Langmuir 1994,10,4039-4047
4039
Volume and Heat Capacity of n-Pentanol in Aqueous Surfactants: Effect of Chain Length and Polarity of the Head Group Daniel H6tu,*lt Christian CamirB,* G6rald Perron,$ and Jacques E. DesnoyersS Universitt de Moncton, Centre Universitaire de Shippagan, Shippagan, C.P. 2000, New Brunswick, Canada EOB 2P0, and INRS-Energie & Mattriaux, C / OIMI-NRC, 75 de Mortagne, Boucherville, Quebec, Canada J4B 6Y4 Received May 2, 1994. In Final Form: August 18, 1994@ Medium chain length alcohols tend to distribute themselves between water and surfactant micelles. In order to better understand the effect of length of the aliphatic chain and polarity of the hydrophilic head of the surfactant on the thermodynamic properties of alcohols in micelles, the volume and heat capacity of transfer of pentanol (PenOH) from water to aqueous solutions of surfactants were either taken from the literature or measured for various cationic, anionic, and nonionic surfactants of chain lengths between 6 and 12. The transfer quantities were analyzed through the principle of relative hydrophobicities (J. Colloid Interface Sci. 1988,122, 4181,which states that “an extremum appears in the transition region of the transfer function only if the transfered solute is more hydrophobic than the main solute”,and with a chemical distribution model (J.Solution Chem. 1984,13,1; 1987,16,529). The distribution constant KD,the volumetric interaction parameter between PenOH and surfactant monomers, and the volume and heat capacity of transfer of PenOH from water to the micelles all vary linearly with the chain length of the surfactant in the direction of stronger hydrophobic interactions. This suggests that, with longer-chain surfactants, there is a stronger tendency for PenOH to dissolve in the interior of the micelle. Tliere appears to be notable dependence of the thermodynamic parameters on the nature of the head group in the case of KD and volumes of transfer. The larger KD and smaller volume of transfer for PenOH with anionic surfactants compared to cationic surfactants are probably related to stronger interactions between the head groups in the palisade layer of the anionic micelle. It is also shown that transfer functions can be used to predict the thermodynamic properties of mixed micelles.
Introduction Aqueous solutions of medium chain length alcohols often exist, a t high mole fraction, as microaggregates which show many of the characteristics of micellar systems.l This explains, at least partially, the success of alcohols as cosurfactants in the preparation of emulsions and microemulsions.2 In recent years, aqueous mixtures of alcohols and surfactants were studied extensively by a variety of experimental techniques in order to better understand the interactions and the structure of these ternary In summary, the main conclusions are the following: (1)Below the critical micellar concentration (cmc) or critical region of both solutes, the alcohol-surfactant interactions can be expressed in the usual way through second virial coefficients. (2) At high surfactant concentrations, medium chain length alcoholsare distributed between the aqueous phase and the surfactant micelles. (3) The alcohol changes the micellization equilibrium ofthe surfactant, either through modificationof the solvent medium or by solubilization in the micelles. (4)Specific interactions will occur between the alcohol and the surfactant in the micelle, and the locus of solubilization will depend on these interactions.
* To whom correspondence should be sent at t h e Universit6 d e Moncton. t Universit6 d e Moncton. INRS-Energie & Matkriaux. Abstract published in Advance ACSAbstracts, October 1,1994. (1)Franks, F.;Desnoyers, J. E. In Water Science Reviews; Franks, F., Ed.; Cambridge University Press: Cambridge, U.K., 1985;Vol 1,p 171. (2)See for example: Desnoyers, J. E.; HBtu, D.; Caron, G. Colloids Surf 1989.35. 169. (3) Mukkjee, P.; Cardinal, J. R. J. Phys. Chem. 1978,82,1620. (4) Nagarajan, R.; Chaiko M. A.; Ruckenstein, E. J. Phys. Chem. 1984,88, 2916.
*
@
(5)The alcohol affects the shape and size ofthe micelles. (6) The alcohol can modify the degree of counterion binding of ionic micelles. (7)At high alcohol concentration, microaggregates of alcohols are formed, and surfactants can be solubilized in these microstructures and can modify them. At finite concentrations of both components, all ofthese effects will contribute to most properties to some extent, and it is very difficult to design experiments that will isolate only some of them. This is why, for example, the value of the distribution constants of alcohols between the aqueous and micellar phases can vary significantly, depending on the property investigated and on the model used. I t is therefore important to apply the same techniques and the same models to many systems if we wish to understand trends in the properties, such as the effect of chain length and geometry of the hydrophobic chains, polarity ofthe hydrophilic head groups, ionization of the surfactant, etc., and indirectly derive information from these on the structure of these systems. (5) Hirsh, E.; Candau S.; Zana, R. J. Colloid Interface Sci. 1984,97, 318. (6)Blokhus, A.M.; Holland, H.; Backlund, S. J . Colloid Interface Sci. 1986,114,9. (7)Oakenfull, D. J. Colloid Interface Sci. 1982,88,562. (8) Holland, H.; Yosland, E.; Backlund, S. J. Colloid Interface Sci 1984,101,467. (9)Candau, S.;Zana, R. J. Colloid Interface Sci. 1981,84, 206. (10)Lianos, P.; Viriot, M.-L.; Zana, R. J.Phys. Chem. 1984,88,1098. (11)Almgren, M.; Grieser, F.; Thomas, J. K.J. Am. Chem. Soc. 1979, 101,279. (12)Hirose, C.; Sepulveda, L. J . Phys. Chem. 1981,85,3689. (13)Simon, S. A.;McDaniel, R. V.; McIntosh, T. U. J . Phys. Chem. 1982,86,1449. (14)Kandori, K.; McGreevy, R. U.; Schechter, R. S. J. Phys. Chem. 1989,93,1506. (15) Abu-Hamdujyah, M.; Kumari, K J . Phys. Chem. 1990,94,2518. (16)Nishikido, N. J. Colloid Interface Sci. 1989,131,440. (17)Holland, H.; Blockus,A. M. NutoASISer., Ser. C 1990,324,139. (18)Wasylihen, R. E.;Kwak, J. C. T.; Zhesheng, G.; Verpoorte, E.; MacDonald, J. B.; F’ickson, R. M. Can. J . Chem. 1991,69,822.
Q743-7463/94/2410-4039$04.5Q/Q 0 1994 American Chemical Society
4040 Langmuir, Vol. 10,No. 11, 1994
Hhtu et al.
Table 1. Apparent Molar Volumes and Heat Capacities of PenOH in Aqueous Solutions of Surfactants at 25 "C m 2a
m 3'
dob
0.099389 0.29974 0.39993 0.50001 0.60000 0.69922 0.79967 0.89986 0.97980 1.0000 1.2000 1.2998 1.4000 1.5944 1.6000 1.8001 1.9000 1.9993 2.5084
0,05499 0.05253 0.05343 0.04670 0.05242 0.05069 0.04952 0.05127 0.03200 0.05064 0.05115 0.05020 0.04962 0.05894 0.05013 0.05037 0.05613 0.05053 0.05042
1.000960 1.008526 1.012193 1.015703 1.019137 1.022432 1.025666 1.028759 1.031783 1.031497 1.037248 1.039681 1.042202 1.046682 1.046776 1.051019 1.053032 1.054960 1.064277
0.010003 0.020003 0.030000 0.040000 0.045002 0.049989 0.059995 0.069830 0.083691 0.089929 0.10000 0.12757 0.14996 0.20228 0.24272 0.29999 0.35006 0.39996 0.42985 0.45000 0.49982 0.51000 0.60620 0.79990 1.00720
0.05121 0.04891 0.05131 0.04922 0.04873 0.05354 0.04686 0.04959 0.05011 0.04859 0.04902 0.053151 0.05117 0.05065 0.04966 0.05062 0.05069 0.04949 0.051347 0.04995 0.05087 0.052791 0.04936 0.04997 0.049801
0.997381 0.997701 0.998033 0.998368 0.998518 0.998690 0.998956 0.999174 0.999503 0.999620 0.999865 1.000490 1.000973 1.002126 1.003077 1.004177 1.005208 1.006196 1.006827 1.007201 1.008152 1.008377 1.010135 1.013551 1.016990
0.0092858 0.018660 0.026445 0.038962 0.041442 0.046178 0.056060 0.069276 0.078835 0.095822 0.10161 0.11530 0.13867 0.21578 0.35067 0.40883 0.65739 0.75961 0.97972 1.1345
0.047000 0.049310 0.047679 0.049520 0.050525 0.042179 0.051648 0.052473 0.050514 0.052753 0.051878 0.047937 0.048762 0.050971 0.068317 0.081078 0.049184 0.050489 0.043630 0.052495
0.99655 0.996877 0.996801 0.996682 0.996653 0.996592 0.996463 0.996268 0.996130 0.995879 0.995789 0.995588 0.995244 0.994125 0.992212 0.991473 0.988601 0.987470 0.984992 0.993544
0.0054524 0.010662 0.019511 0.029105 0.034034 0.040184 0.051289 0.060678 0.069673 0.079234 0.094514 0.10145 0.15623 0.18720 0.35821 0.49873 0.51260
0.049124 0.054260 0.054679 0.058539 0.052543 0.052416 0.048333 0.056582 0.046080 0.053026 0.044357 0.062049 0.046202 0.050803 0.051424 0.052160 0.053958
0.996981 0.996913 0.996795 0.996626 0.996533 0.996425 0.996216 0.996038 0.995872 0.995699 0.995415 0.995289 0.994296 0.993742 0.990795 0.988551 0.988318
CP,OC
(d - do) x 10%
HABr (M.W.: 182.12 mol-l)
4.1496 4.0915 4.0644 4.0370
-0.855 -0.762 -0.803 -0.768 -0.823 3.9845 -0.851 -0.896 3.9340 -1.001 3.9067 -0.686 -1.086 3.8466 -1.269 -1.293 3.8132 3.7717 -1.315 3.7020 -1.619 -1.379 3.7017 3.6476 -1.420 3.5976 -1.599 -1.445 3.5660 3.4058 -1.495 DABr (M.W.: 238.23 gmol-l) 4.1778 -0.703 4.1753 -0.682 4.1739 -0.687 4.1721 -0.690 4.1711 -0.727 4.1701 -0.918 4.1656 -0.773 4.1606 -0.817 4.1519 -0.837 4.1490 -0.819 4.1428 -0.816 4.1281 -0.922 -0.903 4.1161 -0.892 4.0862 -0.901 4.0633 -0.920 4.0360 -0.951 4.0117 -0.877 3.9878 -0.988 3.9772 -0.946 3.9644 -1.035 3.9434 -1.036 3.9423 -0.982 3.8965 -1.008 3.8149 -1.011 3.7383 ODPO (M.W.: 190.26 -01-l) 4.1805 -0.655 4.1816 -0.682 4.1824 -0.667 4.1848 -0.723 4.1859 -0.728 4.1873 -0.686 4.1877 -0.785 4.1855 -0.809 4.1835 -0.803 4.1791 -0.836 4.1775 -0.820 4.1740 -0.767 4.1675 -0.786 4.1468 -0.842 4.1118 -1.229 4.0965 -1.384 4.0392 -0.838 4.0146 -0.864 3.9710 -0.738 3.9361 -0,899 DDAO (M.W.: 201.35 g-mol-l) 4.1802 -0.683 -0.759 4.1808 4.1823 -0.798 -0.861 4.1819 4.1807 -0.793 4.1789 -0.798 4.1756 -0.747 4.1729 -0.889 4.1699 -0.733 4.1666 -0.847 4.1622 -0.703 4.1596 -0.996 4.1428 -0.751 4.1330 -0.843 4.0813 -0.850 4.0416 -0.867 -0.891 4.0371
v+,3e
103.67 101.74 101.84 102.81 101.70 102.36 103.23 104.23 105.64 105.73 108.18 108.75 109.12 109.46 109.46 109.54 109.57 109.40 109.16
( a - uo)/uo x 1ou
CP,d
1.44 1.34 1.36 1.22
539.9 524.8 523.0 527.5
1.31
520.5
0.66 -0.32
472.8 386.6
-2.21 -2.46 -2.67 -3.43 -2.95 -2.99 -3.34 -2.84 -2.74
264.5 243.2 224.8 207.2 205.0 202.2 199.6 210.0 209.5
1.19 1.14 1.22 1.14 1.09 0.55 0.10 -0.12 -0.31 -0.37 -0.44 -0.75 -0.78
523.7 524.5 524.0 523.8 524.1 482.7 445.3 425.6 409.9 404.3 397.1 377.3 372.7
-1.18 -1.22 -1.34 -1.38 -1.47 -1.45 -1.62 -1.72 -2.01 -2.53 -2.64
335.0 331.4 322.3 310.3 312.5 308.7 301.4 295.5 261.1 218.4 205.3
106.42 106.69 106.91 107.01 107.43
1.15 1.25 1.15 1.57 1.44 0.86 0.30 -0.07 -0.19 -0.40 -0.43 -0.47 -0.62 -0.91 -1.68 -2.08 -1.36 -1.36 -1.41 -1.64
530.0 533.5 529.0 563.9 549.7 523.5 457.8 428.5 420.1 403.4 400.1 394.2 381.9 360.4 335.7 326.2 313.8 315.1 289.6 292.2
102.48 102.58 103.20 103.35 103.74 103.88 104.14 104.43 104.63 104.73 104.62 104.88 105.18 105.59 105.90 106.27 106.19
1.16 1.35 0.90 0.36 0.22 0.06 -0.08 -0.24 -0.30 -0.45 -0.47 -0.69 -0.82 -0.97 -1.33 -1.45 -1.49
526.3 532.1 499.5 456.6 449.8 437.4 426.2 416.2 407.2 398.9 389.2 387.6 359.3 354.4 322.1 311.6 311.6
102.25 102.43 101.84 102.43 103.32 105.55 104.85 104.81 104.99 105.14 104.90 105.53 105.77 105.60 106.00 105.90 106.36 106.64 106.30 106.83 106.87 106.71 106.41 102.51 102.41 102.58 103.22 103.03 103.85 104.10 104.60 104.59 104.55 104.76 104.93 105.48
Volume and Heat Capacity of n-Pentanol
Langmuir, Vol. 10, No. 11, 1994 4041
Table 1 (Continued) mza
0.011869 0.016818 0.032737 0.046089 0.075530 0.10179 0.1052 0.12197 0.12667 0.13271 0.14607 0.15550 0.16711 0.17582 0.19725 0.25147 0.27077 0.31158 0.33976 0.38415 0.43268 0.56769 0.66815 0.72369 0.97174 1.0215
m3"
0.048212 0.046368 0.049096 0.044180 0.046691 0.045931 0.048050 0.047239 0.051053 0.049849 0.050936 0.049863 0.051333 0.046081 0.046826 0.053413 0.050499 0.047747 0.051407 0.052078 0.046056 0.051657 0.047314 0.051252 0.046527 0.049786
dob
0.997768 0.998081 0.999025 0.999791 1.001575 1.003117 1.003329 1.004255 1.004519 1.004896 1.005564 1.006085 1.006654 1.007096 1.008179 1.010854 1.011762 1.013666 1.015020 1.017091 1.019223 1.025232 1.029378 1.031757 1.041258 1.043311
CP,OC (d - do) x low NaOS (M.W.: 232.27mol-') 4.1754 -0.6g3 4.1740 -0.655 4.1693 -0.682 4.1653 -0.620 4.1565 -0.673 4.1486 -0.694 4.1479 -0.742 4.1428 -0.777 4.1419 -0.887 4.1392 -0.906 4.1340 -0.954 4.1287 -0.956 4.1225 -0.978 4.1173 -0.868 4.1048 -0.932 4.0732 -1.061 4.0624 -1.019 4.0405 -0.964 4.0236 -1.049 3.9996 -1.063 -0.902 3.9759 -1.100 3.9069 -1.039 3.8623 -1.140 3.8358 -1.025 3.7368 -1.170 3.7134
(a - uo)/uo x 10%
VA3O
102.23 102.57 102.22 102.27 102.45 102.96 103.27 104.17 105.06 105.81 106.29 106.66 106.47 106.19 107.12 106.76 106.95 106.71 106.76 106.51 106.35 106.47 106.45 106.20
CP,0,3C
1.18 1.15 1.21 1.02 1.14 1.09 0.95 0.00 -0.45 -0.74 -1.42 -1.66 -1.77 -1.71 -1.85 -2.28 -2.19 -2.13 -2.36 -2.31 -2.01 -2.28 -2.10 -2.28 -1.86 -2.13
528.6 531.3 529.1 522.5 528.5 527.4 512.2 433.4 400.4 378.4 326.0 304.9 298.7 286.8 280.3 264.6 262.4 255.9 250.3 254.9 252.9 252.6 251.0 249.7 258.7 251.7
1.28 1.38 1.37 1.23 1.38 1.39 1.53 1.78 1.59 1.38 0.11 -1.09 -1.28 -2.56 -3.39 -3.71 -3.69 -3.89 -3.72 -3.81 -3.65 -3.12 -2.92 -2.86 -2.61 -2.56 -2.85
530.8 542.5 530.0 527.5 537.4 542.6 554.2 572.4 556.3 549.7 451.1 357.1 332.2 220.2 175.6 145.8 151.0 129.5 145.6 137.2 149.0 175.6 194.6 206.6 215.3 222.8 234.3
-1.76
253.8
-1.93
260.3
NaNO 0.040886 0.049969 0.071600 0.10001 0.12203 0.13300 0.15000 0.16394 0.17251 0.17991 0.19996 0.21164 0.21996 0.23271 0.25003 0.26624 0.28004 0.30004 0.31999 0.35002 0.39989 0.51066 0.59858 0.70000 0.82573 0.95798 1.1197 1.1310 1.2438 1.4164 1.6244 1.7352
0.051477 0.050339 0.055741 0.051104 0.052783 0.050501 0.050699 0.052852 0.054528 0.050357 0.050369 0.050688 0.049743 0.045239 0.050663 0.050059 0.050157 0.049920 0.050397 0.050339 0.050360 0.047725 0.048533 0.050429 0.048525 0.049830 0.059532 0.049685 0.041143 0.049078 0.048957 0.049534
0.998395 0.998674 0.99393 1.000268 1.001000 1.001346 1.001824 1.002292 1.002564 1.002725 1.003323 1.003708 1.003879 1.004291 1.004648 1.005080 1.005335 1.005762 1.006183 1.006811 1.007862 1.010326 1.012021 1.013635 1.016343 1.018482 1.021349 1.021514 1.022822 1.025469 1.028720 1.030195
4.1770 4.1759 4.1752 4.1730 4.1726 4.1721 4.1707 4.1712 4.1710 4.1700 4.1696 4.1712 4.1703 4.1703 4.1664 4.1618 4.1560 4.1486 4.1409 4.1280 4.1076 4.0615 4.0293 4.0287 3.9920 3.9465 3.8338 3.8335 3.7277
Thermodynamicproperties give little direct information on the structure of the micellar species but are very sensitive to interactions in these systems and lend themselves readily to m0de1ing.I~If the alcohol is kept at low concentration, then alcohol-alcohol interactions and any self-aggregation of alcohols can be neglected. The standard thermodynamic functions of transfer of solute 3 (the alcohol) to a mixture of surfactant 2 in water (W) is given by
where Y is the standard (infinite dilution) partial molar quantity of 3, for the property Y,in water and in the aqueous solution of 2. If the concentration of the alcohol is sufficiently low, Yi can be replaced by the cor(19)Desnoyers, J. E. J. Sutf Sei. Technol. 1989,5, 289.
102.24 102.50 102.29 102.18 102.40 102.24 102.35 103.14 103.78 103.00 105.64 106.82 105.12 109.20 108.92 109.00 109.72 108.93 108.71 108.60 108.30 107.84 107.49 107.32 106.89 106.72 106.70 106.46 106.74 106.40 106.39 106.49
-0.716 -0.727 -0.802 -0.864 -0.810 -0.897 -0.965 -0.863 -0.973 -1.077 -1.071 -1.111 -1.069 -1.071 -1.068 -1.060 -0.998 -1.008 -1.049 -1.005 -1.037 -1.258 -1.040 -0.881 -1.049 -1.067 -1.094
responding apparent molar quantity Y ~inJthe calculation of the transfer functions.20 Many such transfer functions of alcohols to micellar systems have been measured for volumes, compressibilities, enthalpies, and heat capacities. Two main models have been developed to extract fundamental parameters of alcohols in the micelles from the data. Roux et a1.21,22 used a mass-action model for the surfactant and a pseudophase model for solute 3. This model essentially accounts for the three first contributions given above. DeLisi et al.23,24 used a pseudophase separation model for the surfactant and a mass-action model for solute 3. They ~
~~~
(20)AvBdikian, L.;Perron, G.; Desnoyers, J. E. J. Solution Chem. 1975,4 , 331. (21)Row, A. H.; HBtu, D.; Perron, G.; Desnoyers, J. E. J . Solution Chem. 1984,13,1. (22)HBtu, D.; Row, A. H.;Desnoyers, J. E. J. Solution Chem. 1987, 16, 529.
Hktu et al.
4042 Langmuir, Vol. 10, No. 11, 1994 can also account for the distribution of the alcohol between the aqueous and micellar phases and partially for the equilibrium shift. While the approach of Row et al. works best for short-chain surfactants, that of DeLisi et al. is mostly applicable to long-chain ones. Neither of these models accounts forcontributions 4-6above, and any such contribution is necessarily attributed to the distribution constant KOor to theproperties of the alcohol in the micelle. The aim of the present paper is to verify the effect of surfactant chain length and head group on the distribution of alcohols between water and the micellar phase and on the properties of alcohols in the micelles. Nonionic and ionic surfactants of chain lengths 6-12 were used, and pentanol (PenOH) was taken as a representative alcohol used as a cosurfactant. The properties investigated are the volume and heat capacity of transfer at 25 "C. New measurements were obtained for hexylammonium bromide (HABr), decylammonium bromide (DABr), sodium octylsulfate (NaOS), octyldimethylphosphine oxide (ODPO), decyldimethylamine oxide (DDAO), and sodium nonanoate (NaNO). Literature data were used for octylammonium bromide (OABr),z5decyltrimethylammonium bromide (DTAB)F6octyldimethylamine oxide (ODAO),zz sodium dodecyl sulfate NaDDS,zzand sodium decanoate (NaDCLZ7 The analysis of the results is made from the point of view of the relative hydrophobicity principlez8 and from the simulation of the data with the model of Roux et ai.zz
Experimental Section Water was obtained from a Barnstead Nanopure System, equipped with reverse osmosis, and degassed before use. Its specific conductivity was always lower than 2 x lo-' cm42-l. PenOH, of ACS quality, was obtained from Fisher and used as such. The origin and purification procedure for ODPOz9and DDA030 have been described previously. Those for the other surfactants are as follows: (HABr) Hexylamine (Fluka, >99%)was neutralized with concentrated HBr (Caledon Laboratories). Water was removed with 2-PrOH (azeotrope) in a flash evaporator. The salt was washed with diethyl ether and recrystallized in benzene. (DABr) Decylamine (Fluka)was distilled and neutralized with concentrated HBr. Water was removed with 2-PrOH (azeotrope) in a flash evaporator. The salt was washed with diethyl ether and recrystallized in benzene. (NaNO) Nonanoic acid (Aldrich) was recrystallized in ether and neutralized with NaOH t o a pH of 9.8. Water was removed with a flash evaporator. (NaOS)Octyl sulfate (Eastman Kodak) was recrystallized in a mixture of acetone, methanol, and diethyl ether. All solutions were prepared by mass. Ternary solutions containing 0.05 mol-kg-l of PenOH, which represents a good compromise between an easily measurable quantity and infinite dilution, were prepared from aqueous solutions of surfactant and measured against the corresponding aqueous solutions of surfactant. Densities and volumetric heat capacities were respectively determined with a SODEV flow densimeter, Model 03D, and a SODEV flow microcalorimeter,Model CP-C,which were described p r e v i ~ u s l y . ~ lUnder - ~ ~ the best conditions, with these instruments, the changes in density (d - do) between the solution and (23)DeLisi, R.; Genova, C.; Testa, R.; Turco Liven, V. J. Solution Chem. 1964,13,121. (24)DeLisi, R.; Turco Liven,V.; Castagnolo,M.; Inglese, A. J.Solution Chem. 1986,15,23. (25)Desnoyers, J. E.;HBtu, D.; Perron, G. J. Solution Chem. 1983, 12,427. (26)DeLisi, R.;Milioto, S.; Triolo, R. J . Colloid Interface Sci. 1988, 17,673. (27)Yamashita, F.;Kwak,J. C. T. Unpublished data. (28)HBtu, D.; Roux, A. H.; Desnoyers, J. E. J. Colloid Interface Sci. 1968,122,418. (29)Perron, G.;Yamashita, F.;Martin, P.; Desnoyers,J.E. J.Colloid Interface Sci. 1991,144,222. (30)Desnoyers, J. E.;Caron, G.; DeLisi, R.; Roberts, D.; Row, A.; Perron, G. J. Phys. Chem. 1983,87,1397.
Table 2. Apparent Molar Volumes and Heat Capacities of PenOH in Water at 25 "C
0.039331 0.040772 0.044212 0.052099 0.060476 mean: standard deviation:
PenOH (M.W.: 88.15 gm01-l) -0.549 102.51 0.93 -0.565 102.40 0.97 -0.612 102.40 1.07 -0.726 102.50 -0.833 102.35 102.43 0.07
a Units = mol-kg-'. Units = Jsmol-'K-l.
526.4 526.6 528.3
527.2 1.1
. = cm3*mol-'. Units = lo3 g - ~ m - ~ Units
the reference solvent can be detected within f 3 x lon6g - ~ m - ~ and the relative changes in heat capacity per unit volume (a uo)/uowithin f0.3% up to the limit of sensitivity of Au which is 7 x 105J . K - ' T ~ - ~ .The temperature of these instruments was maintained at 25.00 "C with a SODEV temperature controller, Model CT-L .
Results Density and volumetric heat capacity data are given in Table 1. The values of the apparent molar volumes and heat capacities of PenOH in the aqueous solutions of surfactant were calculated from the experimental data, using, respectively, the usual relations:
V,,3 (W
+ 2) = M / d - 1000(d - d,-,)/m3dd,
(2)
where M is the molar mass of PenOH and m3 its molality in mol-kg-l of surfactant solution. The change in specific heat capacity between the ternary solution of PenOH and the corresponding aqueous solution of surfactant, cp- c ~ , ~ , is related to (u - UO)/UOby the following relation:
The values of Ya,3 (W), are already known from the literature, but thevalues for thevolume range from 101.88' to 102.69 cm3m 0 1 - l . ~For ~ the purpose of consistency, the measurements were thus repeated. The results which are given in Table 2 were calculated using eqs 2-4 where do and cp,oare taken, respectively, as the density and the heat capacity of water at 25 "C, 0.997 047 g ~ m and - ~ 4.1793 J-mol-l0K-l. While it has been established that the thermodynamic properties of alcohols in water vary with c ~ n c e n t r a t i o nY , ~ ~(W) at 0.05 mol-kg-l was taken as the average of the values in Table 2. The volumes and heat capacities of transfer of PenOH from water to aqueous surfactants were plotted against mz, the molality of the aqueous solution of surfactant. These results are presented in Figures 1-6 by the full points, and the literature data by open points. The dotted and full lines represent the theoretical simulations obtained with the model of R o w et al. (see Discussion). For the transfer functions, the thermodynamic properties ofthe ternary system are measured against the binary surfactant solution. Experimentally, it is therefore not (31)Picker, P.;Tremblay, E.; Jolicoeur, C. J . Solution Chem. 1974, 377. (32)Picker, P.;Leduc, P.-A.; Philip, P.; Desnoyers, J. E. J . Chem. Thermodyn. 1971,3,631. (33)Desnoyers, J. E.;deVisser, C.; Perron, G.; Picker, P. J.Solution Chem. 1976,5,603. (34)HBtu, D. Ph.D. Thesis, Univ. of Sherbrooke, Sherbrooke, PQ, Canada, 1986. (35)Perron, G.; Desnoyers, J. E. J . Chem. Thermodyn. 1981,13, 1105.
Langmuir, Vol. 10,No.11, 1994 4043
Volume and Heat Capacity of n-Pentanol
Table 3. Parameters Obtained by Least-Squares Fit for the Thermodynamic Properties of the Binary Systems Water Surfactant at 25 "C
+
~
solute HABr OABr DAE!r DTAE! ODPO ODAO DDAO NaNO NaDC NaOS
property volume heat cap. volume heat cap. volume heat cap. volume heat cap. volume heat cap. volume heat cap. volume heat cap. volume heat cap. volume volume heat cap.
Af
Y )
By,2zb
141.9 (0.09) 453.7 (4.2) 173.85 (0.07) 619.0 (1) 205.4 (0.2) 810.8 (4) 256.7 (0.1) 893. (5) 200.9 (0.3) 919.9 (2) 183.07 808.0 215.0 988.0 147.1 (0.07) 685.0 (3) 164.6 171.6 (0.1) 652. (4)
1.42 (0.2) -36.6 (7.8) -3.1 (0.7) 0.0 (0) -3.5 (4) 0.0 (0) -5.7 (3) 0.0 (0) -30.4 (14) 0.0 (0) -2.369 0.0 (0) -34.97
0.0 (0) 0.0 (0) 0.0 (0) 0.0 (0) -3.2 (1) 0.0 (0)
1.865 (0) 28.95 (0) 1.865 (0) 28.95 (0) 1.865 (0) 28.95 (0) 1.865 (0) 28.95 (0) 0.0 (0) 0.0 (0) 0.0 (0) 0.0 (0) 0.0 (0) 0.0 (0) 1.865 (0) 28.95 (0) 1.865 (0) 1.865 (0) 28.95 (0)
YF4
mid
n
149 (0) 200 (0) 182.4 (0.1) 279. (3) 215.24 (0.08) 423. (4) 262.18 (0.03) 501. (4) 206.4 (0.14) 497. (3) 188.6 379.9 221.76 461.5 157.8 (0.2) 293. (6) 176.7 (0.2) 180.7 (0.1) 334.5 (5.6)
1.174 (0.04) 1.331 (0.06) 0.257 (0.005) 0.274 (0.003) 0.056 (0.002) 0.053 (0.001) 0.069 (0.002) 0.077 (0.002) 0.043 (0.002) 0.051 (0.001) 0.2126 0.20896 0.02049 0.0219 0.255 (0.005) 0.236 (0.009) 0.122 (0.001) 0.153 (0.003) 0.130 (0.008)
10.8 (0.3) 11.0 (0) 28.8 (0.5) 29.0 (0) 159.0 (6) 159.0 (0) 135.0 (4) 135.0 (0) 18. (1) 18.4 (0.4) 12.7 13.4 21.7 15.3 18.4 (.4) 18.4 (0) 9.4 (0.1) 13.4 (0.2) 14.0 (0)
AH2e 0.0 (0) 0.0 (0) 0.0 (0) 0.0 (0)
10613.0 (570) 11667.0 10137.0 7635.0 (700) 6761 (1000)
a Units = cm3-mol-' for volumes and J.K-lmo1-l for heat capacities. b Units = cm3.kg-m01-~for volumes and J.kgK-1.mol-2 for heat capacities. Units = Debye-Huckel limiting slopes for VQ in cm3-mol-l and Cp,*in J-K-l.mo1-l. Units = mol-kg-l. e Units = Jmol-I. The origin of the thermodynamic data used for the determination of the parameters of the binary systems is the same as that of the ternary systems given in Table 4.
necessary to know the properties of the binary system. However, as it will be shown in the Discussion, the parameters from the application of a mass-action model to the binary surfactant solution are required to simulate the transfer functions. These parameters can be taken from the literature or calculated from the data on the binary solutions in Table 1 using the model of Roux et aL30 They will be summarized in Table 3. In the case where data are already available on some systems in the literature, a comparison with the present data serves as a check for the purity of the present surfactants. In most cases the agreement is excellent. Some disagreement is observed with NaOS, NaNO, and NaDC. The present sample of NaOS, afier purification, always shows a slight minimum in surface tensions, and the values of Vm,2 and Cp,a,zare systematically lower by -2 ~m~mmo1-l and -8 J.K-l.mo1-l than the published data.36 The impurity present is probably some sodium hexyl sulfate which coprecipitates with NaOS. A comparison of V of NaNO with other alkanoates, by group additivity, suggests that V,,z are too low by -1.1 cm3.mol-'. Also, V i of NaDC, obtained from the fit of the data by KwakF7 is 164.6 cm3*mol-lcompared with the published value of 164.08 ~m~mmol-'.~~ For self-consistency, whenever there was a divergence between two sets of data, preference was given to the binary systems that were measured at the same time as the ternary system. The uncertainty in these data is still acceptable and will not affect significantly the parameters needed for the simulations of the transfer functions.
i
Discussion Principle of Relative Hydrophobicities. The shapes of the transfer functions are typical of systems where a hydrophobic solute distributes itself between water and micelles. The presence of an extremum is related to the shift in the micellization equilibrium induced by the alcohol. Such an extremum has been observed previously for a transfer function of a hydrophobic solute from water to an aqueous surfactant only when the hydrophobicity (36)Musbally, G. M.; Perron, G.; Desnoyers,J. E. J.CoZloidInterface Sci. 1974, 48, 494. (37) DeLisi, R.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1980,58, 959.
of the transfered solute is higher than that of the surfactant.28 The relative hydrophobicities are evaluated by the inverse of the macrosolubilities in water or of the CMC. When the hydrophobicities are the same, the transfer function becomes equivalent to the corresponding partial molar quantity. This has been called the principle of relative hydrophobicities. Ideally, this principle holds for systems involving a transferred solute of the same type as the main solute 2 and where the difference in the hydrophobicities depends only on the relative chain length. However, it has been shown that it can be extended to many systems, especially when the transferred solute has a head group similar to that of the main solute or when the difference in hydrophobicities is high. This is especially true for those thermodynamic properties which are more sensitive to hydrophobic effects than to interactionsinvolvingthe head groups (e.g. heat capacities). It can then be considered that the main effect of these latter interactions is to decrease or increase the hydrophobicity of the main solute. The transfer functions ofPenOH from water to nonionic surfactants, ODAO, DDAO, and ODPO, shown in Figures 1 and 2, are representative of the case where the transferred solute is similar to the main solute. The slight minimum in heat capacities and the uncertain maximum in the volumes show that a molecule of PenOH tends to replace nearly indifferently a molecule of ODAO. In fact, the curves of the transfer functions have then nearly the same shape as the partial molar quantities of the surfactants. In the case of DDAO and ODPO, no extrema are observed. From the principle of relative hydrophobicities, this is interpreted in terms of a larger hydrophobicity ofthese surfactants relative to PenOH. In such a case, the distribution of PenOH between water and the micellar phase is the leading effect. Indeed, DDAO has a longer chain than ODAO and is then obviously more hydrophobic, whereas the high hydrophobicity of ODPO compared to ODAO has been explained by Perron et al.29 by the higher polarity of the head group of ODAO. Concerning the ammonium salts in Figures 3 and 4, the trends are very similarto those ofnonionic surfactants. There is no extremum in the cmc region for the longer and more hydrophobic DABr, whereas the break in heat capacities at higher concentrations of long-chain am-
Hktu et al.
4044 Langmuir, Vol. 10,No. 11, 1994 t
e
0 l
0.0
,
0.4
I
,
0.8
l
I
1.2
I.6
Q (md-kg-9
Figure 1. Volumes of transfer of PenOH from water to aqueous solutions of nonionic surfactants (SI,at 25 "C.The broken and
full lines are the ideal and adjusted simulations. Original data
for ODAO from ref 22.
c
1
e:
Figure3. Volumes oftransferof PenOH from water to aqueous solutions of cationic ammonium bromide surfactants (S),at 25 "C. The broken and full lines are the ideal and adjusted simulations. Original data for OABr from ref 25.
OtL
-"L 1.2
-200
0.0
0.4
1.6
0.8
Q (d-ke-l)
0.0
1
I
1.0
2.0
L
Y?(md-kg-1)
Figure 2. Heat capacities of transfer of PenOH from water to aqueous solutions of nonionic surfactants (SI,at 25 "C. The
Figure 4. Heat capacities of transfer of PenOH from water to aqueous solutions of cationic ammonium bromide surfactants (S), at 25 "C.The broken and fulllines are the ideal and adjusted simulations. Original data for OABr from ref 25.
monium salts has been attributed by Quirion and Desnoyers38 to a change in the counterion binding prior to the sphere to rod transition. For OABr, there is no extremum, which shows that a molecule of PenOH may replace indifferently a molecule of OABr as in the case of ODAO. Finally, for the shorter and less hydrophobic HABr, there is a visible maximum in the volumes and a slight minimum in the heat capacities, which shows that PenOH enhances the micellization of HABr because of its more hydrophobic character. In the case of anionic surfactants, Figures 5 and 6, the situation is much different. Large extrema are observed, except for the heat capacities ofNaOS where the minimum
is slight. From the principle of relative hydrophobicities, this would mean that anionic surfactants appear less hydrophobic relative to PenOH than nonionic or cationic surfactants of the same chain length. Since PenOH can enhance the micellization of anionic surfactants more than that of other surfactants of the same chain lengths, the difference in the trends must be due to interactions involving the polar heads. Chemical Model for the Transfer Functions. The data for the transfer functions were simulated using the model of Roux et a1.21*22 The system is assumed to be composed of three aqueous species which are the free surfactant monomers, free alcohol monomers, and the mixed micelles of surfactant and alcohol. Knowing the values of the micellization and distribution constants, KM and&, respectively, allows the proportion of each species
broken and full lines are the ideal and adjusted simulations. Original data for ODAO from ref 22.
(38) Quirion F.; Desnoyers,J. E. J.Colloid Interface Sci. 1986,112, 565.
Langmuir, Vol. 10,No. 11, 1994 4045
Volume and Heat Capacity of n-Pentanol
AY,(W
-
W + 2) = m$m3(ao - a)AY (1- PI AY
+
+ 2m2a+3By,23(8)
where a, represents the mole fraction of aqueous free monomers in the aqueous solution of surfactant, and AYY and AYF are the variations of the property of solutes 2 and 3 between the aqueous and micellar phases. The last term of eq 8 takes into account contributions for pairwise interactions between monomers of solutes 2 and 3. Self-interactionsbetween monomers of the same solute (By,22) and the Debye-Hiickel slope (AY),for ionic surfactants, are included in AY :: AY
NaNo 0.4
0.8
1.2
-Y
- A,ao1’2m21’2- By,22aom2 (9)
With heat capacities, relaxation effects, which are responsible for the maximum observed in the cmc region, must also be taken into account. This is done by introducing a n extra term R involving the enthalpies of micellization and of transfer AH and AH of solutes 2 and 3 in eq 8:
0 0.0
F=Y
:
1.6
n-2 (m-ks-l)
Figure 6. Volumes of transfer of PenOH from water to aqueous solutions of anionic surfactants (S), at 25 “C. The broken and full lines are the ideal and adjusted simulations.Original data for NaDC from ref 27.
R = (m21m3) (daJdT - da/dr)AH
- aP/aT AH
(10) Parameters for the binary systems of aqueous solutions of surfactants (namely, AY AY ,: By,22, n, and mi, the molality at the inflection point daddm21 were obtained from a least-squares fit using the mass-action model of Roux et al.30for the aqueous surfactants. The parameters of the binary systems are given in Table 3 with their standard deviation in parentheses. A standard deviation indicated as (0)means that this parameter was fxed prior to the least-squares fit. For example, for short-chain surfactants, the values of AYY were obtained from a phase-separation model from a plot of YQ,Zagainst llm since, with the mass-action model, data must be available up to nearly 10times the cmc in order to obtain reasonable values of AY y.29 The simulations for the volumes and heat capacities of transfer of PenOH from water to aqueous surfactants, represented in Figures 1-6 by the broken and full lines, were achieved using the parameters of binary systems of Table 3. Simulations were also made for DTAB but are not shown in the figures. The parameters for the simulations of the volumes of sodium dodecyl sulfate (NaDDS)were taken from R o n et a1.22 The broken lines represent the ideal simulations, neglecting interactions ~ between the monomers of solute 2 and 3 ( B Y , Zand assuming an ideal behavior of PenOH in the micellar phase. The value of AY is then taken as Y - Y where Y and Y are respectively the property of the pure PenOH and of the standard value in water. KD, obtained from eq 5 by assuming that X3’ = 1, is taken as llPom3,where Pom3is the solubility of PenOH in water on a molal scale. In some cases where the cmcs were very low (DDAO and ODPO), problems of convergence of the model were found at high values of m2. I t was then necessary to use values for m3 that are lower than 0.05. This has little effect on the magnitude of the simulation. These ideal simulations give a good idea of the general shape of the curves, but it is obvious that the behavior of PenOH is not ideal and that some other contributions must be taken into account. This is done by adjusting the parameters KD,AY f,and By,23. The values obtained for these parameters are given in Table 4 and presented in Figure 7 as a function of chain length of the surfactants. The values of KO in Figure 7 were taken as the average
i,
00
0.4
0.8
12
16
n-2 (m-ks-l)
Figure 6. Heat capacities of transfer of PenOH from water t o aqueoussolutions ofanionicsurfactants(S), at 25 “C.“he broken and full lines are the ideal and adjusted simulations. in the solution, represented as the molar fraction of aqueous free monomers of solutes 2 and 3, respectively a and P, to be obtained from the bulk molalities of both solutes. This is done by successive approximations using the two equilibrium conditions -(l/n)ln
KM = In am2 - (l/n)ln[(l - a)m$nl +Xi
+
-In K,, = ln(Bm3/Xi) Xi - 1
(5) (6)
where n is the aggregation number and X3’, the mole fraction of solute 3 in the micelle, is defined by
X,’ = (1- P)m,/[(l - P)m3 + (1- a>m21
(7)
The transfer function AY can then be calculated from
i,
Hhtu et al.
4046 Langmuir, Vol. 10,No. 11, 1994 Table 4. Parameters for the Simulations of the Functions of Transfer of PenOH from Water to Water + Surfactant Systems at 25 "C simulation solute HABr
property
volume volume heatcap. heat cap. OABrS volume volume heatcap. heat cap. DABr volume volume heatcap. heat cap. ODPO volume volume heatcap. heat cap. ODAOb volume volume heatcap. heat cap. DDAO volume volume heatcap. heat cap. NaOS volume volume heatcap. heat cap. NaDDSi volume volume NaNO volume volume heat cap. heat cap. NaDCk volume volume DTAB volume volume heat cap.
typd
I A
I A
I A I A
I A
I A
I A I A
I A I A I A I A I A I A I A I A I A I A I A A
K D ~y Y d 0.05 0.0 4.0 6.27 0.05 -0.79 4.3 4.3 4.0 -315 0.05 0.0 0.05 0.0 5.55 -280 0.08 0.0 4.0 6.27 0.08 -1.75 6.5 4.40 0.08 0.0 4.0 -315 0.08 0.0 6.8 -300 0.05 0.0 4.0 6.27 0.05 -3.0 9.5 5.4 0.05 0.0 4.0 -315 0.05 0.0 10.0 -370 0.03 0.0 4.0 6.27 0.03 -2.1 11.0 5.3 4.0 -315 0.03 0.0 0.03 0.0 11.7 -285 0.05 0.0 4.0 6.27 0.05 -2.1 13.0 4.9 4.0 -315 0.05 0.0 0.05 0.0 13.5 -240 0.02 0.0 4.0 6.27 0.02 -3.0 15.4 4.8 0.02 0.0 4.0 -315 0.02 0.0 15.4 -315 0.05 0.0 4.0 6.27 0.05 -2.5 12.9 2.8 0.05 0.0 4.0 -315 0.05 0.0 16.7 -285 0.02 0.0 4.0 6.27 0.02 0.0 22.2 3.5 0.05 0.0 4.0 6.27 0.05 -1.7 13.0 2.5 0.05 0.0 4.0 -315 0.05 0.0 16.4 -230 0.05 0.0 4.0 6.27 0.05 -2.6 14.1 2.4 0.05 0.0 4.0 6.27 0.05 -3.0 10.5 5.6 0.05 0.0 11.1 -360 m3a
BY.23'
0
HABr,OABr,DABr o DTABr
A
NaOS,NaDDS 3
mye
ODA0,DDAO
9740 9740 9740 9740 9740 9740 9740 9740 9740 9740 9740 9740 9740 9740
9740 9740
9740
Units = mol-kg-l. b Units = ~m~.kg-mol-~ for volumes and J.kgK-lmol-2 for heat capacities. Units = kgmol-l. Units = ~ m ~ m ofor l - volumes ~ and J.K-1mol-2for heat capacities.e Units = Jmol-l. f I, ideal simulation;A, adjusted simulation. g Reference 25. Reference 22. Reference 22. j Reference 26. Ir Reference 27. a
values between the volume and heat capacity fits. For NaDDS, the values of the parameters were taken from a previous study.22 Since no least-squares fits have been used for these simulations, there is no indication of the uncertainty of these parameters from standard deviations. These uncertainties depend more on the approximations of the model itselfthan on the fitting of the curves, for which the range is in fact relatively narrow. The errors in AY y are of the order of 10%at most. The results obtained for CS surfactants are the most reliable, since it is generally easy to obtain a very good fit. For longer surfactants, the high concentration trend is not always clear, especially for ionic systems where a postmicellar transition is often observed. This contribution is not taken into account by the model, and the value of AY y can then be more in error than that for CS surfactants. On the other hand, for shorter surfactants such as HABr, the transition occurs at a relatively high concentration. The parameters KD and AY are then more affected by premicellar solute-solute interactions such as deviations from the Debye-Huckel theory and structural interactions. However, the real interest of the parameters obtained lies more in their general trends as a function of the chain length of surfactants than in absolute values.
1
I
I
I
6
0
10
12
NU*OfCl+
I
Figure 7. Parameters obtained from adjusted simulations of the transfer function of PenOH from water to aqueous surfactants at 25 "C as a function of surfactant chain length.
For the simulations of heat capacities, knowledge of the enthalpy of transfer AH is required. The parameter is most probably different from the value calculated from the enthalpy of solution of the pure alcohol in water, but since it appears only in the relaxation term which is small compared with the other terms of eq 8, the ideal value was used in all cases. In the ideal case, the parameters in Figure 7 should be independent of the chain length and polarity of the surfactants. These ideal values are given as a broken line. Experimentally, all the parameters vary essentially linearly with the chain length of the surfactant. The increase in KD indicates that PenOH is more soluble in long-chain surfactants. This suggests that PenOH is located in a more hydrophobic environment or, in other words, that the alcohol is located deeper in micelles with longer chain surfactants. On the other hand, KDdepends to some extent on the nature of the head group since the data for cationic surfactants appear to be systematically lower than those for anionic and nonionic surfactants. This is in disagreement with the observation of Rao and R u c k e n ~ t e i nwho , ~ ~ stated that the nature of the surfactants had little effect on the distribution of the alcohols. The increasingly negative values for Bv,23 are in the direction expected for increasingly hydrophobic interactions between PenOH and the surfactant monomers as the chain length increases. There is little dependence on the nature of the hydrophilic head group. The values of A V y are less positive than the ideal value (V - V but the difference decreases with chain length. The deviation from ideality would be even larger if V in an alkane was used as the standard state for the alcohol in a micelle.40 The specificity of the function
y
i),
(39)Rao, I. V.; Ruckenstein, E. J. Colloid Interface Sci. 1986,113, 375. (40) Desnoyers, J. E.; Caron, G.; Perron, G. Colloids Surf. 1989,38, 263.
Langmuir, Vol. 10, No. 11, 1994 4047
Volume and Heat Capacity of n-Pentanol AV on the head group is important, as seen in Figure The values are less positive for anionic surfactants. The sign and magnitude of AVy are due to the loss of hydrophobic solvation when PenOH moves into the micelle interior and to the polar interactions between the -OH group and the hydrophilic head group of the surfactant in the palisade layer of the micelle. The loss in hydrophobic hydration makes a positive contribution to the volume ( V: > vi) . Volumes are sensitive to electrostatic interactions and lead to a negative contribution to AV r.(V < V ;). For example, a large electrostriction associated with the hydration of ions. This latter interaction decreases in magnitude with longer chain length surfactants since the PenOH is probably more buried in the interior of the micelle.Therefore, the lower values of AV for anionic surfactants probably originate from stronger interactions between the OH group of PenOH and the anionic head group ofthe surfactant in the palisade layer of the micelle. Similar trends for volumes were also observed by DeLisi et al.,23who attributed the lower values of AVY for PenOH in anionic surfactants to a residual hydration of the PenOH in the palisade layer. These smaller values for AV y of anionic surfactant compared those for cationic ones are consistent with the larger observed KD. The nonionic surfactants behave like cationic surfactants in the case of the trends for KD but are more like cationic surfactants for the trends in AV y. We have no obvious explanation for these differences. The dependence on the surfactant chain length and nature of the hydrophilic head group is smaller for AC?,. It is generally accepted that heat capacities depend significantly on structural interactions but much less on electrostatic ones, and the present observations confirm this. The sign and magnitude of this function depend mostly on the loss of hydrophobic hydration when PenOH moves into the micelle interior. Thermodynamic Properties of Mixed Micelles. Thermodynamic properties of mixed micelles of surfactants 1and 2 can be obtained by measuring the properties of a mixture of both surfactants kept at a k e d relative mole ratio. By analogy with mixtures of liquids, the properties of mixed micelles can be interpreted in terms of excess functions, the two reference points being the micellar properties of the two pure surfactants.*l
y
A P X = Y f;”,(W)- X,Y y(W) - X2Y f(W)
(11)
where Y(W)fvI stands for the thermodynamic quantity (cmc, VM, etc.) of the mixed micelle and of each micelle in water. It can be that the reduced excess quantity of a mixture of two liquids 1 and 2 is related to the respective apparent molar quantities by
A ~ x / X l / X 2= {Y&)
- Y ;}/XI = {YQ,1(2)- y
T}/& (12)
where Y stands for the pure liquids. For nearly ideal solutions, the reduced excess quantities vary linearly with the mole fraction of either component and the intercepts are equal to Y p - Y: of both components. By analogy with eq 12, for a nearly ideal mixed micelle (a good approximationin most cases), the reduced excess quantities will vary linearly with the mole fraction of the (41)Scamehorn, J.F.,Ed. Phenomena in Mixed Surfactant Systems; ACS Symp. Ser. 311;1986. (42) Perron,G.;Couture, L.; Desnoyers, J. E. J . Solution Chem. 1992, 21,433.
components of the mixed micelle. The two intercepts will be given by
It is therefore possible to predict the excess functions for the formation of mixed micelles from two transfer functions. For example,the deviation from ideality is negative for all the volumes of transfer of PenOH to surfactants of chain length 12 or less (Figure 7). Similarly, the volumes of transfer of surfactants to alcohol-water mixtures are also generally smaller than the corresponding volume changesfor the surfactant in water.5 Therefore, the excess volume for the formation of mixed micelles will be necessarily negative. The situation is more complex with heat capacities since the measured AC of PenOH will be less negative or more negative than that of an ideal transfer, depending on the chain length (Figure 7). The same approach can be used for any other property where apparent molar quantities can be determined (enthalpies, expansibilities, and compressibilities).
z3
Conclusion The thermodynamic transfer quantities of PenOH to surfactant solutions of medium chain length can be interpreted through the principle of relative hydrophobicities and through a chemical model. From the interpretation of the trends of the various parameters derived from the fit of the data with this model, indirect information is obtained on the locus of solubilizationofthe alcohol. The properties of PenOH in the micelles all change in the direction of stronger hydrophobic interactions with more hydrophobic surfactants, suggesting that the PenOH is buried more inside the micelles in such cases. There is little specificity for the properties of PenOH on the nature of the hydrophilic head group of the surfactant for the interaction parameters B~,23and AC . The less positive values for AV y and the larger values of KDof anionic surfactants compared to those of cationic surfactants suggest that larger attractive interactions exist between the -OH group and the head group of anionic surfactants. This interaction contributes significantly to enhance the micellization of short-chain surfactants and to hold the micellar alcohol molecules nearer the palisade region of the micelles. The locus of solubilization of PenOH in nonionic surfactants relative t o ionic ones is less clear.
g3
If the transfer functions of an alcohol to a surfactant micelle and of a surfactant to an alcohol microaggregate are both known, the corresponding property of a mixed micelle can be predicted. Acknowledgment. The authors are grateful to the Natural Sciences and Engineering Council of Canada, to the University of Moncton and to “Les Ratisseries StHubert’’for financial support. The authors are also grateful to Dr. J . C. T. Kwak for making some data available prior to publication and to Jean-Marc Roy, professor of mathematics at Shippagan and Line Robichaud, summerstudent, for computer assistance.
