Gradient elution it is then, so how do we decide on our gradient conditions. Gradients in HPLC are defined by three parameters: a) Initial %B, b) Final %B, c) and Gradient time (t_{g}). Another important parameter that needs to be taken in to account is the system dwell time (V_{D}), this is the time taken from the gradient composition being mixed in the pump to the point at which this composition enters the column, and therefore, affects analyte retention. This needs to be calculated for each system and details on doing this can be found in CHROMacademy. For this example we will use 1.2 mins.
a) The elution composition of the first peak in our scouting gradient can be used to estimate the Initial %B. In our example this would correspond to:
t_{i} = 12.8 mins
V_{D} = 1.2 mins
Retention time of first peak (t_{i}) adjusted for system dwell = 11.6 mins
To estimate the initial %B we use the %B/min from our scouting gradient (i.e. gradient steepness)
Then calculate as follows:
%B/min x t_{i} + starting gradient composition = 4.75 x 11.6 + 5 = 60.1 %B
b) The elution composition of the final peak in our scouting gradient can be used to estimate the Final %B. In our example this would correspond to:
t_{f} = 21.2 mins
V_{D} = 1.2 mins
Retention time of first peak (t_{f}) adjusted for system dwell = 20 mins
To estimate the initial %B we use the %B/min from our scouting gradient (i.e. gradient steepness)
Then calculate as follows:
%B/min x t_{f} + starting gradient composition = 4.75 x 20 + 5 = 100 %B
c) Finally we need to decide upon the gradient steepness. Gradient steepness is controlled by the mobile phase start and end composition and the gradient time. The steepness of the mobile phase gradient can have a significant effect on the separation.
The equation for the gradient retention factor (k*) shown here can be found in many textbooks. It can be rearranged to allow us to calculate the gradient time for our method.
t_{g} = gradient time (min)
F = flow rate (mL/min)
S = constant determined by strong solvent and sample compound (Small molecules < 500 Da) the value is between 2 and 5; a value of 4 is used by convention when the value is not accurately known. Proteins have much higher values (typically between 50 – 100) and need longer gradient times for separation.
ΔΦ = change in volume fraction of organic (Final %B – Initial %B)
V_{M} = column void volume and is calculated using the equation below
k* = target value of 5 for average separation
Where: d_{c} = column diameter (mm) and L = column length (mm).
For our example
Rearranging the equation so that we can calculate tg gives us
It is best practice to include an isocratic portion at the beginning of the gradient to allow transfer of our method to other HPLC systems. Therefore, our initial gradient method for development is:
Time 
%B 
0 
60 
1.2 (V_{D}) 
60 (Initial %B) 
9.0 (tg+V_{D}) 
100 (Final %B 
