Travelling wave ion mobility spectrometry: determination of size?

I performed an ESI / travelling wave ion mobility spectrometry / MS experiment and observe $\ce{M + H+}$ at $m/z ~701$ and $\ce{M + K+}$ ions with $m/z ~740$. The drift times are 6.75 ms for $\ce{M + H+}$ and 7.0 ms for $\ce{M + K+}$. My first instinct was that this means that the proton adduct is smaller than the potassium adduct. However, if the mass is taken into account as well, i.e. $$7.0 ~\mathrm{ms} ~/ ~740 = 0.0095 ~\mathrm{ms}$$ for the potassium adduct, and for the proton adduct $$6.75 ~ \mathrm{ms} ~/~ 701 = 0.0096 ~\mathrm{ms}$$ which would indicate that the two are very similar in size, the proton adduct being slightly larger. For a linear drift tube it would be very easy for me to calculate the relationship (i.e. Mason-Schamp equation), but for travelling wave IMS I am pretty unsure. Which of the two reasonings is correct?

In terms of practical data analysis standpoint, travelling wave-IMS data can generally be treated similarly as drift tube-IMS for which the technical differences is in resolution (better or worse). However, one point of consideration is that

Low gas pressure in TW IMS means strong fields in E/N terms and thus substantial heating of ions. This may cause fragmentation or distortion of macromolecular structures, complicating their detection and characterization. [1]

Your first instinct to assume that the $\ce{[M + H]+}$ adduct is quite rational, however remember that ion conformation is always in flux and can be influenced by collisions with buffer gas. What you may be experiencing is the proton adduct producing a "looser" structure, resulting in a larger collisional cross section. The $\ce{[M + K]+}$ adduct is heavier in mass but may produce a tighter conformation.

A good example of this is in the fragmentation and mobility of polyethylene glycol (PEG) ions $\ce{[PEG + H]+}$ and $\ce{[PEG + Na]+}$. When carrying out fragmentation studies of PEG, it was found that the sodiated ion produced less extensive fragmentation and required higher collision energy.[2] Ion mobility studies have also found that PEG chelates the $\ce{Na+}$ ion similar to that of crown-ether, producing tightly wound "rigid" structures.[3]

These conditions are highly compound/structure dependent however, it should be something to keep in mind especially in the case of analyzing other molecules such as peptides which respond to adduction in "weird and mysterious" ways.

References

• Especially the second reference looks very promising. Thanks : ) – logical x 2 Nov 22 '16 at 23:36