The phase behavior of a melt of two-scale multiblock copolymers has been theoretically studied in the framework of the Weak Segregation Limit theory with a twocomponent order parameter. The existence of a thermodynamically stable mesophase with two scales of the space periodicity has been revealed for a melt of monodisperse nonperiodic heteropolymers. For the first time a discontinuous change with temperature of the spatial period of the mesophases has been predicted.

An original diagrammatic technique is advanced for calculating, in the first-harmonic approximation of the Weak Segregation Limit theory, the coefficients of the amplitude expansion of the Landau free energy for a melt of a binary incompressible heteropolymer comprising linear macromolecules with arbitrary chemical structure. A universal approach to the calculation of these coefficients for heteropolymer liquids describable using the Landau theory of phase transitions with a two-component order parameter is put forward for the first time. This approach proves to be particularly efficient in a theoretical consideration of the thermodynamic behaviour of multiblock copolymers whose macromolecules contain blocks of two types substantially differing in length. A general algorithm for finding the coefficients of the amplitude expansion of the Landau free energy in such systems is formulated for a number of mesophases showing two characteristic scales of spatial periodicity. The application of this algorithm is exemplified by considering a deformed hexagonally perforated lamellar mesophase.

Abstract:The phase behavior of a melt of periodic two-scale multiblock copolymers has been theoretically studied in the framework of the Weak-Segregation Limit theory. The effect of the structural symmetry of the macromolecules on the vertex functions of the Landau free energy expansion is considered in detail. The existence of a thermodynamically stable mesophase with a two length-scale space periodicity has been revealed for a melt of monodisperse periodic heteropolymers.

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.