Average drift time and average mobility in ion mobility spectrometry

- Ions in an IMS are mostly clustered or hydrated.
- A model is used to describe the average mobility and drift time.
- Four fraction quantities are defined.
- Average mobility is related to the single ion mobilities in the form ofKavg=X0K0+X1K1+X2K2+..., where, Xi is the mole fraction.

Ions in an IMS are mostly clustered or hydrated so that a single ion mobility peak usually contains a mixture of ions differing in their cluster size. In this study, a model is used to describe the average mobility and drift time based on the individual properties of the mixture. For this purpose, the following four fraction quantities are defined: length fraction,Xid, (i.e., the fraction of the drift tube along which the ion travels in the form of i); time fraction, Xit, (i.e., the fraction of the drift time during which the ion travels in the form of i); single ion time fraction, Xito, (i.e., the time an ion spends as i in the drifting mixture divided by the drift time of pure i); and the mole fraction, Xi. It is shown that for a binary mixture of ions, the fraction quantities are related by(XA=XAt)=(XAd=XAto)×(XA+α.XB) , where α=KA/KB is the relative mobility of the two components. It is concluded that average mobility is related to the single ion mobilities in the form ofKavg=X0K0+X1K1+X2K2+...., where, Xi is the mole fraction. However, the observed or the average drift time cannot be described in a similar manner. Rather, it must be inverted to tobs−1 = Xoto−1 + X1t1−1 + X2t2−1 + …. If, in case, it is expanded as tobs = αo to+ α1 t1+ α2 t2+ …, the coefficient αi will differ from the mole fractions.

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