Polymer solutions coil size measurement

The intrinsic viscosity of polymers in dilute solutions is an extremely important measure of the coil size, owing to its simplicity and precision. The Zimm model leads directly to the Fox-Flory equation for intrinsic... 

A very wide distribution of molecular weights or hydrodynamic coil sizes are usually found within each EOR polymer solution. Because of this polydispersity, the molecular weights or hydrodynamic sizes determined by viscosity measurements are only averages. No information on macromolecular polydispersity is obtained from viscosity measurements. However, characterization of polydispersity is important because EOR polymers which have molecular weight or coil size distributions containing a large proportion of smaller... 

The radius of gyration of polymer coils in solution can be measured using small-angle scattering. In the case of small molecules, SAXS or SANS are appropriate techniques, but if the chain is sufficiently large (coil size > X/20, where X is the wavelength of the radiation) it will scatter light anisotropically, so SALS is a suitable experiment. The radius... 

Because of the fundamental nature of the size of polymer coils, considerable effort has been devoted to the experimental measurement of the size of regular star polymers both in good solvents and under 6-conditions. The size of a polymer coil is obtained from the angular dependence of scattered radiation at low angles. The angular dependence of the intensity of light (or neutrons) scattered by a polymer solution is analyzed in terms of the product of the form factor, P Q), and the structure factor, S Q) ... 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

A radius of gyration in general is the distance from the center of mass of a body at which the whole mass could be concentrated without changing its moment of rotational inertia about an axis through the center of mass. For a polymer chain, this is also the root-mean-square distance of the segments of the molecule from its center of mass. The radius of gyration is one measure of the size of the random coil shape which many synthetic polymers adopt in solution or in the amorphous bulk state. (The radius of gyration and other measures of macromolecular size and shape are considered in more detail in Chapter 4.)... 

The second virial coefiicient A2, which is related to the Flory dilute solution parameters by Eq. (3.121), is a measure of solvent-polymer compatibility. Thus, a large positive value of A% indicates a good solvent for the polymer favoring expansion of its size, while a low value (sometimes even negative) shows that the solvent is relatively poor. The value of A2 will thus tell us whether or not the size of the polymer coil, which is dissolved in a particular solvent, will be perturbed or expanded over that of the unperturbed state, but the extent of this expansion is best estimated by calculating the expansion factor a. As defined by Eqs. (3.123) and (3.124), a represents the ratio of perturbed dimension of the polymer coil to its unperturbed dimension. 

Traditionally, solutions have been used to characterize the polymer — to measure its molecular weight averages, e.g., number, weight and z-average M, M, and M, or the size of its macromolecular coil. The latter maybe expressed as the unperturbed end-to-end distance (six times larger) or the radius of gyration, viz. ... 

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