The Column - June 2008 - (Page 20) Tips & Tricks: GPC/SEC The Column www.thecolumn.eu.com June 2008 Figure 2: Calibration curve with polynomial fit function 7th order where the first derivative shows physical meaningless local maxima and minima. Figure 3: Calibration curve with PSS fit function: where maxima and minima are avoided, this function can be used. functions but modified so that typical pitfalls are avoided (PSS calibration functions). For users of on-line light-scattering detectors: Another possibility to measure the relation of molar mass to elution volume is to apply an on-line light scattering detector (LALLS, RALLS, MALLS but not ELSD) and a concentration detector (RI, UV, ELSD). With such a combination a calibration curve valid for this specific sample is measured with the sample itself. To obtain smooth MMDs light-scattering software programs often provide the use of fitted data, where (the same as in conventional calibration curves) the molar mass/elution volume relation is fitted. Proper data analysis also requires the detector constant (calibration constant) of the light-scattering detector and of the concentration detector (response factor). For the concentration detector the constant is comparable to detector calibrations performed in HPLC and obtained in a similar way. Table 2: Influence of the calibration fit function on the regression coefficient. Fit function Linear (square) Polynomial 3 (cubic) Polynomial 5 Polynomial 7* PSS Polynomial 7 How can I decide if the best GPC/SEC calibration fit has been chosen? There are three criteria at hand that help the user decide if the proper function has been selected: • Regression coefficient, R2 • Deviation of the calibration point from the fitted value (e.g., average deviation) • The slope of the calibration curve. Table 2 illustrates this decision making process; it shows the regression coefficients for identical calibration data with different fit functions and the average deviation for all data points. Clearly, the regression coefficient is not a proper parameter to select the best calibration fit function because large average deviations are observed even for a regression coefficient very close to unity. If the data evaluation software provides the regression coefficient as the only selection criterium for the fit function, a value of 0.999 should be achieved for GPC/SEC results with highest precision. Table 2 also shows that the regression coefficient and the average deviation become smaller when selecting a polynomial function with higher degree. However, it is not physically meaningful to use the function with the highest degree that generates the lowest average deviation. More important than small deviations is the shape of the calibration curve which should be in general agreement with the separation mechanism. This means that a lower molar mass is always correlated with a higher elution volume. A good measure for this principle is the first derivative of the calibration curve (slope). Figure 2 shows an ideal first derivative for a GPC/SEC calibration curve. The slope changes only near the exclusion R2 0.9925 0.9986 0.9995 0.9999 0.9998 Average deviation (%) 30.2 10.4 7.35 3.57 4.92 *First derivative discontinuous; this function should not be used. 20 http://www.thecolumn.eu.com
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