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Role of Column Length in Gradient Separations


Changes in column length have a direct and linear effect on theoretical plates and analysis time in isocratic separations. However, column length plays a significantly less important role in gradient techniques. Three chromatograms illustrate how well packed, short HPLC columns yield very similar peptide separations under identical conditions (no adjustment in gradient time for length).

For this study, the 2.1mm I.D. HAISIL 300, C18, 5µm columns ranged in length from 250 to 100mm. Due to the relative increase in gradient time (on the shorter columns) to achieve similar separations, solvent and analysis time savings are minimal. However, column cost savings (one time) are less when using as short a column as possible, with the potential to save time if the separation allows it. The efficacy of a gradient separation is thus controlled by gradient shape and time more than column length.

Scaling Factors and Gradient Adjustment Tables


A common problem in scaling up separations is keeping the slope of the gradient the same on columns of different lengths and/or diameters. The following formulas and tables are designed to help you scale up (or down) your flow rate and modify your gradient tables on your HPLC system to attain this equivalency.

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Formulas:
    Scale Factor (SF) = (D2/D1)2
    Flow Adjustment = SF
    Load Adjustment = SF
   Gradient Time2 Adjustment Factor = [SF x (Flow1) / (Flow2)] x (Length2 / Length1) x (Time1)

Tables:

Table 1. Scaling Factors for Columns Relative to 4.6 mmID.
  Prep Semi-Prep Analytical Narrowbore Microbore Capillary Capillary Nano Capillary Nano Capillary
Column Diameter (mmID) 21.5 10.0 4.6 2.1 1.0 0.500 0.320 0.150 0.075
Scale Factor (SF) 21.8 4.7 1.0 0.208 0.047 0.012 0.0048 0.00106 0.00027

Table 2. Equivalent Linear Velocity Table Relative to 4.6 mmID Flow Rates.
Column Diameter (mmID) 21.5 10.0 4.6 2.1 1.0 0.500 0.320 0.150 0.075
Equivalent Flows (mL/Min) 21.8 4.7 1.0 0.208 0.047 0.012 0.0048 0.00106 0.00027
Equivalent Flows (mL/Min) 43.6 9.4 2.0 0.416 0.095 0.024 0.0097 0.00212 0.00053
Equivalent Flows (mL/Min) 65.4 14.1 3.0 0.625 0.142 0.035 0.0145 0.00318 0.0008

Table 3. Equivalent Gradients for An Equal Column Diameter.
  4.6mmID 4.6mmID 4.6mmID
Flow Rate (mL/Min) + Time 0.5 + 2x T 1.0 + 1x T 2.0 + 0.5x T
Flow Rate (mL/Min) + Time 1.0 + 2x T 2.0 + 1x T 4.0 + 0.5x T
Flow Rate (mL/Min) + Time 1.5 + 2x T 3.0 + 1x T 2.0 + 1.5x T

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Table 4.
Gradient Time Segment Conversion Table (Relative to a 250mm Length Column).
 

250 mmL
150 mmL
75 mmL
50 mmL
1
0.6
0.3
0.2
2
1.2
0.6
0.4
3
1.8
0.9
0.6
4
2.4
1.2
0.8
5
3
1.5
1
6
3.6
1.8
1.2
7
4.2
2.1
1.4
8
4.8
2.4
1.6
9
5.4
2.7
1.8
10
6
3
2
11
6.6
3.3
2.2

Table 5.
Gradient Time Segment Conversion Table (Relative to a 150mm Length Column).

250 mmL
150 mmL
75 mmL
50 mmL
1.67
1
0.5
0.33
3.33
2
1.0
0.66
5.01
3
1.5
0.99
6.68
4
2.0
1.33
8.34
5
2.5
1.67
9.99
6
3.0
2
11.67
7
3.5
2.33
13.33
8
4.0
2.67
14.99
9
4.5
3.0
16.7
10
5
3.33
18.33
11
5.5
3.67

Table 6.
Gradient Time Segment Conversion Table (Relative to a 75mm Length Column).

250 mmL
150 mmL
75 mmL
50 mmL
3.33
2.0
1
0.67
6.65
4.0
2
1.33
10.0
6.0
3
2.0
13.35
8.0
4
2.67
16.65
10.0
5
3.33
20.0
12.0
6
4.0
23.35
14.0
7
4.67
26.67
16.0
8
5.33
30.0
18.0
9
6
33.33
20.0
10
6.67
36.67
22.0
11
7.33

Table 7.
Gradient Time Segment Conversion Table (Relative to a 50mm Length Column).
 

250 mmL
150 mmL
75 mmL
50 mmL
5.0
3.0
1.5
1
10.0
6.0
3.0
2
15.0
9.0
4.5
3
20.0
12.0
6.0
4
25.0
15.0
7.5
5
30.0
18.0
9
6
35.0
21.0
10.5
7
40.0
24.0
12
8
45.0
27.0
13.5
9
50.0
30.0
15
10
55.0
33.0
16.5
11
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Last Updated: 08/20/21