Optimal heating rate in constant pressure and constant flow gas chromatography (2021)

Optimal heating rate is the one resulting in the shortest analysis time for achieving a required separation performance of a column. The previously recommended default heating rate (R<sub>T,Def</sub> ) was optimal for temperature-programmed gas chromatography analyses in constant pressure mode. It has been shown herein that the same recommendation can be extended to constant flow mode with fixed heating rate (R<sub>T</sub> ). The numerical value of R<sub>T,Def</sub> has been herein rescaled from previous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>10</mml:mn> <mml:msup><mml:mspace></mml:mspace> <mml:mo>∘</mml:mo></mml:msup> <mml:mspace></mml:mspace> <mml:mi>C</mml:mi> <mml:mspace></mml:mspace> <mml:mo>/</mml:mo> <mml:mspace></mml:mspace> <mml:msub><mml:mi>t</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> </mml:math> (10°C per void time) where t<sub>M</sub> was measured at 50°C, to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>12</mml:mn> <mml:msup><mml:mspace></mml:mspace> <mml:mo>∘</mml:mo></mml:msup> <mml:mspace></mml:mspace> <mml:mi>C</mml:mi> <mml:mspace></mml:mspace> <mml:mo>/</mml:mo> <mml:mspace></mml:mspace> <mml:msub><mml:mi>t</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> </mml:math> with t<sub>M</sub> measured at 150°C-a round number in the middle of the gas chromatography temperature range, chosen as a reference temperature for numerical values of all temperature-dependent gas chromatography parameters. It has been experimentally found based on theory developed herein that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mrow><mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Def</mml:mi></mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>12</mml:mn> <mml:msup><mml:mspace></mml:mspace> <mml:mo>∘</mml:mo></mml:msup> <mml:mi>C</mml:mi> <mml:mspace></mml:mspace> <mml:mo>/</mml:mo> <mml:mspace></mml:mspace> <mml:msub><mml:mi>t</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> </mml:math> is optimal for columns with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>φ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.001</mml:mn></mml:mrow> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>φ</mml:mi> <mml:mo>=</mml:mo> <mml:msub><mml:mi>d</mml:mi> <mml:mi>f</mml:mi></mml:msub> <mml:mspace></mml:mspace> <mml:mo>/</mml:mo> <mml:mspace></mml:mspace> <mml:mi>d</mml:mi></mml:mrow> </mml:math> is dimensionless film thickness, d and d<sub>f </sub> are the column internal diameter and film thickness, respectively) in constant pressure mode and constant flow mode with fixed R<sub>T</sub> . Theory shows that, for arbitrary φ, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mrow><mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Def</mml:mi></mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>12</mml:mn> <mml:msup><mml:mrow><mml:mo>(</mml:mo> <mml:mn>1000</mml:mn> <mml:mi>φ</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:mn>0.09</mml:mn></mml:msup> <mml:msup><mml:mspace></mml:mspace> <mml:mo>∘</mml:mo></mml:msup> <mml:mspace></mml:mspace> <mml:mi>C</mml:mi> <mml:mspace></mml:mspace> <mml:mo>/</mml:mo> <mml:mspace></mml:mspace> <mml:msub><mml:mi>t</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> </mml:math> . The theory also shows that the fixed R<sub>T</sub> is optimal for constant pressure mode. In constant flow mode, however, the optimal R<sub>T</sub> should gradually increase with increasing temperature (T). The optimal theoretical curves R<sub>T</sub> (T), different for different flow rates, were found. However, only the optimization of the fixed R<sub>T</sub> was experimentally evaluated due to limited capability of existing gas chromatography instrumentation and resources. It has been shown that the separation-time tradeoff in constant pressure mode is slightly better than that in constant flow mode. The experimental data are compiled in the Supporting information.