A nonlinear electrophoretic model for PeakMaster: I. mathematical model

Area of Science:

• Analytical Chemistry
• Physical Chemistry
• Computational Chemistry

Background:

• Electromigration is a fundamental separation technique.
• Existing linearized models have limitations in predicting complex zone behaviors.
• Accurate modeling is crucial for optimizing separation conditions and interpreting results.

Purpose of the Study:

• To extend the linearized electromigration model by incorporating nonlinear dispersion and diffusion.
• To develop a new model capable of accurately predicting electropherograms for various zone shapes and injection conditions.
• To implement the enhanced model in PeakMaster software for practical application.

Main Methods:

• Developed a continuity equation for zone shape function including linear and nonlinear migration and diffusion terms.
• Solved the equation using the Hopf-Cole transformation.
• Applied the solution to Dirac and rectangular pulse initial conditions, deriving Haarhoff-van der Linde (HVL) and HVLR functions.
• Implemented the nonlinear model and HVLR function in PeakMaster 5.3.

Main Results:

• The nonlinear model accurately describes zone migration, diffusion, and dispersion.
• The HVLR function enables prediction of electropherograms, including those with wide injection zones.
• Model predictions were validated against numerical simulations using Simul 5.
• The enhanced model provides a more comprehensive understanding of electromigration phenomena.

Conclusions:

• The extended nonlinear electromigration model offers significant improvements over linearized approaches.
• The HVLR function is a valuable tool for predicting and analyzing electropherograms in PeakMaster.
• This work advances the simulation capabilities for capillary electrophoresis and related techniques.