Growth of wormlike micelles in nonionic surfactant solutions: Quantitative theory vs. experiment

Abstract

Despite the considerable advances of molecular-thermodynamic theory of micelle growth, agreement between theory and experiment has been achieved only in isolated cases. A general theory that can provide self-consistent quantitative description of the growth of wormlike micelles in mixed surfactant solutions, including the experimentally observed high peaks in viscosity and aggregation number, is still missing. As a step toward the creation of such theory, here we consider the simplest system - nonionic wormlike surfactant micelles from polyoxyethylene alkyl ethers, CE. Our goal is to construct a molecular-thermodynamic model that is in agreement with the available experimental data. For this goal, we systematized data for the micelle mean mass aggregation number, from which the micelle growth parameter was determined at various temperatures. None of the available models can give a quantitative description of these data. We constructed a new model, which is based on theoretical expressions for the interfacial-tension, headgroup-steric and chain-conformation components of micelle free energy, along with appropriate expressions for the parameters of the model, including their temperature and curvature dependencies. Special attention was paid to the surfactant chain-conformation free energy, for which a new more general formula was derived. As a result, relatively simple theoretical expressions are obtained. All parameters that enter these expressions are known, which facilitates the theoretical modeling of micelle growth for various nonionic surfactants in excellent agreement with the experiment. The constructed model can serve as a basis that can be further upgraded to obtain quantitative description of micelle growth in more complicated systems, including binary and ternary mixtures of nonionic, ionic and zwitterionic surfactants, which determines the viscosity and stability of various formulations in personal-care and house-hold detergency.

Analytical modeling of micelle growth. 1. Chain-conformation free energy of binary mixed spherical, wormlike and lamellar micelles

“…To generalize the theory for single component micelles [28,44] to the case of two components, let us consider the surfactant chains as continuous strings with extended length l k = N sg,k l sg and volume…”

“…In Ref. [28], it was demonstrated that in combination with the other components of the micelle free energy, Eq. (1.1) provides an excellent theoretical description of the growth of single-component wormlike micelles from nonionic surfactants (polyoxyethylene alkyl ethers).…”

Understanding and Prediction of the Clouding Phenomenon by Spontaneous and Effective Packing Concepts

“…Another approximation is the estimation of the full molecular length l C + I via Tanford's formula (Tanford, 1972) and a mean, estimated EO-EO length, because the ethoxylated chains can arrange in different configurations (Kronberg et al, 2014;Lindman et al, 2016). Moreover, the use of the empirical equation of Sottmann et al (1997) should be checked for its general validity, as well as the "rule of thumb" derived from the work of Danov et al (2018) to estimate the relative evolution of the area at the water/micellar interface with temperature.…”

Rheology of mixed solutions of sulfonated methyl esters and betaine in relation to the growth of giant micelles and shampoo applications

“…The synergism can be due to favorable headgroup interactions (e.g. in a catanionic pair) [32,33], as well as to a mismatch in the surfactant chainlengths [34][35][36].…”