Radius of a chain

We may now reconsider the arguments of the previous section. Equation (9.17), for instance, yields for the radius of a chain in semidilute solution... 

A similar expansion can be obtained for scattering intensity S q,C) oc 1/(1 + q R +...). For very low q, in the Guinier regime qR<, this expansion is the basis for the so-called Zimm plots that are commonly used to determine the radius of a chain and the second virial coefficient of a solution. 

Last section dealt with the concentration profile of the adsorbed large polymers. We saw that in a dilute bulk solution and in the plateau regime, it extends to distances of the order of the radius of a chain. In a semi-dilute solution, we expect the same profile to be... 

Restrict the study to long wavelength properties of the problem by abandoning chemical detail and introduction of a coarse-grained model. It is this approach which will be emphasized in this chapter and many following ones (Chapters 2-4, 6, 7, 9). It is clear that this coarse-graining approach makes sense only for universal properties, and what universal means depends on the problem under study. For example, for dilute polymer solutions one expects that the mean-square gyration radius of a chain varies with Np as for... 

Fig. 26 Hydrodynamic radius of a graft copolymer PVCL-g-14 single chain at low temperatures and of the particles formed above the critical solution temperature (a). Temperature dependence of the hydrodynamic radius of grafted PVCL microgel E4 (b) [181]...

Coefficient coimecting the intrinsic viscosity, the radius of gyration and the molar mass of a chain macromolecule, according to the equation... 

Because there are many possible ends in branched polymers, it is customary to use the radius of gyration S) instead of r for such polymers. The radius of gyration is actually the RMS distance of a chain end from the polymer s center of gravity. S is less than the end-to-end distance (r), and for linear polymers = 6S. ... 

In this expression A(i) is the specific activity of radionuclide i, A(i) (r = 1) is the specific activity of nuclide i at r = 1, r is the radius of a debris particle, and mis a number between 0 and 1. A value of m = 0 implies that the activity is proportional to the volume of the particles. Such a volume dependence results for nuclides which combine with the matrix material in the cooling fireball and applies to the so-called refractory chains, such as the 95-, 11-, and 147-chains. A value of m = 1 or a surface-... 

Q q R i l, i 2 Rb Rd Rg RP Ro r rc S Electric charge (As), heat (J), quality factor of a resonator Heat per unit area (J m-2), integer coefficient Radius of a (usually) spherical object (m), gas constant Two principal radii of curvature (m) Radius of a spherical bubble (m) Radius of a spherical drop (m) Radius of gyration of a polymer (m) Radius of a spherical particle (m) Size of a polymer chain (m) Radius (m), radial coordinate in cylindrical or spherical coordinates Radius of a capillary (m) Entropy (J K-1), number of adsorption binding sites per unit area (mol m-2), spreading coefficient (Nm-1)... 

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