A new phenomenon has been unexpectedly discovered in studying transitions between crystal phases A, B, and C of n-alkanoic acids mixed with ordinary glass powder. Post-melting and pre-freezing events have been observed on scanning temperature at atmospheric pressure by means of a DSC calorimeter and on scanning pressure isothermally using a piezothermal apparatus. These phenomena have been interpreted as the melting and freezing of an assembly of Langmuir-Blodgett-like films of alkanoic acids adsorbed on the glass surface. Freezings and meltings could be observed at temperatures 10 to 15 degrees C higher than the conventional melting point or at pressures as much as 500 bar lower than the expected melting pressures. Optical microscopy allowed the phenomenon to be observed. The glass mixtures with lignoceric acid were thoroughly investigated at two different mass fractions. At atmospheric pressure, independent of the acid content, deposition of acid on the glass surface was achieved only at the end of a slow process of adsorption requiring repeated melting and freezing cycles. In the case of a mixture containing a poor quantity of acid, the adsorption process could be controlled by the gradual diminution and disappearance of the melting and freezing peaks of the bulk acid. On the contrary, the adsorption was completed from the first rise of pressure in the case of the piezothermal scans. In addition, both scan types showed the occurrence of new transitions after the completion of surface melting. They have been attributed to the transformation of the surface crystal into liquid-crystal-like structures onto the glass surface. In piezothermal scans, the pressure range within which transitions occurred became wider with increasing temperature.