by
vmu » Tue May 20, 2025 6:19 pm
Correct determination of the column hold-up volume (Vm, the total mobile phase volume in the column, i.e. the sum of the column
interparticle volume and the sorbent
intraparticle pore volume) is not a simple task. Many papers are devoted to this problem. For example:
Pure Appl. Chem., Vol. 73, No. 6, pp. 969–992, 2001.
RETENTION PARAMETERS IN CHROMATOGRAPHY (IUPAC Recommendations 2001). PART A. HOLD-UP VOLUME CONCEPT IN COLUMN CHROMATOGRAPHY
https://www.degruyterbrill.com/document ... 60969/html
The
accurate value of Vm (which is not so easy to measure) is more important for scientists than for industrial chromatographers. First of all, it is necessary to clearly understand that Vm expressed as a percentage of the column tube volume (Vc = L*pi*(dc^2)/4), i.e. Vm/Vc*100:
- can never be more than 100 % (it can be as high as 85 % in size-exclusion and in silica monolithic columns, but never higher than 100 %; some chromatographers fail to check their experimental values of Vm against this obvious limit);
- usually lies in the approximate range between 50 % and 70 % for the columns filled with porous particles (core-shell and fully porous);
- is usually close to 40 % (36 % to 42 %) for the (rarely used) columns filled with
nonporous particles.
The values of relative volumes in the range from 36 % to 42 % also correspond to the typical
interparticle column volume (aka "external volume", Ve; do not confuse with the extra-column volume) in the columns filled with porous particles. This is the fraction of the column volume available for the analytes totally excluded (via size-exclusion and/or ion-exclusion mechanism) from the pores of the sorbent particles. This volume is used as the dead volume is SEC (where the symbol Vo or V0 is normally used for it).
Also the
interparticle volume Ve is used for the calculations of the
zone retention factor k'' = (Vr - Ve)/Ve in scientific papers devoted to the band broadening theories (Vr is the analyte retention volume). k'' is used to describe the analyte distribution between the moblie
zone (the interparticle volume Ve wherein the eluent flows) and the stationary
zone (Vsz, the whole particles volume that includes the particle material and the stagnant eluent in the intraparticle pores) in the column.
Ve + Vsz = Vc.
k'' is the equilibrium ratio of the analyte
masses in the stationary
zone and in the mobile
zone.
The more widely known
phase retention factor is k' = (Vr - Vm)/Vm. It is used to describe the analyte distribution between the two
phases. The mobile
phase volume is Vm. The stationary
phase quantity can be defined in several ways (as the sorbent surface area, as the solid material volume, as the bonded layer volume, etc) to link k' to the correspondingly defined distribution constant.
k' is the equilibrium ratio of the analyte
masses in/on the stationary
phase and in the mobile
phase.
In SEC, it is common to calculate the distribution constant instead of k'. With the same notation as above, this constant is given by Ksec = (Vr - Ve)/(Vm - Ve). It describes the analyte distribution between the volume of the eluent flowing in the interparticle channels (Ve) and the volume of stagnant eluent in the intraparticle pores (Vm - Ve).
Ksec is the equilibrium ratio of the analyte
concentrations in the
intraparticle
pore volume and in the
interparticle volume.
Ksec varies in the range from 0 to 1.