Vandeemeter equation


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Vandeemeter equation

  2. 2. INTRODUCTION• In the mid 1950s a group of Dutch chemicals engineers began a study of the process that caused band broadening in chromatography.• They derived an expression called as the VAN DEEMETER equation, relating the height equivalent to a theoretical plate(HETP) to a number of experimental parameters , which are7/23/2012 2
  3. 3. 7/23/2012 3
  4. 4. • Diameter of the stationary phase particles.• The diffusion coefficients of the solute in the stationary phase and mobile phase.• Flow rate of the mobile phase.7/23/2012 4
  5. 5. • Van Deemeter equation is useful in optimizing chromatographic performance and is expressed as: HETP = 2λdp + 2νdg + 8 {K / (1+K) 2} df2 x u u π2 dl• u = Velocity of carrier gas• λ = Constant indicating packing of column• dp = Particle diameter• ν = Obstruction factor• dg = diffusion coefficient of the solute molecules in carrier gas ( cm2 / sec)• 8 / π2= Geometrical factor pertaining to the uniformity of the liquid film thickness on the particles• K = Capacity factor• df = Thickness of the film of liquid phase• dl = Diffusion coefficient of the solute in liquid phase (cm2 / sec)7/23/2012 5
  6. 6. • Except u , all other terms in the equation are constant so it can be simplified as follows HETP = A + B / u + Cu• A = EDDY’S DIFFUSION• B = LONGITUDINAL DIFFUSION• C = MASS TRANSFER• µ = VELOCITY OF THE CARRIER GAS7/23/2012 6
  7. 7. COEFFICIENT A• Coefficient A is called the eddy diffusion or multiple –path coefficient and is concerned with the different paths traveled by the molecules of a particular solute during their passage through the column.• The particles of the stationary phase, weather irregularly or spherically shaped, are packed as tightly as possible, and the solute molecules must pass around them to proceed along the7/23/2012 7 column.
  8. 8. …7/23/2012 8
  9. 9. • Because of the large number of possible paths , some molecules of the same kind will reach the end of the column before others .• Faster molecules found in the leading edge of the peak , and slower ones form the tailing edge.• The net effect of this distribution is band broadening.7/23/2012 9
  10. 10. • In a modern chromatographic column ,which is packed with small , uniformly sized particles , the value of A is minimal and the contribution of this term to increasing the HETP is negligible.• In GLC column , which contains no solid particles, the value of A is zero.7/23/2012 10
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  12. 12. COEFFICENT B  In the van dee meter equation is termed the coefficient of longitudinal diffusion. Because the concentration of solute is lower at the edges of the band than in the center ,a gradient exists and, during travel of the band through the column, solute is diffusing continually through the mobile phase away from the center of the band.  This phenomenon occurs at both the leading & trailing edges of the peak & contributes7/23/2012 further to band broadening. 12
  13. 13. FRONTING : Deformation at the beginning of the peak. It is due to saturation ofstationary phase with higher quantity of components.TAILING: Deformation at the end of the peak. It is due to similarity of polarity for acomponent towards stationary phase.7/23/2012 13
  14. 14. • The equation predicts that the contribution to the HETP of this is inversely proportional to the• mobile phase velocity• The effect is more pronounced at low flow rates.• Diffusion effects are more severe in GC than in liquid chromatography because diffusion coefficient are several orders of magnitude higher in the gas.7/23/2012 14
  15. 15. • The contribution of longitudinal diffusion to band broadening can be lessened by the proper adjustment of flow rates.7/23/2012 15
  16. 16. COEFFICENT C• The co efficient of mass transfer, is concerned with the transfer of the solute between the two phases.• Because the mobile phase is moving rapidly, equilibrium between the two phases may not be attained .• Therefore, some solute molecules in the mobile phase are not transferred to the stationary phase quickly enough, and, result are carried ahead of the center of7/23/2012 16 the band.
  17. 17. 7/23/2012 17
  18. 18. • Those in the stationary phase are retained too long and ,hence, lag behind.• In contrast to longitudinal diffusion , the contribution to the plate height of this term directly proportional to the flow rate; thus, to minimize the overall effect, a compromise in flow rate is necessary.• Mass transfer effects also may be lessened by using a very thin coating of the stationary phase so that the area, in7/23/2012 18
  19. 19. • Contact with the mobile phase is maximized while diffusion deep in to the stationary phase is reduced.• An efficient GC column will have several thousand theoretical plates , and capillary columns will have in excess of 10,000 theoretical plates.7/23/2012 19
  20. 20. GRAPH OF HETP7/23/2012 20
  21. 21. Significance:• It explains the factors responsible for band broadening.• It also gives the optimum flow rate of M.P so as to get minimum HETP.• Use full in optimizing the chromatographic performance.7/23/2012 21
  22. 22. 7/23/2012 22