Mass
spectrometry (MS) is a uniquely informative technique in the characterization
of copolymers, where spectra prominently feature peak clustering.
The spacing of these clusters, in general, is dominated by the spacing
of one repeat unit, and contained herein is the theory to explain
this observation. Extension of this theory also explains the more
subtle observation that, even though the spacing is generally that
of one unit, occasionally, the spacing between the maxima of adjacent
clusters shifts by that of the other unit. Furthermore, the theory
predicts that, in the low molecular weight region of the spectrum,
there is a total switch to the spacing of the other unit along with
asymmetric peak clusters that have a “sawtooth” shape.
The analysis uses the Gaussian, log–normal, and Schulz–Zimm
models as well as the random coupling hypothesis to explicitly demonstrate
that (1) the major peak cluster spacing naturally arises from the
unit in the copolymer with the widest distribution, as measured by
the scaled standard deviation, (2) the spacing shift naturally occurs
due to the marginal probabilities away from the spectrum maximum,
and (3) the low molecular weight switch is a natural consequence of
the tail of the distribution of the unit with the widest distribution.
Results are provided to predict which unit in the copolymer will govern
the major peak cluster spacing, how often the spacing will shift to
that of another unit in the middle and high molecular weight regions
of the spectrum, the molecular weight and composition of the maximum
peak in every cluster, and the molecular weight below which the spacing
will be that of the another unit. We believe that our results are
the first to provide tangible theory to explain the previously unknown
origins of these empirically observed phenomena.