ion mobility of a gas-phase ion is the quantity that describes how quickly
the ion moves through a drift cell filled with a high pressure of buffer
gas under the influence of a weak electric field. Small, compact ions
with small collision cross sections drift more quickly than large, extended
ions with large collision cross sections. This is similar to the effect
that causes an extended paper towel to drift to the ground much more slowly
under the influence of gravity and air resistance than a crushed towel
of the same mass. Thus, measuring the mobility of an ion yields information
about its structure, whether it is compact or extended. Mixtures of compact
and extended structures can be separated like in a chromatography experiment
(hence "ion chromatography"). However, structural assignments based on
mobility results generally require comparison with calculated candidate
structures. Those are obtained in our lab by ab initio/density functional
theory calculations or molecular modeling using the AMBER force field.
A pulse of mass-selected ions is injected into the cell.* The force exerted on them by the electric field is offset by the force of friction caused by collisions of the ions with the buffer gas. As a result, ions drift through the cell with a constant velocity vd that is proportional to the electric field.
In this expression, the proportionality constant K is called the ion mobility. The ion mobility is directly proportional to the buffer gas pressure. It is typically converted to a "reduced" mobility K0 using a value of 760 Torr for P0 and 273.15 K for T0.
By combining the equations above, an expression for the amount of time the ions spend in the drift cell td can be obtained in terms of P/V.
The quantity measured experimentally is ion intensity as a function of time, generating a plot called an arrival time distribution (ATD). Arrival time ta is the amount of time between the formation of the initial ion pulse and an ion's arrival at the detector. It is equal to td + t0 where t0 is the amount of time the ions spend outside the drift cell. Plotting ta versus P/V for a given temperature yields a straight line with an intercept equal to t0. The drift time td can be obtained by subtracting t0 from ta. Typical drift times can range anywhere from 100 μs to 10 ms depending on the mobility of the ion and the drift voltage used. The reduced mobility K0 can be obtained from the slope of the line. The Bowers Group uses this type of experiments in several ways (see table below). In general, they involve using the mobility to calculate a collision cross section or using drift times to determine reaction rate constants.
* All the instruments in the Bowers group have mass-selection capabilities before and after the drift cell except for the ESI instrument, which only has it after the cell.