Domain formation theories

Meier D.J., Theory of block copolymers Domain formation in A-B block copolymers, J. Polym. Sci., Part C, 26, 81, 1969. 

Dale Meier has been one of the firsts if not the first who presented a theory of domain formation in block copolymers39. In its original version39, Meier s theory was restricted to AB block copolymers and spherical domains. In a series of following papers40-45, however, Meier has refined his theory considering different shapes of domains, the effect of the presence of a solvent, the dimensions of the interface, the interfacial properties of block copolymers and the solubilization of homopolymers by copolymers. 

A number of statistical thermodynamic theories for the domain formation in block and graft copolymers have been formulated on the basis of this idea. The pioneering work in this area was done by Meier (43). In his original work, however, he assumed that the boundary between the two phases is sharp. Leary and Williams (43,44) were the first to recognize that the interphase must be diffuse and has finite thickness. Kawai and co-workers (31) treated the problem from the point of view of micelle formation. As the solvent evaporates from a block copolymer solution, a critical micelle concentration is reached. At this point, the domains are formed and are assumed to undergo no further change with continued solvent evaporation. Minimum free energies for an AB-type block copolymer were computed this way. 

A number of polymeric systems exhibit domain formation. This results in some polymeric material being confined in regions between the domains. The deformation properties of these systems depend on the types of polymer chains lying between the domains, as well as on the shape and spatial arrangement of the domains. Several theories have been proposed to date for the contribution of the interdomain material to different deformation properties in semicrystalline polymers and block copolymers. We will present and analyze these theories herein. 

A somewhat more sophisticated approach to domain formation and fine structure was taken by Meier (1969,1970). As with Inoue et al. (1970a,f ) and Krause (1969,1970,1971), the A-B junction was restricted to a location somewhere in the interfacial region. Meier s model (Figure 4.11) assumes that random flight statistics and regular solution theory hold, that statistical chain segments (not block lengths) are of equal size, and that chain perturbation is characterized by the usual parameter a ... 

The characteristic feature of block copolymers in the solid state is their microphase separated structure, with domains of the minor component dispersed in a matrix of the major component Domain symmetry is chiefly determined by copolymer composition, however, the route to the solid state (i.e. melt prepared or solvent cast) may influence this factor. The major aim of recent small angle scattering experiments on block copolymers has been the investigation of current statistical thermodynamic theories of domain formation. In this respect, it should also be noted that small angle X-ray scattering has been used to investigate block copolymers, the work of Hashimoto et al. being particularly noteworthy. 

An exhaustive, critical review of the status concerning current statistical thermodynamic analysis of block copolymer domain formation will not be presented here. A precis only of the major theories is given and the predictions from each noted, fuller details are available in the original publications. Furthermore, whilst the earlier theories of Meierand Williams " were important in stimulating interest and defining the questions to be addressed, they are not considered here since the more recent ideas encompass all the features of the earlier theories. 

Domain Formation and Interfaces in Praseodymium and Terbium Oxides Obtained by Reduction of Pr02 and Tb02 A Comparison with Group Theory Predictions, C. Boulesteix and L. Eyring, J. Solid State Chem., 66, 125-135 (1987). 

In this article, the analysis of microdomain and do-main-boundary structures of amorphous block copolymers is first investigated by means of small angle X-ray scattering and electron microscopy. The structures, especially for alternating lamellar microdomains of a series of A-B type block copolymers of styrene and isoprene, are discussed in comparison with those predicted from the current theories of domain formation by Meier and Helfand-... 

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