Theoretical relation between domain

For a more complete description of the time and the temperature dependence of the fibre strength a theoretical description of the viscoelastic and plastic tensile behaviour of polymer fibres has been developed. Baltussen (1996) has shown that the yielding phenomenon, the viscoelastic and plastic extension of a polymer fibre can be described by the Eyring reduced time model. This model uses an activated site model for the plastic and viscoelastic shear deformation of adjacent chains in the domain, in which the straining of the intermolecular bonding is now modelled as an activated shear transition between two states, separated by an energy barrier. It provides a relation between the lifetime, the creep load and the temperature of the fibre, which for PpPTA fibres has been confirmed for a range of temperatures (Northolt et al., 2005). 

Some of the coarse-grained parameters, i e and can be easily measured by experiments or in simulations. The other two parameters, %N and the suppression of density fluctuations, XqN, are thermodynamic characteristics, which are not directly related to the structure (i.e., they cannot be simply expressed as a function of the molecular coordinates). If density fluctuations of the polymeric liquid are small on the length scale of interest (e.g., width of an interface between domains), then the value of the compressibility has only a minor relevance and decreasing it even further will not significantly affect the behavior of the system. Thus, field-theoretic calculations often take the idealized limit of strict incompressibility. In particle-based simulations, however, one often softens the constraint in order to facilitate the motion of the interaction centers and, thereby, reduces the viscosity of the polymer liquid. The Flory-Huggins parameter, in turn, is a crucial coarse-grained parameter and different methods have been devised to extract it from experiments or simulations [16, 20-25]. We shall briefly discuss this important issue in Section 5.2.3, and further refer the reader to the literature, where computer simulations have been quantitatively compared with mean field predictions and where the role of fluctuations on the coarse-grained parameters is discussed [16, 22]. 

A rather common feature of subunit contacts is ft sheet hydrogenbonding between strands in opposite subunits. Theoretically the relationship could be a pure translation or a 2-fold screw axis with a one-residue translation (for a pair of parallel strands), but all the known cases of intersubunit /3 sheet bonding turn out to be between equivalent strands related by a local 2-fold axis. For hydrogen-bond formation, the 2-fold must be perpendicular to the /3 sheet, requiring the two equivalent strands to be antiparallel. Those may be the only two /3 strands (as in insulin, Fig. 63), or they may be part of antiparallel P sheets (as in prealbumin, Fig. 62), or the rest of the sheets may be parallel (as in alcohol dehydrogenase domain 1). 

At the mesoscopic scale, interactions between molecular components in membranes and catalyst layers control the self-organization into nanophase-segregated media, structural correlations, and adhesion properties of phase domains. Such complex processes can be studied by various theoretical tools and simulation techniques (e.g., by coarse-grained molecular dynamics simulations). Complex morphologies of the emerging media can be related to effective physicochemical properties that characterize transport and reaction at the macroscopic scale, using concepts from the theory of random heterogeneous media and percolation theory. 

The fundamental aspects related to the thermochemistry, structure and reactivity of gas-phase ions are usually considered the domain of gas-phase ion chemistry. By extension, some of these same properties are often obtained for simple neutrals and radicals from methods used in gas-phase ion chemistry. A wide range of experimental techniques can be used for this purpose, and instrumental developments have contributed a great deal to our knowledge of gas-phase ions. Theoretical calculations have also played an important role and gas-phase ion chemistry has witnessed a very lively interplay between experiment and theory in recent years. 

Preliminary studies of the interphase between respective domains by Van Bogart et al. (53) indicate the thickness of this region, assuming a linear density gradient, is on the order of 10-20 A for polyester and polyether urethanes (MDI-BD based). Theoretically, the interfacial thickness is inversely related to the square root of the hard segment-soft segment interaction parameter (54). 

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