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Optimizing Gradient HPLC Parameters

Gradient elution is an important technique for the separation of complex mixtures of analytes or for analytes with large molecular weights.  There are several parameters which define a gradient separation (Figure 1) and which should be considered and optimized.  The following article will detail a few simple equations which can be quickly used in conjunction with a scouting gradient to produce a successful gradient elution.

 

Figure 1: Gradient elution parameters.

 

Each of the parameters below should be considered and optimized for gradient elution.

  • Initial %B - starting mobile phase composition (described in terms of the % of the strong solvent ‘B’) – the weakest solvent composition required to retain the most polar analytes

  • Isocratic hold - a period within the gradient in which the eluent composition is held at the Initial %B.  This achieves a degree of analyte focusing but also crucially enables easy method transfer between instruments  with differing Gradient Dwell Volume (VD)

  • Gradient time (tg) - the time during which the eluent composition is changing

  • Final %B - final mobile phase composition – the strongest solvent composition required to elute all analytes

  • Purging - ramping to high %B to elute highly retained components from the column.  Possible isocratic hold at this composition to ensure elution of all analytes, interferents and strongly bound components

  • Conditioning - returning the system (specifically the column) to the initial gradient composition. In practice this step is programmed to occur very rapidly

  • Equilibration - the time taken to ensure the whole of the analytical column is returned to initial gradient composition.  This is an important step and if not properly considered can lead to retention time and quantitative variability

Scouting Gradient

A scouting gradient is the best place to start method development and can provide a plethora of information including whether an isocratic or gradient method should be used, if an isocratic elution method is employed the optimum mobile phase composition, and if a gradient method is to be employed it can be used to optimize parameters such as initial and final %B (Figure 2).

The following example calculation is for a reversed phase HPLC separation.

 

Figure 2: Scouting gradient method.

 

The following calculations can be used to decide whether an isocratic or gradient method should be used, to estimate the optimum isocratic eluent composition, or to optimize essential gradient parameters.

If peaks elute in < 25% of the gradient time (tg) then an isocratic method may be used, if >25% then a gradient approach is recommended (Equation 1).

25% tg = 5 minutes, therefore, gradient elution must be used as Δtg > 25% tg.

Where:

ti = elution time of the initial peak (min.)

tf = elution time of the final peak (min.)

tg = gradient time (min.)

 

If isocratic elution can be The isocratic solvent composition is calculated by initially determining the time midway through the peak elution range (Equation 2).

 

The rate of change of the mobile phase during the gradient (Δ%B/min.) is then calculated (Equation 3).

Where:

%Binitial = initial %B used in the scouting gradient

%Bfinal - final %B used in the scouting gradient

 
The solvent composition when tR(avg) would elute is then calculated and the isocratic solvent composition (%Biso) is determined by subtracting 10% B from this value (Equation 4).

Where:

VD = dwell volume (mL)

F = flow rate (mL/min.)

At this point if optimum separation is not achieved the mobile phase composition can be reduced or increased incrementally in 5-10%B steps.  If the desired resolution is still not achieved the mobile phase solvents used or the column chemistry may need to be reconsidered, or gradient elution employed.

If a gradient separation has been recommended (i.e. Δtg > 25%tg) the initial %B composition for the gradient method (%Binital(gradient)) can be optimized using Equation 5.

Where:

ti = elution time of the initial peak (minutes)

The final mobile phase composition for the gradient method (%Bfinal(gradient)) can also be calculated (Equation 6).

 

Where:

tf = elution time of the final peak (minutes)

Using the calculated values of %Binital(gradient) and %Bfinal(gradient) the gradient profile and resulting chromatogram were obtained (Figure 3).

 

Figure 3: Chromatogram produced using optimized %Binital(gradient) and %Bfinal(gradient).

 

It should be noted that although optimizing initial and final %B in this way can give the desired separation the gradient elution profile can be further optimized.  In the chromatogram in Figure 3 there is a critical peak pair (1) which would indicate that this separation needs further optimization.

The gradient profile can be further optimized by calculating an appropriate gradient slope (tg Equation 7).

 

Where:

k* = gradient retention factor (use 5 as a starting point)

S = shape selectivity factor (for small molecules use 5 or calculate Equation 8)

Δφ = change in %B expressed as a decimal

VM = column interstitial volume (mL)

Using the same values of initial and final %B and the new gradient time the chromatogram in Figure 4 was obtained.

 
Figure 4: Figure 2: Chromatogram produced using optimized %Binital(gradient) and %Bfinal(gradient) and gradient time (tg).
 

If there are still any critical peak pairs the separation may require some further optimization, this may require the use of segmented gradient profiles.

The re-equilibration time of a gradient method is a parameter that should be considered and optimized. 
The optimum re-equilibration time can be calculated using Equation 10.

Where:

VD = dwell volume (mL)

VM = column interstitial volume (mL)

F = flow rate (mL/min.)

For this separation the optimum re-equilibration time would be 7.2 minutes.

 
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