4246
J. Phys. Chem. 1993,97, 4246
COMMENTS Comment on "Does the DLVO Account for Interactions between Charged Spheric Vesicles" C. Washington Department of Pharmaceutical Sciences, University of Nottingham, University Park, Nottingham, U.K. Received: December 2, 1992
I read with interest the recent paper by Carmona-Ribeirol in which DLVO calculations, based on zeta potentials measured by electrophoresis, were used to calculate stability ratios of vesicles of dioctadecyldimethylammonium chloride (DODAC) and sodium dihexadecyl phosphate (DHP). The authorsconcluded that the stability of such vesicles in electrolyte solutions should be very high, since the calculated intervesicle potentials displayed large (>lOOkT) short-range maxima typical of a stable strongly repulsive system. However, in earlier experimental studies,*these vesicles were observed to readily aggregate in NaCl solutions with measurable stability ratios in the range 1-1000. The author suggests that some unusual structural feature, such as regions of damage in the bilayer due to reorganization in the presence of electrolyte, accounts for this large discrepancy between experimental and theoretical stabilities. I suggest that this is not the case and that the observations have an alternative explanation, largely within the bounds of DLVO theory. I have for some time been involved in studies of the stability of colloidal systems stabilized by phospholipids,4 which are wellknown vesicle formers. This has involved the calculation of the stability of phospholipid-stabilized triglyceride emulsions in electrolyte solutions using methods similar to those of CarmonaRibeiro et al. Similar methods have also been used to compute stability ratios of phospholipid vesicles by Lis et ale5 Both Lis et al. and I obtained very reasonable agreement between computed and experimental stability ratios, using only very minor adjustment of the Hamaker constant which did not lead to major alterations in the character of the interparticle potentials. In addition, we included a term for the hydration energy in the interaction potential, but this was only a very short-range force and made little difference to the final analysis. The main difference between our studies and those of CarmonaRibeiro et al. involves the means by which the stability ratio was calculated from the interparticle potential. Carmona-Ribeiro uses the method of Verwey and Overbeek (eq 8 in ref 2 ) which calculates the stability ratio for irreversible flocculation over the repulsive primary maximum when the integration is taken to the limit of zero separation. I agree that this would lead to an extremely large value of W,similar to those reported in ref 1 . However, the rapid flocculation observed in DODAC and D H P vesicle systems by the a ~ t h o r s ,is~ .almost ~ certainly not due to irreversible aggregation over this barrier but is instead due to a reversible aggregation into the longer-range attractive secondary minimum, which lies at about 4 nm particle separation. The authors note the existence of this minimum in their previous publications but do not consider it as a source of instability. Its existence is barely discernible in their Figure 2 of ref 1 , due to the vertical scale of the graph. My experiments have demonstrated that the rapid flocculation of phospholipid-stabilized systems is reversible and that the aggregated systems can be redispersed simply by diluting out the electrolyte. I do not see any reasons why the DODAC and D H P 0022-3654f 93f 2091-4246SO4.00f 0
I .
0
1
2
EmiNkT
Figure 1. Stability ratio vs potential energy minimum depth calculated from the model of Marmur.
systems should behave differently. Calculated interparticle potentials in phospholipid-stabilized dispersion^^.^ show a shallow secondary minimum developing with increasing electrolyte concentration; in triglyceride emulsions it begins to form at a NaCl concentration of 0.1 M (the observed CFC in this system) and deepens to approximately 0.3kT at a NaCl concentration of 0.5 M. Since there is no energy barrier to this minimum, aggregation into it can occur at diffusion-controlled rates; this is directly confirmed by microscopic examination of the flocculating system. The Verwey-Overbeek equation is inappropriate for the calculation of the rate of flocculation into this energy minimum, but a rough approximation of Wcan be obtained by integrating the equation only from the secondary minimum outward to infinity. Lis et al. and I instead used the method described by Marmur: which considers a kinetic model of the aggregation and can be interpreted as describing the equilibrium between freely diffusing particles and those in the secondary minimum. There is a direct relationship between the depth of the secondary minimum and the stability ratio for flocculation into the minimum (Figure 1). It can be appreciated that only modest minima, with a depth of the order of kT, are required to obtain stability ratios of the order of 1-1000, Le., the reported range of stability ratios in the DODAC and D H P systems. I cannot estimate the depth of the energy minimum from the existing data in ref 1 but suggest that if this value is extracted from the existing calculations and inserted into the Marmur relation, the resulting values of the stability ratio will be in better agreement than those previously presented. (Workers in this field wishing to form their own opinions on this matter should note that an error in ref 2 has propagated itself into the literature. We cite the corrected reference.) References and Notes (1) Carmona-Ribeiro, A. M. J . Phys. Chem. 1992, 96, 9555. ( 2 ) Carmona-Ribeiro, A. M.; Yoshida, L. S.;Sesso, A.; Chaimovich, H. J . Phys. Chem. 1985,89, 2928. (3) Carmona-Ribeiro, A. M. J . Phys. Chem. 1989, 93, 2630. (4) Washington, C. Int. J. Pharm. 1990, 64, 61. (5) Lis, L. J.; McAlister, M.; Fuller, N.; Rand, R. P.; Parsegian, V. A. Biophys. J . 1982, 37, 657. (6) Marmur, A. J. Colloid. Interface Sci. 1987, 72, 41.
0 1993 American Chemical Society
