S. Sundaram et Kj. Stebe, EQUATIONS FOR THE EQUILIBRIUM SURFACE PRESSURE INCREASE ON THE PENETRATION OF AN INSOLUBLE MONOLAYER BY A SOLUBLE SURFACTANT, Langmuir, 12(8), 1996, pp. 2028-2034
This study addresses the penetration of a pre-existing insoluble monol
ayer by a bulk soluble surfactant. It is shown that if the adsorption
isotherm is known describing the partitioning of the soluble component
between the interface and the bulk, the equation for the resulting in
crease in surface pressure Delta pi can be derived using the Gibbs ads
orption equation. The relationship is valid for any adsorption isother
m. A framework for studying monolayer penetration is presented based o
n these equations. Two example calculations are presented based on ads
orption site models for the interface that allow closed form solutions
for Delta pi(x(1),C-2), where C-2 is the molality of the soluble comp
onent and x(1) is the fractional coverage of the insoluble component.
First, a Langmuir model is posed, where the insoluble surfactant reduc
es the adsorption of the soluble component. The Delta pi caused by the
soluble surfactant at a given C-2 is exactly equal to the surface ten
sion reduction caused by that surfactant in the absence of the insolub
le monolayer. Second, a Frumkin model is posed, incorporating 1-2 inte
ractions (between the insoluble (1) and soluble (2) components) and 2-
2 self-interactions. The model predicts enhanced Delta pi with x(1) fo
r 1-2 cohesion and 2-2 repulsion and diminishing Delta pi with x(1) fo
r 1-2 repulsion and 2-2 cohesion when compared with the surface tensio
n reduction achieved by the soluble component alone. The Frumkin model
is discussed as a means for quantifying synergistic adsorption into t
he monolayer directly from a family of Delta pi curves for various, fi
xed x(1) as a function of C-2. A brief discussion of data available in
the literature is presented; the trends observed are in qualitative a
greement with the theoretical framework.