The Journal of Physical Chemistry, Vol. 83, No. 7, 1979 093
Communications to the Editor
COMh/lUNICATIONS TO THE EDITOR Laplace Pressure Inside Micelles Publication costs assisted by the National Science Foundation
Sir: A spherical droplet of radius r and surface tension y experiences a pressure P exceeding that in the external medium according to the Laplace equation (eq 1):l P = 2y/r (1) Recently, Laplace forces have been invoked to explain certain micellar proper tie^.^^^ For example, O2 solubility in sodium dodecyl on a mole fraction basis is only 10 X sulfate micellles as compared to 21 X in pure nonane. This result is consistent with a micelle interior where Laplace pressure reduces gas solubility relative to a hydrocarbon solvent a t atmospheric pressure. Using reasonable values of r for surfactants of various chain lengths, one can show that Laplace pressures of up to 400 atm are required to effect the two-fold decrease in O2 solubility.2 In this corrimunication, I demonstrate that micellar properties, including gas solubilization, can be attributed equally well to factors other than Laplace pressure. Calculations of Laplace pressure from gas solubility data rest on the assumption that the micelle interiors (Le., the space occupied by all carbons of the surfactant chains) possess a microenvironment equivalent to hydrocarbon. Such an "oil droplet in an ionic coat"4 description has the virtue of simplicity, but is almost certainly incorrect. We have shown by (2-13 NMR that water penetrates into the micelles up to at least the seventh carbon beyond the ionic head groupe5 Others claim that water permeates into the micelle even deepera6y7Molecular models demonstrate that 50-100 surfactant molecules cannot pack into a sphere or ellipsoid without leaving sizeable voids filled with watere8 Since oxygen solubility in water is two orders of magnitude less than in h.ydrocarbon, water penetration could readily explain the twofold solubility discrepancy between the micelle interiior and n ~ n a n e .Indeed, ~ the twofold effect can be used to estimate the depth of the water layer within a micelle: assuming that the aqueous region of the micelle solubilizes O? to the same extent as bulk water, one can calculate that 22% of a surfactant chain is exposed to water inside a micelle. Of course, this represents a minimum value owing to the fact that O2is undoubtedly less soluble in bulk water than in the complex waterhydrocarbon mixture near the micelle surface. If it is assumed that the solubilizing power of the aqueous portion of the micellle resembles that of isobutyl alcoho15J0 (in which the O2solubility = 8.4 X 10-4),11then water reaches the outer 5096 of the chain carbons as determined from eq 2 (where f H is the fractional micellar volume that contains no water; xm is the observed micellar solubility; xw and Xh are the solubilities of o2in the aqueous and hydrocarbon portions of the micelle). The value of 50% points to a loose micellar structure having deep cavities and a rough surface, in agreement with current concepts.8 Laplace pressure has also been used to explain the fact that the mole ratio of solubilized paraffin to surfactant decreases with increasing volume of solubilizate.2 Thus, a sodium dodecanoate micelle with an aggregation number of 100 can accommodate 18 molecules of n-hexane but only 0022-3654/79/2083-0893$01 .OO/O
3 of n-decane.12 The data, however, can be rationalized equally well by assuming that paraffinic guests adsorb within the water-filled cavities.13 Hydrophobic forces would promote binding in this region with minimum disruption to the micelle structure. Since the space for adsorbing solubilizates thus depends on the availability of cavities, the smaller hydrocarbons bind in greater number. In summary, the fluid-drop model indicating hundreds of atmospheres pressure for small spherical micelles is (1) not required to interpret micellar data and (2) unrealistic in terms of the packing requirements of 50-100 chains in a sphere.
Acknowledgment. This work was supported by the National Science Foundation and the National Institutes of Health.
References and Notes (1) R. Defay, I. Prigogine, A. Beilemans, and D. H. Everett, "Surface Tension and Adsorption", Wiiey, New York, N.Y., 1966. (2) I. B. C. Matheson and A. D. King, Jr., J . Colloidhterface Sci., 66, 464 (1978). (3) P. Mukerjee, Kolloid Z . 2. Polym., 236, 76 (1970). (4) P. Mukerjee and J. R. Cardinol, J . Phys. Chem., 82, 1620 (1978). (5) F. M. Menger, J. M. Jerkunica, and J. C. Johnston, J . Am. Chem. SOC.,100, 4676 (1978). (6) N. Muller and R. H. Birkhahn, J . Phys. Chem., 71, 957 (1967). (7) B. Svens and B. Rosenholm, J . Colloa Interface Sci., 44, 495 (1973). (8) F. M. Menger, Acc. Chem. Res., to be published. (9) The possibility of water penetration is also pointed out by Matheson and King in ref 2. (10) Isobutyl alcohol is only a presumed "average" in what is almost certainly a continuum of micellar environments ranging from highly aqueous in the Stern layer to hydrocarbon-like near the center of the aggregate. (11) E. Wilheim and R. Battino, Chem. Rev., 73, 1 (1973). (12) M. E. L. McBain and E. Hutchinson, "Solubilization and Related Phenomena", Academic Press, New York, N.Y., 1955. (13) At present there are no conclusive data indicating the exact location of hydrocarbon guests inside micelles.
Department of Chemistry Emory University Atlanta, Georgia 30322
F.
M. Menger
Received December 18, 1978
Caging Effects of an I c e Lattice on High-Energy Iodine Geminate Recombination with Biomolecules Publication costs assisted by the U S . Department of Energy
Sir: In an important preliminary study, Willard et al.' found unusually high organic yields of (n,y)-activated high-energy iodine-128 in dilute aqueous solutions of CH31. Because of the lack of suitable analytical procedures, no conclusions could be made as to the mechanism of the process. We have reinvestigated the problem by employing dilute aqueous solutions of biomolecules and determining the products by high performance liquid chromatography (LC). In this communication, we report the caging effects of ice on the geminate recombination of iodine-128 activated by radiative neutron capture in dilute aqueous mixtures of monoiodotyrosine (MIT) and diiodotyrosine (DIT). Polyethylene vials containing 5 mL volumes of dilute aqueous mixtures of MIT or DIT in the liquid and frozen 0 1979 American
Chemical Society
