A simple analytical approach to electrostatics for nanoparticles with torus-like elements in 1:1 electrolyte solution

Modeling Micellar Growth and Branching in Mixtures of Zwitterionic with Ionic Surfactants

Zwitterionic surfactants are widely applied as drag-reducing or thickening agents because their aggregation patterns may drastically change in response to variations of the system composition or external stimuli, which provides controllable viscoelasticity. For predicting aggregation behavior of surfactant mixtures, classical molecular thermodynamic models have been widely used. Particularly, the results of modeling have been reported for zwitterionic/ionic surfactant mixtures. However, for solutions containing a zwitterionic surfactant, no molecular thermodynamic model has been proposed for a micellar branch. In this work we extend the classical molecular thermodynamic aggregation model to describe aggregation in the aqueous mixtures that contain a zwitterionic and an ionic surfactant. We derive analytical expressions (1) for the contribution of dipoles to the electrostatic term of the standard free energy of aggregation into micellar branches and (2) for the dipolar contribution to the persistence length of wormlike micelles. The dependence of micellar branching on the surfactant concentration is taken into account by including the population of micellar branches in the material balance equations. This model is applied to predict aggregation equilibrium in aqueous salt solutions of betaine (oleoylamidopropyl-N,N-dimethylbetaine) mixed with sodium dodecyl sulfate (SDS) and the longer tail sodium n-alkyl sulfates. We discuss the predicted properties of the aggregates and micellar networks and compare our predictions with available experimental data.

Molecular thermodynamic modeling of a bilayer perforation in mixed catanionic surfactant systems

An interplay between electrostatics and deformation of surfactant tails is responsible for the spontaneous formation of pores in self-assembled bilayers.

Micro-mechanical, continuum-mechanical, and AFM-based descriptions of elasticity in open cylindrical micellar filaments

We present theoretical and experimental descriptions of the elasticity of cylindrical micellar filaments using micro-mechanical and continuum theories, and atomic force microscopy. Following our micro-mechanical elasticity model for micellar filaments [M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1-16], the elastic bending energy of hemispherical end caps is found. The continuum description of the elastic bending energy of a cylindrical micellar filament is also derived using constrained Cosserat rod theory. While the continuum approach provides macroscopic description of the strain energy of the micellar filament, the micro-mechanical approach has a microscopic view of the filament, and provides expressions for kinetic variables based on a selected interaction potential between the molecules comprising the filament. Our model predicts the dependence of the elastic modulus of the micellar filaments on their diameter, which agrees with previous experimental observations. Atomic force microscopy is applied to estimate the elastic modulus of the filaments using force volume analysis. The obtained values of elastic modulus yield the persistence length of micellar filaments on the same order of the previously reported values. Consistent with previous studies, our results indicate that semi-flexible linear micelles have a relatively large local strain energy at their end points, which explains their tendency to fuse to minimize the number of end caps at relatively low total surfactant volume fractions. Also, the elastic modulus of micellar filaments was found to increase when the indentation frequency increases, a finding which agrees with previous rheological observations on the bulk shear modulus of micellar solutions.

A molecular model for the free energy, bending elasticity, and persistence length of wormlike micelles

An expression for the elastic free-energy density of a wormlike micelle is derived taking into account interactions between its constituent molecules. The resulting expression is quadratic in the curvature and torsion of the centerline of micelle and thus resembles free-energy density functions for polymer chains and helical filaments such as DNA. The model is applied on a wormlike micelle in the shape of a circular arc, open or closed. Conditions under which linear chains in dilute systems transform into toroidal rings are analyzed. Two concrete anisotropic soft-core interaction potentials are used to calculate the elastic moduli present in the derived model, in terms of the density of the molecules and their dimensions. Expressions for the persistence length of the wormlike micelle are found based on the flexural rigidities so obtained. Similar to previous observations, our results indicate that the persistence length of a wormlike micelle increases as the aspect ratio of its constituent molecules increases. A detailed application of the model on wormlike micelles of toroidal geometry, along with employing statistical-thermodynamical concepts of self-assembly is performed, and the results are found to be well consistent with the literature. Steps to obtain the material parameters through possible experiments are discussed.

Universal sequence of ordered structures obtained from mesoscopic description of self-assembly

Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived by a systematic coarse-graining procedure. For particles interacting with spherically symmetric potentials of arbitrary form, the grand-thermodynamic potential consists of two terms. The first term is associated with microscopic length-scale fluctuations, and has the form of the standard density functional. The second term is associated with mesoscopic length-scale fluctuations, and has the form known from the statistical field theory. For the correlation function between density fluctuations in mesoscopic regions, a pair of equations similar to the Ornstein-Zernicke equation with a new closure is obtained. In the special case of weak ordering on the mesoscopic length scale, the theory takes a form similar to either the Landau-Ginzburg-Wilson (LGW) or the Landau-Brazovskii (LB) field theory, depending on the form of the interaction potential. Microscopic expressions for the phenomenological parameters that appear in the Landau-type theories are obtained. Within the framework of this theory, we obtain a universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. The sequence of phases agrees with experimental observations and with simulations of many self-assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential, we find the bicontinuous gyroid phase ( Ia3d symmetry) that may be related to a network-forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.