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# Multi-Linear Gradient Elution Optimization for Separation of Phenylthiohydantoin Amino Acids Using Pareto Optimality Method

*M.R. Hadjmohammadi* and K. Kamel*

### Department of Chemistry, University of Mazandaran, Babolsar, Iran

Multi-linear gradient elution was applied for simultaneous optimization of resolution and analysis times for ten phenylthiohydantoin amino acids (PTH-AAs) in liquid chromatography. Relation of ln*K* upon *†* for each analyte was determined using isocratic retention time data, and gradient retention time of analytes was predicted using fundamental equation of gradient elution. Then a grid search program was used to predict retention time of solutes in variable space. Two different chromatographic goals-analysis time and minimum difference between adjacent peaks- were simultaneously evaluated using Pareto optimality method. Gradient program in optimum condition was: initially 24% CH_{3}OH/Water for 10 min, linear ramp to 34% over 5 min, to 29% over 5 min, and to 70% over 20 min. The average of calculated relative error in the prediction of the retention time in optimal conditions was -1.67% that shows a good agreement between predicted and experimental values of the chromatographic retention time in optimal condition.

**Keywords:** Multi-linear gradient elution, Optimization, Pareto optimality method, Phenylthiohydantoin amino acids, Separation