A new algorithm for finding vertex functions in the Landau theory of phase transitions in heteropolymer liquids

The phenomenological Landau theory of phase transitions can be employed for the description of the thermodynamic behavior of an equilibrium system, provided the coefficients of the expansion of the Landau free energy of this system in powers of the order parameters are known. These coefficients, referred to as the vertex functions, under the consideration of spatially periodic mesophases, depend on the momenta. An algorithm for finding the vertex function for any term of the Landau free energy expansion is introduced. This algorithm provides a possibility to obtain the explicit expressions for the vertex functions describing a compressible melt of polydisperse multiblock copolymer composed of any number of types of blocks with arbitrary distributions for lengths. Under theoretical consideration of block copolymers, the solution of the problem of finding of the vertex functions in such a general formulation has not been reported in literature so far.