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

∑ Simi∑ Si= k∑nimi/ k∑ni/ [6.3]The right hand side of the equation is the M n of the polymer (equation [4.1]) independent of ksince the k in numerator and denominator cancel out. The same holds for equations for M wand all higher moments and is broadly true if we are in the linear range.We know from the work of Montaudo and coworkers 19 , McEwen and coworkers 20 , andLi and coworkers 15-17 that if the m i span too great a mass range the values for k and/or the n 0cutoff must change dramatically otherwise the MALDI-TOF MS would be able to obtain theMMD correctly for very broad distributions.In general, if we are in the linear range for each oligomer i of a polymer then:S = k n[6.4]iiiwhere k i is now a slowly varying function of i or more simply a slow varying function ofoligomer mass m i for a fixed set of instrument parameters and sample preparations parameters(e.g., matrix material, matrix:salt:polymer concentration, method of sample preparation, etc.).An equation similar to [6.4] has been assumed by Sato, et al. 21 for the relationship betweenfractions obtained from an analytical SEC and signals measured from each fraction byMALDI-TOF MS. Theirs is simply a coarse grained version of our mathematical model.Now if we assume in the above equation that k i is a slowly varying function of i or of m ithen we may make a Taylor's expansion around a mass peak near the center of the MMD,termed M 0 . The center of the MMS is used to assure that the function is changing as little aspossible over the entire width of the MMD. Then:S = k n + Q( m − M ) n + higher order terms in n and m[6.5]ioiioiii15