Using DLS Spectroscopy and Optical Probe Diffusion to examine structure of Brij Micelles

We studied properties of Brij-35 surfactant micelles in solution using Dynamic Light Scattering (DLS) Spectroscopy and Optical Probe Diffusion method. Aqueous solutions of Brij-35 with concentrations ranging from 2 to 100g/L were prepared, both with and without polystyrene latex probes of diameters 24, 50, 186, 282 and 792nm. Solutions were studied at four temperatures of 10, 25, 40 and 70$^{o}$C with DLS to obtain micelle and probe diffusion coefficients (D$_{m}$, D$_{p})$. Using both diffusion coefficients we deduced micelle radius (a$_{m})$, micelle water content ($\delta )$, and number of surfactant molecules per micelle (N) using two different models. First, hard sphere model of micelles/probe interaction was used to analyze the data by two methods, after a$_{m}$ was obtained from intercept of D$_{m}$(c). The first method uses the slope of D$_{m}$(c) and size of probes to determine N and $\delta $. The second method uses the linear least-squares fit of D$_{p}$(c) for different probe sizes to determine N and $\delta $. Both methods reveal that with increase in solution temperature a$_{m}$ increases by 10{\%}, N increases and $\delta $ decreases by a factor of 2. The second model treats micelles as core-shell particles with corona radius (a$_{c})$. This model used two different approaches based on linear least-squares fits of D$_{m}$(c) and D$_{p}$(c). We found a$_{m }$to be 4-4.5nm and a$_{c}$-a$_{m}$ to be 1nm without relying on Stokes-Einstein equation. Results for N and $\delta {\rm g}$ were also consistent.