SEC calibration curve

A range of individual pore size PLgel packing materials is produced and their pore size distribution is conveniently represented by a SEC calibration curve as illustrated in Fig. 12.1. It should be pointed out that the descriptors used for the different pore sizes, 50 A, 100 A, and so on, are not the actual pore sizes of the beads but relate to the size of a polystyrene molecule just excluded from the packing material. This nomenclature comes from the original work carried out by Moore (3) and should only be viewed in the context of differentiating... 

FIGURE 12.1 SEC calibration curves for PLgel individual pore size columns (300 X 7.5 mm), eluent THE at 1.0 ml/min, polystyrene calibrants. 

The use of hexafluoroisopropanol (HFIP) as an SEC eluent has become popular for the analysis of polyesters and polyamides. Conventional PS/DVB-based SEC columns have been widely used for HFIP applications, although the relatively high polarity of HFIP has led to some practical difficulties (1) the SEC calibration curve can exhibit excessive curvature, (2) polydisperse samples can exhibit dislocations or shoulders on the peaks, and (3) low molecular weight resolution can be lost, causing additive/system peaks to coelute with the low molecular weight tail of the polymer distribution... 

In the original works, theoretical models were developed to explain the SEC calibration curve... 

Figure 3. Theoretical SEC calibration curves for various shapes...

Figure 4. SEC calibration curve for silica sol separation (hard sphere particles, single pore size column) (1), Column PSM-1500 (8.9 fim), 30 X 0.78 cm mobile phase O.IU Na.HPO -NaH.PO, pH 8.0...

Figure 5. SEC calibration curves random-coil vs. rigid-rod (8) (SEC column set of several pore sizes, N,N-dimethylacetamide solvent at 80°C)...

One solution to the problem is by way of the universal calibration approach suggested by Benoif. Since SEC separations are based mainly on the hydrodyneimic volvune of the polymer molecules, there should exist a universal SEC calibration curve when hydrodyneimic volumes of molecules are used in the calibration plot. According to the basic theories in polymer science ... 

Using half-generation dendrimers possessing ( —COf Na ) surfaces, Dubin and Tomalia [155] have shown that a single universal (SEC) calibration curve for spheres can be derived which has important implications for protein chromatogra-phy. 

Fig. 6. SEC calibration curves of molar mass vs. elution volume for different polymethacrylates, stationary phase LiChrosphere 300+1000 A, eluent methyl ethyl ketone...

The application of refractive index and differential viscometer detection in SEC has been discussed by a number of authors [66-68]. Lew et al. presented the quantitative analysis of polyolefins by high-temperature SEC and dual refractive index-viscosity detection [69]. They applied a systematic approach for multidetector operation, assessed the effect of branching on the SEC calibration curve, and used a signal averaging procedure to better define intrinsic viscosity as a function of retention volume. The combination of SEC with refractive index, UV, and viscosity detectors was used to determine molar mass and functionality of polytetrahydrofuran simultaneously [70]. Long chain branching in EPDM copolymers by SEC-viscometry was analyzed by Chiantore et al. [71]. 

The experimental dependence M = /(V), i.e. the classical SEC calibration curve usually obtained by using narrow standards, in such a case can be obtained directly without calibration from the on-line LS detector. By combining the experimental function M = /(V) and the concentration profile (from DRI), one can construct the complete MMD of the HA sample. The differential and cumulative MMD of a high molar mass HA sample (Mw = 652 kDa, D = 2.1) are shown in Fig. (10). Starting from the initial MMD, the molecular weight averages and dispersity index (Mn, Mw, Mz, and D) could be easily calculated using the appropriate definitions. 

Fig. 4 Illustration of an SEC calibration curve. High-MW molecules that have K = 0 and low-MW molecules that have K — pass through the column with no separation. For molecules that have 0 < If < 1, size-based separation occurs.

Figure 7.36 SEC calibration curves for the networks prepared by crosslinking linear polystyrene with monochlorodimethyl ether to 100% crosslinking degree in (1) ethylene dichloride at volume concentration of 5.9% and in (2) cyclohexane at volume concentration of 11%.

SEC calibration curves for PMMA, PDMA, PtBMA, PnBMA (reproduced with permission from Ref. 22). 

SEC-MALDI also proves useful in cases where the production of high polymers is accompanied by the formation of sizeable amotmts of cyclic oligomers. The presence of a mixture of linear and cyclic chains in low molar mass polymers causes difficulties in establishing an appropriate SEC calibration curve for such samples. The theoiy predicts that cycles are eluted at later times with respect to linear chains.In fact, for a given polymer there is a small but defined difference between the hydrodynamic volumes of linear and cyclic oligomers of the same molar mass, and this difference is reflected in the elution volumes (Ve) of the linear and cyclic species of the... 

Typical SEC calibration curve logarithm of molecular weight versus retention... 

SEC calibration curves for PLgel MIXED gels, column dimensions 300 x 7.5 mm, eluant tetrahydrofuran, flow rate 1 ml/minute, calibrants narrow polydispersity polystyrene, detector UV 254 nm. 

Typical SEC calibration curves for linear and branched polymers. 

Cellulose standards for use in calibration, especially by the peak position method, can be obtained by a number of methods. The most straightforward method is to utilize a series of celluloses from a variety of sources (eg., pulps, yarns, and avicel) that have a wide range of DPs (15,26). In a second method, celluloses of different DPs are obtained from a single cellulosic source (e.g., cotton) by controlled, acid-catalyzed depolymerization (93). Another method uses fractional precipitation of the appropriate cellulose derivative (10,29). Once obtained, the DP of each cellulose standard can be determined by osmotic and viscometric methods. The SEC calibration curve obtained with these standards is then adjusted numerically until a best fit with the DPs of each of the standards is obtained (93). 

The SEC calibration curve shown in Figure 1.3 indicates how the separation of two peaks depends on their molecular mass and the slope of the calibration curve. Thus a smaller gradient (shallower curve) will increase the separation of... 

Although the Rp-Dp curves are a convenient means for illustrating separation behaviour, for calibration purposes, it is more useful to plot the data as log particle diameter versus the elution volume difference. An example of such a plot is shown in Figure 10.5 where the similarity to an SEC calibration curve is apparent. In this form, several features of HDC behaviour can be seen. First, in the low ionic strengths region, the calibration curves are... 

Despite the evident role of coulombic protein-substrate interactions, SEC calibration curves on derivatized silica do not always reveal expected differences among proteins in various charge states. Le Maire et al. (78) found... 

An estimate of the pore size can be derived frcm the inflexion point of the SEC calibration curve, as suggested by Freeman and Poinescu (38). Hcwever, their derivation was based on Bgn. 7 rather than the gmieral Bgn. 9 and unfortunately a misinterpretation of Egn. 7 (i.e. Bps. 33 and 35 in Ref. 75) have introduced an additional factor of two into their results (38, 76). A general derivation of the pore size at the inflexion point is... 

The theoretical relationships between the physical structure of a porous SEC packing (i.e. its particle shape, particle diameter, pore size distribution, cp) and the width of the fractionation range as well as the linearity of the SEC calibration curve... 

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