dynamics of exchange at gas-zeolite interfaces i: pure...

Dynamics of Exchange at Gas-Zeolite Interfaces I: Pure Componentn-Butane andIsobutane

M. Chandross*,† E. B. Webb III, † G. S. Grest,† M. G. Martin, ‡ A. P. Thompson,‡ andM. W. Roth§

Mail Stop 1411, Sandia National Laboratories, Albuquerque, New Mexico 87185, Mail Stop 1111Sandia National Laboratories, Albuquerque, New Mexico 87185, and Texas A&M UniVersity,Department of Physical and Life, Sciences, Corpus Christi, Texas 78412

ReceiVed: August 15, 2000; In Final Form: February 23, 2001

We present the results of Molecular Dynamics and Monte Carlo simulations ofn-butane and isobutane insilicalite. We begin with a comparison of the bulk adsorption and diffusion properties for two differentparameterizations of the interaction potential between the hydrocarbon species, both of which have beenshown to reproduce experimental gas-liquid coexistence curves. We examine diffusion as a function of theloading of the zeolite, as well as the temperature dependence of the diffusion constant at loading and forinfinite dilution. Both force fields give accurate descriptions of bulk properties. We continue with simulationsin which interfaces are formed between single component gases and the zeolite. After reaching equilibrium,we examine the dynamics of exchange between the bulk gas and the zeolite. In particular, we examine theaverage time spent in the adsorption layer by molecules as they enter the zeolite from the gas in an attemptto probe the microscopic origins of the surface barrier. The microscopic barrier is found to be insignificantfor experimental systems. Finally, we calculate the permeability of the zeolite forn-butane and isobutane asa function of pressure. Our results underestimate the experimental results by an order of magnitude, indicatinga strong effect from the surface barrier in these simulations. Our simulations are performed for a number ofdifferent gas temperatures and pressures, covering a wide range of state points.

I. Introduction

Zeolites are microporous materials that are ideally suited toa number of different industrial applications such as catalyticcracking or hydroisomerization of hydrocarbon molecules aswell as ion exchange in desiccant or purification applications.Zeolites with medium pore sizes, such as silicalite (structuretype MFI),1 are additionally useful for separations processes,as their openings are approximately the same size as the kineticdiameter of many small molecules. As such, the utility of anygiven zeolite in a separations application is strongly dependenton the preferential adsorption, as well as the relative diffusivitiesof the sorbed species.

There exists a large body of theoretical2-6 and experimental7-14

work that investigates the diffusion properties of small alkanesin zeolites. Simulations are generally performed with eitherMolecular Dynamics (MD) or Monte Carlo (MC) methods,15

both of which give calculated diffusivities that agree well witheach other, although the MC methods, not having a true timedependence, rely on transition state theory for rate constants.The experimental situation is much less clear. Experimentaldiffusion constants can be measured through both microscopicand macroscopic methods, with the calculated diffusivitiesdiffering by an order of magnitude or more between the twomethods. Although macroscopic studies measure the diffusion

of the molecules indirectly, as in supported membrane studieswhere the diffusion is calculated from the permeation flux, themicroscopic measurements directly follow the mean-squareddisplacement of individual molecules. This is the same methodthat is traditionally used in simulations, and it is for this reasonthat simulations tend to agree more with microscopic diffusionstudies rather than macroscopic. It has been suggested that thedifference between the macroscopic and the microscopicmeasurements lies in the improper assumption of Fickiandiffusion in the former16 or the difference between the diffusionof gas-phase and adsorbed components,17 but this discussionlies outside the scope of this paper. With the above in mind,when both macroscopic and microscopic measurements areavailable for comparison with our simulations, we only use themicroscopic measurements.

Simulations of molecular adsorption on zeolites have tradi-tionally been MC studies of adsorption isotherms.18-22 AlthoughMC methods are much more efficient for computing equilibriumproperties of the gas/zeolite system than MD, MC is not wellsuited for calculating time dependent properties. We areprimarily interested in the dynamics of exchange between thegas and adsorbed phases through direct analysis of moleculartrajectories which are not available from MC interface simula-tions. In fact, although our MC studies include a gas phase inthe simulation, most do not, instead relying on parameterizedequations of state that equate a calculated chemical potentialwith a gas pressure.22 It is for these reasons that we have focusedour transport studies on MD simulations. We have verified thatMD simulations equilibrate to the state points as given by the

† Mail Stop 1411, Sandia National Laboratories, Albuquerque, NewMexico 87185.

‡ Mail Stop 1111 Sandia National Laboratories, Albuquerque, NewMexico 87185.

§ Texas A&M University, Department of Physical and Life, Sciences,Corpus Christi, Texas 78412.

5700 J. Phys. Chem. B2001,105,5700-5712

10.1021/jp002967v CCC: $20.00 © 2001 American Chemical SocietyPublished on Web 05/25/2001

adsorption isotherms from MC (see below). With the demon-strated success of MD simulations in both the gas and the zeolite,as well as at the interface (i.e., adsorption isotherms), we feelthat the specifics of molecular exchange between the gas andthe zeolite are equally well represented, and elucidate thedynamics of a process that cannot presently be investigatedexperimentally.

For this work, we restrict ourselves ton-butane (hereafterbutane) and isobutane. The use of these small molecules avoidsthe computational burden associated with longer molecules,while still allowing us to compare fast and slow diffusingspecies.

The remainder of the paper is arranged as follows: In sectionII, we present the details of our simulation methodology,including descriptions of the parameter sets used. We continuein section III with the results of our simulations of bulk zeolitecrystals. These include adsorption isotherms and diffusionstudies. Our interface simulations are presented in IV, wherewe examine the exchange dynamics for systems in equilibrium.We present nonequilibrium permeation studies, in which aconcentration gradient appears on either side of the zeolitemembrane in section V. We conclude and discuss our futurework in section VI.

II. Simulation Details

We perform MD simulations of butane and isobutane usingan united atom (UA) representation for the CHn groups, in whicheach group is treated as a single pseudo-atom. For the diffusionand interface simulations we used two different simulationcodes, one of which constrained all CsC bond lengths to 1.54Å using the RATTLE algorithm,15 whereas the other used aharmonic potential between UAs with a spring constant of452 900 K/Å2.23 The simulations with the constrained bondsused a 5 fstime step and a Langevin thermostat.15 Those withthe harmonic potential used a multiple time step rRESPAalgorithm24 with a 1.25 fs time step for the bonds, a 2.5 fs timestep for the angles, and a 5 fs time step for the interactionbetween nonbonded CHn UAs. Temperature control in thesesimulations used a Nose´-Hoover thermostat. The formersimulations were run with the same code as in our previouswork,3,25,26 whereas the latter were run with the large-scaleparallel MD code LAMMPS.27 We have verified that these twodifferent approaches equilibrate to the same points on theisotherms. We have found slight differences in the exchangedynamics between the two codes when run as described above.These differences, however, disappeared when both codes wereimplemented with a Langevin thermostat. For technical reasons,the multitime step rRESPA algorithm is not presently imple-mented with Langevin dynamics. Hence, to compare exchangedynamics from Nose´-Hoover and Langevin thermostats, simu-lations were run with both codes using a single time step of1.25 fs. A Nose´-Hoover thermostat is essentially a velocityrescaling scheme, which adds no randomness to the system,velocities of all particles are scaled so as to make the kinetictemperature match the prescribed temperature. This type ofthermostat is most applicable in dense systems, such as liquids,where frequent molecular collisions serve to randomize veloci-ties. The Langevin thermostat, on the other hand, couples theparticles to a heat bath via a random force and viscous damping,which are coupled through the fluctuation-dissipation theorem.The Langevin thermostat is most appropriate for our interfacesimulations, as it simulates both collisions with a carrier gas aswell as the effect of a vibrating crystal lattice for molecules

sorbed inside the zeolite. It is for these reasons that most ofour simulations are performed with a Langevin thermostat,especially where dynamical information is desired.

Both codes include three body bendingVb and four bodytorsionVt terms15 of the forms below.

wherekb is the angular spring constant,θ (θb) is the (equilib-rium) angle between three neighboring atoms, andφ is thetorsional angle as described in ref 15. All nonbonded interactionsare governed by a 12-6 cut and shifted Lennard-Jones (LJ)interaction

with a cutoff of rc ) 10 Å unless otherwise indicated. For theadsorption isotherms in section IIIA we also present results forlarger values of the cutoff,rc ) 14 and 18 Å. We use twodifferent parametrizations for the LJ interactions, both developedby Siepmann and co-workers to accurately predict vapor-liquidcoexistence curves for linear and branched alkanes of variouslengths28-33 (see Tables 1 and 2). We refer to these parameter-izations as mSKS (modified Siepmann, Karaborni, Smit)28-31

and TraPPE (Transferable Potentials for Phase Equilibria),32,33

respectively. In both force fields, methyl, methylene, andmethine groups are described by a single set of parametersregardless of their neighbors. Note that although this is theprescription for the TraPPE force field, the original SKS forcefield had a methyl group whose parameters depended upon itsneighbors. To reduce confusion we refer to our SKS force field(i.e., with constant methyl group parameters) as mSKS.

The reason for using two different potential sets is 2-fold.First, although the TraPPE force field reproduces the experi-mental vapor-liquid coexistence curves better than SKS, it isunknown how the two sets compare for dynamical measure-ments, such as diffusion constants. Second, our previous workon the diffusion of long linear and branched alkanes used themSKS potential set,3,25,26and this study can help to understandhow the results from that work relate to the new potential set.

The zeolite structure in our simulation is taken from thedatabase contained in the Insight II software from MolecularSimulations, Inc.34 and is assumed to be rigid. The LJ interaction

TABLE 1: Lennard -Jones Potential Parameters

model group σ (Å) ε (kcal/mol)

TraPPE CH3 3.750 0.195CH2 3.950 0.0914CH 4.680 0.0199

mSKS CH3 3.930 0.227CH2 3.930 0.093CH 3.850 0.064

TABLE 2: Angular Potential Parameters

traPPE & mSKS units

bond length 1.54 Åkb (bending) 124.18 kcal/(mol rad2)θb 114.0°a0 (torsion) 2.007 kcal/mola1 4.012a2 0.271a3 -6.290

Vb(θ) )kb

2(θ - θb)

2 (1)

Vt(φ) ) ∑i

ai cosi(φ) (2)

VLJ(r) ) 4ε[(σr )12- (σr )6] (3)

Pure Componentn-Butane and Isobutane J. Phys. Chem. B, Vol. 105, No. 24, 20015701

between the atoms of the zeolite and the UAs of the alkanes istaken from the work of June et al.,35 with a slight modification.In the original work, all UAs (i.e., CH3 and CH2) were treatedas identical units. For this work, we have normalized thisinteraction to decane in order to arrive at separate parametersfor the different UAs, as described previously.3,26 Theseparameters are not optimized for diffusion or adsorption andthus perform adequately at best, particularly for isobutane, butthis is not of concern as our primary purpose is to compare thedynamics within the given alkane models, using the samealkane/zeolite interaction.

Isotherms were computed using a combination36,37of coupled-decoupled33 configurational-bias MC simulations38-41 and theisobaric-isothermal version of the Gibbs ensemble.42-44 Thisformulation is useful for comparison to experimental isothermsin which the temperature and pressure of the gas are heldconstant. One simulation box contained 12 unit cells of silicaliteand was kept at a constant volume, whereas the other simulationbox exchanged volume with an external pressure bath. Thesystem contained 400 solute molecules which were allowed toexchange between the two simulation boxes. Simulations wererun for 10 000 cycles, where each cycle consisted of 400 MCmoves. Moves were chosen at random with a fixed probabilityof performing a volume move (0.01), molecule exchange (0.19),molecule regrowth (0.2), translation of the center of mass (0.3),and rotation about the center of mass (0.3). The maximumvolume, translational, and rotational displacements were auto-matically adjusted to achieve an acceptance rate of 50%.

For our diffusion studies, our zeolite crystal contained 96 unitcells, four each in the (100) and (001) directions, and six in the(010) direction. Periodic boundary conditions were applied inall directions. For all diffusion studies, guest molecules wereinserted along the straight channels of the zeolite and allowedto diffuse at high temperature (e.g., 900 K). The temperaturewas gradually reduced to the desired temperature for a givenrun, and the system was then allowed to equilibrate before datawere taken. In the dilute limit (i.e., noninteracting sorbatemolecules) we simulated 96 molecules, whereas for finitedensity, the number of molecules ranged from 96 to 768. Ourinterface runs used the same zeolite crystal as the diffusionstudies with the addition of a large (∼100 Å) gas regionalongside the (010) crystal face. Because the gas is exposed tothe external surface of the zeolite, the true nature of this surfacebecomes relevant. For example, the surface will likely bereconstructed, and consist of a mixture of undercoordinated andovercoordinated oxygen atoms. As our MD simulations cannotprobe the true nature of the surface, we have instead investigatedthe effects of differing termination by first examining the twoextremes of fully coordinated and fully undercoordinatedoxygens at the surface. We have further modified the lattersurface to include the effects of hydroxylation by changing theLJ interaction of these oxygens. We found no dramaticdifferences in these simulations and will not discuss them here.45

Our interface simulations were performed in three stages. Thefirst stage was a gas equilibration run in which a given numberof molecules (typically 800-2000) were equilibrated at constanttemperature. The simulation box for this stage had periodicboundary condition in thex andz directions, but was confinedin they direction by walls with a 9-3 LJ potential. Thex andz box dimensions matched those of the zeolite crystal in the(100) and (001) directions. The spacing between the LJ wallswas adjusted to give a desired gas density. After equilibriumwas reached, we began the second stage of the simulation, wherethe LJ walls were removed and the gas was placed alongside

the zeolite with periodic boundary conditions in all directions.The gas molecules adsorbed onto the zeolite crystal and anequilibrium state point was reached when the pressure in thegas and the loading of the zeolite matched the adsorptionisotherm for the system temperature. We show in Figure 1representative snapshots of one of our interface simulations. InFigure 1a, we show a side view of our simulation box, with thebutane molecules in the gas, adsorption layer and zeolite coloredred, yellow, and light blue, respectively, and the zeoliterepresented by purple bonds. Figure 1a shows a gas region witha pressure of approximately 5.5 MPa, and the correspondinghighly loaded zeolite. In Figure 1b and (c) we show closeupsnapshots of the adsorbed surface layer for dilute and densegas regions, respectively. Because we specify the system volumeV, the number of moleculesN, and the temperatureT only, thepressureP, and loading that are finally reached cannot bespecified in advance, although with careful selection ofN for agiven T andV, we can come close to any desired point on theisotherm.

The membrane permeation simulations were performed usingthe parallel grand-canonical (GC) MD code LADERA.46 Twozeolite membranes were positioned in a simulation box of totallength 137.30 Å, oriented so that the straight-channels traversedthe membrane, and the sinusoidal channels lay in the plane ofthe membrane. Each membrane had cross-sectional dimensionsof 2 unit cells in the (001) direction and 3 units cells in the(100) direction (approximately 40 Å× 40 Å). The zeolitemembranes separated the remaining volume into two gasregions, each approximately 29 Å thick. Periodic boundaryconditions were applied in all three directions. Hence, thesimulation box represented an infinite set of infinite parallelzeolite membranes separated by gas regions of alternating highand low pressure. A constant chemical potential was maintainedwithin a 15 Å thick region at the center of each gas region.This was done by performing insertions and deletions of gasmolecules according to the grand canonical MC algorithm.46

Using this method, the pressures and densities on the high andlow sides were maintained at constant but different values. Atthe same time, trajectories of all the molecules in the simulationbox were followed using a conventional molecular dynamicsalgorithm, based on the LAMMPS code.27 As a result, thesimulation evolved in time to a condition of steady-state, witha constant net flux of molecules moving from the high-pressureside, through both zeolite membranes, to the low-pressure side.This flux was maintained by a net addition of molecules in thehigh-pressure control volume and a net removal of moleculesin the low-pressure control volume.

For the permeation studies, the zeolite and gas moleculeinteraction potentials were identical to those described above,with two exceptions. First, the Lennard-Jones interactions weretruncated at 10 Å but were not shifted. This has no effect onthe permeation of molecules through the zeolite, which is onlydependent on the forces, but it is important for the definitionof chemical potential. Second, in the MD portion of thecalculation, which used the velocity-Verlet algorithm withconstant volume and temperature and a time step of 3 fs, thetemperature was controlled by velocity rescaling. We have foundno difference when we ran the same state points with aNose-Hoover thermostat. A set of insertion and deletionattempts were performed in the control volumes every 1000time steps. Each set consisted of 32 attempts in each controlvolume, with insertions and deletions chosen at random withequal probability.

5702 J. Phys. Chem. B, Vol. 105, No. 24, 2001 Chandross et al.

III. Bulk Properties

Before discussing the dynamics of the gas-zeolite interfaces,we present our results for a bulk zeolite. These include thethermodynamic properties of zeolite adsorption as probedthrough adsorption isotherms, and diffusion studies in the infinitedilution limit and at finite loading.

A. Thermodynamic Properties.We begin with a comparisonof the adsorption isotherms from both potential sets andexperiment for both molecules. In Figure 2(a) we show thecomparison forn-butane with the mSKS and TraPPE force fieldsat 353 K with a cutoff of 10 Å. We have chosen theseparameters to match those used in the MD simulations below.We also show in Figure 2a the experimental data from Sun et

Figure 1. (a) Snapshot of an interface simulation at 500 K. Butane molecules in the gas, adsorption layer and zeolite are red, yellow, and lightblue, respectively, whereas the zeolite is represented by purple bonds. The density of the adsorption layer and the filling of the zeolite can be clearlyseen. (b) Close up view of the adsorption layer with a dilute gas region (see text). (c) Same as (b) for a dense gas region.


al.47 at the same temperature. The agreement is excellent forthe TraPPE force field and fair for mSKS, but quite acceptable,considering that neither parameter set was optimized foradsorption studies.

We show the comparison for isobutane in Figure 2b. Theagreement between TraPPE and mSKS is reasonable, but neitherforce field can accurately reproduce the experimental data. Inparticular, both force fields fail to exhibit the plateau in theisotherm in the region of 4 molecules/unit cell, and overshootthe maximum filling by nearly a factor of 2. This difficulty infitting isobutane adsorption has also been seen by Macedoniaand Maginn in their work with a consistent-valence force fieldall-atom method.22 That work found better agreement with aUA method with parameters that were optimized for zeoliteadsorption. The lack of agreement between our calculated andexperimental isotherms is a symptom of the hybrid origin ofthe force fields, and demonstrates the sensitivity of adsorptionsimulations on the parameterization of large molecules (i.e.,those with kinetic diameters close to the pore size). Weemphasize that our purpose in this section is to compare ourstate points with experiment, not to fit them. We are moreinterested in verifying that our MD interface simulations haveconverged to the correct state points for a given model, and theisotherms shown in Figure 2 serve that purpose.

In Figure 3a and 3b, we show the MC isotherms for butaneand isobutane, respectively, as a function of temperature. Forcomparison, we also show results from the MD interface runsat 500 K. We stress, however, that while isotherms can besuccessfully reproduced with the MD simulations, the directintegration of molecular trajectories leads to long equilibrationtimes (in excess of 20 ns for isobutane), and thus extremely

long run times. The MC method is much better suited toisotherm calculations, but is unable to give the dynamics ofexchange that are the ultimate goal of this work.

The calculated isotherms can be fit well with a simpleLangmuir isotherm

whereq(P) is the filling of the zeolite,qsatis the saturation fillingandK is the Langmuir constant. This has been shown previouslyby other authors.18 We show these fits for 500 K in Figure 3aand 3b. The good fits from the Langmuir isotherm suggest thatthe molecules have preferential adsorption sites within thezeolite. The Langmuir fits begin to fail at lower temperaturesand higher pressures, due to the presence of additional adsorp-tion sites that are relatively energetically unfavorable. Forexample, isobutane is known to preferentially load the intersec-tions between the straight and sinusoidal channels in silicalitedue to its large kinetic diameter.21 At higher pressures, however,the intersections become filled, and the sorbed molecules areforced into the channels of the zeolite. These multiple adsorptionsites are taken into account by a double Langmuir fit forisobutane.

To conclude our thermodynamic studies, we investigate theeffect of the LJ cutoff on the calculated isotherms. We performthe bulk of our simulations with a 10 Å cutoff, and show belowthat the effect of the cutoff on dynamic properties, such as thediffusivity at constant loading is small. The effect of the cutoff

Figure 2. Adsorption isotherms for (a) butane and (b) isobutane insilicalite at 353 K. Experimental data from Sun et al. is shown as asolid line. Simulation results are shown for TraPPE with a 10 Å cutand shift (diamonds) and mSKS with a 10 Å cut and shift (squares).Dotted lines are shown as a guide to the eye.

Figure 3. Adsorption isotherms for (a) butane and (b) isobutane insilicalite as a function of temperature. Simulation results using TraPPE10 Å cut and shift are shown at 400 K (circles), 500 K (squares), and600 K (diamonds). The data are connected with lines as a guide to theeye, with the exception of the case of 500 K, where the lines are fitsfrom a Langmuir isotherm. In both (a) and (b), the simulation resultscalculated at 500 K using the MD interface code are shown as stars.Experimental data are not available at these temperatures.

q(P) ) qsatKP

1 + KP(4)


on the adsorption isotherms, however, is more severe. TheTraPPE force field was originally parameterized using a 14 Åcutoff with the standard analytical tail corrections.32,33 Tailcorrections are applied with the implicit assumption that thepair-pair correlation function attains a constant value of 1beyond the cutoff, an assumption that is incorrect inside azeolite, as demonstrated by Macedonia and Maginn.22 Thebehavior of the model for infinite cutoff within a zeolite istherefore unknown. With this in mind, we present in Figure 4our MC isotherms for butane on silicalite as a function of thecutoff in the potential. The isotherms shift monotonically tohigher fillings at a given pressure as the cutoff is increased.This is to be expected, since a larger cutoff leads to increasedattractive energy. In the figure, the isotherms seem to beconverging, though still changing, as the cutoff is increased from14 to 18 Å. It is certainly possible to increase the cutoff untilthe isotherms converge, but such an exercise is beyond the scopeof this work. Rather, we simply point out that the choice ofcutoff is a model parameter that affects the calculated thermo-dynamic properties of any system. In Figure 4, we also showthe calculated isotherm with the TraPPE potential as published,i.e., with a 14 Å cutoff and tail corrections.32,33 Even with thecaveats above, this isotherm seems close to what would beexpected for an infinite cutoff.

B. Diffusion Studies.With an understanding of the thermo-dynamics of sorption, we now move on to the behavior of themolecules within the zeolite. We begin with the calculateddiffusion constantD in the infinite dilution limit. For all ourdiffusion measurements, we find the mean squared displacementof individual molecules, and calculate the diffusion constantbased on the Einstein relation

where⟨r2⟩ is the mean squared displacement andt is the time.In Figure 5, we show the calculated diffusivities over thetemperature range of 400 K to 800 K for both butane andisobutane with the mSKS and TraPPE potential sets. The resultsfor butane show that over the given temperature range the twopotential sets perform identically. This result is not surprisinggiven that the parameterization for butane is almost unchangedbetween the two force fields. Both parameterizations calculatesimilar activation energies, 1.01 and 0.78 kcal/mol for the mSKSand TraPPE potentials, respectively. These values compare well

with experimentally measured activation energies for butane insilicalite, which range from 1 to 3 kcal/mol.12-14,48

For isobutane, there is a substantial difference in thecalculated diffusivities for the two parameter sets at allT. Thisdifference is clearly due to the different treatment of theCHUA in the two parameter sets. In the mSKS parameterization,theCH UA has a radiusσ ) 3.85 Å and well-depthε ) 6.4×10-2 kcal/mol, whereas in the TraPPE parameterization thevalues areσ ) 4.68 Å andε ) 1.99× 10-2 kcal/mol. Whilethe difference inσ is perhaps at first the most surprising, andthe size comparison between CH and CH2 and CH3 for theTraPPE potential is counter-intuitive, we feel that this is notthe cause of the differing diffusivities in Figure 5. Althoughσis so large for the CH UA, the surrounding CH3 UAs effectivelyshield the CH group from the zeolite atoms. Instead it is thevalue ofε, which is smaller by a factor of 3.2 in the TraPPEpotential that leads to the higher diffusivity. A smaller well depthnecessarily implies less attraction to the walls of the zeolite,and it is this attraction that contributes most strongly to thediffusion constant in the infinite dilution limit. The weakerattraction is, of course, tempered somewhat by the larger valueof σ, which implies more attraction at a longer distance. Bothmodels do, however, give similar activation energies of 3.12and 4.34 kcal/mol for TraPPE and mSKS, respectively. Thesevalues also compare well with experimentally measured activa-tion energies, which are generally around 5 kcal/mol.13,14,48

The good agreement with experimental activation energiesis somewhat surprising, given that experiments cannot truly beperformed at infinite dilution. With this in mind, we have alsoinvestigated the diffusivities of butane and isobutane at variousloadings of the zeolite cages. In Figure 6 we show the diffusionof butane in silicalite for both potential sets as a function ofloading. Again, it is clear that the small differences in thedescription of butane within the two force fields results in aminimal difference in the calculated diffusivity. In Figure 6,we also include experimental data taken from Heink et al.11

These data should not be taken as a strict comparison as theywere not tabulated and were inferred from a figure. However,the agreement between simulation and experiment is still quitegood.

Even better agreement between simulation and experimentin seen in Figure 7 where we show the diffusion of butane insilicalite as a function ofT at a fixed loading of eight moleculesper unit cell. As we have found little difference between themSKS and TraPPE potential sets, we will hereafter restrict ouranalyses to TraPPE, as it is designed to treat branched and linearmolecules in a consistent fashion. The experimental data wereagain inferred from a Figure in Heink et al.,11 but we still find

Figure 4. Adsorption isotherms for butane in silicalite at 500 K as afunction of the cutoff. Simulation results are shown for the TraPPEforce field with a potential truncation of 10 Å cut and shift (circles),14 Å cut and shift (diamonds), 18 Å cut and shift (squares), and 14 Åwith tail corrections (crosses). Simulation results are connected by linesas a guide to the eye.

Figure 5. Diffusion constantD of butane and isobutane as a functionof temperature in silicalite in the infinite dilution limit. Open (closed)circles refer to the mSKS (TraPPE) potential set for butane, while open(closed) triangles refer to the same potential sets for isobutane.

⟨r2⟩ ) 6Dt (5)


excellent agreement between simulation and experiment. It isimportant to note, however, that in Figure 6 the points for eightmolecules per unit cell are already very close, and thus theexcellent agreement in Figure 7 is somewhat fortuitous. Hadwe chosen a different loading, although the activation energywould change only slightly, there would be a constant factorbetween the simulated and experimental diffusivities at alltemperatures. This is clear from a comparison of the activationenergies at infinite dilution and finite loading presented here.Also shown in Figure 7 is the calculated diffusivity at thisloading and temperature with a cutoff of 14 Å. It is clear fromthe figure that the large cutoff has no effect on the diffusionconstant at this loading. Because this loading is near to themaximum for butane in silicalite, any effect of the cutoff shouldbe large here. We are now fully justified in our use of the smallercutoff of 10 Å for our diffusion studies.

We conclude our study of diffusion in silicalite with Figure8 where we show the simulated and experimental diffusivity ofisobutane at a variety of temperatures and loadings. The statepoints for the simulations were chosen to coincide with thoseused in the experimentals of Millot et al.49 because of thedifficulty in finding experimental diffusion studies of isobutanein a temperature range accessible to simulations. We show thetemperatures and corresponding loadings for these data in Table3. The agreement here between simulation and experiment isfair, but we note two important points. First, the error bars onthe experiment are quite large (a factor of 3), which can greatlyaffect the slope of the line in the figure. Second, the experimentaldata here are from macroscopic membrane experiments, which

are well-known to disagree with MD simulations by an orderof magnitude or more. With these points in mind, the agreementis quite acceptable.

IV. Interface Studies

A. State Points.Although relative diffusion rates and bulksorption studies are of interest in separations applications, thetendency of a given species to adsorb preferentially over otherspecies will also play an important role. As an example, wepoint to the permeation studies of Krishna and van den Broeke.50

This work has shown that for binary mixtures of methane andbutane, the flux is characterized by an initial sharp peak ofmethane, which quickly dies out and is replaced by a largersteady flux of butane. The authors ascribe the initial methaneflux to its higher relative diffusivity. The relative adsorption,however, eventually leads to a higher filling of butane overmethane, and then a higher butane output flux. From a practicalstandpoint, the adsorption properties must be understood firstfor pure component gases before the inherently more compli-cated behavior of mixtures is investigated. We discuss here theresults of our interface studies for pure gases only, and willpresent our simulations of mixtures in a future paper.45

Though most of the experiments on separations are at or nearroom temperature, we often found it necessary to work at moreelevated temperatures. Accurate interpretations of the dynamicsof exchange between the gas and the zeolite require statisticsgathered over a large number of actual exchange events. This,in turn, places requirements on the possible densities, and thuspressures, of the gas phase of the simulations. For good statistics,we need to run our simulations at gas pressures on the order of100 kPa. Lower pressures imply extremely dilute gas regions,while higher pressures lead to fully loaded zeolites. Both thesesituations make exchange events rare. Pressures around 100 kPathen restrict us to high temperatures. At the lower temperaturesoften used in the experiments, pressures close to this wouldresult in the zeolite being loaded to capacity and a thick wettinglayer on the crystal surface (see Figure 1). At higher temper-atures diffusivities of the sorbed species are enhanced, which

Figure 6. Diffusion constantD as a function of loading for butane insilicalite at 400 K. Simulated (experimental) points are represented bycircles (crosses), and the open (filled) circles represent points calculatedwith the mSKS (TraPPE) force field. The experimental data is takenfrom Heink et al.11

Figure 7. Diffusion constantD of butane in silicalite as a function oftemperature at a finite loading of the zeolite cage (8 molecules/unitcell). Agreement between simulation data (filled circles) and experiment(crosses) are excellent. Also shown is the calculated diffusion at 400K with a cutoff of 14 Å (open triangle). The change in cutoff has noeffect onD.

Figure 8. Diffusivities of isobutane in silicalite at various temperaturesand loadings (see text). The temperatures and loadings were chosen sothat the simulated state points (closed triangles) coincide with theexperimentally available data (upside down triangles).49

TABLE 3: Temperatures and Corresponding Loadings forthe Diffusion Data in Figure 8

T (K)loading

(molecules/unit cell)

398 3.5473 2.5573 1.0673 0.5


greatly reduces the computational burden. This is especiallysignificant in the case of isobutane, which takes millions of timesteps just to equilibrate, even at 500 K.

We show the state points of our butane MD simulations inFigure 9, where we also show the vapor liquid coexistence curve(VLCC) for the TraPPE potential with a 10 Å cut and shiftedpotential. The VLCC for this potential set deviates considerablyfrom the curve for the full TraPPE potential,32 which showsexcellent agreement with experiment. The purpose of this figure,however, is not to compare to experiment, but rather to indicatethe state points at which our simulations are performed. As isclear from the figure, we have focused on two different systems,a dilute system, which remains to the left of the coexistencecurve at nearly all temperatures studied, and a dense system,which undergoes a phase separation as the temperature islowered below the critical pointTc. In Figure 9, it can be seenthat the density of the adsorption layer of the dense system doesnot exactly match the liquid densities of the VLCC belowTc.This is primarily due to the definition of the adsorption layer,which is somewhat arbitrary. Small variations in this definitioncan lead to changes in the reported liquid densities in Figure 9.In more dilute systems, liquid layers formed during phaseseparation may be unable to achieve the density that would bereached were an infinite particle bath available. For this reason,we will not include phase separated state points in the bulk ofour discussions below.

B. Simulation Results. There are many different pathsavailable for probing the dynamics of the exchanges betweenthe gas and the zeolite. For example, one could choose toexamine the mean adsorption time of molecules in the zeolite,or the mean timetads required for a gas molecule to becomeadsorbed. As these times can essentially be deduced from thediffusivities of the molecules, we have decided not to investigatethese properties. Rather, we have chosen to investigate therelationship of the adsorbed surface layer to the exchanges. Ourquestion is posed as follows: given a molecule which is in thegas at timet0, leaves the gas at timetg, and enters the zeolite atsome timetz g tg, what is the meantime this molecule spendsin the adsorption layer for timestg e t e tz? Furthermore, whatare the variables that affect this mean time?

The surface residence time has previously been proposed asthe microscopic origin of the surface barrier51,52which leads todiscrepancies between diffusion constants as measured bymicroscopic and macrosopic experimental methods. Vigne´-Maeder et al., studied the entrance of Ar and Xe into both MFIand MOR, and found insignificant surface residence times, while

Ford and Glandt used a simpler system with single Lennard-Jones particles entering slit pores. Both these works consideredsmall systems in the infinite dilution limit only, and theapplicability of their results to true experimental systems isunknown. Our present results are, to the best of our knowledge,the first simulations to examine the effects of the surface barrierfor dense alkane gases exposed to large zeolite surfaces.

To begin, we show in Figure 10 a center of mass densityprofile typical of our equilibrated interface simulations forbutane. In this figure, the gas region extends from 80 to 184 Å,where the pressure is approximately 1.2 MPa. The small peaksof the adsorption layer can be seen near 82 and 182 Å and areapproximately 5 Å thick. The butane molecules can be seen topreferentially load the sinusoidal channels of the zeolite, asreported by other authors.21 The smaller peaks in the zeoliteportion of the density profile correspond to the straight chan-nels, which become populated by butane as the gas pressureincreases.

A molecule is identified as residing in the gas at some timetg when its center of mass lies outside the zeolite and theadsorption layer.53 Adsorbed molecules are identified by asimilar criterion. As discussed below, the actual thickness ofthe adsorption layer is not strictly defined, and can affect resultsquantitatively, though not qualitatively. Consider the case shownin Figure 11. The path shown by the dashed line represents acommon trajectory in which a molecule rapidly exchangesbetween the gas and the adsorption layer before settling intothe layer and later entering the zeolite, represented by the solidline z. If the adsorption layer is chosen to be at dotted line 1,this molecule would be counted as spending a long time,t1 in

Figure 9. State points of the butane MD simulations. The density ofthe gas (adsorption layer) of the dilute system is shown as closed (open)circles, whereas that for the dense system is shown as closed (open)squares. The vapor liquid coexistence curve for this potential set isalso shown as stars with a dotted line to guide the eye.

Figure 10. Typical density profile along the (010) crystal direction.The state point in the figure represents 800 butane molecules at 500K, which leads to a gas pressure of 1.2 MPa and a loading of 7.3molecules per unit cell. The two adsorption layers are centered atapproximatelyy ) 82 Å andy ) 182 Å and are approximately 5 Åthick.

Figure 11. Schematic diagram of a molecule rapidly exchangingbetween the gas and adsorption layer before residing in the adsorptionlayer and entering the zeolite.


the adsorption layer. However, if the adsorption layer werechosen to be at either dotted line 2 or 3, the exchanges wouldnot be counted, and the value oftads would be a much smallertime, t2 or t3.

In Figure 12 we show the distribution of time spent in theadsorption layer,tads, by molecules entering the zeolite fromthe gas for the dilute and dense system, representing a pressurerange of approximately 1-20 MPa atT ) 500 K. Note that thedistribution in the figure is dramatically different from theoverall lifetime of molecules in the adsorption layer, which hasan exponential form as shown in the inset. From Figure 12, itis clear that ballistic entry makes up only a small part of theexchange events. A rough calculation indicates that a moleculeentering the zeolite ballistically should spend approximately 1ps in the adsorption layer at 500 K. It is clear from the figurethat the bulk of the molecules spend substantially longer than1 ps in the adsorption layer, and the mean time is, in fact, onthe order of 10 ps. It is also clear from the figure that thepressure dependence, and therefore the dependence on zeoliteloading, is extremely weak, at least for the pressure range shownin the figure. The distribution is normalized so that the integralunder the curve gives one.

We have fit the distribution fortadsshown in Figure 12 witha simple binomial distribution of the form

whereB is the total probability,p is the probability of successin a single trial,n is the number of trials, andν is the numberof successes.54 We also show the fits from eq 6 in Figure 12.For these data, the time step was reduced to 1.25 fs withmolecular configurations saved every 0.5 ps in order to increasethe resolution. As can be seen in the figure, the fits are quitegood for a value ofp ) 0.33. The fits are most accurate atsmall tads, but begin to underestimate the data at longer times.This effect is primarily due to our choice of the width of theadsorption layer. The choice of the layer width can clearly affectthe distributions shown in Figure 12, as shown in Figure 11.However, as this choice is somewhat subjective, rather thanattempt to explain the slight differences between the fits andthe data, we point out that the fits demonstrate a physicallyreasonable functional form for the lifetimes.

A binomial distribution suggests that there are a number ofdistinct adsorption sites on the (010) surface of the zeolite, andadsorbed molecules quickly jump from site to site until theyeither enter the zeolite or return to the gas. We note that the

naive interpretation of this distribution, in which hops on thesurface are viewed as failures, and the pore entry is considereda success does not lead to a binomial distribution. This isbecause such a model requires that a single success occursafter all failures, removing the prefactor from eq 6 and changingthe distribution. To obtain a binomial distribution, it is necessaryto consider that there are at least two distinct adsorption siteson the surface (labeled arbitrarily as successes or failures), andthat molecules actually hop among these sites before enteringthe pore mouth or returning to the gas. We have examined thevalidity of this conclusion by calculating the density profile ofthe center of mass of physisorbed molecules, shown in Figure13(a) and (b) for butane and isobutane, respectively. For thesefigures, we show a contour plot of the density of physisorbedmolecules averaged over the entire production phase of thesimulation, with white (black) representing regions of high (low)density. For clarity, we only show a subsection of the totalsystem in the figures. In the figures, it can be seen that thereare a number of distinct adsorption sites surrounding the poremouths that are preferentially occupied by the butane andisobutane molecules. The highest density is seen to be directlyover the pore mouth, indicating that the molecules do not snaketheir way into the zeolite, hugging close to the surface, but ratherhop directly into the potential well of the pore mouth. Thispicture is consistent with Burggraaf,55 who showed that whenthe ratio of the kinetic diameter of the sorbed molecules to the

Figure 12. Time spent in the adsorption layer by butane molecules asthey enter the zeolite from the gas. The squares and circles representP ≈ 1 and∼10 MPa, respectively, whereas the solid and dashed linesare fits of the low and high pressure points, respectively, to a binomialdistribution as described in the text. The inset shows the overall lifetimeof molecules in the adsorption layer.

Bn,p(ν) ) (nν ) pν(1 - p)n-ν (6)

Figure 13. Density profile of (a) butane and (b) isobutane moleculesin the adsorption layer over the entire simulation at 500 K. The profileis overlayed over the bonds of the unit cell for clarity. There are anumber of distinct adsorption sites present on the surface.


pore opening is close to 1, as is the case for butane and isobutanein silicalite, sorbed molecules feel a deep potential well insidethe pores, with nearly equal contributions from both walls. It isinteresting to note that the distributions for butane and isobutaneare identical.

In addition totadsfor molecules entering the zeolite, we haveinvestigated the related distribution for molecules that leave thezeolite and enter the gas. In Figure 14 we show the distributionfor tadsfor T ) 500 K andP ) 1200 kPa for molecules enteringthe zeolite from the gas (i.e., the same distribution shown inFigure 12) as well as that for molecules leaving the zeolite andentering the gas. The two distributions are identical withinstatistical error, indicating that ballistic transport is, again, arelatively unfavorable process. This result also suggests thatthere are different desorption points for molecules entering thegas and the zeolite. As discussed above, from Figure 13, it isclear that molecules entering the zeolite do so by first hoppingto an adsorption site directly above a pore mouth. Moleculesleaving the zeolite and entering the adsorption layer must firstexit a pore via this same site. If this site were also the site fordesorption into the gas, then the probability for ballistic exit(or very smalltads) in Figure 14 would dominate. This is notthe case. Rather, molecules leaving the zeolite enter theadsorption layer via the adsorption site directly over the poremouth, and then hop from adsorption site to adsorption site untilthe preferred site for desorption into the gas is reached. This,coupled with the lack of variation oftads over a wide pressurerange, indicates that even for extremely low back-pressures, suchas those realized in membrane permeation experiments withsweep gases, desorbing and adsorbing molecules will feel thesame resistance to transport into or out of the zeolite.

In Figure 15 we show the mean value oftads for our diluteand dense systems as a function of temperature. For the reasonsdiscussed above, we do not show the meantimes for the densesystem belowTc in the figure. From the figure, it is clear thatthe mean time is nearly insensitive to pressure at all temperaturesand shows a weak temperature dependence. The effect oftemperature on the mean shows that entry into the zeolite is anactivated process related to surface diffusion. The insensitivityto pressure implies that identical surface barriers exist on bothsides of membranes in permeation simulations and experiments.Also shown in the figure are representative points for isobutanemolecules entering the zeolite. It is an interesting and unexpectedresult that the mean time is nearly identical for butane andisobutane. The implication is that surface diffusion processesare more closely related to gas diffusion (which should besimilar for butane and isobutane) than to diffusion inside thezeolite.

A distinct difference between the dilute and dense butanesystems exists in the orientation of surface adsorbed molecules.The angular orientation of the adsorbed butane molecules canbe found by finding the distribution of the angles between theend-to-end vector of all adsorbed molecules and the (010)surface of the zeolite. To remove artifacts caused by the finitewidth of the adsorption layer, we show the differences be-tween angular distributions, rather than the individual distribu-tions themselves. The effect of the width should be the samefor all distributions, and should thus cancel out for thedifferences.

In Figure 16 we show the difference in angular distributionbetween the dilute and dense systems for two different tem-peratures, 500 and 200 K. Although 200 K is well belowTc forthe dense system, we have chosen to show this temperaturebecause the effect on the angular distribution becomes morepronounced at lower temperatures. Additionally, although theliquid densities of systems at these low temperatures may notreach the same level as systems coupled to an infinite particlebath, these effects should be more pronounced at the vapor/liquid interface, while the vapor/solid interface (represented hereby the first adsorption layer) should not be strongly affected.In the Figure 16 it is clear that at 500 K, where both systemsare supercritical fluids, there is little difference in the angulardistributions. At 200 K, however, there is a strong difference.Because the figure shows the dense system distribution sub-tracted from the dilute system distribution, an excess in the

Figure 14. A comparison oftads for butane molecules entering thezeolite from the gas (squares) and those entering the gas from the zeolite(circles). The data are forT ) 500 K andP ) 1200 kPa, and areidentical within statistical error.

Figure 15. Mean time spent in the adsorption layer by butanemolecules as a function of temperature. The times for the dense (dilute)system are shown as squares (circles). We do not show points belowTc for the dense system. Representative times for a dilute system ofisobutane are shown as open diamonds.

Figure 16. Difference between the angular distributions of the denseand dilute systems of butane molecules in the adsorption layer. Excessin the dilute (dense) system is shown as a positive (negative) peak.There is no difference at 500 K, whereas at 200 K molecules in thedilute (dense) system tend to lie on (stick up from) the surface.


former (latter) will be realized as a negative (positive) peak. At200 K, physisorbed molecules in the dilute system tend to lieflat on the surface. Such a conformation is allowed because ofthe low density of physisorbed molecules, and preferred becauseit maximizes their energy of adsorption. In the dense system at200 K, the adsorption layer become so densely packed that themolecules must begin to stand on end. This change in angulardistribution can also be seen in Figure 17, where we show thedistributions at 200 K subtracted from those at 500 K for bothsystems. Again, it is clear that molecules in the dilute systemlie down on the surface at low temperatures, whereas those inthe dense system tend to stick out. Representative snapshots ofthe adsorption layers of the dilute and dense systems at 200 Kare shown in Figure 1b and (c), respectively. The orientationof the molecules in the dense system suggests that the meantimewill actually be shorter than in the dilute system at lowertemperatures. This is because in the dense system, moleculesare already in the preferential position to enter the zeolite, andsimply need to find a pore mouth, whereas in the dilute system,the molecules must additionally lift themselves off the surface,losing adsorption energy, to enter a pore. We have performeda similar analysis of the angular distribution of physisorbedisobutane molecules, using the angle between the plane formedby the three CH3 UAs and the surface of the zeolite. However,we have not found any appreciable difference in the distributionsas a function of temperature or density for the systems westudied.

V. Permeation Studies.We performed simulations for purebutane and pure isobutane at temperatures of 400 K and 500 Kand several different pressure drops. Each simulation consistedof a series of consecutive runs, lasting from 10 to 20 ns. Duringeach run, the density profile across the membrane and the fluxacross the membrane were measured. The flux was calculatedfrom the average of the net number of molecules added on thehigh-pressure side and the net number of molecules deleted onthe low-pressure side, divided by the membrane area and theduration of the run. Once all of these quantities stopped changingfrom one run to the next, steady-state was assumed to have beenreached, and the results from the final run were used. The timerequired to reach steady-state ranged from 10 to 100 ns.

The pressures in the upstream and downstream gas phaseswere calculated from the gas-phase densities. On the low-pressure side, this was done using the ideal gas law. On thehigh-pressure side, we used pressure-volume isotherms ob-tained by direct isobaric-isothermal MC simulation of the bulk

gas. The permeabilityΠ was calculated using the followingequation

whereJ is the flux rate of molecules across the membrane,∆Pis the difference between the upstream and downstream gaspressures, andL is the membrane thickness (40 Å). In all cases,the downstream pressure was much smaller than the upstreampressure, so the pressure-drop and upstream pressure werealmost equal in magnitude. The variation of butane andisobutane permeability with pressure-drop and temperature isshown in Figure 18. In all cases, we see the same generalbehavior. For low pressure drops, the permeability is inde-pendent of the pressure. As the pressure drop increases, thepermeabilities start to decrease strongly. Both of these behaviorsare correctly captured by the simple permeation model basedon the Langmuir isotherm. The constant permeability at lowpressure corresponds to the Henry’s law regime, where loadingincreases linearly with pressure. At sufficiently high pressures,excluded volume interactions cause the isotherm to flatten out,resulting in a monotonically decreasing permeability.

As a comparison, we also show in Figure 18 the theoreticalpermeabilities as a function of pressure for butane and isobutaneat the simulation temperatures. Following Burggraaf,55 we havecalculated the permeability based on our Langmuir isothermfits from section IIIA, and diffusivities from section IIIB. Thetheoretical flux is given as

whereDc is the transport diffusivity andPf(Pm) is the pressureon the feed (membrane) side. This equation is easily extendedto the case of a double Langmuir isotherm for isobutane.Following Maginn et al.,56 we have used the self-diffusivity inthe infinite dilution limit as a value forDc. As can be seen inthe figure, the theoretically predicted permeabilities are con-sistently an order of magnitude greater than those from thesimulation. Actual experimental measurements of butane andisobutane permeation at low-pressure drops show permeabilitiesof about 10-10 and 10-11 (mol/m2/s)/(Pa/m), respectively,57 andagree well with the theoretical results.

Figure 17. Differences in angular distributions as a function oftemperature for butane molecules in the adsorption layer of the diluteand dense systems. Excess at 500 K (200 K) is shown as a positive(negative) peak. As the temperature changes from 500 to 200 K,molecules in the dilute (dense) system tend to lie on (stick up from)the surface.

Figure 18. Permeability of butane and isobutane through a silicalitemembrane as a function of pressure drop and temperature. Butane andisobutane are shown as open and closed figures, respectively, whereasthe circles and squares represent 500 and 400 K, respectively. Alsoshown are the theoretical permeabilities for butane at 500 K (dashedline) and isobutane at 400 K (dotted line).

Π ) J∆P/L

J ) qsat

Dc

Lln( 1 + KPf

1 + KPm) (7)


One reason for this underprediction can be inferred from thedensity profiles obtained from the simulations. For example,Figure 19 shows the profiles for butane at 500 K for both highand low pressure drops. Each membrane exhibits four densitypeaks corresponding to the sinusoidal channels of the zeolite,as discussed in section IVB. The outer peaks are slightly lowerthan inner peaks due to the lower number of zeolite atomsinteracting with the butane molecules that are near the surface.What is striking about the profile is the perfect symmetry withineach membrane, i.e., there is no concentration gradient. Thisindicates that the molecules within the zeolite are at equilibrium.This implies that the flux rate is limited by processes other thandiffusion through the interior of the zeolite. The limitingprocesses are likely dominated by the transition from theadsorption layer to the zeolite on the upstream surface and fromthe zeolite to the adsorption layer on the downstream surface.The same absence of gradient is seen in all the butane runs.

Figure 20 shows the corresponding profiles for isobutane. Inthis case, we do see the formation of a concentration gradientin the direction of flow, and this is also true for the otherisobutane simulations. It appears that switching from butane toisobutane results in a decrease in the relative importance of thesurface resistance. This is understandable, given our resultsabove. In section IVB, we showed that the mean time spent inthe adsorption layer by butane and isobutane are identical,implying identical surface barriers. The diffusivity of isobutaneinside the zeolite, however, is lower than that of butane by anorder of magnitude. This is the same difference seen in Figure18, implying that the permeation of isobutane is controlled bydiffusion within the zeolite itself.

The absence of internal density gradients has also beenobserved by Pohl and Heffelfinger,58 and more recently by Nitta

et al.59 The presence of surface barriers could be viewed as ananomaly associated with the extremely thin membrane samplewhich we have used. In fact, it could explain why ourpermeability predictions lie far below the experimental range.One might expect that as the membrane thickness is increased,surface effects will become negligible. However, it is not clearif this is true for the zeolite particles used in typical membranes.

VI. Conclusions

We have presented the results of molecular dynamicssimulations of interfaces between single component gases ofbutane and isobutane and silicalite. After verifying that ourpotential parameters give accurate results for the experimentallymeasured bulk adsorption and diffusion, we investigated thedynamics of exchange between the gas and the zeolite. Inparticular, we have found that molecules from the gas enter thezeolite primarily via the adsorption layer, where they hop amongpreferred adsorption sites until entering a pore mouth. Moleculesdesorbing from the zeolite undergo a similar process in reverse.For both processes,tads is found to be on the order of 10 ps,and is unchanged over a wide range of gas pressures, and onlyweakly affected by system temperature. This surface residencetime is the microscopic origin of transport resistance and ispresent at both the feed and permeate sides of membranepermeation experiments and simulations. However, the averagesurface residence times are too small in comparison to bulktransit times (approximately 20 ps per unit cell) to account forthe differences between macroscopic and microscopic diffusionstudies. We have simulated the permeation of butane andisobutane through thin silicalite membranes and found signifi-cant differences between our results and theoretical permeationsbased on Langmuir isotherms and bulk diffusion. The mostlikely cause of the discrepancy is the microscopic barrier, whichcan be significant for thin membranes.

Future work will investigate the preferential adsorption ofbinary gas mixtures and its role in separations processes.

Acknowledgment. We thank Tina Nenoff for many usefuldiscussions. We thank Scott Sides for insightful discussions,assistance with the nonlinear fitting, and the generation ofgraphics. We also thank Mike Macedonia and Ed Maginn fortheir initial calculations of butane isotherms with the TraPPEpotential. Sandia is a multiprogram laboratory operated bySandia Corporation, a Lockheed Martin Company, for theUnited States Department of Energy under Contract DE-AC04-94AL85000.

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dynamics of exchange at gas-zeolite interfaces i: pure...

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