Theory of surface light scattering from a fluid–fluid interface with adsorbed polymeric surfactants

Abstract

We present a microscopic theory for the interfacial rheology of a fluid–fluid interface with adsorbed surfactant and calculate the effect of this on surface light scattering from the interface. We model the head and tail groups of the surfactant as polymer chains, a description that becomes increasingly accurate for large molecular weight surfactants, i.e., polymeric surfactants. Assuming high surface concentrations so that we have a double-sided polymer brush monolayer, we derive microscopic scaling expressions for the surface viscoelastic constants using the Alexander–deGennes model. Our results for the surface elastic constants agree with those in the literature, while the results for the viscous constants are new. We find that four elastic constants, i.e., γ (surface tension), ε (dilational elasticity), κ (bending modulus), λ (coupling constant), and three viscous constants, i.e., ε′,κ′,λ′ (the viscous counterparts of ε, κ, and λ, respectively) are required for a general description of interfacial viscoelasticity (neglecting in-plane shear). In contrast to current phenomenological models, we find (1) there is no viscous counterpart to γ, i.e., γ′≡0; (2) there are two additional complex surface constants (i.e., λ+iωλ′ and κ+iωκ′) due to the finite thickness of the monolayer. Excellent agreement is found comparing our microscopic theory with measurements on diblock copolymer monolayers. We further derive the dispersion relation governing surface hydrodynamic modes and the power spectrum for surface quasielastic light scattering (SQELS) for a general interface parameterized by all the surface viscoelastic constants. Limiting results are presented for (1) liquid–air interfaces; (2) liquid–liquid interfaces with ultralow γ. The significant contribution of κ in the latter case opens up the possibility for a direct measurement of κ using SQELS for polymeric surfactant monolayers. Finally, we show that the coupling constant λ can lead to apparent negative values of ε′, as observed in many experimental systems. This is the first time that this result has been explained for insoluble monolayers using a physically realistic model. Based on our theory, we speculate the existence of a thick sublayer (on the length scale of a micron) in recent experiments on insoluble copolymer systems where negative surface viscosities have been found. We also suggest methods to detect the presence of such a sublayer if it does exist.