Role of dislocation loops on the elastic constants of lyotropic lamellar phases

We study the role of dislocation loops defects on the elasticity of lamellar phases by investigating the variation of the lamellar elastic constants, ¯ and K, induced by the proliferation of these defects. We focus our interest on one particular lamellar phase made up of a mixture of C12E5 and DMPC in water, which is already well-characterised. This lamellar phase undergoes a second-order (or weakly first-order) lamellar-to-nematic phase transition at about 19°C and dislocation loops are seen to proliferate within the lamellar structure when temperature is decreased below 30°C. The values of both elastic constants of this given lamellar phase are measured as a function of temperature, approaching the lamellar-to-nematic transition, with the help of Quasi-Elastic Light Scattering (QELS) on oriented lamellar phases. Very surprisingly we observe a strong and rapid increase in both ¯ and K as the lamellar-to-nematic transition temperature is approached. These increases are seen to start as soon as dislocation loops can be observed in the lamellar phase. We interpret our results as being the consequence of the appearance and proliferation of dislocation loops within the lamellar structure. According to a simple model we developped we show that ¯ and K are proportional to the density of dislocation loops in the lamellar phase.