Potential Model Development Using Quantum Chemical Information for Molecular Simulation of...

Potential Model Development Using Quantum Chemical Information for MolecularSimulation of Adsorption Equilibria of Water-Methanol (Ethanol) Mixtures in ZeoliteNaA-4

Eva Csanyi,† Tamas Kristof,*,† and Gyorgy Lendvay*,‡,§

Department of Physical Chemistry, UniVersity of Pannonia, H-8201 Veszprem, P.O. Box 158, Hungary,Department of General and Inorganic Chemistry, UniVersity of Pannonia, H-8201 Veszprem,P.O. Box 158, Hungary, and Chemical Research Center, Hungarian Academy of Sciences,P.O. Box 17, H-1525 Budapest, Hungary

ReceiVed: March 20, 2009; ReVised Manuscript ReceiVed: May 11, 2009

A theoretical examination of two simple Lennard-Jones + Coulomb type potential models of zeolite NaA-4was performed by quantum chemical calculations using density functional theory. A comparison of potentialcurves obtained from model parameters with those from quantum chemical calculations as a function of theposition of a Na+ ion with respect to an appropriately chosen fragment of zeolite was used as a primaryindicator in testing how realistic the behavior of the applied models is. This comparison provides a goodstarting point for further parameter tuning of a potential model using experimental data. The potential modelswere tested in different aspects: structural and adsorption equilibrium properties (quantum chemical structuresvs pair correlation functions as well as equilibrium amount of adsorption) were calculated with pure water,methanol, and ethanol. Tuning the potential parameters resulted in a new model that satisfactorily reproducesthe quantum chemical equilibrium location of the three adsorbates with respect to the zeolite framework.From the pair correlation functions, the behavior of the new potential model was found to be between thoseof the two investigated earlier models. Monte Carlo simulation of adsorption for water-methanol andwater-ethanol mixtures showed that, at higher pressures (above p ) 1 kPa), the newer model predicts greateradsorption selectivity of water to alcohols than the earlier models, which fits to available membrane permeationexperiments better.

1. Introduction

Zeolites are porous materials consisting of a silicon-alumi-num-oxygen network with the positive charge of the Al ionsbeing supplemented by mobile cations. They have excellentadsorption and molecular sieve properties, making them goodcatalysts and ion-exchange agents. They are stable in harshchemical environments and at high temperatures. The size ofthe pores in different zeolites covers a wide range, andaccordingly, the type of molecules that can penetrate them andbe sorbed varies widely for different types of zeolites. Asynthetic variant, zeolite NaA-4, is characterized by small porediameters (∼0.8 nm). This type of zeolite can be used fordehydration of organic solvents. An important application ofzeolite NaA-4 is the dehydration of ethyl alcohol, being usedindustrially in bioethanol production. The performance of zeoliteNaA-4 as a drying agent can, in principle, be determinedexperimentally. However, due to the complexity of suchexperiments, only a limited set of experimental data is available.A possible way to collect the missing information is a theoreticalapproach, such as molecular simulation. Using properly param-etrized molecular simulations, one can determine properties,such as the equilibrium amount of adsorption, heat of adsorption,and kinetic parameters, for example, diffusion coefficients.

The most important criterion for an atomistic-level molecularsimulation to produce successful and realistic information onadsorption is that an appropriate potential function characterizingthe interaction of the atoms within the adsorbent as well asbetween atoms of the adsorbent and adsorbate be available. Forcondensed-phase systems, in principle, one can use the methodsof electronic structure theory to derive the potential energy ofan atomistic system, but the efficiency of the computationalimplementations does not yet allow productive simulation of azeolite-adsorbent system. Instead, model potentials are usedthat are expected to properly describe the interactions betweenadsorbate and adsorbent and adequately reflect the polarproperties of the adsorbent and the structure of the adsorbentas well as that of the adsorbent/adsorbate system. The modelpotentials are most often constructed from atom-atom pairpotentials depending only on the distance between the respectiveatoms. For these pair potentials, appropriate functional formsare chosen and their parameters are determined empirically-withproper guidelines-to ensure that the experimental data on theproperties to be modeled are reproduced satisfactorily well. Thepair potentials often differ significantly from those measuredor calculated ab initio for a single pair of particles (as it is thecase with some of the most widely used potentials, such asSPC/E for water1). This is not surprising because (1) they areexpected to characterize a condensed-phase system where thelocation of the numerous neighboring particles influences theapparent two-body interactions so that the latter can be describedby pair potentials only if proper effectiVe parameters are selectedand (2) our target is the description of one or more macroscopic

* Corresponding author. Email: [email protected] (T.K.); [email protected] (G.L.).

† Department of Physical Chemistry, University of Pannonia.‡ Department of General and Inorganic Chemistry, University of

Pannonia.§ Hungarian Academy of Sciences.

J. Phys. Chem. C 2009, 113, 12225–12235 12225

10.1021/jp902520p CCC: $40.75 2009 American Chemical SocietyPublished on Web 06/17/2009

observables that, reflecting the average behavior of a largenumber of particles, only indirectly depend on the interactionof individual atom pairs. According to the generally appliedapproach, the pair potentials are constructed from terms corre-sponding to dispersive and Coulomb interactions. The dispersioninteraction is usually described by the Lennard-Jones (LJ)potential. To model the Coulomb interactions, the charge ofthe atoms/ions may differ from the integer values normallyconsidered in chemistry, again to produce an effective, averageinteraction.

Model potentials for simulation of adsorption of moleculesin zeolites have to be able to describe the interaction of theatoms of the zeolite framework with each other as well as withthose of the adsorbate. There are several models for the zeoliteframework that can be classified as flexible,2 rigid,3-5 andsemiflexible.6 The rigid model implies that the atomic positionsare fixed in the calculations. In a semiflexible model, thelocations of the framework atoms are fixed but the sodium ionscan move. The flexible model allows the framework atoms alsoto move. Furthermore, there are oxygen atoms in variouspositions in the framework that can be characterized by differentparameter sets.

Recently we have studied the adsorption characteristics ofzeolite NaA-4 by molecular simulations.7,8 We used several forcefields for the zeolite framework taken from the literature, butnone of them proved to be completely satisfactory. To be ableto provide results on the selectivity of adsorption of water withrespect to alcohols, we found that it is necessary to develop anew zeolite framework model.

We decided to develop such a potential model by modifyingan earlier force field by varying the parameters using a newparadigm. According to this paradigm, we sequentially assessthe performance of the actual model potential in two respects:(1) how do the potential curves calculated with the model alongsome selected lines in the configuration space of the systemmatch those obtained using electronic structure theory and (2)how well does the molecular simulation reproduce macroscopicproperties, such as the amount of adsorption measured experi-mentally. We perform the molecular simulation only if the firstcriterion is satisfied. We expect that the comparison withquantum chemical potential data ensures that the potentialparameters are realistic, and so they provide a good startingpoint for parameter tuning using experimental data. This way,we can get a reasonably accurate model that enables us to makepredictions. In principle, we could fit the parameters of themodel so that the quantum chemical potential curves arereproduced as well as possible. However, our own experience9,10

and those of others11,12 with potential surface fitting show thatthe number of parameters in a simplified model potentialconsisting of pairwise interaction functions is too little toguarantee that a complex potential surface, with all its minima,steepness of walls, etc., could be uniformly well reproduced.An additional reason making the attempt of a full potentialsurface fit less desirable is that quantum chemical calculationscan be performed for only a subset of the complete system,and if we fitted the parameters of the model potential to thequantum chemical potential surface for the subset, we couldeasily face the contradiction mentioned above, namely, that theaccurate potential that is valid for a limited number of particlesseparated from the rest of the system does not match the modelpotential that best reproduces the macroscopic data.

An advantage of our paradigm is that it makes the search forgood parameters of the pair potentials more efficient. Bychecking whether a parameter combination proposed during

parameter search is realistic, we can discard the ones that willprobably produce unacceptable results in a complete moleculardynamics or Monte Carlo (MC) simulation, this way reducingthe number of attempts that actually involve the rather time-consuming step, simulation.

In our search for good potential parameters for zeolite NaA-4, we supplemented the parameter improvement procedure wereported earlier (and sketch below) with additional stepsaccording to the strategy described above. The first model weused is the zeolite model proposed by Lee et al.6 (in thefollowing, model A). This model predicted too high equilibriumloadings in our simulations for pure methanol and ethanol withrespect to the corresponding experiments.13 To correct thisweakness of the model, we developed a new model (model B7)in which we kept the semiflexible concept of the framework.The atomic positions of the zeolite NaA-4 framework were takenfrom X-ray diffraction experiments, and the point charges aswell as the Lennard-Jones interaction sites were assigned topoint masses corresponding to the framework atoms. Forsimplicity, all types of oxygen atoms were characterized by thesame parameter set and the dispersion (as well as the soft-sphererepulsion) interactions of framework atoms were taken intoaccount only through the effective LJ potential of O. Model Bshows better agreement with the experimental data for theloadings of water, methanol, and ethanol. Furthermore, insimulations of mixtures, the selectivity of water to alcohols ispredicted to be higher and, in contrast to model A, model Bdoes not exhibit any inversion of selectivity in a wide range ofpressure.7 The main advantage of model B is its transferability:it can also be applied to zeolites with a variable Si/Al ratio.However, in simulations of the adsorption of CO2 in zeoliteNaA-4, the experimental equilibrium loadings were significantlyunderestimated.14 As CO2 is a nonpolar gas under normalconditions, we conjectured from this result that the model istoo polar. The body of information listed above served as astarting point for improvement according to the above-mentionedparadigm. We calculated potential curves, that is, cuts of thepotential energy surface, using the methods of electronicstructure theory. These calculations, in addition to providinginformation on the interaction of the Na+ ion and the zeoliteframework, also supported our assumption that the chargeparameter of the Na+ ion needs to be reduced. As describedabove, comparison of the model potential curves with thequantum chemical ones provided a quick way of selecting theparameter domain that produces realistic interaction potentials,and the time-consuming molecular simulations were performedonly within this domain. Using only two-body (Lennard-Jonesand Coulomb) potentials, we cannot expect that fitting to thequantum chemical potential surface would make sense. Instead,the target of parameter optimization-within the domain ap-proved by the quantum chemical calculations-was the bestperformance of the model potential in classical MC simulationsof adsorption of pure water, methanol, and ethanol on zeoliteNaA-4.

In this paper, we first describe the methods and proceduresused in the electronic structure calculations, followed by thesummary of the methods of molecular simulations. The basicprinciples and the parameters of the group of models wedeveloped are presented in section 3. In section 4, we comparethe performance of models B and C in simulation of adsorptionof pure adsorbates in zeolite NaA-4 and test how realistic theatom-atom pair potentials are by comparing them with the DFTpotential curves. Finally, the results of modeling simultaneous

12226 J. Phys. Chem. C, Vol. 113, No. 28, 2009 Csanyi et al.

adsorption, the main goal of the development of the new model,are presented.

2. Computational Details

Density Functional Theory Calculations. We used first-principles electronic structure methods, namely, density func-tional theory (DFT)15-18 with the B3-LYP combination offunctionals19,20 and the SVP basis set.21 Since these calculationsare relatively time-consuming, they were performed using afragment of the zeolite that can still adequately represent thebehavior of the zeolite adsorbent. Adsorption takes place in theinterior of the supercage of the zeolite framework. After somepreliminary calculations, we have chosen a corner of the super-cage, which consists of one 8R, two 6R, and two 4R windowsconnected to each other, as seen in Figure 1 (the referencecoordinate system used is also shown). The terminal O atomswere capped by H atoms. The geometry of the fragment wasfrozen during the calculations because the zeolite frameworkwas kept fixed during the classical simulations, too. We havechecked and found that minor modifications of the geometryof the fragment do not cause any significant difference in theresults of the DFT potential curve calculations. All quantumchemical calculations were carried out with the Gaussian 03suite of programs.22

The geometry corresponding to the minima on the potentialenergy surface of the Na+ ion + zeolite system was calculatedby restricted geometry optimization, keeping the zeolite fragmentfrozen. The optimum positions were determined for one as wellas for two Na+ ions. The obtained positions agree with theresults of X-ray diffraction experiments.23 Note that at least oneof the Na+ ions is very mobile. One Na+ ion is located close tothe center of the 6R ring. If a second Na+ ion is also present,the potential energy is the lowest if the first ion is at the centerof the 6R ring and the second is near the center of the 8R ring.Later, when we optimized the location of the adsorbates, thesodium atoms were initially placed at these positions but wereallowed to move. We also calculated DFT potential energycurves by systematically varying the position of the Na+ ions,which served as a reference for testing the pair potential models.

The Na+ ion was translated along various straight lines anchoredto the zeolite fragment, which are expected to provide satisfac-tory information for fitting of the parameters of the Na+-zeolitepotential.

The adsorption of water, methanol, and ethanol moleculesin the supercage of zeolite NaA-4 was simulated in DFTcalculations including the model zeolite fragment, two sodiumions, as well as one adsorbate molecule. The potential minimacorresponding to the lowest-energy position of the adsorbatewith respect to the Na+ + zeolite fragment were located byrestricted geometry optimization. The framework of the zeolitefragment was frozen; the Na+ ions and the adsorbate moleculewere allowed to move. The initial positions of Na+ ions wereat the positions obtained in previous optimization in the ab-sence of the adsorbate and remained essentially there duringthe optimization. The structure of the adsorbate molecule in theDFT calculations was set initially identical to the structure usedin the classical molecular simulations (as it is shown in Table2), but after the optimum location of the adsorbate moleculewas found, this restriction has been relaxed and a full optimiza-tion of the adsorbate with respect to the (frozen) zeoliteframework was performed.

Monte Carlo Simulations. The molecular simulation ofadsorption was carried out using the grand canonical MCmethod. The partial pressure values of the adsorbate moleculesin the gas phase were given indirectly by specifying thecomponent’s chemical potential that was calculated from theideal gas law. In our earlier work, the suitability of the idealgas law was verified by test simulations.7 The LJ interactionsbetween sites of the zeolite and the adsorbate molecules, suchas water, methanol, and ethanol, were calculated by theLorentz-Berthelot combining rules. The Wolf method24 wasused to treat the Coulomb interactions. The advantage of thismethod is that it lacks the inherent periodicity of Ewaldsummation,25 and consequently, the computation time can bereduced. It was shown earlier26 that the Wolf method is anefficient alternative to the Ewald summation, and in mostsystems, the best agreement can be achieved with rc ) L/2 andR ) 2/rc (where L is the box length, rc is the cutoff radius, andR is the convergence parameter). In our system, these parametersare the following: L ) 2.4555 nm, rc ) 1.22775 nm, and R )1.6290 1/nm.

The grand canonical simulations with pure componentsconsisted of an equilibration period (in the order of 108 MCmoves) and a subsequent averaging period (at least 2 × 108

MC moves), where the ratio of insertion and deletion steps was70-80%. In these simulations, we used the configurational-bias technique27 to increase the sampling efficiency. In mixturesimulations, the sampling efficiency was further increased byidentity change attempts28 and, in the case of water-ethanolmixtures, a special, so-called energy biased identity changemethod was used.29 The creation of molecules inside the sodalitecages was prevented artificially by placing purely repulsivedummy atoms at the center of these cages because the standardrandom insertion of molecules cannot take into account thephysical diffusion pathways in the zeolite. The accessibility ofthe sodalite cages for adsorbate molecules is still an openquestion; there is some disagreement in the literature concerningit.30,31 Sodalite cages are very probably not accessible formolecules such as methanol and ethanol. However, in contrastto some experimental reports (e.g., ref 32), our previoussimulation results suggest that smaller molecules such as waterare also unable to pass through the windows of the sodalitecage.

Figure 1. Zeolite fragment (a corner of the supercage) used in QCcalculations. The Si, Al, and O atoms are denoted by yellow, gray,and red, respectively. The reference coordinate system (axes x, y, z)and the different types of O atoms are also shown.

Water-Methanol (Ethanol) Mixtures in Zeolite NaA-4 J. Phys. Chem. C, Vol. 113, No. 28, 2009 12227

When we calculated the potential curves using various modelpotentials for comparison with the corresponding reference DFTresults, no periodic boundary conditions and long-range cor-rections were applied: each atom-atom pair energy wascalculated from the terms of the direct pair (Lennard-Jonesand Coulomb) interactions. Separate classical molecular simula-tions were also performed for comparison of the most probablepositions of adsorbate molecules with the DFT optimizedgeometries. The most probable positions in the simulations weredetermined from site-site pair correlation functions. The latterwere obtained from simulations with one adsorbate particle (inthe grand canonical simulation, the chemical potential wasadjusted to ensure that only one particle is present, on average,in the simulation box). We calculated the distances betweenthe sites of the adsorbent and adsorbate molecules from the first(and possibly second) peaks of the pair correlation functions,and these were used in the comparison with the DFT results.

3. Model Potentials

Our model for the zeolite framework is semiflexible: theframework atoms are fixed at the atomic positions taken fromX-ray diffraction experiments,23 and the nonframework Na+ ionsare allowed to move. Zeolite NaA-4, as other zeolites, cor-respond to the general formula Mx/n[(AlO2)x(SiO2)y], where thenonframework cations (the valence of which is n) are denotedby M. The primary unit of the zeolite structure is the TO4

tetrahedron, which can have either Si or Al in its center. Theseunits are generally organized into secondary units called rings.Zeolite NaA-4 is of framework type LTA (Linde type A) andhas three types of rings: 4R, 6R, and 8R containing 4, 6, and 8O atoms, respectively. The interconnection of 4R and 6R ringsforms nearly spherical cages, which are called sodalite cages.The O bridges connect the sodalite cages to each other so thatthey form supercages23 with a diameter of about 1.2 nm. Thecrystal structure of zeolite NaA-4 belongs to the fm3c spacegroup with a lattice parameter of 2.4555 nm.

The MC simulation box consisted of 576 framework atoms(96 Si, 96 Al, 384 O atoms) and 96 Na+ ions. In the model,each AlO4 tetrahedron is connected to a SiO4 tetrahedron tofulfill the Lowenstein rule that prohibits Al-O-Al linkages.The potential models are defined by the positions of the

interaction sites and their parameters, namely, the Lennard-Jonesenergy (ε) and size (σ) parameters and the point charges (q).Earlier, we used the semiflexible potential model proposed byLee et al.6 (model A). In all simulations of adsorption, we foundthat this model predicts higher equilibrium loadings for pureadsorbates, such as methanol and ethanol, than the correspondingexperimental results. Therefore, we changed to an other literaturemodel, the potential model of Faux et al.,2 and the model wasmodified by optimizing its parameters to the equilibriumadsorption of pure water, methanol, and ethanol (model B). Theparameters of models A and B are given in Table 1. The mainchanges in model B with respect to model A are (1)the assumption that all oxygen atoms in the framework are ofthe same type (i.e., each O atom has the same parameter set),(2) the significantly larger charge parameter of Na+ ions (beingset to 1), and (3) reduction of the LJ parameters for Si and Alto 0 (i.e., these atoms participate only in Coulomb interactions).Although the charge parameters were adopted from ref 2 onlywith slight modifications, it is important to emphasize that thedifference between the charge parameters of Si and Al in modelB was set equal to the charge parameter of Na+ ions The modelparameters were optimized for the equilibrium amount ofadsorption of water, methanol, and ethanol (normal liquids) andof the much less polar hydrogen sulphide (normal gas). As aresult, the simulations of adsorption of water-alcohol mixturesproduced better results for both the amount of adsorption andthe selectivity data using model B than with model A. We testedmodel B for other adsorbates. For carbon dioxide adsorption,we found that the results do not match the correspondingexperimental data.14 This suggests that model B is too polar inthe simulations with nonpolar adsorbate molecules, suggestingthat the model needs to be further improved. The main problemis the selection of the charge parameter of the Na+ ion becausethe polarity of the model strongly depends on it, significantlyaffecting the adsorption behavior of the zeolite. Following adetailed structure examination of models A and B, we assumedthat model B could be improved by decreasing the chargeparameter of Na+ ions (which calls forth some changes in theLJ parameters). We found that this parameter should be between0.55 and 1, and the charge parameters of the framework atomsneed to be changed accordingly to fulfill electroneutrality. We

TABLE 1: Lennard-Jones Energy (ε) and Size (σ)Parameters and Partial Charges (q) of Models A,6 B,7 and C

model A

sites Na+ Si Al Oa Ob Oc

(ε/k)/K 2507.3 64.18 64.18 78.02 78.02 78.02σ/nm 0.1776 0.4009 0.4009 0.289 0.289 0.289q/(electron

charge)0.5502 0.6081 0.6081 -0.4431 -0.4473 -0.438

model B

sites Na+ Si Al O

(ε/k)/K 20.0 100.0σ/nm 0.32 0.34q/(electron charge) 1.0 3.7 2.7 -1.85

model C

sites Na+ Si Al O

(ε/k)/K 100.0 200.0σ/nm 0.25 0.33q/(electron charge) 0.7 2.4 1.7 -1.2

a Member of 4R and 8R. b Member of 6R and 8R. c Member of4R and 6R.

TABLE 2: Lennard-Jones Energy (ε) and Size (σ)Parameters, Partial Charges (q), and Geometry Data (BondLength δ, Bond Angle r and Dihedral Angle θ) for Water,Methanol, and Ethanol

model sites (ε/k)/K σ/nm q/(electron charge)

water34

O 78.197 0.3166 0.8476H 0.4238

δ(O-H) ) 0.1 nm, R(H-O-H) ) 109.47°

methanol36

CH3 105.2 0.374 0.265O 86.5 0.303 -0.700H 0.435

δ(O-H) ) 0.0945 nm, δ(O-CH3) ) 0.1425 nmR(H-O-CH3) ) 108.53°

ethanol35

CH3 104.17 0.3775CH2 59.38 0.3095 0.265O 85.55 0.3070 -0.700H 0.435

δ(O-H) ) 0.0945 nm, δ(O-CH2) ) 0.1430 nmδ(CH2-CH3) ) 0.1530 nm

R(CH3-CH2-O) ) 108°, R (H-O-CH2) ) 108.5°θ(H-O-CH2-CH3) ) 180°


selected for the new model the Na+ and Al parameters proposedby Maurin et al.:33 qNa ) 0.7 and qAl ) 1.7 (Table 1). We thenvaried the LJ parameters, and with each, the potential curveswere calculated at the locations of the Na+ ion used in the DFTcalculations (the Na+ ion moving along straight lines). This isa very quick calculation (requires only fragments of a second)in contrast to the full MC simulations (requiring several days).By comparing to the DFT data, it was easy to discard unrealisticcombinations of the charge and LJ distance parameters thatpoorly match the corresponding DFT data. When a promisingparameter set was found, we performed classical test simulationsand calculated the equilibrium adsorption data for pure water,methanol, and ethanol. During model optimizations, the LJ sizeparameters of model B decreased and the energy parametersincreased to some extent. The model with the resulting parameterset will be called model C in this paper.

In the simulations, we used the well-known SPC/E34 model,the OPLS35 model, and an OPLS-type model36 for the repre-sentation of the water, ethanol, and methanol molecules,respectively. These models are suitable for the reproduction ofthermodynamic properties of the pure substances. The interac-tion parameters as well as the geometry parameters of theadsorbates are summarized in Table 2.

4. Results and Discussion

Performance of Model C in Simulations of Adsorption ofPure Substances in Zeolite NaA-4. For the final parametriza-tion of model C, the experimental adsorption data for pure water,methanol, and ethanol at T ) 298 K13 were used. Theequilibrium adsorption loadings at p ) 1 and 0.1 kPa are shownin Table 3 (some data are taken from our previous work7).Comparing the three models, we can say that models B and Cyield a reasonably good reproduction of the experimentalloadings for all three adsorbates. The results for models B andC are quite similar, especially for methanol and ethanol. Thequality of reproduction of the experimental data for model A isnot as good as that of models B and C and becomes worse inthe order of water, methanol, and ethanol.

From pair correlation functions, we can get information aboutthe relative strength of the different interactions and the featuresof hydrogen bonding. As the main differences between modelsB and C are associated with the Na+ ions and the O atoms, theO(zeolite)-adsorbate and the Na(zeolite)-adsorbate interactionsare the key properties to be examined. Three types of O atomsare determined by site symmetries: O1 is a member of a 4Rand an 8R ring, O2 is a member of a 6R and an 8R ring, and O3

is a member of a 4R and a 6R ring. As expected, the paircorrelation functions plotted in Figure 2 for the adsorbate’s Hatom and the framework O atoms are quite similar for modelsB and C. There is a significant difference in the intensity of

peaks and a slight dissimilarity (0.01-0.03 nm) in the positionof peaks, especially in the O1-H(adsorbate) interactions. Formodel C, the adsorbent-adsorbate interactions seem to beweaker than those for model B. In all three zeolite models,the positions of the first O1-H(adsorbate) peaks indicate theexistence of hydrogen bonding between the adsorbent and theadsorbates. Even though the LJ distance parameter of O issmaller in model C, these curves suggest that the adsorbatescannot approach the zeolite framework atoms as close as inmodel B. The comparatively featureless O3(zeolite)-H(adsorbate)pair correlation functions are not presented, as they do notprovide any new information.

From the Na(zeolite)-O(adsorbate) pair correlation functionsplotted in Figure 3, we can observe that the positions of thefirst peaks are more or less identical in the case of models Aand C, and the relative intensity of these interactions is nearlythe same for models B and C. These results justify what wehave expected, namely, that the performance of model C isbetween those of models A and B.

Comparison of the Model Potentials with DFT. As wementioned above, in models B and C there is only one parameterset for O instead of three parameter sets as in model A, and itis necessary to examine in detail the influence of this dissimilar-ity. We compared the potential energy curves as a function ofthe location of the Na+ ion calculated with the model potentialsand with DFT. The quantum chemical results can be consideredas a reliable reference because the minimum energy positionsof Na+ ions according to the DFT calculations-one close tothe center of the 6R ring and one near the center of the 8Rring-are the same as those in the X-ray diffraction experi-ments.23 Three characteristic straight lines were chosen alongwhich the Na+ ions are moved in the zeolite fragment, startingfrom the potential energy minima corresponding to the Na+ ionsbeing in the 8R or in the 6R ring. We have not consideredpositions of Na+ ions in the 4R ring or very near to it.Accordingly, the lines along which the potential energy issampled run (1) perpendicular to the 8R plane, passing throughthe center of the 8R ring (parallel to the x axis in Figure 1), (2)along one of the medians of the 8R ring (the z axis in Figure1), and (3) perpendicular to the 6R plane, passing through thecenter of the ring. These potential curves are the ones that weused to guide our potential parameter optimization, as describedin the Introduction. In Figure 4a-c, we plotted the potentialenergy curves obtained with the DFT method and with the threemodel potentials. The energy along each curve is referred tothe respective energy minimum. We found that the energyminima are obtained at the same position with each methodalong the line perpendicular to the 8R plane through the centerof the 8R ring (see Figure 4a). It is seen that the curve of modelC runs the closest to the DFT results. If the Na+ ion goes alongthe diameter of the 8R ring (see Figure 4b), the shapes of thecurves are very similar but the minimum of model A is closerto the QC minimum than those of the other two models (forwhich the location of the minimum is nearly the same). Thereason for this difference is that the LJ size parameters of theO atoms and Na+ ions are larger in models B and C because,in these models, the consequence of the omission of the LJinteractions for the framework atoms, Al and Si, had to becounterbalanced by the LJ size parameters of O atoms. Thisdifference appears in Figure 4c, too, where the Na+ ion passesthrough the center of the 6R ring. There is a local maximumon the curves at the DFT minimum for all models; however,the curve of model A fits the DFT results better. The appearanceof the maximum is an artifact: the diameter of the 6R ring is

TABLE 3: Simulated and Experimental Data13 for theAmount of Adsorption (na)a

number of adsorbate molecules per unit cell (na)b

water methanol ethanol

p 1 kPa 0.1 kPa 1 kPa 0.1 kPa 1 kPa 0.1 kPa

experimental 195 184 76 70 46 44model A 203(2) 182(2) 95(1) 93(1) 63(1) 60(1)model B 197(2) 185(2) 77(1) 73(1) 49(1) 48(1)model C 187(2) 173(2) 77(1) 73(1) 48(1) 47(1)

a Simulated data for models A and B are taken from ref 7.b Numbers in parentheses represent statistical uncertainties of thesimulations in the last reported digits.


relatively small, and even a slight enhancement of the sizeparameters can cause a large difference in the potential energiesif the framework atoms of the 6R ring are close to the Na+ ion.

The consequence is that, in contrast to the DFT and X-rayresults, the most probable position of the Na+ ions in theclassical simulations is not exactly the center of 6R ring but

Figure 2. O1(zeolite)-H(adsorbate) and O2(zeolite)-H(adsorbate) pair correlation functions with one adsorbent molecule of water, methanol, andethanol at 378 K. The dashed, dotted, and solid lines correspond to models A, B, and C, respectively.


slightly outside of its plane. This is, in a sense, the price wehave to pay to get a much better simulation performance of amacroscopic system.

We also tested how realistic are the zeolite models combinedwith the zeolite-adsorbate interaction by finding the mostprobable positions of the adsorbate molecules, water, methanol,and ethanol. The reference QC calculations were performed withthe selected zeolite fragment (Figure 1) supplemented by twoNa+ ions, as described in section 2. After the initial constrainedoptimizations with rigid adsorbates, the geometry of water,methanol, or ethanol was relaxed, and the optimized structuresshowed negligible deviations from the structures used insimulations (the largest change was 2 pm in the bond lengths,3° in bond angles, and 2° in torsional angle). The position ofthe Na+ ions did not change significantly either. One of themalways stayed in its most favorable position, that is, in the centerof the 6R ring. The other Na+ ion followed the movement ofthe adsorbate molecule, but it stayed essentially on the centerline of the 8R ring. The optimized positions of the adsorbatesare shown in Figure 5. The Na+ ion helps the adsorption of theadsorbate molecules through an orientation effect: the O atomof the adsorbate tends to take a position close to the Na+ ion inthe 8R ring in such a way that the H atoms of the adsorbate’sOH group point toward the O atoms of the framework. Thecalculations show clearly that, unlike methanol and ethanolmolecules, the water molecule is bound to the zeolite frameworkby two hydrogen bonds. The presence of the additional hydrogenbond is reflected by the binding energies of the adsorbates to

the zeolite, which are 168.5, 115.2, and 111.2 kJ mol-1 for water,methanol, and ethanol, respectively. Although we do not thinkthese numbers can be considered very accurate, the tendency iscertainly correct. The significantly larger binding energy of wateras compared to that of the alcohols justifies why wateradsorption is preferred on this type of zeolite, which causesimproved selectivity of water to alcohols.

For the zeolite models A, B, and C, the most probablepositions of adsorbate molecules were determined from grandcanonical simulations using one adsorbate particle, where thefirst peaks of the calculated pair correlation functions (for allpairs of interaction sites) provided the distances betweendifferent adsorbent-adsorbate atom pairs. Shown in Figure 6is the comparison of the simulation versus the DFT results forthe distances between the O and H atoms of the adsorbate andthe nearest O, Si, and Al atoms and the Na+ ion (located in the8R ring) of the zeolite. The figures show the deviation of thedistance obtained in molecular simulations from that found byquantum chemical geometry optimization. Figure 6a shows thatmodels B and C describe well the water-zeolite interactions;the overall performance of model A is somewhat poorer. Thedistances obtained with model C are quite similar to those frommodel B. In the case of the Na+-O(water) interaction, modelB is somewhat better. It is seen that the results for model A arealso in good agreement with the DFT results, except for theO(zeolite)-H(water) and Na(zeolite)-O(water) interactions.Figure 6b illustrates that model C provides the best overallagreement with the DFT calculations in the case of methanol.

Figure 3. Na(zeolite)-O(adsorbate) pair correlation functions with one adsorbent molecule of water, methanol, and ethanol at 378 K. The dashed,dotted, and solid lines correspond to models A, B, and C, respectively.


The results of model B are quite similar to those of model C,except for the Na(zeolite)-O(methanol) distances, where modelB produces a more than 0.1 nm worse overestimate. It is visiblethat model A gives the worst results for the different interatomicdistances, except that between Na(zeolite) and O(methanol). In

the case of ethanol (Figure 6c), models B and C describe theinteractions between the framework atoms and the adsorbatemolecules quite well; only the Na(zeolite)-O(ethanol) distanceis too large for model B. From Figure 6, we can make theconclusion that, overall, model C predicts more realistically thebehavior of the system for the adsorption of water, methanol,and ethanol.

5. Simulation of Adsorption of Water-Alcohol Mixtureson Zeolite NaA-4

Our main purpose with the development of model C is anadequate modeling of the adsorption selectivity for water-alcohol mixtures. We performed such simulations at T ) 378K. Because this temperature is above the normal boiling pointsof the components, the maximum pressure was set to p ) 100kPa, the pressure of the available gas permeation experimentsfor water-alcohol mixtures.13 A detailed comparison of modelsA and B was made in our earlier work, simulating at differentpressures and mole fractions of bulk phase.7 For model C, wecarried out simulations at equimolar composition of the bulk

Figure 4. Potential energies for different positions of one Na+ ion:(a) when the ion is translated along a line perpendicular to the planeof ring 8R (the line parallel to the x axis in Figure 1), passing throughthe center of 8R (the negative direction corresponds to locations outsideof the supercage, i.e., the negative z axis in Figure 1), (b) when the ionis translated along one of the medians of the 8R ring (the z axis inFigure 1), and (c) when the ion is translated along a line perpendicularto the plane of ring 6R passing through the center of 6R (a line in thex-z plane in Figure 1). The energy is measured from the lowest energyof each curve. The solid blue line corresponds to the quantum chemicalcalculation; the dashed, dotted, and solid lines correspond to modelsA, B, and C, respectively.

Figure 5. Optimized positions of water (a), methanol (b), and ethanol(c). The Si, Al, O, H, and Na+ atoms are denoted by yellow, gray, red,white, and blue, respectively.


water-alcohol mixtures. We present here the comparison ofthe simulation results obtained with the three model potentialsunder the latter conditions.

The comparison of the results of mixture adsorption (shownin Figure 7) clearly indicates the difference between the three

models. Model A predicts a reversal of equilibrium selectivityat relatively high pressures (around 20 kPa) in both water/methanol and water/ethanol mixtures: at higher pressures, wateradsorption is preferred, whereas at lower pressures, methanolor ethanol adsorption is preferred. In the case of model B, the

Figure 6. Distances between the atoms of the zeolite framework and the O (Ow, Om, Oe) as well as H (Hw, hydroxyl-Hm, hydroxyl-He) atoms ofa (a) water, (b) methanol, or (c) ethanol molecule at the lowest energy position with respect to the zeolite, as obtained from MC simulationscompared with the corresponding DFT values. The distances for the MC simulations are equal to the location of the first or highest maximum ofthe pair correlation functions. The dashed, dotted, and solid lines correspond to models A, B, and C, respectively.


inversion of selectivity cannot be observed even at very lowpressure (see ref 7). The results of model C differ from thoseof the other two models; namely, at low pressures (around 1Pa), the amount of adsorbed water and methanol/ethanol isapproximately equal. In addition, model C shows the bestselectivity rate at higher pressures (above p ) 1 kPa). Notethat zeolite NaA-4 is applied industrially at higher pressures(around p ) 140 kPa), for example, for ethanol dehydrationduring the high-efficiency pressure swing adsorption process.Experimental data are available at ambient pressure only frommembrane permeation experiments,13 the results of whichdepend not only on the difference in adsorptivity but also onthe diffusivity of the components. As a result, no directcomparison can be made with our simulation results. Neverthe-less, we can assume that model C predicts the amount ofadsorption better than the earlier models used for water/methanoland water/ethanol mixtures because the experiments show veryhigh selectivity of water to alcohols. The observation mentionedin section 4, namely, that, according to the DFT calculations,the binding energy of water to the zeolite is much larger thanthat of alcohols, supports that the high selectivity predicted bymodel C is realistic.

6. Conclusion

We developed a new potential model for zeolite NaA-4 basedon a new paradigm. During parameter optimization, we utilizedpotential curves obtained in quantum chemical calculations usingdensity functional theory for judging the quality of the modelpotentials. In contrast to an often used approach, instead of fittingthe model potential to these curves, we used the DFT results toscreen parameter sets that occurred during model developmentand discarded the ones that produced unrealistic potential curves.

The quantum chemical reference calculations compared withthe results of classical MC simulations of two published models(models A6 and B7) suggested a possible way to improve thepotential model for zeolite NaA-4. Namely, the charge of theNa+ ion should be set lower than 1 (and, of course, such achange involves the modification of the rest of the pair potentialparameters). Considering the results of structure examinations,we proposed a new parameter set starting from the later model(model B). When the calculated equilibrium amounts ofadsorption obtained in simulations using the three models at T

) 298 K are compared with available experimental data, it canbe established that the new model provides a reasonably goodreproduction of the experimental loadings for water, methanol,and ethanol.

The simulation results for water-methanol and water-etha-nol mixtures showed that, at higher pressures (above p ) 1 kPa),the newer model (model C, which, in all other aspects, is morerealistic than the others) predicts a larger relative amount ofadsorption of water than that of the earlier models. This resultmay be of great importance considering that zeolite NaA-4 isapplied industrially at higher pressures. The higher selectivityof water to alcohols at higher pressures agrees better with themembrane permeation experiments.13 The higher selectivity isin good agreement with the larger binding energy found in theDFT calculations for the water to zeolite versus the alcohol tozeolite connections.

Our earlier studies concerning the adsorbent-adsorbate paircorrelation functions suggested that model B is more realisticthan model A,7 so here, we compare the results of model C tothose of model B. We found the pair correlation functions ofmodels B and C to be quite similar, except that the intensity ofthe peaks differs. The lower peak intensities for model C indicateweaker adsorbent-adsorbate interactions. The O1(zeolite)-H(adsorbate) pair correlation functions of the newer modelsuggest that the adsorbates, even though the LJ distanceparameter of O(zeolite) is smaller in model C, cannot approachthe zeolite framework atoms as close in this model as in thecase of the other two models. As it can be expected on the basisof the model parameters, the Na(zeolite)-O(adsorbate) paircorrelation functions (especially the first peaks) also show thatthe performance of model C lies between those of models Aand B.

Examination of the potential curves calculated as a functionof a Na+ ion with respect to a fragment of zeolite proved thatthe newer model describes the framework-Na+ interactionsbetter than our previous models and even coincides, almostperfectly, with one of the quantum chemical curves. Theseresults also confirm that, in the course of model development,we managed to partially counterbalance the unrealistic compo-nents of the model potential (namely, that the LJ parametersfor Si and Al were set to 0). The comparison of the optimumpositions of the adsorbate molecules water, methanol, and

Figure 7. Simulation results for the amount of adsorption (na) for equimolar mixtures of water-methanol and water-ethanol on zeolite NaA-4 at378 K. Dashed, dotted, and solid lines represent models A, B, and C, respectively. The circles and squares correspond to water and methanol orethanol, respectively. The statistical uncertainties of the calculated loadings do not exceed the symbol size. The results for model A are taken fromref 8.


ethanol obtained in quantum chemical calculations with thosederived from molecular simulations also supports that the newmodel presented in this paper behaves more realistically thanall earlier ones.

Acknowledgment. This work was supported by the Hungar-ian Scientific Research Fund (Grant Nos. OTKA K 75132 andK 77938).

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