Volume, hydrodynamic

FIGURE 12-39 Schematic diagram illustrating the slicing of the SEC chromatogram. 

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

FIGURE 12-41 Schematic diagram illustrating different calibration curves at the same temperature in the same solvent 

These factors would seem to make SEC or GPC a tedious method that is only of limited use. Not so—there have been a couple of developments that make SEC the preferred method of obtaining molecular weight data. 

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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. 

Calibration curves for PS and PMMA are shown in Figs. 15.3-15.5. The slight differences in courses of calibration curves for PS in THF, chloroform, and toluene, as well as the curve for PMMA in THF (Fig. 15.3), can be explained by the flow rate variations for different pumping systems and by the hydrodynamic volume effects, respectively. The calibration curves for PMMA in mixed eluents THF/toluene are shown in Fig. 15.4. Three percent of THF in toluene assured a reasonable SEC elution of PMMA. However, more chloroform was needed to obtain a good SEC elution of PMMA in mixed eluent chloroform/toluene... 

It is surprising to note that for all four columns there is good agreement between the M determined in water and in water/methanol, despite the fact that PEO and polyvinylpyrrolidone have different hydrodynamic volumes in these two mobile phases and that the column packings may swell or shrink differently in these two mobile phases. 

Solvent can affect separation in two different ways. Because water is a better solvent for these four columns than water/methanol, based on the swelling or void volume of the columns in Table 17.9, the separation should be better in water than in water/methanol. The relative viscosity of a 0.5% PEO standard from Aldrich (Lot No. 0021kz, MW 100,000) in water and in water/methanol with 0.1 M lithium nitrate is 1.645 and 1.713, respectively. This indicates that the hydrodynamic volume of PEO in water is smaller than in water/methanol. The difference in hydrodynamic volume between two PEO standards should also be larger in water/methanol than in water. Hence, the separation for PEO should be better in water/methanol than in water. The results in Table 17.8 indicate that separation efficiency is better in water than in water/methanol... 

Several factors can contribute to the difference in retention times for PEO in different mobile phases the viscosity of a mobile phase, the hydrodynamic volume of a PEO, and the swelling or void volume of a column. Shodex and TSK columns should swell more in water than in water/methanol, and PEO should therefore come out later in water than in water/methanol. PEO should also elute later in water than in water/methanol because water/methanol is a better solvent for PEO than water. The viscosity of the 50 50 water/methanol mobile phase is higher than the viscosity of water. PEO should therefore elute later in water/methanol than in water due to the difference in viscosity. The results in Table 17.9 indicate that the difference in retention time for PEO in water and in water/methanol depends more on the swelling of columns and the hydrodynamic volumes of PEO than the viscosities of mobile phases. 

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... 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

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. 

The second and third samples represent inimer-type polymerizations. Figure 7.14 shows a typical SEC trace, with populations of distinctively different hydrodynamic volumes. 

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