Employing our free-standing film calorimetric system, we have identifi
ed three remarkable layer-by-layer transitions in several liquid-cryst
al compounds. Each of these transitions can be well described by the s
imple power-law form: L=L(0)t(-nu). The layering transitions found nea
r the smectic-A-hexatic-B and smectic-A-crystal-B transitions are well
characterized by the exponent nu approximate to 1/3. This value is co
nsistent with models based on a van der Waals-like dominant intermolec
ular interaction. Another novel layer-by-layer thinning transition has
been discovered above the bulk smectic-A-isotropic transition of a pe
rfluorinated liquid-crystal compound. The value of the exponent obtain
ed, nu approximate to 3/4, cannot be easily explained using familiar m
odels.