NMR Studies on Selectivity of β-Cyclodextrin to Fluorinated

Jun 27, 2007 - Abdalla H. Karoyo , Paul S. Sidhu , Lee D. Wilson , Paul Hazendonk , and Alex Borisov. The Journal of Physical Chemistry C 2015 119 (38...
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J. Phys. Chem. B 2007, 111, 8089-8095

8089

NMR Studies on Selectivity of β-Cyclodextrin to Fluorinated/Hydrogenated Surfactant Mixtures Hang Xing,† Shrong-Shi Lin,† Peng Yan,† Jin-Xin Xiao,*,†,‡ and Yong-Ming Chen*,§ Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking UniVersity, Beijing 100871, China, Beijing FLUOBON Surfactant Institute, Beijing 100080, China, and State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100080, China ReceiVed: January 10, 2007; In Final Form: April 25, 2007

The interactions between β-cyclodextrin (β-CD) and the equimolar/nonequimolar mixtures of sodium perfluorooctanoate (C7F15COONa, SPFO) and sodium alkyl sulfate (CnH2n+1SO4Na, CnSO4, n ) 8, 10, 12) were investigated by 1H and 19F NMR. It showed that β-CD preferentially included the fluorinated surfactant when exposed to mixtures of hydrogenated (CnSO4) and fluorinated (SPFO) surfactants, notwithstanding whether the hydrogenated surfactant CnSO4 was more or less hydrophobic than the SPFO. Such preferential inclusion of the fluorinated surfactant continued to a certain concentration of β-CD at which time the CnSO4 was then observed to be included. The longer the hydrocarbon chain of CnSO4 the lower the concentration of β-CD at which the hydrogenated surfactants began to show inclusion. The inclusion process can be qualitatively divided into three stages: first, formation of 1:1 β-CD/SPFO complexes; second, formation of 1:1 β-CD/ CnSO4 complexes; and finally, formation of 2:1 β-CD/SPFO complexes upon further increase of β-CD concentration. In the concentration range studied, during the last stage of inclusion both 2:1 β-CD/C12SO4 and 2:1 β-CD/SPFO complexes appear to be simultaneously formed in the system of β-CD/SPFO/C12SO4 but not in either the systems of β-CD/SPFO/C8SO4 or β-CD/SPFO/C10SO4. The selective inclusion of the shorter fluorocarbon chain surfactant might be attributed to the greater rigidity and size of the fluorocarbon chains, compared to those of the hydrocarbon chains, which provide for a tighter fit and better interaction between the host and guest. This latter effect appears to dominate the increase in hydrophobic character as the carbon chain length increases in the hydrogenated series.

Introduction β-Cyclodextrin (β-CD) is a cyclic molecule composed of seven D(+)-glucopyranose units.1,2 It has a hydrophobic interior and hydrophilic exterior. Such a special structure makes β-CD an important host to capture hydrophobic guest molecules into its cavity.1 Surfactants have both hydrophilic and hydrophobic groups, and they can be included by β-CD through forming host-guest complexes. The interaction between β-CD and surfactants is a widely investigated topic. However, previous works have focused on the systems containing single surfactants;3-8 mixed surfactants were rarely involved. As mixed surfactants have a much greater significance, especially in the realm of industrial applications, we herein investigated the interactions between β-CD and mixed surfactants. The selective inclusion of β-CD to different guest molecules is very useful in the process of separation, synthesis, enzyme modeling, and biochemical reactions.2 For the study of mixed surfactants/β-CD systems, it is important to know whether β-CD has selectivity to different surfactants. As far as we know, the selective inclusion of β-CD in mixed surfactant systems has not been reported. * Authors to whom correspondence should be addressed. J.-X.X.: E-mail: [email protected]. Telephone: 0086-10-62764973. Fax: 008610-62751708; Y.-M.C.: [email protected]. Telephone: 0086-1062659906. Fax: 0086-10-62559373. † Peking University. ‡ Beijing FLUOBON Surfactant Institute. § The Chinese Academy of Sciences.

In this work, the interactions between β-CD and the mixtures of hydrogenated and fluorinated surfactants were studied. The surfactant mixtures were composed of sodium octyl/decyl/ dodecyl sulfates (CnSO4) and sodium perfluorooctanoate (SPFO) with molar ratios of 1:1 and 5:1 (CnSO4/SPFO). 1H and 19F NMR were applied to measure the chemical shift changes (∆δ) of CnSO4 and SPFO in the presence of β-CD. The details of the inclusion process, such as structural differences and stoichiometries of inclusion compounds, were analyzed. Binding constants of single surfactant systems were also obtained with an NMR method. Experimental Section Materials. β-Cyclodextrin (β-CD) (g99% HPLC, Fluka), perfluorooctanoic acid monohydrate (ACROS), D2O (99.8 atom % D, ACROS), sodium decyl sulfate (C10SO4) (HPLC, ACROS), sodium dodecyl sulfate (C12SO4) (99%, ACROS), and sodium octyl sulfate (C8SO4) (>98%, Fluka) were used as received. Sodium perfluorooctanoate (C7F15COONa, SPFO) was prepared by neutralizing perfluorooctanoic acid with sodium hydroxide. The solid product was obtained by freeze-drying under vacuum. The purities of all surfactants were further examined by surface tension measurement with drop volume method.9 No minima were observed in the surface tension curves, indicating the absence of surface-active impurities.9 Equipment and Methods. The 1H NMR experiments were performed on a Bruker ARX 400 (1H: 400.13 MHz) spectrom-

10.1021/jp070198a CCC: $37.00 © 2007 American Chemical Society Published on Web 06/27/2007

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Xing et al.

eter with D2O as solvent at 25 °C. Methanol (3 × 10-4 M) was used as the internal reference (3.343 ppm).10,11 The 19F NMR experiments were performed on a Varian Mercury Plus 300 (19F: 282.31 MHz) spectrometer in D2O at 25 °C. All fluorine chemical shifts were referenced to the external trifluoroacetic acid (-79.46 ppm), with field frequency locked. The experiments were carried out by addition of β-CD into CnSO4/SPFO mixtures. In order to avoid the formation of micelles, the total concentration (Ct) of surfactant mixtures was fixed to a concentration below critical micelle concentration (cmc). The changes of chemical shifts of 1H and 19F, ∆δ(H) and ∆δ(F), respectively, were analyzed among different concentration ratios of β-CD, RCD ) [β-CD]/Ct. Here ∆δ(H) ) δobsd - δmono and ∆δ(F) ) δobsd - δmono are defined respectively, where δobsd is the chemical shift observed in CnSO4/SPFO/β-CD mixtures and δmono is the chemical shift of monomers of CnSO4 or SPFO in their respective single solution. Results 1.1H and 19F NMR Results of Equimolar CnSO4/SPFO Mixtures with β-CD. When surfactants are captured into the cavity of β-CD, the chemical shifts (δ) of the nuclei in surfactant molecules are changed. As reported in the literature for the systems of single hydrogenated surfactants,4 the δ of proton ω (terminal methyl) increases during the formation of a 1:1 complex, while those of protons R and β (methylene protons next to the headgroup) decrease. For the hydrogenated surfactants with a long hydrophobic chain, the δ of protons R and β are hardly influenced when 1:1 complexes are formed. However, when a second β-CD covers the chain of the surfactant, the δ values of protons ω, R, and β decrease. Similar results were obtained in our work for the single surfactants of CnSO4 with β-CD (Figures 5-7). Previous works have shown that during the formation of 1:1 β-CD/SPFO complexes, the δ curves of all fluorine nuclei go up. When 2:1 β-CD/SPFO complexes are formed, the δ values of fluorine nuclei R and β increase, while those of other fluorine nuclei decrease.12,13 It is consistent with our results of the system of SPFO and β-CD (Figure 8). Therefore, by analyzing the chemical shifts, the details of the inclusion process in β-CD/single surfactant systems can be obtained. In our work, there are multiple, coupled equilibria occurring in solution. It is hard to decouple the equilibria in such complicated mixtures. The combination of 1H and 19F NMR was designed to obtain the inclusion information of CnSO4 and SPFO in surfactant mixtures with β-CD. We simplified the analysis of the NMR results of β-CD/CnSO4/SPFO systems on the basis of the mixtures of β-CD and single surfactants. The simplification was based on the following considerations: (i) There is no micelle in solution because the total concentration (Ct) of surfactant mixtures was fixed to a concentration below cmc. (ii) It is known that hydrogenated and fluorinated substances do not mix easily.14 (iii) Both CnSO4 and SPFO are anionic surfactants. Therefore, the synergistic and cooperative interactions between free CnSO4 and SPFO monomers could be ignored, which is also proved by the almost zero values of ∆δ(H) and ∆δ(F) at RCD ) 0. (The discrepancy between the values of δobsd and δmono was within the NMR instrumental error.) Thus, the complexation between CnSO4 (or SPFO) and β-CD could be treated approximately as independent, coexistent equilibria, and the equilibria compete in the concentration region of β-CD. For such reasons, when the shift of 1H and 19F NMR signals of β-CD/mixed surfactant systems show trends similar

Figure 1. Chemical shift change of protons (∆δ(H)) of C8SO4 (A), C10SO4 (B), and C12SO4 (C) versus molar ratio of β-CD, RCD, in the equimolar mixtures of sodium alkyl sulfate (CnSO4) and sodium perfluorooctanoate (SPFO) at 25 °C. ∆δ(H) ) δobsd - δmono, where δobsd is the chemical shift directly observed from 1H spectra of CnSO4/ SPFO/β-CD mixtures under investigation; δmono is the chemical shift of monomers of CnSO4. RCD ) [β-CD]/Ct, where Ct is the total concentration of surfactants. Ct was fixed to 10 mM in all experiments.

to those in β-CD/single surfactant systems, the qualitative information of the formation of inclusion complexes could be approached. Figures 1 and 2 show the respective chemical shift changes of 1H (∆δ(H)) and 19F (∆δ(F)) in CnSO4/SPFO mixtures upon the addition of β-CD. The total concentration of the

Interactions between β-CD and Mixed Surfactants

Figure 2. Chemical shift change of 19F (∆δ(F)) of SPFO versus RCD at 25 °C in the equimolar mixtures of SPFO and C8SO4 (A), C10SO4 (B), and C12SO4 (C). ∆δ(F) ) δobsd - δmono, where δobsd is the chemical shift directly observed from 19F spectra of CnSO4/SPFO/β-CD mixtures; δmono is the chemical shift of monomers of SPFO. RCD ) [β-CD]/Ct, where Ct was fixed to 10 mM in all experiments.

equimolar surfactant mixtures (Ct) was fixed to 10 mM, i.e., the concentrations of CnSO4 and SPFO were 5 mM. Since Ct is below the cmc of 1:1 CnSO4/SPFO mixture, there is no micelle in the systems investigated. Initially the ∆δ(H) values remained constant in Figure 1AC, indicating that no β-CD/CnSO4 complex was formed significantly until RCD (RCD ) [β-CD]/Ct) reached a certain level.

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8091 However, ∆δ(F) went up from the very beginning (Figure 2AC), which suggested that β-CD included SPFO to form 1:1 complexes as soon as β-CD was added. The results above showed that β-CD preferentially included SPFO when added to the surfactant mixtures. In other words, β-CD exhibited significant selectivity to the fluorinated surfactant, whether the hydrophobicity of hydrogenated surfactant was lower or higher than that of the fluorinated surfactant. The selective inclusion process differed significantly, however, with the variation of the hydrophobicity of CnSO4 (Figures 1-2). The curves of ∆δ(H) and ∆δ(F) showed two turning points in Figures 1 and 2, and the positions of the turning points were related to the hydrophobic chain length of CnSO4. 1.1. Inclusion Process from RCD ) 0 to the First Turning Points. SPFO was included to form a 1:1 β-CD/SPFO complex as soon as β-CD was added. The inclusion was almost saturated when the curves reached the first turning points in Figure 2. CnSO4 was not observed to be included until the first turning points in Figure 1. So the first turning points in Figures 2 and 1 approximately indicated the saturation of 1:1 inclusion of SPFO and the start of 1:1 inclusion of CnSO4, respectively. It was interesting to compare the first turning points of different CnSO4/SPFO/β-CD systems in Figures 1 and 2. The positions of the first turning points differed with the hydrophobic chain length of CnSO4. When n increased from 8 to 12, we could find that the concentration of β-CD at which CnSO4 began to be significantly included (at the first turning points in Figure 1) was decreased; correspondingly, the first turning points in Figure 2, which indicated the saturation of 1:1 inclusion of SPFO, was increased. In other words, although β-CD preferentially included SPFO, the level of such selectivity was decreased with the increase of the hydrophobicity of CnSO4. Both the curves R and β in Figure 1C gave only one turning point around RCD ) 1, which was almost identical to the second turning point of the curve ω. The R- and β-CH2 of C12SO4 might be outside the cavity of β-CD due to the long hydrocarbon chain, so that the formation of 1:1 β-CD/C12SO4 complexes showed no significant effect on the R- and β-CH2 of C12SO4. 1.2. Inclusion Process between the First and the Second Turning Points. CnSO4 was significantly included to form a 1:1 β-CD/CnSO4 complex between the first and the second turning points in Figure 1. The ∆δ(F) in this region stayed almost constant (Figure 2B-C), which indicated no further β-CD/SPFO inclusion compounds were significantly formed. However, the ∆δ(F) in Figure 2A changed slightly, which implied that minor 2:1 β-CD/SPFO complexes were formed in this region for the C8SO4/SPFO/β-CD system. 1.3. Inclusion Process from the Second Turning Points. In Figure 2, the curves γ, δ, , λ, and ω began to drop down while the curves R and β went up from the second turning points, which was attributed to the formation of 2:1 β-CD/SPFO complexes in all the systems. However, the ∆δ(H)’s in Figure 1A-C were different because of the variation of hydrophobicity of CnSO4. In Figure 1A, the curve ω went on increasing, indicating that minor 1:1 β-CD/C8SO4 complexes simultaneously kept on forming. In Figure 1B, the curves reached nearly a plateau from the second turning points, indicating that C10SO4 was saturatedly included. In Figure 1C, the curves R and β began to go down from the second turning points, which was attributed to the formation of 2:1 β-CD/C12SO4 complexes. It was interesting to note the different trends of ∆δ(H) of protons R and β in Figures 1A-C. In Figure 1A, the ∆δ(H) of

8092 J. Phys. Chem. B, Vol. 111, No. 28, 2007

Figure 3. Chemical shift change of protons (∆δ(H)) of C8SO4 (A), C10SO4 (B), and C12SO4 (C) versus molar ratio of β-CD, RCD, in the mixtures of sodium alkyl sulfate (CnSO4) and sodium perfluorooctanoate (SPFO) with molar ratio (CnSO4/SPFO) of 5:1 at 25 °C. ∆δ(H) ) δobsd - δmono, where δobsd is the chemical shift directly observed from 1H spectra of CnSO4/SPFO/β-CD mixtures under investigation; δmono is the chemical shift of monomers of CnSO4. RCD ) [β-CD]/Ct, where Ct is the total concentration of surfactants. Ct was fixed to 10 mM for the mixtures of SPFO and (A) C8SO4, (B) C10SO4; Ct was fixed to 8 mM for the mixture of SPFO and (C) C12SO4.

R-CH2 of C8SO4 changed more than that of β-CH2, because R-CH2 was nearer to the polar headgroup and thus more

Xing et al.

Figure 4. Chemical shift change of 19F (∆δ(F)) of SPFO versus RCD in the mixtures of sodium alkyl sulfate (CnSO4) and sodium perfluorooctanoate (SPFO) with molar ratio (CnSO4/SPFO) of 5:1 at 25 °C. The systems are the mixtures of SPFO and (A) C8SO4, (B) C10SO4, (C) C12SO4, respectively. ∆δ(F) ) δobsd - δmono, where δobsd is the chemical shift directly observed from 19F spectra of CnSO4/SPFO/βCD mixtures; δmono is the chemical shift of monomers of SPFO. Ct was fixed to 10 mM for the mixtures of SPFO and (A) C8SO4 and (B) C10SO4. Ct was fixed to 8 mM for the mixture of SPFO and (C) C12SO4.

dehydrated when the 1:1 β-CD/C8SO4 complex was formed. In Figure 1B, the changes of ∆δ(H) of R- and β-CH2 of C10SO4 seemed almost equally small; ∆δ(H) of β-CH2 was even a little more negative than that of R-CH2. The reason might be that

Interactions between β-CD and Mixed Surfactants

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8093

TABLE 1: cmc Values of Single Surfactants and Binding Constantsa of Complexes of β-CD/Single Surfactants cmc/mM K1/M-1 K2/M-1

C8SO4

C10SO4

C12SO4

SPFO

120b 7.8(2.3) × 102 3.43(0.11) × 102 c

30b 7.0(2.9) × 103 2.24(0.15) × 103 c

8.2b 4.9(2.6) × 104 2.1 × 104 d 2.68(0.25) × 104 e 1.0(1.0) × 102 210d 440(90)e

31b 7.4(2.8) × 104 8.85(4.4) × 104 f

41(31)

9.0(3.8) × 102 7.64(3.8) × 102 f

a K and K are the binding constants of 1:1 and 2:1 β-CD/surfactant complexes, respectively, determined from the systems of β-CD and single 1 2 surfactants on the basis of the models and calculations in the Appendix. b Determined by surface tension (drop volume method).9 c From ref 7. d From ref 17. e From ref 20. f From ref 12, in which the unit of K2 is M-2.

both R- and β-CH2 of C10SO4 were outside the cavity of β-CD for the 1:1 β-CD/C10SO4 complex, and β-CH2 was probably nearer to the open annulus of β-CD. In Figure 1C, the ∆δ(H) of R- and β-CH2 of C12SO4 began to decrease around RCD ) 1, owing to the formation of the 2:1 β-CD/C12SO4 complex. The formation of 1:1 complexes seemed to have no significant effect on its R- and β-CH2 because both of them were entirely outside the cavity of β-CD. 2. Selectivity in the Three Stages of Inclusion Process in the Equimolar Mixtures. The two turning points of the ∆δ(H) and ∆δ(F) curves in Figures 1-2 suggested that the inclusion process qualitatively underwent three stages. In the C8SO4/SPFO/β-CD system (Figures 1A and 2A), β-CD selectively included SPFO to form 1:1 complexes. Then 1:1 β-CD/C8SO4 complexes were significantly formed, with a small amount of 2:1 β-CD/SPFO complexes. Finally 2:1 β-CD/SPFO complexes were mainly formed with the continuous formation of minor 1:1 β-CD/C8SO4 complexes. In C10SO4/SPFO/β-CD system (Figures 1B and 2B), β-CD preferentially included SPFO to form 1:1 complexes, then 1:1 β-CD/C10SO4 complexes were mainly produced, and finally 2:1 β-CD/SPFO complexes were observed. Figures 1C and 2C showed that, in the C12SO4/SPFO/β-CD system, β-CD selectively included SPFO to form 1:1 complexes, then 1:1 β-CD/C12SO4 complexes were significantly formed, and finally both the formations of 2:1 β-CD/SPFO and 2:1 β-CD/C12SO4 complexes were observed. 3. Selectivity of β-CD in CnSO4 Excess Systems of CnSO4/ SPFO Mixtures. The results above showed that there was obvious selectivity of β-CD to SPFO in the equimolar mixtures of CnSO4 and SPFO. The 1H and 19F NMR results of CnSO4/ SPFO mixtures with a molar ratio of 5:1 upon the addition of β-CD are presented in Figures 3 and 4, respectively. The shapes of the plots were quite similar to those of the equimolar mixtures (Figures 1 and 2), which indicated that even when the concentration of CnSO4 was 5 times that of SPFO, β-CD still showed significant selectivity to SPFO. However, the first turning points in Figure 3 occurred at lower values of RCD compared with that shown in Figure 1. It is consistent with the concentration effect in the competitive equilibria. Discussion It was generally supposed that hydrophobic interaction was the main driving force for the formation of inclusion compounds between surfactants and β-CD.1,15 However, the cmc values of C8SO4, C10SO4, and C12SO4 are higher than, similar to, and lower than that of SPFO, respectively (Table 1). In other words, whether the hydrophobicity of the hydrogenated surfactants was higher or lower than that of SPFO, β-CD still exhibited significant selectivity for SPFO in the mixtures, which suggested that there might be other effects responsible for the selectivity.

The molecular structures of the two types of surfactants might play an important role in the selectivity. It is known that the cavity diameter of β-CD is about 7 Å,1 and the diameters of CH3 and CF3 are estimated to be 4 and 7 Å, respectively.13,16 Therefore, fluorocarbon chains match the cavity of β-CD better than hydrocarbon chains do. Moreover, fluorocarbon chains are more rigid than hydrocarbon chains. The rigidity and the size of fluorocarbon chains might make SPFO more favorable to obtain an all-trans conformation which reduces the energy without kinks.13,17 In conclusion, the selective inclusion could be attributed to the special rigidity and size of fluorocarbon chains. Such speciality results in a much stronger complexation ability of SPFO than the increase of the hydrophobicity of CnSO4 did. Therefore, in spite of the increase of the hydrophobicity of CnSO4 when n increased from 8 to 12, β-CD always showed significant inclusion selectivity to SPFO. However, the hydrophobicity of CnSO4 still exhibited certain effects on the details of the inclusion process, such as the concentration of β-CD at the first turning points, the level of selectivity, and the stoichiometries of β-CD/surfactant complexes, as shown in sections 1.1-1.3 above. The above mechanism of selectivity in the inclusion process can be supported by the binding constants K of the β-CD/ surfactant complexes. In this work, the values of K were obtained based on NMR results of β-CD/single surfactant systems. The models and calculations of K are shown in the Appendix. The data of single surfactant systems in our work are listed in Table 1, where K1 and K2 correspond to the binding constants of 1:1 and 2:1 β-CD/surfactant complexes, respectively. It should be noted that all K1 values of β-CD/CnSO4 complexes are smaller than the K1 of the β-CD/SPFO complex. This is consistent with the selectivity of β-CD to include SPFO prior to CnSO4. The value of K1 of the β-CD/C8SO4 complex was close to the K2 of the 2:1 β-CD/SPFO complex. This could explain the observed sequence of the formation of complexes in the mixture: 1:1 β-CD/C8SO4 complexes were mainly formed with a small amount of 2:1 β-CD/SPFO complexes (between the first and the second turning points). Then 2:1 β-CD/SPFO complexes were significantly formed with the continuous formation of minor 1:1 β-CD/C8SO4 complexes. The value of K1 of the β-CD/C10SO4 complex was between the K1 and K2 of β-CD/SPFO complexes. This was consistent with our finding that the formation of 1:1 β-CD/C10SO4 complexes was observed to mainly appear between 1:1 β-CD/ SPFO complexes and 2:1 β-CD/SPFO complexes. The value of K2 of the β-CD/C12SO4 complex was close to the K2 of the β-CD/SPFO complex. Therefore, 2:1 β-CD/SPFO and 2:1 β-CD/C12SO4 complexes could be significantly formed simultaneously after the second turning points (Figures 1C and 2C).

8094 J. Phys. Chem. B, Vol. 111, No. 28, 2007 Conclusions

Xing et al. Then the following equation is obtained:

It was shown that β-CD exhibits significant inclusion selectivity to fluorinated surfactant in the mixtures of hydrogenated/fluorinated surfactants. The formation of β-CD/SPFO inclusion compounds was more favored than that of β-CD/CnSO4 ones, which was attributed to the molecular structures of the two kinds of surfactants. This finding might be helpful in the fields of separation and reaction control in industrial processes, such as catalysis involving β-CD18 and specific separation processes involving mixed hydrogenated/fluorinated species, e.g. in fluorinated compound synthesis, where chromatographic techniques might be applied when β-CD is attached to some solid substrate. Acknowledgment. We thank Professor Changwen Jin for helpful discussions. This project was financially supported by National Natural Science Foundation of China (Nos. 20273006 and 20573007).

CS ) (CS)2 - C0‚CS - S0‚CS + C0S0 K1 The expression of the value of chemical shift change:

∆δ ) δobsd - δS )

CS (δ - δS) S0 CS

The curves can be described as the equation below:

(∆δ)2‚S02 (δCS - δS)

2

(

- C0 + S0 +

)

∆δ‚S0 1 + C0S0 ) 0 ‚ K1 (δCS - δS)

Appendix Models and Calculations of Binding Constants of β-CD/ Surfactant Complexes in Single Surfactant Systems by NMR Studies.

By nonlinear least-squares fitting (Marquardt-Levenberg algorithm) of the experimental data, the parameters K1 and δCS in the equation can be obtained.

Nomenclature and Abbreviations C S CS C2S C0 S0 δS

δobsd

∆δ

β-CD surfactant 1:1 inclusion complex of β-CD/surfactant 2:1 inclusion complex of β-CD/surfactant initial concentration of β-CD initial concentration of surfactant chemical shift of monomers of surfactant, which can be determined directly from the solution of a single surfactant chemical shift observed in β-CD/surfactant mixtures. It is the weighted average value of the components according to their mole fraction content in solution. change of chemical shift, ∆δ ) δobsd - δS

There are two types of host-guest stoichiometries involved here: Type 1:

C + S T CS

Figure 5. Chemical shift change (∆δ(H)) of the protons in the system of single sodium octyl sulfate (C8SO4) versus the concentration of β-cyclodextrin (β-CD), C0. The concentration of C8SO4 was fixed to 5 mM. The dotted lines are the simulated curves.

Type 2:

C + S T CS CS + C T C2S Therefore, δobsd is shown as the following expressions:

δobsd ) δS

S CS + δCS (Type 1) S0 S0

δobsd ) δS

C2S S CS + δCS + δC2S (Type 2) S0 S0 S0

1. Type 1 C + S T CS CS K1 ) C‚S C0 ) C + CS S0 ) S + CS

The simulated dotted curves are shown in Figure 5 of the Appendix, which are consistent with the experimental data. 2. Type 2

C + S T CS CS + C T C2S K1 )

CS C‚S

K2 )

C2S CS‚C

C0 ) C + CS + 2C2S S0 ) S + CS + C2S

Interactions between β-CD and Mixed Surfactants

Figure 6. Chemical shift change (∆δ(H)) of the protons in the system of single sodium decyl sulfate (C10SO4) versus the concentration of β-cyclodextrin (β-CD), C0. The concentration of C10SO4 was fixed to 5 mM. The dotted lines are the simulated curves.

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8095

Figure 8. Chemical shift change (∆δ(F)) of fluorine in the system of single sodium perfluorooctanoate (SPFO) versus the concentration of β-cyclodextrin (β-CD), C0. The concentration of SPFO was fixed to 5 mM. The dotted lines are the simulated curves.

The Newton-Raphson method19 is employed to obtain the concentration of CS. The best fitting values of K1 and K2 are determined by minimizing the sums of the squares of the residuals, ∑i (∆δobsd,i - ∆δcalc,i)2, where ∆δobsd and ∆δcalc are the observed experimental data and their calculated values, respectively. The simulated dotted curves are shown in Figures 6-8 , which are consistent with the experimental data. References and Notes

Figure 7. Chemical shift change (∆δ(H)) of the protons in the system of single sodium dodecyl sulfate (C12SO4) versus the concentration of β-cyclodextrin (β-CD), C0. The concentration of C12SO4 was fixed to 5 mM. The dotted lines are the simulated curves.

Combining the equations above, the following two equations are obtained:

(

K2 -

)

(

)

4K22 4K2 (CS)3 + 1 - 2K2S0 (CS)2 + K1 K1

(

2K2S0C0 - C0 - K2C02 - S0 C2S ) K2

)

1 CS + C0S0 ) 0 K1

CS‚(C0 - CS) 2K2‚CS + 1

The expression of the value of chemical shift change:

∆δ ) δobsd - δS ∆δ )

C2S CS (δCS - δS) + (δ - δS) S0 S0 C2S

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