Domains in certain Langmuir monolayers support a texture that is the two-dimensional version of the feature known as a boojum. Such a texture has a quantifiable effect on the shape of the domain with which it is associated. The most noticeable consequence is a cusplike feature on the domain boundary. We report the results of an experimental and theoretical investigation of the shape of a domain in a Langmuir monolayer. A further aspect of the investigation is the study of the shape of a ''bubble'' of gaslike phase in such a monolayer. This structure supports a texture having the form of an inverse boojum. The distortion of a bubble resulting from this texture is also studied. The correspondence between theory and experiment, while not perfect, indicates that a qualitative understanding of the relationship between textures and domain shapes has been achieved. ͓S1063-651X͑97͒06407-6͔ PACS number͑s͒: 68.15.ϩe, 68.55.Ln, 68.18.ϩp, 68.60.Ϫp FIG. 1. ͑a͒ Excluded angle ⌿ plotted as a function of 1/R. ͑b͒ Definition of the excluded angle ⌿.

The surface pressure-temperature diagram of Langmuir monolayers of mixtures of heneicosanoic acid with heneicosanol has been determined from 10 °C to 40 °C by direct observation with Brewster angle microscopy. The measurements focused on the way in which the boundary between the L′2 and L2 phases change with composition. As previously observed by Shih et al. [J. Chem. Phys. 101, 9132 (1994)], it moves to lower pressure and higher temperature with increasing concentration of alcohol. We have discovered that the boundary between the Ov and L2 phases, which had not been studied before, moves in the opposite direction and that the L′2 and Ov phase regions merge, an unanticipated result.

Surface pressure-temperature phase diagrams have been determined by Brewster-angle microscopy for Langmuir monolayers of heneicosanoic acid with the esters methyl and ethyl heneicosanoate and octadecanoic acid with methyl, ethyl, and propyl octadecanoate. The behavior is similar to that found previously in mixtures of an acid and an alcohol. In each case with increasing ester concentration the L 2 /L 2 Ј phase boundary moves toward lower pressure and higher temperature while the L 2 /Ov boundary moves toward lower pressure and lower temperature. The L 2 Ј and Ov phases eventually merge and the boundary with the L 2 phase moves to zero pressure. The phase diagram of eicosyl acetate is similar to that of the fatty acids. We attribute the variations in the diagrams to the extent of hydrogen bonding between the head group and the subphase.

To examine the relative stability of monolayer phases with nearest-neighbor (NN) and next-nearest-neighbor (NNN) tilt directions, we have performed grazing incidence X-ray diffraction and Brewster-angle microscopy studies on mixtures of hexadecanoic acid with methyl n-hexadecanoate. We have determined how the boundary between the L2 (NN) and Ov (NNN) phases change with composition. Beyond a mole fraction of ester x = 0.70, the boundary moves sharply toward lower temperature with increasing concentration of the ester, and eventually the only tilted mesophase remaining has NN tilt. This is in contrast to many other esters that have been studied for which there is only a NNN mesophase. It is argued that the stability of the NN phase is the result of disorder in the chain ends of the amphiphile.

Grazing incidence x-ray diffraction and Brewster-angle microscopy measurements have been undertaken for a mixed Langmuir monolayer of octadecanoic acid and methyl octadecanoate. For the composition studied (49.7 mol % ester) there are two noncrystalline tilted phases, one at low pressure in which the chains point to their nearest neighbors (L2 phase) and a higher-pressure phase in which the tilt is toward next-nearest neighbors. The higher-pressure phase arises from a merger of the L2′ and Ov phases, which are separated in the pure acid. A continuous change between the two regions is observed rather than a first-order transition, as had been suggested. The results are discussed with reference to different proposals for the origin of two distinct next-nearest neighbor tilted mesophases: the presence of one-dimensional chain backbone order [V. M. Kaganer and E. B. Loginov, Phys. Rev. E 51, 2237 (1995)] and a coupling between tilt and distortion [E. Sirota, Langmuir 13, 3849 (1997)].