Three-dimensional visualization and physical properties of dendrites in thin samples of a hexagonal columnar liquid crystal

Using the optical birefringence of the hexagonal columnar mesophase of the hexaoctyloxytriphenylene, we show that two types of stationary dendrites exist in thin samples, depending on the ratio of the diffusion length ℓd over the sample thickness d. Either ℓd/d>50 and the dendrites are “ 2D ” and fill the whole sample thickness, or ℓd/d < 10 and they are “ 3D ” and separated from the limiting surfaces by a film of isotropic liquid. The 2D-dendrites satisfy the Ivantsov relation and have a stability constant σ*2D ≈0.041 independent of the sample thickness. By contrast and surprisingly, when their velocity is large enough (ℓd/d < 1), the 3D-dendrites have an apparent stability constant σ*3D ≈0.005 independent of the thickness even if they do not verify the Ivantsov relation.