Hydrodynamic molecular volume

Retention volume in SEC is proportional to the size of the polymer molecules in solution. In addition, as discussed in Section 6.2, equation (6-2), the product of the intrinsic viscosity of the polymer and its molecular weight is proportional to the hydrodynamic molecular volume. These relationships allowed Benoit et al. [5, 6] to introduce a universal molecular weight calibration. 

GPC/SEC is a controlled separation technique in which molecules are separated on the basis of their hydrodynamic molecular volume or size [26], With proper column calibration or using molecular weight-sensitive detectors, such as light scattering, viscosimetry, or mass spectrometry, the MWD and the statistical molecular weight averages can be readily obtained. In their review, Barth et al. [26] mentioned that the GPC/SEC is the premier technique to evaluate these properties for both synthetic polymers and biopolymers. 

The column packing in SEC comprises porous, spherical gel beads with a defined pore size distribution. Most often, these beads are made from poly(styr-ene-divinylbenzene). (For GFC, cross-linked dextran and agarose gels are often used. ) The sample is dissolved in a suitable solvent that is often used as the mobile phase as well. Separation occurs as a result of differences in accessibility of pore volume. Small molecules can freely access the whole pore volume as a result, the column retards these molecules the greatest. As molecular volume increases, less and less pore volume is accessible for molecules to sample, and elution times decrease. For all molecules with hydrodynamic volumes that are too large to penetrate into the pores of the packing, elution occurs at the (interstitial) void volume of the column. The retention volume for each solute can be described mathematically as ... 

Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

In order to apply the Smoluchowski equation (Equations (1.3), (2.1), (3.29)), we need values for the least distance of approach (rAn) and the diffusion coefficient (Dab)- The value of tab can be estimated from molecular volumes (Section 2.5.1.2). The diffusion coefficient can be determined by various methods, but experimental values are available only for a minority of the myriad possible situations. A common practice is to use the Stokes-Einstein relation (Section 1.2.3), which rests on the assumption that solute molecules in motion behave like macroscopic particles to which classical hydrodynamic theory can be applied. We shall first outline (a) the relation between the diffusion coefficient D and the mechanics of motion of particles in fluids, leading to the Stokes-Einstein equation relating D to solute size and solvent viscosity and (b) the direct experimental determination of D. We shall then (c) compare the results and note the reservations that are required in relying on the Stokes-Einstein estimates of D in various cases. 

Why Chromatography Gel permeation chromatography is accurate and routine for average molecular weight determinations in excess of 50,000. Chromatographic methods separate complex mixtures resolved in time. For example, in a GPC an oligomer mixture is separated by hydrodynamic size (volume). 

Fig. 5 Cumulative pore volume distribution, described by the inaccessibility kna as a function of the molecular weight MW (a,c) and as a function of the hydrodynamic molecular radius MR (b.d), determined interferometrically for cartilage (a.b), cornea, and contact lenses (c.d) with test molecules ranging from mono- and oligosaccharides to proteins and excluded dextran (o PEGS, a others). LLFs are used for fitting to cornea and cartilage.

The elution volume, F/, and therefore the partition coefficient, is a function of the size of solute molecule, ie, hydrodynamic radius, and the porosity characteristics of the size-exclusion media. A protein of higher molecular weight is not necessarily larger than one of lower molecular weight. The hydrodynamic radii can be similar, as shown in Table 4 for ovalbumin and a-lactalbumin. The molecular weights of these proteins differ by 317% their radii differ by only 121% (53). 

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). 

The elution volume of a molecule in HPSEC is determined by its hydrodynamic size and the pore size of the column packing. In setting up an HPSEC experiment, the chromatographer must match the pore size of the column to the molecular size range of the sample. 

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... 

---