From molecular flexibility to shape, curvature and thermotropic transitions in pure surfaces

A material surface of pure constituents with a flexible molecular chain (amphiphilics) is considered; thermodynamic behaviour is studied in the chain length-temperature plane. The Hamiltonian of the system is modelled as the sum of a formation term which refers to the polymer nature of the chain, and of a fluctuation term with a specific elastic form. For closed systems the model exhibits phases with uniform curvature and conformational order/disorder or, alternatively, modulated phases; a critical chain length is found for the existence of modulated phases; the dependence of transition temperature on energy parameters is determined. A critical region is found for open systems, where conformational disorder drives spontaneous generation of curvature; this lies above a characteristic chain length and around the shape transition temperature.