Random coil, macromolecules modeled

In the model presented by Hammond, the HS, tied together by a polydiacetylene backbone, are oriented laterally in lameUar-like hard domains oriented in random directions before stress is applied, and possibly forming spherulitic type superstructures. The SS are randomly coiled macromolecules spaced between the hard domains. At low moderate strains, when the material is stretched, stress is transferred to the hard domains. The HS orient perpendicular to the stress direction. Upon removal of the stress, the SS relaxation allows the hard domains to return in a random orientation. This results in a small residual hard domain orientation. Therefore, the two-phase microstructure of the material is not highly interconnected. It consists of discontinuous hard domains dispersed throughout a continuous SS phase [364]. 

The above model does not change the generally accepted views on the shape of a macromolecule in solution, but only gives a more detailed picture of the macromolecules single sections which have a spiraled, and not a randomly coiled, conformation. 

Fig. 1. Various conformation models for macromolecules adsorbed on an interface, a) chain lying totally on the interface b) loop-train conformation c) loop-train-tail conformation d) adsorbed at one chain end e) random coil adsorbed at a single point f) rod-like macromolecules adsorbed at one end g) rod-like macromolecules adsorbed located totally on an interface...

As discussed earlier, solid polymers can be distinguished into amorphous and the semicrystalline categories. Amorphous solid polymers are either in the glassy state, or - with chain cross linking - in the rubbery state. The usual model of the macromolecule in the amorphous state is the "random coil". Also in polymer melts the "random coil" is the usual model. The fact, however, that melts of semi-crystalline molecules, although very viscous, show rapid crystallisation when cooled, might be an indication that the conformation of a polymer molecule in such a melt is more nearly an irregularly folded molecule than it is a completely random coil. 

In this Section, the general characteristics of the conformation of a polymer molecule in solution are considered. The general model for a linear polymer molecule in solution is based on a randomly coiled, flexible chain, the average form of which possesses spherical symmetry. The distribution of chain ends about the center of this sphere is further supposed to be Gaussian. Since the total number of conformations which the macromolecule may adopt is exceedingly large, only an average dimension can... 

The summary of dimensions at the bottom of Fig. 1.33 demonstrates the effects of the various restrictions on the model compound. The random flight model gives for polyethylene already an answer within a factor of about 2.5. Comparison with the experiment is possible by analyzing the dimensions of a macromolecule in solution, as will be discussed in Chap. 7. One can visualize a solution by filling the vacuum of a random flight of the present discussion with the solvent molecules. The 0-temperature listed as condition for the experiment is the temperatme at which the expansion of the molecule due to the excluded volume is compensated by compression due to rejection of the solvent out of the random coil. This compensation of an excluded volume is similar to the Boyle-temperature of a real gas as illustrated in... 

The x-ray patterns of natural rubber in the relaxed and extended states led J.R. Katz and others to develop a random coil model for polymer chains. The "Katz Effect" which was repeated by H. Mark helped to establish a relationship between mechanical deformation and concomitant molecular events in all macromolecules. 

The existence of dilute solutions of macromolecules was denied by many experts until the macromolecular hypothesis was largely accepted in the time period from 1930 to 1940. The dilute-solution state is still the basis for characterizing individual macromolecules and the interactions of pairs of macromolecules and the solvent. The structural, thermodynamic, and hydro-dynamic properties of polymer solutions are explained in terms of the random-coil model developed by Kuhn, Debye, Flory, Kirkwood, Yamakawa, and deGennes. While this subject alone could easily be the basis for a one-semester course, the topics are developed so that the material could be presented as part of a complete development of the subject. 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

Fig. II. The Baranov-Frenkel-Lobanov-Ueberreiter two-dimensional model for the segment-s ment contact origin of as visualized by us in Fig. 9 of lef. 1. Polymer chains are shown for convenience as segments of random coils. Three chains are indicated as macromolecules, mm-1, mm-2, and mm-n. They can associate with other segments in their own chains as well as the three interactions depicted, and also with other macnmudecuies not shown, all in three dimensions.

Lindenmeyer does not illustrate his chain folded model but we assume it to be similar to that of Privalko and Lipatov, Fig. 14, and of Yehl°Ll02 shown in Figure 15. Lindenmeyer did quantify his model by estimating that one folded macromolecule would interact with at most 5-10 other macromolecules instead of 50-100 other macromolecules as in the random coil situation. 

Completely statistical (random) arrangements of the macromolecules without a regular order or orientation, i.e., without constant distances, are known as amorphous states. There is no long-range order whatsoever. The valid model for such states is the statistical coil. This is the dominating secondary structure in synthetic polymers and polymeric solutions. Its determinant parameter is coil density. 

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