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The theory for gradient chromatography revisited

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Information about The theory for gradient chromatography revisited
Education

Published on February 7, 2008

Author: Sebastiana

Source: authorstream.com

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The Theory for Gradient Chromatography Revisited:  The Theory for Gradient Chromatography Revisited by Jan Ståhlberg Academy of Chromatography www.academyofchromatography.com Objective of the presentation:  Version: 05/20/07 (c) Academy of Chromatography 2007 2 Objective of the presentation Discuss the background of the traditional theory for gradient chromatography. Show how a more fundamental and general theory for gradient chromatography can be obtained. Show some applications of the general theory. Brief review of the traditional theory (1):  Brief review of the traditional theory (1) Version: 05/20/07 The traditional derivation starts with the velocity of the migrating zone as a function of the local retention factor. Zone velocity Local retention factor as a function of mobile phase composition F Mobile phase velocity F(x,t) us Brief review of the traditional theory (2):  Brief review of the traditional theory (2) Version: 05/20/07 Brief review of the traditional theory (3):  Brief review of the traditional theory (3) Version: 05/20/07 In many cases the retention factor of a solute decreases exponentially with F, i.e.: Where S is a constant characteristic of the solute. Brief discussion of the traditional theory (4):  Brief discussion of the traditional theory (4) Version: 05/20/07 Mass balance approach(1):  Mass balance approach(1) Version: 05/20/07 A fundamental starting point for an alternative gradient theory is the mass balance equation for chromatography: c= solute concentration in the mobile phase n= solute concentration on the stationary phase F= column phase ratio D= diffusion coefficient of the solute x= axial column coordinate t= time Mass balance approach(2):  Mass balance approach(2) Version: 05/20/07 Mass balance approach(3):  Mass balance approach(3) Version: 05/20/07 The mass balance equation becomes:. Here, the diffusive term has been omitted. The equation is the analogue of the ideal model for chromatography. The term ∂n/∂Φ is a function of c, i.e. In the limit c→0, the traditional representation of gradient chromatography theory is obtained. Mass balance approach(4):  Mass balance approach(4) Version: 05/20/07 For a solute it is often found that: Where c is the concentration of the solute in the mobile phase and k0 the retention factor of the solute when Ф =0. The function ∂Ф/∂t is known and determined by the experimenter. For a linear gradient it is equal to the slope, G, of the gradient.   Mass balance approach(5):  Mass balance approach(5) Version: 05/20/07 Mass balance approach(6):  Mass balance approach(6) Version: 05/20/07 Gradient equation; Gaussian injection;S*G=5:  Gradient equation; Gaussian injection;S*G=5 Version: 05/20/07 Solution of the gradient equation for a Gaussian profile, red line. Numeric simulation of the complete mass balance equation, H=10mm, for the same input parameters. c0=10 mmol, t0=50,s ki=10, ,ti=10s Gradient equation; Gaussian injection;S*G=1:  Gradient equation; Gaussian injection;S*G=1 Version: 05/20/07 Solution of the gradient equation for a Gaussian profile, red line. Numeric simulation of the complete mass balance equation, H=10mm, for the same input parameters. c0=10mmol, t0=50,s ki=10, ,ti=10s Gradient equation; Gaussian injection;S*G=0.1:  Gradient equation; Gaussian injection;S*G=0.1 Version: 05/20/07 Solution of the gradient equation for a Gaussian profile, red line. Numeric simulation of the complete mass balance equation, H=10mm, for the same input parameters. c0=10 mmol, t0=50,s ki=10, ,ti=10s Gradien equation; Gaussian injection;S*G=0.05:  Gradien equation; Gaussian injection;S*G=0.05 Version: 05/20/07 Solution of the gradient equation for a Gaussian profile, red line. Numeric simulation of the complete mass balance equation, H=10mm, for the same input parameters. c0=10 mmol, t0=50,s ki=10, ,ti=10s Gradient equation; Gaussian injection: S*G=0.01:  Gradient equation; Gaussian injection: S*G=0.01 Version: 05/20/07 Solution of the gradient equation for a Gaussian profile, red line. Numeric simulation of the complete mass balance equation, H=10mm, for the same input parameters. c0=10 mmol , t0=50,s ki=10, ,ti=10s Mass balance approach(7):  Mass balance approach(7) Version: 05/20/07 Mass balance approach(8):  Mass balance approach(8) Version: 05/20/07 Conclusions:  Conclusions Version: 05/20/07

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