THEORY OF SURFACE LIGHT-SCATTERING FROM A FLUID-FLUID INTERFACE WITH ADSORBED POLYMERIC SURFACTANTS

We present a microscopic theory for the interfacial rheology of a flui d-fluid interface with adsorbed surfactant and calculate the effect of this on surface light scattering from the interface. We model the hea d and tail groups of the surfactant as polymer chains, a description t hat becomes increasingly accurate for large molecular weight surfactan ts, i.e., polymeric surfactants. Assuming high surface concentrations so that we have a double-sided polymer brush monolayer, we derive micr oscopic scaling expressions for the surface viscoelastic constants usi ng the Alexander-deGennes model. Our results for the surface elastic c onstants agree with those in the literature, while the results for the viscous constants are new. We find that four elastic constants, i.e., gamma (surface tension), epsilon (dilational elasticity), kappa (bend ing modulus), lambda (coupling constant), and three viscous constants, i.e., epsilon', kappa', lambda' (the viscous counterparts of epsilon, kappa, and lambda, respectively) are required for a general descripti on of interfacial viscoelasticity (neglecting in-plane shear). In cont rast to current phenomenological models, we find (1) there is no visco us counterpart to gamma,i.e., gamma'=0; (2) there are two additional c omplex surface constants (i.e., lambda+i omega lambda' and kappa+i ome ga kappa') due to the finite thickness of the monolayer. Excellent agr eement is found comparing our microscopic theory with measurements on diblock copolymer monolayers. We further derive the dispersion relatio n governing surface hydrodynamic modes and the power spectrum for surf ace quasielastic light scattering (SQELS) for a general interface para meterized by all the surface viscoelastic constants. Limiting results are presented for (1) liquid-air interfaces; (2) liquid-liquid interfa ces with ultralow gamma. The significant contribution of kappa in the latter case opens up the possibility for a direct measurement of kappa using SQELS for polymeric surfactant monolayers. Finally, we show tha t the coupling constant lambda can lead to apparent negative values of El. as observed in many experimental systems. This is the first time that this result has been explained for insoluble monolayers using a p hysically realistic model. Based on our theory, we speculate the exist ence of a thick sublayer (on the length scale of a micron) in recent e xperiments on insoluble copolymer systems where negative surface visco sities have been found. We also suggest methods to detect the presence of such a sublayer if it does exist. (C) 1998 American Institute of P hysics.