Column Diameter, Linear Velocity and Column Efficiency

Feb 01, 2010

I recently had a question regarding some changes that took place in the 2009 edition of the US Pharmacopeia. In USP 32, General Chapter 621,1 the adjustments allowed to meet system suitability for liquid chromatography (LC) methods include a change in column internal diameter of ±25%. A change was made in USP 32 Supplement 2.2 This stated that column internal diameter "can be adjusted provided that the linear velocity is kept constant." The person was not sure how this adjustment of linear velocity should be made and wondered about what effect it would have on column efficiency.

Adjustment of Flow Rate

Much of the band broadening that takes place within an LC column is a result of slow diffusion of the analyte in and out of the pores in the column packing. This means that the mobile phase flow rate can have an affect on the volumetric width of a peak. By volumetric width, I mean the peak width in units of volume (for example, millilitres or microlitres), not time. In the days when 10 μm diameter particles were used as column packing, a noticeable reduction in column efficiency could be observed when the flow rate was increased.

The smaller the particle diameter, the less the dependence of column efficiency upon flow rate. Although it is easy to demonstrate a loss in efficiency with an increase in flow rate for very well-behaved analytes with 3 and 5 μm diameter particles, a two-fold change in flow rate is rarely noticed with real applications. With sub-3 μm particles, flow rate has little influence on column efficiency, even with well-behaved compounds.

In this discussion, I have referred to flow rate, but the important variable is not flow rate, but linear velocity. Linear velocity is the speed at which the mobile phase travels through the column, for example, in millimetres per second. For comparison of equivalent conditions between columns of different internal diameters, the linear velocity should be kept constant. To keep linear velocity constant, the flow rate should be adjusted in proportion to the column cross-sectional area, which is directly proportional to the square of the ratio of column diameters. For the current discussion, let's consider two cases. The first is a change from a 4.6 mm i.d. column to a 2.1 mm i.d. column:

(4.6/2.1)2 = 4.8 ≈ 5

and the change from 4.6 mm to 1.0 mm:

(4.6/1.0)2 = 21.2 ≈ 20

In both cases, we'll consider the approximations as close enough for practical work and certainly easier to remember and use for mental calculations.

This means that for equivalent linear velocities, a change from a 4.6 mm i.d. column operated at 1 mL/min to a 2.1 mm i.d. column would require a flow rate adjustment of five-fold, or to 1.0/5 = 0.2 mL/min. A change to a 1.0 mm i.d. column would mean a new flow rate of 1.0/20 = 50 μL/min.