Soft Condensed Matter

Paired defects in bilayer membranes with nematic monolayers

Ordinary membranes are self-assembled bilayers of surfactants, or lipids, which form a fluid flexible surface. The polar heads of the molecules, when seen from above, appear as an isotropic two-dimensional fluid.

Since both nature and chemists know how to attach several lipids together in order to build surfactants with elongated polar heads (gemini surfactants, natural cardiolipins, surfactants to come...), we have studied the potential properties of exotic membranes such as that depicted in Fig. 1. Several facts indicate that similar systems may already exist (Candau et al., 1998).

Figure 1: A hypothetical membrane with two nematic monolayers.
\begin{figure} \centerline{\epsfxsize=8cm\epsfbox{memnem.eps}}\end{figure}

We have studied in particular the effect of a weak coupling between the two nematic fields in the planar geometry of the nematic bilayer. There are interesting consequences on the nature the nematic disclination defects, as illustrated in Fig. 2. Along most of the sample the nematic director in both layers has the same direction. Defects appear as mismatch lines, which start and end at disclinations. Quite interestingly, the presence of a disclination in one layer can force the appearance of a "virtual disclination" in the other layer. This results in a number of interesting recombining rules.

Figure 2: (a) Two interacting strength +1 defects, one in each monolayer. They are joined by two adjacent $\pi /2$ walls (b). Walls have recombining rules (c).
\begin{figure} \centerline{\epsfxsize=9cm\epsfbox{bidefects.eps}}\end{figure}



J.-B. Fournier and L. Peliti. Phys. Rev. E 58, R6919 (1998).

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