Polymers hydrodynamic volume

A quantity J which is proportional to the polymer hydrodynamic volume (3) then was calculated ... 

As demonstrated by numerous experiments, temperature does not well influence the exclusion processes (compare Equation 16.6) in eluents, which are thermodynamically good solvents for polymers. In this case, temperature dependence of intrinsic viscosity [ii] and, correspondingly, also of polymer hydrodynamic volume [p] M on temperature is not pronounced. The situation is changed in poor and even theta solvents (Section 16.2.2), where [p] extensively responds to temperature changes. 

An interesting outgrowth of these considerations is the idea that In r versus K or Vj should describe a universal calibration curve in a particular column for random coil polymers. This conclusion is justified by examining Eq. (9.55), in which the product [i ]M is seen to be proportional to (rg ), with r = a(rg 0 ) - This suggests that In rg in the theoretical calibration curve can be replaced by ln[r ]M. The product [r ]M is called the hydrodynamic volume, and Fig. 9.17 shows that the calibration curves for a variety of polymer types merge into a single curve when the product [r ]M, rather than M alone, is used as the basis for the cafibration. 

These groups are found in the various polymers discussed here. Truly unique in its abiUty to interact and promote water solubiUty is the —O—CH2—CH2— group. The interactions of these groups with water and their placement in the polymer stmcture influence the water solubiUty of the polymer and its hydrodynamic volume. 

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. 

Approximately a minimum of 1 to 5,000 is required before complexation is no longer dependent on molecular weight for small anions such as KI and l-ariiLinonaphthaLine-8-sulfonate (ANS) (86,87). The latter anion is a fluorescent probe that, when bound in hydrophobic environments, will display increased fluorescence and, as expected, shows this effect in the presence of aqueous PVP. PVP, when complexed with Hl, shrinks in si2e as it loses hydrodynamic volume, possibly because of interchain complexation. ANS, on the other hand, causes the polymer to swell by charge repulsion because it behaves like a typical polyelectrolyte (88). 

Gels made in this way have virtually no usable porosity and are called Jordi solid bead packings. They can be used in the production of low surface area reverse phase packings for fast protein analysis and in the manufacture of hydrodynamic volume columns as well as solid supports for solid-phase syntheses reactions. An example of a hydrodynamic volume column separation is shown in Fig. 13.2 and its calibration plot is shown in Fig. 13.3. The major advantage of this type of column is its ability to resolve very high molecular weight polymer samples successfully. 

Eor low molecular weight polymers the separation of the system peaks from the low molecular weight end of the polymer peak is very critical in obtaining accurate MWD and the percentage of low molecular weight materials in the polymer. The water/methanol mixture is a better solvent for PVP than water. PVP K-15 and K-30 should be better separated from the system peaks in the water/methanol mixture than in water because the difference in hydrodynamic volumes between PVP K-15 or K-30 and system peaks is larger in... 

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

Interactions with xanthan were investigated for some GAX fractions of wheat bran [109]. Whereas, for lowly substituted GaMs a synergy in viscosity was observed at low total polymer concentrations, yielding a maximum of the relative viscosity at nearly equal proportions of both polysaccharides [124], the xanthan/xylan mixtures at the same experimental conditions showed no synergy. The observed decrease in the relative viscosity values upon addition of the xylan indicates that a certain interaction with xanthan takes place, but that it leads to a contraction in the hydrodynamic volume. The authors suggested that structural and conformational differences between GaM and GAX might be the reason for this observation. 

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. 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

Hyperbranched poly(ethyl methacrylate)s prepared by the photo-initiated radical polymerization of the inimer 13 were characterized by GPC with a lightscattering detector [51]. The hydrodynamic volume and radius of gyration (i g) of the resulting hyperbranched polymers were determined by DLS and SAXS, respectively. The ratios of Rg/R are in the range of 0.75-0.84, which are comparable to the value of hard spheres (0.775) and significantly lower than that of the linear unperturbed polymer coils (1.25-1.37). The compact nature of the hyperbranched poly(ethyl methacrylate)s is demonstrated by solution properties which are different from those of the linear analogs. 

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

Size exclusion chromatography (SEC) separates molecules of a polymer sample on the basis of hydrodynamic volume. When the chromatograph is equipped only with a concentration-sensitive detector, i.e. conventional SEC, a molecular weight distribution (MWD) can be obtained from the chromatogram only through use of a calibration function relating molecular weight and elution volume V (2). 

The hydrodynamic volume separation mechanism of SEC, along with the different molecular size/weight relationships of branched and linear polymers of identical chemical composition, can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper both conventional SEC and SEC/LALLS are used to obtain data about branching in samples of poly(vinyl acetate) (PVA) and polychloro-prene (PCP). 

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. 

To study the bulk copolymerization of styrene n-butyl methacrylate both conventional and unconventional GPC analyses were used. The normally obtained chromatograms, (from dual U.V. detectors) primarily provided area ratios intficative of composition as a function of retention volume. However, even this information was only obtainable after average compositions had been otherwise determined. Furthermore, in general, since the GPC normally separates on the basis of hydrodynamic volume, the polydispersity of aU polymer molecular properties at e h retention time is of serious concern. 

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

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