J. Phys. Chem. 1996, 100, 17873-17880
17873
Monte Carlo Simulations of Polyelectrolytes at Charged Micelles. 2. Effects of Linear Charge Density Torsten Wallin* and Per Linse Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund UniVersity, P.O. Box 124, S-221 00 Lund, Sweden ReceiVed: April 8, 1996; In Final Form: August 14, 1996X
A simple model system was used to examine the complexation between a charged micelle and an oppositely charged polyelectrolyte. Structural data of the micelle-polyelectrolyte complex and thermodynamic quantities of the complexation as a function of the polyelectrolyte linear charge density at two different chain flexibilities were calculated from Monte Carlo simulations and thermodynamic integration. The presence of the polyelectrolyte was found to reduce the critical micellar concentration, i.e., the lowest surfactant concentration at which micelles are formed. The largest reduction of the cmc occurred for the highest linear charge density and the most flexible polyelectrolyte (110 times smaller), whereas the smallest reduction occurred for the lowest linear charge density and the more rigid polyelectrolyte (10 times). The complexation is caused by the strong attractive electrostatic interaction between the micelle and the polyelectrolyte and is manifested by (i) a decrease of the electrostatic energy due to small micelle-polyelectrolyte charge separations and (ii) an increase of the entropy due to the release of the counterions of the macroions. The predicted results are in accordance with experimental data of systems with different linear charge densities and chain flexibilities of the polyelectrolyte.
Introduction Aqueous solutions of mixtures of polyelectrolytes and charged surfactants have now been studied for some time.1-19 One feature of these mixtures that has received attention is the large difference between the critical micellization concentration of solutions containing charged surfactant without added polyelectrolyte (cmc) and the critical aggregation concentration of similar solutions with added oppositely charged polyelectrolyte (cac).12-19 The cmc and cac are defined as the lowest concentration at which micelles are formed without and with polyelectrolyte present in the solution, respectively. In many experiments cationic surfactants of the type alkyltrimethylammonium bromide (CnTAB) have been used in combination with different anionic polyelectrolytes. Hayakawa et al.2 and Thalberg et al.14 have shown that addition of polyacrylate to C14TAB can lower the cmc of C14TAB up to 1000 times. In a recent study, Hansson et al.18 examined how the cac of C12TAB depends on the degree of charged substituence of sodium (carboxymethyl)cellulose (NaCMC). They found that the cac was reduced as the linear charge density of the NaCMC was increased. Furthermore, Kiefer et al.15 investigated the interaction between C14TAB and poly(acrylic acid) at different degree of neutralization. In contrast to what they expected, at a low degree of ionization (
