Swelling Kinetics of Layered Structures: Triblock Copolymer Mesogels

We consider the swelling kinetics of layered structures. We focus on the case of triblock copolymer mesogels, although our results are applicable to other layered structures including clays. We assume the mesogels are swollen by a solvent that is good for the bridging block but poor for the non-bridging block. At long times the penetration front moves as in ordinary diffusion, i.e., as $t^{1/2}$. At short times, however, the bending elasticity of the non-bridging layers becomes important. This bending elasticity leads to a $t^{1/6}$ relaxation of the penetration front at early times. The crossover length between these two regimes is approximately the width of a single layer. However, for a large number of lamellae there is a cooperative effect which leads to a large enhancement of this crossover length.