GPC calibration curves

GPC calibration curves are established based on the radius of gyration of known-molecular-weight polymers, such as well characterized, narrow-molecular-weight distribution polystyrene. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. Thus, as branching increases the GPC numbers become less and less accurate and so should only be used for trends, and not exact calculations as some authors have done. 

The hmax obtained from the GPC calibration curve by estima-... 

Determination of Pore Size Distributions. The shape and range of a GPC calibration curve are, in part, a reflection of the pore size distribution (PSD) of the column packing material. A consideration of the nature of PSDs for the ULTRASTYRAGEL columns to be used in this work is therefore appropriate. The classical techniques for the measurement of PSDs are mercury porisimetry and capillary condensation. The equipment required to perform these measurements is expensive to own and maintain and the experiments are tedious. In addition, it is not clear that these methods can be effectively applied to swellable gels such as the styrene-divinylbenzene copolymer used in ULTRASTYRAGEL columns. Both of the classical techniques are applied to dry solids, but a significant portion of the pore structure of the gel is collapsed in this state. For this reason, it would be desirable to find a way to determine the PSD from measurements taken on gels in the swollen state in which they are normally used, e.g. a conventional packed GPC column. 

The use of a continuous GPC viscosity detector in conjunction with a DRI detector permits the quantitative determination of absolute molecular weight distribution in polymers. Furthermore, from this combination one can obtain Mark-Houwink parameters and the bulk intrinsic viscosity of a given polymer with a GPC calibration curve based only on polystyrene standards. Coupling these two detectors with ultraviolet and infrared detectors then will permit the concurrent determination of polymer composition as a function of molecular weight and... 

Figure 2 shows a co hvent i ona 1 GPC calibration curve for the standards, that is, a plot of GPC retention vs log M. These dat.a were fitted to a Fth order polyriomial and the molecular weights of all the standards recomputed from this fit using the measured retention volumeis. These values are shown in column 7 of Table I. 

This is the case of parallel calibration curves discussed in the previous paper. Equation 4 shows that when the calibration curves are parallel, the equivalence ratio, r, is constant to the elution volume V. It varies with the latter when aA aB—i.e., the calibration curves are not parallel. For that case Equation 3 would have to be used. Equation 4 also shows that the equivalence ratio can be calculated from the Mark-Houwink parameters K and a. It offers a way to determine r in addition to obtaining it from the GPC calibration curves of homopolymers. 

Moreover, no general valid mathematical expression is available for the GPC-calibration curve because the GPC-resolution mechanism has not yet been described mathematically to a sufficient extent. However, as the GPC-calibration curve is temperature-independent, spline polynomials 16) can well be used here, or a 4-para-meter-formula propsed by Yau and Malone 281 can be applied (cf. also the papers of Rosen and Provder quoted in Ref. 27i). 

Figure 2. GPC calibration curve using Dextran T standards.

The distribution curve of molar masses of analyzed macromolecular substance is constructed using g, and values, GPC calibration curve, and the equation for molar mass distribution ... 

Figure 1. GPC calibration curves, using VPO, shows that different pitches have different calibration curves.

Different pitches have different GPC calibration curves and each sample should be used to define its own /elution volume relationship. A quantitative evaluation performed on the CPTI sample shows a higher UV absorption coefficient for high MW species. This quantum nature of the absorption coefficient makes the definition of a continuous relationship between absorption coefficient and MW difficult. 

Figure 6. Comparison of GPC calibration curves for CTC derived from intrinsic viscosity ond GPC/LALLS (9-0-) methods...

The usual means of measuring molar mass distributions (MMDs) is gel permeation chromatography (GPC) which is described in Section 11.2.2.5. Denote the GPC trace as the signal G as a function of elution volume Veil it is assumed that the baseline has been subtracted. Appropriate calibration with monodis-perse standards yields the GPC calibration curve, which is the volumes at which monodisperse standards elute as a function of the molar mass M of the standard this is denoted V(A/ )... 

Equation (5.55) has the important implication that if the appropriate circumstances are satisfied, then the instantaneous MMD is independent of conversion, and hence that the cumulative and instantaneous MMDs are the same (to within an arbitrary normalization constant). In this case, the number MMD is a single exponential, and that suggests that a most informative way to plot experimental MMDs is as In P(M) against M (recalling that if the GPC calibration curve is linear, then P(M) = GPC trace/Af ), The result should be a straight line whose slope yields the transfer constant. 

Fig. 4. GPC calibration curve for Corning porous glasses with various pore sizes O, CPG 10-240 , CPG 10-370 x, CPG 10-1250 and , CPG 10-2000 (172). Courtesy of John Wiley Sons, Inc.

FIGURE 5.10 GPC calibration curve. Narrow polydispersity <1.1 polystyrene samples... 

Fig. 3.24 So/ne typical GPC calibration curves for polystyrene in tetrahydrofuran. The curves are for six different GPC columns packed with gels of porosity (a) 10 A, (b) 10 A, (c) 10" A, (d) 10 A, (e) 500A, (f) 50 A (courtesy of Polymer Laboratories Ltd). In each case the curve is approximately linear over the range of resolvable molar masses.

Fig. 3.23 Universal GPC calibration curve for different types of polyethylene dissolved in o-dichlorobenzene at 403 K. The solid points are for linear polymer fractions and the open circles are for fractions of branched polymer. (Data taken from Wild and Guliana, J. Polym. Sci. A2, 5 (1967) 1087). The product [r)] M has units of m moT ...

The number MWD may in turn be found from the GPC signal as a function of elution volume, G(V), as follows [34,39]. Let l M) be the GPC calibration curve (i.e.. Vis the volume at which a monodisperse molecular weight sample of molecular weight M elutes). One then can show ... 

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