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Using the method of cumulants, we investigate the distribution of diffusion coefficients in polydisperse systems. We consider the intensity weighting for distributions of spherical particles having the same polarizability. Results of computer simulations are presented for a variety of polydisperse situations. Also, comparisons are made between predicted and measure results for mixtures of Dow latex spheres.

Using the method of dynamic light scattering we have measured the diffusion coefficients D of cetyltrimethylammonium hydroxide (CTAOH) micelles as a function of CTAOH and NaOH concentrations at 25°C for 0.01 ≤ [CTAOH] ≤ 0.05 M and 0.02 ≤ [NaOH] ≤ 0.5 M. Substantial enhancements in the diffusivity were observed at low [NaOH] due to the presence of strong intermicellar electrostatic repulsions. We obtained good theoretical fits to the D versus [CTAOH], [NaOH] data over the range 0.01 ≤ [NaOH] ≤ 0.5 M using linear interaction theory (including both thermodynamic and hydrodynamic corrections to D ) with a DLVO-type pair interaction potential. From these fits we obtained estimates of the mean micellar hydrodynamic radius, R h ∼ 23.4 A, and the micellar fractional ionization, α ∼ 0.5.

Quasi-elastic light scattering measurements have been performed on aqueous solutions of CTAB (cetyltrimethylammonium bromide). Theoretic fits to the measured diffusion coefficients at low NaBr were obtained by using the generalized Stokes-Einstein equation expanded to first order in the surfactant concentration (including both thermodynamic and hydrodynamic terms), with a pair-interaction potential taken from Dlvo theory. Good fits are obtained at low NaBr concentrations by assuming a constant micellar radius for each temperature and assuming that the remaining parameters (aggregation number, fractional ionization, and Hamaker coefficient) are independent of temperature. This procedure yields an unambiguous value for the fractional ionization alpha for CTAB micelles: alpha = 0.22. The limits of validity of the theoretic fitting procedure (previously applied by Corti and Degiorgio to the system sodium n-dodecyl sulfate (SDS) + NaCl) are discussed. 65 references.

The diffusion coefficient and correlation radius associated with the droplet particles in oil-in-water microemulsions (CTAB, octane, butanol, NaBr and water) were determined by dynamic light scattering- Unlike the case of CTAB micelles, there is a maximum in the correlation radius versus temperature plot.

The cationic surfactant dodecyl ammonium chloride (DAC) undergoes a one- to two-fluid phase transition with decreasing temperature T at constant [NaCl]. In the case of [DAC]= 0.025M, there is phase separation in the region T ≳ 16°C provided that [NaCl] ≳ 0.23M. Below [NaCl] ∼ 0.23M the apparent micellar hydrodynamic radius Rh aPP, determined by dynamic light scattering from the diffusion coefficient D, increases with decreasing T. This behavior is typical of a variety of ionic micellar systems in the presence of added salt and has been ascribed to micellar growth (e.g. SDS + NaCl). However, with DAC + NaCl for [NaCl] > 0.23M, there may be an additional mechanism which causes Rh aPP to increase greatly with decreasing T -- i.e., critical-type fluctuations at the approach to a phase boundary. This behavior is qualitatively similar to that observed for nonionic micelles and micro- emulsions. In these systems the decrease in D (i.e. increase in Rh app) upon the approach to a cloud point or phase boundary is believed to be due to long-range correlated diffusion of micelles/droplets of basically unchanging size. Hence, the diffusivity results for DAC + NaCl at [NaCl] > 0.23M may be due to either micellar growth or critical-type behavior, or a combination of the two.

Using the method of dynamic light scattering, we have determined the diffusion coefficients of micelles in aqueous solution as a function of surfactant and salt concentrations for three related systems: CTAB (C16H33N(CH3)3Br) + NaBr, MyTAB(C14H29N(CH3)3Br) + NaBr and CTACl(C16H33N(CH3)3Cl) + NaCl. For each system there is a well-defined salt concentration below which the micellar diffusivity increases linearly with surfactant concentration. In this low-salt region, in which the net intermicellar interaction is repulsive, we have obtained good fits to the diffusivity data using linear interaction/DLVO theory. From this procedure we have determined the “minimum-sphere” micellar radius as a function of temperature as well as estimates of the micellar fractional ionization α and the Hamaker constant A for the above systems as well as for SDS(C12H25SO4Na) + NaCl. Hence, by this approach one is able to relate variations in these physical parameters to subtle changes in surfactant composition (e. g. alkyl chain length) and counterion properties. Interestingly, significant micellar growth apparently commences at the salt concentration at which the net intermicellar interaction shifts from repulsive to attractive.

Using the technique of dynamic light scattering, we have examined the effect of interactions (predominantly electrostatic repulsions) on micellar diffusion coefficients, D, for two related cationic surfactants, CTAOH (C16H33N(CH3)30H) and CTACl (C16H33N(CH3)3C1), under conditions of little-to-moderate micellar growth -- 0 to 0.5M electrolyte and 0.01 to 0.05M surfactant at 25°C -- where variations in D are due primarily to changes in intermicellar interactions. We obtained systematic plots of D vs [surfactant] with positive slopes and common diffusivities, Do, extrapolated to the cmc. Diffusivities increase with decreasing [electrolyte] due to inadequate screening of the intermicellar Coulombic repulsions. With no added electrolyte D exceeds Do by a factor of almost 5 at 0.05M surfactant. Plots of D vs [surfactant] are linear for CTAOH with [NaOH] ≥ 0.03M and for CTAC1 with [NaCl] ≥ 0.01M. At lower [electrolyte] the curvature of the D vs [surfactant] plots is due to screening by anions dissociated from the micelle. Following Corti and Degiorgio we applied linear interaction theory to the D vs [surfactant], [electrolyte] plots, taking into account theormodynamic and hydrodynamic corrections to D, using the DLVO pair interaction potential, which is overwhelmingly repulsive in dilute electrolyte.

We have investigated the influence of dilute tertiary amyl alcohol (t-AmOH) on micellar size and charge by dynamic light scattering using two related surfactant/salt systems: CTABr (C16H33N(CH3)3-Br) + NaBr, and CTAC1 (C16H33)N(CH3)3C1) + NaCl. These were chosen because of their contrasting sensitivity to added salt with respect to micellar growth. For CTABr there is substantial growth at 25°C for [NaBr] > 0.05M, whereas for CTAC1 there is negligible growth below [NaCl] ∼ 1M. We measured the micellar diffusion coefficient D as a function of [surfactant] and [salt] at 25°C over the range 0.25% ≤ [t-AmOH] ≤ 7% (w/w) , approaching the solubility limit of t-AmOH in water, ca. 11%. We focused our attention on relatively low salt concentrations, where interlicellar interactions are predominantly repulsive and micellar growth is either small-to-moderate (CTABr) or negligible (CTAC1). For the CTACl-related ternary system we applied linear interaction theory (with a DLVO-type pair potential) to estimate the hydrodynamic radius Rh and fractional ionization a, from fits to D vs [surfactant] for various [salt]. Over the range of t-AmOH investigated, in general Rh decreases and a increases somewhat with increasing [t-AmOH], consistent with previous findings in the literature.