Surface equation of state and transitional behavior of adsorption layers of soluble amphiphiles at fluid interfaces

Generally, the equilibrium surface tension vs concentration isotherm of any amphiphile has to be described by a surface equation of state that makes allowance for a transition state in the adsorption layer. The transition state is assumed to continuously connect two adsorption stales attributable to two different surface configurations of the adsorbed amphiphile. By the investigation of various types of nonionic amphiphiles, it is shown that the transition range sets on at rather low surface pressures, i.e., in the Henry region. The width of the transition range depends on the amphiphilic structure. The transition behavior can be described mathematically by various functions. Here, we used a polynomial (POLY), the tangens hyperbolicus (TANH), and two analytical expressions related to the distribution of the configurations' different cross-sectional area (AREA) and/or surface tension (SELF) values in the transition region. These functions lead To almost identical results. It turns out that from the evaluation of the AREA transition in terms of molecular space constraints, only the surface accommodation of straight-chain surfactants with small terminal head group can reasonably well be understood. Rising head group size, addition of more hydrophilic entities, and nonterminal binding of the hydrophilic group(s) result in area ratios far beyond those derived from the molecules' coordinates. Obviously, amphiphiles of such molecular structure possess a comparatively high mobility in the adsorption layer. Thus, it is concluded that there is no uniform mechanism for the amphiphiles' surface accommodation at the onset of the transition region.