Pyrene to β-CD Solutions

[I–] (mol dm–3) (Kapp)corr (×10–3 mol−1dm3)

0.02 5.500.04 8.600.06 13.10.08 18.40.10 21.4



to the similar charge of the receptor and the quencherthe inclusion of the latter in the receptor is not possible.By comparing Tables I and III a good agreement canbe seen between Kapp and (Kapp)calc. This confirms ourtreatment and the additional hypothesis employed inthe case of β-CD solutions.

CONCLUSIONS

A treatment has been presented justifying the for-mal application of the pseudophase model to data ofquenching processes in the slow exchange limit, that is,when the lifetime of the excited state of the quenchedspecies is short. However, in this case, the binding con-stants appearing in the equations of the pseudophasemodel are apparent binding constants. These apparentconstants depend on the quencher concentration, asfollows from Eqs. (17) and (18).

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