(453g) Application of Thermodynamic Models in the Context of Liquid Chromatography

Applying the assumption of dilute conditions, the use of thermodynamic
models in the context of liquid chromatography is most often avoided.
Chromatographic models are commonly based on component mass balances which
consider a single convective phase and a thermodynamic equilibrium between
adsorbed phases and liquid phases which is described through an isotherm, being
a function of liquid phase concentrations. In some cases, however, the common
assumption of dilute conditions is not valid, and one has to account for highly
concentrated, non-ideal liquid phases, which might even result in a phase split
and subsequent multiphase flow [1,2]. Examples for such non-ideal behavior are
certain reactions in chromatographic reactors, or systems where interactions of
adsorbing components lead to a considerable enrichment of these components. Under
these non-dilute conditions, the thermodynamic equilibrium between adsorbed
phase and convective phase(s) is consistently described as a function of liquid
phase activities (rather than liquid phase concentrations), and, in the case
that solubility limits are exceeded, the phase split and compositions of the
convective phases have to be determined. For these problems, a thermodynamic
model for the liquid phase(s) is required.

In this contribution, we consider the quaternary system phenetole (PNT), 4-tert-butylphenole (TBP), methanol and
water at 296 K and ambient pressure, and its interaction with the adsorbent Zorbax 300SB-C18. In order to describe the dynamic, chromatographic
behavior of this system under non-dilute conditions, accounting for adsorption
and possible phase separations/ two-phase flow, we have to characterize the
thermodynamic behavior of this system.

In a first step, we characterize the thermodynamic behavior of the convective
phase(s), i.e. of the quaternary system in the absence of
the adsorbent, through liquid-liquid, solid-liquid, and solid-liquid-liquid
equilibrium experiments. A  UNIQUAC model
is used to quantitatively describe the thermodynamic properties of the system
(see Figure 1), with model parameters fitted to the experimental data.

Secondly, the thermodynamic equilibrium between the convective phase(s)
and the adsorbed phase has to be analyzed. For this purpose, adsorbed phase
concentrations of the adsorbing components PNT and TBP are determined
experimentally through dynamic column experiments as a function of the liquid
phase composition (compare Figure 2a). Liquid phase activities can be
calculated from the liquid phase composition applying the established UNIQUAC
model. Determined adsorbed phase concentrations can be related to liquid phase
activities through simple isotherms (see Figure 2b). The established isotherms describe
the adsorption behavior for a very broad range of conditions (diluted to highly
concentrated and multi-phase conditions), while common isotherms, being a
function of liquid phase concentrations, are only valid in a low concentration
range of the adsorbing component and for a constant solvent (methanol : water)
ratio.

Application of the established UNIQUAC model and adsorption isotherms in
the chromatographic model provides an accurate description of the
chromatographic behavior for a broad range of conditions.

Figure 1: Thermodynamic model of the
quaternary system PNT-TBP-methanol-water (prediction by UNIQUAC model)

Figure 2: (a)
experimental adsorption data for PNT at different solvent ratios r (methanol content in solvent in mass
fractions), over the liquid phase concentration of PNT, (b) adsorption data for
PNT, with liquid phase compositions converted to liquid phase activities by
applying the UNIQUAC model.

References

[1] Jermann
S., et al., (2015), J. Chrom. A, 1425, 116-128

[2] Ortner F., Mazzotti M., (2017), in preparation