Equation of state of a charged bilayer system: Measure of the entropy of the lamellar–lamellar transition in DDABr

Abstract

The synthetic cationic double-chain surfactant didodecyldimethylammonium bromide shows two distinct thermodynamically stable lamellar phases; a dilute Lα phase stabilized predominantly by electrostatic forces, and a condensed Lα′ phase stabilized by “hydration” forces. Using six different experimental methods, applying osmotic stress from 102 to 109 Pa and varying temperature from 20 °C to 70 °C, we have measured the osmotic pressure vs interbilayer distance and thus mapped the phase diagram with an equation of state. In this binary system, the area per headgroup as well as bilayer thickness vary with concentration and temperature. Hence, lateral compressibility has to be taken into account in the free energy balance. The osmotic stress needed to effect the swollen-to-collapsed lamellar phase transition is determined as a function of temperature. From these data the entropy of the Lα–Lα′ transition is found to be a strong function of temperature. Below 40 °C, condensation from the dilute Lα phase, the change of entropy is negative as might be expected. Above 40 °C the entropy of condensation is positive, demonstrating that there is a release of degrees of freedom associated with the bilayer condensation. These data allow us to think far more critically about the forces that stabilize bilayer systems.