Pendular Ions in FAIMS The Matter of Rotational Hysteresis

5 Pendular Ions in FAIMS The Matter of Rotational Hysteresis 

The timescale (Jr) of adjusting to the variation of E is controlled by two phenomena limiting the speed of ion rotation— the inertia and viscous friction with characteristic times of tjn and tyis, respectively. One may approximate 

The inertia depends only on the ion (and not gas) properties—the principal moments of inertia 7r of which 3D geometries have three. To estimate ti for typical globular proteins, we may represent them as filled spheres. For a uniform sphere, all three 7r equal 

Objects rotate in media slower than in vacuum because of viscous friction, which may be quantified using the Stokes-Einstein-Debye equation. For a sphere 

For proteins with m between 9 kDa for ubiquitin and 66 kDa for albumin (Table 2.4), one finds ri 18-33 A and, assuming Tr = 300 K, that tin 0.4-2.2 ns by Equation 3.61, tin 2.4—51 ns by Equation 3.63, and tvis 0.1-0.6 ns by Equation 3.64. Elevation of Tr by rotational ion heating (2.7.2) would somewhat reduce both tin and tvis, with tvis proportional to decreasing more than ti proportional to So the rotational diffusion of typical proteins is 

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