A 2-dimensional, linear-splay elastic constant K1 is evidenced in ultrathin prefreezing (and prewetting) films of a tilted smectic liquid crystal (MHTAC). Though small, ∼ −1×10 −11 Jm −1 , K1 may produce visible effects in quasi-2D systems. We show, in particular, that K1 is able to promote a purely elastic instability in the film, corresponding to a continuous rotation of the c director. This instability is characterized by typical patterns of stripes with a 4-fringe periodicity between crossed polarizers, which denote variations of the molecular tilt angle in the splay regions. K1 should also exist in Langmuir and biological films as well.

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The prefrozen films that may be observed at the surface of isotropic liquid crystal droplets, close to the isotropic-smectic phase transition, or surface-induced films, are essentially asymmetric. If moreover, the molecules are tilted inside the smectic layers, as in the smectic-C (SmC) or smectic-C(A) (SmC(A)) phases, the c director that we may define as the order parameter of the film, is a real vector. Thus, the surface-induced films of MHTAC exhibit vectorial or polar properties, though the molecules are not chiral. The film free energy therefore contains a surface-elasticity term, K(1)c(2) c, that is a linear function of the splay distortion, and that may be negative enough to promote a mechanical instability. A spontaneous c distortion, or c modulation, then invades the whole film and produces an array of parallel stripes, with a typical four-fringe periodicity when observed between crossed polarisers. Here, we present optical measurements of the distortion for different film thicknesses, and we propose a linear analysis of the data to test our model. Due to the limitations inherent to the Fourier expansion that we use, the calculations are valid only between two limits: a large q limit where splay domains collapse into disclination lines, and a small q borderline below which the distortion evolves towards a system of independent solitons. We find that the sign of the spontaneous splay elastic constant K1 alternates as a function of the number of layers, N, a property that is reminiscent of the alternate structure of the SmC(A) phase. We argue that the two-dimension elastic constant, K1, originates from the interactions between the molecules in contact to the isotropic phase, and we deduce K1 approximately -(-1)(N)x10(-11) N and the elastic anisotropy, with a ratio of the splay over bend elastic constants K(s)/K(b) approximately 4.5. Similar properties could be observed also in other types of ultrathin films, e.g., in free-standing, ferroelectric (SmC*) or antiferroelectric (SmC(*)(A)), films, in Langmuir films, and even in particular biological films. In some cases, a second, electric instability may occur and superimpose onto the elastic one.

A texture of circular concentric disclination walls is produced in a smectic C* free standing film on applying an in-plane ac electric field. Intensity light profiles taken in the radial section of the circular walls allows us to evidence modulations of the tilt of the molecules. These molecular tilt angle modulations are due to , a new elastic term K*c2(rotc).N in the free energy. We deduce the linear bend constant K , which originate from the chiral property of the system. We find K*/b -2.5 pm.

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