by jan st hlberg academy of chromatography www academyofchromatography com l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
The Theory for Gradient Chromatography Revisited PowerPoint Presentation
Download Presentation
The Theory for Gradient Chromatography Revisited

Loading in 2 Seconds...

play fullscreen
1 / 20

The Theory for Gradient Chromatography Revisited - PowerPoint PPT Presentation


  • 273 Views
  • Uploaded on

by Jan Ståhlberg Academy of Chromatography www.academyofchromatography.com. The Theory for Gradient Chromatography Revisited. Objective of the presentation. Discuss the background of the traditional theory for gradient chromatography.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'The Theory for Gradient Chromatography Revisited' - bernad


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
by jan st hlberg academy of chromatography www academyofchromatography com
by

Jan Ståhlberg

Academy of Chromatography

www.academyofchromatography.com

The Theory for Gradient Chromatography Revisited
objective of the presentation
(c) Academy of Chromatography 2007Objective 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)

The traditional derivation starts with the velocity of the migrating

zone as a function of the local retention factor.

us

Mobile phase velocity

F(x,t)

Zone velocity Local retention factor as a

function of mobile phase

composition F

brief review of the traditional theory 2
Brief review of the traditional theory (2)

Introduce the coordinate z where:

Assume that a given composition of the mobile phase migrates through the column with the same velocity as the mobile phase, i.e. u0. Let the solute be injected at x=0 and t=0.

The equation for the migrating zone can now be written:

brief review of the traditional theory 3
Brief review of the traditional theory (3)

The retention time is found from the integral:

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)
  • For a linear gradient with slope G and for a solute with retention factor ki at t=0, integration gives:
mass balance approach 1
Mass balance approach(1)

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)

The stationary phase concentration is a function of the mobile phase composition, Φ, i.e. n=n(c,Ф(x,t)) .

This means that:

For a linear adsorption isotherm F*δn/ δ c is equal to the retention factor k(Ф(x,t)).

mass balance approach 3
Mass balance approach(3)

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)

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)

For this particular case the mass balance equation is:

Where ki is the initial retention factor at t=0.

The solution of this equation is of the form:

where f(x,t) is determined by the boundary and initial conditions.

mass balance approach 6
Mass balance approach(6)

Example:

Assume that the solute is injected at x=0 as a Gaussian profile according to

The solution of the differential equation is found to be:

gradient equation gaussian injection s g 5
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=5
gradient equation gaussian injection s g 1
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=1
gradient equation gaussian injection s g 0 1
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=10sGradient equation; Gaussian injection;S*G=0.1
gradien equation gaussian injection s g 0 05
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
gradient equation gaussian injection s g 0 01
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
mass balance approach 7
Mass balance approach(7)

Example:

Assume that the solute is injected at x=0 as a profile according to

The solution of the differential equation is:

mass balance approach 8
Mass balance approach(8)

Example:

Assume that the solute concentration is constant and independent of time. The solution of the

differential equation is:

conclusions
Conclusions
  • A fundamental and general theory for gradient chromatography can be obtained from the mass balance equation for chromatography.
  • The traditional theory for gradient chromatography is a special case of a more general theory, it is valid in the limit c(solute) 0.
  • By neglecting the dispersive term in the mass balance equation, algebraic solutions are easily found.
  • Practical consequences:
  • By comparing experimental data with the exact solution, the effect of dispersion can be quantified.
  • ……..