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Register a new userSurface tension model for surfactant solutions at the critical micelle concentration
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A model for the limiting surface tension of surfactant solutions (surface tension at and above the critical micelle concentration, cmc) was developed. This model takes advantage of the equilibrium between the surfactant molecules on the liquid/vacuum surface and in micelles in the bulk at the cmc. An approximate analytical equation for the surface tension at the cmc was obtained. The derived equation contains two parameters, which characterize the intermolecular interactions in the micelles, and the third parameter, which is the surface area per surfactant molecule at the interface. These parameters were calculated using a new atomistic modeling approach. The performed calculations of the limiting surface tension for four simple surfactants show good agreement with experimental data (~30% accuracy). The developed model provides the guidance for design of surfactants with low surface tension values.
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The interfacial tension between immiscible liquids is studied as a function of a model linear surfactant length and concentration using coarse grained, dissipative particle dynamics numerical simulations. The adsorption isotherms obtained from the simulations are found to be in agreement with Langmuir model. The reduction of the interfacial tension with increasing surfactant concentration is found to display some common characteristics for all the values of chain length modeled, with our predictions being in agreement with Szyszkowski equation. Lastly, the critical micelle concentration is predicted for all surfactant lengths, finding exponentially decaying behavior, in agreement with Kleven model. It is argued that these findings can be helpful guiding tools in the interpretation of available experiments and in the design of new ones with new surfactants and polymers.
We propose and study a simplified model for the surface and bulk structures of crosslinked polymer gels, into which voids are introduced through templating by surfactant micelles. Such systems were recently studied by Atomic Force Microscopy [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, ``clumpy bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C_q(x)= <|h(x_0+x)-h(x_0)|^q>. The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.
We carry out the calculation of the surface tension for a model electrolyte to first order in a cumulant expansion about a free field theory equivalent to the Debye-Huckel approximation. In contrast with previous calculations, the surface tension is calculated directly without recourse to integrating thermodynamic relations. The system considered is a monovalent electrolyte with a region at the interface, of width h, from which the ionic species are excluded. In the case where the external dielectric constant epsilon_0 is smaller than the electrolyte solutions dielectric constant epsilon we show that the calculation at this order can be fully regularized. In the case where h is taken to be zero the Onsager-Samaras limiting law for the excess surface tension of dilute electrolyte solutions is recovered, with corrections coming from a non-zero value of epsilon_0/epsilon.
We present a reformulation of the reactive rod model (RRM) of Dutta and Graham [Dutta, Sarit and Graham, Michael D., JNNFM 251 (2018)], a constitutive model for describing the behavior of dilute wormlike micelle solutions. The RRM treats wormlike micelle solutions as dilute suspensions of rigid Brownian rods undergoing reversible scission and growth in flow. Evolution equations for micelle orientation and stress contribution are coupled to a kinetic reaction equation for a collective micelle length, producing dynamic variations in the length and rotational diffusivity of the rods. This model has previously shown success in capturing many critical steady-state rheological features of dilute wormlike micelle solutions, particularly shear-thickening and -thinning, non-zero normal stress differences, and a reentrant shear stress-shear rate curve, and could fit a variety of steady state experimental data. The present work improves on this framework, which showed difficulty in capturing transient dynamics and high-shear behavior, by reformulating the kinetic equation for micelle growth on a more microstructural (though still highly idealized) basis. In particular, we allow for micelle growth associated with strong alignment of rods and breakage due to tensile stresses along the micelles. This new formulation captures both steady and transient shear rheology in good agreement with experiments. We also find good agreement with available steady state extensional rheology.
The contact between a spherical indenter and a solid is considered. A numerical finite element model (F. E. M) to taking into account the surface tension of the solid is presented and assessed. It is shown that for nano-indentation of soft materials, the surface tension of the solid influences significantly the reaction force due to indentation. The validity of the classical Hertz model is defined. In very good approximation, the force vs. indentation depth curve can be fitted by a power law function $F=a^delta b$ where $F$ denotes the force acting on the indentor, $d$ the indentation depth, $a$ and $bin ]1,1.5]$ are constants depending on the materials and the size of the indentor.
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