Molecular weight calibration function

When the total polymer response, is known as a function of retention volume, the molecular weight distributlon can be obtained in the usual manner with the appropriate molecular weight calibration curve. The molecular weight calibration curve can be obtained (a) by using the Runyon (65) copolymer molecular weight scale approach, or (b) by using a hydrodynamic volume approach if the Mark-Houwink constants for the polymer of interest are known or can be determined, or (c) by using a hydrodynamic volume approach in conjunction with an on-line viscosity detector. 

Fig. 2. Effect of the uv detector noise on the estimation of the molecular weight as function of elution volume for a narrow polystyrene standard. The symbols represent molecular weights obtained using the universal calibration and viscosity measurements on collected fractions...

Figure 11. Copolymer composition (Plv), average styrene sequence length (Ns) and number average molecular weight as function of the retention volume. Molar feed composition is 0.90. PS is the polystyrene calibration curve. Key , Mn A>...

Typically, the elution of small molecules has been described as a linear function of log M and the elution volume, Vg. Molecular weight calibration curves obtained with members of a specific homologous series often give very good linearity with remaining members of the series, within the limit of the included volume of the column system used. An example of this application with oligosaccharides and several monosaccharides is shown in Figure 1. The predictive ability of such log M curves decreases as the solute studied... 

Individual pore size columns have variable pore volume, and because the column dimensions are fixed, the combination of different columns must result in variable slope of the overall calibration curve and hence variable degrees of resolution as a function of molecular weight. 

This analogy of functional forms between Equations 7 and 4 indicates that the SEC-[n] calibration curve must also be linear. This is experimentally verified by the data in Figure 4. One assumption made here is that the K and a in the E and E2 expressions are not significantly dependent on MW, which is usually the case. The method will be less accurate in the molecular weight ranges where this assumption becomes a poor approximation. ... 

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). 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

Upon applying the calibration constants obtained from the data of one sample to evaluate the SEC data of the other samples, the calculated Mn and values correspond fairly well (within 10-20%) with the absolute MW parameters of the samples. This agreement also suggests that the samples probably have similar chain structures. The distribution functions for samples PN-1 and IL-22 are plotted in Figures 4 and 5. The molecular weight distributions of both polymers are similar to distribution curves reported for derivatized poly(organo)phosphazenes (4-10). 

Figure 5. A typical chromatogram. The solid curve is the part of the data that is used to characterize the molecular weight distribution. The dashed portions represent data that are not used. The solid straight line represents the baseline under the chromatographic peak. The vertical lines define the limits of the calibration function for the column set.

Other analysis methods dependent on multiple detectors can be implemented using this automated system. Two methods under development are the use of a continuous viscometer detector with a refractive index detector to yield absolute molecular weight and branching, utilizing the universal calibration curve concept (4), and the use of a UV or IR detector with the refractive index detector to measure compositional distribution as a function of molecular weight. 

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