Thermopermeation in bicontinuous lyotropic crystals

Abstract

In 1982, P. G. de Gennes wrote two articles on two apparently disjoined subjects: (1) the Ludwig–Soret effect in porous media filled with pure liquids and (2) bicontinuous structures in microemulsions. In the study of bicontinuous cubic lyotropic crystals subjected to temperature gradients which we present here, these two subjects are now intimately related. Our experiments consist of the observation, by means of an optical microscope, of crystal shapes in three types of phase coexistence: Ia3d-in-vapour, Pn3m-in-L1 and Im3m-in-L1. In all three cases, we infer from changes in the crystal shapes that the surfactant is transferred, along the unique periodic bilayer, from the warm to the cold extremities of crystals. In order to explain this phenomenon of ‘thermopermeation’ of the surfactant, inspired by de Gennes we assume that: (1) the periodic bilayer acts as a viscoelastic matrix and (2) a slip occurs at the surfactant/water interface.

Keywords:

• Ludwig–Soret effect
• bicontinuous lyotropic crystals
• crystal shapes

Acknowledgements

This study of thermopermeation in lyotropic liquid crystal was exceptionally long (about 10 years) and as such it involved numerous collaborations, first of all, with students who worked with me specifically on other topics: C. Even, D. Rohe, L. Sittler, M. Bouchih, N. Ginestet, S. Popa-Nita, T. Plötzing, J. Grenier, S. Leroy, J. Okal, P. Faye, R. Sheska, G. Saquet and J. Rizzi. Throughout this work, I also benefitted from interactions with experts in related topics. In particular, I had illuminating discussions with Paul Sotta, Vittorio Luzzati, Gregoire Porte and Christophe Blanc on the nature of bicontinuous phases and with Antonio Figueiredo Neto, Simone Wiegand, Roberto Piazza, Werner Köhler and Alois Würger on the Ludwig–Soret and related effects. I am also indebted for technical assistance to V. Klein, S. Saranga, D. Brunello, P.-J. Leroux, J.-L. Signoret, F. Quenault, J.-P. Dalac, Ch. Millien and C. Gendreau. This work was realised partially thanks to the financial support from BQR ‘Étude physique des gouttes ou des films de cristaux liquides lyotropes placés sous humidité contrôlée’.

Last but not least, I would like to express my gratitude to P. G. de Gennes who always manifested his interest for my work and encouraged me to take the roads “less travelled by”.

Note added in proof: After submission of this article the author has learnt that Reynolds ( 46 ) discovered thermophilic behaviour of gases in porous materials which has been termed “thermal transpiration” and this effect has been explained by Maxwell ( 47 ).