Optimization of Electric Field Traveling Waves in SLIM Platforms for Improved Resolution via Analytical Solutions of the Nernst–Planck Equation

Ion mobility spectrometry (IMS) is increasingly recognized as a powerful technique in analytical chemistry, enabling the separation of gas-phase ions based on their size-to-charge ratio. Among the most advanced implementations of IMS are the Structures for Lossless Ion Manipulations (SLIM) platform, and the cyclic IMS system, which use traveling electric waveforms across precisely patterned electrodes to transport and separate ions. Most SLIM and cyclic IMS systems employ square voltage waves to transmit the ions; however, due to fringing effects, the ions usually observe pseudosinusoidal electric fields as they travel. This fringing effect has not been addressed despite a myriad of studies of different waveforms. In this work, we derive and solve the axisymmetric two-dimensional Nernst-Planck equation under several linearly varying electric field conditions to analyze waveform performance. By comparing field profiles, we show that a linearly decreasing field offers a unique advantage: it suppresses longitudinal diffusion. This condition, in which the standard deviation of the ion distribution remains constant or even shrinks during transport, sets a theoretical benchmark for field-based separations. Practically, however, a decreasing field must always be paired with an increasing field to complete the traveling-wave cycle, which partially neglects the effect. We discuss the implications of this solution, offering guidance for next-generation SLIM device design, while theoretically showing that resolving powers in the thousands are attainable through waveform optimization.