INTRODUCTION TO CHROMATOGRAPYPART II

REVIEW: RESOLUTION

Rs = ¼ (-1/) (k/k+1) N½

The effect on Rs of:increasing a…?increasing k…?increasing N…?

H - Theoretical Plate Height

H = A + B/u + (Cs + Cm) u

u = the average linear mobile phase velocityA is a term expressing multipath diffusionB/u is the term for longitudinal diffusionCs is the mass transfer term in the stationary phase Cm is the mass transfer term in the mobile phase

A - Multiple Flow Paths

A = 2ldp

Where l is is a constant that depends on the quality of the packing, dp is the diameter of the packing particle

B/u - Longitudinal Diffusion

B=

2Dm

uu

Where g is a constant that depends on the quality of the packing, Dm is the diffusion coefficient in the mobile phase

Mass Transfer in the Stationary Phase

Csu = fs(k)df2

Dsu

Where fs(k) means “a complex function of k”df is the thickness of the liquid coatingDs is the diffusion coefficient in the stationary

phase.

Mass Transfer in the Mobile Phase

Cgu =fg(k)di

2

Dg

u

Cmu =fm(k)dp

2

Dm

u Packed Columns

Capillary Columns

Mass Transfer in the Mobile Phase

The smaller the spaces betweenparticles the faster the transfer from the mobile phase.

In capillary gas chromatography, common mobile phases (carrier gases) differ considerably in their diffusion coefficients which will have an effect on plate height, in this case nitrogen being the best.

Nitrogen = 0.15 cm2/sHelium = 0.40 cm2/s Hydrogen = 0.56 cm2/s

Mass Transfer in the Mobile Phase

However, longitudinal diffusion is most important at low mobile phase velocities, and at the higher velocities often used in chromatography, the Cgu term is more important, and hydrogen and helium are often preferred over nitrogen.

Nitrogen = 0.15 cm2/sHelium = 0.40 cm2/s Hydrogen = 0.56 cm2/s

Mass Transfer in the Mobile Phase

Mass Transfer in the Mobile Phase

Cgu =fg(k)di

2

Dg

u

The effects of capillary column internal diameter on plate height.

A) 0.53 mm, B) 0.25 mm, C) 0.05 mm

Assuming it was 30 M long, What would “N” be for column B at a flow rate of 30 cm per second?

Average Linear Velocity (u)

The average linear velocity term used in these equations is simply calculated by the following

formula:

u = L/to

L = Column lengthto = retention time of an unretained compound

The Effect of Resolution on Total Analysis Time

T =16Rs

2Hu

- 1( ) (1 + kb)

kb

32

2

T =16Rs

2Hu

- 1( ) (1 + kb)

kb

32

2

Doubling of resolution (all other things being equal) would require 4x longer time. Since we know that Rs is proportional to N from

previous equations, then doubling of resolution could be achieved by using a 4x longer column (this 4x longer column taking 4x

longer time for analysis).

The Effect of Resolution on Total Analysis Time

T =16Rs

2Hu

- 1( ) (1 + kb)

kb

32

2

The Effect of Resolution on Total Analysis Time

The effect of the efficiency factor

Analysis Time is directly proportional to H

T =16Rs

2Hu

- 1( ) (1 + kb)

kb

32

2

What would be the effect on analysis time of changing a from 1.05 to 1.10?

The Effect of Resolution on Total Analysis Time

The effect of the selectivity factor

T =16Rs

2Hu

- 1( ) (1 + kb)

kb

32

2

Compare retention factor terms using:k = 0.3 ? k = 2.0 ?k = 10 ?

The Effect of Resolution on Total Analysis Time

The effect of the retention factor

0

5

10

15

20

25

30

0.1 1 10 100

Retention Factor Kb

Re

lati

ve

Tim

e

Retention Factor kb

The Effect of Resolution on Total Analysis Time

Peak Shape

Peaks on a chromatogram have a bell shaped curve often this shape is modeled based on a normal

(Gaussian) distribution. A Gaussian shape results when the partition coefficient is constant

Peak ShapeIn real columns, the ratio CS/CM changes somewhat as

the total quantity of solute increases, and the resulting band shapes are skewed.

Peak Shape

Skewed peak shapes result in changes in retention time.

The General Elution Problem

The solution to this problem is actually quite simple. The separation of the first pair of peaks (1 & 2) is

optimized and then the chromatography conditions are changed to maximize the separation of the next

pair of peaks, and so on.

The General Elution Problem

In HPLC changing the mobile phase during a chromatographic run is called gradient elution.

In gas chromatography, changing the temperature of the column during the run is standard practice and is

called temperature programming.

Extra Column Effects

Besides the column, there are other places in the chromatographic system where band broadening

can take place. These areas are known as extra-column volumes and consist of the volume between the injection point and the head end of the column,

and the volume between the outlet of the column and the detector.

The retention time of an analyte is determined by 9 factors:

1. the chemistry of the analyte2. the composition of the solvent containing the analyte3. the injection volume4. the physical and chemical properties of the column packing5. the dimensions of the column6. the composition of the mobile phase7. the temperature of the system8. the flow rate9. the extra-column volume