Error analysis for NMR polymer microstructure measurement without calibration standards.

We report an error analysis method for primary analytical methods in the absence of calibration standards. Quantitative (13)C NMR analysis of ethylene/1-octene (E/O) copolymers is given as an example. Because the method is based on a self-calibration scheme established by counting, it is a measure of accuracy rather than precision. We demonstrate it is self-consistent and neither underestimate nor excessively overestimate the experimental errors. We also show the method identified previously unknown systematic biases in a NMR instrument. The method can eliminate unnecessary data averaging to save valuable NMR resources. The accuracy estimate proposed is not unique to (13)C NMR spectroscopy of E/O but should be applicable to all other measurement systems where the accuracy of a subset of the measured responses can be established.