Response of Soft Continuous Structures and Topological Defects to a Temperature Gradient

Thermophoresis, which is mass transport induced by a temperature gradient, has recently attracted considerable attention as a new way to transport materials. So far the study has been focused on the transport of discrete structures such as colloidal particles, proteins, and polymers in solutions. However, the response of soft continuous structures such as membranes and gels to a temperature gradient has been largely unexplored. Here we study the behavior of a lamellar phase made of stacked surfactant bilayer membranes under a temperature gradient. We find the migration of membranes towards a low-temperature region, causing the increase in the degree of membrane undulation fluctuations towards that direction. This is contrary to our intuition that the fluctuations are weaker at a lower temperature. We show that this can be explained by temperature-gradient-induced migration of membranes under the topological constraint coming from the connectivity of each membrane. We also reveal that the pattern of an edge dislocation array formed in a wedge-shaped cell can be controlled by a temperature gradient. These findings suggest that application of a temperature gradient provides a novel way to control the organization of soft continuous structures such as membranes, gels, and foams, in a manner essentially different from the other types of fields, and to manipulate topological defects.