Rigid solution properties

Our aim is to analyze the solution properties of the variational inequality describing the equilibrium state of the elastic plate. The plate is assumed to have a vertical crack and, simultaneously, to contact with a rigid punch. 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

Other structural variations on the rigid-rod PBZXs have encompassed a variety of changes that affect the backbone geometry. Deviation from 180° para-catenation has been investigated by a number of researchers for improved processability. Solution properties are of particular interest in an effort to determine concentration effects on the ability to form liquid crystalline solutions. Most notable backbone deviations have been the ABPBT, ABPBO and ABPBI systems which are characterized by catenation angles of 162°, 150°, and 150° respectively. They are classified as extended chain systems because of the unrestricted rotation between the repeat units. The polymer backbone can... 

All the flexible polyquinolines are readily soluble in chlorinated hydrocarbons such as methylene chloride and chloroform. Semirigid polyquinolines are soluble in tetrachloroethane or / /-cresol, but rigid polyquinolines are soluble only in strong acids like sulfuric and trifluoromethane sulfonic acid. Dilute solution properties of polyquinolines have been investigated by techniques such as membrane osmometry, light scattering, viscometry, and gel-permeation chromatography (96,97). 

Comparison of the values of C for the polymers with a flexible C-C or Si-O-Si backbone (as occurs in siloxane polymers) of about 6-10 with the value for the rigid-rod polymer of 125 demonstrates the fundamental difference in the solution properties of the latter polymer which has a highly extended conformation characteristic of liquid-crystal polymers. Equation (1.5) also shows that for a real chain the value of Rq would be expected to increase as the half power of the number of repeat units, i.e. the degree of polymerization, DP. ... 

The solution properties of these materials are unusual. They form optically anisotropic solutions in both amide and acid solvent systems over quite wide ranges of concentration and polymer molecular weight. In other words they are among the few known examples of synthetic polymers which can form lyotropic liquid crystals. (That is to say liquid crystals formed by the action of a solvent.) The usual example quoted in this context is poly(y-benzyl-L-glutamate) which forms cholesteric mesomorphic solutions in certain organic solvents. The helical structure adopted by the polypeptide in these solvents behaves as a rigid rod and it is... 

Aharoni SM, Walsh EK (1979) Rigid backbone polymers. 4. Solution properties of two lyotropic mesomorphic poly(isocyanates). Macromolecules 12 271-276... 

Computer simulation has also been used to study the solution properties of rigid-rod polymers (161,279,362). It has been foimd that the local structure and d5mamics of different rigid-rod polymers may be quite different but global motions in dilute and semidilute solutions are expected to be very similar (375). Based on the Broersma and Tirado-de la Torre relations, the translational and rotational coefficients, A and Dr, of rigid-rod polymers in dilute (or semidilute) solutions can be written in the forms... 

Part of the difficulty in studying the solution properties of such rigid-rod polymers is that the solubility is limited to strongly acidic media. In a number of cases, the solubility of polyaromatics has been improved by the attachment of phenyl groups on the main chain. Polyquinoline 5 (x=2) already has two pendent... 

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