6442 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA J. Phys. Chem. 1992, 96, zyxwvu 6442-6449 Electrostatic Properties of Zwitterionlc Micelles zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED Mauricio da Silva Baptista, Iolanda Cuccovia, Hernan Chaimovich, Mario J. Politi,* Departamento de Bioquimica, Instituto de Quimica, Universidade de SBo Paulo, P.O. Box 20780, zyx Siio Paulo, Brazil and Wayne F. zyxwvut Reed* Physics Department, Tulane University, New Orleans, Louisiana 70118 (Received: December zyx 5, 1991; zy In Final Form: January 30, 1992) The electrostatic properties of zwitterionic micelles of 3-(N-hexadecyl-N~-dimethylammonio)propanesulfonate (HPS) have been investigated by light scattering and conductivity,and a simple electrostatic model in the Debye-Hueckel approximation, containing no adjustable parameters, is presented which accounts qualitatively for the main experimental results on second virial coefficientsand conductivity,as well as for fluorescence quenching reported in earlier work. Additional photochemical data concerning reprotonation rates of 8-hydroxy- 1,3,6-pyrenetrisulfonate in HPS micelles are also presented and interpreted by the electrostatic model. The model involves the superposition of solutions for concentric, oppositely charged spherical micelles. This leads to a broad maximum in the curve of the absolute value of surface potential and second virial coefficient vs ionic strength. It further implies a significant sequestering of mobile anions in the dipole layer (positive inner surface, negative outer) and low net mobile ion charge densities outside the micelle. These effects are observed experimentally. Introduction Despite their importance, zwitterionic interfaces have peculiar properties still poorly understood. With aqueous zwitterionic micelles made from monomers such as betaines, lysolecithin (lys-PC), etc., a controversial picture remains. While previous light scattering datal reported a value of zero for the second virial coefficient A2 (CGS units for A2 are cm3.mol/g2 and are used throughout this work) and other data have reported insensitivity of zwitterionic micelle stability to ionic strength? anion enrichment and selectivity (in the order Br- zyxwvutsrq > C1- > Fl- > OH-) were found for 3-(N-hexadecyl-N,N-dimethylammonio)propanesulfonate (HPS) micelles and l ~ s - P c . ~ In these latter cases no effects were observed for different cation species. It was argued in these studies that micellar aggregates having the positive layer closer to the micellar core than the negative one (monomers radially oriented) will present a higher surface positive charge density and might therefore be compared with a nondissociated cationic micelle.38 In order to obtain more details on the electrostatic properties of HPS micelles, we investigated A2 and ion distributions at the interface by static and dynamic light scattering, ionic conduc- tivities, and laser induced pH jump reprotonation kinetics. These phenomena may be best understood with reference to the dis- tribution of electrostatic potentials and mobile ions around the zwitterionic micelles. A very simple electrostatic model for the zwitterionic micelle, which is equivalent to a double shell concentric spherical capacitor immersed in an electrolyte solution, is pres- ented, and the consequences are investigated with respect to the various experimental results. This simple model is successful in accounting for qualitative and some quantitative aspects of the diverse data. It shows the electrostatic behavior of zwitterionic micelles to be fundamentally different from that of ionic micelles. Simple Electrostatic Model for Zwitterionic Micelles The simplest zwitterionic micelle model is a sphere with an inner positive charge layer of radius RA, and an outer negative charge layer with radius RB = RA + S, where S represents the thickness of the dipole layer (see Figure 2a for a graphical representation). All electrostatic calculations are in the MKSA (meterskilo- grams.seconds*amperes) system. Three regions are distinguished in the model of Figure 2a: The region outside the micelle, r 1 RE, whose potential and net charge are denoted as &(r) and pl(r), respectively. The second region is in the dipolar layer, RA I r I RE, and its associated quantities To whom correspondence should be addressed. are denoted with the subscript 11. The impenetrable micelle core is region 111. The boundary conditions which the potentials must satisfy are at r = RB (IC) a91 a611 -Q -e1 - + €1, - = - ar ar 4?r~B2 Here Q = Ze and represents the absolute magnitude of the charge on each dipole surface, where Z is the micelle aggregation number and e the elementary charge. Z is given by M/m, where M is the micelle molecular weight and m is the monomer weight (Z is the same on both surfaces). Here tI and cII in each region are the permittivity of free space (8.85 X C2/(N.m2)) times the dielectric constant in media I and 11, respectively. We use the bulk water dielectric constant of 78 in both regions, so that q1 = €1. At this point numerical solutions to the Poisson-Boltzmann (P-B) equation could be generated with the boundary conditions la-c. The focus of this work, however, is to obtain simple ana- lytical expressions which allow a wide variety of experimental data to be rationalized. Hence, the DebyeHueckel ( B H ) linearization of the P-B equation is assumed. The use of the D-H approxi- mation must be approached cautiously, however, since potentials on the inner surface reach Q/htRA 1100 mV at no added salt (the outer surface potential is zero in this case) and remain well above kBT even as electrolyte is added. Direct application of the D-H approximation to the zwitterionic micelles whose dipole layer is freely permeable to mobile ions hence should lead to overes- timates of the potentials within the dipole layer and underestimates of the net charge density, which in turn will lead to underestimates of surface potentials, second virial coefficients, and differential conductivities. The solution for the D-H approximation where the dipole layer is freely permeable to ions and satisfies eqs la-c is presented in the Appendix, and illustrative curves resulting from those potentials are indicated with dotted lines on certain curves in the text. There is no contradiction with the uniqueness of the solution to Poisson's equation here because, even though the solutions to be presented below and those in the Appendix satisfy eqs la-c and the Poisson equation, the values of the potential on the surfaces RA and RB are different in each case. These surface values seem to be in zyxwvutsrqp 0 1992 American Chemical Societv