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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