Section 3

What is the Best Column
Configuration for Your Method?

 

Will a Shorter Column Work for Your Application?

It is not necessary to actually install, equilibrate and run a sample on a shorter column to determine if it will provide sufficient resolution for your sample mix. if you already have data from a longer column, a few quick calculations will tell you if a shorter column having the same particle size will work.

Estimating Change in Rs
Resolution, Rs, changes directly with the square root of the change in column plate number. Since plate number changes directly with column length, we know that resolution will change directly with the square root of the ratio of column lengths (L).

Rs2 = Rs1 x (L2/L1)0.5

Where:
Rs1 = Resolution with column #1
Rs2 = Resolution with column #2 
L1 = Column #1 length
L2 = Column #2 length

    Estimating Changes in Analysis Time and Back Pressure
In similar fashion, we can predict how analysis time (T) and back pressure (P) will change with column length. 

T2 = T1 x L2/L1
P2 = P1 x L2/L1 

Where:
T1 = Analysis time with column #1
T2 = Analysis time with column #2
P1 = Pressure with column #1
P2 = Pressure with column #2

An Example

Figure 3-1

Column: 4.6 x 150 mm;  Pressure: 1050 psi
Analysis time: 18 min; Rs(3,4) = 3.7



Column: 4.6 x 150 mm;  Pressure: 630 psi
Analysis time: 11 min; Rs(3,4) = 2.9

Suppose that you are using a 25 cm column. The resolution between the least resolved peak pair is 3.7, the total analysis time is 18 minutes and the back pressure is 1050 psi. If resolution greater than 2.5 is required for this analysis, could a 15 cm column be used in place of the 25 cm column? How would the analysis time and pressure change?

Rs2 = 3.7 x (15/25)0.5 = 2.9
T2 =18 min x 15/25 = 10.8 min
P2 =1050 psi x 15/25 = 630 psi

Where:
Rs2 = Resolution with 15 cm column
T2 = Analysis time with 15 cm column
P2 = Pressure with 15 cm column

It is clear from the analysis that a 15 cm column could be substituted and perform satisfactorily. This change would result in using 40% less solvent and reducing analysis time by 7 minutes.

The example above shows that you can quickly determine if a shorter column will work for a particular analysis without having to actually install and run the column. This can save you many hours of trial-and-error work in the laboratory.
 
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