The Journal of
Physical Chemistry
0 Copyright, 1989, by the American Chemical Society
VOLUME 93, NUMBER 24 NOVEMBER 30,1989
LETTERS Influence of Hydrocarbon Chaln Length on Micellar Size S. BorbBly, L. Cser,*.+ Hahn-Meitner Institut, 0-1000, Berlin 39, Postjach 3901 28, Federal Republic of Germany
Yu. M. Ostanevich, Joint Institute for Nuclear Research, Dubna P.O.B. 79, Moscow, USSR
and Sz. Vass Central Research Institute for Physics, H-1525, Budapest 114, P.O.B. 49, Hungary (Received: March I , 1989; In Final Form: September 20, 1989)
The average aggregation number of sodium alkyl sulfate micelles will be investigated as a function of the alkyl chain length. It will be shown that the balance between hydrophobic and electrostatic interactions of charged sulfate head groups determines the value of the aggregation number. A simple model which is based on the above assumptions and agrees nicely with our observations will be presented.
Introduction The micelle formation of sodium dodecyl sulfate (SDS) amphiphiles has broadely been studied by different experimental and theoretical methods.'-5 Three competing effects were found to be responsible for the micelle size formation, viz., the hydrophobic interaction, the electrostatic interaction of polar head groups, and the interaction between formed micelles. Small-angle neutron scattering (SANS) is an adequate tool to obtain detailed information about micelle sizes and the average aggregation n ~ m b e r . ~ - ~ We used the SANS method to study of micelles formed by sodium alkyl sulfates of varying chain length and to investigate the significance of the chain length for the forming of micellar sizes at relatively high (comparing to cmc) amphiphile concentration. 'On leave from Central Research Institute for Physics.
Materials and Methods Sodium dodecyl and tetradecyl sulfate amphiphiles were dissolved in pure (99.8%) freshly distilled heavy water at uniform amphiphilic concentration of 0.25 MIL. A mixture of octyl and decyl sodium sulfate (proportion 1:l) was also investigated at the (1) Lindman, B.; WennerstrBm, H. Micelles Amphiphile Aggregations in Aqueous Solutions. In Topics in Current Chemistry; Springer Verlag: Berlin,
Heidelberg, 1980 Vol. 87. (2) Hayter, J. B.; Penfold, J. J . Chem. Soc., Faraday Trans. I 1981, 77, 1851. (3) Bendedouch, D.; Chen, S. H.; Koehler, W. C. J . Phys. Chem. 1983, 87, 2621. (4) Bezzobotnov, V. Yu.;BorbEly, S.; Cser, L.; Farago, B.; Gladkih, I. A.; Ostanevich, Yu. M.; Vass, Sz. J . Phys. Chem. 1988, 92, 5738. (5) Cabane, B.; Duplessix, R.; Zemb, T. J . Phys. 1985, 46, 2161.
0022-3654/89/2093-7967$01.50/0 0 1989 American Chemical Society
7968 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 TABLE I: Values of the Average Aggregation Number (N) and Length of Hydrocarbon Chains (I4) Evaluated by Tanford’s Formula as a Function of Number of Carbon Atoms (n,) sample mixture of sodium octyl and decyl sulfate sodium dodecyl sulfate sodium tetradecyl sulfate
n,
N
9 12 14
75 124 181
I,
Letters
la
A
13.5 16.7 19.2
same total concentration and dissolved in the same solvent. The technical grade (Merck quality) sodium alkyl sulfates were properly purified, and the purity was checked by combined liquid chromatography-mass spectroscopy. Less than 0.6% sodium alkyl analogues were found in any material investigated.6 The SANS experiments were carried out on a small-angle time-of-flight spectrometer installed at the IBR-2 impulse reactor of the Joint Institute for Nuclear Research, Dubna.’ At this time-of-flight spectrometer the value of transferred momentum q usually varies from 0.02 to 0.22 A-’ with a neutron flux of lo7 neutrons s-l. The neutron scattering intensity obtained was carefully corrected for background and instrumental resolution. The differential coherent scattering cross section was obtained by a vanadium standard scatterer. All measurements were performed at 30 “C. The temperature was stabilized with an accuracy of 0.1 OC. In order to obtain the value of the average aggregation number, the differential cross section was regarded as a product of the single-particle scattering form factor P(q) and the apparent interparticle structure factor S(q). At a given concentration the shape of the particles is expected to be a prolate ellipsoid of rotation with an axial ratio a / b of less than 2 . As it was shown,8 in this case P(q) belongs to an ellipsoid of rotation that cannot be distinguished from an equivalent sphere of the same volume. For S(q) the screened Coulomb structure factor proposed by Hayter and Penfold9 was used. This approximation does not deal with the polydispersity effect, and it was shown to be valid for high concentrations.2 It was concluded that the SANS intensity distribution can be well fitted by a model with a monodisperse micellar form factor using the corresponding least-squares fit2-10 because the interparticle structure factor is not too sensitive to polydispersity and the effective single-particle form factor is a smoothly varying monotonic Gaussian-like function.” The good agreement of the data we4 and Hayter12 had obtained for sodium dodecyl sulfate micelles encouraged us to use the same data processing method in the present work.
Experimental Results For all three micellar solutions the shape of the scattering intensity distribution versus the transferred momentum curves was quite similar to the SDS spectra previously observed by Hayter12 and by US.^ The data show a well-pronounced maximum which is a characteristic feature of strongly interacting particles in medium of high concentration (see Figure 1). The values of the average aggregation number (N) were obtained by the equivalent mean sphere approximation mentioned above and are given in Table I . Discussion Since the scattering amplitude density of the sulfate head group region ps is 6.32 X 10” A-*, which is within the experimental error range equal to the D 2 0 solvent value, to neutrons the micelle looks (6) Decsy, Z. Personal communication, 1982. (7) Vagov, V. A.; Kunchenko, A. B.; Ostanevich, Yu.M.; Salamatin, I. M. JINR Report No. P14-83-898-, Dubna, USSR, 1983; in Russian. (8) Kotlarchyk, M.; Chen, S . H. J . Chem. Phys. 1983, 79, 2481. (9) Hayter, J. B.; Penfold, J. J . Mol. Phys. 1981, 42, 109. (10) Sheu, E. Y.; Wu, C. F.; Chen, S.H.; Blum, L. Phys. Reu. A 1985, 32, 3807. ( 1 1 ) Sheu, E. Y.; Chen, S.H. J . Phys. Chem. 1988, 92, 4466. (12) Hayter, J. B. Presented at the International School of Physics “Enrico Fermi”, Varenna, July, 1983.
‘I
5
Ii
/A I o
I1 h
--.-
C
Figure 1. Differential cross section per unit volume versus transferred momentum. 0, sodium tetradecyl sulfate; 0,sodium dodecyl sulfate; 1:l sodium octyl sodium decyl sulfate. (Dashed line represents the result of the least-squares fit. The line corresponding to results of the octyl-decyl mixture is omitted because the experimental points are too closely spaced.)
+,
+
TABLE 11: Values of the Longer Axis of the Micellar Ellipsoids ( a ) , Ratio a / b , Radius of Equivalent Spheres ( r ) , Average Distance between the Micelles ( R J , and Ratio R,/r: as a Function of n , n, a. A alb r, 8, R., 8, R*Ir. 9 26.5 2.0 16.8 128 5.6 12 33.0 1.9 21.8 170 5.4 14 36.4 1.7 25.9 193 5.3 “ r e = r - 2.8 A,where 2.8 8, stands for the half linear size of the sulfate head group.
like a homogeneous particle consisting only of hydrocarbon chains. Tanfordi3proposes an empirical rule to evaluate the length of a fully stretched chain
I , = 1.5
+ 1.265nC
(1)
where n, is the number of carbon atoms. From the values of I , and N the length of the longer axis of the ellipsoids can be calculated. From these values the ratio a / b and the radii of the equivalent spheres can be computed. The data obtained (see Table 11) show that the condition a / b 6 2, required for the applicability of the equivalent main spheres method, is fulfilled for all three systems. From the amphiphile concentration and the aggregation numbers the average distance between the micelles was estimated. The result is given in Table 11. In order to interpret the values of the average aggregation number, we follow a rationale similar to that given in our previous work.4 As mentioned in the Introduction, there are three main types of interactions which determine the aggregation number. Contrary to the other two types of interactions, the interaction between the micelles can be neglected if the concentration is relatively low. First, the average distance between the charged head groups is 5-6 times smaller then that between the different micelles (see Table 11). Second, the effective charge of the in(13) Tanford, C. The Hydrophobic Ejjecr; Wiley: New York, 1980.
J. Phys. Chem. 1989, 93, 7969-7973
7969
termicellar interaction term is much more appreciably screened than that of the head groups belonging to the same micelle. Let us now denote the effective binding energy of hydrophobic interaction by e,. The total energy of this interaction is E, = t o n g (2) The electrostatic repulsive interaction of charged head groups inside one micelle can be calculated by the following formula:
E2 = K ( M / r )
(3)
where r denotes the average distance between head groups and the constant K includes the effective charge of the head groups. The shape of the micelles can roughly be estimated by an equivalent sphere of the radius R . (It can be shown that r = (4/7rR.) It is now obvious that r R n,. Thus, expression 3 can be rewritten as
- -
E2 = K ’ ( M / n , ) Both E, and E2 vary by n,. In the case of equilibrium dEl = dE2
(4)
which leads to a differential equation
(y ;)-:
( N + nfl7c0 = 2K’ -- -
where N’is the differentiation of the aggregation number with respect to n,. Rearranging (6) N’(2KJNn,- con:) - Nn2c0 - K’M = 0 (7) The solution of this differential equation is quite simple:
N = An:
(8)
A = c,/K’
(9)
where
v r
0
m
&
nc2
-
Figure 2. Average aggregation number (N) as a function of the squared value of the number of carbon atoms in hydrocarbon chain (nc).
Equation 8 predicts a quadratic dependence of the aggregation number on the number of carbon atoms in the aliphatic chain. From Figure 2 it is obvious that the experimentally determined aggregational numbers vary linearly by the square of n,. This coincidence as well supports the basic ideas involved in the derivation of (7) as validity of the simple model proposed. It is worthwhile to note that the aggregation number also shows a quadratic dependence on n, near the critical micellar concentration.I4 However, the value of the proportionality constant A in ref 14 obtained from simple geometrical considerations is about half the value determined from the slope of the straight line in Figure 2. This difference can be explained by the fact that, near cmc, micelles have a minimal size, their hydrocarbon chains are packed much more compactly than in larger micelles existing at higher concentrations, and the effective charge of the head groups is larger. This means an increase of K’ value which according to (9) causes a decrease of the constant A . (14) Missel, P. J.; Mayer, N. A.; Benedek, G . B.;Carey, M. C. J. Phys. Chem. 1983, 87, 1264.
Ion-Molecule Clusterlng Thermochemistry by Laser Ionization High-pressure Mass Spectrometry M. Samy El-Shall,*i+Kenneth E. Schriver, Robert L. Whetten,* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024-1 569
and M. Meot-Ner (Mautner) Department of Chemistry, University of Canterbury, Christchurch 1, New Zealand (Received: June 22, 1989; In Final Form: October 4, 1989)
A laser ionization source has been developed and applied to measure the equilibrium thermochemistry of the clustering of neutral molecules with atomic metal ions. This high-pressure mass spectrometric method enables cluster association reactions to be studied at pressures that ensure both atomic ion thermalization and collisional stabilization of the nascent cluster ions. Initial application to the thermochemical properties of the association reactions of Cu+ with Kr, Nz(up to five molecules), H20, CH30H, and CH3COCH3is described. The binding energies for Cu+.Kr and Cu+.Nz are similar to the analogous Naf complexes, as expected from predominantly electrostatic interactions. The binding energies show reasonable variations with the proton affinity of the molecule.
Introduction Clustering of neutral molecules with a metal ion is of great current interest, because an understanding of the many-body interactions between a metal ion and neutral molecules is prerequisite to the development of proper theories for important
phenomena such as ion solvation, charge-transfer and other condensed-phase processes, electrostatic effects in biological systems, and ion-induced nucleation, with numerous implications in atmospheric and interstellar chemistry, combustion, dnd cata1ysis.’-3
‘Permanent address: Department of Chemistry, Virginia Commonwealth University, Richmond, VA 23284.
(1) Srrucrure, Reactiuify and Thermochemistry oflons; Ausloos, P., Lias, S. G . , Eds.; NATO-ASI; Kluwer Academic Publishers: Norwell, MA, 1986.
0022-3654/89/2093-7969$01 S O / O
0 1989 American Chemical Society
