Size, of polymers

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. 

The major advantage of the capillary hydrodynamic chromatography is that the mobile phase does not need to have similar solubility parameter as the sample and packing material. (In SEC, nonsize exclusion effects may be observed if the solubility parameter of the sample, packing material, or mobile phase is considerably different.) Therefore, the hydrodynamic size of polymers can be studied in a 0 solvent and even in a solvent that is not compatible with any currently available SEC packing material (9). Figure 22.4 is an example of polystyrene separation in both THF and diethyl malonate. Diethyl malonate is the 0 solvent of polystyrene at 31-36 C. 

The study of filler distribution by the methods of optical and electronic microscopy has shown that in all compositions obtained by method 4 the filler is distributed rather uniformly as in an individual polymer. In the mixtures of incompatible polymers, obtained by methods 1 and 2, the filler is distributed nonuniformly and there are zones of high concentration of the filler and almost empty ones. The size of such zones is close to the size of polymer regions known for mixtures of thermodynamically incompatible polymers — 1 to 10 p. 

The resulting active end-groups have a covalent structure, rather than ionic, with tetrahedrally bound ligands persisting unaltered during the lifetime of the polymeric chains 46). This persistence of the various initially formed structures accounts for the multimodal distribution of the molecular sizes of polymers initiated by Grignard compounds46). 

After insignificant transformations the Flory-Renner s equation can be obtained. Such equation helps to calculate the sizes of polymer link between the cross bonds Mc... 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

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

In any 2D HPLC, it is important to attain certain degree of both the complementarity and the orthogonality between the two separation dimensions [255-257]. The so far most universal approach to 2D polymer HPLC assumes the partial or possibly full suppression of the molar mass effect in the first dimension of the separation so that the complex polymer is separated mainly or even exclusively according to its chemical structure. Selected coupled methods of polymer HPLC are to be applied to this purpose. In the second dimension of separation—it is usually SEC—the fractions from the first dimension are further discriminated according to their molecular size. Exceptionally, SEC can be used as the first dimension to separate complex polymer system according to the molecular size. This approach is applicable when the size of polymer species does not depend or only little depends on their second molecular characteristic, as it is the case of the stereoregular polymers... 

This model was used in dispersion polymerization to predict the size of polymer particles stabilized through grafting on hydrophilic polymers such as PVPo. It provides a reasonable description of, for example, PVPo-stabilized polymerization of styrene in polar solvents. The present model does not apply to other types of dispersion polymerization where grafted comb or block copolymer stabilizers are active. The key controlling parameters in this model are the availability of graft and the minimum and maximum coverage, Qmin and Qmax. 

In both systems (2a and 2b) the size of polymer particles decreased and the number of particles strongly increased with increasing macromonomer (neu-... 

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. 

The following ratios of kinetic events determine the average size of polymer chains ... 

The parameters l0, Kb, 0o, K , K,p, n, 8, ay, by, qit qy and r belong to the fit parameters, which can be determined by fitting of Equation 1.1 to a sufficient set of data calculated by QM and/or determined experimentally (e.g., X-ray scattering, IR spectroscopy, heats of formation). From a numeric point of view the pair interaction terms (van der Waals and Coulomb) are most demanding. In this connection the typical size of polymer packing models is limited to typically 3000-10000 atoms (leading to lateral sizes of bulk models of a few nm), although in other connections now also models with up to 100000 atoms have been used. 

We now consider the second alternative, the concentrated solutions of polymers in solvents, where the concentration of solvent can be changed over a wide range. Here the polymer molecules will evenly distribute among the solvent molecules and a new set of interactions between solvent and solute molecules sets up, which results in a solvation structure. There are many interaction configurations, called solvation structures. Specification of solvation structures is very important in such disciplines as bioscience [75], pharmacy [76], and lavation [77], The polymer solvation structure has been the subject of studies in recent years. In the concept of polymer solvation, since the overall size of polymer also changes in solution, therefore, the solvation... 

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