Rigid chain polymers gyration

Kozlov, G. V Temiraev, K. B. Mikitaev, A. K. The correlations coil gyration radius— Kuhn segment size for rigid-chain polymers the fractal analysis. Proceedings of Higher Educational Institutions. Chemistry and Chemical Technology, 2002,45(2), 30-33. 

Assuredly, differences exist between random-coil polymers and colloidal particles. The interior of a colloidal particle is solid, perhaps with interstices that have imbibed modest amounts of solvent. Most of the volume within the radius of gyration of the center of mass of a random-coil polymer is filled, at least in dilute solution, with solvent. Even though chain segments cannot interpenetrate, entire polymer chains can interpenetrate by passing through each other s void spaces. Furthermore, most colloidal particles are rigid long-chain polymers are flexible. 

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. 

In equation (5.33), as previously defined, An is the second virial coeffi-cient of the / -biopolymer component on the molal scale (cm mol- ) and RGl is the radius of gyration of the / -biopolymer component. For a flexible polymer chain the value of the penetration parameter y/ lies in the range 0.6-0.7, while for a semi-rigid/worm-like polymer we have y/ - 0.3 (Tanford, 1961). The shorter the polymer chain, the closer is its effective conformation to that of the equivalent hard sphere. 

Hence, the stated above results have shown, that the introduction of the changed groups in copolymer changes macromolecular coil in solution structure, reducing its fractal dimension, gyration radius and increasing chain rigidity. Within the frameworks of fractal analysis it was demonstrated, that the indicated factors could influence essentially on both polymers synthesis process and polymer effectiveness as flocculator [5],... 

As one-dimensional objects, cylindrical micelles and polymer nanotubes have many features in common with semi-flexible polymer chains, but on a different size scale. Nanotubes tend to be longer, thicker, and more rigid than individual polymer molecules, but both are characterized by a distribution of end-to-end lengths, a radius of gyration, and a persistence length. Figure 9 compares the structures of a poly(n-hexyl isocyanate) or PHIC chain, a PS-... 

Figure 4.16 Mean square radius of gyration versus the aggregate particle number. Open squares represent aggregates formed without the presence of rigid polymer chains. Black squares correspond to aggregates formed with the presence of rigid polymer chains (particle chain concentration ratio equal to 12.5).

The characteristic ratio is a measure of chain flexibility. Flexible chains have C close to unity, while semiflexible and rigid polymers have usually much larger values of C . The mean-square radius of gyration for freely jointed chain is ... 

The excluded volume, self-avoiding sheet (SAS) deforms and wrinkles propagate as its particles execute their stochastic motion. The conformation and dynamics of the sheet can be studied by keeping track of the rms displacement of the center of mass of the sheet and that of its center (interior) particle, radius of gyration, as a function of molecular weight and rigidity of the covalent bonds. Effects of the quality of the solvent and entanglement barriers (e.g., polymer chains matrix) can be incorporated (see below). A few observations from our computer simulations are briefly discussed in the next section. 

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