890
Langmuir 1996, 12, 890-901
Energetics of Water-Dodecyl Surfactant-Macrocyclic Compound Ternary Systems R. Crisantino, R. De Lisi,* S. Milioto, and A. Pellerito Dipartimento di Chimica Fisica, Universita` di Palermo, via Archirafi 26, 90123 Palermo, Italy Received December 29, 1994. In Final Form: September 28, 1995X Enthalpies of dilution and osmotic coefficients of sodium dodecyl sulfate (NaDS) and dodecyltrimethylammonium bromide (DTAB) in water + 18-crown-6 ether (CR) and water + β-cyclodextrin (CD) at a fixed cosolvent concentration were measured at 298 and 310 K, respectively, as functions of the surfactant concentration (mS). Enthalpies of transfer ∆H (W f W + S) of CR (0.03 m) from water to NaDS and DTAB aqueous solutions as functions of mS were also determined at 298 K. From the enthalpies of dilution the apparent (LΦ,S) and partial (L2,S) molar relative enthalpies of both surfactants were calculated. Despite CR forms inclusion complexes with the anionic surfactant only, the L2,S vs mS profiles are similar and the enthalpies of micellization are lower than those in water by about -5 kJ mol-1. In the case of CD as a cosolvent, the L2,S vs mS profile for DTAB is similar to that for NaDS in the postmicellar region but very different in the premicellar one. The trends in the premicellar region are discussed in terms of different solute-solute hydrophilic interactions other than encapsulation while those in the postmicellar region are discussed in terms of the micellization process. The enthalpies of micellization are very large because of the complexed monomers contribution. ∆H (W f W + S) data for CR in DTAB micellar solutions were fitted through an equation previously reported which permits simultaneously obtaining the distribution constant of the uncomplexed CR and its enthalpy of transfer from the aqueous to the micellar phases. The equations were reviewed for CR in NaDS micellar solutions to account for the CR complexation and for the distribution of both the complexed and uncomplexed CR between the aqueous and the micellar phases. The derived properties are briefly discussed. The osmotic coefficient (ΦS) vs mS curve of both surfactants in W + CD shows a minimum at mS equal to the CD concentration (mCD) and a maximum at mS ) mCD + cmc. These peculiarities are ascribed to the inclusion complex formation between the macrocyclic compound and the apolar chain of the surfactant. The addition of CR to water leads to the shift of the osmotic coefficient toward lower values. This shift is not very important for DTAB while it is for NaDS for which negative ΦS values were obtained. Sodium perfluorooctanoate behaves like NaDS. Since the osmotic coefficients for NaCl in W + CR are close to those in pure water, the results are interpreted in terms of complexed CR solubilization in the micellar phase.
Introduction Cyclodextrins and crown ethers are macrocyclic compounds which undergo inclusion complex formation. In particular, the former, having a hydrophilic external surface and a hydrophobic inner cavity, can encapsulate hydrophobic alkyl chains while the latter, having a hydrophobic external surface and hydrophilic inner cavity, can encapsulate alkali cations.1-4 Therefore, anionic surfactants can form complexes with both cyclodextrins and crown ethers. Different techniques (conductivity,5 potentiometry,6 spectrophotometry,7 ultrasound velocity8) have been used to obtain the complexation constant and the stoichiometry of the complex. Thermodynamic techniques are scarcely used especially in the case of complex formation between macrocyclic compounds and surfactants. In addition, thermodynamic studies of water-surfactant-macrocyclic compound systems were performed in the premicellar region9 or just beyond it so that information on the effect of the complexation on the micellization process is not available. As far as we know, the few studies dealing with the complex formation in micellar solutions concern the enthalpies of X
Abstract published in Advance ACS Abstracts, January 1, 1996.
(1) Gokel, G. Crown Ethers & Cryptands; The Royal Society of Chemistry: Cambridge, 1991. (2) Li, S.; Purdy, W. C. Chem. Rev. 1992, 92, 1457. (3) Bhattacharyya, K.; Chowdhury, M. Chem. Rev. 1993, 93, 507. (4) Høiland, H.; Ringseth, J. A.; Brun, T. S. J. Solution Chem. 1979, 8, 779. (5) Saint Aman, E.; Serve, D. J. Colloid Interface Sci. 1990, 138, 365. (6) Wan Yunus, W. M. Z.; Taylor, J.; Bloor, D. M.; Hall, D. G.; WynJones, E. J. Phys. Chem. 1992, 96, 8979. (7) Dale, J.; Kristiansen, P. O. Acta Chem. Scand. 1972, 26, 148. (8) Junquera, E.; Aicart, E.; Taradajos, E. J. Phys. Chem. 1992, 96, 4533. (9) Evans, D. F.; Sen, R.; Warr, G. G. J. Phys. Chem. 1986, 90, 5500.
0743-7463/96/2412-0890$12.00/0
mixing10 of various surfactants (sodium dodecyl sulfate (NaDS), hexadecyltrimethylammonium bromide, and Triton X-100) with R-, β-, and γ-cyclodextrins, the partial molar volumes and compressibilities of sodium decanoate in aqueous crown ether11 solutions, and the free energies of transfer of crown ethers from water to NaDS and dodecyltrimethylammonium bromide (DTAB) micellar phases.12 Also, we reported elsewhere volume and heat capacity data for water-surfactant (NaDS and DTAB)macrocyclic compound (β-cyclodextrin and 18-crown-6 ether) ternary systems.13,14 It was shown that the above properties for CR in DTAB do not depend on the surfactant concentration while they do in NaDS. Therefore, it was not possible to rationalize the apparent molar volume for CR in NaDS by considering all the equilibria involved, i.e. the distribution of CR in the complexed and uncomplexed form between the aqueous and the micellar phases and the CR complexation in both the aqueous and the micellar phases. As far as CD is concerned, while in the postmicellar region the presence of CD practically does not affect the properties of DTAB and NaDS, in the premicellar region it does but the very few experimental points analyzed and their uncertainties (due to the low cmc) were unsuccessful to improve our knowledge on these systems. Generally, enthalpy is one thermodynamic property most sensitive to solute-solute interactions at low concentrations and to the distribution processes especially in (10) Turco Liveri, V.; Cavallaro, G.; Giammona, G.; Pitarresi, G.; Puglisi, G.; Ventura, C. Thermochim. Acta 1992, 199, 125. (11) Vikingstad, E.; Bakken, J. J. Colloid Interface Sci. 1980, 74, 8. (12) Stilbs, P. J. Colloid Interface Sci. 1982, 87, 385. (13) Bakshi, M. S.; Crisantino, R.; De Lisi, R.; Milioto, S. Langmuir 1994, 10, 423. (14) Milioto, S.; Bakshi, M. S.; Crisantino, R.; De Lisi, R. J. Solution Chem. 1995, 24, 103.
© 1996 American Chemical Society
Energetics of Ternary Systems
Langmuir, Vol. 12, No. 4, 1996 891
the case of low distribution constants. For example, for methanol in NaDS15 the binding constant is 0.4 kg mol-1 and the enthalpy of transfer 4.6 kJ mol-1 while, as for CR in DTAB, the volume of transfer is zero.16 Therefore, in order to obtain more information on water-macrocyclesurfactant systems, we decided to extend our previous studies to the enthalpy. In addition, osmotic coefficients were also studied since they are usually simple to interpret and rationalize because of their dependence on the number of particles only, the other thermodynamic properties needing extra terms. In particular, the enthalpies of dilution at 298 K and osmotic coefficients at 310 K of the two surfactants in aqueous solutions of both the macrocyclic compounds at a fixed concentration and the enthalpies of mixing at 298 K of surfactant and CR aqueous solutions were performed. Experimental Section Materials. 18-Crown-6 ether (CR) and β-cyclodextrin (CD), Sigma products, were dried in a vacuum oven at 308 K for at least 4 days before the use. From several K. Fischer analyses performed by using a Metrohm 655 Dosimat, it was found that β-cyclodextrin contained 11.6% (w/w) of water. Since CD is hygroscopic, the product was kept in the oven and before use the correct amount of water in each sample was determined from density measurements as described elsewhere.14 Sodium dodecyl sulfate (NaDS), Fluka, and dodecyltrimethylammonium bromide (DTAB), Sigma, were crystallized from ethanol and ethanolethyl acetate mixture, respectively, and dried in a vacuum oven at 333 K for 2 days. Perfluorooctanoic acid, Fluka product, was crystallized from carbon tetrachloride and dried at room temperature. Sodium perfluorooctanoate (NaPFO) was prepared by neutralizing the perfluorooctanoic acid with a sodium hydroxide aqueous solution. NaPFO was crystallized twice from the ice-cold solution and dried in a vacuum oven at 60 °C for at least 2 days before its use. All solutions were prepared by mass using degassed conductivity water and their concentrations were expressed as number of solute moles per kilogram of the solvent. Equipment. The enthalpies of dilution of CR in water and of surfactants in CR (≈0.45 m) or CD (≈0.02 m) aqueous solutions and the enthalpies of mixing between CR and surfactant aqueous solutions were carried out with a flow LKB 2107 microcalorimeter at 298 ( 0.01 K. In order to obtain more accurate data for the enthalpies of mixing, the measurements were performed by taking as baseline for the mixing process the enthalpy of dilution of the same surfactant solution with water. Enthalpies of mixing were carried out at a constant CR concentration (≈0.06 m) as a function of the surfactant concentration. The injection of the solutions into the microcalorimeter was made by means of a Gilson peristaltic pump (Minipuls 2) and the flow of each solution was determined by weight. The additive and the surfactant concentrations after the dilution (or mixing) are given by the initial ones (mi) times the corresponding dilution factor fi
fi )
Fw i Fw i
+
Fw j
fj ) 1 - fi
(1)
w where Fw i and Fj indicate the flow of the solvent in the two solutions. The osmotic coefficients (ΦS) were measured by means of an Osmomat 070 (Gonotec) vapor pressure osmometer equipped with an automatic control unit. The following equation was used
ΦS ) K∆R/νm
(2)
where ∆R is the difference in the readings when the solvent is replaced by the solution in one of the two thermistors. K is the (15) De Lisi, R.; Milioto, S. J. Solution Chem. 1988, 17, 245. (16) De Lisi, R.; Lizzio, A.; Milioto, S.; Turco Liveri, V. J. Solution Chem. 1986, 15, 623.
Table 1. Enthalpies of Dilution of 18-Crown-6 Ether in Water at 298 Ka mCR
fCRmCR
CR -∆Hid
0.02540 0.06010 0.09390 0.1476 0.1883 0.2529 0.3061 0.3451 0.3758 0.4650
0.01153 0.02766 0.04231 0.06629 0.08138 0.1081 0.1301 0.1461 0.1655 0.2040
0.081 0.18 0.29 0.44 0.58 0.76 0.92 1.02 1.08 1.32
a Units are mol kg-1 for concentrations and kJ mol-1 for enthalpies.
calibration constant, and ν is the number of ions into which the solute dissociates. The measurements were made at 310 K, the lowest operating temperature suggested for aqueous solutions. The instrument was calibrated using aqueous NaCl solutions at given osmolalities.17 The accuracy on ΦS is better than 2%. The osmotic coefficient measurements of DTAB and NaDS in water + CR and water + CD mixtures were carried out as functions of mS and those of NaCl in CR aqueous solutions as functions of NaCl concentration.
Results and Discussion Enthalpies of Dilution of Macrocyclic Compounds in Water. The enthalpies of dilution (∆HCR id ) of CR in water together with the initial (mCR) and the final (fCRmCR) concentrations are summarized in Table 1. They were fitted as a function of concentration according to the following equation18
∆HCR id (fCR - 1)mCR
) hxx + hxxx[(fCR + 1)mCR]
(3)
where hxx and hxxx represent the pair and triplet interaction parameters, respectively. The values of these parameters, i.e. the intercept and slope of eq 3, are hxx ) 5.75 ( 0.06 kJ kg mol-2 and hxxx ) 1.17 ( 0.10 kJ kg-2 mol-3. In the case of CD, the very low solubility did not make possible the study of the enthalpies of dilution as a function of concentration. The only dilution process analyzed was that from mCD ) 0.017 m to mCD ) 0.0085 m for which -1 ∆HCD id ) 0.10 kJ mol . Enthalpies of Dilution of Surfactants in Macrocyclic Aqueous Solutions. The apparent molar relative enthalpies (LΦ,S) of surfactants in the aqueous solution of the macrocyclic compound at fixed concentration were derived from the enthalpies of dilution (∆HSid) using the equation
∆HSid ) (LΦ,S)f - (LΦ,S)i
(4)
where (LΦ,S)f and (LΦ,S)i refer to the final and initial states, respectively. The enthalpies of dilution together with the final (fSmS) and initial (mS) surfactant concentrations are collected in Tables 2-5. In the premicellar region, LΦ,S in the solvent mixture was expressed as a function of mS as19
LΦ,S ) ALmS1/2 + BLmS + CLmS3/2 + ...
(5)
where AL is the Debye-Hu¨ckel limiting slope and BL and CL are the pair and triplet interaction parameters, (17) Janz, G. J.; Gordon, A. R. J. Am. Chem. Soc. 1943, 65, 218. (18) De Lisi, R.; Milioto, S.; Turco Liveri, V. J. Colloid Interface Sci. 1987, 117, 64. (19) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147.
892
Langmuir, Vol. 12, No. 4, 1996
Crisantino et al.
Table 2. Enthalpies of Dilution and Apparent and Partial Molar Relative Enthalpies of Dodecyltrimethylammonium Bromide in Water-18-Crown-6 Ether Mixture 0.4063 m at 298 Ka
Table 4. Enthalpies of Dilution and Apparent and Partial Molar Relative Enthalpies of Dodecyltrimethylammonium Bromide in Water-β-Cyclodextrin Mixture 0.01749 m at 298 Ka
mS
fSmS
S ∆Hid
(LΦ,S)i
(LΦ,S)f
(L2,S)i
(L2,S)f
mS
fSmS
S ∆Hid
(LΦ,S)i
(LΦ,S)f
(L2,S)i
(L2,S)f
0.003 34 0.003 96 0.005 75 0.007 40 0.012 16 0.012 50 0.015 74 0.018 32 0.021 18 0.028 15 0.032 59 0.049 91 0.078 16 0.117 4 0.154 7 0.191 9 0.249 1 0.283 8 0.417 5 0.503 7 0.788 7
0.001 65 0.001 96 0.002 77 0.003 65 0.005 85 0.006 17 0.007 57 0.009 05 0.011 94 0.013 39 0.015 35 0.023 47 0.036 54 0.054 64 0.072 26 0.088 73 0.100 7 0.114 2 0.167 0 0.242 8 0.351 6
-0.14 -0.19 -0.61 -0.23 -0.26 -0.36 -0.38 -0.39 0.05 1.47 1.78 2.47 1.91 1.65 1.40 1.34 1.21 1.10 0.98 1.04 0.95
0.36 0.40 0.53 0.63 0.87 0.88 1.00 1.08 0.76 -0.34 -0.95 -2.17 -3.24 -4.07 -4.52 -4.82 -5.02 -5.08 -5.63 -6.06 -6.29
0.21 0.24 0.31 0.38 0.53 0.55 0.64 0.72 0.86 0.92 0.99 0.32 -1.24 -2.40 -3.08 -3.53 -3.76 -4.03 -4.65 -5.02 -5.34
0.62 0.70 0.90 1.06 1.38 1.40 1.52 1.58 -2.40 -3.83 -4.20 -5.00 -5.51 -5.75 -5.85 -5.90 -5.94 -5.95 -6.99 -7.03 -7.09
0.37 0.42 0.54 0.66 0.91 0.94 1.07 1.19 1.37 1.43 1.51 -3.30 -4.45 -5.13 -5.44 -5.60 -5.68 -5.74 -5.87 -5.93 -5.97
0.002 09 0.002 55 0.004 77 0.006 47 0.009 88 0.012 98 0.018 64 0.022 58 0.026 29 0.028 89 0.031 85 0.040 92 0.049 49 0.058 31 0.067 05 0.073 40 0.087 35 0.098 80 0.116 0 0.135 9 0.150 4 0.176 8 0.196 7 0.228 2 0.266 0 0.311 8 0.362 6
0.001 02 0.001 20 0.002 31 0.003 16 0.004 78 0.006 29 0.009 05 0.010 94 0.013 32 0.014 63 0.016 14 0.020 71 0.024 08 0.028 33 0.032 58 0.039 21 0.046 46 0.052 58 0.056 65 0.071 70 0.072 25 0.092 70 0.094 02 0.107 9 0.125 0 0.145 6 0.168 6
0.40 0.44 0.74 0.99 1.39 1.59 0.36 -2.01 -3.69 -4.31 -4.81 -4.57 -4.07 -3.29 -2.78 -1.99 -1.60 -1.35 -1.29 -0.88 -0.94 -0.57 -0.55 -0.46 -0.35 -0.17 -0.06
-0.74 -0.90 -1.60 -2.09 -2.95 -3.63 -3.00 -1.18 -0.10 0.55 1.13 2.40 3.18 3.68 4.00 4.19 4.47 4.64 4.86 5.00 5.08 5.16 5.20 5.24 5.29 5.29 5.30
-0.36 -0.44 -0.82 -1.10 -1.60 -2.03 -2.75 -3.20 -3.70 -3.96 -3.76 -1.98 -0.68 0.45 1.31 2.18 2.92 3.36 3.59 4.14 4.15 4.56 4.58 4.77 4.94 5.06 5.14
-1.46 -1.75 -3.02 -3.86 -5.28 -6.28 2.70 5.50 6.50 6.80 6.88 6.75 6.54 6.40 6.28 6.20 6.06 5.98 5.89 5.80 5.74 5.64 5.58 5.51 5.44 5.38 5.34
-0.74 -0.89 -1.60 -2.12 -3.03 -3.78 -4.96 -5.65 -4.50 -2.50 0 4.90 6.00 6.70 6.90 6.80 6.60 6.50 6.41 6.22 6.20 6.03 6.02 5.93 5.89 5.75 5.67
a Units are mol kg-1 for concentrations and kJ mol-1 for enthalpies.
Table 3. Enthalpies of Dilution and Apparent and Partial Molar Relative Enthalpies of Sodium Dodecyl Sulfate in Water-18-6 Ether Mixture 0.4690 m at 298 Ka
a
mS
fSmS
S ∆Hid
(LΦ,S)i
(LΦ,S)f
(L2,S)i
(L2,S)f
0.003 50 0.004 50 0.005 57 0.007 01 0.014 91 0.019 17 0.029 58 0.039 98 0.063 14 0.112 6 0.131 2 0.185 4 0.195 5 0.265 1 0.339 5 0.419 9
0.001 88 0.002 24 0.003 00 0.003 81 0.008 05 0.010 21 0.015 72 0.021 22 0.033 20 0.053 23 0.068 88 0.087 08 0.101 2 0.123 6 0.171 2 0.195 0
-0.12 -0.20 0.31 0.77 1.42 1.41 1.17 1.00 0.71 0.61 0.55 0.45 0.40 0.32 0.25 0.23
0.36 0.44 0.04 -0.38 -2.06 -2.61 -3.42 -3.86 -4.32 -4.74 -4.84 -5.00 -5.02 -5.14 -5.22 -5.29
0.22 0.25 0.32 0.39 -0.67 -1.14 -2.19 -2.83 -3.60 -4.17 -4.40 -4.58 -4.68 -4.80 -4.96 -5.02
0.66 0.82 -2.06 -2.65 -4.20 -4.54 -4.96 -5.13 -5.29 -5.37 -5.38 -5.40 -5.40 -5.41 -5.41 -5.41
0.39 0.45 0.58 0.71 -2.98 -3.51 -4.28 -4.66 -5.03 -5.24 -5.31 -5.34 -5.36 -5.38 -5.40 -5.40
a
For units see Table 2.
respectively. Equations 4 and 5 can be combined and rearranged in the following form
∆HSid - AL[(fS1/2 - 1)mS1/2] (fS - 1)mS
) BL + CL
(fS3/2 - 1) mS1/2 (6) fS - 1
from which BL and CL can be evaluated as intercept and slope, respectively, provided that AL is known for the given mixed solvent. Since this is not the case here, the AL value in pure water (1973 J mol-3/2 kg1/2) was used19 and, then, BL and CL (whose values are reported in Table 6) are to be considered as simply curve fitting parameters. For the dilution processes whose final and initial concentrations are smaller and larger, respectively, than the cmc (LΦ,S)f was calculated by means of eq 5 and the BL and CL parameters, while (LΦ,S)i, by means of eq 4; therefore, LΦ,S in a larger concentration interval is obtained; by repeating the procedure LΦ,S values in the whole range of mS were obtained. They are collected in Tables 2-5 together with
For units see Table 2.
Table 5. Enthalpies of Dilution and Apparent and Partial Molar Relative Enthalpies of Sodium Dodecyl Sulfate in Water-β-Cyclodextrin Mixture 0.01773 m at 298 Ka mS
fSmS
S ∆Hid
(LΦ,S)i
(LΦ,S)f
(L2,S)i
(L2,S)f
0.001 93 0.002 64 0.002 70 0.003 87 0.004 09 0.005 26 0.005 82 0.007 06 0.007 81 0.011 08 0.012 02 0.013 70 0.019 41 0.024 33 0.025 24 0.027 78 0.028 90 0.033 76 0.036 35 0.038 80 0.042 03 0.042 65 0.045 71 0.049 12 0.053 89 0.057 88 0.062 00 0.064 43 0.073 01 0.078 93 0.093 40 0.119 2 0.153 9
0.000 918 0.001 29 0.001 32 0.001 84 0.002 12 0.002 57 0.002 83 0.002 53 0.003 81 0.005 46 0.005 93 0.006 88 0.009 73 0.011 90 0.012 68 0.013 60 0.014 49 0.016 92 0.017 80 0.019 43 0.021 48 0.020 90 0.023 06 0.024 70 0.027 08 0.027 80 0.029 70 0.030 80 0.035 39 0.038 79 0.046 20 0.063 00 0.075 31
-0.05 -0.78 -0.77 -1.00 -1.73 -1.90 -1.82 -2.47 -2.47 -3.02 -3.37 -3.40 -5.65 -7.72 -8.25 -8.49 -8.73 -7.99 -8.89 -7.94 -7.47 -7.59 -7.00 -6.58 -6.27 -6.34 -5.85 -5.86 -5.05 -4.46 -3.68 -2.45 -2.10
1.15 1.56 1.59 2.25 2.38 3.04 3.35 4.05 4.47 6.30 6.83 7.77 10.95 13.69 14.19 15.40 15.87 17.54 18.25 18.84 19.51 19.62 20.15 20.67 21.28 21.71 22.10 22.31 22.93 23.28 23.95 24.74 25.39
0.57 0.78 0.80 1.10 1.26 1.51 1.66 1.49 2.22 3.15 3.41 3.95 5.55 6.76 7.20 7.71 8.21 9.56 10.05 10.96 12.10 11.78 12.98 13.90 15.09 15.41 16.18 16.58 18.00 18.83 20.23 22.19 23.07
2.25 3.06 3.12 4.44 4.69 6.00 6.63 8.01 8.85 12.50 13.55 15.42 21.76 27.23 27.24 27.46 27.47 27.51 27.53 27.54 27.55 27.55 27.56 27.57 27.58 27.58 27.59 27.59 27.60 27.60 27.61 27.61 27.62
1.10 1.53 1.56 2.15 2.47 2.98 3.27 2.93 4.37 6.23 6.75 7.81 11.00 13.41 14.28 15.31 16.30 19.00 19.98 21.79 24.06 23.42 25.82 27.64 27.45 27.46 27.48 27.49 27.52 27.54 27.56 27.59 27.60
a
For units see Table 2.
the partial molar relative enthalpies (L2,S). The latter in the premicellar region were calculated by means of the following equation
Energetics of Ternary Systems
Langmuir, Vol. 12, No. 4, 1996 893 Table 6. Partial Molar Relative Enthalpies of Sodium Dodecyl Sulfate and Dodecyltrimethylammonium Bromide in Unmicellized and Micellized Forms and Enthalpy of Micellization in the Presence of 18-Crown-6 Ether (CR) and β-Cyclodextrin (CD) Water-CRa DTAB
NaDS
Water-CDa DTAB
NaDS
93 ( 11 69 ( 8 -460 ( 20 550 ( 20 BL (kJ kg mol-2) CL (kJ kg3/2 mol-5/2) -360 ( 8 0 1400 ( 200 0 exp -7.0 9.0 L2,m (kJ mol-1) L2,m (kJ mol-1) 0.5 0.9 4.2 21.5 L2,M (kJ mol-1) -7.0 -5.4 7.5 27.6 CD 14.5 18.6 ∆Hm (kJ mol-1) ∆Hm (kJ mol-1) -7.5 -6.3 3.3 6.1 a
For CR and CD concentrations see Tables 2-5.
Figure 1. Partial molar relative enthalpies of sodium dodecyl sulfate (NaDS) and dodecyltrimethylammonium bromide (DTAB) in pure water (W) and W + 18-crown-6 ether (CR): (s), NaDS in W; (- - -) DTAB in W; (b) NaDS in W + CR 0.47 m; (O) DTAB in W + CR 0.41 m.
L2,S ) 1.5ALmS1/2 + 2BLmS + 2.5CLmS3/2
(7)
and in the postmicellar region according to
L2,S )
∂(mSLΦ,S) ∆(mSLΦ,S) ≈ ∂mS ∆mS
(8)
by drawing the best curve for the apparent molar relative enthalpies as a function of mS and by taking points interpolated at regular intervals. The enthalpies of micellization (∆Hm) were evaluated according to the pseudophase transition model by extrapolating at the cmc the trends above and below the cmc of L2,S as a function of molality20
∆Hm ) L2,M - L2,m
Figure 2. Partial molar relative enthalpies of sodium dodecyl sulfate (NaDS) and dodecyltrimethylammonium bromide (DTAB) in pure water (W) and W + β-cyclodextrin (CD): (s) NaDS in W; (- - -) DTAB in W; (b) NaDS in W + CD 0.018 m; (O) DTAB in W + CD 0.017 m.
(9)
where L2,M and L2,m are the partial molar relative enthalpies for the surfactant in the micellized and unmicellized states, respectively. Surfactants in Water + Crown. As shown in Figure 1, the L2,S vs mS profiles for both surfactants in the CR solution (≈0.45 m) do not differ from those in pure water. For DTAB the presence of CR allows an increase of L2,S in the premicellar region and a decrease in the postmicellar one, while for NaDS, the presence of CR scarcely affects L2,S in the premicellar region but has an effect in the postmicellar one. The change in the slope in the L2,S vs mS curve at about 0.35 m for DTAB can be ascribed to the postmicellar transition already detected at the same concentration from heat capacity data in pure water21 and from L2,S data in urea aqueous solutions.22 Since no change in the slope is present in the L2,s vs mS curve in pure water, it seems that the cosolvent effect of CR can enhance the transition. This effect does not seem to be important as far as the NaDS transition is concerned.23 Probably, the CR complexation with Na+ and its solubilization at the NaDS micellar surface13 can account for the different CR effect on the transition of the two surfactants. Therefore, these results suggest that only CR in the uncomplexed form can reinforce the postmicellar transition. (20) De Lisi, R.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1980, 58, 959. (21) De Lisi, R.; Milioto, S. J. Solution Chem. 1987, 16, 767. (22) Caponetti, E.; Causi, S.; De Lisi, R.; Floriano, M. A.; Milioto, S.; Triolo, R. J. Phys. Chem. 1992, 96, 4950. (23) Roux-Desgranges, G.; Roux, A.; Viallard, A. J. Chim. Phys. 1985, 82, 441.
The values of L2,m, L2,M, and ∆Hm for DTAB and NaDS are reported in Table 6. The ∆Hm values are about 6 kJ mol-1 more negative than those in pure water (-0.7 and -1.1 for NaDS24 and DTAB,25 respectively). So, despite the fact that the interactions between CR and NaDS involve phenomena (complexation of CR with sodium ions in the aqueous phase and solubilization of the complexed CR in the micellar phase)13 which are absent in the interactions between CR and DTAB, the addition of CR affects ∆Hm essentially in the same manner. Surfactants in Water + β-Cyclodextrin. Figure 2 shows the plots of L2,S vs mS for DTAB and NaDS in water + CD (≈0.017 m) and in pure water. As it can be seen, the curves are deeply modified by the presence of CD. In the case of DTAB the cmc (corresponding to break point) is close to that in pure water. Similar experimental evidence was observed for other thermodynamic properties (volumes and heat capacities, for instance)14 while conductivity14 and ultrasound26 data gave cmc values corresponding somewhat to the sum of the cmc in pure water and the CD concentration (mCD). The latter finding could explain the apparent only break at ≈0.02 m observed in the L2,S vs mS trend for NaDS in W + CD. So, on this basis the micellization enthalpy is zero while that for DTAB is very large (see later). To clarify this puzzling point, we plot (Figure 3) experimental data according to eq 6 for NaDS27 and DTAB25 in pure water and in W + CD. As it can be (24) Woolley, E. M.; Burchfield, T. E. J. Phys. Chem. 1984, 88, 2155. (25) De Lisi, R.; Milioto, S.; Castagnolo, M.; Inglese, A. J. Solution Chem. 1987, 16, 373. (26) Junquera, E.; Taradajos, E.; Aicart, E. Langmuir 1993, 9, 1213.
894
Langmuir, Vol. 12, No. 4, 1996
Figure 3. Plots of eq 6 for sodium dodecyl sulfate (filled symbols) and dodecyltrimethylammonium bromide (open symbols) in pure water (circles) and in water + β-cyclodextrin (triangles): ordinate scale, 105 kJ kg mol-2 for surfactants in W + CD and 104 kJ kg mol-2 for surfactants in W; abscissa scale, kg1/2 mol-1/2. The intercepts and slopes of the lines in pure water were calculated by means of eq 5 and the LΦ,S data in the premicellar region reported in the literature for NaDS (ref 27) and DTAB (ref 42).
seen, as a general feature, three regions delimited by the breaks at the cmc and at 2-3 times the cmc are present: the first region deals with the dilution processes involving dispersed surfactant in both the initial and final states; the intermediate region involves the micellization process and its extension is due to the fact that micellization is not a real phase transition; the third region deals with the dilution processes involving micellized surfactant in both the initial and final states. In the case of NaDS in W + CD, the large BL and small CL values in the premicellar region (eq 6) minimize the above effects in the micellization region. Consequently, it is justified to assume that the cmc for NaDS in W + CD is equal to that in pure water. In the premicellar region, by increasing mS the partial molar relative enthalpy strongly increases for NaDS and decreases for DTAB. To explain this difference, recall that the reference state for L2,S is the infinite dilution of the surfactant in the given solvent so that the enthalpy for the inclusion complex formation (∆HW C ) is buried in the reference state. Therefore, the only effect to be considered concerns the decomplexation of the surfactant with mS. We reported elsewhere14 that the mole fraction of the complexed surfactant (XS,CD) slightly decreases by increasing mS from 0 to the cmc. In the worst case (lowest literature value for the complexation constant), it decreases by about 0.06 for NaDS and 0.14 for DTAB. It was shown10 that the inclusion complex formation is exothermic regardless the nature of the head group of the surfactant and that for NaDS and hexadecyltrimethyl-1 ammonium bromide (CTAB) ∆HW C ≈ -13 kJ mol . By assuming that ∆HW for DTAB is equal to that of the C longer homologous CTAB, the contributions at the cmc of the decomplexation process to L2,S are 0.8 and 1.8 kJ mol-1 for NaDS and DTAB, respectively. Consequently, the dependence of L2,S on mS essentially does not reflect the surfactant encapsulation by CD but rather the solutesolute interactions (the solute being essentially in the complexed form). Since these interactions depend on the nature of the solute, positive or negative slopes can be obtained. (27) Berg, R. L. BERC/TPR-77/3, Bartlesville Energy Research Center, Bartlesville, OK, 1977.
Crisantino et al.
For both surfactants, at the cmc there is a more or less abrupt change on the property which corresponds to the enthalpy of micellization. This quantity, evaluated through eq 9, is very large (Table 6) compared to that in pure water where ∆Hm is about -1 kJ mol-1 for both surfactants. So, the effect of 0.02 m CD on the enthalpy of micellization (∆HCD m ) is surprisingly large with respect, for example, to that of 7 m urea on DTAB (∆Hm ≈ -3 kJ mol-1).22 Consider that the very large ∆HCD m values refer to the difference at the cmc between the surfactant solubilized in the pure micelle (the partial molar relative enthalpy being L2,M) and the monomeric surfactant which is essentially in the complexed form (the partial molar exp ). To obtain the effect of CD relative enthalpy being L2,m as cosolvent only, the L2,S value of the monomeric surfactant in the uncomplexed form L2,m (see eq 9) should cmc be evaluated. By indicating with XS,CD the mole fraction of the complexed surfactant at the cmc, we roughly have exp cmc CD L2,m ) L2,m + XS,CD ∆HW C and, therefore, ∆Hm (complexed monomers) is related to the enthalpy of micellizacmc tion (uncomplexed monomers) by ∆Hm ) ∆HCD m + XS,CD W ∆HC . The ∆Hm values (Table 6) were calculated by cmc taking the XS,CD values of 0.96 and 0.90 for NaDS and DTAB, respectively.14 They show that the presence of CD as a cosolvent allows a reasonable increase of the enthalpy of micellization with respect to that in pure water. Enthalpies of Mixing. The enthalpies of mixing between surfactant and macrocyclic compounds solutions were determined for CR only since for CD they are reported in the literature.10 The measured enthalpy (∆Hexp), i.e. the difference between the enthalpy of mixing and the enthalpy of dilution of the surfactant (corrected for the enthalpy of dilution of CR) corresponds to the enthalpy of transfer of the additive from water to the surfactant solution ∆H(WfW+S)15
∆H(WfW+S) ) ∆Hexp - ∆HCR id
(10)
At the given CR concentration, the ∆HCR id value was calculated by means of eq 3 and the hxx and hxxx values reported above. The ∆Hexp values together with the final CR (fCRmCR) and surfactant (fSmS) concentrations are collected in Table 7. CR in DTAB. Figure 4 shows that the profile of ∆H(WfW+S) of CR from water to DTAB surfactant solutions possesses the feature of the solubilization of the solute in the micellar phase having a large enthalpy of transfer and a small distribution constant (smooth curvature).15,18 This supports the literature findings,12 following which in DTAB micellar solutions CR behaves like a normal nonionic amphiphilic solute which distributes between the aqueous and the micellar phases. Therefore, ∆H(WfW+S) was rationalized according to the following equation18,28
∆H(WfW+S) ) ∆Hw t - (∆Ht - Acdc∆Hm)Nf
(11)
where ∆Hw t and ∆Ht are the standard enthalpies of transfer of CR from water and from the aqueous phase to the micellar phase, respectively; ∆Hm is the enthalpy of micellization and Acdc indicates the shift of the micellization equilibrium due to the additive. Acdc and Nf were rationalized in terms of the distribution constant (KD) of the additive between the aqueous and the micellar phases (28) Milioto, S.; Romancino, D.; De Lisi, R. J. Solution Chem. 1987, 16, 943.
Energetics of Ternary Systems
Langmuir, Vol. 12, No. 4, 1996 895
Table 7. Enthalpies of Mixing, Corrected for the Enthalpies of Dilution of Surfactants in Water, between 18-Crown-6 Ether and Sodium Dodecyl Sulfate and Dodecyltrimethylammonium Bromide Aqueous Solutions at 298 Ka NaDS
DTAB
fSmS
fCRmCR
-∆Hexp
fSmS
fCRmCR
-∆Hexp
0.001 31 0.002 27 0.004 38 0.008 61 0.012 48 0.019 06 0.026 12 0.037 85 0.055 30 0.069 66 0.088 60 0.123 7 0.126 6 0.174 5 0.223 8 0.270 8
0.025 55 0.027 43 0.027 37 0.027 00 0.026 85 0.026 84 0.026 88 0.025 65 0.025 81 0.025 94 0.026 22 0.026 25 0.031 21 0.026 04 0.026 43 0.026 69
0.20 0.20 0.25 0.43 0.60 0.92 1.25 1.73 2.20 2.52 2.86 3.39 3.40 3.79 4.13 4.21
0.000 65 0.001 33 0.001 59 0.002 53 0.005 37 0.009 11 0.017 50 0.032 79 0.056 72 0.075 76 0.108 9 0.146 6 0.188 4 0.247 9 0.267 0 0.302 5 0.358 4
0.024 89 0.024 06 0.024 21 0.024 02 0.024 21 0.026 64 0.026 82 0.026 97 0.025 10 0.025 60 0.025 29 0.026 30 0.026 10 0.026 87 0.028 60 0.028 32 0.025 63
0.17 0.16 0.16 0.15 0.03 0.00 -0.18 -0.31 -0.43 -0.52 -0.70 -0.81 -0.91 -1.12 -1.27 -1.34 -1.57
a
Units are mol kg-1 for concentratiosn and kJ mol-1 for enthalpies.
Figure 4. Enthalpy of transfer of 18-crown-6 ether from water to dodecyltrimethylammonium bromide micellar solutions as a function of the surfactant concentration: (s) best fit to the experimental points according to eq 11.
from the aqueous to the micellar phases are given by
∆Gto ) -RT ln(KD/VS)
(14)
T∆Sto ) ∆Ht - ∆Gto
by29
1 Nf ) 1 + KD(fSmS - cmc) Acdc )
(12)
cmc {2.3Ks + (1 + β)KD} 2
where Ks is the Setchenov constant and β is the degree of the counterion dissociation of the micelle; the numerical coefficient 2 accounts for the complete dissociation of the monomeric surfactant. Approximations introduced in deriving eqs 11 and 12 were discussed elsewhere.18,28 In the present case, the Acdc term can be evaluated only roughly due to the lack of literature values for Ks. However, since low absolute values are expected for Ks and KD, the chemical displacement contribution can be simply evaluated as
Acdc )
cmc - cmcW+CR fCRmCR
(13)
where cmcW+CR indicates the critical micellar concentration in the presence of CR at mCR. The three-parameter (KD, ∆Hw t and ∆Ht) eq 11, was solved by a no linear regression by taking literature values for ∆Hm,25 cmc,30 and cmcW+CR.13 The best fit to the experimental points, shown in Figure 4, gave the values reported in Table 8. The KD value, which agrees with that reported by Stilbs from NMR studies,12 indicates a scarce solubilization of the uncomplexed CR in the micelles. Nevertheless, the solubilization involves a large enthalpic effect. Note that both KD and ∆Ht values are comparable to those of a very short alkyl chain amphiphilic additive like methanol in DTAB.18 By converting KD into the partition constant in the molarity scale (KD/VS,25 where VS is the partial molar volume of the micellized surfactant), the standard free energy (∆Gto) and entropy (∆Sto) for the transfer process (29) De Lisi, R.; Turco Liveri, V.; Castagnolo, M.; Inglese, A. J. Solution Chem. 1986, 15, 23. (30) Treiner, C. J. Colloid Interface Sci. 1983, 93, 33.
By taking the value of 0.295 dm3 mol-1 for VS,29 the thermodynamic properties of transfer, summarized in Table 8, were calculated. CR in NaDS. It was observed13 that the apparent molar volume of CR at a fixed low mCR in DTAB solutions essentially does not depend on mS, and consequently, in the rationalization of this property for CR in NaDS it was assumed that the uncomplexed CR does not distribute between the aqueous and the micellar phases. This assumption is too drastic in the case of enthalpy due to the large ∆Ht value obtained for the transfer process of CR from the aqueous to the DTAB micellar phase. Therefore, eq 11 must be reviewed to account not only for the complexation of CR in the aqueous phase but also for the distribution of CR in both the complexed and uncomplexed forms between the aqueous and the micellar phases. To this purpose, by indicating with FS and FCR the flows (in terms of the number of kg of water per second) of the surfactant and CR solutions, the mixing process in the postmicellar region can be schematized as shown in Scheme 1, where W, CR, Sn, S, CRf, and CRb indicate Scheme 1 FCR kg of W FS kg of W (FS + FCR) kg of W FCRmCR + FS(mS-cmc) f (FS + FCR)[m] moles of S moles of CR moles of Sn FScmc moles of S FSmS - (FS + FCR)[m] moles of Sn FCRmCRNf,c moles of CRf,c FCRmCRNf,u moles of CRf,u FCRmCRNb,c moles of CRb,c FCRmCRNb,u moles of CRb,u
water, crown in water, micellized surfactant, unmicellized surfactant, crown in the aqueous phase, and crown in the micellar phase, respectively. In addition, the subscripts c and u indicate the crown in the complexed and uncomplexed forms in both phases, respectively; [m] stands for the dispersed surfactant concentration in the presence of CR. Since CR can solubilize in the two pseudophases in both the complexed and uncomplexed forms, by taking into account eq 13 the original equation18,28 leading to eq 11 can be written as
896
Langmuir, Vol. 12, No. 4, 1996
Crisantino et al.
Table 8. Thermodynamic Properties of Transfer of 18-Crown-6 Ether in the Complexed and Uncomplexed Forms from Water and from the Aqueous Phase to the Micellar Phases of Sodium Dodecyl Sulfate and dodecyltrimethylammonium Bromidea DTAB KD ) 0.7 ( 0.4
∆Gto ) -2.1
KuD ) 0.7 ( 0.4
∆Gto ) -2.5
KcD ) 33 ( 1 KM C ) 288 ( 170 KW C ) 6.1 ( 1.0
∆Gto ) -12.1 ( 0.1 ∆Go,M C ) -14.0 ( 1.2 ∆Go,W C ) -4.5 ( 0.3
∆Ht ) 6.6 ( 2.3 ∆Htw ) 6.4 ( 2.9
T∆Sto ) 8.7
∆Ht,u ) -4.2 ( 0.1 w ∆Ht,u ) -3.3 ( 0.3 ∆Ht,c ) 4.6 ( 0.7 ∆HM C ) -0.6 ( 0.2 ∆HW C ) -9.4 ( 0.4
o T∆St,u ) 1.7 ( 1.2
NaDS
a
o T∆St,c ) 16.7 ( 0.8 o,M T∆SC ) 13.4 ( 1.4 T∆So,W C ) -4.9 ( 0.7
Units are kg mol-1 for the distribution constant and kJ mol-1 for the free energy, enthalpy, and entropy of transfer.
cmc - cmcW+CR ∆Hm ) fCRmCR Nf,cHf,c + Nf,uHf,u + Nb,cHb,c + Nb,uHb,u - HCR (15)
∆Hexp - ∆HCR id -
where HCR indicates the enthalpy of CR in water. By indicating with Xf,c and Xf,u the mole fractions of the complexed and uncomplexed crown in the aqueous phase and with Xb,c and Xb,u those in the micellar phase, we have
Nf,c ) Xf,cNf; Nf,u ) Xf,uNf; Nb,c ) Xb,cNb; Nb,u ) Xb,uNb (16) Since Xf,c + Xf,u ) 1, Xb,c + Xb,u ) 1, and Nf + Nb ) 1, from eqs 15 and 16 we obtain
∆Hexp - ∆HCR id -
Figure 5. Mole fraction of the complexed 18-crown-6 ether (CR) as a function of the sodium ion concentration: (s) calculated by neglecting the complexed CR concentration with respect to sodium ion concentration; values used, 6.1 kg mol-1 for complexation constant, 0.03 mol kg-1 for CR concentration.
cmc - cmcW+CR ∆Hm ) fCRmCR
w M - ∆Ht,uNf + Xf,cNf∆HW ∆Ht,u C + Xb,cNb∆HC ) w W M ∆Ht,u + Xb,c∆HM C - (∆Ht,u - Xf,c ∆HC + Xb,c∆HC )Nf
(17) M where the quantities ∆HW C ()Hf,c - Hf,u) and ∆HC ()Hb,c - Hb,u) correspond to the enthalpies for the complex formation in the aqueous and micellar phases, respectively, while the quantities ∆Ht,u ()Hb,u - Hf,u) and w ∆Ht,u ()Hb,u - HCR) correspond to the enthalpies of transfer of the uncomplexed crown from the aqueous to the micellar phase and from pure water to the miceellar phase, respectively. We can check the self-consistence of eq 17 by considering its physical meaning for mS f cmc and mS f ∞. In the first case, since Nf f 1 the quantity at the left hand side of eq 17, subtracted from the contribution due to the complex formation in the aqueous phase (Xf,c ∆HW C ), corresponds to the enthalpy of transfer of CR from water w - ∆Ht,u); for mS f ∞, since to the aqueous phase (∆Ht,u Nf f 0 and Xb,c f 1 the quantity at the left hand side w of eq 17 corresponds to the enthalpy of transfer (∆Ht,u + M ∆HC ) of CR from pure water (where it is in the uncomplexed form) to the micelles (where it is in the complexed form). Despite the approximations introduced, the latter is a quite involved equation since it depends from the equilibrium constant for the complex formation in the aqueous M (KW C ) and micellar (KC ) phases through Xf,c and Xb,c and from the total distribution constant (KD) of CR through Nf. As it will be seen later, KD is related to the distribution constants (KcD and KuD) of the two species and depends on the surfactant concentration because of the complexation equilibrium of CR with Na+. In addition, in eq 17 the enthalpies related to the complex formation in the two phases and to the transfer of crown in the uncomplexed
form from water and from the aqueous phase to the micellar phase are to be determined. To account for the above points, we, firstly, consider the complexation equilibrium in both the aqueous and the micellar phases. Since mCR is sufficiently low, we can assume that the complexed CR concentration is negligible with respect to that of Na+. This approximation is not drastic, as shown in Figure 5, where the mole fraction of the complexed CR, evaluated with and without the above approximation, is reported as a function of the sodium ion concentration (mNa+). Calculations were made by taking the value of 6.1 kg mol-1 for KW C as that in sodium decanoate.11 Therefore, Xf,c and Xf,u are given by
Xf,c )
KW C mNa+ 1 + KW C mNa+
Xf,u ) 1 - Xf,c )
(18)
1 1 + KW C mNa+
Similarly, the mole fractions in the micellar phase are given by
Xb,c )
KM C mNa+ 1 + KM C mNa+
Xb,u ) 1 - Xb,c )
(19)
1 1 + KM C mNa+
where mNa+ in eq 18 is given by (mS - cmc)β + cmc and in eq 19 by (mS - cmc)(1 - β) being β the degree of
Energetics of Ternary Systems
Langmuir, Vol. 12, No. 4, 1996 897
dissociation of micelles. Since the β value13 is close to 0.5 and the cmc negligible, mNa+ values in eqs 18 and 19 are equal. To decrease the number of unknown parameters, Xb,c can be expressed in terms of Xf,c. According to eq 12, we can write
Xb,c )
mb,c mb,c ) mb mfKD(mS - cmc)
(20)
mb,c
) KcD(mS - cmc), where mf,c KcD indicates the distribution equilibrium constant of the complexed CR, from eq 20 it follows Since mf,c ) Xf,cmf and
Xb,c )
mb,c mf,cKD(mS - cmc)
Xf,c )
KcD X KD f,c
(21)
In order to solve eq 17, Nf should be expressed in terms of the distribution constants of the complexed and uncomplexed CR. By using again eq 12, we can write
KD(mS - cmc) )
Nb mb mb,c + mb,u ) ) ) Nf m f mf,c + mf,u mb,c mb,u + (22) mf,c + mf,u mf,c + mf,u
Since Xf,c ) mf,c/(mf,c + mf,u) and Xf,u ) mf,u/(mf,c + mf,u) and recalling that Xf,u ) 1 - Xf,c, from the latter equation it follows
KD ) KcDXf,c + KuDXf,u ) KuD + (KcD - KuD)Xf,c (23) Equation 17 through eqs 12, 18, 21, and 23 is a seven w W M parameter (KcD, KuD, KW C , ∆Ht,u, ∆Ht,u, ∆HC , and ∆HC ) equation which was reduced to a three-parameter equation by taking the literature values of 6.1 kg mol-1 for 11 -1 for ∆HW,31 33 kg mol-1 for Kc ,13 and KW C , -9.4 kJ mol C D the value of 0.7 kg mol-1 for KuD reported above for the distribution of the uncomplexed CR between the aqueous and the DTAB micellar phases. So, eq 17 was solved by a no linear regression to obtain w ∆Ht,u , ∆Ht,u, and ∆HM C . The best fit to the experimental data, shown in Figure 6, gave the values summarized in Table 8. Since the uncertainties on the introduced parameters (see Table 8) can make the fit results unreliable, the procedure was repeated by taking them into account. Within the uncertainties, the derived enthalpies w ) -3.84 ( 0.33 agree also in the worst conditions (∆Ht,u -1 kJ mol , ∆Ht,u ) -3.97 ( 0.12 kJ mol-1, and ∆HM C ) 0 ( 0.3 kJ mol-1) with those reported in Table 8. Free energies of transfer of the complexed and uncomplexed CR from the aqueous to the NaDS micellar phases were calculated according to eq 14 by using32 0.250 dm3 mol-1 for VS. The enthalpy of transfer of the complexed CR from the aqueous to the NaDS micellar phase (∆Ht,c) was evaluated W M M as ∆Ht,c ) ∆Ht,u + ∆HM C - ∆HC and KC as KC ) W c u KC KD/KD. The thermodynamic properties related to the distribution process of both the uncomplexed CR between the aqueous and the micellar phases of DTAB and NaDS (31) Izzatt, R. M.; Terry, R. E.; Haymore, B. L.; Hansen, L. D.; Dalley, N. K.; Avondet, A. G.; Christensen, J. J. J. Am. Chem. Soc. 1976, 98, 7620. (32) De Lisi, R.; Genova, C.; Testa, R.; Turco Liveri, V. J. Solution Chem. 1984, 13, 121.
Figure 6. Enthalpy of transfer of 18-crown-6 ether from water to sodium dodecyl sulfate micellar solutions as a function of the surfactant concentration: (s) best fit to the experimental points according to eq 17.
and the complexed CR between the aqueous and the micellar phases of NaDS together with the thermodynamic properties related to the CR complexation process in both the aqueous and the micellar phases are summarized in Table 8. It is to be noted that the large uncertainty on u KM C derives from that on KD because of its very small value. We focus our attention on the main information which can be drawn from the thermodynamic properties collected in Table 8. (i) KcD is 50 times larger than KuD indicating that in the NaDS micellar phase CR exists essentially in the complexed form. This result is clearly supported by the KM C value, i.e. the complexation constant in the micellar phase. (ii) The complex formation involves exothermic effects in both phases; that in the aqueous phase (-9.4 kJ mol-1) is very large with respect to that in the micellar phase (-0.6 kJ mol-1). On the contrary, the standard free energy of the process in the aqueous phase (-4.5 kJ mol-1) is smaller than that in the micellar phase (-14.0 kJ mol-1). Consequently, the entropy change is large and positive in the micellar phase and small and negative in the aqueous phase. In other words, the CR complexation in the aqueous phase is an enthalpy-driven process while that in the micellar phase is an entropy-driven process. While the energetics for the complex formation in water can be explained in terms of desolvation of both cation and macrocycle, it is not so in the micellar phase. In this case, other phenomena such as conformational changes in the macrocycle, different micellar site of solubilization of the macrocycle in the complexed and uncomplexed form, changes in the micelle structure, etc., should be taken into account. Since only the present data are available for the CR complexation in the micellar phase, it is hazardous to interpret the energetics of the process. (iii) The interactions between the uncomplexed CR and the surfactant are not negligible; accordingly, its enthalpy of transfer at the cmc from water to the NaDS aqueous w - ∆Ht,u, is 0.66 ( 0.15 kJ mol-1. phase, given by ∆Ht,u This value is close to that (0.4 kJ mol-1) evaluated from data in the premicellar region in DTAB. In the latter w - ∆Ht,u case, the evaluation of this quantity from ∆Ht,u is meaningless because of the large uncertainties on both properties of transfer. (iv) The nature of the head group of the surfactant is fundamental as far as the thermodynamics of the uncomplexed CR distribution is concerned. In fact, the
898
Langmuir, Vol. 12, No. 4, 1996
Crisantino et al.
Table 9. Osmotic Coefficients of Sodium Dodecyl Sulfate (NaDS), Dodecyltrimethylammonium Bromide (DTAB), Sodium Perfluorooctanoate (NaPFO), and Sodium Chloride (NaCl) in Water-18-Crown-6 Ether (CR) and NaDS and DTAB in Water-β-Cyclodextrin at 310 Ka mNaDS
φNaDS
mCR ) 0.2000 0.01035 0.03000 0.05258 0.1009 0.1486 0.1980 0.2472 0.3004 0.3494 0.4003 0.4989
0.248 -0.032 -0.110 -0.153 -0.142 -0.129 -0.091 -0.077 -0.057 -0.028 -0.002
mDTAB
φDTAB
mCR ) 0.3989 0.00996 0.02084 0.02422 0.04735 0.06952 0.09023 0.1396 0.1999 0.2505 0.3005 0.3476 0.3999
0.952 0.577 0.429 0.256 0.175 0.148 0.084 0.134 0.067 0.137 0.101 0.114
mNaPFO
φNaPFO
mCR ) 0.4000 0.00992 0.01639 0.01991 0.02999 0.05861 0.1023 0.1744 0.2370 0.3179
0.614 0.027 0.146 -0.164 -0.264 -0.287 -0.312 -0.315 -0.215
mNaCl
φNaCl
mCR ) 0.4000 0.04997 0.1002 0.1497 0.1996 0.2497 0.2985 0.3497 0.3977 0.4474 0.4997
0.910 0.886 0.887 0.951 0.931 0.947 0.945 0.991 0.970 0.939
mCR ) 0.3969 0.00987 0.04843 0.1001 0.1502 0.1993 0.2499 0.3008 0.3505 0.3999 0.4486 0.4999
0.320 -0.373 -0.402 -0.352 -0.330 -0.282 -0.272 -0.235 -0.205 -0.190 -0.168
mCD ) 0.01752 0.00779 0.01168 0.01312 0.01901 0.02220 0.02573 0.03160 0.04255 0.05439 0.07418 0.0849 0.1257 0.1856 0.2567 0.3162 0.3838 a
0.545 0.468 0.380 0.324 0.389 0.460 0.395 0.313 0.251 0.253 0.246 0.192 0.153 0.137 0.119 0.078
mCD ) 0.01747 0.00799 0.01293 0.01708 0.02199 0.02857 0.03246 0.04240 0.06568 0.09447 0.1283 0.1588 0.2211 0.2949 0.3602 0.4276
0.572 0.516 0.477 0.555 0.546 0.609 0.480 0.365 0.257 0.197 0.169 0.134 0.116 0.080 0.096
Units are mol kg-1 for concentrations.
enthalpy of transfer is positive for the cationic surfactant and negative for the anionic surfactant. This result is reminiscent of that observed for the enthalpy of transfer of phenol from the aqueous to the micellar phases of the same surfactants.33 (v) The enthalpy of transfer of the complexed CR from the aqueous to the NaDS micellar phase is endothermic and the process is entropy driven. The thermodynamic properties related to this process are close to those found for medium chain length alcohols in the same surfactant.15 Osmotic Coefficients. Osmotic coefficients of surfactants in macrocyclic compounds solutions (ΦS) were measured to evaluate the nonideal contribution to the free energies and, through L2,S data, entropies. Actually, calculations were not made because of the peculiar ΦS vs mS profiles observed for all the systems here investigated. Experimental ΦS values for DTAB and NaDS in water + CR and water + CD mixtures together with data for NaCl in water + CR are summarized in Table 9. In the (33) Causi, S.; De Lisi, R.; Milioto, S. J. Solution Chem. 1990, 19, 995.
Figure 7. Osmotic coefficients of sodium dodecyl sulfate (NaDS) and dodecyltrimethylammonium bromide (DTAB) in pure water (W) and W + β-cyclodextrin (CD) as functions of the surfactant concentration: (- - -), DTAB in W; (s) NaDS in W; (O) DTAB in W + CD 0.017 m; (b) NaDS in W + CD 0.017 m.
case of NaDS in water + CR, measurements were carried out at two different CR concentrations. Surfactants in β-Cyclodextrin Solutions. Figure 7 shows the plots of ΦS as a function of mS for DTAB and NaDS in 0.017 m CD aqueous solution. In the same figure ΦS data for DTAB34 and NaDS35 in pure water are also shown. In order to clarify the anomalies shown in the figure, the osmotic coefficients are plotted against the reduced concentration calculated by using the cmc of surfactants in pure water (0.0083 and 0.0152 mol kg-1 for NaDS13 and DTAB,30 respectively). As seen, the addition of CD deeply modifies the profile of ΦS vs mS. In fact, for both surfactants a minimum localized at about mS ) mCD and a maximum localized at about mS ) mCD + cmc are present (see insert in Figure 7). Beyond this concentration ΦS decreases, becoming close to the value in pure water. The initial sharp decrease in the dilute region must be ascribed to the complex formation. In fact, ΦS reflects the deviation from ideality not only in terms of solute-solute interactions but also in terms of change of the number of particles. In this region, since the reference solvent is the CD solution, the measured number of osmoles correspond to those of the surfactant (2mSΦS,CD, where the subscript S,CD indicates the surfactant in the complexed form) subtracted from those of the complexed CD (mSΦCD). According to this idea, the slope of the plot of the experimental number of osmoles against the surfactant concentration is 1 in W + CD and 2 in pure water. Beyond the minimum, ΦS increases because the addition of the surfactant allows monomer formation since all the CD molecules are already in the complex form. At mS ) mCD + cmc, the micellization process occurs and, therefore, ΦS decreases because of the decrease of both the number of particles and the osmotic coefficient. The above simple interpretation of the ΦS vs mS plot disagrees with experimental evidence for other thermodynamic properties (volume,14 heat capacity,14 and enthalpy). In fact, the latter properties indicate that the micellization occurs at the cmc of the surfactant in pure water while osmotic coefficients (as specific conductivities14 and speeds of sound8) indicate that it occurs at mS ≈ mCD + cmc. An explanation of this contradictory result could be searched on the different nature of the above thermodynamic properties. In fact, the micellization process implies a change in the property for volume, heat capacity, (34) De Lisi, R.; Fisicaro, E.; Milioto, S. J. Solution Chem. 1988, 17, 1015. (35) Crisantino, R.; De Lisi, R.; Milioto, S. J. Solution Chem. 1994, 23, 639.
Energetics of Ternary Systems
Figure 8. Osmotic coefficients in water + 18-crown-6 ether (CR) 0.4 m of NaCl (×), dodecyltrimethylammonium bromide (2), sodium perfluorooctanoate (+), and sodium dodecyl sulfate (b) as functions of their concentrations; (O) NaDS in water + CR 0.2 m; (s) NaDS in pure water.
and enthalpy but not for osmotic coefficients and conductivities. Therefore, the former properties could be more sensitive to this process and could immediately detect it. Speeds of sound and specific conductivities like densities are bulk properties and, therefore, do not display a change in the property at the cmc as their derived apparent and partial molar properties do; therefore, it should be interesting to know data for the isoentropic compressibilities. An alternative interpretation of the ΦS vs mS profile could consider that the initial decrease is due to the complex formation and that, despite the presence of CD, the micellization occurs at the cmc; by increasing mS, the minima and maxima observed could be due to the simultaneous increase of the micellized and unmicellized surfactant molecules. The latter are in the complexed form at lower mS and in the uncomplexed form at higher mS. At mS g mCD + cmc, the added surfactant is always in the micellized form and, then, ΦS decreases with increasing mS. Surfactants in 18-Crown-6 Ether Solutions. The effect of CR on the ΦS vs mS curves for NaDS and DTAB is shown in Figure 8 where, for sake of comparison, data for NaDS in pure water are also plotted. In the same figure experimental data for NaCl and sodium perfluorooctanoate (NaPFO) at mCR ) 0.4 m are also reported. As a general feature, the presence of CR scarcely affects the osmotic coefficient in the premicellar region as well as that for NaCl in the whole range of concentrations analyzed. This means that either the presence of CR as a cosolvent and the Na+ complexation by CR are more or less ineffective on the ΦS values. This finding does not disagree with that observed in CD solutions for which the inclusion complex formation deeply lowers ΦS even if mCD is 20 times smaller than mCR. In fact, in the case of CD the complexed surfactant concentration is very close to the stoichiometric one while in the case of CR it is negligible with respect to the stoichiometric one because of the very different complexation equilibrium constant values. Consequently, in the case of CR the slight decrease of the number of particles due to the complex formation could be compensated by the different osmotic coefficients. As Figure 8 shows, in the postmicellar region the presence of CR shifts the osmotic coefficients toward lower values with respect to those in pure water. However, this shift is not very important for DTAB while it is for NaDS for which negative values were obtained. The latter surprising results suggested that we measure ΦS for NaDS in a more dilute CR solution (0.2 m). The ΦS vs mS curve,
Langmuir, Vol. 12, No. 4, 1996 899
Figure 9. Excess osmotic coefficients, with respect to those in pure water, of sodium dodecyl sulfate in water + 18-crown-6 ether 0.2 m (b) and 0.4 m (O), and of dodecyltrimethylammonium bromide (2) in water + 18-crown-6 ether 0.4 m as functions of surfactant concentration. Simulations according to eq 27 by using (‚‚‚) β ) 0.4 (ref 13) and (s) β ) 0.2 (ref 37) for NaDS and (- - -) β ) 0.24 (ref 13) for DTAB.
shown in Figure 8, clearly shows the effect of mCR: the decrease of mCR shifts the ΦS vs mS curve toward that in pure water. In addition, the ΦS vs mS curve for NaPFO at 0.4mCR essentially superimposes to that for NaDS at the same mCR. All these results can be explained in terms of the CR solubilization in the micellar phase rather than in terms of a more or less important deviation from the ideality for a given species. In fact, as reported above, the distribution is more effective than the complexation in water in the case of NaDS while they are comparable in the case of DTAB. Accordingly, the ΦS vs mS curve for DTAB is close to that in water while the curve for NaDS is greatly shifted toward lower values. In other words, by increasing mS the CR solubilization in the micelles allows an increase of the number of surfactant particles smaller than the number of CR particles solubilized in the micellar phase making the W + CR reference solvent more concentrated than that in the solution. Accordingly, the difference between the osmotic coefficient of the surfactant in the CR solution and that in water (∆ΦS) is negative. As a general feature, at a given mCR the higher the distribution equilibrium constant of CR the more negative ∆ΦS is, as the comparison between DTAB and NaDS shows; also, for a given surfactant, by increasing mCR, ∆ΦS decreases (Figure 9). To test this idea ∆ΦS was rationalized according to the above models for micellization and for the solute distribution between the aqueous and the micellar phases. It is to be stressed that by neglecting the electrostatic interactions the approach to osmotic coefficients is simpler than that to other thermodynamic properties such as enthalpies, for instance. In fact, for osmotic coefficients: (i) the shift of the chemical equilibrium for micellization due to the addition of the solute does not contribute to osmotic coefficient since its property of micellization does not exist; (ii) the solubilization of CR (complexed or uncomplexed) into micelles does not imply a change of the number of micelles if it is assumed that the aggregation number is not affected; (iii) according to the above mentioned results for the NaCl-CR-water system, the complexation of Na+ has a little effect on the osmotic coefficient of the solute in the aqueous phase. Since the osmotic coefficients were calculated by assuming the surfactant to be a strong 1:1 electrolyte at all concentrations (eq 2), by neglecting
900
Langmuir, Vol. 12, No. 4, 1996
Crisantino et al.
Figure 10. Osmotic coefficients of sodium dodecyl sulfate in water as a function of the reduced concentration: (b) experimental data; (‚‚‚) simulation according to eq 24 by using β ) 0.4; (s) simulation according to eq 24 by using β ) 0.2.
electrostatic interactions, in the postmicellar region the osmotic coefficient of the surfactant in water (ΦW S ) is given by34
ν cmc (mS - cmc)/N β(mS - cmc) ΦW + + ) S ) Φm νmS νmS νmS mS - cmc 1 cmc β Φm + + ) mS mS νN ν cmc (24) ΦM + (Φm - ΦM) mS
(
)
where N and β indicate the aggregation number and the degree of counterion dissociation, respectively, while Φm is the osmotic coefficient at the cmc; ΦM is given by
ΦM ) (β + 1/N)/ν
(25)
which shows that at high mS values the osmotic coefficient tends to 1/N for nonionic surfactants and to β/ν for ionic surfactants since, in this case, 1/N is negligible with respect to β. With the exception of the electrostatic contribution, the mass action model approach reported in the literature36 is fundamentally based on eq 24. It is to be noted that (Φm - ΦM) is not the property of micellization since ΦM is not the property of micelles. In fact, if micelles are considered pure phases, the ideal osmotic coefficient of monomers in the phase is 1; therefore, ΦM < 1 is simply a scaled property. In other words, we talk about the existence of the property of micellization if the given property of monomers in the two phases is different such as occurs, for example, for enthalpy. Figure 10 shows the experimental ΦW S for NaDS as a function of the reduced concentration (mS/cmc) together with the simulated curves obtained according to eq 24 by using 0.9 for Φm and the values of 0.237,38 and 0.413 for β. As can be seen, there is a very good agreement between experimental and calculated values for β ) 0.2. According to eq 24, the osmotic coefficients for surfac) is given by tants in CR solution (ΦW+CR S
ΦW+CR ) ΦW+CR + S M (ΦW+CR m
-
cmcW+CR ΦW+CR ) M mS
-
ΦW CR
mb (26) νmS
where mb is the concentration of CR solubilized in the (36) Burchfield, T. E.; Woolley, E. M. J. Phys. Chem. 1984, 88, 2149. (37) Caponetti, E.; Chillura Martino, D.; Floriano, M. A.; Triolo, R.; Wignall, G. D. Langmuir 1995, 11, 2464. (38) Anacker, E. W.; Underwood, A. L. J. Phys. Chem. 1981, 85, 2463.
micellar phase and transferred from pure water where its W osmotic coefficient is ΦCR . In the above equation we assumed that there is no difference between the osmotic coefficients of the surfactant in the aqueous phase in the presence or not of CR (Φm ) ΦW+CR ). This is a first-order m approximation since in the premicellar region negligible differences were observed in the two cases. This means that the osmotic coefficient of the surfactant, whose counterion is complexed or not, scarcely depends on the CR concentration. Thus, contrarily to what is observed for volumes and enthalpies, for which the property of the surfactant in the complexed form is quite different from that in the uncomplexed form, the CR solubilization into micelles implies a change of the CR concentration in the aqueous phase but not of the osmotic coefficient in this W pseudophase. Going further, since ΦCR ≈ 1, for 1:1 ionic surfactants, which is the case here, from eqs 24, 25, and 26 one obtains
βW+CR - β + 2 W+CR W+CR /2)cmc - (Φm - β/2)cmc mb (Φm - β mS 2mS (27)
∆ΦS ) ΦW+CR - ΦW S S )
which permits evaluation of ∆ΦS as a function of mS by considering that (i) Φm of different dodecyl surfactants are ≈0.90 regardless the nature of the surfactant,19,34 (ii) the cmc values in water, 0.2 mCR, and 0.4 mCR are 0.008, 0.006, and 0.005 mol kg-1, respectively,13 (iii) two sets of β and βW+CR values are reported in the literature13,37 and both were used, and (iv) mb values can be calculated according to eqs 12 and 23; in the latter no approximations were made in the Xf,c calculations. The simulated ∆ΦS for the systems here investigated are reported in Figure 9 together with points interpolated in the experimental curves. As can be seen, experimental and calculated profiles are quite similar and also there is a reasonably good agreement between them for mS > 0.1 mol kg-1. The approximations introduced in deriving eq 27, basically due to the neglected electrostatic interactions and the use of KcD, KuD, cmc, and β values at 298 K instead of those at 310 K, could justify the quantitative disagreement between the experimental and calculated ∆ΦS values. Moreover, remember that the KcD and KuD values were obtained by using equations strictly valid at low mCR while experimental data are available at mCR ) 0.2 and 0.4 m. This is not trivial since the distribution constant of an additive between the aqueous and the micellar phases is effectively constant when the mole fraction of the additive in the micellar phase is lower than 0.339 which is not the case here. Finally, although a quantitative agreement is not verified, especially in the surfactant dilute region, the above results support the idea that the CR solubilization in the micellar phase is responsible for the negative osmotic coefficients of surfactants in CR aqueous solutions. Conclusions Enthalpy and osmotic coefficient data for the systems water + CD + DTAB, water + CD + NaDS, water + CR + DTAB, and water + CR + NaDS are reported as functions of the surfactant concentration. The experimental data dealing with the cationic surfactant in water (39) Abuin, E.; Lissi, E. A. J. Colloid Interface Sci. 1983, 95, 198.
Energetics of Ternary Systems
+ CR were analyzed by means of a previously reported chemical model which accounts for the CR distribution between the aqueous and the micellar phases. The model was reviewed for the anionic surfactant to account also for the complexed CR distribution between the aqueous and the micellar phases. By some literature data introduced in the resulting equation, free energy, enthalpy, and entropy changes for the CR complexation in the micellar phase were derived. It was observed that the energetics (kJ mol-1) of the process in the micellar phase (∆G° ) -14.0, ∆H° ) -0.6, T∆S° ) 13.4) is different than that in water31 (∆G° ) -4.5, ∆H° ) -9.4, T∆S° ) -4.9), in the 70% water + methanol solution40 (∆G° ) -15.8, ∆H° ) -20.5, T∆S° ) -4.7) and acetone41 (∆G° ) -25.3, ∆H° ) -34.0, T∆S° ) -8.7) reflecting the peculiar solvent properties of micelles. The above mentioned model accounts also for the negative osmotic coefficients observed. (40) Izzatt, R. M.; Terry, R. E.; Haymore, B. L.; Hansen, L. D.; Dalley, N. K.; Avondet, A. G.; Christensen, J. J. J. Am. Chem. Soc. 1976, 98, 7626. (41) Buschmann, H. J.; Cleve, E.; Schollmeyer, E. J. Solution Chem. 1994, 23, 569. (42) Woolley, E. M.; Burchfield, T. E. J. Phys. Chem. 1985, 89, 3173.
Langmuir, Vol. 12, No. 4, 1996 901
The profiles of the partial molar relative enthalpy of DTAB and NaDS in W + CD as functions of the surfactant concentration are similar in the postmicellar region but very different in the premicellar one. Since the property is an excess with respect to the infinite dilution state, where the surfactant is completely complexed by CD, the profiles indicate that (i) in the premicellar region, as far as enthalpy is concerned, surfactant-complexed CD interactions strongly depend on the nature of the hydrophilic moiety of the surfactant, (ii) the macrocycle does not solubilize into micelles, and (iii) the observed very large enthalpies of micellization are due to the presence of the inclusion complex in the aqueous phase. The complex formation between dispersed surfactant and CD accounts also for the maxima observed in the plot of osmotic coefficients against surfactant concentration. Acknowledgment. The authors are grateful to the National Research Council of Italy (CNR, Contract No. 93.02944.CT03) and to the Ministry of University and of Scientific and Technological Research (MURST) for financial support. LA941048R
