Langmuir 1999, 15, 6035-6042
6035
Correlation and Prediction of Liquid-Phase Adsorption on Zeolites Using Group Contributions Based on Adsorbate-Solid Solution Theory† C. Berti,* P. Ulbig, A. Burdorf, J. Seippel, and S. Schulz Universita¨ t Dortmund, Fachbereich Chemietechnik, Lehrstuhl fu¨ r Thermodynamik, Emil-Figge-Str. 70, 44227 Dortmund, Germany Received October 9, 1998. In Final Form: March 16, 1999 Both correlation as well as prediction of experimental data for the adsorption of various binary liquid mixtures of alkanes and alkenes on NaX at different temperatures are presented. The theoretical background is based on the adsorbate-solid solution theory which conceives the adsorbed phase to be a mixture of the adsorbed species (adsorbate) and the adsorbent as an additional component. With the introduction of the Gibbs excess energy GE* for this hypothetical mixture, activity coefficients and composition of the adsorbed phase may be calculated. The Gibbs excess energy and thus the activity coefficients of the adsorbed species depend strongly on the energetic heterogeneity of the solid surface which may be described by use of so-called group contribution models. These approaches, until now widely applied to predict fluid-phase equilibrium, are derived from statistical thermodynamics and take into account the energetic interactions between the respective components. For the application of this approach on thermodynamics of adsorption zeolites have to be divided into different functional groups such as SiO2, AlO2-, and the respective cations. The interaction energies between these active sites and the functional groups of the adsorbed liquid molecules represent fundamental parameters of activity coefficient models based on group contributions such as UNIFAC. These parameters were determined by fitting four different adsorption systems. With the fitted values, six other systems were predicted. Both correlation and prediction include adsorption data at different temperatures. All calculations show excellent results with a mean relative deviation of 4.2% for the correlation and a mean deviation in the range of 8-17% for the predictions.
1. Introduction Despite numerous possible applications in the chemical industry, liquid-phase adsorption is only rarely considered to be an alternative process for the separation of liquid mixtures. One of the most obvious reasons is the lack of both experimental data and suitable models to predict the adsorption behavior of multicomponent mixtures, the like of which that they typically occur in separation processes. This applies particularly if the prediction is to include the solid, that is, if a suitable solid has to be chosen for a given separation problem. However, the selection of a suitable separation process for basic engineering relies on corresponding possibilities to calculate equilibrium behavior of multicomponent mixtures in advance since a measurement of these properties is very time-consuming and cost-intensive. In the case of dilute solutions and sometimes even at higher concentrations, several isotherms actually applied for gas adsorption are used to calculate liquid-phase adsorption.1,2 Aside from empirical equations, models with interaction parameters (e.g., Langmuir-Freundlich) or association constants3 were developed in order to fit the experimental * To whom correspondence should be addressed. E-mail:
[email protected]. † Presented at the Third International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Polid, August 9-16, 1998. (1) Reschke, G. Untersuchungen zur Wasserreinigung durch Adsorption an Aktivkohlen WAP 1995, 31-39. (2) Reschke, G.; Seidel, A.; Gelbin, D.; Kluge, G.; Nagel, G. Zur Modellierung der konkurrierenden Adsorption von zwei in Wasser gelo¨sten organischen Stoffen an Aktivkohle im Festbett. Chem. Technol. 1987, 39, 254. (3) Derylo-Marczewska, A. A General Model for Adsorption of Organic Solutes from Dilute Aqueous Solutions on Heterogeneous Solids: Application for Prediction of Multisolute Adsorption. Langmuir 1997, 13, 1245.
data. Some approaches make use of the classical formulation of phase equilibrium for adsorption as introduced by Gibbs in combination with activity coefficient models.4 However, the above-mentioned equations may only be used for correlations while they lack the possibility to predict surface excess isotherms. Simulation methods like the Monte Carlo5 method may offer the possibility to predict surface excess isotherms but are rarely used until now, particularly since they are limited to simple systems with respect to the pore shape and the adsorbed species. At this point the success of group contribution methods in the prediction of vapor-liquid equilibrium (VLE) or liquid-liquid equilibrium (LLE) suggests a similar approach for the calculation of adsorption processes. A thermodynamic description of interfacial phenomena is far more difficult though than the description of classical phase equilibria (e.g., VLE) since there is no twodimensional, sharp phase boundary between an adsorbed phase and an uninfluenced bulk phase, but a threedimensional transition region with a continuous change of the respective thermodynamic state variables.6,7 The classical approach divides the total amount of fluid molecules no in two independent phases that are assumed to be homogeneous, the adsorbed or surface phase(s) with ns moles of the liquid mixture and the uninfluenced bulk (4) Chitra, S. P.; Govind, R. Application of a Group Contribution Method for Predicting Adsorbability on Activated Carbon. AIChE J. 1986, 32, 167. (5) Borowko, M.; Borowko, P.; Rzysko, W. Adsorption from Binary Solution in Slit Shaped Pores. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1050. (6) Heuchel, M.; Bra¨uer, P.; Messow, U.; Jaroniec, M. Phenomenological Thermodynamics of Adsorption from Binary Non-electrolytic Liquid Mixtures on Solid Surfaces. Chem. Scr. 1989, 29, 353. (7) Schay, G. Adsorption of Solutions of Nonelectrolytes. In Surface and Colloid Science; Matijevic, E., Ed.; (Wiley-Interscience: New York, 1969; Vol. 2, p 155.
10.1021/la981415p CCC: $18.00 © 1999 American Chemical Society Published on Web 05/07/1999
6036 Langmuir, Vol. 15, No. 18, 1999
Figure 1. Classical description of adsorption systems (a) and definition of the adsorbate-solid solution (b).
phase (b) (see Figure 1a). By introducing activity coefficients for both phases, one may derive relations of phase equilibrium for each adsorbed component i from which the respective activity coefficients in the surface phase may be estimated by use of experimental data.8-10 However, the resulting functions γsi ) f(xsi ) show a complex variation with composition, for example, extreme values, inflection points, or nonmonotonic behavior, thus questioning the physical meaning of these activity coefficients.7,10,11 Moreover, for the pure component adsorption the respective activity coefficient equals 1 though the measurable enthalpy of immersion proves the existence of interactions between the adsorbent and the pure liquid which actually are described by γsi . Finally, apart from the condition of phase equilibrium, there is no independent relation between the activity coefficients in the surface phase and the free energy of immersion though both variables describe the same physical process, which suggests that they must be interrelated in some way.7 These difficulties led to the formulation of the adsorbate-solid solution theory as a thermodynamically consistent framework that incorporates the adsorbent’s properties by conceiving adsorption systems as a solution of the solid and the liquid adsorbates.12 This enables the influence of different structural groups of the adsorbent on the adsorption behavior to be estimated, thus forming a basis for a description of adsorption systems with a group contribution method that includes the adsorbent. 2. Theory 2.1. Surface Excess and Model of Adsorption. In contrast to gas adsorption in liquid-phase adsorption the total amount adsorbed ns is not a meaningful variable to describe the process of adsorption since it is not directly measurable and depends on the extension of the surface phase. Therefore, the separation of mixtures is generally described by the surface excess of each component i:13,14 (8) Kaul, B. K.; Sweed, N. H. Adsorption Equilibrium Data and Model Needs. Fundamentals of Adsorption, Proceedings of the Engineering Foundation Conference, Schloss Ellmau, Bayern, 1983; Engineering Foundation: New York, 1983; p 249. (9) Larionov, O. G.; Myers, A. L. Thermodynamics of adsorption from nonideal solutions of nonelectrolytes. Chem. Eng. Sci. 1971, 26, 1025. (10) Minka, C.; Myers, A. L. Adsorption from Ternary Liquid Mixtures on Solids. AIChE J. 1973, 19, 453. (11) Li, M.-H.; Hslao, H.-C.; Yih, S.-M. Adsorption Equilibria of Xylene Isomers on a KBa-Y Zeolite. J. Chem. Eng. Data 1991, 36, 244. (12) Berti, C.; Ulbig, P.; Schulz, S. Correlation and Prediction of Adsorption from Liquid Mixtures on Solids by Use of GE-Models. Adsorption 1998 Aug, accepted. (13) Everett, D. H. Thermodynamics of Interfaces: an Appreciation of the Work of Geza Schay. Colloids Surf. A: Physicochem. Eng. Aspects 1993, 71, 205. (14) Sircar, S.; Novosad, J.; Myers, A. L. Adsorption from Liquid Mixtures on Solids: Thermodynamics of Excess Properties and Their Temperature Coefficients. Ind. Eng. Chem. Fundam. 1972, 11, 249.
Berti et al.
Γei ≡ Γo(xoi - xbi )
(1)
) Γs(xsi - xbi )
(2)
where Γo is the total amount of the liquid mixture and Γs the total amount adsorbed referring to a quantity of adsorbent (i.e., Γ ≡ n/m0), respectively. The second relation which is easily derived from the first one by means of a mass balance enables the surface excess to be calculated at any concentration in the bulk phase zbi if the composition of the surface phase xsi and the total amount adsorbed Γs are known. The latter variable is somewhat arbitrary and depends on the definition or extension of the surface phase that is fixed by a model of adsorption. In the case of the adsorption of a binary liquid mixture, the total amount adsorbed Γs may be estimated according to
xs1 xs2 1 ) + Γs Γsm1 Γsm2
(3)
which is the underlying relation for the most common models of adsorption of liquid mixtures like the pore filling model or monolayer model.15 When the pore-filling model s (Table 1) may is applied, the surface-phase capacities Γmi be assessed by the pore volume of the solid vp and the molar volume of the respective fluid v0i: s ) Γmi
vp voi
(4)
Table 1. Surface-Phase Capacity component
Γm1 (mmol/g)
n-hexane (293.15 K) n-hexane (303.15 K) n-hexane (313.15 K) 1-hexene (293.15 K) 1-hexene (303.15 K) 1-hexene (313.15 K) n-octane (293.15 K) 1-octene (293.15 K) 1-decene (293.15 K) n-dodecane (293.15 K) 1-dodecene (293.15 K) 1-tetradecene (293.15 K) 1-hexadecene (293.15 K)
2.04 1.73 1.53 2.1 1.80 1.60 1.78 1.88 1.41 1.21 0.9 1.05 0.9
2.2. Adsorbate-Solid Solution Theory. The evaluation of eq 2 still requires the calculation of the composition of the surface phase xsi from the condition of equilibrium which is a general thermodynamic relation that does not depend on specific models. As already mentioned, the difficulties connected with the classical description of adsorption systems led to the development of the adsorbate-solid solution theory which is represented briefly in the following section. A more detailed description and derivation of all relations is reported elsewhere.12 For the definition of an adsorbate-solid solution as a reference system the bulk phase is considered to be uninfluenced by the solid (see Figure 1b). The formulation of mole fractions for the reference system has to include the solid, that is, one has to assign a molar quantity n0 to the solid. By introducing a molar weight M0 for the adsorbent, the mole fraction of each component i in the (15) Messow, U.; Bra¨uer, P.; Heuchel, M.; Pysz, M. Zur experimentellen U ¨ berpru¨fung der Vorhersage von Gleichgewichtsdiagrammen bei der Adsorption bina¨rer flu¨ssiger Mischungen in poro¨sen Festko¨rpern. Chem. Tech. 1992, 44, 56.
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customary definition of the Gibbs excess energy,18 one may formulate the free Gibbs energy for the adsorbatesolid solution in accordance with
adsorbate-solid solution yields
x/i )
M0Γsi
∑i
1 + M0
(5) Γsi
1
x/0 )
(6)
∑i Γsi
1 + M0
In these equations the index 0 refers to the solid. The definition of a molar weight for the solid is closely connected with its functional groups and will be dealt with in section 2.4. It has to be stressed that these definitions are only sensible for a system in'equilibrium, that is, for a system that contains more fluid molecules than necessary to cover all adsorption sites (no > ns and thus x/0 ∈ [0, 1]). Hence, the boundaries of the domain of definition are given by the borderline case of the pure component adsorption for each component i which corresponds to a binary adsorbate-solid solution. For this case, the amount of the respective component i in the s in surface phase Γsi equals its surface-phase capacity Γmi eqs 5 and 6. The connection with the variables of the surface phase is given by
ns ) n*(1 - x/0)
(7)
x/i ) xsi (1 - x/0)
(8)
Usually, the derivation of general thermodynamic relations for the description of the surface phase starts with the formulation of the fundamental equation for the abovementioned reference system of an adsorbate-solid solution:16,17
dG* ) -S* dT + V* dp + µ/0 dm/0 +
k
µ/i dn/i ∑ i)1
(9)
where
φ* ≡
∂G* ∂m0
(10)
is the change in the free Gibbs energy of the adsorbatesolid mixture when a small mass of solid is added to the system. Thus, φ* may be described as the chemical potential of the adsorbent in the presence of the adsorbate, containing the chemical potential of the pure, uninfluenced solid in the absence of the adsorbates (µ0) and the free Gibbs energy of adsorption gad that takes into account the interactions between the adsorbent and the liquids:
φ* ) φ0 + gad
k
G* )
(11)
At this point the Gibbs excess energy of the adsorbatesolid mixture may be introduced to derive a connection to the Gibbs energy of adsorption, thus enabling the interactions between the solid and the adsorbed liquids to be described by a suitable GE model. By applying the (16) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons, Inc.: New York, 1984. (17) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogenious Surfaces; Academic Press, London, 1992.
nsi goi + G0 + GE* ∑ i)1
(12)
where goi is the molar free Gibbs energy of the component i and G0 the free Gibbs energy of the pure, uninfluenced adsorbent, respectively. From eq 9 and the definition of GE* finally the relation between the free energy of adsorption and the Gibbs excess energy of the adsorbatesolid solution may be derived:12
GE* ) Gad + GEs
(13)
where GEs refers to the Gibbs excess energy of a hypothetical mixture with the composition of the surface phase uninfluenced by the solid. Equation 13 indicates that GE* contains both the perturbations of molecules of the solid and the liquid because of the adsorption process (Gad) as well as the interactions of the pure fluid mixture in the absence of the solid. In the case of the pure liquid E adsorption the latter term equals zero, so that GE* ≡ Goi ad / ) Goi . The corresponding result may be obtained by an enthalpy balance for an immersion experiment which is in addition necessary to derive a relation between the excess enthalpy of the adsorbate-solid mixture and the enthalpy of immersion, thus incorporating another experimentally accessible variable that plays an important role in the design of adsorption processes. Since this work focuses on the correlation and prediction of equilibrium data, the corresponding equations are not presented. When activity coefficients γ/i are introduced for each component of the adsorbate-solid solution, the expressions for the chemical potential of the liquid species i in the adsorbate-solid mixture are obtained: / / (T, φoi ) ) + RT ln(γ/i x/i ) µ/i (T, φ*) ) µoi
(14)
/ represents the standard chemical In this equation µoi potential of the respective component i which is identical to the chemical potential of the pure adsorbed component i in the same state as the adsorbed mixture. This corresponds to the classical approach.9,10 Now, the formulation of the conditions of phase equilibrium is straightforward. By equating the chemical potentials of the fluid components in each phase, one finally obtains an equilibrium relation for the calculation of the mole fraction of each liquid in the adsorbate-solid solution:
(
xoi γbi ) x/i γ/i exp -
)
/ φ* - φoi s RTΓmi
(15)
where the difference of the chemical potential of the influenced adsorbent / ) φ* - φoi
1 E (GE* - GEs - Goi /) m0
(16)
is given by eqs 11 and 13 and may be calculated if the Gibbs excess energy of the adsorbate-solid solution is (18) Gmehling, J.; Kolbe, B. Thermodynamik; VCH Verlagsgesellschaft mbH: Weinheim, 1992.
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known. Usually, it is more convenient to express the Gibbs excess energy in terms of activity coefficients; in the case of GEs
GEs
k
)
RT
nsi ln γi(xsi ) ∑ i)1
(17)
Note that γi(xsi ) is the activity coefficient of the component i in a hypothetical, autonomous phase that is uninfluenced by a solid and may not be confused with the activity coefficient γsi in the surface phase in the classical formulation which contains the perturbation of the atoms of the solid. GEs may be estimated by use of any suitable GE model. Similarly, the definition of activity coefficients for the adsorbate-solid solution yields their connection with the Gibbs excess energy in accordance with E
G * RT
k
)
∑ i)0
n/i
ln
γ/i
(18)
where the index 0 again refers to the solid component to which one has to assign an activity coefficient as well. These equations represent the connection between the activity coefficients and the free Gibbs energy of adsorption gad. For the pure component adsorption, the respective / / are given by eq 5 and 15 (φ* f φoi ): activity coefficients γoi / )1+ γoi
1
/ / γGE,i (xoi ) represents the activity coefficient of a binary adsorbate-solid solution, that is, the pure (adsorbed) liquid and the solid adsorbent, as it is given by the chosen GE model. The introduction of a reference point does not have any effect on the qualitative variation of the activity coefficients with concentration but represents a simple normalization. In the case of pure component adsorption, the activity coefficient of the solid is directly given by the GE model. At this point a GE model has to be introduced to calculate the Gibbs excess energy of the adsorbate-solid solution. For a first evaluation of a group contribution method for the description of the adsorbate-solid solution, the widely used modified UNIFAC model was chosen. The concentration-dependent part of the activity coefficients is split into a combinatorial and residual part:18
/ ln γGE,i ) ln γCi / + ln γRi /
For the activity coefficients of the liquid components, eq 21 may be directly incorporated in the expression, that is, /
C C /(x/i ) - ln γGE,i /(xoi ) ln γCi / ≡ ln γGE,i
(23)
R R / /(x/i ) - ln γGE,i /(xoi ) ln γRi / ≡ ln γGE,i
(24)
For the solid each of the second terms is dropped. The combinatorial part is given by18
(
(19)
s Γmi M0
C ln γGE,i / ) 1 - Vi + ln Vi - 5qi 1 -
Obviously, in the borderline case of pure component adsorption, the activity coefficient of the respective fluid does not equal 1 but a fixed value that depends on the respective system of adsorbent and pure liquid, that is, the respective binary adsorbate-solid mixture. 2.3. GE* Model Using Group Contributions. The equations given in the previous chapter are general thermodynamic relations that do not depend on a particular model to describe the Gibbs excess energy of the adsorbate-solid solution. These relations will be dealt with in the following chapter. GE* may in principle be calculated by application of any GE model that is suitable to describe solutions containing at least three components, as long as the model is not limited to small values of the excess enthalpy. However, the concept of an adsorbate-solid solution offers an excellent basis to incorporate a group contribution methodology that takes into account the influence of different structural groups of the solid adsorbent with respect to adsorption. Since in the case of adsorption the borderline case is the pure liquid adsorption, that is, a binary adsorbatesolid solution, the respective boundary values according to eq 19 have to be incorporated in any GE* model that is suitable to describe the adsorbate-solid solution. This is achieved by splitting the activity coefficient of the respective fluid into two parts (i > 0): / / + ln γGE,i ln γ/i ) ln γoi
(20) / γGE,i
a concenwhere γoi is the boundary value and ln tration-dependent part of the activity coefficient that is / has to equal zero given by the chosen GE model. ln γGE,i at the concentration border: / / / / ) ln γGE,i (x/i ) - ln γGE,i (xoi ) ln γGE,i
(21)
(22)
)
Vi Vi + ln Fi Fi
(25)
where Vi and Fi depend on the composition of the adsorbate-solid solution:
Vi )
Fi )
ri
∑rjx/j qi
∑qjx/j
(26)
(27)
For both the fluid and the solid, the parameters ri and qi can be calculated from the relative van der Waals volumes RK or surfaces QK:
ri )
ν(i) ∑ K RK K
(28)
qi )
ν(i) ∑ K QK K
(29)
and may thus be estimated for each zeolite from structural data, if the respective number of the structural groups of type K in the solid ν(0) K is known. In the original form of UNIFAC, the residual part is given by
ln γRi )
(i) ν(i) ∑ K (ln ΓK - ln ΓK ) K
(30)
where ΓK represents the group activity coefficient of the mixture and Γ(i) K the group activity coefficient of the pure component i. Equation 30 is necessary to attain the normalization γi(xi f 1) ) 1 for fluid mixtures.19 In the case of adsorption, Γ(i) K does not represent a meaningful
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Table 2. Fitted UNIFAC Parameters for the Interactions of Group M with group K in the adsorbate-solid-solution λMK (Parameters for the Interactions between the Same Groups or between the Functional Groups of the Solid Equal to 0) K M group 1 2 3 4 5
1
2
3
4
5
CHn
CHnd
SiO2
AlO2-
Na+
CHn 0.00 847.27 444.52 -952.54 -912.60 CHnd 1343.05 0.0 -1186.50 2055.28 1332.10 SiO2 -3098.98 2583.71 0.0 0.0 0.0 AlO2187.45 13958.34 0.0 0.0 0.0 Na+ -2275.53 2409.67 0.0 0.0 0.0
variable and is consequently replaced by the group activity coefficient of the pure adsorbed component if eq 24 is incorporated into the residual part of the activity coefficient. One obtains (oi) ν(i) ∑ K (ln ΓK - ln ΓK ) K
R ln γGE,i /)
The group activity coefficient is given by
(
ln ΓK ) QK 1 - ln( where
∑ M
ΘMΛM) -
ΘM )
XM )
∑ M
ΘMΛMK
(31)
)
∑P ΘPΛPM
QMXM
(32)
(33)
QNXN ∑ N
Figure 2. Correlated and predicted excess isotherms for 1-hexene(1)/n-hexane(2) on NaX at different temperatures. Symbols refer to experimental data (Herden et al.); lines refer to the correlation or prediction with ASST.
∑j ν(j)Mx/j
(34)
∑j ∑ N
/ ν(j) N xj
are the surface fraction ΘM or the mole fraction XM of group M in the adsorbate-solid solution. In original UNIFAC, the temperature-dependent parameter is given by
ΛMK ) exp(-λMK)/T
(35)
where λMK is the interaction parameter describing the energetic interactions between the groups of type M and K, respectively (Table 2). 2.4. Molar Weight of the Adsorbent. The inner surface that is significant for adsorption is composed of different functional groups. Thus, the entire inner surface may be calculated from the van der Waals group surfaces Q K:
A ) am0 )
νKQK ) ν0 ∑ ∑ K K
X(0) K QK
(36)
where a is the specific surface of the adsorbent, νK the number of functional groups of type K in the solid, X(0) K the corresponding fraction of all functional groups, and ν0 the total number of all functional groups in the respective amount of the solid m0. (19) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 6.
For crystalline adsorbents like zeolites the definition of the unit cell as a molecule yields a detailed expression for the molar weight of the adsorbent. The total number ν0 of functional groups in the solid may then be expressed in terms of the number of functional groups per unit cell ν0,uc and the number of these unit cells in the solid Nuc:
ν0 ) Nucν0,uc
(37)
Defining the molar quantity of the solid according to n0 ≡ Nuc/NA, the molar weight of the zeolite is given by
X(0) ∑ K MK K
M0 ) Muc ) ν0,uc )
νK,ucMK ∑ K
(38)
where νK,uc is the number of all functional groups of type K in the unit cell. Considering the structural formula
Mx/n [(AlO2)x(SiO2)y]‚zH2O
(39)
which applies to most zeolites,20,21 eq 38 yields
Muc ) x
(
)
MKat + MAl + 2MO + y(MSi + 2MO) n
(40)
(20) Breck, D. W. Zeolite Molecular Sieves; John Wiley & Sons: New York, 1974. (21) Smith, J. V. Definition of a Zeolite. Zeolites 1984, 4, 309.
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Figure 3. Correlated excess isotherms for the adsorption on NaX at 293.15 K (system 1, 1-octene(1)/n-octane(2); system 2, 1-decene(1)/n-hexane(2)).
Figure 4. Predicted excess isotherms for the adsorption on NaX at 293.15 K (system 1, 1-tetradecene(1)/n-hexane(2); system 2, 1-tetradecene(1)/n-dodecane(2)).
3. Calculation and First Results
of the bulk phase by calculating the respective activity coefficients with modified UNIFAC. All corresponding parameters are shown in the Appendix. 3.1. Correlation of Isotherms. The first aim is to examine the ability of ASST to correlate different isotherms. Figures 2 and 3 show the results for equilibrium data and the activity coefficients of the adsorbate-solid solution. All surface excess isotherms are represented well with only little deviations between correlation and experimental data. The first two systems with 1-hexene as the preferably adsorbed component at different temperatures are represented best. The activity coefficients of the adsorbed solution show a monotonic behavior with an increase in the activity coefficient of 1-hexene on a value at infinite dilution which is typically observed for liquid mixtures. Similar results are obtained for the systems 1-octene(1)/n-octane(2) and 1-decene(1)/n-hexane(2) on NaX. 3.2. Prediction of Isotherms at Different Temperatures. To examine the ability of the adsorbate-solid solution theory (ASST) to predict surface excess isotherms at different temperatures, the system 1-hexene(1)/n-
In contrast to the classical formulation of the condition of equilibrium the mole fraction of each fluid in the adsorbate-solid solution has to be calculated by iteration of eq 15 since the activity coefficients of the adsorbatesolid solution and φ* depend on the concentration. The surface excess is then given by eqs 8, 3, and 2. All optimizations for the determination of the UNIFAC parameters have been carried out by using the evolution strategy with the error function:
)
1
N
∑
N k)1
|
|
e e Γ1,calc - Γ1,exp e Γ1,exp
(41)
Since enthalpies of immersion are not available for the examined systems, only surface excess data could be consulted to determine the interaction parameters. The surface-phase capacities are taken from the respective publications orsif not availablesassessed from the surface excess isotherm by a procedure described by Schay.7 For the calculations adsorption equilibrium data of different binary mixtures of alkanes and alkenes on NaX were taken from literature.22-25 For the zeolite the molar weight has been estimated from the structural formula according to eq 40 (M ) 13 418 g/mol). All systems have been calculated taking into consideration the nonideality (22) Herden, H.; Einicke, W.-D.; Scho¨llner, R. Adsorption of n-Hexane/ n-Olefin Mixtures by NaX Zeolites from Liquid Solution. J. Colloid Interface Sci. 1981, 79, 280.
(23) Herden, H.; Einicke, W.-D.; Jusek, M.; Messow, U.; Scho¨llner, R. Adsorption Studies of n-Olefin/n-Paraffin Mixtures on X- and Y-Zeolites I. Comparison of Liquid Phase and Vapor Phase Adsorption of Hexene-1 and n-Hexane on NaX-Zeolite. J. Colloid Interface Sci. 1984, 97, 559. (24) Herden, H.; Einicke, W.-D.; Messow, U.; Quitzsch, K.; Scho¨llner, R. Adsorption Studies of n-Olefin/n-Paraffin Mixtures on X- and Y-Zeolites II. Adsorption of Tetradecene-1/n-Dodecane Mixtures on Modified X- and Y-Zeolites. J. Colloid Interface Sci. 1984, 97, 565. (25) Einicke, H.; Herden, W.-D.; Messow, U.; Volkmann, E.; Scho¨llner, R.; Ka¨rger, J. Liquid Phase Adsorption Studies of Octene-1 and Octane on X-Zeolites. J. Colloid Interface Sci. 1984, 102, 227.
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heterogeneity of the solid surface or the interactions between its active sites with the liquid molecules are taken into consideration by use of a group contribution method and a new formulation of the conditions of phase equilibrium. Both correlations as well as predictions of surface excess isotherms at different temperatures are presented. The prediction of surface excess isotherms of binary liquid mixtures only on the basis of other binary adsorption data proves the physical meaning of the UNIFAC parameters. The activity coefficients show a monotonic variation with composition revealing first regularities; however, at present it is not yet possible to give a complete physical interpretation of these variables. Future research will focus on the expansion of the database including equilibrium data (i.e., surface excess data) and the integration of caloric data to enable the interaction parameters to be determined more accurately with the aim to predict the adsorption behavior of multicomponent mixtures. Moreover, the predictions are to include the solid which finally means that the respective zeolite with the optimal composition for a given separation problem may be chosen on the basis of the calculations. Nomenclature
Figure 5. Predicted excess isotherms for the adsorption on NaX at 293.15 K (system 1, 1-octene(1)/n-hexane(2); system 2, 1-dodecene(1)/n-hexane(2); system 3, 1-hexadecene(1)/n-hexane(2)).
hexane(2) on NaX was chosen. With the UNIFAC parameters determined at 293.15 K the surface excess isotherms were predicted at 303.15 and 313.15 K. The result is also shown in Figure 2. The order of magnitude of the maximum as well as its shift toward higher concentrations is represented well. The change of the surface excess with temperature results from both a change of the activity coefficients as well as a change of the surface-phase capacities with temperature. 3.3. Prediction of Isotherms. If the interaction parameters have a physical meaning, it should be possible to predict surface excess isotherms by using the UNIFAC parameters found during the correlation. Figures 4 and 5 show the experimental adsorption equilibrium of five binary mixtures on NaX investigated by Herden et al. To predict these surface excess isotherms, the fitted UNIFAC parameters from the correlation could be used since the investigated systems contain exclusively the same functional groups. The results for all five predictions are shown in Figures 4 and 5. They show excellent agreement with the experimental data. Larger deviations are partly caused by the mean variation of the experimental data especially at lower concentrations because of the high gradient of the surface excess isotherms. However, the order of maxima of the isotherms are represented satisfactorily for all five isotherms. 4. Conclusion A new model for the correlation and prediction of surface excess isotherms has been developed. The energetic
R ) specific surface of adsorbent (m2/kg) A ) total surface of adsorbent (m2) G ) Gibbs energy (J) g ) molar Gibbs energy (J/mol) GE ) Gibbs excess energy (J) gad ) specific Gibbs energy of adsorption (J/kg) Gad ) Gibbs energy of adsorption (J) m ) mass (kg) M ) molar weight (kg/mol) n ) molar quantity (mol) N ) number of experimental data NA ) Avogadro constant (1/mol) Nuc ) number of unit cells p ) pressure (Pa) QK ) van der Waals group surfaces of group K (m2) RK ) van der Waals group volumes of group K (m3) R ) gas constant (J/(mol K)) S ) entropy (J/(mol K)) T ) temperature (K) V ) volume (m3) v ) molar volume (m3/mol) vp ) pore volume (m3/mol) x ) molar fraction / x0i ) molar fraction of the pure adsorbed component i in the adsorbate-solid-solution X ) fraction of a functional group Greek Letters ) mean relative error γ ) activity coefficient ΛMK ) temperature-dependent interaction parameter (interactions of groups M, K) λMK ) interaction parameter describing the interactions of groups M, K (K) µ ) chemical potential (J/mol) νK ) number of groups of type K φ0 ) chemical potential of the pure solid (J/kg) φ* ) chemical potential of the wetted solid (J/kg) / φ0i ) chemical potential of the wetted solid, at adsorption of the pure component i (J/kg) Γ ) specific molar quantity (mol/g of adsorbent) (mol/g) ΓK ) group activity coefficient Γs ) total specific amount adsorbed (mol/g) Γsi ) total specific amount adsorbed of component i (mol/g) Γei ) specific surface excess (mol/g)
6042 Langmuir, Vol. 15, No. 18, 1999 s Γmi ) specific surface-phase capacity of component i (mol/g) ΘM ) surface fraction of group M in the adsorbate-solidsolution
Subscripts 1, 2, i ) component 1, 2, or i calc ) calculated oi ) pure component i or pure adsorbed component i 0 ) adsorbent exp ) experimentally GE ) calculated from a GE model K ) group of type K Kat ) cation uc ) unit cell
Berti et al. Superscripts (0) ) adsorbent (i), (j) ) component i, j (oi) ) pure adsorbed component i b ) bulk phase C ) combinatorial part of the activity coefficient s ) surface phase o ) total amount (of fluid/before wetting) * ) adsorbate-solid-solution ad ) adsorption E ) excess quantity e ) surface excess quantity R ) residual part of the activity coefficient LA981415P
