DYNAMIC SURFACE-TENSION OF AQUEOUS SURFACTANT SOLUTIONS .2. DIFFUSION-KINETIC-CONVECTIVE CONTROLLED ADSORPTION

A qualitative theory of the dynamic surface tension is developed for the diffusion-kinetic-convective theoretical models obeying any adsorption isotherms and any adsorption kinetics when the diffusion coefficient in the adsorbed layer depends on the fraction of the total surface coverage. The effect of the convective transfer is estimated in an analytical form for short and long times. The time-dependent adsorption over a wide range of time is obtained in an analytical form any adsorption isotherms and any adsorption kinetics for the diffusion-kinetic theoretical model. It is shown that the dynamic surface tension over a wide range of time may be described by using two linear equations in the form of the relaxation function F(t) - log[gamma0 - gamma(t))/(gamma(t) - gamma(e))] = n log(t/t(rel)) versus log(t). The parameter of n is equal to 1.0 for the kinetic-controlled adsorption and equal to 0.5 for the diffusion-controlled adsorption. Formulae were derived to calculate (a) the rate constant for adsorption/desorption, (b) the diffusion coefficient, and (c) the activation energy of diffusion in the adsorbed layer by using kinetic adsorption data at different adsorbate concentrations. It is shown that the dynamic surface tension over a wide range of surfactant concentrations may be described by using the following models: (1) the kinetic-controlled adsorption for short times (0 less-than-or-equal-to t less-than-or-equal-to t(cr1)), (II) the diffusion-kinetic-controlled adsorption for intermediate times (t(cr1) less-than-or-equal-to t less-than-or-equal-to t(cr2)), and (III) the diffusion-controlled adsorption for long time (t greater-than-or-equal-to t(cr2)). Formulae were derived to calculate the critical times t(cr1) and t(cr2). The existence of the (I), (II), and (III) regimes are justified by using the experimental data for the dynamic surface tension of N-dodecyl-N-benzyl-N-methylglycine (C12BMG) in water. (C) 1994 Academic Press, Inc.