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Electronic Supplementary Material (ESI) for RSC Advances. This journal is © The Royal Society of Chemistry 2014 SUPPORTING INFORMATION Obtaining equation 8 Consider a solution containing two (or more) receptors that can interact with a fluorophore that can be quenched by a given species (quencher) present in the solution. These receptors in the present case are cyclodextrins, but the following treatment can be applied to other receptors, such as surfactant monomers and micelles, for example. In the absence of a quencher, the intensity of emission of the fluorophore, in the presence of two cyclodextrins, CD1 and CD2, would be: (I em ) 0 (I em ) f (I em )1 K 1 [CD1 ] (I em ) 2 K 2 [CD 2 ] 1 K 1 [CD1 ] K 2 [CD 2 ] S-1 In this equation (Iem)f corresponds to the emission intensity of the probe in the absence of receptors, (Iem)1 to the situation in which all the probe molecules are bound to CD1 and (Iem)2 to CD2. This equation follows from the fact that the concentrations of free fluorophore and fluorophore bound to CD1 and CD2 are given by: In the presence [R f ] 1 [R ] 1 K 1 [CD1 ] K 2 [CD 2 ] [R 1 ] K 1 [CD1 ] [R ] 1 K 1 [CD1 ] K 2 [CD 2 ] [R 2 ] K 2 [CD 2 ] [R ] 1 K 1 [CD1 ] K 2 [CD 2 ] of a quencher, consequently, 23 S-2 (I em ) Q (I em ) Qf (I em ) Q1 (I em ) Q 2 and (I em ) 0 (I ) (I em ) 01 (I em ) 02 em 0 f (I em ) Q (I em ) Qf (I em ) Q1 (I em ) Q 2 S-3 In this equation (Iem)0f, (Iem)01 and (Iem)02 represent the emission intensities of Rf, R1 and R2 in the absence of the quencher and (Iem)Qf, (Iem)Q1 and (Iem)Q2 in the presence of the quencher. Of course, (I em ) 0i 1 (K SV ) i [Q] (I em ) Qi i f , 1, 2 S-4 Thus (I em ) 0i (I em ) Qi (I em ) Qi (K SV ) i [Q] i f , 1, 2 S-5 Introducing equation S-5 in equation S-3, (I em ) Qf (K SV ) f (I em ) Q1 (K SV )1 (I em ) Q 2 (K SV ) 2 (I em ) 0 1 [Q] (I em ) Q (I em ) Qf (I em ) Q1 (I em ) Q 2 S-6 Now, (Iem)Qi can be written as: (I em ) Qi i l i 0 [R i ] i S-7 In this equation I is the molar extinction coefficient of species i, l is the light path length of the cuvette, i0 is the intensity of the incident beam on the sample and I is the quantum yield for the emission of species i, in the presence of the quencher. Of course, [Ri] are given by equations S-2. Introducing equations S-2 and S-7 in equation S-6 one obtains: 24 l f ε f i 0 (K SV ) f l ε i (K ) K [CD1 ] l 2 ε 2 i 0 (K SV ) 2 K 2 [CD 2 ] 1 1 0 SV 1 1 (I em ) 0 1 K 1 [CD1 ] K 2 [CD 2 ] 1 K 1 [CD1 ] K 2 [CD 2 ] 1 K 1 [CD1 ] K 2 [CD 2 ] 1 [Q] l f ε f i 0 l1ε 1i 0 K 1 [CD1 ] l 2 ε 2 i 0 K 2 [CD 2 ] (I em ) Q 1 K 1 [CD1 ] K 2 [CD 2 ] 1 K 1 [CD1 ] K 2 [CD 2 ] 1 K 1 [CD1 ] K 2 [CD 2 ] a a (K SV ) f 1 (K SV )1 K 1 [CD1 ] 2 (K SV ) 2 K 2 [CD 2 ] af af 1 [Q] a1 a2 1 K 1 [CD1 ] K 2 [CD 2 ] af af S-8 with ai= ii. Thus, as (I em ) 0 1 (K SV ) obs [Q] (I em ) Q S-9 it results in (K SV ) obs a (K SV ) f 1 af a (K SV )1 K 1 [CD1 ] 2 (K SV ) 2 K 2 [CD 2 ] af a a 1 1 K 1 [CD1 ] 2 K 2 [CD 2 ] af af S-10 or (K SV ) obs (K SV ) f (K SV )1 (K app )1 [CD1 ] (K SV ) 2 (K app ) 2 [CD 2 ] 1 (K app )1 [CD1 ] (K app ) 2 [CD 2 ] a (K app ) i i K i a f This is equation 8. 25 S-11