Journal of Chromatography A, 1092 (2005) 65–75
Adsorbed solution model for prediction of normal-phase chromatography
process with varying composition of the mobile phase
Wojciech Piatkowski
a
, Igor Petrushka
b
, Dorota Antos
a,∗
a
Rzeszow University of Technology, Chemical Engineering and Process Control Department, al. Powsta´ nc´ ow Warszawy 6, 35-959 Rzesz´ ow, Poland
b
Lvov Polytechnic Institute, Faculty of Chemical Engineering and Industrial Ecology, Bandera Str. 12, Lviv 13, Ukraine
Available online 26 August 2005
Abstract
The adsorbed solution model has been used to predict competitive adsorption equilibria of the solute and the active component of mobile phase
in a normal-phase liquid chromatography system. The inputs to the calculations were the single adsorption isotherms accounting for energetic
heterogeneity of the adsorbent surface and non-ideality of the mobile phase solution. The competitive adsorption model has been coupled with a
model of the column dynamics and used for simulating of chromatography process at different mobile phase composition. The predictions have
been verified by comparing the simulated and experimental chromatograms. The model allowed quantitative prediction of chromatography process
on the basis of the pure-species adsorption isotherms.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Non-linear chromatography; Adsorption equilibria; Mobile phase composition; Surface heterogeneity
1. Introduction
Chromatographic separations are usually realized in isocratic
mode, i.e., with constant temperature, pressure or solvent com-
position of the mobile phase during the process. However, it
is well known that the adsorption behaviors of the system can
be strongly affected by changes of these operating parameters.
Changes of adsorption properties are commonly used for bed
regeneration in cyclic adsorption processes such as thermal and
pressure swing-adsorption and displacement-purge adsorption
[1,2].
In liquid chromatography, the idea of affecting the adsorp-
tion behavior by a modulation of the mobile phase composition
is often exploited to improve the separation performance in chro-
matographic processes.
The effect of the mobile phase composition on the reten-
tion in normal-phase systems operating under conditions of a
linear isotherm has been described using theoretical models of
adsorption developed in [3–6]. In these models, the adsorption
on a polar adsorbent surface was understood as a competition
between the molecules of the solute and the modifier on the
adsorption sites. Despite some differences, all the models lead
∗
Corresponding author. Tel.: +48 17 865 1730.
E-mail address: dorota antos@prz.rzeszow.pl (D. Antos).
after simplifications to the same simple equation describing the
retention of solute as a function of concentration of a strong
solvent (the modifier):
k
′
0
= k
′
(c
mod
)
-m
(1)
where k
′
0
is the retention factor of the solute in the pure strong
solvent, m is the empirical constant, which is determined by fit-
ting to the set of experimental retention data acquired at different
modifier content in the mobile phase. κ
′
0
is the retention factor
correlated with the slope of the isotherm of the solute at c → 0:
k
′
0
= F
∂q
∗
∂c
c→0
, (2)
where F = (1 - ε
t
)/ε
t
is the phase ratio.
If the mobile phase composition varies during the process
(solvent gradient), the retention of the solute is correlated with
the profile of the modifier concentration propagating along the
space z and time t co-ordinate, i.e., c
mod
(z, t ). Various models
for retention predictions of the solute under gradient conditions
accounting for possible adsorption of the modifier are discussed
in [7].
For predictions of non-linear chromatography processes real-
ized at constant mobile phase composition as well as at varying
elution strength empirical or semi-empirical approaches domi-
nate. The idea behind these approaches is to measure adsorption
0021-9673/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.chroma.2005.08.031