PROPERTIES OF POLYURETHANES
Modern understanding of polyurethane structure-property relationships is conventionally first associated with the work of Cooper and Tabolsky in 1966 . Their recognition that modulus values of TPU could not be modeled using standard equations for filler reinforcement led to detailed understanding of these materials. Greater theoretical insight awaited further experimental progress. Koberstein and Stein  suggested that phase separation of a reactive block copolymer system such as polyurethane occurs only after the attainment of a critical hard segment length (or average number of repeat units). Consistent with the conclusion of Cooper and Tablosky, they ruled out a random two-phase morphology on the basis of their X-ray scattering curves. They estimated a critical hard segment length of between 2 and 3 depending on numerous hard segment and processing factors. Subsequent work by Ryan et al.  suggested a minimum critical length slightly lower than this.
With experimental description of the polyurethane structure at many length scales, and theoretical formalisms of polymer superstructure from block-copolymer theories, composite models were developed that could account for the properties of polyurethane foams and elastomers. Block copolymer theory (see Section 4.1) had suggested that block copolymers could arrange themselves into spherical, cylindrical, lamellar, and gyroid structures, for instance, and various microscopy techniques were enlisted to detect morphologies that were forming during reactive polyurethane processing. In fact many block copolymer structures that can be observed have indeed been observed in polyurethanes. Spherical (Fig. 4.8), cylindrical (Fig. 4.4), and lamellar (Fig. 4.5) morphologies have been observed by the author and others [15, 30]. Gyroidlike morphologies are also observable (see Fig. 5.9). What has not been observed is ordered packing of the hard segment phases such as is observed in ideal block copolymers. Thus cyclindrical hard segment phases can be observed, but hexagonal packing of those cylinders for instance is not.
Regardless of the phase separation temperature or molecular weight, the calculation of properties based for a specific structure are significantly affected by the assumptions made in the composite model. Simple equations can result from sophisticated analyses and subtle assumptions.