Size-Exclusion Chromatographic Determination of Polymer Molar Mass Averages Using a Fractal Calibration

Abstract

The characterization of polymers by size-exclusion chromatography basically consists of the determination of the weight-average molar mass (Mw), number-average molar mass (Mn), and polydispersity index (I). An accurate estimation of these magnitudes requires the use of a reliable and trusted calibration curve. Three procedures for building up a calibration curve are analyzed in this work. The first is the classical universal calibration (UC), based on the elution of tetrahydrofuran-polystyrene in a system as reference. The second is based on the proper calibration curve made with standards of the sample under study. However, two main drawbacks arise when using these methodologies: the nonfulfilment of the UC when secondary mechanisms, other than pure size-exclusion, are present in the separation process; and the lack of a broad set of narrow standards of the sample under analysis in the second procedure. In order to circumvent these difficulties, a third, recently-proposed approach based on fractal considerations is applied. The accuracy and reliability of this method is proven through the calculation of the deviations observed in the estimation of the Mw values for polymer samples in different solvent-gel chromatographic systems. Whereas the classical UC shows a mean deviation of approximately 80% relative to the values given by the manufacturer, the fractal calibration yields a mean deviation of approximately 16%, similar to that obtained from the proper calibration. Moreover, the fractal procedure only needs one polymeric sample to generate the calibration curve.

The fractal calibration method applied to the characterization of polymers in solvent mixtures and in mixed gel packings by SEC

“…Summarizing, the data in Table 3 also corroborate the goodness of the fractal procedure to characterize polymers eluted in mixed gel columns. Moreover, the comparison between the results obtained in the present work with those recently published by our group for other systems and/or columns [12,13] shows that the mean deviations diminish when using mixed solvents (case of l-styragel) or when mixing gel packings (case of TSK Gel H HR + XL + HR ). Figure 4 shows, as an example, the overlays of the MMD (as w i vs. M i ) obtained with the three calibration approaches here compared, Eqs.…”

“…Overall, for this packing, the mean dM X values are 55, 15 and 6% corresponding to calculations made with the UC, SC and FC methods, respectively. These results show that the fractal method [12,13] is also valid to explain the SEC elution behaviour of systems in which the solvent is a mixture of two liquids that can undergo secondary mechanisms during the separation process and, therefore, it serves to properly characterize samples eluted in such solvents. Similar calculations have been performed for different solvent/polymer systems eluted in , mixed' gels.…”

“…This coefficient can be related with the fractal characteristics of the chromatographic support, i. e. the available pore size, L, and the fractal dimension of the pore surface, D f [22,23]. The procedure to obtain log M[g] and V e with the FC method has been explained in detail elsewhere [13]. Briefly, it requires the knowledge of the sample elution profile (chromatogram), the elution volume, the intrinsic viscosity and the MHS constants of the system under study.…”

“…MMD to proceed with the molar mass estimations. The deconvolution of an experimental chromatogram has been recently described in detail [13]. For the sake of clarity, let us briefly recall the main steps of the procedure: the raw data collected by the refractive index detector were divided in equidistant slices with a corresponding elution volume, V e,i .…”

“…Most of chromatographers use the wellknown , universal calibration' (UC) method [11] that is specifically useful when the separation process accounts by pure or , ideal' SEC, otherwise it fails. For this reason, the present work compares the results obtained with three different procedures: universal (UC), specific (SC) and fractal (FC) calibrations [12,13]. All of them have been applied to polymer systems eluted in solvent mixtures or in gel packing mixtures, where secondary separation mechanisms occur besides the main size-exclusion mechanism.…”