by
Hollow » Sat May 05, 2012 10:26 pm
Flow and injection volume are directly proportional to the column volume.
disagree for flow rate!
(I know, PhEur states this as well and would even scale the flow rate of an isocratic method in relation to the column volume...)
Instead, the flow rate should be scaled in proportion to the cross-sectional area (=diameter) of the columns. -> in one model (w/o diffusion coefficients), the x-axis of the Van-Deemter is the the flow velocity u=L/t0 and is in mm/s.
t0 is determined by the column volume / flow, therefore u = L/t0 = L/(VCol/F) = L*F/VCol;
with VCol = dc^2*pi*e*L/4 >> the length will clear out and the linear flow velocity u = F*4/(dc^2*pi*e) >> u = F / dc^2
"e" = porosity = ca. 0.66) [make sure you use the correct units...)
Therefore 1 ml/min on a 4.6mm column would translate to 0.21 ml/min on a 2.1mm column, independent of the column length.
Otherwise you're moving along the Van-Deemters curve and maybe change your plate heights = column efficency.
For my last point, I try to explain it with an example:
Code: Select all
Column1 Column2
dc1 4.6 mm dc2 2.1 mm
lc1 250 mm lc2 150 mm
e 0.65 - e 0.65 -
dp1 5 um dp2 3 um
F1 1 ml/min F2 0.3 ml/min
L/dp1 50000 - L/dp 2 50000 - (proportional to plate count)
VC1 2.70 ml VC2 0.34 ml
v1 1.54 mm/s v2 2.22 mm/s
tg1 Vg1 VCg1 VCg2 Vg2 tg2
min ml Vcol Vcol ml min
0 0 0.00 0.00 0.00 0.00
10 10 3.70 3.70 1.25 4.17
15 15 5.55 5.55 1.88 6.25
30 30 11.11 11.11 3.75 12.50
- tg1 are the time steps of gradient1
- with the flow rate of 1, these steps will give the volume of mobile phase used at that time (Vg1)
- express the volume of mobile phase (Vg1) in units of column volumes (VCg1 = Vg1/VC1)
- hold this ratio constant for the new column (VCg1=VCg2)
- calculate the volume of mobile phase for the new column dimension (Vg2 = VCg2*VC2)
- calculate the time needed to deliver this volume with the new flow rate (Vg2/F2)
-- remarks:
a) no correction for the dwell volume is made yet
b) notice that the particle size of column 2 is reduced to 3 um to maintain a constant L/dp ratio of 50000. If the same particle size would be used, the L/dp and therefore the plate count would be reduced by about 40% (50000 vs. 30000 > resolution reduced by about 20%)
c) the flow of condition2 is not strictly scaled (see above)
d) "Klaus I." was effectively doing the same with his flow rate translation of 0.3 > 2.4 and holding the gradient steps constant, but due to the above explanation I would not do it this way...
Another nice translator is from University of Geneva:
"HPLC Calculator" (Excel)
http://www.unige.ch/sciences/pharm/fana ... gement.htm