New approach to model fitting in multi-detector GPC

The main limitation of multi-detector GPC arises from the nature of detecto r sensitivities in the tails of a polymer distribution. In the low molecula r weight tail of this distribution, molecular weight-sensitive detectors (s uch as a capillary viscometer or a static laser light-scattering photometer ) have low sensitivity while concentration detectors (e.g., differential re fractometer) have high sensitivity. This situation is reversed in the high molecular weight tail. These imbalances in sensitivity raise the question of how best to obtain an estimate of column calibration curves. The question is central to the succ essful application of the multi-detector GPC technique. For example, the ac curacy and precision with which structural information for polymers with br oad molecular weight distribution, especially with long-chain branches, can be obtained depends critically on the accurate estimation of such calibrat ion curves in the tails. Traditionally, calibration curves are fit to the logarithm of the ratios of detector responses. However, the logarithm of a ratio will not give meanin gful values in the regions where at least one of the responses is near zero . Thus, low detector sensitivity in the tails requires that a calibration c urve be fit only to the heart of the peak, where all detectors have good re sponse. The optimized curve is then extrapolated to the regions in the tail s that were excluded from the fit. This data truncation has two consequences that limit the accuracy and preci sion of the multi-detector GPC technique. Truncation eliminates potentially useful responses with which to constrain the calibration curves, and the r esulting curves can be sensitive to the choice of the fitting region. We describe a new data analysis method for multi-detector GPC where the com plete chromatographic profile obtained from one detector is compared, in a least-squares sense, to a model that is a function of responses from the ot her detector. This formulation of least-squares avoids the use of logarithm s, ratios, and eliminates the need for extrapolation. The approach allows t he inclusion of regions in the least-squares fit that contain low detector' s signal, e.g., near baseline responses that fluctuate about zero from eith er, or both, detectors. We apply this approach to obtain column calibration curves with each of two molecular weight-sensitive detectors, coupled to a GPC system. Such calibr ation curves are the necessary intermediate steps in determining the polyme r's molecular weight and intrinsic viscosity distributions. If suitable cal ibration standards are available, we further show how the polymer's intrins ic viscosity law can be obtained directly from dual-detector responses with out requiring - or depending on - a sample-dependent calibration curve.