ARTICLE pubs.acs.org/Langmuir
Atomistic Simulation of the Formation of Nanoporous Silica Films via Molecular Chemical Vapor Deposition on Nonporous Substrates Taslima Akter, Thomas C. McDermott, J. M. Don MacElroy, Damian A. Mooney, and Denis P. Dowling UCD School of Chemical and Bioprocess Engineering, the SEC Strategic Research Cluster and the Centre for Synthesis and Chemical Biology, the Conway Institute, University College Dublin, Belfield, Dublin 4, Ireland ABSTRACT: To distinguish thin deposited film characteristics clearly from the influence of substrate morphological properties, the growth mechanism and the macroscale and nanoscale properties of nanoporous SiO2 films deposited on nonporous silica (SiO2) substrates from chemical precursors Si(OH)4 and TEOS (tetraethoxysilane) via low-pressure chemical vapor deposition are the primary targets of this study. This work employs a kinetic Monte Carlo (KMC) simulation method coupled to the Metropolis Monte Carlo method to relax the strained silica structure. The influence of the deposition temperature (473, 673, and 873 K) on the properties of the SiOx layers is addressed via analysis of the film growth rates, density profiles of the deposited thin films, pore size distributions, carbon depth profiles (with respect to TEOS), and voidage analysis for layers of different thicknesses (818 nm). A comparison of simulation with experimental results is also carried out.
1. INTRODUCTION To date, membranes that could be used to separate gas mixtures at high temperatures (notably process gas streams at temperatures of T > 750 K) have been developed with only limited success (see, for example, refs 17), and it is apparent that this modest pace of growth is, in part, due to the lack of a detailed understanding of the membrane fabrication process at an atomistic level. Porous inorganic silica membranes have played a significant role in these studies in view of their chemical and thermal stability at high temperatures. The objective of much of this earlier work has been focused on the development of fabrication protocols for composite membranes whose end use is for the separation of H2 from process gas streams. Because the focus has been on hydrogen, which is molecularly small relative to the other process gases, the twofold objectives of high permselectivity and comparatively high permeation rates have been achieved with relative ease. However, in the separation/capture of carbon dioxide (CO2) from combustion gas mixtures the primary component of the gas mixture is N2 and the enrichment of CO2 relative to this constituent is one of the major difficulties encountered in the CO2 capture process. At the high temperatures involved in the CO2/N2 separation, the primary mechanism associated with the separation that could lead to a substantial enrichment of CO2, normally referred to as molecular sieving, is kinetic in origin (for example, see ref 8), with permselective transport of the (kinetically) smaller CO2 species taking place within the fine pores of the nanomembrane material. Permselective membranes are normally prepared by depositing a thin nanoporous layer onto a micro/mesoporous support using a variety of deposition techniques (e.g., chemical vapor deposition (CVD),57,9,10 plasma-enhanced CVD,1113 or sol gel techniques1417). However, the pore size, density, and thickness r 2011 American Chemical Society
of the deposited layer all play crucial roles in the separation process. In principle, by controlling the deposition process parameters the desired deposited structure can be achieved. In earlier work reported by this group,1820 the possibility of generating membranes with both high kinetic selectivities for CO2 capture and acceptable permeability has been demonstrated. However, the influence of the experimental conditions employed during the CVD fabrication process on the fundamental microscopic details of the membranes formed still needs to be clarified. In this work, we investigate the creation of silica films via direct simulation of the CVD process at intermediate to high temperatures. In this preliminary work, we focus on the deposition of silicic acid (Si(OH)4) and TEOS (tetraethoxysilane), the kinetic expressions for which have been reported in a number of sources2123 but not yet applied to the molecular-level simulation of the formation of porous films via CVD. To model the creation of nanoporous silica layers via CVD, we apply a hybrid kinetic Monte Carlo (KMC)24,25 method. Lattice KMC26 is used for the elementary reactions, and an off-lattice method2729 is employed for the silica network. A range of conditions are simulated to investigate the influence of various processing conditions on the nanoscale features of the deposited layers. The structural properties of the simulated nanolayers such as density, pore size distribution, cavities, and composition are examined.
2. SIMULATION METHOD A combination of lattice kinetic Monte Carlo (KMC) and off-lattice Monte Carlo is employed to investigate the growth Received: August 11, 2011 Revised: September 20, 2011 Published: September 21, 2011 13052
dx.doi.org/10.1021/la2031329 | Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Table 1. Chemical Reactions for SiO2 Deposition from TEOS reaction no.
reactions
R2
A. Deposition Reaction SiðO CH2 CH3 Þ4 þ OH f O SiðO CH2 CH3 Þ3 þ C2 H5 OH
Figure 1. Snapshot of the initial amorphous 3.57 nm 3.57 nm 1.5 nm substrate used for deposition in this model. The green atoms represent the bottom surface, and the pink atoms correspond to the top surface hydroxyl groups that serve as reactive seed sites for the deposition process.
R3
process for the CVD deposition technique. In this work, both silicic acid, Si(OH)4, and, independently, tetraethoxysilane, Si(OCH2CH3)4 (TEOS), are employed as the deposition precursors involved in the reaction-controlled growth of silica (SiOx) layers on the surface of an amorphous silica substrate at temperatures below 1000 K. The silica substrate is an atomistic model of amorphous glass at a bulk density of 2.2 g/cm3 initially prepared by a combination of methods similar to those reported by Wooten et al.29 and MacElroy and Raghavan.30 A section of a 3D periodically imaged bulk amorphous silica (SiO2) cube was cut along the xy plane at two z locations to produce a substrate base material on the upper side (+z direction) of which the deposition would take place. While being sectioned, the bridging oxygen atoms connected to the two silicon atoms that share both the top and bottom planes of the substrate were converted to hydroxyl groups (OH), and each of the two silicon atoms was assigned to one OH group. Finally, a structure with dimensions of 3.57 nm 3.57 nm 1.5 nm (xyz) was generated and served as the substrate for silica deposition. The periodic boundary condition along the z axis was then removed, and the OH groups on the top surface were treated as the initial reacting sites to commence the growth of the SiOx layer. The bottom part of the substrate (1.0 nm) was kept rigid, and the top 0.5 nm was taken into account for Monte Carlo moves during atomic relaxation in the thin film deposition process. The film growth took place along the +z direction of the substrate, and periodic boundary conditions were applied in the x and y directions in order to minimize edge effects. Figure 1 shows the initial SiOx structure and the front view of the cleaved surface employed as the substrate in this study. 2.1. Reaction Kinetics. The reactions that are deemed to take place in this model system are as follows. In the case of silicic acid, Si(OH)4, the deposition occurs as21 jOH þ SiðOHÞ4 f jOSiðOHÞ3 þ H2 O
ðR1Þ
In the simulation of the deposition of TEOS, the nine irreversible reactions listed in Table 1 are considered to take place.22 Furthermore, in both the Si(OH)4 and TEOS deposition studies the surface condensation (annihilation) reaction jOH þ HOj f jOj þ H2 O
ðR11Þ
also takes place. For simplicity in all of the simulations conducted here, only reactions that may be considered to take place on the solid surface or within the growing film have been simulated and gasphase decomposition/dissociation of the TEOS has been neglected.
B. Dissociation Reactions SiðO CH2 CH3 Þ3 f SiðOHÞðO CH2 CH3 Þ2 þ C2 H4
R4
SiðOHÞðO CH2 CH3 Þ2 f SiðOHÞ2 ðO CH2 CH3 Þ þ C2 H4
R5
SiðO CH2 CH3 Þ f tSiðOHÞ þ C2 H4
R6
SiðO CH2 CH3 Þ2 f dSiðOHÞðO CH2 CH3 Þ þ C2 H4
R7
SiðOHÞðO CH2 CH3 Þ f dSiðOHÞ2 þ C2 H4 C. Dissociation Reactions in the Presence of a Siloxane Bond (SiO2) SiðOHÞðO CH2 CH3 Þ2 f tSiðO CH2 CH3 Þ þ C2 H5 OH
R8 R9
SiðOHÞ2 ðO CH2 CH3 Þ f tSiðOCH2 CH3 Þ þ H2 O
R10
SiðOHÞ2 ðO CH2 CH3 Þ f tSiðOHÞ þ C2 H5 OH
Table 2. Arrhenius Parameters for Si(OH)4 and TEOS Deposition Reactionsa reaction no. R1
b
frequency factor 3
activation energy (kJ/mol)
1 1
3.45 10 (cm mol 15
s )
110
R2c
1.70 1020 (cm3 mol1 s1)
249
R3 R4
5.1 1012 (s1) 3.4 1012 (s1)
197 197
R5
1.7 1012 (s1)
197
R6
1.7 1012 (s1)
197
R7
1.7 1012 (s1)
197
R8
2.0 1012 (s1)
184
R9
2.0 1012 (s1)
184
R10
2.0 1012 (s1)
184
R11d
1013 (s1)
see eq 3
a
All parameters for reactions R3R10 are based on estimates reported by Coltrin et al.22 All other parameters are from the following sources: b Pelmenschikov et al.,4 Pereira et al.,14 and Zhdanov.32 c Estimated from cold molecular beam data reported by Coltrin et al.22 d Based on estimates reported by Bogillo et al.23
The results therefore serve as a model of low-pressure chemical vapor deposition (LPCVD) reactors and are also representative of the conditions employed in low-temperature molecular beam deposition studies. The Arrhenius parameters, in appropriate units, for reactions R1 R10 are provided in Table 2. For reaction R1 with forward rate constant k1f, the parameters are based on activation energy estimates reported by Pelmenschikov et al.21 and Pereira et al.31 and estimates of the frequency factors of bimolecular surface reactions cited by Zhdanov.32 The Arrhenius parameters for reactions R3R10 in Table 2 are taken directly from earlier work reported by Coltrin et al.22 The activation energy for reaction R2 refers to a net contribution associated with the adsorption of TEOS onto the silica film 13053
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
followed by reaction within the layer. In the studies reported here, the rate expression employed for this process is rðrÞ ¼ k2f cOH ðrÞ cTEOS ðrÞ k2f ¼ hKTEOS ðrÞicOH ðrÞpTEOS RT
ðR2Þ
where k2f is the reaction rate constant, cOH(r) and cTEOS(r) are the local molar concentrations of silanol groups and TEOS reagent within the growing film at r, respectively, ÆKTEOS(r)æ is the TEOS partition coefficient, pTEOS is the TEOS partial pressure within the gas phase, and R and T are the universal gas constant and absolute temperature, respectively. Preproduction kinetic Monte Carlo simulations (details of the KMC methodology employed are provided in section 2.2 below) were conducted to ascertain initial estimates of the equilibrium values of the TEOS partition coefficients, ÆKTEOS(r)æ, and the silanol group loadings as functions of position, r, within the film over the temperature range of 473873 K. These results were then employed in combination with the experimental cold molecular beam data reported in ref 22 to estimate the activation energy and the frequency factor of the rate constant, k2f. There are two distinct differences in the manner in which this parameter is treated in this work in contrast to that in ref 22. In ref 22, the Arrhenius frequency factor for R2 is cited in terms of a reactive sticking coefficient based on surface area; the frequency factor reported in Table 2 is in units appropriate to a bulk second-order reaction with the surface silanol groups distributed within the three dimensionally growing nanoporous silica film. The activation energy for the TEOSsilanol reaction is also significantly larger than the value reported in ref 22. (In ref 22, this value was cited as 183 kJ/mol.) This is due to the separate and explicit evaluation of the equilibrium distribution coefficient ÆKTEOS(r)æ in the work reported here. Interestingly, the activation energy reported in Table 2 for the TEOSsilanol reaction is similar in magnitude to the activation energy for the homogeneous gas-phase dissociation of TEOS to produce intermediate Si(OH)(OC2H5)3. We feel that this demonstrates that reaction R2 as depicted in Table 2 and in ref 22 is not elementary even though the overall reaction is second order as evidenced by a comparison with experimental observations. Intermediate Si(OH)(OC2H5)3 itself requires very little activation22 to complete the deposition reaction sequence with the surface silanol. Forward reaction R11 (the self-healing reaction of Pelmenschikov et al.21) is modeled on the basis of the reported observations of Bogillo et al.23 The rate constant and its activation energy, EA,11, are expressed as EA, 11 k11 ¼ 1013 ðs1 Þ exp RT ð1Þ EA, 11 ¼ 5:81 ðkJ=molÞ expð8:8164rSiSi ðnmÞÞ where the distance scale is the relative separation of the two silicon atoms to which the condensing hydroxyls are attached. (Note that the estimate of the frequency factor, 1013 s1, comes directly from Pelmenschikov et al.21 and is in agreement with estimates reported by Zhdanov32 for monomolecular reactions in the adsorbed state.) The reaction is considered to be pseudofirst-order, with the relative frequency computed for each individual pair of hydroxyls. Note that should the condensation reaction result in the formation of a two-membered (diamondlike) ring,
which are not normally observed in real systems, then the reaction is not allowed to proceed. In section 2.2, we describe the kinetic Monte Carlo method employed in the execution of the formation of the thin silica films based on (a) reactions R1 and R11 for silicic acid deposition and (b) reactions R2R11 for TEOS deposition. 2.2. KMC Algorithm. The evolution of the silica (SiOx) film is simulated using the BortzKalosLebowitz24 lattice kinetic Monte Carlo (KMC) method in conjunction with a hybrid offlattice relaxation process to be described below. In the KMC process, the reactive deposition precursor (silicic acid or TEOS) from the vapor phase is incorporated within the growing solid film and transformed into surface sites. The simulation space is discretized into small subcells each of dimensions 0.51 nm 0.51 nm 0.5 nm (= ΔV). During the growth process, each subcell of the 3D simulation box can be occupied by one or more silicon sites that are bonded to a combination of molecular groups (OH, OCH2OCH3, or bridging oxygens), and the occurrence of one of the reactions at one of the sites is termed an event. At each KMC step, the frequency of each reaction event in each subcell is calculated and the choice of reaction event, r, to be undertaken is determined by the probability, Pr, that is proportional to the frequency of the associated surface reaction relative to the sum of all such frequencies. To illustrate the application of this procedure, the algorithm associated with the deposition of silicic acid as a precursor is outlined below. In the case of thin film formation via silicic acid deposition, the two reactions of concern are R1 and R11. The selection of which reaction event should be sampled at any given time is determined by the frequencies of the reactions given by ν1 ðrÞ ¼ ΔVRTcOH ðrÞ cSiðOHÞ4 ðrÞ D E ¼ KSiðOHÞ4 ðrÞ NOH ðrÞpSiðOHÞ4 ν11 ðrÞ
ð2Þ
k11 ¼ RT NOHHO ðrÞ k1f
where νm(r) is the scaled frequency for reaction m and is directly related to the reaction frequency vm(r) (s1) by νm ðrÞ ¼
RT νm ðrÞ k1f
Furthermore, ci is the local concentration of i, Ni is the number of sites of type i within volume element ΔV, and pi is the bulk vaporphase partial pressure of i. Note that the designation of the number of pairs of condensable silanol groups, NOHHO, is such that at least one of the OH groups is within the volume element ΔV and the second OH group is from a biased sample (i.e., only those within a specific radius of the first group and also not a nextto-nearest bonded neighbor). Also, in view of the inhomogeneity of the deposition process, the reaction frequencies are functions of position within the layer as it forms. The local partition coefficients for the reagents, ÆKi(r)æ, that are employed to determine the local concentration of these species relative to prespecified bulk vapor pressures are computed via a two-step process involving a Widom insertion algorithm33 coupled to topological constraints associated with the accessibility of the nanocavities within the deposited layer to vapor/gas molecules exterior to the medium. As noted above, the deposition region is subdivided into small cubic elements of volume ΔV (0.13 nm3) centered at r, 13054
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
and the partition coefficients are computed using 1 Z Uðr0 , rÞ K i ðrÞ ¼ exp dr0 ΔV ΔV kB T Ω i
Table 3. Lennard-Jones and Coulombic Partial Charge Parametersa ð3Þ
where the energy U(r) is computed from the potential interactions between the individual atoms of the inserted molecule (Si(OH)4 or TEOS) and the atoms of the silica layer. The angular bracket ÆæΩ in eq 3 refers to the canonical average over orientations, represented by the solid angle Ω, of the inserted species. The insertion cycle involves placing the test particle in question at a randomly selected position r0 with a random orientation within a subcell in the simulation box. Typically, the partition coefficients are evaluated by averaging over 103 trial cycles of insertion per subcell. These individual atomatom pair interactions include both Lennard-Jones, ULJ(rij), and Coulombic, Uel(rij) (partial charge), potential terms Uðrij Þ ¼ ULJ ðrij Þ þ Uel ðrij Þ The Lennard-Jones interaction is 0 !12 !6 1 σij σ ij A ULJ ðrij Þ ¼ 4εij @ rij rij
ð4Þ
ð5Þ
where rij is the distance between atoms i and j, εij represents the magnitude of the minimum well depth, and the distance σij characterizes the separation between the two atoms at which repulsion dominates the interaction. A cutoff radius for the Lennard-Jones interaction of 1.2 nm was employed in the simulations. The Coulombic potential in its screened form as proposed by Wolf et al.34 is employed in this work to estimate the potential interactions between pairs of partial charges in the system. This is a computationally viable approach for large 2D periodically disordered systems of the kind investigated in this work, and in its shifted force form (Fennell and Gezelter35), the Wolf method involves the following modification to the Coulomb energy for rij e Rc: Uel ðrij Þ ¼ ( þ
qi qj erfcðαrij Þ erfcðαRc Þ Rc 4πε0 rij
! ) erfcðαRc Þ 2α expð α2 Rc 2 Þ þ pffiffiffi ðrij Rc Þ Rc 2 Rc π ð6Þ
where rij is the distance between two partial atomic charges qi and qj on particles i and j, respectively, ε0 is the electrical permittivity of space, and erfc is the complementary error function 2 Z ∞ t2 e dt erfcðxÞ ¼ pffiffiffi π x The spherical cutoff Rc and shielding factor α appearing in eq 6 must be determined empirically. When α is zero, this expression reduces to a standard shifted force potential.
atom
ε/kB (K)
σ (nm)
charge, qi(eo)
O(silica)
185.0
0.2708
0.64025
O(ethoxy) Si(silica)
185.0 0.0
0.2708 0.0
0.64025 +1.2805
O(OH)
185.0
0.3
0.533
H(OH)
0.0
0.0
+0.206
CH2
108.2
0.36
0.0
CH3
153.5
0.37
0.0
a
All of the atomic parameters are taken from Schumacher et al.,28 with the exception of the united atom (CH2 and CH3) parameters, which are taken from Mayo et al.46
qi qj 1 1 þ Uel ðrij Þ ¼ 4πε0 rij Rc
! 1 ðrij Rc Þ ðrij e Rc Þ Rc 2
The parameters used in this work (α = 0, Rc = 1 nm) are those suggested by Carre et al.,36 who have shown that the method can provide accurate results for amorphous silica systems. The Lennard-Jones and electrostatic (partial charge) parameters on each atom used in the deposition model are reported in Table 3. In this work, the OH groups (and the CH2 and CH3 groups in the case of TEOS deposition) are treated as united atom structures with the charge on the OH group defined by combining the individual charges on the oxygen and hydrogen atoms. In the TEOS simulations, the charges on united atom structures CH2 and CH3 are assumed to be 0.0. To assign the charge on the surface silicon atoms qSi during the growth process, a simple equation has been employed that is given by qSi ¼ qOH NOH qOðsiloxaneÞ NOðsiloxaneÞ qOðethoxyÞ NOðethoxyÞ ð7Þ An additional refinement introduced into the simulations is an acknowledgment of the fact that the volume of the nanoporous silica medium cannot be fully accessible to the depositing species. This constraint is applied by sampling only those sites for deposition reactions to take place that are located on topologically permitted pathways within the growing nanoporous solid film. To this end, a lower bound in the critical percolation threshold of 0.03 is selected for the Henry’s law constants in this work. Regions of the solid that are characterized by this value of K or lower are considered to be inaccessible. This lower bound corresponds to a conservative estimate based on the known percolation limit for partitioning in media composed of random assemblies of spheres,3740 which nanoporous silica closely resembles.18 During the deposition process, a percolation analysis is carried out to define the accessible path for the percolating reagent molecule through the porous structure. In this work, both lattice41 and nonlattice42 versions of the HoshenKopelman (HK) algorithm were employed to label percolation clusters within the solid film. The accessible cluster analysis employs the 3D cubic subcell lattice (grid) with periodic imaging in the x and y directions. Lattice HK was employed to explore accessible pathways through the entire deposited structure, and to establish the number of percolating clusters in the structure, the nonlattice form of the HK algorithm was implemented. The nonlattice HK algorithm requires only simple data structures (connectivity 13055
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Table 4. Potential Parameters Used for the Relaxation of the Deposited Solid Films bond-stretching constant
bond-bending constant
equilibrium distance
(MJ/mol/nm2)
(kJ/mol)
(nm)
atomic interaction SiO
260.6
angle (deg)
0.161
SiOSi
193
θSiOSi,0 = 144
OSiO
417
θOSiO,0 = 109.471
SiOc
292.9
0.1487
CH2CH3
292.9
0.143
OcCH2
292.9
0.132
SiOcCH2 OcCH2CH3
θSiOcCH2,0 = 120 θOcCH2CH3,0 = 109.471
558 471
SiOH
292.9
0.1487
The pure silica parameters (bond length SiO and bond angles SiOSi and OSiO) are taken from von Alfthan et al.45 The remaining parameters are those reported by Mayo et al.46 tables) to describe the network connectivity, and the algorithm can handle an arbitrary set of connected bonds (links) and sites (nodes) on any lattice or nonlattice environment of any dimensionality. To establish the number of clusters in the structure, only nodes (corresponding to atoms in the connectivity table) need be considered, and thus the original node-link algorithm can be simplified as suggested by Al-Futaisi and Patzek.42 A single cycle of the lattice KMC algorithm is completed, with the selection of which reaction event to be undertaken. For the case of the silicic acid KMC simulations involving two reactions (see eq 4), the probability of which reaction to execute is given by Pm, j ¼
νm, j NBIN
2
∑ ∑
i¼1 m¼1
ð8Þ νm, i
where NBIN is the instantaneous number of subcells, each of volume ΔV, within the growing film at that given time. To implement this, a random number, ξ1, uniformly distributed in the range of (0, 1) is generated and the event (reaction i) to be undertaken is determined by νm, j
i1
∑
j, m ¼ 1
NBIN
2
∑ ∑
k¼1 m¼1
< ξ1 e νm, k
νm, j
i
∑
j, m ¼ 1
NBIN
2
∑ ∑
k¼1 m¼1
ð9Þ νm, k
Within this lattice KMC, one reaction is allowed to take place at one site in each KMC step. After an event has occurred, the simulation time is updated and the process is continued until the KMC cycle reaches a predefined number of events. At each simulation step, the time increment τinc is computed as τinc ¼ N
lnðξ2 Þ 2
∑ ∑ BIN
k¼1 m¼1
ð10Þ
νm, k
where ξ2 is another random number uniformly distributed in the range of (0, 1). The time increment as given by eq 10 is adjusted dynamically and stochastically to accommodate the fastest possible event at each simulation step. In the TEOS deposition studies, the same approach was employed for the extended set of reactions R2R11. To minimize the energy and relax the structure independently of reactions R1R11, the canonical Metropolis Monte Carlo
scheme as outlined by Burlakov et al.27 and Schumacher et al.28 has been employed at intervals between each KMC event. Initial studies to investigate the relative importance of the switching of pairs of siloxane bonds via reversible bond-switching reactions R12 and R13 (the Wooten, Winer, and Weaire formalism29) jOj þ HOj T jOH þ jOj
ðR12Þ
jOj þ jOj T jOj þ jOj
ðR13Þ
confirmed that these reactions are extremely rare at the temperatures investigated in this work (confirming observations reported by Cabriolu and Ballone43). In the Metropolis MC simulations, the energy is computed prior to and after the move using Keating SiO bond stretching and the OSiO, Si OSi bond-angle-bending interaction potential.44,45 This potential represents the energy of the solid as a function of the nearestneighbor positions and is given (in its simplified form44) by E¼
∑ kbi ½ri ri0 2 þ ij ∈∑angles 2 kθij ½cos θij cos θij0 2 i ∈ bonds 2 1
1
ð11Þ In this equation, ri is the distance between two bonded atoms, ri0 is the (average) equilibrium length of bond i, θij represents the bond angle between bonds i and j, and θij0 is the corresponding equilibrium value. kbi and kθij are the bond-stretching and bondbending force constants, respectively. The parameters of the Keating potential for the Si(OH)4 and Si(OCH2CH3)4 deposition models used in this study are provided in Table 4. In the case of TEOS, a reaction between the depositing molecule and the surface of the substrate results in carbon atoms being confined within the layer during the growth process. Mayo et al.46 reported the parameters for organic molecules using the Dreiding force field that are employed in this work for the prediction of the structure. The kbi and kθij values for the carbon atoms are obtained from the Dreiding potential and converted to correlate with the Keating potential. The bondstretching force constant kbi is taken to be the same as the corresponding coefficient kbi(Drieding)reported by Mayo et al.,46 and the value of kθij employed in this study is given by kθij ¼ 13056
kθijðDreidingÞ sin2 θij0
ð12Þ dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
This approach may lead to marginally lower accuracy but allows reasonable predictions to be made for novel combinations of the elements simulated in this work. A repulsive potential45 is also used along with the Keating potential in this study to prevent the overlapping of unbonded atoms during energy relaxation of the structure. This potential acts between atoms and does not consider nearest or second nearest neighbors with respect to the bond topology. The form of the repulsive potential selected to calculate the repulsive interaction in this work is 8 > : 0, rij g rc
∑
where Ur is the repulsive energy between two atoms, kr is the spring constant, and rc is a cutoff radius. In this study, the radius of the interaction has been chosen to be 0.26 nm, which is the distance between the nearest-neighbor oxygen atoms in silica, and the spring constant kr was set to 8000 eV/nm4 = 772 MJ/mol/nm4. During the relaxation process, the acceptance or rejection of a new trial configuration follows the usual Metropolis Monte Carlo prescription. At least 105 trial MC simulation moves (500 on average per atom) are conducted immediately after each KMC event on all atoms within a 1 nm radius of the site of the event. This number was selected to ensure adequate relaxation of the local stresses of the structure (as determined by the relaxation of the local structural energy), and independent evaluations (not reported here) of the OSiO/SiOSi configurational properties, such as the atomic radial distribution functions and bond angle distributions, have confirmed that the final structures formed are consistent with the equilibrium structures observed for random networks of amorphous silica. In all of the runs conducted in this study, the total length of the growth trajectory during the CVD simulation of the formation of a single layer was fixed at 8000 reaction events to ensure that a distinctly homogeneous region of the film evolved during the deposition process and that the properties of this region assumed a steady state. For each thermodynamic condition (temperature and precursor pressure) and for reagents Si(OC2H5)4 and Si(OH)4, five independent layers were fabricated; the results reported in the following section therefore correspond to averages over 40 000 reaction events in each case.
3. RESULTS The internal architecture of nanoporous composite membranes formed during CVD has a significant influence on the equilibrium and/or kinetic selectivity of the resultant membrane for separating fluid mixtures. Therefore, to develop a more complete understanding of the key features of the deposited structure and the manner in which the experimental deposition conditions play a role in determining the membrane properties, one needs to characterize these nanoporous media in terms of morphological parameters such as local atomic and mass density distributions, pore sizes, and voidage and spatial details of the membrane's chemical composition. 3.1. Film Growth Rates. The most direct comparison with experiment that can be made is through the solid film growth rate, a macroscopic observable normally reported in studies of nanoscale thin film deposition. In Figure 2, we report the film
Figure 2. SiOx film growth rate as a function of precursor pressure. (---) Silicic acid precursor; () TEOS precursor. Deposition temperature: (9) 473 K; (0) 673 K; (b) 873 K. The large open diamond ()) corresponds to the deposition rate reported in ref 22 for a cold molecular beam of TEOS deposited at 1.7 103 Torr onto a substrate maintained at a temperature of 873 K.
growth rates at three temperatures for the films simulated in this work over a range of precursor reagent pressures of 104 < pR < 1.5 Torr. For most of the conditions investigated, the growth rates are linear in pressure as implied by the expression for the time increment (eq 10). The exception is at the lowest temperature of 473 K for TEOS. Under stationary conditions, the denominator of eq 10 with TEOS as the precursor may be expressed as ! NBIN Ndiss
pTEOS ri, j þ k2f ½ KTEOS, j NOH, j RT j¼1 i¼3
∑ ∑
EA, i Ai NC2 H5 , i, j exp þ k11 ½NOHHO, j RT j¼1 i¼3
pTEOS þ k2f ½ KTEOS, j NOH, j RT ! Ndiss NBIN EA, i ¼ NC2 H5 , i, j Ai exp RT i¼3 j¼1 NBIN
¼
Ndiss
∑ ∑
∑ ∑
þ k11
NBIN
∑ NOHHO, j
j¼1
!
þ k2f
pTEOS RT
NBIN
∑
j¼1
KTEOS, j NOH, j
!!
ð14Þ During the deposition process at low temperatures, the ethoxy dissociation reactions (on the left of the last expression in eq 14) occur at frequencies commensurate with the TEOS deposition term shown on the right of the above expression. The growth rate, however, is not a simple linear function of pressure in view of the direct increase in the ethoxy concentration level (the first term on the left of eq 14) within the deposited film at higher deposition pressures. This results in the nonlinearity in the growth curves observed in Figure 2 at low temperatures. At high temperatures (and at low pressures in all cases), the ethoxy dissociation reactions occur very frequently relative to the deposition reaction, with the result that for each TEOS molecule deposited the three ethyl moieties remaining in the surface group as indicated on the right-hand side of reaction R2 must first be 13057
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Figure 3. SiOx film growth rate as a function of temperature at a fixed precursor reagent pressure of 0.25 Torr. (9) Kinetic Monte Carlo simulation results for TEOS employing reactions R2R11. (b) Kinetic Monte Carlo simulation results for Si(OH)4 employing reactions R1 and R11. (0) Experimental data reported by Desu47 for the temperature range of 8931083 K. (The dashed line is the extrapolation of a fit to the experimental data proposed by Desu.)
stripped before another TEOS molecular deposition can take place. As will be demonstrated below, this does indeed lead to low levels of carbon in the deposited films. Although the dissociation reactions do take place independently of all other reactions in the system, there are exceptions to this sequence of full carbon depletion prior to the deposition of a TEOS molecule. Hidden constraints exist for the dissociation reactions because suitable “glass bond” siloxane oxygens are required in the neighborhood of these ethoxy groups for each of these reactions to proceed. The absence of such an oxygen will result in the retention of the ethoxy moiety. A subsequent reaction may produce a suitable glass bond oxygen and allow for its removal; however, it is clear that in general ethoxy dissociation is not entirely independent of the other reactions. The open diamond symbol shown in Figure 2 at a pressure of 1.7 103 Torr and 873 K is the growth rate under these conditions estimated from data reported by Coltrin et al.22 for cold (25 C) molecular beam deposition onto a substrate surface maintained at 873 K. Under these conditions, it has been noted that the molecular dissociation of TEOS in the gas phase is negligible. At high gas-phase temperatures, however, Coltrin et al. have clearly demonstrated that dissociation reactions within the gas phase prior to deposition are of paramount importance. This is evident from the simulation results shown in Figure 3 and the experimental data of Desu47 for CVD at high temperatures. Coltrin et al.22 have made a detailed comparison with the experimental observations reported by Desu and have concluded that the gas-phase dissociation reaction SiðOC2 H5 Þ4 f SiðOHÞðOC2 H5 Þ3 þ C2 H4 257:15 ðkJ=molÞ k ¼ 4:9 1013 ðs1 Þexp RT
ð15Þ
is the most significant gas-phase decomposition reaction and greatly influences the thin solid film growth rate at high temperatures. By including the dissociation reaction in eq 15 within
the set reported in Table 1, they have demonstrated good agreement with the data reported by Desu over the reaction limiting range from 893 to 1000 K. (At higher temperatures, the deposition process becomes diffusion-limiting as indicated by the nonlinearity in the data in Figure 3 for T > 1000 K.) The omission of gas-phase reactions in the studies reported here and in particular the formation of the intermediate Si(OH)(OC2H5)3 in the gas phase serve to explain, at least in part, the underprediction by the KMC simulation results for TEOS in Figure 3. At 873 K, the KMC growth rate is approximately 6 times smaller than the estimate provided by Desu’s correlation (the dashed line in Figure 3). While the agreement would appear to be improved at lower temperatures (within a factor of 3 at 473 K), it is clear that, in general, for a more complete analysis of the deposition process, computations based on additional data provided by a knowledge of the specific configuration, internal gas-phase distribution pattern, and thermal states within the CVD reactor involved would be required. The KMC method employed in this work should provide reliable results for systems with low gas-phase reaction times or low-temperature molecular beam deposition onto hot surfaces. The Si(OH)4 simulation results reported in Figures 2 and 3 are indicative of an upper bound in the deposition rates for the limiting case in which TEOS and other alkoxysilanes have been stripped of their carbon content in the gas phase prior to deposition. At 873 K, the growth rate for silicic acid as the precursor is approximately 3 orders of magnitude larger than estimated for undissociated TEOS and 2 orders of magnitude larger than the film growth rate provided by the experimental data reported by Desu47 for TEOS in which, as noted above, reactive intermediate Si(OH)(OC2H5)3 is considered to play a major role in the deposition process. As will be shown below, this also has a direct bearing on the precursor dependence of the atomic structure of the resulting thin films formed during layer growth. 3.2. Film Mass and Number Density Profiles. The mass density profiles obtained for a selected set of simulation runs are shown in Figure 4. The background substrate (Figure 1) corresponds to the region z < 0, and the densities in this region for the deposited material start at 0.0 where the penetration of deposited silicic acid or TEOS cannot take place. In the inhomogeneous region at the surface of the substrate (z = 0), the density initially passes through a maximum before leveling off at a layer thickness of approximately 1 to 2 nm. From the profiles, it is clear that the average densities of the silica films (Figure 5) in the homogeneous region of z > 2 nm decrease with increasing substrate/ deposition temperature and, for Si(OH)4 deposition, with increasing precursor pressure. (Statistically, with standard errors of ∼(2%, the densities of the TEOS films are essentially independent of pressure, although the low-temperature deposition results do indicate a systematic density reduction of approximately 2.3% at the highest pressure studied.) To explain these observations, we note that there are two competing effects relating separately to temperature and pressure involved during the deposition process. High-temperature conditions encourage minimal hydroxyl content through hydroxyl group condensation (reaction R11), and this is evident from the results for the atomic number density profiles shown in Figures 6 and 7. During deposition, the removal of OH groups via condensation at a given pressure results in fewer sites for subsequent deposition and leads to a lowering of the density locally within the medium and a more open pore structure. Local condensation reactions deep within the layer also result in the appearance of nanocavities, and 13058
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Figure 5. Average mass density as a function of deposition pressure for silicic acid deposition () and TEOS deposition (---) at (9) 473, (0) 673, and (b) 873 K.
Figure 6. Oxygen atomic number density profiles with Si(OH)4 employed as a precursor. The open and filled squares correspond to siloxane (or bridging) oxygens, and the open and filled triangles correspond to the hydroxyl oxygens. The open symbols refer to the lowest temperature (473 K) and the highest pressure (pSi(OH)4 = 0.1 Torr), and the filled symbols refer to the highest simulated temperature (873 K) and lowest precursor pressure (1 104 Torr).
Figure 4. Mass density as a function of layer depth for silicic acid deposition ((O) 1 104 Torr and (0) 0.1 Torr) and TEOS deposition ((b) 2.84 104 Torr and (9) at 1.42 Torr) at (a) 473, (b) 673, and (c) 873 K.
both of these effects are most significant for high-temperature deposition conditions. Conversely, at a given temperature, increasing
the deposition pressure enhances the deposition rate, and during Si(OH)4 CVD, this leads to a significantly higher OH content. The latter effect results in a greater degree of steric exclusion of neighboring atomic groups by dangling silanol groups prior to silanol condensation with the subsequent creation of larger voids within the evolving film. Furthermore, whereas the presence of the ethyl moieties during TEOS deposition encourages the formation, on dissociation, of larger nanocavities (and hence lower densities than solid films based on silicic acid), the trend toward lower densities at higher temperatures in these media would also appear to be primarily related to silanol condensation and dehydration. The carbon content of the films formed during TEOS deposition is also sensitive to temperature and pressure, with the least carbon remaining, as anticipated, at the highest temperature 13059
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Figure 8. Ethyl number fraction in the 3.5-nm-thick surface layer of the TEOS-based CVD films as a function of precursor pressure at (9) 473, (0) 673, and (b) 873 K. The lines shown are simply guides to the eye.
Figure 7. Oxygen and carbon atomic number density profiles with TEOS employed as a precursor (a) at 473 K and a precursor pressure of 1.42 Torr and (b) at 873 K and a precursor pressure of 2.84 104 Torr. The open symbols correspond to the oxygen atoms: (0) siloxane (or bridging oxygens), (Δ) hydroxyl oxygens, and (r) ethoxy oxygens. The filled circles (b) correspond to the carbon atoms (in both CH2 and CH3). Note the change in both (a) and (b) on the reference axis for the ethoxy oxygens and the carbon atoms.
and lowest pressure. However, even in this case there is still a significant level of carbon remaining in the film (primarily within 3 nm of the surface). This “contamination” is common in CVD processes employing alkoxysilanes as precursors, with the carbon content being particularly high at high precursor pressures (flow rates) and/or low temperatures.11 To illustrate more clearly the carbon composition dependence on temperature and pressure, the results for the number fraction xC2H5 of the ethyl groups (relative to the total number density of the silicon, siloxane oxygens, hydroxyl groups, ethoxy oxygens, and ethyl groups) remaining in the top 3.5 nm of the deposited films as a function of TEOS pressure are reported in Figure 8. (We note that no residual carbon was observed deeper within the layers.) These results were obtained from running averages over samples of the 3.5 nm surface interfacial zone during the last half of the film growth trajectory. At 473 K, the carbon content is highest, increasing significantly with increasing TEOS pressure. As the deposition temperature is increased, the carbon levels at a given precursor pressure diminish
only marginally, and it is clear that even at high temperature and low pressures between 0.4 and 0.5% carbon can remain in the top 3 to 4 nm interfacial region of the solid film. In a process setting, the removal of this would normally require thermal treatment (continued dissociation via reactions in the absence of deposition) and/or oxidation with O2 or O3. An important outcome of the KMC simulations is the demonstration of the dependence of the film mass density and molecular structure not only on the thermodynamic conditions for the deposition process but also on the precursor employed. The films obtained with the molecularly larger of the two precursors result in layers with significantly lower densities. For example, from Figure 5 the density within the homogeneous region of the Si(OC2H5)4 film deposited at 873 K is approximately 2.1 g/cm3 whereas that for Si(OH)4 deposition is close to 2.3 g/cm3. The lower densities observed for TEOS are not an uncommon observation in experimental CVD studies48,49 in which film densities that are as much as 10% lower than the density of bulk amorphous glass have been observed. The precursor-controlled SiOx film density has also been proposed for applications as low-k dielectric films (e.g., ref 50). These materials and techniques, with the appropriate selection of the thermodynamic deposition conditions, may also be employed in the development of controlled pore composite membranes for molecular-size-selective separation of the components of gas and liquid mixtures. 3.3. Pore Size Distributions and Void Accessibilities. Selected results for the pore size distributions (PSDs) for the homogeneous regions of the density profiles reported in Figure 4a, c are shown in Figure 9. These distributions were determined using the algorithm developed by Bhattacharya and Gubbins.51 According to this method, the pore size in the structure at a given point is defined by the largest diameter of a sphere that encompasses the given point without overlapping the neighboring atoms in the system. Enumerating the pore sizes in this manner, it is straightforward to establish the normalized pore size distribution for each of the simulated structures formed via the KMC CVD algorithm. For high-deposition temperatures, the PSDs are relatively broad with maximum pore radii of 4.1 and 3.0 Å for TEOS and silicic acid, respectively, clearly illustrating the influence of the molecular size of the individual precursors. The influence of 13060
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Figure 10. Average pore radius for the simulated nanoporous layers as a function of precursor pressure: upper curves, TEOS; lower curves, Si(OH)4). (9) 473, (0) 673, and (b) 873 K.
Figure 9. Pore size distributions for CVD layers formed by the deposition of Si(OH)4 and TEOS. (a) T = 473 and (b) T = 873 K. Filled symbols correspond to the highest pressure investigated ((9) 0.1 Torr for Si(OH)4 and (2) 1.42 Torr for TEOS), and open symbols refer to the lowest pressure investigated ((0) 104 Torr for Si(OH)4 and (Δ) 2.84 104 Torr for TEOS).
precursor pressure in controlling the pore size is also seen in the low-temperature TEOS deposition results with a significant reduction in the maximum pore radius from 4.0 to 3.4 Å. The results at high temperature, however, are only marginally affected by pressure. The influence of precursor molecular size and to a lesser extent the deposition thermodynamic conditions is also very much in evidence from the average pore radii of ∼1.651.85 Å (TEOS) and ∼1.051.25 Å (Si(OH)4) as shown in Figure 10. These results, and particularly the average pore diameters of 3.33.7 Å for TEOS, are consistent with observations by Altemose52 on silica glasses and the recent estimates of the silica film pore size reported by McCann.13 The results for the average pore radii inversely follow the trends observed in Figure 5 for the average density of the films. For both precursors, the average pore radii increase with temperature, which we believe is due to the lower OH content within the high-temperature films. For fluid mixture separations,
however, the added variability, and hence control, of the pore size depending on the precursor employed is significant and should be a key factor for consideration in the fabrication of size (or kinetically) selective membranes. To provide additional insight into the influence that the morphological characteristics of the simulated layers can have on the pore space accessibility of simple gases, a series of computations have been performed to evaluate the hard-core partitioning of a range of species between the bulk gas and the pores of the films formed in these simulations. A simple random insertion routine has been employed in the homogeneous region of the films in the ranges of 1.5 nm < z < 12.0 and 1.5 nm < z < 5.0 nm for layers formed by silicic acid and TEOS as precursors, respectively, for a hard-point particle, helium (with a hard-sphere atomic diameter equal to its Lennard-Jones collision diameter of σ = 0.228 nm (Chakravarty53)), oxygen (diatomic with a hard atomic diameter of σ = 0.3106 nm and an interatomic distance of l = 0.09699 nm), nitrogen (diatomic with a hard atomic diameter of σ = 0.3321 nm and an interatomic distance of l = 0.10464), and carbon dioxide (a triatomic linear molecule with hard atomic diameters of σ = 0.3064 nm (O) and 0.2785 nm (C) with a carbonoxygen interatomic distance of l = 0.1161 nm) (Schumacher et al.28). In Figure 11, the atomic structure of one of the silica films formed via TEOS deposition is shown alongside void accessibility maps for gases N2, CO2, and He. This figure illustrates clearly the nanocavities referred to earlier and also highlights morphological features of the deposited structures that can be inferred only from the pore size distributions plotted in Figure 9. In particular, the rather broad pore size distributions computed for these systems are seen to arise from the presence of a relatively small number of nanocavities of varying size interconnected by narrow channels. For the case of larger molecules N2 and CO2, many of the these cavities are isolated and the transport of N2 and CO2 within composite films of the kind produced via TEOS deposition will be determined to a significant extent not by the average pore radii reported in Figure 9 but more by the relatively high level of exclusion indicated in Figure 11 in contrast to the helium void map and, most importantly, by the topology of the pore network through 13061
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir
ARTICLE
Figure 12. Parity plot for the accessible pore volumes predicted using eq 16 and the results obtained by direct MC simulation: (9) helium, (0) oxygen, (2) nitrogen, and (Δ) carbon dioxide.
Figure 11. (a) Atomic structure of a silica film formed during TEOS deposition at 873 K and 2.84 104 Torr (yellow, silicon; red, oxygen/ OH; light blue, CH2/CH3. (bd) Void accessibility plots for (b) N2, (c) CO2, and (d) He, respectively, within the region enclosed by the blue contour box shown in a.
interconnecting narrow channels of the kind illustrated in Figure 11b,c. Further perspectives into the structure of the silica films are provided by ensemble averages of the accessible void volumes for each of the gases mentioned above. A simple relationship based on models of the inserted gas particles as a hard sphere (helium) or a hard spherocylinder (O2, N2, or CO2) that correlates all of the data for a given precursor quite well is given by Raghavan and MacElroy54 ln ψAcc σf 3 3 lf σf 2 ð16Þ ¼ 1 þ þ 1 þ 2 σs ln ψAcc ð0Þ σs σs where ψAcc is the accessible void fraction of the silica medium to hard-core fluid particles of diameter σf (the cylinder diameter in the case of the spherocylinder model) and length l f and ψAcc(0) is the corresponding value for particles of zero volume (points). Density variations between configurations are canceled to a significant degree in the ratio on the left-hand side of eq 16. The single fitting parameter in this expression is σs, the effective diameter of the solid exclusion “particles” that make up the silica structure. Equation 16 is based on the assumption that the solid exclusion particles are overlapping spheres distributed at random within the medium, and whereas the correlation of the void accessibility data is very good, the actual silica structures are not entirely random (in particular, long-range topological constraints are present
because of bond connectivity throughout the silica network). For this reason, the fitting parameter σs does depend to some extent on the origin of the film (notably the precursor employed): for all of the layers formed with silicic acid as the precursor, σs = 0.324 nm, and for the TEOS-based systems, σs = 0.422 nm, which is intermediate between the size of the siloxane oxygen/ hydroxyl group and an effective size for the silica tetrahedra. The parity plot provided in Figure 12 demonstrates the relative accuracy of eq 16 for all of the simulations conducted in this work. Most of the helium data are in the region of or above the limiting value of 0.03, and the results represented by the open squares and triangles in the vicinity of ψ = 0.03 are the data for TEOS-related layers. The results in the lower left-hand corner of Figure 12 are for O2, N2, and CO2 distributing within silicic acidbased films. Although in general the ability of eq 16 to correlate the data over three to four decades of voidage values is very good, there does appear to be some dependence on the deposition temperatures. The variation across the parity line, from left to right, for a given gas would appear to be correlated primarily with increasing temperature and a reduction in the concentration of OH groups at high temperatures. In particular, for the layers formed via silicic acid deposition, the order of magnitude increase in simulated values of ψAcc for O2, N2, and CO2 as the deposition temperature increased from 473 to 873 K suggests that it is the removal of silanols via condensation within the narrow interconnecting channels as well as within the nanocavities in the silica films that leads to the opening of the pore structure for these gases. This is supported by the significant shift to larger pores in the pore size distributions observed in Figure 9a,b (see also Figure 10) as the deposition temperature is increased from 473 to 873 K.
4. CONCLUSION The aim of this work has been to develop a thin silica film deposition model for the simulation of TEOS and Si(OH)4 on nonporous silica substrates and to investigate the growth process using a hybrid kinetic Monte Carlo (KMC) algorithm. Although good quantitative agreement with reported experimental data has 13062
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
Langmuir been demonstrated for layer growth rates, the primary objective of these studies has been to demonstrate that the KMC algorithm is able to provide valuable molecular-level details of the nanoporous thin films formed during the CVD process. The main observations to be drawn from the results are as follows: (a) High-density films are formed during the CVD process. The densities, in the range of 2.1 to 2.4 g/cm3, are sensitive to the precursor employed and, to a lesser extent, the thermodynamic conditions of the CVD process itself. (b) The morphological details of the silica films are similarly sensitive to the precursor employed. In particular, depending on the alkoxysilane, Si(OH)4 x(O(CH2)nCH3)x, and its pretreatment within the gas phase, the average pore diameter within the silica film formed via CVD may lie within a broad range from 0.2 to 0.4 nm, with the tightest pores being formed when x f 0. (c) Closer scrutiny of the morphology of the silica films formed during deposition indicates that the comparatively broad pore size distributions computed for the structures arise from the presence of nanocavities interconnected via narrow channels. For the tight pore sizes observed for the silicic acid-based layers, pore accessibility and hence molecular sieving selectivity are also found to be very sensitive to the deposition temperature employed.
’ AUTHOR INFORMATION Corresponding Author
E-mail:
[email protected].
’ ACKNOWLEDGMENT T.C.M. gratefully acknowledges the financial support provided by grant EU-FP6 STREP Project FUSION, and T.A. acknowledges the support of Science Foundation Ireland grant 05RFP/ENG0044. ’ REFERENCES (1) Tsapatsis, M.; Gavalas, G. R. J. Membr. Sci. 1994, 87, 281. (2) Kim, S.; Gavalas, G. R. Ind. Eng. Chem. Res. 1995, 34, 168. (3) Tsapatsis, M.; Gavalas, G. R. AIChE J. 1997, 43, 1849. (4) Mulder, M. Basic Principles of Membrane Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. (5) Lee, D; Zhang, L.; Oyama, S. T.; Niu, S.; Saraf, R. F. J. Membr. Sci. 2004, 231, 117. (6) Araki, S.; Mohri, N.; Yoshimitsu, Y.; Miyake, Y. J. Membr. Sci. 2007, 290, 138. (7) Li, K. Ceramic Membranes for Separation and Reaction; John Wiley & Sons: Chichester, U.K., 2007. (8) K€arger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; John Wiley & Sons: New York, 1992. (9) Sea, B.-K.; Watanabe, M.; Kusakabe, K.; Morooka, S.; Kim, S.-S. Gas Sep. Purif. 1996, 10, 187. (10) Prabhu, A. K.; Oyama, S. T. J. Membr. Sci. 2000, 176, 233. (11) Ramamoorthy, A.; Rahman, M.; Mooney, D. A.; MacElroy, J. M. D.; Dowling, D. P. Surf. Coat. Technol. 2008, 202, 4130. (12) Kafrouni, W.; Rouessac, V.; Julbe, A.; Durand, J. Appl. Surf. Sci. 2010, 257, 1196. (13) McCann, M. T. P. Plasma Deposition of Nanoporous Inorganic Membranes for Gas Separation. Ph.D. Thesis, University College Dublin, Ireland, 2010. (14) de Lange, R. S. A.; Hekkink, J. H. A.; Keizer, K.; Burggraaf, A. J. Microporous Mater. 1995, 4, 169.
ARTICLE
(15) Lin, Y. S.; Kumakiri, I.; Nair, B. N.; Alsyouri, H. Sep. Purif. Methods 2002, 31, 229. (16) Stoitsas, K. A.; Gotzias, A.; Kikkinides, E. S.; Steriotis, T. A.; Kanellopoulos, N. K.; Stoukides, M.; Zaspalis, V. T. Microporous Mesoporous Mater. 2005, 78, 235. (17) Koutsonikolas, D.; Kaldis, S.; Sakellaropoulos, G. P. J. Membr. Sci. 2009, 342, 131. (18) MacElroy, J. M. D. Mol. Phys. 2002, 100, 2369. (19) Mooney, D. A.; MacElroy, J. M. D.; Kozachok, M.; Cuffe, L.; Tacke, M. 16th International Congress of Chemical and Process Engineering; CHISA: Prague, the Czech Republic, 2004. (20) Cuffe, L.; MacElroy, J. M. D.; Tacke, M.; Kozachok, M.; Mooney, D. A. J. Membr .Sci. 2006, 272, 6. (21) Pelmenschikov, A.; Leszczynski, J.; Petterson, L. G. M. J. Phys. Chem. A 2001, 105, 9528. (22) Coltrin, M. E.; Ho, P.; Moffat, H. K.; Buss, R. J. Thin Solid Films 2000, 365, 251. (23) Bogillo, V. I.; Pirnach, L. S.; Dabrowski, A. Langmuir 1997, 13, 928. (24) Bortz, A. B.; Kalos, M. H.; Lebowitz, J. L. J. Comput. Phys. 1975, 17, 10. (25) Knizhnika, A. A.; Bagaturyantsa, A. A.; Belova, I. V.; Potapkina, B. V.; Korkin, A. A. Comput. Mater. Sci. 2002, 24, 128. (26) Battaile, C. C.; Srolovitz, D. J. Ann. Rev. Mater. Res. 2002, 32, 97. (27) Burlakov, V. M.; Briggs, G. A. D.; Sutton, A. P.; Tsukahara, Y. Phys. Rev. Lett. 2001, 86, 3052. (28) Schumacher, C.; Gonzalez, J.; Wright, P. A.; Seaton, N. A. J. Phys. Chem. B 2006, 110, 319. (29) Wooten, F.; Winer, K.; Weaire, D. Phys. Rev. Lett. 1985, 54, 1392. (30) MacElroy, J. M. D.; Raghavan, K. J. Chem. Phys. 1990, 93, 2068. (31) Pereira, J. C. G.; Catlow, C. R. A.; Price, G. D. Chem. Commun. 1998, 13, 1387. (32) Zhdanov, V. P. Elementary Physicochemical Processes on Solid Surfaces Plenum Press: New York, 1991. (33) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1987. (34) Wolf, D.; P. Keblinski, P.; S. R. Phillpot, S. R.; Eggebrecht, J. J. Chem. Phys. 1999, 110, 8255. (35) Fennell, C. J.; Gezelter, J. D. J. Chem. Phys. 2006, 124, 234104. (36) Carre, A.; Berthier, L.; Horbach, J.; Ispas, S.; Kob, W. J. Chem. Phys. 2007, 127, 114512. (37) Kertesz, J. J. Phys. Lett. 1981, 42, 393. (38) Park, I.-A.; MacElroy, J. M. D. Mol. Simul. 1989, 2, 105. (39) Rintoul, M. D. Phys. Rev. E 2000, 62, 68. (40) Hofling, F.; Franosch, T.; Frey, E. Phys. Rev. Lett. 2006, 96, 165901. (41) Hoshen, J.; Kopelman, R. Phys. Rev. B 1976, 14, 3438. (42) Al-Futaisi, A.; Patzek, T. W. Physica A 2003, 321, 665. (43) Cabriolu, R.; Ballone, P. Phys. Rev. B 2010, 81, 155432. (44) Keating, P. N. Phys. Rev. 1966, 145, 637. (45) von Alfthan, S.; Kuronen, A.; Kaski, K. Phys. Rev. B 2003, 68, 073203. (46) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897. (47) Desu, S. B. J. Am. Ceram. Soc. 1989, 72, 1615. (48) Haupfear, E. A.; Olson, E. C.; Schmidt, L. D. J. Electrochem. Soc. 1994, 141, 1943. (49) Yin, M.-Z.; Yao., X.; Zhang., L.-Y. J. Zhejiang Univ., Sci. 2004, 5, 422. (50) Mountsier, T. W. Chemical Vapor Deposition of Low Density Silicon Dioxide Films. U.S. Patent 6,054,206, 2000. (51) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726. (52) Altemose, V. O. J. Appl. Phys. 1961, 32, 1309. (53) Chakravarty, C. J. Phys. Chem. B 1997, 101, 1878. (54) Raghavan, K.; MacElroy, J. M. D. Mol. Simul. 1991, 8, 93.
13063
dx.doi.org/10.1021/la2031329 |Langmuir 2011, 27, 13052–13063
