“…For the mesophases studied in a planar orientation with the columns subjected to a normal dilation, we can predict the undulation instability of columns by minimizing the elastic free energy, by taking into account the symmetry of the arrangement of the columns in a hexagonal network. Thus, with previous calculations that describe the undulations of the smectic layers and of the columns in the columnar–hexagonal mesophases,11, 16, 21, 26, 27 we derive Equations (1–3), , , where m, K 3 , B , δ c , and λ are, respectively, the De Gennes characteristic length, the curvature elastic constant, the elastic modulus, the threshold dilation, and the curvature wavelength. $\rm{{\it m}\,=\,\left({{{\it K}_{3}} \over {{\it B}}}\right)1/2}$ δ c = 2π m λ 2 = 4π md …”