Standard Reference Material 2881 - National Institute of Standards ...

6.2 Mathematical Model for Gravimetric BlendingAs discussed in Section 4, to estimate the Type B uncertainty in an instrumental methodone needs a mathematical model based on either physical principals or comprehensivephenomenological observations. A quantitative, predictive physical model of the MALDIprocess and the TOF mass spectrometer seems out of reach at this time. However, a heuristicmathematical model is available and will serve as our starting point. The experimental worksdescribed previously 12-17 each implicitly assume that there is a point in the parameter space ofthe instrument and the sample preparation where the signal intensity, S i , for an oligomer ofmass m i is linearly proportional to n i , the number of polymer molecules at that oligomermass. Mathematically this is given by:Si= kn i[6.1]where for a narrow enough range of m i we assume k is a constant independent of m i and therange of linearity, 0 < n i < n 0 , is the same for all oligomers. From the work of Goldschmidtand Guttman, 18 working with a 7900 u PS in a matrix of either retinoic acid or dithranol,there was found a linear relationship between signal intensity and analyte concentration over awide concentration range provided there is a large molar excess of Ag salt. Furthermore, at ahigh polymer-to-matrix ratio, the curve becomes nonlinear and the signal intensity approachessaturation. This cutoff was shown to be a weak function of molecular mass.If we assume we are in the linear region for all the oligomers of a polymer, the totalmeasured signal is given by:∑ imi= k∑nimiS [6.2]with n i m i summed over all oligomers i. This is valid as long as the polymer is evenlydistributed throughout the matrix on the target spot. Then we can obtain:14