Random copolymer FH theory

An additional dependence on the copolymer compositions x and y beyond that predicted by simple random copolymer FH theory appears in Eq. 24b through the front conversion factor C/S1S2 as well as through factors of 51/52 and 52/51. The main novel feature of Eq. 24b, however, lies in the presence of the temperature-independent portion of xsans. This term represents the influence of monomer structural asymmetry on the nonrandom chain packing and coincides with the leading contribution of the LCT for binary blends in the incompressible, high molecular weight, athermal, fully flexible chain limit. 

As illustrated in the next subsections, the BLCT has successfully been applied to a wide variety of copolymer blends whose thermodynamics cannot be described by random copolymer FH theory. While both theories share the inability to distinguish between random, diblock, or alternating copolymers of the same composition, the sensitivity of computed thermodynamic properties to the detailed monomer molecular structure of the blend components makes the BLCT a much more powerful theoretical tool than random copolymer FH theory. The relative simplicity of Eq. 24b and the readily computed entropic factors n and ri render the BLCT useful for interpreting thermodynamic data and for generating new predictions. 

The observation by Delfohe et al. [96] that the miscibility of norbornene-co-ethylene (NxEi-x/NyEi- ) binary copolymer blends improves significantly when both components are rich in norbornene, i.e., when x > 1/2 andy > 1/2, stands in sharp contrast to the predictions (Eq. 27) of random copolymer FH theory [88], which imphes that the blends are miscible when the composition difference x-y is less than a critical constant value. The general theory of Sect. 8.1 that has been used to explain this observation is described elsewhere in some detail [96]. Here we summarize the main results of this theoretical analysis to illustrate some computational aspects of the BECT. 

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