The Van Deemter Equation PDF

Preview

Summary

lecture notes Dr. Hu...

Description

H= 1+

A Cm

The Van Deemter Equation

+

B +C s u+C m u1/ 2 u

u1/ 2

1. H = measure of column efficiency, smaller is better, H is length of column required for one partition step to occur

H= a.

L N



The smaller the plate height (H) the better the separation

( )

tr N =5 . 54⋅ w1

2

2

b.  

N- # of theoretical plates, efficiency of plates ↑N  ↑efficiency of column  the more plates you have the more efficient the separation 2. A = “eddy diffusion” term (broadening due to longer path some molecules take) a. Explains part of the rational for peak broadening (some molecules take a straightforward path through the column and come out early= leading edge of the peak) b. Most of the molecules follow an intermediate delayed path and they form the bulk of the molecule peak c. There are a few molecules that take a more torturous path and come out last forming the tailing edge of the peak  forming a gaussian distribution o A = 0 in open tubular columns as there is no packing to create eddy diffusion currents o ↑ Cm  ↓ A o ↑ μ  ↑ A (b/c cross multiplication)

3. B = 2Dm  longitudinal diffusion -

Rate of diffusion of the molecule in the liquid phase (small in LC, becomes more significant at low flow rates)

-

This only occurs in the mobile phase

-

B term is longitudinal diffusion, as the molecules go through the column they can diffuse and so early on the band is very tight and later on the band is much broader if the compound stays on the column a very long time

-

A term and B term contribute to band broadening but the B term is really only important at very low flow rates -

At high flow rates or normal flow rates we get very little time for diffusion

-

At low flow rates diffusion can occur, so B becomes more important

-

Dm is the diffusion coefficient of the analyte in the mobile phase, this is something that can be measured, is a value that refers to  after a short period of time the sample is fairly narrow + after a long period of time on the column it is much broader  so Dm takes into account the diffusion of the analyte in the mobile phase, how well does it diffuse back and forth  2Dm can be substituted for B

-

↑ Dm  ↑ band broadening.

-

↓ Dm  won’t get as much longitudinal diffusion - a way to keep Dm small is to ↑ μ, not let flow get too small

4. μ = linear velocity/flow rate of the mobile phase, cm/s of an unretained molecule a. ↑ μ  ↑ Csu and ↑ Cmu1/2 

Csu increases more b/c Cmu1/2 is taking the square root

b. ↑ μ  ↑A  so the whole value of A/ 1+Cm/u1/2 is going to ↑ c. ↑ μ  ↓ B/μ -

If μ gets too low, then B starts increasing

d. ↑ μ  ↑H

1/2

5. Equilibration time = the C term: C s u+C m u a. Cs = resistance to mass transfer in the stationary phase: - Depends on diffusion coefficient in the stationary phase and upon the thickness of the stationary phase coated onto silica gel 2 d thickness C s= Ds o d2 thickness: square of the stationary phase film thickness -

Each particle on a packed particle system has some kind of coating + the analyte must diffusion in and out of the coating

-

↑ d2thickness  ↑Cs

o Ds: diffusion coefficient of the analyte in the stationary phase The thicker that stationary phase the more the particle is going to diffuse, the more it’s going to get absorbed + the greater Cs value will be b. Cm = resistance to mass transfer/diffusion due to the diameter and shape of the stationary phase particles -

-

2 d packing C m= Dm

The smaller and more regular the shape of the particles, the less this term contributes to band broadening o d2packing: square of the stationary-phase particle diameter - diameter of the particle size in the stationary phase - ↓ d2packing  ↓ Cm ↑ d2packing ↑ Cm  ↑H  ↓ efficiency o Dm: the diffusion coefficient of the analyte in the mobile phase -

-

  

↑column temp  ↑rate of diffusion (B) + ↓ mass transfer effects (C terms) ↑ μ  effect of Csμ term predominates ↓ μ  B predominates -





↑Dm  ↓ efficiency of A term and ↑efficiency of Cm term, but effect is less impactful to the A term

have to make a balance between analysis time and flow rate

Column efficiency (N) increased by: - Small particle size of stationary phase (↓d2packing) - Thin stationary-phase coating (↓d2 thickness) - Regularly shaped particles of stationary phase - ↑ Temp - Even stationary-phase coating - Uniform stationary-phase particle size - High diffusion coefficient in the mobile phase (↑Dm) - High diffusion coefficient in the stationary phase (↑Ds) Column efficiency (N) decreased by: - Very low flow rate (↓ μ) - Large particle size of stationary phase (↑d2packing) - Thick stationary-phase coating (↑d2 thickness) - Irregularly shaped particles of stationary phase - ↓ Temp - Uneven stationary-phase coating - Non-uniform stationary-phase particle size - Low diffusion coefficient in the mobile phase (↓Dm) - Low diffusion coefficient in the stationary phase (↓Ds)...