Vertex functions in the Landau theory of phase transitions in melts of Markovian multiblock copolymers

A modified diagram technique has been developed for obtaining the vertex functions of the Landau free energy of the melt of an m-component linear stochastic multiblock copolymer whose macromolecules are of arbitrary architecture. The derivation of the expressions for the vertex functions by means of this diagram technique for block copolymers with molecular structure distribution described by the Markov chain is considered in detail. Expressions for all contributions to the free energy up to the fourth order and local contributions of the fifth and sixth orders have been found for the first time for the compressible melt of this copolymer. As to nonlocal contributions of these orders, the expressions for the most singular of them have been obtained for the incompressible melt of m-component Markovian copolymers. Some considerations have been made concerning the appearance of the nonlocal contributions of an arbitrary order.