Architecture, nonlinear

Polymers without configurational regularity are called atactic. Configurationally regular polymers can fonn crystalline stmctures, while atactic polymers are almost always amorjihous. Many polymers consist of linear molecules, however, nonlinear chain architectures are also important (figure C2.1.2). 

Figure C2.1.2. Polymers witli linear and nonlinear chain architectures. The nonlinear polymers can have branched chains. Short chains of oligomers can be grafted to tire main chain. The chains may fonn a. stor-like stmcture. The chains can be cross-linked and fonn a network.

However, dendrimeric and hyperbranched polyesters are more soluble than the linear ones (respectively 1.05, 0.70, and 0.02 g/mL in acetone). The solution behavior has been investigated, and in the case of aromatic hyperbranched polyesters,84 a very low a-value of the Mark-Houvink-Sakurada equation 0/ = KMa) and low intrinsic viscosity were observed. Frechet presented a description of the intrinsic viscosity as a function of the molar mass85 for different architectures The hyperbranched macromolecules show a nonlinear variation for low molecular weight and a bell-shaped curve is observed in the case of dendrimers (Fig. 5.18). 

The architecture of macromolecules is another important synthetic variable. New materials with controlled branching sequences or stereoregularity provide tremendous opportunity for development. New polymerization catalysts and initiators for controlled free-radical polymerization are driving many new materials design, synthesis, and production capabilities. Combined with state-of-the-art characterization by probe microscopy, radiation scattering, and spectroscopy, the field of polymer science is poised for explosive development of novel and important materials. New classes of nonlinear structured polymeric materials have been invented, such as dendrimers. These structures have regularly spaced branch points beginning from a central point—like branches from a tree trunk. New struc-... 

The MINLP-model instances comprised 200 binary variables, 588 continuous variables and 1038 constraints. The linearization not only eliminates the nonlinearity but also leads to a reduced number of398 continuous variables and 830 constraints (the number of 200 binary variables is unchanged). The MINLP-problems were solved by the solver architecture DICOPT/CONOPT/CPLEX, and the MILP problems were solved by CP LEX, both on a Windows machine with an Intel Xeon 3 GHz CPU and 4 GB RAM. 

The chemistry of metal complexes featuring alkyne and alkynyl (acetylide) ligands has been an area of immense interest for decades. Even the simplest examples of these, the mononuclear metal acetylide complexes L MC=CR, are now so numerous and the extent of their reaction chemistry is so diverse as to defy efforts at a comprehensive review. " The utility of these complexes is well documented. Some metal alkynyl complexes have been used as intermediates in preparative organic chemistry and together with derived polymeric materials, many have useful physical properties including liquid crystallinity and nonlinear optical behaviour. The structural properties of the M—C=C moiety have been used in the construction of remarkable supramolecular architectures based upon squares, boxes, and other geometries. ... 

Nord and Jacobsson [97] proposed several approaches to interpret ANN models. The results were compared with those derived from a PLS regression model where the contributions of variables were studied. Notably, they employed simple architectures composed of a unique hidden layer. They discovered that the variable contribution term in ANN models is similar to that in PLS models for linear relationships, although this may not be the case for nonlinear relations. In such cases, the proposed algorithms can give additional information about the models. 

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