We investigated the oriented overgrowth of a series of diacetylene molecules by epitaxy on a single crystal of potassium acid phthalate (KAP). By changing the chemical architecture of the deposited molecule, we were able to modify the molecular interactions between the deposited molecule and the crystal surface. Thus we synthesized four new asymmetrical diacetylenes (DA) bearing a carbazolyl group on one side of the diacetylene core and a urethane at the end of a flexible spacer on the other side Of the DA moiety. The different conditions of the film growth under high vacuum were implemented by a systematic investigation of the different kinetic parameters acting on the molecule arrangement at the crystal surface, such as the monomer evaporation rate or the substrate temperature. The morphology and the structure of the films were studied by atomic force microscopy (AFM) imaging and transmission electron microscopy (TEM) and compared to the morphologies of the bis(carbazolyl) derivative {poly[1,6-bis(9-carbazolyl)-2,4-hexadiyne], abbreviated pDCH}. We found, for the monosubstituted carbazolyl derivative {poly[9-(9-carbazolyl)-5,7-nonadiyn-1-ol ethylurethane], abbreviated (pCNEU)}, that the molecular interactions leading to epitaxy were of several types on the (010) plane of KAP. First, a pi-pi type interaction induced one prevailing position of the DA molecules (the aromatic sides of the carbazolyl substituent were inserted between phenyl rows of KAP stacked along c). Second, another geometrical interaction induced two secondary positions of the DA molecules (the flexible moiety lying in shallow ditches lined along the (101) directions of KAP). Related to the thin film morphologies, the static optical spectroscopies were also investigated and discussed. Improvements in orientational order were observed on pCNEU as on pDCH at slow evaporation rates and on heating the crystal substrate in the temperature range 50-100 degrees C.