Simulation and optimisation in ion chromatography

Ion chromatography (IC) is the premier technique for the separation of inorganic and organic ions. Two fundamental elution regimes, namely isocratic and gradient elution, are available for separation but both are often inadequate for the separation of complex mixtures. Hence, complex elution profiles involving multiple isocratic and linear gradient steps have become the most attractive solution to accomplish the desired separations. However, the number of parameters requiring trial-and-error optimisation of such elution profiles demands a huge investment in time. This problem can be solved through the development of in-silico (computerised) simulation, and ultimately optimisation, methods. The Virtual Column Separation Simulator (Dionex Corporation, Sunnyvale, CA, USA) is an efficient commercial software package for simulating and optimising IC separations. However, it has a number of limitations. The objective of this study was to address the limitations of the Virtual Column Separation Simulator and improve its prediction and optimisation abilities. This project focussed on improving the algorithms used for simulation and modelling of retention and peak width. This study commenced with an evaluation of the maximum tolerable prediction error thresholds for retention time and peak width needed for an accurate in-silico optimisation. A sample mixture is normally designed to be separated within a time window of less than 30 minutes. So the acceptable maximum prediction error evaluation was analysed based on a 30-min separation. This analysis indicated that retention time had a much greater influence than peak width on the accuracy of in-silico optimisation. It was found that the acceptable average error limits for representative prediction were 2.5% and 35% for retention time and peak width respectively. Three retention time algorithms and two peak width models were proposed in this study for modelling IC separations. Prediction of analyte retention times under complex eluent profiles using these methods relied on monitoring the analyte displacement through the chromatographic column. The three devised algorithms mapped the position of the analyte in different ways where the position mapping methods of the three algorithms relied on mathematical iteration (which this algorithm was entitled the linear analyte displacement model‚ÄövÑvp), integrated displacement equations and numerical segmented isocratic steps. The three algorithms were found to be highly similar in their predictive errors, which were all 4% on average. Peak width modelling was much more difficult due to well known peak broadening processes. Two empirical peak width models were found to be viable for peak width simulation of analyte under complex eluent profiles. The first peak width model measured the compression exerted from each individual step using a weighting function with a compression term calculation. The second peak width model simulated the peak width using only the eluting retention factor under isocratic conditions. Both models were found to deliver predictive errors of 17% on average. In summary, this study indicated that the retention time simulation of analytes using the newly derived models can be predicted with an average error of ‚Äöv¢¬ß 4%, which is very close to the target acceptable average error limit of 2.5% required for reliable prediction. The second aspect of the modelling process investigated the broadening of the chromatographic during a separation. It was found that the width of an analyte peak could be simulated reliably using both of the derived models with an average error of ‚Äöv¢¬ß 17%. This can be compared to the error threshold of up to 35% that was determined to be manageable for reliable peak width simulation. Hence, two peak width models investigated were deemed to achieve this target. Retention prediction in the Virtual Column Separation Simulator requires the input of analyte information. This information is stored inside the pre-existing data library and is known as embedded data. This data has been collected over a period of 5 years, and to use this embedded data to predict analyte retention on newer columns could be problematic due to the variability in column manufacture and tubing configuration. This incompatibility issue was more obvious when this older embedded data, collected on 4 mm i.d columns, was used to predict separations on the new micro-bore (2 mm) and capillary (0.4 mm) IC columns as a result of the changes in column internal diameter that results in changes related to wall effects, phase ratios and total ion-exchange capacities. These changes will somewhat alter the overall separation selectivity. A method, which was coined porting‚ÄövÑvp, has been used to calibrate the pre-existing data library with minimal experimental input. This process allowed the data to be refreshed‚ÄövÑvp for newer columns, along with those of different internal dimensions, and allowed retention time simulation to be reliably performed. By incorporation of this porting methodology for calibration and the linear analyte displacement model for retention prediction, a predictive error of 3% was achieved for these newer column formats while employing data collected on older column formats.