Size of Polymer Molecules

In any event one does not encounter single polymer chains (except in theoretical discussions) what is more relevant to the present discussion is the solid state of a 

FIGURE 3.3 Approximate simulation of a polymer chain with freely jointed chain model. The value of r is the end-to-end distance. 

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The fully extended molecular length is not representative of the spatial extension that a molecule actually displays. The latter is sensitive to environmental factors, however, so the extended length is convenient for our present purposes to provide an idea of the spatial size of polymer molecules. 

J. D. Honeycutt, D. Thirumalai. Influence of optimal cavity shapes on the size of polymer molecules in random media. J Chem Phys 92 6851-6858, 1990. 

Xp Effective size of polymer molecule (j) Solids concentration (volume fraction) jU Liquid viscosity... 

Spouge [ 21 ] has shown that for any kernel of this form the Smoluchowski equation can be solved analytically, i.e., the distribution of molecular size of polymer molecules at any extent of reaction prior to the gel point (if any) or at least moments of the distribution can be expressed explicitly. 

Because of the huge size of polymer molecules, the van der Waals forces between the molecules are very strong. Thus, their boiling and melting points are very high in comparison to their monomers. They are hard, strong and have a wide usage. 

While the chemistry of polymer synthesis can be explained by the usual themes of organic reactions, the large size of polymer molecules gives them some unique physical properties compared to small organic molecules. 

Thus a four-fold increase in initiator concentration would result in halving the size of polymer molecules, though the rate of polymerization [Eq. (6.26)] would be doubled by this change in initiator concentration. 

A more satisfying procedure for determining molecular weight and size of polymer molecules by light scattering was developed by Zirnm. The method is based on the same general principle of destructive interference... 

Fia. 15-13. Use of light scattering for determining molecular weight and size of polymer molecules. Zimm plot of polystyrene in diehloroethylene at 22°C. [Otder, Carr, and Zivm, J. Chem. Pkys. 18, 830 (1950).]... 

SEC can be used as a measure of both the size and the MW dispersity of a polymer that is, it has the capability of finding the distribution of the sizes of polymer molecules. If standards of a known size are run previously, then a calibration curve can be created to determine the sizes of polymer molecules of interest in the solvent chosen for analysis often tetrahydrofuran (THE). Alternatively, techniques such as light scattering and/or viscometry, which do not rely on the calibration using standards of known MW, can be used online with SEC to yield absolute MWs. Because of the difference in size of two different polymers... 

When atoms and molecules approach one another closely, they begin to exert forces on one another that do not result from the sharing or transfer of electrons. These forces are known as intermolecular forces if the forces are between two neighboring molecules and are called intramolecular forces if they are between different parts of the same molecule. These forces are much weaker than covalent or ionic bonds but are very important to the properties of polymers because the huge size of polymer molecules results in a proportionally huge number of these attractions. 

Because of the very large size of polymer molecules, both interatomic and intermolecular forces play a crucial role in their formation and properties. A brief review of the most important atomic forces follows. 

The mean square end-to-end distance divided by nf- is used to quantify the relative size of polymer molecules of a given molecular weight (Table 3.1). The high value for polystyrene reflects the expansion in the chain size necessary to accommodate the large phenyl side groups. The... 

However, the contour length L of the chain is not as useful a measure of the size of polymer molecules as R ). An alternate measure of the size of a polymer molecule is the root mean square of its radius of gyration, Rg. It is defined as the average distance of a chain element from the center of gravity of the chain. The mean end-to-end distance R) for such a chain is zero. Therefore, the second moment (/ ) is used instead. 

The solution properties of polyelectrolytes in general are markedly different from those of polyelectrolyte solutions with added salts. These differences are very strikingly revealed in their viscometric behaviors. Viscosity, as pointed out in the previous section, is related to the size of polymer molecules and therefore is affected by molecular expansion. When a small amount of a simple salt, such as sodium chloride, is added to a dilute polyelectrolyte solution, the ionic strength of the solution outside of the polymer coil is increased relative to the strength of the solution inside of the coil. Consequently, some of the mobile electrolyte diffuses into the polyion coil and the thickness of the ionic atmosphere around the polymer chain is reduced. This effect produces a significant contraction of the polyion coil and is reflected in decreased values of the viscosity. 

The phase behavior of polymers, whether in solution or in mixtures with other polymeric components, differs considerably from that of small molecules. This difference is a direct consequence of the large size of polymer molecules. For mixtures of small molecules the driving force for miscibility is a result of the large gain in entropy that takes place on mixing, but this is not the case for polymers. The entropy of mixing is particularly small for pol5mier/polymer mixtures and, as a result, one-phase systems are obtained only in a limited number of cases. 

This chapter extends the survey of literature of dilute and semi-dilute polymer solution properties - both theoretical and experimental aspects - begun in Part I of this series, to include literature appearing in the years 1979 and 1980. Our brief, introduced only shortly here, is to examine those aspects of the above properties that depend on the shape and size of polymer molecules, but not specifically upon their chemical nature. Some of the topics examined here will, judging by experience gained with the first volume, also appear in other chapters of this volume. In particular, reference should be made to the chapters covering neutron scattering (11), polymer characterization (12), and computer applications (19). 

Analytical Gel Pomeation Chromatt raphy.—Since its discovery in 1964, analytical GPC has rapidly become the single most important technique for characterization of the size of polymer molecules. The basic experiment has changed very little, the major development being the adaptation of high speed chromatographic methods to GPC giving much shorter analysis times. The literature up to 1976 has been extensively reviewed. ... 

Kirkwood derived an equation to correlate the diffusion coefficient D with the size of polymer molecule Ry) in the form... 

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