Hydrodynamic volume of polymers

With use of a THF/n-Heptane mixture for example, in GPC 2 the hydrodynamic volume of polymer mola ules rich in one monomer component can be much more affected than those rich in the other. Steric exclusion paration can then distinguiA compsitional differences. 

Hydrodynamic volume of polymer (here considered equivalent to the separation parameter KM Table II for GPC calibration)... 

A direct consequence of the development of hydrodynamic volume theory In SEC has been the universal calibration method as introduced by Benoit (17). Universal calibration methodology is based upon the fact that retention in SEC can be described as a function of the hydrodynamic volume of polymer molecules. 

FIGURE 12-40 Schematic diagrams illustrating different hydrodynamic volumes of polymers. 

Rudin and Hoegy [43] have considered the assumption, inherent in the universal calibration procedure, that the hydrodynamic volume of a polymer at the concentration range adopted in SEC analysis is that which pertains at infinite dilution, and discuss whether this can account for apparent failures in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations and provide a universal calibration. Polypropylene is one of the examples used to illustrate the size of the effect. 

In a hydrocolloid system, the effective hydrodynamic volume of polymer coils may be characterized by intrinsic viscosity [r]]. The number of coils... 

The presence of inorganic salts in solutions of poly(ethylene oxide) also can reduce the hydrodynamic volume of the polymer, with attendant reduction in intrinsic viscosity this effect is shown in Figure 7. 

Yet as long ago as 1966 the problem of calibration in GPC was solved. In that year, Benoit and his co-workers recognised that GPC separates on the basis of the hydrodynamic volume of the polymer molecules in solution. The intrinsic viscosity [rj] is related to the hydrodynamic volume, V, by the equation ... 

Chen R.H., Chen W.Y., Wang S.T., Hsu C.H., Tsai M.L. 2009. Changes in the Mark-Houwink hydrodynamic volume of chitosan molecules in solutions of different organic acids, at different temperatures and ionic strengths. Carbohydrate Polymers 78, 902-907. 

Equivalent hydrodynamic volume of a polymer molecule (Chap. XIV). 

The second new program allows the user to compare the shapes of molecular weight distributions. For example, if we have the cumulative distribution of hydrodynamic volume for two polymers we can plot the hydrodynamic volume corresponding to the 10th percentile of the distribution for polymer A against the similarly defined hydrodynamic volume for polymer B. Such a plot, made for the entire distribution of both polymers, is called a "quantile... 

For some polymers, like polystyrene or poly(methyl methacrylate), narrow standards of known molar mass and small polydispersity are commercially available, which can be used for calibration. Unfortunately, such standards are not available for all polymers and then the obtained true molar masses of a specific polymer might differ by a factor of two from the value obtained by calibration with, e.g., polystyrene [30] (see Section 9.1). This problem can be resolved by the so-called universal calibration, which is based on the finding that the retention volume of a polymer is a single-valued function of the hydrodynamic volume of the polymer, irrespective of its chemical nature and... 

It has been shown, by theories of the frictional properties of polymer molecules in solution, that the intrinsic viscosity is proportional to the effective hydrodynamic volume of the molecule in solution divided by its Molecular weight. The effective volume is proportional to the cube of a linear dimension... 

In the mucosal environment, effects of salt, pH, temperature, and lipids need to be taken into consideration for possible effects on viscosity and solubility. A pH range of 4-7 and a relatively constant temperature of 37°C can generally be expected. Observed solution properties as a function of salt and polymer concentration can be referred to as saline compatibility. Polyelectrolyte solution behavior [27] is generally dominated by ionic interactions, such as with other materials of like charge (repulsive), opposite charge (attractive), solvent ionic character (dielectric), and dissolved ions (i.e., salt). In general, at a constant polymer concentration, an increase in the salt concentration decreases the viscosity, due to decreasing the hydrodynamic volume of the polymer at a critical salt concentration precipitation may occur. 

Viscometrv. It has been reported that complexation of two polymers leads to a decrease of the mixture viscosity and the minimum in viscosity corresponds to the mean stoichiometry of the complex (8-10). This was generally attributed to a compact structure for the complex. The hydrodynamic volume of the complex is small relative to the sum of hydrodynamic volumes of the original macromolecules. 

Relative methods measure properties that depend clearly on molecular weight, for example, the hydrodynamic volume of the polymer coils (GPC, vis-cosimetry) or their solubility as a function of chain length. However, these measurements can only be evaluated with respect to the molecular weight of the mac-... 

Certain SEC applications solicit specific experimental conditions. The most common reason is the limited sample solubility. In this case, special solvents or increased temperature are inavoid-able. A possibility to improve sample solubility and quality of eluent offer multicomponent solvents (Sections 16.2.2 and 16.8.2). The selectivity of polymer separation by SEC drops with the deteriorating eluent quality due to decreasing differences in the hydrodynamic volume of macromolecules with different molar masses. The system peaks appear on the chromatograms obtained with mixed eluents due to preferential solvation of sample molecules (Sections 16.3.2 and 16.3.3). The multicomponent eluents may create system peaks also as a result of the (preferential) sorption of their components within column packing [144,145]. The extent of preferential sorption is often sensitive toward pressure variations [69,70,146-149]. Even if the specific detectors are used, which do not see the eluent composition changes, it is necessary to discriminate the bulk sample solvent from the SEC separated macromolecules otherwise the determined molecular characteristics can be affected. This is especially important if the analyzed polymer contains a tail of fractions possessing lower molar masses (Sections 16.4.4 and 16.4.5). 

FIGURE 16.10 The SEC chromatogram of a statistical copolymer. Each slice contains macromolecnles of nearly the same size but their molar masses may differ depending on their overall composition and architecture (blockines) hydrodynamic volume of macromolecnles depends on all molecular characteristics of polymer species. 

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