J . Phys. Chem. 1993,97, 3900-3903
3900
Application of Scaled Particle Theory to the Problem of Micellization. 2. Cationic and Nonionic Surfactants Nilashis Nandi and Indra N. Basumallick' Department of Chemistry, Visva Bharati, Santiniketan 731235 (W.B.),India Received: September 24, 1992
Scaled particle theory (SPT) has been applied to calculate cavity-forming free energies (AGOcav)of micellization for a series of cationic and nonionic surfactants. These cavity terms along with other free energy components were used to calculate free energy of micellization (AGOmic) of these surfactants. The observed close agreement between the predicted and experimental values of AGOmic for cationic and nonionic surfactants suggests that cavity-forming free energies play an important role in the process of micellization. Present results also support the conclusion drawn on the basis of similar calculations on anionic surfactants.
Introduction
In a recent paper' emphasis has been given to understanding the role of cavity-forming free energy to the process of micellization. The magnitude of this energy as estimated' earlier for a series of anionic surfactants has been found to be comparable to that of the hydrophobiceffect. Whileestimation of freeenergy of the hydrophobic effect is a subject of intense debate and discussion,2 cavity free energy can be estimated easily by use of scaled particle theory (SPT). SPT has been applied to a wide variety of systems consisting of small,4 large,5 and spherical6 as well as nonspherica17molecules. In almost all the cases the results of such applications have clearly established that cavity energy plays an important role in the process of solute solvation. Since the process of micellization is often visualized as dissolution of surfactant to oil-like hydrocarbon core, it is presumed that there should be some relation between cavity-forming free energy and free energy of micellization. Theobjectiveof the present paper is toextend thecavity energy calculation for a series of cationic and nonionic surfactants in search of additional support to the concept of cavity free energy as an important driving force in the process of micellization. The model used for the cationic surfactant is essentiatly the same as that used for the anionic surfactant.' However, proper attention has been given to the hydration of ethoxy linkages and partial penetration of the first ethoxy groups near the nonpolar core for the nonionic surfactants. The surfactants studied are shown in Tables I-IV, and the model used is depicted in Figure 3. Computational Method Cationic Surfactants. For cationic surfactants the computational procedure is essentially the same as that for anionic surfactants as discussed earlier.' Here we have calculated the following free energy terms: (i) cavity-forming free energy due to tail and head group of the amphiphile, (ii) free energy due to the hydrophobic effect, (iii) free energy due to dispersive and inductive interactions, (iv) free energy due to loss of translational and rotational degrees of freedom, (e) free energy change due to change in the nature of interface, and (0 free energy due to head group repulsion. The necessary parameters for such calculation are cited in Tables I-IV. NonionicSurfactants. Since nonionic surfactants largely differ from ionic surfactants in head group behavior, the, calculation of free energy of head group repulsion has been modified for these surfactants. A detailed method of computation for each component, except for the head group component, is the same as that ~~~~
* To whom correspondence should be addressed.
~
for ionic surfactants' and hence not repeated here. But at present, no unique and unambiguous method is known for computing the free energy contribution of nonionic head groups. However, empirical methods8-l0are available for such a calculation. Since a considerable amount of hydration occursi in the ethylene oxide layer in contrast to the micellar core, which is free of water, it is known that the polyoxyethylene linkages are partially transferred'* from the aqueous phase to the micelle during micellization. The first ethoxy groups near the nonpolar core of the micelle lose some of their water of hydration and thus become partially dehydrated, presumably due to the need for close packing of nonpolar tails. In the long chain, the ethoxy groups beyond the sixth one are located sufficiently far from each other so that their local environment changes very littlel compared to the monomer. Aggregation of surfactant molecules leads to some alteration of the unmicellized polar chain conformation; as a consequence, ethoxy hydration shell overlaps. Obviously, hydration shell overlaps decrease with distance from the core due to geometric reasons. We have taken the values of AGw from the literature, as the method of computation of such a component is very complicated.
Assessment of Uncertainty in Different Free Energy Terms Apart from the calculation of different component free energies, in this paper major emphasis has been given to the estimation of uncertainties associated with each free energy component, so that the results of such a calculation can be properly justified. Cavity components of free energy are calculated on the basis of input parameters cited in Table V. Among these parameters, the calculation is most sensitive to the solute and solvent diameters. As the diameters of the solvents considered here (water and liquid hydrocarbons) are well confirmed by several workers,IS we have examined here a variation in the AG term with the variation of solute (surfactant) diameter to a large extent of f0.05 A, and the results are shown in Table V. A close look at the input parameters in the AGLJterm indicates that major uncertainties in this term are incorporated through LJ diameters and LJ potential parameters ( e l k ) . These parameters for solvents like water and liquid hydrocarbons are wellreported. Here we have varied c/k by a large extent of f4 units and LJ diameters by f0.04 A units synchronously. The results of such variation are shown in Table V. In AG,I-rOL, AGinler,and AGeleCterms the uncertainty in AGC8l may be incorporated via aggregation number. Other terms also depend on aggregation number. We have taken here a maximum variation of f4 units for the aggregation number. The results of such variation are shown in Table V.
0022-3654/93/2091-3900S04.00/00 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3901
Application of Scaled Particle Theory to Micellization
TABLE I: Parameters for Calculation of Different Free Energy Components of Micellization of Cationic Surfactants at 298.15 K surfactant (no. of carbon atoms)
mol wt" of tail head 1 I4 142 170.00 198.00 198.0
OTAB (C-8) DTAB (C-IO) DDTAB (C-12) TTAB (C-14) TTAC (C-14)
139.03 139.03 139.03 139.03 94.57
densities" tail head 0.6985 0.7301 0.7511 0.7645 0.7645
hard core diametersh tail head 6.63 7.07 7.47 7.84 7.84
1.2973 1.3129 1.3226 1.3340 1.2056
c/kb (K)
polarizabilityC
650 8 50 1050 1250 1250
15.42 19 22.5 26.5 26.5
4.70 4.70 4.70 4.70 4.31
pX
IO2'
agg no.
3.69 3.1 2.66 2.33 2.33
388 35' 531 70.81 62.31
'
Dictionary of Organic Compounds, 4th ed.; Eyre & Spottiswoode Publishers: London, Vols. 2-5. Nandi, N.; Basumallick, I. N. J . Phys. Chem. 1990, 94, 2537. Calculated from: Lippincot, E. R.; Stutman, J. M. J . Phys. Chem. 1964.68, 2926. Calculated by methods cited in: Ben-Amotz, D.; Herschbach, D. R. J . Phys. Chem. 1990, 94, 1038. e Calculated for largest spherical micelle from: Nagarajan, R.; Ruckenstein, E. J . Colloid lnterfuce Sci. 1979, 71, 580. f Imae, T.; Ikeda, S.J . Phys. Chem. 1986, 90, 5216. 9 Oakenfull, D. J . Colloid Inrerface Sci. 1982, 88, 562. [
TABLE II: Values of Different Components of Free Energies of Micellization in kJ mol-' for Cationic Surfactants at 298.15 K surfactants (no. of carbon atoms) OTAB (C-8) DTAB (C-IO) DDTAB (C- 12) DDTAB DDTAB DDTAB TTAB ((2-14) TTAB ((2.14) TTAC (C- 14)
AGOcav
tail -23.99 -29.12 -34.30 -34.30 -34.30 -34.30 -39.61 -39.61 -39.61
head -0.40 -0.50 -0.58 -0.58 -0.58 -0.58 -0.61 -0.61 +0.11
AGOLJjlnd
AG'trans-rot
12.59 14.18 16.96 16.96 16.96 16.96 20.24 20.24 20.24
5.02 7.46 9.3 I 9.31 9.31 9.31 12.32 12.32 12.22
AGOinterracc
8.83 10.82 14.15 14.15 14.15 14.15 14.12 14.12 14.96
AG0h -21.36 -27.46 -33.56 -33.56 -33.56 -33.56 -39.66 -39.66 -39.66
AGOeIec
AG'culd
AGOcxpt
4.85 6.36 7.13 7.69 7.81 7.77 10.80 10.94 1 1.30
-14.46 -18.26 -20.29 -20.33 -20.21 -20.25 -22.40 -22.26 -20.44
-13.01" -16.61" -20.27' -20.21' -20.42' -20.36' -23.72h -23.96' -21.85''
Zielinsky, R.; Ikeda, S.;Nomura, H.; Kato, S.J . Colloid Interface Sci. 1989, 129, 175. Roe, J. M.; Barry, B. W. J . Colloid Interface Sci. 1983, 94, 582. ''Imae, T.; Ikeda, S.J . Phys. Chem. 1986, 90, 5216.
TABLE III: Parameters for Calculation of Different Free Energy Components of Micellization of Nonionic Surfactants at 298.15 K surfactant ChEh CaE6 Cioh CIZE~ ClhE, (X
17,32,44,63)
mol wt" of tail"
densities"
hard core diameters'
elkb (K)
polarizabilityC
86.18 1 I4 142 170 226
0.6548 0.6985 0.7301 0.7511 0.76996
5.959 6.63 7.07 7.47 8.29
517 650 8 50 1050 15689
11.77 15.42 19.0 22.5 28.44
p X
IO2'
4.58 3.69 3.1 2.66 2.05
agg no. 13d 4Ir 73' 1581 87d
a Dictionary of Organic Compounds, 4th ed.; Eyre & Spottiswoode Publishers: London, Vols. 2-5. Ben-Amotz, D.; Herschbach, D. R. J . Phys. Chem. 1990, 94, 1038. Calculated from: Lippincot, E. R.; Stutman, J. M. J . Phys. Chem. 1964,68, 2926. Calculated for largest spherical micelle from: Nagarajan, R.; Ruckenstein, E. J . Colloid Interface Sci. 1979, 71, 580. Balmbra, R. R.; Clunie, J. S.;Corkill, J. M.; Goodman, J. F. Trans. Furaduy SOC.1964, 60, 979. /Corkill, J. M.; Goodman, J. F.; Ottewill, R. H. Trans. Faraday SOC.1961, 57, 1627. z Calculated by methods cited in ref b.
TABLE I V Values of Different Components of Free Energies of Micellization in kJ mol-' for Nonionic Surfactants at 298.15 K surfactants ChEh CsEh CioEh CIZ& CihE17 c 1hE3?
c I6E44 c I hE63
AGOcnv
-18.10 -23.99 -29.12 -34.30 -44.52 -44.52 -44.52 -44.52
AGO Ll/lnd 10.38 12.59 14.18 16.96 18.52 18.52 18.52 18.52
AGOtrans-rot
AGointsrrace
AGOh
-1.68 4.33 7.96 12.10 14.36 14.36 14.36 14.36
10.15 6.19 5.25 3.14 8.51 8.5 1 8.51 8.51
-15.26 -21.36 -27.46 -33.56 -45.77 -45.77 -45.17 -45.77
AGOw 1.75 1.75 1.75 1.75 10.53 11.75 12.92 13.17
AGOcnld
AGOcxpi
-12.76 -20.49 -27.44 -33.91 -38.37 -37.15 -35.98 -35.73
-1 5.47"
-21.32" -27.17" -33.02" -39.33' -38.1 2h -36.95' -36.70'
Corkill, J. M.; Goodman,'J. F.; Harrold, S.P. Trans. Furaduy SOC.1964,60,202. Barry, B. W.; El-Eini, D. 1. D. J . Colloid Interface Sci. 1976, 54, 339.
Discussion Free energies of micellization for different ionic and nonionic surfactants have been computed earlier by several worker^.^^.'^ While in the present calculation we have included a term, viz, cavity-forming free energy of micellization, it has not hen used explicitly in earlier calculations,~6though this effect has been included in earlier calculations partially through terms like the solvent structural effect, hydrocarbon-hydrocarbon interaction, It is Seen from the Table v that, uncertainties in the calculation, the calculated values of free energy of micellization of these cationic surfactants are well in agreement with those of experimentalvalues. For thenonionicsurfactants, theagreement between calculated and experimental values is only fair, probably because of a larger uncertainty in the free energy of head group transfer.
Recently, we haveapplied SPT to predict partitioncoefficientsi7 of some larger hydrocarbons between water and some organic solvents, and it has been shown that the cavity energy is almost parallel to thoseof the hydrophobiceffect indictating partitionary behavior of these hydrocarbons between the organic solvents. It is interesting to note that for micellization of these surfactants the contribution of the cavity term is almost comparable to that of the hydrophobic effect. The cavity model of micellization can predict well the ease of formation of the micelle for a surfactant It is Seen from the that with a larger while the cavity energy for the CS hydrocarbon iS-23.63 kJ/mol is -39*13 kJ/mol* that for the c14 Presently, we have considered two different series of nonionic surfactants: while in one case the length of the hydrocarbon tail changes, in the other (C16Ex) the number of polyoxyethylene
P H
TABLE V
s a d y of the Effect of Variatiom in Input Parameters of Different Components of Free Energies of Miallizatioll in W mo-’ for Cationic and Nonionic !Surfactsots at 298.15 K ’rr
OTAB (C-8) NTAB (C-9) DTAB (C-IO) DDTAB (C-12) TTAB (C-14) ChEn CXEn ClOEh ClZh Ci&n
6.63 f 0.04 6.86 f 0.04 7.07 0.04 7.47f0.04 7.84f0.04 5.959f0.04 6.63 0.04 7.07 0.04 7.47 f 0.04 8.2 f 0.04
*
-23.99 f 1.78 -26.81 f 1.78 -29.12 f 1.79 -34.30f 1.80 -39.61 f 1.80 -18.10f 1.02 -23.99 f 1.78 -29.1 2 f 1.79 -34.30 f 1.80 -44.52 f 1.76
4.40
4.54 -0.55 4.58 4.61
650 f 4,6.63 f 0.04 750 f 4.6.86 f 0.04 850 f 4.7.407 f 0.04 1050f4.7.47f0.04 1250f4,7.84f0.04 517 f 4.5.959 f 0.04 650 f 4.6.63 f 0.04 850 f 4.7.07 f 0.04 I050 f 4,7.47 f 0.04 1568 f 4.8.2 f 0.04
12.59 f 0.48 13.53 f 0.50 14.18 f 0.55 16.96f0.58 20.24f0.60 10.38 f 0.44 12.59 fO.48 14.18f0.55 l6.96f0.58 l8.52f 0.69
38 f 4 33.5 f 4 35 f 4 53f4 70.8f4 13 f 4 41 f 4 73f4 158f4 87 f 4
2.40 f 0.23 3.41 f 0.22 4.76 f0.21 9.31f0.50 12.32f0.07 -1.68 f 0.33 4.33 f 0 . 2 6 7.96*0.13 12.10f0.08 14.36 f 0 . 0 8
10.46 f 0.72 12.45 f 0.71 13.46f0.72 14.15f0.60 14.12f0.35 10.15 f 2.2 6.19 f 0 . 5 4 5.25f0.29 3.14f0.22 8.51 f 0 . 2 9
-21.36 -22.77 -27.46 -33.56 -39.66 -15.26 -21.36 -27.46 -33.56 45.77
4.85 f 0.51 4.63 f 0.56 6.36 f0.58 7.73f0.28 10.80f0.61 1.75 1.75 1.75 1.75 10.53
-15.45 f 1.32 -15.60 f 1.35 -18.37 f 1.31 -20.29f1.40 -22.40f 1.53 -12.76 f 1.29 -20.49 f 1.02 -27.44 f 1.08 -33.91 f 1.08 -38.37 f 0.86
-13.01 -15.25 -16.61 -20.27 -23.72 -15.47 -21.32 -27.17 -33.02 -39.33
~
- 2
ER Dcs
2. 5 4
Application of Scaled Particle Theory to Micellization In Figures 1 and 2 experimentalfree energies and corresponding cavity-forming free energies have been plotted against the number of carbon atoms in the alkyl chain of the surfactant. These curves reveal that a large part of the favorablefree energy of micellization is contributed by the cavity-forming freeenergy. Again, another interesting feature of these plots is that while in plot I the AG,,, and AG,,, are separated by a large gap, and this gap increases with number of carbon atoms at the tail part of the surfactant. The reverse is the case for the nonionic surfactants (vide plot 11). Hence, it seems that thecavity-formingfreeenergyofmicellization is dominating in the case of nonionic surfactants.
The Journal of Physical Chemistry, Vol. 97, No. 15, I993 3903 (2) Tanford, C. The Hydrophobic Effect; 2nd ed.; Wiley-lnterscience: New York, 1979. (3) (a) Reiss, H.; Frisch, H. L.; Lebowitz, J. L. J . Chem. Phys. 1959, 31, 369. (b) Nandi, N. Doctoral Thesis, Visva Bharati University. (4) Reiss, H.; Mayer, S.W. J . Chem. Phys. 1961, 34, 2001. (5) Desrosiers, N.; Desnoyers, J. E. Can. J . Chem. 1976, 54, 3800. (6) Pierotti, R. A. Chem. Rev. 1976, 76, 717. (7) Cotter, M. A.; Martier, D. E. J . Chem. Phys. 1970. 52, 1909. (8) Barry, B. W.; El-Eini, D. 1. D. J. ColloidInterJaceSci. 1976,54,339. (9) Corkill, J. M.; Goodman, J. F.; Harrold, S.P. Trans. Faraday SOC. 1964,60, 202.
(IO) Corkill. J. M.; Goodman, J. F.; Ottewill, R. H. Trans. Faraday Soc. 1961, 57, 1627.
Conclusion Results of cavity calculation for cationic and nonionic surfactants along with uncertainties of such a calculation clearly indicate that, like anionic surfactants, the cavity-forming free energy is a major driving force for these surfactants, too. Again, its role seems to be significant for the nonionic surfactants.
References and Notes ( I ) Nandi, N.; Basumallick, 1. N. J . Phys. Chem. 1990, 94, 2537.
( I I ) Elworthy, P. H.: Macfarlane, C. B. J . Chem. Soc. 1962, 537. (12) Crook, E. H.; Trebbi, G. F.; Fordyce, D. B. J . Phys. Chem. 1964,68, 3592. (13) Ray, A.; Nemethy, G. J . Phys. Chem. 1971, 75, 809. (14) (a) Schick, M. J.; Atlas, S.M.; Eirich, E. R. J . Phys. Chem. 1962, 66, 1326. (b) Schick, M. J. J . Phys. Chem. 1963, 67, 1796. (15) Ben-Amotz, D.; Herschbach, D. R. J . Phys. Chem. 1990.94, 1038. (16) Ruckenstein, E.; Nagarajan. R. J . Colloid Interface Sri. 1979, 71, 580. (17) Nandi,N.;Basumallick,l.N.Z.Phys.Chem.(Munich) 1991,173(S), 179.
