INTRODUCTION TO CHROMATOGRAPY PART II

Rs = ¼ (a-1/a) (k/k+1) N½ The effect on Rs of: Review: Resolution increasing a…? increasing k…? increasing N…?

H - Theoretical Plate Height H = A + B/u + (Cs + Cm) u u = the average linear mobile phase velocity A is a term expressing multipath diffusion B/u is the term for longitudinal diffusion Cs 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 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 Where fs(k) means “a complex function of k” df is the thickness of the liquid coating Ds is the diffusion coefficient in the stationary phase.

Mass Transfer in the Mobile Phase Cmu = fm(k)dp2 Dm u Packed Columns Cgu = fg(k)di2 Dg u Capillary Columns

Mass Transfer in the Mobile Phase The smaller the spaces between particles the faster the transfer from the mobile phase.

Mass Transfer in 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/s Helium = 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/s Helium = 0.40 cm2/s Hydrogen = 0.56 cm2/s

Mass Transfer in the Mobile Phase Assuming it was 30 M long, What would “N” be for column B at a flow rate of 30 cm per second? The effects of capillary column internal diameter on plate height. A) 0.53 mm, B) 0.25 mm, C) 0.05 mm

u = L/to 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 length to = retention time of an unretained compound

The Effect of Resolution on Total Analysis Time T = 16Rs2H u a a - 1 ( ) (1 + kb) kb 3 2

The Effect of Resolution on Total Analysis Time 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 The effect of the efficiency factor Analysis Time is directly proportional to H

The Effect of Resolution on Total Analysis Time The effect of the selectivity factor 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 retention factor Compare retention factor terms using: k = 0.3 ? k = 2.0 ? k = 10 ?

The Effect of Resolution on Total Analysis Time Retention Factor kb

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 Shape In real columns, the ratio CS/CM changes somewhat as the total quantity of solute increases, and the resulting band shapes are skewed.

Skewed peak shapes result in changes in retention time.

The General Elution Problem

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. 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 analyte 2. the composition of the solvent containing the analyte 3. the injection volume 4. the physical and chemical properties of the column packing 5. the dimensions of the column 6. the composition of the mobile phase 7. the temperature of the system 8. the flow rate 9. the extra-column volume