From Surface Tension to Molecular Distribution: Modeling Surfactant Adsorption at the Air-Water Interface.

Surfactants are centrally important in many scientific and engineering fields and are used for many purposes such as foaming agents and detergents. However, many challenges remain in providing a comprehensive understanding of their behavior. Here, we provide a brief historical overview of the study of surfactant adsorption at the air-water interface, followed by a discussion of some recent advances in this area from our group. The main focus is on incorporating an accurate description of the adsorption layer thickness of surfactant at the air-water interface. Surfactants have a wide distribution at the air-water interface, which can have a significant effect on important properties such as the surface excess, surface tension, and surface potential. We have developed a modified Poisson-Boltzmann (MPB) model to describe this effect, which we outline here. We also address the remaining challenges and future research directions in this area. We believe that experimental techniques, modeling, and simulation should be combined to form a holistic picture of surfactant adsorption at the air-water interface.

Quantifying the Counterion-Specific Effect on Surfactant Adsorption Using Modeling, Simulation, and Experiments.

Ionic surfactants behave differently in the presence of various counterions, which plays an important role in many scientific and engineering processes. Previous work has shown that the counterion-specific surface tension can be reproduced with classical adsorption models, but the underlying origin of this effect has not been explained. In this paper, we extend our previously developed adsorption model to account for the specific counterion adsorption. This model can accurately predict the surface tension of surfactant solutions like sodium dodecyl sulfate (SDS) in the presence of the monovalent salts LiCl, NaCl, KCl, and CsCl. The predicted surface excess and surface potential are validated by corresponding sum-frequency generation (SFG) spectroscopy experiments. We also used molecular dynamic (MD) simulation to explain the origin of the counterion-specific effect for surfactant behavior. Our study shows that for SDS, binding of the counterion to both the headgroup and a few CH2 fragments close to the surfactant head contributes to the counterion-specific effect. In general, SDS behaves like a large ion, and it prefers to bind with large counterions such as Cs+, which is consistent with Collins's law of matching water affinity. Therefore, large counterions enhance the surface adsorption and lower the surface tension the most.

Detecting the undetectable: The role of trace surfactant in the Jones-Ray effect.

The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration, the surface tension decreases. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we use both experimental surface tension measurements and numerical solution of the Poisson-Boltzmann equation to demonstrate that very low concentrations of surfactant in water create a Jones-Ray effect. We also demonstrate that the low concentrations of the surfactant necessary to create the Jones-Ray effect are too small to be detectable by surface sensitive spectroscopic measurements. The effect of surface curvature on this behavior is also examined, and the implications for unexplained bubble phenomena are discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces.

Salting-Up of Surfactants at the Surface of Saline Water as Detected by Tensiometry and SFG and Supported by Molecular Dynamics Simulation.

Surfactant adsorption at the air-water interface is critical to many industrial processes but its dependence on salt ions is still poorly understood. Here, we investigate the adsorption of sodium dodecanoate onto the air-water interface using model saline waters of Li+ or Cs+ at pH values 8 and 11. Both cations enhance the surfactant adsorption, as expected, but their largest effects on the adsorption also depend on pH. Specifically, surface tension measurements, sum-frequency generation spectroscopy, and microelectrophoresis show that small (hard) Li+ enhances the surfactant adsorption more than large (soft) Cs+ at pH 11. This effect is fully reversed at pH 8. We argue that this salting-up (increasing adsorption) reversal is attributable to the conversion of the neutralized carboxylic (-COOH) headgroup at pH 8 into the charged carboxylate (-COO-) headgroup at pH 11, which, respectively, interact with Cs+ and Li+ favorably. Molecular dynamics simulation shows that the affinity of Cs+ to the interface is decreased and eventually overtaken by Li+ as the carboxylic groups are deprotonated. This study highlights the importance of the charge and size of salt ions in selecting surfactants and electrolytes for industrial applications.

Adsorption of ionic surfactants at the air-water interface: The gap between theory and experiment.

We review the experimental and theoretical results for the adsorption and structure of ionic surfactants at the air-liquid interface. The results show that ionic surfactants form thick adsorption layers at the interfacial region. We also review several adsorption models for ionic surfactants, which become increasingly complex as they capture the many features of adsorption layers. However, the adsorption layer structures determined by experiments and the structures predicted by models do not match because most models assume very thin adsorption layers. We show the discrepancies between measured and predicted surface properties and provide several explanations. We conclude that the mismatch in the adsorption layer structure provided by experiments and the structure provided by adsorption models is the main reason for the discrepancies in the surface excess and the surface potential.

Significant Effect of Surfactant Adsorption Layer Thickness in Equilibrium Foam Films.

Foam films formed at the air-water interface do not have fixed adsorption sites where adsorbed surfactants can arrange themselves, resulting in the formation of thick adsorption layers. Current theories of equilibrium foam films fail to account for this feature and significantly underestimate the adsorption layer thickness. Here we show that this thickness has a significant effect on the disjoining pressure in foam films. If ignored, the theory predicts unphysical electrostatic potential profiles, which underestimate the disjoining pressure. We apply a previously developed adsorption model that incorporates a realistic thickness for the adsorption layer. This new model reproduces experimental measurements of the disjoining pressure of foam films very well over a wide surfactant concentration range without fitting parameters. Our work shows that a thick adsorption layer is less effectively screened by counterions, resulting in a higher electrostatic potential inside the film and therefore a higher disjoining pressure.

Surface Potential Explained: A Surfactant Adsorption Model Incorporating Realistic Layer Thickness.

Soluble surfactants form thick adsorption layers at the air-liquid interface, but classical adsorption models fail to account for it as they treat the adsorption layer as a mathematical plane (of zero thickness). This simplification has produced several inconsistencies between theoretical predictions and experimental results, especially for the surface potential. Here, we develop a new adsorption model for ionic surfactants at the air-water interface that incorporates the effect of the adsorption layer thickness using a modified Poisson-Boltzmann equation that integrates information from molecular dynamics simulation. We show that the surface potential depends sensitively on both the thickness of the adsorption layer and the interfacial depth at which the surface potential is probed. This model, therefore, provides a much more accurate picture of the surface potential than classical models.

A critical review of the model fitting quality and parameter stability of equilibrium adsorption models.

We reviewed eight commonly used equilibrium adsorption models and examined their underlying assumptions, fitting qualities, and parameter stabilities. We compared several objective functions that have been applied to curve fitting analysis and a few statistics tests that have been performed to evaluate regression quality. The iteratively reweighted least squares algorithm was selected as the most suitable regression method for adsorption models in the presence of heteroscedasticity. The fraction of unexplained variance was selected to indicate the model fitting quality. Two sources of parameter instability were identified: residue instability and function instability. While the definition of the instability caused by residue is well established, we are the first to consider the instability caused by an adsorption model. The models discussed in this article can be applied to many surfactants, such as normal alcohols, polyglycol ethers, and sodium dodecyl sulfate at different salt concentrations. Our results show that both the model fitting quality and parameter instability increase with the number of parameters subject to curve fitting. For the Frumkin-type of reorientation model, the parameter instability can be as high as 25%. The high degree of instability in some complicated adsorption models may invalidate the estimated parameters. Therefore, additional measurements or simulations are required for complicated models to extract reliable model parameters.