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Description of adsorption in liquid chromatography under non-ideal conditions Franziska Ortner, Chantal Ruppli, and Marco Mazzotti Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00552 • Publication Date (Web): 17 Apr 2018 Downloaded from http://pubs.acs.org on April 17, 2018
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Description of adsorption in liquid chromatography under non-ideal conditions Franziska Ortner, Chantal Ruppli, and Marco Mazzotti
∗
Institute of Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland E-mail:
[email protected] Abstract A thermodynamically consistent description of binary adsorption in reversed phase chromatography is presented, accounting for thermodynamic nonidealities in the liquid and the adsorbed phase. The investigated system involves the adsorbent Zorbax 300SB-C18, as well as phenetole (PNT) and 4-tert -butylphenol (TBP) as solutes and methanol and water as inert components forming the eluent. The description is based on adsorption isotherms which are a function of the liquid phase activities, in order to account for non-idealities in the liquid phase. Liquid phase activities are calculated with a UNIQUAC model established in this work, based on experimental phase equilibrium data. The binary interaction in the adsorbed phase is described by the adsorbed solution theory (AST), assuming an ideal (IAST) or real (RAST) adsorbed phase. Implementation of the established adsorption model in a chromatographic code achieves a quantitative description of experimental elution pro les, with feed compositions exploiting the entire miscible region, and involving a broad range of dierent eluent compositions (ratio methanol:water). The quantitative agreement of model and experimental data serves as a con rmation of the underlying physical (thermodynamic) concepts, and of their applicability to a broad range of operating conditions.
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Introduction In liquid chromatography, adsorption equilibria are commonly described assuming ideal (i.e. dilute) behavior both in the liquid and in the adsorbed phase.
13
Single component isotherms
are assumed to be a function of the liquid phase concentrations (ideal liquid phase). Interactions between multiple adsorbing components are often described by binary (or multicomponent) isotherms obtained by empirically combining single-component isotherms,
3
in a thermodynamically consistent way by applying the ideal adsorbed solution theory
or
4,5
(assuming an ideal adsorbed phase). However, operating at high solute concentrations may result in considerable nonidealities in the liquid and/or the adsorbed phase, such that models based on the assumption of ideality might fail outside a very limited range of operating conditions.
3,6
In this work, we apply
thermodynamic concepts to describe adsorption in an experimental system in a thermodynamically consistent manner and over a broad range of operating conditions, accounting for nonidealities in both liquid and adsorbed phase.
The system under investigation involves
tert -
the adsorbent Zorbax 300SB-C18, two adsorbing components phenetole (PNT) and 4-
butylphenol (TBP), and the solvent components water and methanol (both assumed to be non-adsorbable). Methanol can also be viewed as a modi er, altering both the solubility and the adsorption behavior of the solutes. In order to account for nonidealities in the liquid phase, the description of the adsorption behavior is based on liquid phase activities. To calculate liquid phase activities from liquid phase compositions, a thermodynamic model for the liquid mixture is required, which is established for the quaternary system in the rst part of this work (UNIQUAC model). Single component adsorption isotherms are then established as a function of the liquid phase activities. Such isotherms have been used previously in the context of separating concentrated acids and carbohydrates on elastic ion exchange resins,
7,8
where the eluent consisted of water
only. In this work, with the eluent being a binary mixture of methanol and water, single component isotherms based on liquid phase activities are applied to a broad range of eluent
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compositions, in which the solubility of the solutes, and thus the investigated concentration range, changes considerably.
An isotherm based on liquid phase activities established for
PNT (in the same experimental system as discussed here) was recently shown to be applicable even beyond the solubility limits, i.e. in the presence of two convective, liquid phases in thermodynamic equilibrium.
6
In the presence of two (or multiple) adsorbing components, competition or cooperation for adsorption sites has to be accounted for. so is the adsorbed solution theory,
4,5
A thermodynamically consistent method to do
which is based on the Gibbs adsorption isotherm and
treats the adsorbed phase as a solution, which can be assumed to be ideal (ideal adsorbed solution theory - IAST) or not (real adsorbed solution theory - RAST). While the IAST provides a description of the binary (or multicomponent) adsorption behavior based on the single-component isotherms without the necessity of further parameters, the RAST requires a thermodynamic model to describe nonidealities in the adsorbed phase. In this work, we consider both the IAST and the RAST for the description of the binary adsorption behavior. While these concepts have been used extensively to describe binary isotherm data or a limited number of binary elution pro les,
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we consider this work novel because of the broad
applicability of the established model, which is demonstrated by a high number of experimental binary elution pro les in quantitative agreement with simulated pro les (a total of 19 dierent feed conditions of PNT and TBP exploiting the soluble region at three dierent eluent compositions of methanol and water). This paper is structured as follows: First, we provide theoretical background to the chromatographic model applied, the adsorbed solution theory and its application to the BET isotherm. We describe the experimental methods used is this work, before presenting and discussing results. We start with an assessment of volume additivity in the liquid and the adsorbed phase, which we assume in the chromatographic model. Experimental phase equilibrium data of the quaternary system is presented, based on which a thermodynamic model (UNIQUAC model) is established. The single component adsorption behavior of PNT and
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TBP is investigated and described, with isotherms based on liquid phase activities, which are calculated using the UNIQUAC model established previously. The binary adsorption behavior is investigated experimentally, and described applying IAST and RAST, which make use of the previously established single-component isotherms. Finally, the main ndings are summarized and conclusions are drawn.
Theoretical background Chromatographic model In order to calculate chromatographic elution pro les at dierent operating conditions and compare them with experimental data, a simpli ed version of the lumped kinetic model established in Ref. 17 was used, accounting for only one instead of multiple convective phases. The model is based on component mass balances:
∂ni ∂ci ∂(ci ) + (1 − ref ) + = 0; ∂τ ∂τ ∂ξ
i = 1...Nc − 1,
(1)
with an empirical mass transfer term (linear driving force) lumping kinetic eects such as dispersion and mass transfer resistances:
∂ni = Sti (neq i − ni ); ∂τ The variable
ci
i = 1...Nc − 1.
(2)
i
in mass per volume liquid
is the liquid phase concentration of component
phase, whereas
ni
is the adsorbed phase concentration, in mass per volume of adsorbent
in the completely regenerated (reference) state, i.e. The number of components (assumed to be inert, i.e. as
τ = tu/Lc
and
Nc
comprises both solutes (adsorbing) and solvent components
ns = 0).
ξ = x/Lc ,
without any components adsorbed.
The dimensionless time and space variables are denoted
with
u
and
Lc
being the constant super cial velocity and
the column length, respectively. In the mass transfer term,
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neq i
corresponds to the adsorbed
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phase concentration in thermodynamic equilibrium with the liquid phase composition, which can be calculated from the isotherm model used. The dimensionless Stanton number
Sti
is
de ned as
Sti = ki where
ki
A and V
Lc A , Vu
(3)
correspond to the surface area and volume of the adsorbent, respectively, and
is the mass transfer coe cient of component
i.
Since the investigation of kinetic eects
is not the focus of this work, and the purpose of the lumped kinetic term is to reduce the sharpness of the fronts in the chromatographic pro les (and thus reduce numerical issues), a constant value for the Stanton number,
Sti = 200,
identical for all components i, is utilized.
In order to ful ll the overall mass balance, i.e. the sum of all component mass balances, a variable porosity
is accounted for:
= ref − (1 − ref )
Nc X ni i=1
(4)
ρi
The reference porosity ref corresponds to the porosity of the column at the completely regenerated state. Equation 4 accounts for the volumetric change in the adsorbed phase, assuming that components require the same volumetric space in the liquid as in the adsorbed phase, which is de ned by the speci c volume
i.
vi = ρ−1 i ,
with
ρi
being the density of component
The latter assumption also implies volume additivity of the components in liquid and
adsorbed phase. As we are dealing with Riemann problems (i.e. stepwise constant initial value problems), the initial condition is de ned as
ci (ξ, 0) = c0i ;
ni (ξ, 0) = n0i ,
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(5)
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where the superscript 0 indicates the initial state in the column. Furthermore, a Dirichlet boundary condition is applied at the column entrance:
ci (0, τ ) = cFi
(6)
The superscript F indicates the feed injected into the column. For the solution of the model equations, liquid and adsorbed phase concentrations were normalized by the density of the corresponding component
ρi .
A semi-discrete nite volume
scheme with a VanLeer ux limiter was applied as suggested in,
18
discretizing the partial
dierential equations 1 in space and thus reducing them to ordinary dierential equations with respect to time. The resulting ODEs (discretized equations 1 and equations 2) were solved with a built-in Matlab routine (ode113).
Adsorbed solution theory The adsorbed solution theory treats the adsorbed phase as a solution, which can be assumed to be ideal (IAST) or not (RAST). Assuming thermodynamic equilibrium between liquid and adsorbed phase and an adsorption behavior described by the Gibbs adsorption isotherm, this theory allows for the thermodynamically consistent description of binary and multicomponent adsorption equilibria on the basis of single-component isotherms. was originally established in the context of gas adsorption, applicable for liquid chromatography.
5
4
The theory
but was later adjusted to be
A recent review article
19
provides a good overview
over model assumptions, equations and applications. In the following, we want to shortly summarize the theory as it is applied in this work. Since it is based on the assumption of thermodynamic equilibrium between liquid and adsorbed phase, and the investigation of this equilibrium is the focus of this work, we will in the remainder of this work omit the superscript eq when referring to adsorbed phase concentrations
ni
in thermodynamic equilibrium.
the context of the AST, we use liquid and adsorbed phase concentrations
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c¯i
and
n ¯i
In
in moles
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per volume of adsorbed phase.
For the implementation into the chromatographic model,
these can be easily transformed into concentrations
ci
and
ni
in mass per volume, through
multiplication by the corresponding molecular weight. The Gibbs isotherm provides the relationship between adsorbed phase concentrations spreading pressure
π
at a constant temperature
n ¯i
and
n ¯s
(7)
denote the adsorbed phase concentrations of the
the solvent, respectively. Accordingly,
µai
and
and
T:
N c −1 X A dπ = n ¯ i dµai + n ¯ s dµas V i=1
The variables
n ¯i
µas
Nc − 1
solutes and
are the chemical potentials of solutes and
solvent in the adsorbed phase. In our system, we de ne water to be the solvent component, while methanol (the modi er) in this context is one of the
Nc − 1
solutes, which however
does not adsorb. The Gibbs-Duhem equation in the liquid phase can be written as
N c −1 X
c¯i dµli + c¯s dµls = 0,
(8)
i=1
with
c¯i and c¯s denoting the liquid phase concentrations of solutes and solvent, respectively, in
moles per volume, and the superscript
l indicating the liquid phase.
Substituting equation 8
in equation 7, and assuming thermodynamic equilibrium between adsorbed and liquid phase
a (i.e. identical chemical potentials in both phases dµi
= dµli ),
yields:
N c −1 X A a dπ = n ¯ cor i dµi , V i=1
(9)
with
n ¯ cor =n ¯i − i
c¯i n ¯s. c¯s
(10)
The second term in equation 10 is negligible under the conditions that concentrations), or that
n ¯ i >> n ¯s
(strongly adsorbing solutes),
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c¯i
