Optimization of Separation Efficiency in Temperature Programmed Gas Chromatography : Application of Response Surface Methodology
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- Department of Chemistry 
Chromatographic efficiency can be defined as the maximal number of chromatographic peaks that can be separated within a section of a chromatogram. In isothermal gas chromatography (GC) it is usually measured by number of theoretical plates and modeled by the van Deemter equation. Number of theoretical plates is not a valid measure of efficiency in temperature programmed GC due to its variability with temperature. The van Deemter equation is also not useful since it does not account for the temperature factor. Thus the purpose of this work has been to investigate how the efficiency depends on carrier gas velocity and temperature rate in temperature programmed GC by expanding the van Deemter equation to a function that accounts for temperature rate in addition to carrier gas velocity, and to develop methodology for optimizing the separation efficiency. Fatty acid methyl esters of saturated homologous and unsaturated fatty acids were used as analytes. The study involved nine different columns of varying polarity using helium, hydrogen and nitrogen as a carrier gases. Efficiency was defined as the inverse of peak width in retention index units and thus peak width was used to measure efficiency where its minimum corresponds to maximum efficiency. Peak width was then used to model van Deemter equation where carrier gas velocity and temperature rate were varied. The data obtained from measurements at different levels of combinations of the varied factors resulted in good fit of van Deemter models at all levels of temperature rate and for all carrier gases used (overall mean R2 = 0.9885). Then by adding the temperature rate factor the ordinary van Deemter curve was expanded to a response surface function which explains peak width in retention index units as a function of carrier gas velocity and temperature rate. The response surface function contained main, interaction and quadratic terms. But since the interacting factors may vary and there is no theoretical basis that explains which of the terms in the response surface function are significant, a backward elimination procedure was employed to detect significant terms. The result revealed that five terms are always required to define the models obtained using each column and every carrier gas. The terms that appear significant depend on the type of carrier gas used. Experiments were carried out in general at 9 levels of carrier gas velocities and 3 levels of temperature rates. Experimental designs of full 9 x 3, 5 x 3, 3 x 3, skewed 3 x 3 and Doehlert designs of carrier gas velocity and temperature rate were compared. From comparison of predicted optimum velocity and peak width measurements the 5 x 3 design showed similar result as the full 9 x 3 design. The 3 x 3, skewed 3 x 3 and Doehlert design had lower performance than the 5 x 3 design. Nevertheless they may be good enough for practical purposes. The maximum difference in predicted optimum velocity from results of full design was 0.98 cm/s for velocities measured in the range of 10-15, 20-30 and 30-40 cm/s for nitrogen, helium and hydrogen respectively whereas the difference in peak width measurements were less than 0.0005 equivalent chain length units. In chromatography there is normally a trade-off between analysis time and separation efficiency. The time of analysis which was best represented with the retention time of the last eluting compound is related to both carrier gas velocity and temperature rate by power functions. This was taken as a basis for deriving response surface function of the retention time of the last eluting compound, which was combined with the models of efficiency. An optimum line of best time efficiency trade-off was then found by an iterative procedure from the overlapped plots and was found to lay 2-5%, 3-6% and 3-8% above the velocity that gives the minimum in van Deemter curve in optimum velocity for helium, hydrogen and nitrogen respectively. Comparison of the carrier gases indicated that at similar efficiency with helium hydrogen as carrier gas reduces the time of analysis by 24-31% whereas there is 80-92% increase in retention time with nitrogen as a carrier gas. On the other hand at similar retention time with helium hydrogen gives 6-8% more efficiency than helium while 12-18% decreases in efficiency with nitrogen is observed. The performance of different polar columns with the right selectivity for FAME was evaluated and compared. The efficiency of the columns was found to depend on polarity of the columns. The less polar DB-23 and BP-20 columns are the most efficient columns whereas the more polar BPX70 and IL100 columns have moderate and less efficiency than the others. On the other hand at similar retention time with helium hydrogen gives 6 - 8 % more efficiency than helium while 1 2 - 18 % decreases in efficiency with nitrogen is observed . The performance of different polar columns with the right selectivity for FAME was evaluated and compared . The efficiency of the columns was found to depend on polarity of the columns . The less polar DB - 23 and BP - 20 columns are the most efficient columns whereas the more polar BPX70 and IL100 colu mns have moderate and less efficiency than the others.