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Simulations of the Structure and Properties of Amorphous Silica Chemical Engineering Science 56 (2001) 4205–4216 www.elsevier.com/locate/ces Simulations of the structure andproperties of amorphous silica surfaces Jeanette M. Stallons, Enrique Iglesia ∗ Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA Received10 December 1999; accepted26 December 2000 Abstract The structure andtransport properties of solidsurfaces have been describedusingmodelsof varying complexity andrigor without systematic comparisons among available methods. Here, we describe the surface of amorphous silica using four techniques: (1) an orderedsurfacecreatedby cutting the structure of a known silica polymorph ( -cristobalite); (2) an unrelaxedamorphous surface obtainedby cutting bulk amorphous silica structures createdby molecular dynamicsmethods;(3) a relaxedamorphous surface createdby relaxing the amorphous surface; and(4) a randomsurface createdby Monte Carlo sphere packing methods. Calculations of the adsorption potential surface and simulation of the surface di4usion of weakly bound adsorbates (N2, Ar, CH4) interacting via Lennard–Jones potentials with these surfaces were used to compare surface models and to judge their ÿdelity by comparisons with available experimental values. Similar heats of adsorption were obtained on the relaxed, unrelaxed, and random surfaces (±0:5kJ=mol), but the relaxed surface showed greater heterogeneity with a wider distribution of adsorption energies. Surface di4usion on the relaxed surface was slower than on the other surfaces, with slightly higher activation energies (0:5–1:0kJ=mol). Rigorous comparisons between simulatedandexperimental surface di4usivitiesare not possible, because of scarce surface di4usion data on well-characterized surfaces. The values obtained from simulations on silica were similar to experimental surface di4usivities reported on borosilicate glasses. ? 2001 Publishedby Elsevier Science Ltd. Keywords: Porous media; Simulation; Transport processes; Di4usion; Surface di4usion; Adsorption 1. Introduction the adsorption and surface di4usion properties of amor- phous silica. Amorphous solids are used because they Simulations are increasingly useful tools in the design pose more formidable simulation challenges than known of porous solids by helping to understand and to pre- andwell-deÿnedcrystallinestructures. Silica was cho- dict the structure and transport properties of these solids sen as an example because of its widespread use as ad- (MacElroy & Raghavan, 1991; Reyes & Iglesia, 1993; sorbents, catalyst supports, andporous membranes. Sev- Drewry & Seaton, 1995; Keil, 1996). Most surface mod- eral previous studies of the bulk and surface structures of els, however, neglect the details of the surface structure amorphous solidshave been carriedout on silica andthe andthey adoptinsteadthe pragmatic approach of de- requiredinteratomic potentials are available from these scribing surfaces using simple lattice models with math- studies (Feuston & Garofalini, 1989, 1990; Athanasopou- ematically convenient distributions of binding sites. A los & Garofalini, 1992; Kohler & Garofalini, 1994; Litton systematic study of how these approaches lead to vary- & Garofalini, 1997). ing degrees of accuracy, ÿdelity, and predictive value Recent studies have introduced heterogeneity into sim- appears to be currently unavailable. Here, we attempt ple lattice models in order to attempt to describe the such a systematic comparison by describing surface struc- chemical non-uniformity of amorphous surfaces. For ex- tures using several methods, di4ering in approach and ample, adsorption energy distributions were assigned to level of complexity, andcomparing their ability to predict various available lattice sites (Nicholson & Silvester, ∗ Corresponding author. Tel.: +1-510-642-9673. fax: +1-510-642- 1977; O’Brien & Myers, 1985). Surface features, such 4778. as steps, terraces, holes, or grooves have been placed E-mail address: [email protected] (E. Iglesia). on square lattices (Haus & Kehr, 1987; Bojan & Steele, 0009-2509/01/$ - see front matter ? 2001 Publishedby Elsevier Science Ltd. PII: S 0009-2509(01)00021-5 4206 J. M. Stallons, E. Iglesia / Chemical Engineering Science 56 (2001) 4205–4216 1988; Gomer, 1990; Rudzinski & Everett, 1992; Steele, radialstructure functions andbondangle distributions). 1997; Zgrablich, 1997). The smaller holes andbarriers are The choice of potential energy function is critical, be- distributed randomly on the surfaces; the larger dimen- cause it determines the positions of atoms at the surface. sions andspacing of the steps andgrooves are approxi- Few studies have included this level of detail in describ- matedfrom experimental microscopy data(Gomer, 1990; ing surfaces. Garofalini et al. have examinedthe structure Steele, 1997). Disorder of the underlying surface struc- of silica surfaces (Feuston & Garofalini, 1989; Athana- ture itself has been introduced using lattices with more sopoulos & Garofalini, 1992; Kohler & Garofalini, 1994) complex topology, for example, by perturbing all vertex andthe surface di4usionof silicon andoxygen lattice positions in a square lattice by a random displacement atoms at high temperatures (Litton & Garofalini, 1997). vector (Benegas, Pereyra, & Zgrablich, 1987). These ap- Bakaev (1999) andBakaev andSteele (1999a, b) have proaches retain the assumption that random, heteroge- recently addressed the incomplete surface annealing in neous surfaces can be described by distributions of sites the Garofalini methods, which leads to pendant oxygens on regular or distorted ordered structures, without in- suggestedto account for OH groups experimentally found cluding the detailed topological connectivity among sur- at the surface of silica. These authors proposedthat hy- face atoms or between surface atoms andthe bulk atoms drophobic silica surfaces require the substantial absence immediately below. Nevertheless, it seems that connec- of OH groups andrequire much higher annealing tem- tivity andinteractions with sub-surface atoms shouldin- peratures in the structural simulations of the surface. Sil- Iuence strongly the transport andbindingproperties of ica surfaces usedas adsorbentsandas catalyst supports, these amorphous surfaces. however, contain signiÿcant OH surface densities; thus, Bakaev andSteele (1992) useda “Bernal surface” the Garofalini methodappears to be more realistic in the (Finney, 1983), createdby randomlypacking spheres, simulation of silica surfaces formedby abrupt termina- representing oxygen atoms, within a three-dimensional tion of particle growth in aqueous media followed by container with periodic boundary conditions using Monte thermal treatments at temperatures well below the glass Carlo methods. The sphere size was set as the diameter transition temperature. MacElroy andRaghavan (1990, of lattice oxygen anions. Riccardo and Steele (1996) 1991) exploredthe di4usionof methane andsilicon hex- usedthis Bernal surface to simulate Ar surface di4u- aIouride within random microporous silicas. Both groups sion on amorphous titania. The interactions of Ar with usedmolecular dynamicsor Monte Carlo simulations to surface oxygens were described by Lennard–Jones place Si andO atoms accurately within bulk silica and potentials parameterizedby comparing experimental and then createda surface by cutting and,in some cases, re- simulatedadsorptionisotherms. Surface “roughness” laxing the bulk structure. was variedby randomremoval of some surface spheres; In this study, various silica surfaces were created and the resulting “roughness” hada markede4ect on surface their adsorption and transport properties were compared transport rates at low temperatures (85–160 K). For ex- with one another andwith available experimental results ample, di4usion activation energies increased from 4.7 in order to assess the level of detail required for the faith- to 7:1kJ=mol as three monolayers of atoms were ran- ful representations of these heterogeneous random sur- domly removed from the initial Bernal surface. Fractal faces. Speciÿcally, surfaces were createdby simple or dimensions (Df) of 2.2–2.5 were calculatedfrom the ef- relaxedcuts of simulatedbulk silica (unrelaxedandre- fects of the diameter of the adsorbates on the maximum laxedsurfaces, respectively) andby Monte Carlo packing achievable coverage (monolayer capacity) on various methods (random surface). The properties of these amor- simulatedsurfaces. The approximate agreement observed phous surfaces were comparedwith those of orderedsys- between these andexperimental fractal dimensionsfor tems, in which uniform adsorption sites are placed in a silica surfaces (Df =2:03–2.30) was taken as evidence lattice corresponding to -cristobalite, a crystalline silica of the ÿdelity of the simulation approach. The activation polymorph (ordered surface). Both the thermodynamics energies andsurface di4usivitiesobtainedin these simu- of adsorption and the dynamics of surface transport of lations on roughenedBernal surfaces were not compared weakly bound adsorbates are simulated. with experimental results. Clearly, atoms on surfaces are not locatedat random positions but at positions of minimum energy, andthese 2. Bulk silica simulation positions are not static but they relax both after the sur- face is ÿrst formedby fracturing, abrupt termination of 2.1. Method particle growth, or cooling from melts, and during ad- sorption anddi4usionof molecules. The forces among Bulk silica was described using well-established surface atoms, those in subsurface
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