The 12,4 Hard-Core Potential Model

The 12,4 hard-core potential model takes into account repulsive (power of 12 dependence on the distance of approach) and attractive (power of 4 dependence) potentials that arise when the ion and nentral molecule approach each other at short ranges (see Equation 10.20). When a short-range repulsive term is added to the polarization Umit potential of Equation 10.18, the interaction potential is modified to a (n,4) 

A slightly more sophisticated model includes a third interaction potential and is called the 12,6,4 hard-core potential model. This is formulated by adding a further term to the 12,4 potential to include some attractive energy in the form of an term as shown in Equation 10.21  

The validity of the models described can be tested by comparing experimentally measured reduced mobilities of several ions in the linear IMS with the predicted coefficients calculated according to the three models. The main features of interest were the correlations of mass with mobility and temperature with mobility another interesting feature is the effect of the drift gas on mobility coefficients (the last two are discussed in Chapter 11). Six parameters are needed in the modeling a, r, z, polarizability, reduced mass, and temperature. The last three arise from direct physical measurements, while the other parameters (fl, r, z) are optimized by a fitting procedure to minimize the deviation between calculated and measured mobility constants. The values of T and were calculated from a, r, and z, and the dimensionless collision cross section (1 was taken from Table 1 in Reference 9. In practice, a discrete value of a was chosen, and initial values for and z were estimated. The parameters Tq and z were then optimized to obtain a good fit with experimental data points by minimizing the squared sum of deviations between theory and experiment. Special attention 

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The motion of ions in a buffer gas is governed by diffusive forces, the external electric field and the electrostatic interactions between the ions and neutral gas molecules. Ion-dipole or ion-quadrupole interactions, as well as ion-induced dipole interactions, can lead to attractive forces that will slow the ion movement, mainly due to clustering effects. The interaction potential can be calculated according to different theories, and three such approaches—the hard-sphere model, the polarization limit model, and the 12,4 hard-core potential model— were introduced here. Under... 

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