Foam film stratification studies probe intermicellar interactions

Ultrathin foam films containing supramolecular structures like micelles in bulk and adsorbed surfactant at the liquid–air interface undergo drainage via stratification. At a fixed surfactant concentration, the stepwise decrease in the average film thickness of a stratifying micellar film yields a characteristic step size that also describes the quantized thickness difference between coexisting thick–thin flat regions. Even though many published studies claim that step size equals intermicellar distance obtained using scattering from bulk solutions, we found no reports of a direct comparison between the two length scales. It is well established that step size is inversely proportional to the cubic root of surfactant concentration but cannot be estimated by adding micelle size to Debye length, as the latter is inversely proportional to the square root of surfactant concentration. In this contribution, we contrast the step size obtained from analysis of nanoscopic thickness variations and transitions in stratifying foam films using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols, that we developed, with the intermicellar distance obtained using small-angle X-ray scattering. We find that stratification driven by the confinement-induced layering of micelles within the liquid–air interfaces of a foam film provides a sensitive probe of non-DLVO (Derjaguin–Landau–Verwey–Overbeek) supramolecular oscillatory structural forces and micellar interactions.

Molecules in simple liquids and supramolecular structures in complex fluids can stratify or undergo confinement-induced layering induced by symmetry breaking at a solid–liquid or a fluid–fluid interface (1–8). In freestanding or foam films, the confinement-induced layering of supramolecular structures including micelles (9–17), lipid layers (18, 19), polyelectrolyte–surfactant complexes (20, 21), nanoparticles (9, 22), and liquid crystalline assemblies (23) can result in drainage via stratification. Due to thin film interference, foam films visualized under white light illumination display iridescent colors for thick films (h > 100 nm) (24–28), but ultrathin films (h < 100 nm) exhibit shades of gray that get progressively darker as the film gets thinner (9–21). In reflected light microscopy, micellar foam films exhibit coexisting thick−thin regions with distinct shades of gray. Interferometry-based measurement of the average film thickness over time decreases in a stepwise fashion yielding a step size, Δh (9–17). Many published studies argue (9–12, 22, 29–34) that foam films containing charged micelles or latex particles stratify analogously due to the formation of “ordered colloidal crystals” (OCCs) and step size, Δh, equals the intermicellar distance, d, in bulk solutions. However, a comparison of concentration-dependent Δh obtained from the dynamic foam stratification studies (influenced by confinement effects) with d measured using small-angle X-ray or neutron scattering (SAXS or SANS) or other direct measurements of static equilibrium structure, and related evidence for or against the formation of OCCs in micellar foam films, are lacking in the literature. Thus, the motivations of this contribution are threefold: 1) contrast the step size, Δh, obtained via stratification studies with the intermicellar distance, d, and micelle dimensions determined using SAXS; 2) examine the SAXS data for any evidence of OCCs; and 3) elucidate the influence of ionic micelles on foam film stability and topography, as well as on colloidal forces, in multicomponent complex fluids.Micelles, formed by self-assembly of soaps and detergents and ever present in typical household foams, facilitate cleaning and detergent action by solubilizing oils and oil-soluble dirt within their hydrophobic core (2, 34, 35). Micelles formed by biosurfactants like bile salt and rhamnolipids can be used for delivering nonpolar, bio-active polyunsaturated oils, flavonoids, vitamins, and hydrophobic drugs (36–38). Therefore, understanding the stability and lifetime of micellar foams is essential toward molecular engineering of formulations, controlling foams in industrial reactors, rivers, and lakes and developing bio-surfactants (36–38). Foam film drainage involves interfacial flows that are influenced both by bulk rheology and interfacial rheology as well as Laplace or capillary pressure, Pc=σC (set by surface tension, σ and curvature, C) (27, 28, 39–41). Additionally, thickness transitions and variations in ultrathin (h < 100 nm) freestanding as well as supported (containing one or two solid boundaries) films (41–43) depend on disjoining pressure, Π(h)=−(∂G/∂h)P,T,A,Ni, defined as the free energy required to change unit thickness at constant temperature, T, pressure, P, surface area, A, and mole number, N_i (1, 34, 40–42). Intermolecular and surface forces determine the strength and range of disjoining pressure, Π(h), as well as of colloidal interaction forces, F(h) (1–3, 35, 40–42). Physical properties of surfactant solutions like surface tension and conductivity show distinct change around a critical micelle concentration (CMC), beyond which spheroidal micelles can form (2, 34, 35), and rod-like micelles, lamellar phases, etc., emerge at higher concentrations (44–46). In foam films formed with ionic surfactant at c < CMC, drainage below h < 30 nm often leads to the formation of relatively long-lived common black (CB) film attributed to counterbalancing of P_c by ΠDLVO(h), the disjoining pressure due to DLVO (Derjaguin–Landau–Verwey–Overbeek) forces contributed by van der Waals and electrostatic double-layer interactions (1–3, 35, 39, 40). Even thinner Newton black (NB) films attest to the role of shorter-range, non-DLVO surface forces (14, 25–27, 40, 41). In contrast, in micellar foam films (c > CMC), a non-DLVO, oscillatory structural force, ΠOS(h), counterbalances P_c at multiple flat thicknesses, manifested as distinct shades of gray in reflected light microscopy (9–17, 21, 40, 47–50).For micellar fluids containing charged micelles, the step size, Δh, obtained using thickness–time plots from stratification experiments, and periodicity, λ, of ΠOS(h) directly measured using thin-film balance (47, 48) show that both periodicity and step size exceed micelle size, a, implying λ>a and Δh>a. In 1971, Bruil and Lyklema (51) were the first to report that the concentration-dependent decrease in step size measured for sodium dodecyl sulfate (SDS) solutions followed a power law of the form Δh∝csoap−1/3 and wrote that step size values “seem to be related to intermolecular distance in the (unmicellized) bulk solution.” In 1988, Nikolov et al. (9) reported that foam films containing latex particles stratified in a fashion similar to micellar foam films and argued that diffusion-driven, layer-by-layer removal of micelles or particles from an ordered colloidal crystal (OCC) structure drives stratification. In their OCC or “micelle-vacancy diffusion” mechanism, they proposed that the effective film viscosity increases with decrease in stratified film thickness (9, 10, 29–31, 33). Contrastingly, in the “hydrodynamic” mechanism, Bergeron and Radke (13, 47) described stratification using a thin-film equation, by incorporating ΠOS(h) and bulk solution viscosity. Nikolov et al. (9, 10, 29–31) suggested that the step size, Δh, was equal to an effective diameter, deff=2lSDS+κ−1, computed by adding the fixed length of SDS molecules, l_SDS, to the Debye length, κ−1, that captures the range of screened electrostatic interactions. However, the step size Δh∼c−1/3 and the Debye length κ−1∼c−1/2 display distinct power laws, and the measured step size exceeds the micelle size, a, as well as the computed effective diameter, d_eff, for ionic micellar systems, or typically Δh>a and Δh>deff.Studies on charged nanoparticle dispersions find that the periodicity, λ, of the oscillatory structural force, F(h), measured directly with surface force apparatus (SFA), or colloidal probe atomic force microscopy (CP-AFM), correlates well with the interparticle distance, d, obtained using scattering and simulations (4, 5, 52–55). Furthermore, the periodicity, λ≈d≫a, is primarily set by the particle number density, ρ, and is relatively independent of added salt, charge at solid surfaces, and particle size, a (4, 5, 53–55). Assuming that analogy between λ∝ρ−1/3 in the nanoparticle studies and Δh∝c−1/3 in stratified foam studies arises due to similar underlying physics, Danov et al. (32) and Anachkov et al. (11) argued that Δh≈d or step size equals the intermicellar distance, d, in bulk solutions and hypothesized that step size from stratification studies could be used for determining aggregation number as Nagg≈(c−CMC)(Δh)3. However, Yilixiati et al. (17) showed that on salt addition, the measured Δh values for micellar SDS solutions do not collapse onto a single curve even if plotted against micellar number density, ρ, as micelle number and dimensions can change on the addition of salt (or surfactant) (2), whereas nanoparticle dimensions remain constant. Furthermore, solid boundaries that can impact SFA and AFM measurements are absent in stratifying foam films. However, the thickness of stratifying films is rather heterogeneous, and the average thickness changes in a stepwise fashion. Thus, the analogy between stratifying micelles in foam films and stratifying nanoparticle dispersions under confinement between solid surfaces requires further investigation. In particular, a comparison between multiple length-scales including micelle dimensions, Debye length, intermicellar distance, d and step-size, Δh, and the consequences of thickness heterogeneities within foam films are warranted.In this study, we contrast the concentration-dependent changes in step-size measured in foam stratification studies with micellar dimensions and intermicellar distances in bulk solutions obtained using SAXS for aqueous solutions of SDS. For the range of concentrations (25 mM ≤ c_SDS ≤ 250 mM) explored here, bulk rheology, interfacial tension, micelle shape and size, and interfacial charge (or potential) are nearly constant. Hence, the observed concentration-dependent changes in step-size and nanoscopic topography in stratifying films are dictated by the corresponding changes in intermicellar interactions and the resulting disjoining pressure, ΠOS(h). We visualize and analyze nanoscopic thickness variations and transitions in stratifying foam films using IDIOM (Interferometry Digital Imaging Optical Microscopy) protocols (16) (Fig. 1A) that provide requisite spatiotemporal resolution (thickness ∼1 nm, in-plane < 1 μm, time < 1 ms). We analyze SAXS data to compute micelle dimensions, volume fraction, and microstructure (order) in bulk solutions and obtain the intermicellar distance from structure factor peak in SAXS data. Finally, we discuss the ramifications of the close comparison between step size from the foam film stratification studies and micellar dimensions and intermicellar distance determined using SAXS analysis on the intermicellar interactions and the mechanistic basis of stratification.Open in a separate windowFig. 1.Schematic of the setup used for examining stratification using IDIOM protocols and illustrative examples of stepwise thinning. (A) The Scheludko-like cell contains a plane-parallel film and surrounding meniscus that emulates a single foam film and its Plateau border. The cell is placed in a closed container and stratification is visualized using reflected light microscopy. A finite volume of fluid is inserted into the cell using the side-arm connected to a syringe. No liquid is added or withdrawn during the stratification experiment, and drainage from the film into the meniscus occurs freely and spontaneously. (B) Spatiotemporal variation in interference intensity I(x, y, t; λ) is used for computing thickness transitions and variations in stratifying films. (C) Average film thickness plotted as a function of time shows stepwise thinning for foam films made with aqueous SDS solutions. The spikes and dips in thickness plots appear when mesas or domains emerge in the region selected for computing average thickness. The data are shifted horizontally for clarity.