Skip to main content
SpringerLink
Log in

Kinetic Monte Carlo study of binary diffusion in silicalite

  • Published:
Adsorption Aims and scope Submit manuscript

Abstract

We report a Kinetic Monte Carlo (KMC) study of the diffusion of linear n-hexane (nC6) and 2,2-dimethylbutane (22DMB) mixture in zeolite silicalite. We first investigated the loading dependences of single component self- and corrected diffusivities of nC6 at 300 K. Anisotropic transition rates are implemented to account for the distribution of the molecules within the zeolite framework. Repulsive guest-guest interactions are modeled using the parameter introduced by Reed and Ehrlich (Surf. Sci. 102:588–601, 1981). The results are in good agreement with recent experimental Quasi Elastic Neutron Scattering data of Jobic et al. (J. Phys. Chem. B 110:2195–2201, 2006), although the influence of the adsorption isotherm inflection is not reproduced. The binary diffusion study of nC6/22DMB mixtures was performed by implementing the nC6 transition rates used for the single component study while 22DMB molecules propagate via intersection-intersection hops. This KMC model allows for different saturation capacities and accounts for interactions between molecules by introducing f ij parameters. Results show the large impact of guest-guest interactions between nC6 and 22DMB on both self- and corrected diffusivities of the two components. Molecule-size effects are found to be predominant near 22DMB saturation capacity. Acceleration/deceleration effects already described in the literature are confirmed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

Reed–Ehrlich parameter, dimensionless

b :

Reed–Ehrlich parameter, dimensionless

b A :

Langmuir constant of the DSL model, Pa−1

b B :

Langmuir constant of the DSL model, Pa−1

D self :

self-diffusion coefficient, m2 s−1

D C :

corrected diffusivity, m2 s−1

f :

Reed–Ehrlich parameter, dimensionless

k i→j :

transition rates from site i to site j, s−1

k STR :

transition rates along straight channels, s−1

k ZZ :

transition rates along zigzag channels, s−1

K :

transition rates ratio, dimensionless

n :

number of nearest neighbours, dimensionless

N :

number of molecules, dimensionless

Q :

parameter defined by (7), dimensionless

R :

gas constant, J mol−1 K−1

R(t):

vector position of the center of mass at a time t, m

r i (t):

vector position of molecule i at a time t, m

t :

time, s

T :

absolute temperature, K

ξ :

random number, dimensionless

δ E :

variation of the activation energy, J mol−1

θ :

loading or fractional occupancy, dimensionless

Θ i :

number of molecules of species i, molecules per unit cell

Θ i,sat :

saturation capacity of specie i, molecules per unit cell

Δt :

mean residence time of a given configuration, s

sat :

referring to saturation

int :

referring to intersection

str :

referring to straight channel

zz :

referring to zigzag channel

References

  • Auerbach, S.M., Henson, N.J., Cheetham, A.K., Metiu, H.I.: Transport theory for cationic zeolites: diffusion of benzene in Na-Y. J. Phys. Chem. 99, 10600–10608 (1995)

    Article  CAS  Google Scholar 

  • Bouyermaouen, A., Bellemans, A.: Molecular simulations of the diffusion of n-butane and i-butane in silicalite. J. Chem. Phys. 108, 2170–2172 (1998)

    Article  CAS  Google Scholar 

  • Cavalcante, C.L.J., Ruthven, D.M.: Adsorption of branched and cyclic paraffins in silicalite. 2. Kinetics. Ind. Eng. Chem. Res. 34, 185–191 (1995)

    Article  CAS  Google Scholar 

  • Dubbeldam, D., Beerdsen, E., Vlugt, T.J.H., Smit, B.: Molecular simulations of loading-dependent diffusion in nanoporous materials using extended dynamically corrected transition state theory. J. Chem. Phys. 122, 224712 (2005)

    Article  CAS  Google Scholar 

  • Eic, M., Ruthven, D.M.: Intracrystalline diffusion of linear paraffins and benzene in silicalite studied by the ZLC methods. Stud. Surf. Sci. Catal. 49B, 897–905 (1989)

    Article  Google Scholar 

  • Fichthorn, K.A., Weinberg, W.H.: Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys. 95, 1090–1096 (1991)

    Article  CAS  Google Scholar 

  • Fichthorn, K.A., Weinberg, W.H.: Influence of time-dependent rates of mass transfer on the kinetics of domain growth. Phys. Rev. Lett. 68, 604–607 (1992)

    Article  Google Scholar 

  • Frenkel, D., Smit, B.: Understanding Molecular Simulations: From Algorithms to Applications, 2nd edn. Academic, San Diego (2002)

    Google Scholar 

  • Gergidis, L.N., Theodorou, D.N., Jobic, H.: Dynamics of n-butane-methane mixtures in silicalite, using quasi elastic neutron scattering and molecular dynamics simulations. J. Phys. Chem. B 104, 5541–5552 (2000)

    Article  CAS  Google Scholar 

  • Jobic, H., Laloué, N., Laroche, C., van Baten, J.M., Krishna, R.: Influence of isotherm inflection on the loading dependence of the diffusivities of n-hexane and n-heptane in MFI zeolite. Quasi elastic neutron scattering experiments supplemented by molecular simulations. J. Phys. Chem. B 110, 2195–2201 (2006)

    Article  CAS  Google Scholar 

  • Jolimaître, E., Ragil, K., Tayakout-Fayolle, M., Jallut, C.: Separation of mono- and dibranched hydrocarbons on sicalite. AIChe J. 48, 1927–1937 (2002)

    Article  Google Scholar 

  • June, R.L., Bell, A.T., Theodorou, D.N.: Transition-state studies of xenon and SF6 diffusion in silicalite. J. Phys. Chem. 95, 8866–8878 (1991)

    Article  CAS  Google Scholar 

  • June, R.L., Bell, A.T., Theodorou, D.N.: Molecular dynamics studies of butane and hexane in silicalite. J. Phys. Chem. 96, 1051–1060 (1992)

    Article  CAS  Google Scholar 

  • Keil, F.J., Krishna, R., Coppens, M.O.: Modeling of diffusion in zeolites. Rev. Chem. Eng. 16(2), 71–197 (2000)

    CAS  Google Scholar 

  • Koriabkina, A.O., de Jong, A.M., Hensen, E.J.M., van Santen, R.A.: Concentration and temperature dependence of the diffusivity of n-hexane in MFI-zeolites. Microporous Mesoporous Mater. 77, 119–129 (2005)

    Article  CAS  Google Scholar 

  • Krishna, R., Calero, S., Smit, B.: Investigation of entropy effects during sorption of mixtures of alkanes in MFI zeolite. Chem. Eng. J. 88, 81–94 (2002)

    Article  CAS  Google Scholar 

  • Krishna, R., Paschek, D., Baur, R.: Modeling the occupancy dependence of diffusivities in zeolites. Microporous Mesoporous Mater. 76, 233–246 (2004a)

    Article  CAS  Google Scholar 

  • Krishna, R., van Baten, J.M., Dubbeldam, D.: On the inflection in the concentration dependence of the Maxwell–Stefan diffusivity of CF4 in MFI zeolite. J. Phys. Chem. B 108, 14820–14822 (2004b)

    Article  CAS  Google Scholar 

  • Leroy, F., Rousseau, B., Fuchs, A.H.: Self-diffusion of n-alkanes in silicalite using molecular dynamics simulations: a comparison between rigid and flexible frameworks. Phys. Chem. Chem. Phys. 6, 775–783 (2004)

    Article  CAS  Google Scholar 

  • Maceiras, D.B., Sholl, D.S.: Analysis of binary transport diffusivities and self-diffusivities in a lattice model for silicalite. Langmuir 18, 7393–7400 (2002)

    Article  CAS  Google Scholar 

  • Metiu, A.I., Lu, Y.T., Zangh, Z.Y.: Epitaxial growth and the art of computer simulations. Science 255, 1088–1092 (1992)

    Article  CAS  Google Scholar 

  • Millot, B., Methivier, A., Jobic, H.: Adsorption of n-alkanes on silicalite crystals. A temperature-programmed desorption study. J. Phys. Chem. B 102, 3210–3215 (1998)

    Article  CAS  Google Scholar 

  • Paschek, D., Krishna, R.: Monte Carlo simulations of self- and transport-diffusivities of 2-methylhexane in silicalite. Phys. Chem. Chem. Phys. 2, 2389–2394 (2000)

    Article  CAS  Google Scholar 

  • Paschek, D., Krishna, R.: Diffusion of binary mixtures in zeolites: kinetic Monte Carlo versus molecular dynamics simulations. Langmuir 17, 247–254 (2001a)

    Article  CAS  Google Scholar 

  • Paschek, D., Krishna, R.: Kinetic Monte Carlo diffusion of transport diffusivities of binary mixtures in zeolites. Phys. Chem. Chem. Phys. 3, 3185–3191 (2001b)

    Article  CAS  Google Scholar 

  • Pascual, P., Ungerer, P., Tavitian, B., Pernot, P., Boutin, A., Development of a transferable guest-host force field for adsorption of hydrocarbons in zeolites. I. Reinvestigation of alkane adsorption in silicalite by grand canonical Monte Carlo simulation. Phys. Chem. Chem. Phys. 5, 3684–3693 (2003)

    Article  CAS  Google Scholar 

  • Reed, A.D., Ehrlich, G.: Surface diffusion, atomic jump rates and thermodynamics. Surf. Sci. 102, 588–601 (1981)

    Article  CAS  Google Scholar 

  • Runnebaum, R.C., Maginn, E.J.: Molecular dynamics simulations of alkanes in the zeolite silicalite: evidence for resonant diffusion effects. J. Phys. Chem. B 101, 6394–6408 (1997)

    Article  CAS  Google Scholar 

  • Saravanan, C., Auerbach, S.M: Modeling the concentration dependence of diffusion in zeolites. II. Kinetic Monte Carlo simulations of benzene in Na-Y. J. Chem. Phys. 107, 8132–8137 (1997)

    Article  CAS  Google Scholar 

  • Shuring, D., Jansen, A.P.J., van Santen, R.A.: Concentration and chainlenght dependence of the diffusivity of alkanes in zeolites studied with MD simulations. J. Phys. Chem. B 104, 941–948 (2000)

    Article  CAS  Google Scholar 

  • Skoulidas, I., Sholl, D.S.: Transport diffusivities of CH4, CF4, He, Ne, Ar, Xe and SF6 in silicalite from atomistic simulations. J. Phys. Chem. B 106, 5058–5067 (2002)

    Article  CAS  Google Scholar 

  • Skoulidas, A.I., Sholl, S., Krishna, R.: Correlation effects in diffusion of CH4/CF4 mixtures in MFI zeolite. A study linking MD simulations with the Maxwell–Stefan formulation. Langmuir 19, 7977–7988 (2003)

    Article  CAS  Google Scholar 

  • Song, L., Rees, L.V.C.: Adsorption and transport of n-hexane in silicalite-1 by the frequency response technique. J. Chem. Soc. Faraday Trans. 93, 649–657 (1997)

    Article  CAS  Google Scholar 

  • Smit, B., Maesen, T.L.M.: Commensurate ‘freezing’ of alkanes in the channels of a zeolite. Nature 374, 42–44 (1995)

    CAS  Google Scholar 

  • Smit, B., Loyens, L.D.J.C., Verbist, G.L.M.M.: Simulation of adsorption and diffusion of hydrocarbons in zeolites. Faraday Discuss. 106, 93–104 (1997)

    Article  CAS  Google Scholar 

  • Snurr, R.Q., Kärger, J.: Molecular simulations and NMR measurements of binary diffusion in zeolites. J. Phys. Chem. B 101, 6469–6473 (1997)

    Article  CAS  Google Scholar 

  • Vlugt, T.J.H., Krishna, R., Smit, B.: Molecular simulations of adsorption isotherms for linear and branched alkanes and their mixtures in silicalite. J. Phys. Chem. B 103, 1102–1118 (1999)

    Article  CAS  Google Scholar 

  • Zhu, W., Kapteijn, F., van der Linden, B., Moulijn, J.A.: Equilibirum adsorption of linear and branched C6 alkanes on silicalite-1 studied by the tapered element oscillating microbalance. Phys. Chem. Chem. Phys. 3, 1755–1761 (2001)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IFP-Lyon, BP 3, 69360, Solaize, France

    N. Laloué, C. Laroche & A. Méthivier

  2. IRCELYON, Institut de Recherches sur la Catalyse et l’Environnement de LYON, CNRS, Université de Lyon, UMR5256, 2 Avenue A. Einstein, 69626, Villeurbanne, France

    H. Jobic

Authors
  1. N. Laloué
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Laroche
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Jobic
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Méthivier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Laroche.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laloué, N., Laroche, C., Jobic, H. et al. Kinetic Monte Carlo study of binary diffusion in silicalite. Adsorption 13, 491–500 (2007). https://doi.org/10.1007/s10450-007-9067-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10450-007-9067-8

Keywords

Search

Navigation