**1. Introduction**

The study of polyelectrolyte oppositely charged surfactant solutions, either in bulk or close to interfaces (fluid and solid ones), has grown very fast in the last two decades [1], mainly as result of its interest for a broad range of technological and industrial fields, e.g., drug delivery systems, food science, tertiary oil recovery, or cosmetic formulations [1–9]. Most of such applications take advantage of the chemical nature of the compounds involved, structural features of the formed complexes, and the rich phase diagrams appearing in this type of system [10–12].

Despite the extensive research, the description of the physico-chemical behavior of these colloidal systems remains controversial, in part because the self-assembly processes of polyelectrolytes and surfactants bearing opposite charges leads to the formation of non-equilibrium complexes [10,13–16]. They are expected to impact significantly on the properties of the solutions and in their adsorption at

the interfaces [7]. This makes it necessary to pay attention to aspects such as the polymer-surfactant mixing protocol, the elapsed time from the preparation of solutions until their study, or the addition of inert electrolytes when comparisons between different studies are performed [17–19]. The role of the above-mentioned aspects in the physico-chemical properties and the phase diagrams of polyelectrolyte-surfactant solutions have been the focus of many studies, which have evidenced the complex behavior of polyelectrolyte-surfactant solutions [6,8,17–19]. It is worth mentioning that the non-equilibrium nature of the complexation process of polymer-surfactant solutions has an extraordinary impact on the interfacial properties of such solutions, as was recently stated by Campbell and Varga [20].

The role of the presence of non-equilibrium aggregates on the adsorption of polymer-surfactant solutions at fluid interfaces was already evidenced by the seminal works of the groups of Campbell and of Meszaros, focused on the analysis of the surface tension of polyelectrolyte-surfactant solutions [7,21–23]. However, it was necessary to use neutron reflectometry, which provides information on the composition and structure of the interfaces to deepen the most fundamental aspects of the physico-chemical behavior of these systems [24–26]. The studies of Penfold's group were a preliminary step toward the understanding of the correlations existing between the aggregation occurring in polyelectrolyte-surfactant solutions and the behavior of these complexes' fluid interfaces [27–31]. However, such works used an extended Gibbs formalism to describe the adsorption at fluid interfaces, i.e., provide a thermodynamic description. This approach was able to account for the non-regular dependences of the surface tension on the bulk concentration (surface tension peaks), even though it neglects the impact of non-equilibrium aspects [32,33]. More recently, Campbell et al. [17,18,34–39], using surface tension measurements and neutron reflectometry combined with ellipsometry, Brewster angle microscopy, and different bulk characterization techniques, tried to link the interfacial properties of the solutions to the bulk phase behavior, paying special attention to the role of the non-equilibrium effects. Their physical picture takes into account the role of the depletion of the interface as a result of the aggregation in the bulk [40], and the enrichment of the interface in virtue of direct interactions of the formed aggregates [19].

Most studies that analyze the behavior of the adsorption of polyelectrolyte-surfactant solutions at fluid interfaces only consider the interfaces as static systems. However, a comprehensive description of their behavior requires taking into consideration the response of such systems against mechanical deformations, i.e., the rheological response of the interfaces [7,41–45]. The understanding of such aspects is essential because most technological applications of interfacial systems, e.g., foam stabilization [42], rely on the response of the interfaces against mechanical perturbations [43]. The seminal studies on the rheological characterization of polyelectrolyte-surfactant layers at the water–vapor interface done by Regismond et al. [26,46] pointed out the strong synergetic effect on the interfacial properties as result of the influence of the bulk complexation process in the interfacial properties. More recent studies by Bhattacharyya et al. [47] and Monteux et al. [48] correlated the interfacial rheological response of polyelectrolyte-surfactant solutions with their ability to stabilize foams. They found that the formation of gel-like layers at the interface hindered destabilization processes such as bubble coalescence and foam drainage. Deepening the understanding of the rheological response of polyelectrolyte-surfactant solutions, Noskov et al. [26,42,43,45,49] showed that the mechanical behavior of the interface is controlled by the heterogeneity of layers, which is reminiscent of the structure of the complexes formed in solution.

It is worth mentioning that most studies in the recent literature deal with solutions containing relative low polymer concentrations, which hold limited interest from an industrial point of view. It is expected that polymer concentration can present an important contribution in both the complexation process and the interfacial properties of polyelectrolyte-surfactant solutions [19,41,43]. Previous studies have shown that, whereas in diluted polyelectrolyte-surfactant solutions, equilibrium between free surfactant molecules and complexes is always present in solution, the role of the free surfactant is rather limited when polymer concentration is increased. For the latter, the binding degree of surfactant molecules to the polymer chain reach values above 90%, which makes it possible to assume that they are mostly complexes that are presented in solution, even for compositions in the vicinity of the onset of the phase separation region [50]. The differences in the complexation phenomena occurring in concentrated and diluted mixtures may significantly affect the interfacial assembly of polymer-surfactant solutions, with concentrated mixtures leading to the formation of interfacial layers, with composition mirroring the composition of the bulk solutions. The latter is far from the scenario found for diluted solutions [50,51].

This work presents a comparative study of the equilibrium and dynamic properties of interfacial layers formed upon adsorption at the water–vapor interface of solution formed by poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants: sodium lauryl-ether sulfate (SLES) and sodium N-lauroyl-N-methyltaurate (SLMT). PDADMAC was chosen as the polymer because of its common utilization as a conditioner in cosmetic formulations for hair care and cleansing. Furthermore, SLES and SLMT have been recently included in formulations of shampoos to replace sodium dodecylsulfate (SDS) due to their softness and mildness, which limits skin and mucosa irritation [1].

The main aim of this work is to unravel the different interfacial behavior appearing in polycation-oppositely charged surfactant mixtures. The adsorption at the water–vapor interface is studied by surface tension measurements obtained with different tensiometers. It is worth mentioning that although polyelectrolyte-surfactant may be out of equilibrium, for simplicity we will refer to the effective property measured in this work as surface tension. In addition to the steady state measurements of the surface tension, we will follow the adsorption kinetics of the complexes at the water–vapor interface by the time evolution of the surface tension (dynamic surface tension) and the mechanical performance of the interfaces against dilation using oscillatory barrier experiments in a Langmuir trough [52]. The obtained results will be combined with the information obtained from the study of the self-assembly phenomena taking place in solution. This will provide a comprehensive description of the equilibration processes occurring during the formation of interfacial layers in this type of system. It is expected that the results contained here may help to shed light on the complex physico-chemical behavior of these systems.
