Quantitative modeling of threadlike micellar solution rheology

Abstract

A mesoscopic simulation method, the “pointer algorithm,” is here shown to capture accurately the rheology of a variety of surfactant solutions, including CTAB/NaNO₃, CPyCl/NaSal, and CTAB/NaSal, at different salt and surfactant concentrations presented in the literature. In addition, correlations derived from this method are shown to allow the average micelle length $\langle L\rangle$ to be estimated from $\frac{{G}_{\mathrm{min}}^{\mathrm{^{\prime}}}}{{G}_{\mathrm{min}}^{^{\prime\prime} }}=0.317{\left(\frac{\langle L\rangle }{{l}_{\mathrm{e}}}\right)}^{0.82}$ where ${G}_{\mathrm{min}}^{\mathrm{^{\prime}}}$/${G}_{\mathrm{min}}^{^{\prime\prime} }$ is the ratio of storage to loss modulus at the frequency where G″ exhibits a local minimum, and ${l}_{\mathrm{e}}$ is the entanglement length, which can be estimated from the modulus. We also obtain from the pointer algorithm a formula whereby the micelle breakage time (τ_br) can be estimated from the longest relaxation time (${\tau }_{\mathrm{R}}$). The pointer algorithm’s predictions are also shown to match those of a more microscopic slip-spring model, which had been previously validated by comparison to polymer rheological data. Thus, the work provides both a method and example estimates of these parameters as functions of surfactant and salt concentration, filling a major gap in characterization of these solutions. Finally, we investigate the determination of the micelle persistence length from high-frequency data.