Domain theories

In the case of the polycrystalline polyester thermoplastic rubbers the simple domain theory does not seem to apply. With these rubbers it would appear that they contain spherulitic structures consisting of 4GT radial lamellae with inter-radial amorphous regions that are mixtures of PTMEG soft segments and noncrystalline hard segments. 

Domain theory. A set of rules and facts to be used in explaining how the training example is an example of the target concept. 

The domain theory consists of the horn clauses that represent... 

The way we have stated the domain theory for the state-space representation has enabled us to avoid making explicit reference to the alphabet symbol properties. However, if in other formulations we need to refer to these properties, we would again use a recursive parsing of the list of symbols to enable generalization over the size of the alphabet. 

Analysis of behavior in single pores is certainly an excellent place to start an understanding of adsorption hysteresis. On the other hand, real porous materials eu e in most cases not simply described in terms of single pore behavior. At the very least a distribution of pores of different sizes should be contemplated. The first analysis of hysteresis loops using a theory of adsorption in single pores together with a pore size distribution was the independent domain theory of Everett and coworkers (Everett, 1967). The most sophisticated application of this kind of approach was made by Ball and Evans (1989) who used density functional theory for adsorption in a distribution of cylindrical pores and compared the hysteresis loops obtained with those for xenon adsorbed in Vycor glass. 

Larson, R.G. Doi, M. Mesoscopic domain theory for textured liquid-crystalline polymers. J. Rheol. 1991, 35 (4), 539-563. 

The role of domain theory is mainly placed in facilitating the identification, elicitation, and formalization of domain knowledge. Furthermore, concepts for supporting experience reuse were developed, based on similarity mappings and classifications. 

A completely fresh and different approach to polymer solutions is being studied in at least two places under the auspices of the Paint Research Institute. Some years ago, Prausnitz (25) reported on polymer segment-interaction theory to predict phase separation. This was based on a lead by Wilson (24) who proposed a local volume fraction concept or domain theory for explaining deviations from ideality. More recently, Prausnitz (27) reported on further work involving anomalous viscosities in high solid polymer solutions. High viscosities may occur when solvent mixtures are used which have values near the extreme ends of the solu-... 

We suggest that the S-B-S thermoplastic rubbers and the domain theory have produced a paradigm upon which the block polymer field advanced significantly. In reviewing the technological discovery of the S-B-S thermoplastic rubbers and the virtually simultaneous formation of a theory that enabled us to move rapidly toward commercialization, it was of interest to us to trace a pathway to discovery for the relatively small group concerned with it. We have set forth in Table II some selected events that we believe enabled us to very rapidly understand the physical phenomena and proceed. Table II is, then, not intended in any way to be a comprehensive illustration of the history of block polymers but is rather a discrete list of events leading to the discovery of S-B-S and S-I-S thermoplastic rubbers in our laboratory. 

Shell team—Formal domain theory. S-B-S and S-I-S physical chemistry and rheology. 

At this point, we had the first four of the seven characteristic features of A-B-A thermoplastic elastomers, as shown in the box. That is, we were completely confident that we had a three-block polymer, rubbery behavior with high tensile strength in the unvulcanized state, and also complete solubility. We concluded from these properties that these polymers were two-phase systems. We then generated the essentials of the two-phase, domain theory and visualized the physical structure illustrated schematically in Figure 1. We also visualized applications in footwear, in injection-molded items, and in solution-based adhesives. Positive confirmation of the two-phase structure quickly followed, by detection of two separate glass transition temperatures, as well as observation of the thermoplasticlike reversibility of bulk- and... 

Although we did not publish our domain theory in 1965, it was fairly evident to those acquainted with the historical developments in Table II that the new products were three-block polymers. Researchers in the field very rapidly commenced to use these polymers as models for comparison and as subject for physicochemical studies. Evidence for this may be seen in the work reported by Cooper and Tobolsky (42) in 1966, in which they correlated the behavior of polyester-polyurethane thermoplastic rubbers (Estane products) (37) with those of a Shell S-B-S polymer. They concluded that the presence of segregated hard and soft phases in the Estane... 

Structural and thermodynamical aspects of the phase separation, domain theory, were presented in 1967 to the International Rubber Conference (21) in the United Kingdom and to a symposium (18) at the California Institute of Technology later in the year. Network properties of the A-B-A polymers were also described (18). Following the commercial announcement in 1965 and the meetings in 1967, there was an explosion of requests for samples of S-B-S and S-I-S products. We then prepared laboratory samples and offered these along with detailed molecular characterization data to outside research workers for study. 

For these reasons, we feel that the discovery of A-B-A thermoplastic rubbers and the domain theory gave the block polymer field a paradigm (22) that greatly accelerated research on a worldwide basis. The content as well as the volume of literature support this view (Figure 3). The usefulness of the paradigm was based on the well-characterized block polymers that can be produced from the anionic polymerization system as shown in the box and on the readily understood basics of the domain theory. 

Kittel, C. (1986). Introduction to Solid State Physics, 6th edition. Wiley, New York. Kittel, C. Galt, J. K. (1956). Ferromagnetic domain theory. Solid State Physics, 3, 437-564. 

Larson, R. G., and Doi, M., Mesoscopic domain theory for textures liquid-crystalline polymers,... 

Weiss, Pierre Ernest (1865-1940) was born in Mulhouse in the Alsace region of eastern France. He proposed the domain theory of ferromagnetism in 1907 while he was working at the Polytechnic Institute in Zurich. 

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