Dynamic interfacial mechanics due to transiently adsorbing ionic surfactants

Abstract An analysis of the transient adsorption of monovalent ionic surfactant to an initially clean, planar interface is performed. We invoke the thin-double-layer limit and solve for the surfactant interfacial concentration when the surfactant adsorbs according to Langmuir kinetics and the counterion does not. We analyze the early-time behavior and the approach to equilibrium of the system, deriving asymptotic approximations for the surfactant interfacial concentration, and the bulk ion concentration and electric potential dynamics. We extend our analysis to incorporate the effect of added monovalent, non-adsorbing electrolyte and find an analogous asymptotic expression for the surface concentration dynamics. We use these analyses to compute dynamic interfacial mechanics in two scenarios: (i) when ionic surfactant transiently adsorbs to an initially clean interface and (ii) when the equilibrated interface undergoes small-amplitude area oscillations. In case (i) the adsorption dynamics resemble kinetically limited adsorption with ambipolar diffusion in the bulk, and at early times the growth of the interfacial concentration of surfactant is linear in time. In case (ii) we show that the Langmuir desorption rate constant can be obtained by finding the frequency of oscillation at which $$\text {Re}(E/E_0) = \frac{1}{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Re</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> , where E is the complex surface compression elastic modulus, $$E_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> is that for an insoluble surfactant, and Re denotes the real part.