Heat Capacity Study to Evidence the Interactions between

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Heat Capacity Study to Evidence the Interactions between Cyclodextrin and Surfactant in the Monomeric and Micellized States R. De Lisi, G. Lazzara, S. Milioto,* N. Muratore, and I. V. Terekhova† Dipartimento di Chimica Fisica “F. Accascina”, Universita` di Palermo, Viale delle Scienze, Parco D’Orleans II, 90128 Palermo, Italy Received February 11, 2003. In Final Form: May 21, 2003 The heat capacities of transfer (∆Cpt) of hydroxypropyl-R-cyclodextrin and hydroxypropyl-γ-cyclodextrin (0.05 mol kg-1) from water to aqueous solutions of sodium hexanoate, sodium decanoate, and sodium dodecanoate were determined at 298 K. The measurements were extended to both the pre- and the postmicellar regions. The shape of the ∆Cpt as a function of the surfactant concentration curve is system specific. As well, the ∆Cpt magnitude depends on the macrocycle cavity being largely negative for HP-γ-CD. The qualitative analysis of the experimental data highlights that the features of the heat capacity are different from those of the enthalpy due to the important effect of temperature on the equilibria in solution. The experimental points were treated by means of a new equation based on the following contributions: (i) the formation of host-guest complexes in the aqueous phase, (ii) the shift of the micellization equilibrium induced by the cyclodextrin, and (iii) the interaction between micelle and cyclodextrin (free and complexed). The resulting equation is involved since it contains not only the terms related to the various equilibria in solution but also those relative to their shift with temperature. Despite its complexity, the equation fitted very well the experimental points in the absence and the presence of micelles.

Introduction Cyclodextrins are well-known for including various guest molecules, and this unique ability makes them functional in cosmetics, pharmaceutical science, and several other fields.1 These macromolecules have been modified to improve their performance, and consequently, the physicochemical properties have been changed. The solubility in water of the alkylated cyclodextrins, for example, is larger than that of the natural ones.2 Also, the methylated β-cyclodextrin solubility shows a negative temperature slope contrarily to that of β-cyclodextrin.3 Hydroxypropyl-cyclodextrins (HP-CD) are nontoxic and biodegradable and, hence, widely usable without risk for the environment.2 They can be employed to remove nonaqueous phase liquids from contaminated soils and groundwater as they enhance the water solubility of nonpolar organic compounds4 and their biodegradation5 and reduce their sorption onto the soil.6 The HP-CD/water characterization in the presence of a third component, such as an alcohol or a surfactant, may verify whether a synergic effect in the solubility increase of such nonpolar compounds takes place. There is evidence7 that the complexation of pyrene by γ-cyclodextrin, for example, is * To whom correspondence should be addressed. E-mail: milioto@ unipa.it. † On leave of absence from the Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya str., 1, 153045 Ivanovo, Russia. (1) Haggins, J. Chem. Eng. News 1993, May 18, 25. (2) Tanada, S.; Kawasaki, N. In Encyclopedia of Surface and Colloid Science; Hubbard, A. T., Ed.; Marcel Dekker: New York, 2002; p 1344. (3) Frank, J.; Holzwarth, J. F.; Saenger, W. Langmuir 2002, 18, 5974 and references therein. (4) Ko, S.; Schlautman, M. A.; Carraway, E. R. Environ. Sci. Technol. 1999, 33, 2765. (5) Wang, J.; Marlowe, E. M.; Miller-Maier, R. M.; Brusseau, M. L. Environ. Sci. Technol. 1998, 32, 1907. (6) Brusseau, M. L.; Wang, J.; Hu, Q. Environ. Sci. Technol. 1994, 28, 952. (7) Zung, J. B.; Munoz, P. A.; Ndou, T. T.; Warner, I. M. J. Phys. Chem. 1991, 95, 6701.

enhanced by the presence of amphiphilic molecules. Furthermore, the surfactant can allow the removal of large amounts of nonpolar substances which dissolve themselves in the micellar aggregates. The thermodynamic properties are very sensitive to the hydrophobic, hydrophilic, and, to a lesser extent, electrostatic interactions, and therefore they have been revealed as suitable to study the aqueous cyclodextrin/ surfactant systems. Most of the studies8-10 were extended to the premicellar region to determine the equilibrium constant for the formation of the cyclodextrin/surfactant inclusion complex and its stoichiometry. At this stage, investigations on modified cyclodextrin/surfactant mixtures essentially based on NMR,11 enthalpy,12-15 and volume15-18 measurements are scarce. The properties second derivatives of Gibbs free energy are very uncommon since few heat capacities are available16,17 whereas the compressibilities only deal with the natural cyclodextrins.19-21 Knowledge of the thermodynamics of HP-CD/ surfactant mixtures is consequently very limited. We (8) Funasaki, N.; Ohigashi, M.; Hada, S.; Neya, S. Langmuir 2000, 16, 383. (9) Mwakibete, H.; Crisantino, R.; Bloor, D. M.; Wyn-Jones, E.; Holzwarth, J. F. Langmuir 1995, 11, 57. (10) Ramos Cabrer, P.; Alvarez-Parrilla, E.; Meijide, F.; Seijas, J. A.; Rodrı´guez Nuń˜ez, E.; Va´zquez Tato, J. Langmuir 1999, 15, 5489. (11) Wilson, L. D.; Verrall, R. E. Langmuir 1998, 14, 4710. (12) Inoue, Y.; Liu, Y.; Tong, L. H.; Shen, B. J.; Jin, D. S. J. Am. Chem. Soc. 1993, 115, 10637. (13) De Lisi, R.; Milioto, S.; Muratore, N. Langmuir 2000, 16, 4441. (14) De Lisi, R.; Milioto, S.; Muratore, N. J. Phys. Chem. B 2002, 106, 8944. (15) De Lisi, R.; Lazzara, G.; Milioto, S.; Muratore, N. J. Phys. Chem. B, submitted. (16) De Lisi, R.; Milioto, S.; Pellerito, A.; Inglese, A. Langmuir 1998, 14, 6045. (17) De Lisi, R.; Milioto, S.; De Giacomo, A.; Inglese, A. Langmuir 1999, 15, 5014. (18) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1998, 102, 480. (19) Gonza´lez-Gaitano, G.; Compostizo, A.; Sańchez-Martin, L.; Tardajos, G. Langmuir 1997, 13, 2235. (20) Gonza´lez-Gaitano, G.; Sańchez-Garcıà, L.; Tardajos, G. Langmuir 1999, 15, 7963.

10.1021/la0342316 CCC: $25.00 © 2003 American Chemical Society Published on Web 07/17/2003

Interactions between Cyclodextrin and Surfactant

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previously determined the enthalpy13,15 and the volume15,16 of aqueous HP-CD/sodium alkanoate systems where the cyclodextrins differed in the cavity size (HP-R-CD, HPβ-CD, and HP-γ-CD made up of 6, 7, and 8 R-D-glucopyranose units, respectively) and the surfactants in the alkyl chain length allowing us to discriminate both the hydrophobic and the hydrophilic moieties. The cavity size of the cyclodextrin and the hydrophobicity of the surfactant play a relevant role in the thermodynamics of the cyclodextrin/surfactant inclusion complex formation and, to a lesser extent, in that for the cyclodextrin-micelle mixed aggregate formation. Heat capacity data16 are fragmentary despite their high sensitivity to the interactions as the reports on the surfactant behavior in water document.22-25 In fact, the second derivative of Gibbs free energy (heat capacity, compressibility, etc.) detects not only the micellization equilibrium but also the micellar structural transitions23,24 which are not evidenced by the corresponding property first derivative (enthalpy, volume, etc.). On this basis, to shed more light on the understanding of the mechanism of interaction between cyclodextrins and surfactants, we determined accurate heat capacity data of aqueous HP-CD/sodium alkanoate systems and modeled them with a new theoretical approach. The availability of several thermodynamic properties (enthalpy,13,15 volume,15,16 and heat capacity) provides a quite complete picture on the energetics regulating these mixed systems. Experimental Section Materials. Sodium hexanoate (NaHex), sodium decanoate (NaDec), and sodium dodecanoate (NaL) (Sigma) were used as received. The pH of their aqueous solutions was ca. 8.5, but it was increased to 10.5 for some NaL solutions which exhibited solid particles. The standard partial molar volumes of the surfactants, evaluated from density measurements, agree with those reported elsewhere.16,26 Hydroxypropyl-R-cyclodextrin (HPR-CD) and hydroxypropyl-γ-cyclodextrin (HP-γ-CD), both Aldrich products, were used as received. The average molar substitution for each glucopyranose residue is 0.6 for both the cyclodextrins. The water content of the cyclodextrin was determined by using the procedure reported elsewhere.16 All solutions were prepared by mass using degassed conductivity water, and their concentrations were expressed as molalities. Heat Capacity Measurements. The relative differences in the heat capacities per unit volume (∆σ/σ0) were determined with a Picker flow microcalorimeter (Setaram) at 298.426 ( 0.001 K. Using a flow rate of about 0.01 cm3 s-1 and a basic power of 19.7 mW, the temperature increment was approximately 0.5 K. The reproducibility of the specific heat capacity measurement is 1 × 10-4 J K-1 g-1. The specific heat capacity (cp) of a solution of density d is related to ∆σ/σ0 through the equation

cp ) σ0{1 + ∆σ/σ0}/d

(1)

(21) Gonza´lez-Gaitano, G.; Crespo, A.; Tardajos, G. J. Phys. Chem. B 2000, 104, 1869. (22) Desnoyers, J. E.; Perron, G.; Roux, A. H. In Surfactant Solutions: New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987. (23) De Lisi, R.; Milioto, S. In Solubilization in Surfactant Aggregates; Christian, S. D., Scamehorn, J. F., Eds.; Marcel Dekker: New York, 1995. (24) De Lisi, R.; Milioto, S.; Verrall, R. E. J. Solution Chem. 1990, 19, 639. (25) Yamashita, F.; Perron, G.; Desnoyers, J. E.; Kwak, J. C. T. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series No. 311; American Chemical Society: Washington, DC, 1986. (26) Milioto, S.; Crisantino, R.; De Lisi, R.; Inglese, A. Langmuir 1995, 11, 718.

Table 1. Physicochemical Properties for the Water-Surfactant and the Water-Surfactant-Cyclodextrin Systems at 298 Ka

KM n BL CL LM Cp0S BC CC CpM

NaHex

NaDecb

NaL

(21 ( 3) × 10-4 8 0.62 ( 0.05c 1.46 ( 0.07c 11.0 ( 0.3c 420 ( 1e 7 ( 2e

7.6 × 1015 20 13.51

(4 ( 3) × 1025 20 -16 ( 3d 300 ( 18d 9.67d 937 ( 8f

290

10.00 771.8 -70.37 40.15 302

KM 1:1 ∆Ht,1:1 KS

HP-R-CDg 15 ( 4 -18 ( 3 2.9 ( 0.3

KM 1:1 ∆Ht,1:1 KS

HP-γ-CDg 20 ( 3 -43 ( 2 2.3 ( 0.5

423 ( 7

a Units: K , kgn-1 mol1-n; B , kJ kg mol-2; C , kJ kg3/2 mol-5/2; M L L LM and ∆Ht,1:1, kJ mol-1; Cp0S and CpM, J K-1 mol-1 ; BC, J K-1 kg M mol-2; CL, J K-1 kg3/2 mol-5/2; K1:1 and KS, kg mol-1. b From ref 25. c From ref 13. d From ref 32. e From ref 16. f From ref 28. g From ref 15.

where σ0 corresponds to the heat capacity per unit volume of the reference solvent, which is water in our case. The σ0 27 as well as the solution density15 values were taken from elsewhere. The apparent molar heat capacity (CΦ,C) of the cyclodextrin in the given solvent mixture was calculated as

CΦ,C ) M cp +

103(cp - cp0) mC

(2)

where M is the molecular weight of the cyclodextrin and mC represents the moles of the cyclodextrin per kilogram of watersurfactant mixture; cp and cp0 are the specific heat capacity of the water-surfactant-cyclodextrin and the water-surfactant mixtures, respectively. The cp0 values were taken from the literature data16,26,28 which, sometimes, were combined with the present ones. The cyclodextrin concentration value of 0.05 mol kg-1 was chosen to obtain a relatively small error in CΦ,C (5 J K-1 mol-1). The heat capacity of transfer of the cyclodextrin from water to the aqueous surfactant solution (∆Cpt) was calculated as difference between CΦ,C and the apparent molar heat capacity of the cyclodextrin in water. Water-Surfactant Binary Systems. Some heat capacity measurements of the aqueous NaHex solutions were carried out at mS > 1.2 mol kg-1 due to the lack of literature data. Some experiments were also done on aqueous NaL solutions. From the data in the micellar region, the partial molar heat capacity of both NaHex and NaL in the micellized form was calculated according to the literature approach.29 As will be seen later, for the micellization process the models of the pseudophase and mass action30 were assumed. Namely, a mass action model was applied to the volumes of NaHex16 and NaL in water to determine the equilibrium constant for micellization (KM) and the aggregation number (n) (Table 1). The data for NaDec were taken from the literature.25 (27) Stimson, M. F. Am. J. Phys. 1955, 23, 614. (28) De Lisi, R.; Inglese, A.; Milioto, S.; Pellerito, A. J. Colloid Interface Sci. 1996, 180, 174. (29) De Lisi, R.; Marongiu, B.; Milioto, S.; Pittau, B.; Porceddu, S. J. Solution Chem. 1997, 26, 891. (30) Desnoyers, J. E.; Caron, G.; De Lisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397.

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Figure 1. Heat capacity (top) and enthalpy (bottom) of transfer of HP-R-CD (filled symbols) and HP-γ-CD (open symbols) from water to the aqueous sodium hexanoate solutions as functions of the surfactant concentration. Enthalpy data are at mC ) 0.02m (ref 13).

De Lisi et al.

Figure 2. Heat capacity (top) and enthalpy (bottom) of transfer of HP-R-CD (filled symbols) and HP-γ-CD (open symbols) from water to the aqueous sodium decanoate solutions as functions of the surfactant concentration. Enthalpy data are at mC ) 0.02m (ref 15).

The enthalpy and the heat capacity of micellization (∆Ym) were calculated by using the following equation:30

∆Ym ) YM - Y0S - YD-H[m0]1/2 - BY[m0] - CY[m0]3/2 (3) where [m0] is the monomer concentration; YM and Y0S are the partial molar property of the surfactant in the micellized and the standard states, respectively; YD-H is the Debye-Hu¨ckel parameter (28.95 J K-1 mol3/2 kg1/2 for the heat capacity31 and 1973 J mol3/2 kg1/2 for the enthalpy31); and BY and CY are the pair and triplet interaction parameters, respectively. Their values13,16,25,28,32 are collected in Table 1.

Results The dependence of ∆Cpt on the surfactant concentration (mS) for the present systems is shown in Figures 1-3 where, for sake of comparison, literature13,15 enthalpy of transfer (∆Ht) data are also plotted. The ∆Cpt versus mS curve of HP-R-CD/NaHex (Figure 1) is very peculiar: the heat capacity of transfer decreases with mS to ca. 1.2 mol kg-1 with a change in the slope at ca. 0.12 mol kg-1; ∆Cpt exhibits a maximum at higher concentration (ca. 2 mol kg-1), and thereafter it smoothly tends to a constant value. The corresponding trend13 for ∆Ht is different, as illustrated in Figure 1, which shows a minimum at mS ≈ 0.07 mol kg-1 in the range of the surfactant concentration investigated (to ca. 0.6 mol kg-1). This curve was interpreted by invoking the simultaneous presence of the 1:1 and 1:2 (1 cyclodextrin/2 surfactant molecules) complexes and ascribing the minimum to the appearance of the 1:2 complexes. Due to the small value of the equilibrium (31) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147. (32) Milioto, S.; Causi, S.; De Lisi, R. J. Colloid Interface Sci. 1993, 155, 452.

Figure 3. Heat capacity (top) and enthalpy (bottom) of transfer of HP-R-CD (filled symbols) and HP-γ-CD (open symbols) from water to the aqueous sodium dodecanoate solutions as functions of the surfactant concentration. Enthalpy data are at mC ) 0.02m (ref 15).

constant (K1:2) and the restricted range of mS analyzed, both K1:2 and the relative enthalpy change were not determined. For HP-γ-CD/NaHex (Figure 1), ∆Cpt versus mS is a sigmoid decreasing curve to mS ≈ 1.0 mol kg-1;


thereafter ∆Cpt increases, exhibiting a maximum at ca. 2 mol kg-1. In the surfactant region where ∆Cpt displays a shoulder, ∆Ht increases almost linearly (Figure 1) according to the low values of the equilibrium constants for the formation of the complexes.13,15 The dissimilarity between the ∆Cpt versus mS curves of the HP-CD/NaHex systems in the dilute surfactant region seems to evidence different phenomena although the enthalpy data of both systems were consistent with the presence of 1:1 and 1:2 complexes. The shape of the ∆Cpt versus mS trends of the HP-CD/NaDec mixtures (Figure 2) is independent of the cyclodextrin cavity size. The property of transfer decreases with mS to ca. 0.10 and 0.13 mol kg-1 for HP-R-CD/NaDec and HP-γ-CD/NaDec, respectively; thereafter it increases, tending to a constant value. The minima are localized at mS values close to the critical micellar concentration in water (cmcw ) 0.108 mol kg-1).33 These curves are diverse from those of the enthalpy of transfer.15 Namely, for HPR-CD/NaDec, ∆Ht shows a smooth minimum and maximum at ca. 0.04 and 0.08 mol kg-1, respectively, beyond which it decreases, tending to a constant value; for HPγ-CD/NaDec, ∆Ht increases to ca. 0.1 mol kg-1 and thereafter it decreases. Despite the unlike profile of the ∆Ht versus mS trends in the surfactant dilute region, both mixtures present the 1:1 and 1:2 inclusion complexes whose formation is regulated by enthalpic and entropic effects specific to the system. The ∆Cpt points of HP-RCD/NaL and HP-γ-CD/NaL (Figure 3) superimpose on each other to ca. 0.03 mol kg-1, the value of which is equal to cmcw,26 and then diverge, increasing for HP-R-CD/NaL and slightly decreasing for HP-γ-CD/NaL. These curves are dissimilar from those of ∆Ht:15 for HP-R-CD/NaL, ∆Ht apparently decreases in a monotonic manner with mS, whereas for HP-γ-CD/NaL the ∆Ht versus mS trend exhibits a maximum at mS ≈ cmcw. The enthalpic data to 0.03 mol kg-1 agreed with the 1:1 complex formation for HP-R-CD/NaL and with the simultaneous presence of 1:1 and 1:2 complexes for HP-γ-CD/NaL. The qualitative understanding of the heat capacity trends has not been facilitated by the examination of the enthalpy. No further support may be provided by the inspection of the volume of transfer,15 which basically presents the same enthalpy features. To comprehend these curves, it is useful to examine the heat capacity of surfactants in water22,25 or polar solutes (alcohols, for example) in micellar solutions.23,25 The decrease in the heat capacity accompanying the micellization or the solubilization of a solute in the micelles is basically due to the loss of hydrophobic hydration of the chain of the surfactant or the solute. Therefore, the ∆Cpt decrease exhibited by all the systems in the surfactant dilute region is consistent with the formation of inclusion complexes involving the transfer of the surfactant from water to the hydrophobic cavity of the cyclodextrin. This explanation is supported by the enthalpy13,15 and the volume15,16 results. The profile of the decreasing curves is system specific and may be an indication of the different relaxation terms which are functions of the magnitude of the equilibrium constant for the inclusion complex formation as well as the associated enthalpy. More complex is the interpretation of ∆Cpt in the surfactant concentrated region; the ∆Cpt increase generally observed for the investigated systems may reflect hydrophilic interactions likely present between the cyclodextrin polar surface and the shell of the micelles. Notwithstanding, apart from the terms appearing in the surfactant dilute region, others (33) De Lisi, R.; Milioto S.; Munafo`, M.; Muratore, N. J. Phys. Chem. B 2003, 107, 819.

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related to the shift of the micellization equilibrium and the cyclodextrin/micelle interactions together with their dependence on temperature are expected to contribute to ∆Cpt. These hypotheses can be verified by quantitative calculations which shall be done in the following section. Theoretical Approach When small amounts of surfactant are added to a cyclodextrin solution, the onset of binding between the surfactant and the cyclodextrin leading to the formation of the surfactant/cyclodextrin inclusion complex usually takes place; by increasing mS, the surfactant reaches the conditions for the micellization and, therefore, micellar aggregates are formed. The very few literature studies34-36 have ruled out that micelles and cyclodextrins interact with each other. Conversely, there is thermodynamic evidence on the affinity of the cyclodextrin toward the micelles controlled by hydrophilic interactions. These results arise from the modeling of enthalpy14,15 and volume15 data done by means of a thermodynamic model based on three contributions: (i) the formation of hostguest complexes in the aqueous phase, (ii) the shift of the micellization equilibrium induced by the cyclodextrin, and (iii) the process of interaction between micelles and cyclodextrin (free and complexed). If complexes of 1:1 and 1:2 stoichiometry do form, for the enthalpy one may write w ∆Ht ) ∆Ht(w f w + s) + Xw 1:1∆H1:1 + X1:2∆H1:2 +

XM 1:2(∆Ht,1:2 - 2∆Hm + ∆H1:2) + XM 1:1(∆Ht,1:1 - ∆Hm + ∆H1:1) + XC,M∆Ht,C +

{

∆Hm

}

cmcw - cmc′ w - Xw 1:1 - 2X1:2 mC

(4)

The fractions of the free cyclodextrin and the 1:1 and w w 1:2 complexes in the aqueous phase (Xw C , X1:1, and X1:2) are given by w Xw 1:1 ) XC K1:1cmc′

w 2 Xw 1:2 ) XC K1:2(cmc′)

(5)

M Xw C ) {K1:1cmc′[1 + K1:1(mS - cmca)] +

K1:2(cmc′)2[1 + KM 1:2(mS - cmca)] + -1 (6) KM C (mS - cmca) + 1} M whereas those in the micellar phases (XC,M, XM 1:1, and X1:2) are expressed as

w M 2 XM 1:2 ) XC K1:2K1:2(cmc′) (mS - cmca) w M XM 1:1 ) XC K1:1K1:1cmc′(mS - cmca) (7) M XC,M ) Xw C KC (mS - cmca)

(8)

where cmc′ is the free surfactant concentration in the presence of the cyclodextrin in equilibrium with the micelles and cmca is the apparent critical micellar concentration, essentially given by the sum of cmcw and the concentration of the surfactant in the complexed form;13,14 K1:1 and K1:2 are the equilibrium constants for (34) Dorrego, B.; Garcıà-Rıò, L.; Herve´s, P.; Leis, J. R.; Mejuto, J. C.; Pe´rez-Juste, J. J. Phys. Chem. B 2001, 105, 4912. (35) Jobe, D. J.; Reinsborough, V. C.; Wetmore, S. D. Langmuir 1995, 11, 2476. (36) Junquera, E.; Penã, L.; Aicart, E. Langmuir 1997, 13, 21.

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the 1:1 and 1:2 complex formation in water, and ∆H1:1 and M ∆H1:2 are the corresponding enthalpy changes. KM C , K1:1, M and K1:2 indicate the binding constants between the micelles and the free cyclodextrin, the 1:1 complex, and the 1:2 complex, respectively, and the associated enthalpies are ∆Ht,C, ∆Ht,1:1, and ∆Ht,1:2. ∆Hm is the enthalpy of micellization. Equation 4 cannot be applied to the heat capacity because the shift of the equilibria in solution with temperature must be also considered. Therefore, it was derived with respect to temperature, and the following equation was obtained:

δXw δXw 1:1 1:2 ∆H1:1 + ∆H1:2 + δT δT δXM 1:2 (∆Ht,1:2 - 2∆Hm + ∆H1:2) + δT δXC,M δXM 1:1 (∆Ht,1:1 - ∆Hm + ∆H1:1) + ∆Ht,C + δT δT δ cmcw - cmc′ w - Xw 1:1 - 2X1:2 ∆Hm + δT mC

∆Cpt )

{

}

∆Cpt(w f w + s) + cmcw - cmc′ w - Xw 1:1 - 2X1:2 + mC

{

∆Cpm Xw 1:1∆Cp1:1

}

M + Xw 1:2∆Cp1:2 + X1:2(∆Cpt,1:2 - 2∆Cpm ∆Cp1:2) + XM 1:1(∆Cpt,1:1 - ∆Cpm + ∆Cp1:1) +

+

equilibria for the inclusion complex formation and the shift of the micellization appear, and (3) the concentrated region (mS > cmca) where the processes for the interaction between micelle and cyclodextrin are present together with the equilibria of the middle region. (1) Analysis Extended to the 0 < mS e cmcw Region. Equation 9 assumes the following form to describe the phenomena in this interval: w ∆Cpt ) Xw 1:1∆Cp1:1 + X1:2∆Cp1:2 +

δXw δXw 1:1 1:2 ∆H1:1 + ∆H1:2 (10) δT δT The third and the fourth terms on the right-hand side of eq 10 represent the shift of the 1:1 and 1:2 complex formation equilibria with temperature, respectively. Their evaluation needs the knowledge of the equilibrium constants for the complex formation at a given temperature and the corresponding enthalpy variations. ∆Cpt corrected w for them can be divided by Xw 1:1 and plotted against X1:2/ w X1:1 to evaluate ∆Cp1:1 and ∆Cp1:2 as intercept and slope, respectively, of the obtained straight line. (2) Analysis Extended to the 0 < mS e cmca Region. This range represents the premicellar region of the watersurfactant-cyclodextrin ternary system wider than that of the water-surfactant binary mixture. Consequently, to ∆Cpt contribute not only the terms related to the equilibria for the complex formation but also the shift of the micellization equilibrium (Eshift∆Cpm) and its relaxation term, (δEshift/δT)∆Hm:

XC,M∆Cpt,C (9) where ∆Cp1:1 and ∆Cp1:2 are the heat capacity changes for the 1:1 and 1:2 host-guest complex formation, respectively. ∆Cpt(w f w + s) is the interaction contribution between the dispersed surfactant and the free cyclodextrin, which in the presence of complexes is negligible.14 ∆Cpt,C, ∆Cpt,1:1, and ∆Cpt,1:2 represent the heat capacity of transfer of the free cyclodextrin and the 1:1 and the 1:2 complexes from the aqueous to the micellar phases, respectively. ∆Cpm is the heat capacity of micellization. The other symbols assume the same meaning as above. Equation 9 is an involved relationship where the first six terms on the right-hand side are relaxation contributions. Equations formally identical to eq 9 must be written for the properties second derivatives of Gibbs free energy. The latter can be described by relationships such as eq 4 only when the relaxation contributions are negligible. The magnitude of these terms cannot be predicted, and its evaluation needs the acquaintance of the thermodynamics of the corresponding property first derivative. This aspect is sometimes missed. Gonza´lez-Gaitano et al.,20,21 for example, determined the adiabatic compressibility changes for the 1:1 complex formation of surfactant/β-cyclodextrin by using the Young model which is valid for the properties first derivatives. Treatment of the Experimental Data. On the basis of the pseudophase transition model for the micellization, the surfactant forms micelles in water at mS ) cmcw and in the water-cyclodextrin mixtures at mS ) cmca15,16,37 which is larger than cmcw. Therefore, the surfactant region investigated for the present systems may be ideally divided into three parts: (1) the dilute region (0 < mS e cmcw) where the complex formation equilibria are only present, (2) the middle region (cmcw < mS e cmca) where the (37) Junquera, E.; Pena, L.; Aicart, E. Langmuir 1997, 13, 219.

w ∆Cpt ) Xw 1:1∆Cp1:1 + X1:2∆Cp1:2 +

δXw 1:1 ∆H1:1 + δT

δXw δEshift 1:2 ∆H1:2 + ∆Hm + Eshift∆Cpm (11) δT δT

{

}

δEshift δ cmcw - cmc′ w ∆Hm ) - Xw 1:1 - 2X1:2 ∆Hm δT δT mC (12) Eshift ∆Cpm )

{

}

cmcw - cmc′ w - Xw 1:1 - 2X1:2 ∆Cpm mC

Despite its complexity, eq 11 was applied to the experimental data by considering that the equilibria for the complex formation and the micellization are simultaneously present. A mass action model30 described the micellization process. All the systems13,15 were analyzed according to the 1:1 and 1:2 model with the exception of HP-R-CD/NaL which presents only 1:1 complexes. The values of KM and n (Table 1) were used to calculate the monomer surfactant concentration in the absence of the cyclodextrin ([m0]) through the Newton-Raphson method. The concentration of the complexes and the monomer surfactant concentration in the presence of the cyclodextrin ([m]) were calculated through the Newton-Raphson method extended into two dimensions by using KM, n, and the values of the equilibrium constants for the complex formation13,15 (Table 2). Both [m0] and [m] replaced cmcw and cmc′, respectively, in eq 12. To evaluate (δEshift/δT), the KM temperature slope was calculated through the van’t Hoff equation by using ∆Hm and ∆Cpm, obtained from eq w 3, at 298 K. The Xw 1:1 and X1:2 temperature dependences were evaluated by assuming that the enthalpy is temperature independent (Table 2). The values of K1:2 and ∆H1:2 for HP-R-CD/NaHex and ∆H1:1 and ∆H1:2 for HP-


Langmuir, Vol. 19, No. 18, 2003 7193

Table 2. Thermodynamic Properties for the Inclusion Complex Formation between Hydroxypropyl-cyclodextrins and Sodium Alkanoates at 298 Ka HP-R-CD bK

1:1 b∆H 1:1

∆Cp1:1 bK

1:2 b∆H 1:2

∆Cp1:2

HP-γ-CD

NaHex

NaDec

NaL

NaHex

NaDec

NaL

445 ( 31c -6.44 ( 0.06c -352 ( 4 22d 16d -5070 ( 110

700 -19.9 ( 0.6 -520 ( 30 21 × 103 -16.1 ( 0.9 -750 ( 30

700 ( 400 -24.3 ( 1.8 -515 ( 8

0.82 37d -1940 ( 70 1.9 39d -1830 ( 60

55 17.4 ( 0.6 -560 ( 50 1.3 × 103 5(1 -1680 ( 50

155 17.4 ( 0.8 -700 ( 20 6.4 × 103 -21 ( 4 -1870 ( 50

Units: K1:1, kg mol-1; K1:2, kg2 mol-2; kJ mol-1 for enthalpy; J K-1 mol-1 for heat capacity. b From ref 13. c From ref 15. value (see text). a

d

Extrapolated

Figure 4. Experimental data (symbols) and values calculated through eq 11 (line) for heat capacity of transfer of HP-R-CD from water to the aqueous sodium hexanoate solutions as functions of the surfactant concentration (top). Bottom: (a) relaxation term for the 1:2 complex formation equilibrium, (b) shift of the micellization equilibrium contribution, (c) relaxation term of the shift of micellization equilibrium, (d) relaxation term for the 1:1 complex formation equilibrium, and (e) contribution for the complex formation equilibria.

Figure 5. Experimental data (symbols) and values calculated through eq 11 (line) for heat capacity of transfer of HP-γ-CD from water to the aqueous sodium dodecanoate solutions as functions of the surfactant concentration (top). Bottom: (a) shift of the micellization equilibrium contribution, (b) relaxation term for the 1:2 complex formation equilibrium, (c) relaxation term for the 1:1 complex formation equilibrium, (d) relaxation term of the shift of the micellization equilibrium, and (e) contribution for the complex formation equilibria.

γ-CD/NaHex were extrapolated from the data of the higher homologues. According to eq 11, ∆Cpt, corrected for the terms in eq 12 and the relaxation contributions of the equilibria of complex formation (∆Cpt,cor), was divided by w w Xw 1:1 and plotted against X1:2/X1:1. ∆Cp1:1 and ∆Cp1:2 were evaluated as intercept and slope, respectively, of the obtained straight line (Table 2). For NaL/HP-R-CD, ∆Cp1:1 was obtained as slope of the ∆Cpt,cor versus Xw 1:1 straight line. The ∆Cpt points calculated by means of eq 11 match very well the experimental ones in a more or less wide range of mS depending on the mixture as evidenced by some examples represented in Figures 4-6. For each system, when the amount of the micellized surfactant concentration becomes appreciable (ca. 2 × 10-4 mol kg-1) the experimental and the calculated data start to diverge. The mS value at which this occurs corresponds to that of cmca. The different shapes of the ∆Cpt versus mS trends fitted by eq 11 may be understood by analyzing the various terms which contribute to the property of transfer. The

equilibria for the HP-R-CD/NaHex complex formation are the only ones responsible for the decrease in ∆Cpt to 0.12 mol kg-1; at larger concentration, the additional positive (δXw 1:2/δT)∆H1:2 term generates a change in the slope and mainly defines the peculiar trend to 1.8 mol kg-1 (Figure 4). For HP-R-CD/NaL and HP-R-CD/NaDec, the ∆Cpt decrease is due to the complexation processes whereas Eshift∆Cpm causes the ∆Cpt increase. The complexation equilibria and their shift with temperature determine the ∆Cpt versus mS trend to 1.2 mol kg-1 for HP-γ-CD/NaHex. As Figure 5 shows, the same terms contribute to ∆Cpt of HP-γ-CD/NaL to 0.03 mol kg-1 above which Eshift∆Cpm is mainly responsible for the smaller slope of ∆Cpt. Finally, for HP-γ-CD/NaDec, ∆Cpt essentially diminishes because of the complex formation equilibria whereas its increase is due to the shift of the micellization equilibrium and its temperature dependence (Figure 6). In conclusion, ∆Cpt has been revealed as a very complex property to study which contains several contributions, the importance of which cannot be stated a priori. From the above analysis, in fact, it turns out that the predomi-

7194


De Lisi et al.

Figure 7. Heat capacity of transfer of HP-R-CD (b) and HPγ-CD (O) from water to the aqueous sodium decanoate micellar solution corrected for Eshift∆Cpm, the relaxation terms and the 1:1 and 1:2 complex formation contributions (eq 9) as a function of the fraction of the 1:1 complex bound to the micellar phase.

Figure 6. Experimental data (symbols) and values calculated through eq 11 (line) for heat capacity of transfer of HP-γ-CD from water to the aqueous sodium decanoate solutions as functions of the surfactant concentration (top). Bottom: (a) shift of the micellization equilibrium contribution, (b) relaxation term for the 1:1 complex formation equilibrium, (c) relaxation term of the shift of micellization equilibrium, (d) relaxation term for the 1:2 complex formation equilibrium, and (e) contribution for the complex formation equilibria.

nance of a given term over another is strictly dependent on the nature of the cyclodextrin/surfactant mixture. (3) Analysis Extended to the Micellar Solutions. The deviation of the experimental points from those calculated through eq 11 may reflect the cyclodextrin-micelle interaction contributions and the relative relaxation terms as well as the shift of the micellization equilibrium due to the cyclodextrin-micelle interactions and its temperature slope. The quantitative description of ∆Cpt in the micellar region is thereby very complicated (eq 9). A correct analysis needs the knowledge of the thermodynamics (free energy and enthalpy) of the cyclodextrin-micelle interactions which is available for the systems15 containing NaL and NaDec. Nevertheless, the points available for NaL being few (due to the experimental problems), we shall analyze the HP-CD/NaDec systems. For sake of simplicity, we assume the pseudophase transition model for the micellization and that only the 1:1 complex interacts with the micelles because the free cyclodextrin amount in water is negligible and the interactions between the micellar surface and the doubly charged complexes are unfavorable. This statement is supported by thermodynamic results of other cyclodextrin/ionic surfactant mixtures.14 The shift of the micellization equilibrium was calculated through eq 13:

[

∆Cpm

]

cmcw - cmc′ ) mC w w (∆Cpm cmc′/2)[2.3KS(Xw 1:1+ X1:2+ XC ) +

(1 +

w β)(KM 1:2X1:2

+

w KM 1:1X1:1

+

w KM C XC )]

(13)

where KS is the Setchenov constant, which was assumed equal for the two complexes and free cyclodextrin, and β

is the degree of ionization of the micelles, the value of which was taken from the literature.33 In evaluating the (δEshift/δT)∆Hm term, KS was assumed to be temperature independent because the corresponding parameter for enthalpy is not detected13-15 in the presence of inclusion complexes. Also, the cmc′ shift with temperature was calculated by using ∆Hm at 298 K evaluated at cmcw. To the best of our knowledge, δβ/δT for NaDec is unknown, and therefore, the value of 3.4 × 10-3 reported38 for dodecyltrimethylammonium bromide was employed. This approximation is reliable since the magnitude of the term relative to δβ/δT is small. The heat capacity of transfer was corrected for the various calculated contriM butions (∆CpM t,cor) and plotted against X1:1 (Figure 7). The M ∆Cpt,cor points of both the systems, within their uncertainties (ca. 100 J K-1 mol-1), fall on a single straight line with intercept and slope close to zero. These findings agree with other thermodynamic results14,15 which evidenced interactions between cyclodextrins and micelles. The independence of the free energy on the hydrophobicity of the surfactant and the negative enthalpy values of the analyzed systems14,15 agree with the hydrophilic interactions between micelles and cyclodextrin. The heat capacity change is expected to be positive, but likely due to its small value and to the large errors on ∆CpM t,cor points, a reliable value cannot be determined. The evidence of cyclodextrin/micelle aggregates is a significant result also in view of the recent attention paid to amphiphilic cyclodextrins,39,40 which are promising molecules for drug encapsulation and delivery because of their properties as macrocyclic hosts and of self-assembly. These macromolecules show very low solubility in water and produce thermodynamically unstable systems. The actual efforts40,41 have been, thereby, devoting to overcoming these limits. Our cyclodextrin-micelle structures present the features of the aggregates formed by the amphiphilic cyclodextrin and, also, are thermodynamically stable. Thus, the appropriate choice of the macrocycle and the surfactant may allow one to design microstructures with functional properties for specific applications. (38) De Lisi, R.; Milioto, S. J. Solution Chem. 1987, 16, 676. (39) Auze´ly-Velty, R.; Peán, C.; Djedaı¨ni-Pilard, F.; Zemb, Th.; Perly, B. Langmuir 2001, 17, 504. (40) Mazzaglia, A.; Ravoo, B. J.; Darcy, R.; Gambadauro, P.; Mallamace, F. Langmuir 2002, 18, 1945 and references therein. (41) Auze´ly-Velty, R.; Djedaı¨ni-Pilard, F.; De´sert, B.; Perly, B.; Zemb, Th. Langmuir 2000, 16, 3728.


Figure 8. Dependence on the number of carbon atoms in the surfactant alkyl chain of the heat capacity for the formation of 1:1 complexes (open symbols) and 1:2 complexes (filled symbols) between HP-R-CD/sodium alkanoates (triangles), HP-β-CD/ sodium alkanoates (circles), and HP-γ-CD/sodium alkanoates (squares).

Heat Capacity Changes for the Cyclodextrin-Surfactant Inclusion Complex Formation Figure 8 illustrates the dependence of ∆Cp1:1 and ∆Cp1:2 on the number of carbon atoms in the surfactant alkyl chain (nc). The ∆Cp1:1 values16 for HP-R-CD/sodium butanoate, HP-R-CD/sodium octanoate (NaOct), and HPγ-CD/NaOct are also represented. For sake of comparison, the ∆Cp1:1 data for the sodium alkanoate/HP-β-CD systems are plotted.16 The negative values are consistent with the transferring of the surfactant alkyl chain from water to the cyclodextrin cavity. ∆Cp1:1 decreases and increases with nc in a nonlinear manner for the complexes formed by HP-R-CD and HP-γ-CD, respectively, and the additivity group, thereby, does not hold. However, a rough evaluation of the methylene group contribution provides the value of -70 ( 15 and 280 ( 20 for HP-R-CD and HP-γ-CD, respectively. The former, within the uncertainties, is very close to the value obtained as the difference between the CH2 group in an apolar solvent42 (30 J K-1 mol-1) and in (42) De Lisi, R.; Milioto, S.; Inglese, A. J. Phys. Chem. 1991, 95, 3322.

Langmuir, Vol. 19, No. 18, 2003 7195

water43 (88 J K-1 mol-1) and smaller than that evaluated for the alcohol/R-cyclodextrin12 and the HP-β-CD/sodium alkanoate.16 In these cases, the loss of freedom degree of the hydrocarbon chain in the cyclodextrin cavity was invoked. The positive value of the ∆Cp1:1(CH2) for HPγ-CD can be due to the release of several water molecules from the cyclodextrin. On the other hand, it is expected that HP-γ-CD is more hydrated than HP-R-CD and HPβ-CD because of its larger size. We recall that the methylene group contribution to the standard free energy for the 1:1 complex formation between sodium alkanoates and HP-R-CD15,16 or HP-β-CD16 is -4.1 kJ mol-1 whereas it is -2.3 kJ mol-1 for the γ-CD/ω-phenylalkanoic acids.44 To our knowledge, the present ∆Cp1:2 values are the only ones available in the literature. For both the cyclodextrins, ∆Cp1:2 < ∆Cp1:1. Direct information on the mechanism of the interaction between each surfactant molecule and the macrocycle may be drawn by comparing ∆Cp1:1 to ∆Cp′ (∆Cp′ ) ∆Cp1:2 - ∆Cp1:1) which represents the process of interaction between the second surfactant molecule and the 1:1 complex. For the HP-γ-CD/sodium alkanoate systems, the ∆Cp′ versus nc slope (-170 ( 50) may reflect the tighter binding of the methylene group to the inner cyclodextrin cavity with respect to the first one. This result is consistent with free energy15,44 and enthalpy data.15 The positive slope of the ∆Cp′ versus nc trend for the HP-R-CD/surfactant systems may be ascribed to a different mechanism of interaction controlled by the release of water molecules from the torus extended by the hydroxypropyl groups where the CH2 group may be lodged. This explanation agrees with other thermodynamic findings.14,15 Acknowledgment. The authors are grateful to the MIUR and the University of Palermo (Bando CORI 2002) for the financial support. Supporting Information Available: Tables of the apparent molar heat capacities for sodium hexanoate and sodium dodecanoate in water and for HP-R-CD and HP-γ-CD in aqueous surfactant solutions. This material is available free of charge via the Internet at http://pubs.acs.org. LA0342316 (43) Perron, G.; Desnoyers, J. E. Fluid Phase Equilib. 1979, 2, 239. (44) Rekharsky, M.; Inoue, Y. J. Am. Chem. Soc. 2000, 122, 10949.

Heat Capacity Study to Evidence the Interactions between

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