(125f) Relating Characteristic Times for Dilatational Moduli with Those of Surfactant Adsorption

The characteristic frequency for soluble surfactant exchange between the interface and the subphase, , ω₀ , determines the relationship between the frequency and concentration dependence of the dilatational modulus, ε = ∂γ/(∂(lnA). For oscillatory area change frequencies faster than ω_0, the surfactant is trapped at the interface, the surface concentration, Γ, changes as the interface is compressed and expanded, and hence the surface tension, γ, changes, resulting in a finite dilatational modulus. However, if oscillations are slower than ω₀, the soluble surfactant can diffuse off the interface, Γ and γ remain constant and ε → 0. These characteristic frequencies are surfactant concentration dependent and can be determined from linear oscillatory dilatational rheology measurements using a capillary microtensiometer. We find that ω₀ is small and changes little below the CMC of lysopalmitoylphosphatidylcholine, consistent with a depletion layer of thickness h developing below the interface, in which h =Γ/C_B , in which C_B is the bulk surfactant concentration. Above the CMC, ω₀ increases as a power law in surfactant concentration, suggesting that the depletion layer is minimized by the exchange between a surfactant reservoir created by micelles and the monomer surfactant in the depletion layer. For a diffusion limited process, we expect ω₀ ~ D/h ² ~ DC_B²/Γ². We find that this same ω₀ from dilatational measurements can be used to scale dynamic surface tension relaxation as surfactants adsorb to a bare interface at different bulk concentrations. We show that when the surface tension is scaled as θ = (γ-γ_eq)/(γ_o -γ_eq ), in which γ_eq is the equilibrium surface tension for a given concentration and γ_o is the bare water (solvent) surface tension vs t' = tω₀ in which t is the adsorption time, the dynamic surface tension collapses into two curves, one for concentrations at and below the CMC, and a second curve above the CMC, even though the actual relaxation times vary by orders of magnitude. This scaling directly connects the dilatational and adsorption experiments and suggests a common diffusion limited mechanism for both. The distinct difference between the measurements above and below the CMC suggest that micellar transport is important to both adsorption and the dilatational modulus at higher concentrations.