## Geometric Analysis of Shapes in Ion Mobility-Mass Spectrometry

Experimental ion mobility-mass spectrometry (IM-MS) results are often correlated to three-dimensional structures owing to theoretical chemistry calculations. The bottleneck of this approach is the need for accurate values, both experimentally and theoretically predicted. Here, we analyze experimental and theoretical collision cross-section (CCS) evolutions instead of interpreting absolute CCS values. Experimentally, the CCS trends of synthetic homopolymers are analyzed as a function of increasing degrees of polymerization (DP) for different charge states. Then, shape evolutions of modeled shape deformations yield theoretical CCS trends, calculated using new software called MoShade (projected area calculations). The shapes are modeled using computer-aided design software where we considered only geometric factors: no atoms, chemical potentials or interactions are taken into consideration to make the method orthogonal to classical methods for 3D shape assessments using time-consuming computational chemistry. We are able to correlate modeled shape evolutions to experimentally-obtained polymer CCS trends. We thus modeled the apparent volume or envelope of their ion-drift gas interactions as sampled by IM-MS. Moreover, the CCS of convex shapes could be directly related to their surface area. The relation seems to hold even for concave shapes which could be correlated to geometry-optimized structures of ions obtained by conventional computational chemistry methods. Modeling beads-on-a-string shape evolutions allows extracting precise dimension relations between two homopolymers, without modeling any chemical interactions.