Znd. Eng. Chem. Res. 1994,33, 2607-2617
2607
Chemical Vapor Deposition of Solid Oxides in Porous Media for Ceramic Membrane Preparation. Comparison of Experimental Results with Semianalytical Solutions George Xomeritakis and Yue-Sheng Lin' Department of Chemical Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0171
Explicit equations correlating chemical vapor deposition (CVD) conditions and substrate parameters to the deposition zone thickness, location of maximum deposition, and pore size evolution of a modified counterdiffusion CVD process (MCVD)are derived from recently developed semianalytical solutions. The permeability reduction ratio and the substrate average pore size as a function of deposition time are calculated using the semianalytical solutions and substrate pore size distribution data. Recently reported experimental data of CVD of ZrOz, TiO2, and A1203 in porous substrates are compared with the theoretical results in terms of the location of maximum deposition, deposition zone thickness, permeability reduction ratio, change in average pore size, and pore closure time. The theoretical results agree reasonably well with the experimental findings and provide a n improved insight into the MCVD process for ceramic membrane fabrication.
Introduction Inorganic membranes have recently attracted increasing attention because of their unique properties like mechanical, chemical, and thermal stability as well as their potential for use in high temperature gas separation and membrane reactor applications (Lin and Burggraaf, 1993). Inorganic membranes are conveniently divided, based on their structure, into porous and dense membranes. Conventional porous and dense membranes have rather different characteristics as regards separation ability. Porous membranes usually exhibit good mechanical strength and high permeation flux because of their open pore structure, but relatively low separation factors which limit their applications mostly in liquid-phase separations. Dense membranes offer greater potential for gas separations because of the higher selectivity for permeation of specific gases that are compatible with their crystal structure. However, their poor mechanical strength and low permeation flux compromise their unique characteristic of high specific gas selectivity (Uemiya et al., 1991). A potential technology that may maximize the separation power (=permeation flux selectivity) of inorganic membranes is the preparation of inorganic membrane composites that may combine the advantageous properties of both porous and dense inorganic membranes. Such composite membranes consist of a thick, porous membrane substrate and a thin permselective layer (either dense or microporous) supported upon or inside the porous substrate. The separation action of the membrane is accomplished mainly in the thin permselective layer while the role of the porous substrate is to provide the required mechanical strength for the former, without imposing significant mass transport resistance to the permeating mixture. By using the concept of composite membranes, it is possible t o achieve a unique combination of good mechanical strength for the membrane together with high perme-
+
* To whom correspondence should be addressed. E-mail:
[email protected] oaaa-5aa~t9412633-2607$04.50/0
ation flux and selectivity toward specific gases (Lin and Burggraaf, 1992). Various types of inorganic composite membranes may be prepared by the chemical vapor deposition (CVD) route. One particular type of membrane composite consists of a thin dense permselective layer, usually solid oxide having high selectivity for a particular gas. The permselective layer may be oxygen semipermeable yttria stabilized zirconia (Lin et al., 1992) or hydrogen semipermeable silica, titania, alumina, and boria (Gavalas et al., 1989; Tsapatsis et al., 1991; Tsapatsis and Gavalas, 1992) supported inside or upon a porous membrane substrate. Such a membrane may be prepared by a relatively new counterdiffusion CVD or modified CVD (MCVD) process. In this process, vapor precursors of the dense layer (usually a metal chloride and an oxidant) are separately introduced from opposite sides of a porous membrane substrate. The precursors are allowed to counterdifise inside the membrane pores and react to form solid product which plugs its pores. Since any remaining porosity allows direct contact of the vapor precursors, it is assured that a gas-tight solid layer will be formed by this CVD process. The CVD process may also be applied in order to modify the pore size or pore surface chemistry of ultrafilrtation membrane top-layers coated on coarse pore substrates by the sol-gel process (Miller and Koros, 1990; Kitao and Asaeda, 1991; Lin and Burggraaf, 1992) or of porous glass membranes having a symmetric structure (Okubo and Inoue, 1989; Megiris and Glezer, 1992). Although CVD offers the potential for preparation of inorganic membranes with high separation power, only a few studies have been devoted t o the experimental and theoretical investigation of this interesting application of CVD. However, considerable research efforts are anticipated in the near future for the development by the CVD or CVD/EVD (electrochemical vapor deposition) processes of various types of composite inorganic membranes useful for gas separation. The success of such efforts depends critically on a theoretical understanding of the CVD process for inorganic membrane preparation. Of major importance for the development
0 1994 American Chemical Society
2608 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 1. Definition of Dimensionless Parameters in CVD Semianalytical Solutions" N = 1. M = CP oarameter N > 0. M > 0
LE
A
-
-+ -L--
---L'"-
ir----
LA
- 1
k-
B
28
L
z
( 0). They deposit was inside the substrate (i.e., 2 also reported that 20 min deposition of ZrO2 in the a-Al2O3 substrate narrowed the substrate average pore size (determined by permporometry) down to 20 nm (with LB = 5 pm and a = 0.95). These results are different from those of Lin and Burggraaf (1992) and can be explained by the difference in the experimental conditions between these two studies. In the work of Cao et al., a higher CA"(ZrCl4 vapor concentration) and lower deposition temperature could increase the consumption rate of water vapor. As a result, the water vapor was not in excess in their CVD experiments and a quasi-zero reaction order with respect to water vapor could not be assumed. Therefore, CVD of ZrO2 from ZrC4 and water vapor under the conditions reported by Cao et al. could be better described by reaction kinetics with N = 1 and M = 2. This kinetics would give 2 , > 0, as shown by eq 4c in Table 2. For N = 1 and M = 2, the permeability reduction ratio a(t) and the average pore size, R a m , at the location of maximum deposition Z,, which is that actually measured by permporometry (Cao et al., 1993b1, were calculated using eqs 11 and 17:
with known PSD for the substrate (in Figure 4) and LB = 5 pm. The calculated a(t) and Ram/Rkvois plotted vs t in Figure 8 (assuming a value of c B o =1.0 x mol/ m3),and a semiquantitative agreement is observed with the experimental data. Based on this simulation, pore closure takes place after about 40 min deposition, which
is consistent with the experimentally observed value (about 50 min) of Cao et al. (1993~). CVD of YSZ in porous alumina substrates was also reported by Carolan and Michaels (1987). The results of this work are summarized in Table 8. In this work, two different substrates were used. In one type of substrate with 0.5 pm pores, the thin YSZ film was penetrating the chloride surface of the substrate up to a thickness of 5 pm. In another type of substrate with 30 pm pores, the film was penetrating the substrate up to a thickness of about 60 pm. The calculated pore closure time was about 31 min for the 30 pm pore substrate and about 11min for the 0.5pm pore substrate, based on the model with N = 1 and M = 2, while the experimentally observed pore closure times varied from 10 to 30 min in this study. Therefore, the predictions based on our solution are in good agreement with the experimental results of Carolan and Michaels. Note that the model with N = 1,M = 0 resulted in an almost 100-fold underprediction of the pore closure times of the substrates used in this study. The reaction rate constant for CVD of ZrO2 in a - A l 2 0 3 substrates of Carolan and Michaels (1987) was also calculated from their reported experimental results. These data of K are also given in Table 8. The rate constants calculated for each case of N and M are slightly different for the two types of substrates used, i.e., those for substrate 2 are 2-3 times larger than those for substrate 1. Since estimation of K is very sensitive to the value of LB as suggested by eq 6, the observed differences may be attributed t o the error in estimating LB. The reaction rate constants for CVD reaction of Carolan and Michaels with N = 1 and M = 2 are about 10 orders of magnitude larger than those of Lin and Burggraaf (see Table 7). The chemical reaction and substrate material were the same in the two studies. The difference in the pore size and deposition temperature in the two works cannot explain such a large difference in the reaction rate constant. It is possible that the origin of this difference is the selected value of the CVD rate order, M . As can be seen from eqs 6b and 6c in Table 3, the estimation of K is very sensitive to the value of M , whereas the estimation of t,l is not, as can be seen from eqs 7b and 7c in the same table. For example, assumption of CVD rate orders N = 1 and M = 1 would result in K = 6.8 x lo6 m4-rnol-%l, which is numerically much smaller than the value reported in Table 8. Therefore, it is suggested that the significantly larger value of K for the results of Carolan and Michaels has resulted from the selected value of M , since the true values of N and M are unknown. Gavalas and his co-workers employed the CVD method to prepare Ha-semipermeable dense oxide membranes
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2615 Table 9. Results of Gavalas and Co-workers(Gavalas et al., 1989; Tsapatsis et al., 1991; Tsapatsis and Gavalas, 1992)O precursor (A) precursor (B) oxide (S) T("0 CA' (moVm3) Cg0 (moVm3) LB e m ) Z, ern) exptl t,] (min) K(m4-mol-1.s-1) ( N = 1 , M = 1) K(m7.mol-2.s-1) (N= 1 , M = 2 ) calcd t , (min) ~ ( N = 1 , M = 1) calcd t,l (rnin) (N= 1,M=2)
450 3.33 1.99 45 100 30 1.8 x
Tic4 HzO Ti02 600 2.75 1.65 30 100 20 8.2 x
3.2 x
2.5 x
32.8
24.0
23.8
40.1
21.3
15.7
15.5
26.1
HzO Azo3
lo-* lo-*
450 3.33 1.16 28 40 15 8.0 x
3.7 x
800 2.24 0.78 40 75 30 5.0 x low4
lo-'
2.4 x 10-1
a Deposition in porous Vycor glass substrates (L= 1.1mm, ro = 2 nm, t = 3). "he K were evaluated by eqs 6 and experimental
t,l were evaluated by eqs 7 and LB values. A corrected value of CA' was used based on experimental
LB values. The calculated
zn.
supported in porous Vycor glass tubes. In one particular study (Tsapatsis et al., 19911, thin dense films of Si02, TiOz, A12O3,and BzO3 were deposited by the reaction of the corresponding chloride precursors with water vapor. Their results of deposition of Ti02 are summarized in Table 9. The Ti02 films deposited in Vycor tubes were located 100 pm inside the membrane pores from the chloride side and had a thickness ranging from 30 to 45 pm, depending on the deposition temperature. The experimental pore closure times were 30 and 20 min for deposition at 450 and 600 "C. The estimated pore closure times were 21-33 and 16-24 min, respectively, which suggests that the predictions of our solution are in good agreement with these results, shown in the second column of Table 9. More detailed characterization data together with a kinetic model were presented by Tsapatsis and Gavalas (1992) for deposition of Si02 and A 1 2 0 3 inside Vycor glass tubes by the vapor phase hydrolysis of the corresponding chlorides. The solid deposit profiles obtained by electron microprobe analysis (EMA) exhibited a rather wide oxide distribution starting from the chloride side of the membrane which was followed by a sharp maximum a few tenths of microns inside the membrane. This distribution may be explained by an initial conventional MCVD stage until membrane pores are plugged to a critical extent, followed by a second stage where only water vapor can further diffuse through the remaining openings toward the chloride side to react close to the other membrane side. From the results reported in this study, those reported for formation of A 1 2 0 3 only are summarized in Table 9, since only the profiles of this oxide resembled those of our simulations. The results of silica deposition however where not used because it was not possible to define the profile created by the initial MCVD stage. It is also suggested by the authors that the deposition of Si02 may proceed by a rather different mechanism involving the reaction of Sic14 and H20 vapors with silica surface groups and subsequent condensation of the latter to produce siloxane groups. The A 1 2 0 3 films that were deposited at 450 "C had a thickness of c.a. 28 pm and gave a maximum EMA signal at distance of 40 pm from the chloride side. The
films that were deposited at 800 "C were slightly thicker (40 pm) and gave a maximum EMA signal at a distance of 75 pm from the chloride side. The deeper penetration of the film deposited at 800 "C may be attributed to the lower mass transfer resistance for vapors to enter the membrane pores at this higher temperature. The experimental pore closure times were 15 and 30 min for the films deposited at 450 and 800 "C, respectively. The model predictions are in very good agreement with these figures, i.e., 15-24 and 26-40 min, respectively, as shown in Table 9. The reaction rate constants for CVD of Ti02 and A1203 in the Vycor glass substrates were also calculated from the results reported by Gavalas and co-workers. The predicted results are summarized in Table 9. The reaction rate constants for these two CVD reactions in the Vycor glass substrates are much smaller than those of the reaction for deposition of ZrOz in alumina substrates calculated from the results of Lin and Burggraaf (see Table 7) and Carolan and Michaels (see Table 8). The lower CVD temperature in the works of Gavalas and co-workers may be partially responsible for the much lower reaction rate constants of their results. The entirely different substrate materials and precursors used in these groups of CVD experiments are the major reason for such a large difference in the reaction rate constants.
Conclusions Semianalytical solutions for the counterdiffusion CVD process for ceramic membrane preparation were reported for three specific reaction kinetics. The effects of CVD conditions and substrate parameters on the deposition zone thickness, location of maximum deposition, and pore size evolution could be predicted using the explicit equations summarized in Tables 2 and 3 for the three reaction kinetics. These explicit equations could also be employed to calculate the reaction rate constants from the experimental results of CVD. The permeability reduction ratio and substrate average pore size as function of deposition time were calculated using the semianalytical solutions and substrate pore size distribution data. Recently reported experimental data of CVD of ZrOz, TiOz, and A 1 2 0 3 in porous substrates were compared with the theoretical results in terms of the location of maximum deposition, deposition zone thickness, permeability reduction ratio, change in average pore size, andlor pore closure time. The theoretical results are in good agreement with most of the experimental findings. The explicit equations also provide a better insight into the CVD process and suggest guidelines for the control of the deposition characteristics by varying the CVD experimental conditions. Both the theoretical and experimental data show that for a given deposition time the extent of the permeability reduction depends mainly on the deposition zone thickness, LB,which is controlled by several experimental parameters. If the substrate has uniform pores or the CVD experiments are performed under conditions with nonzero reaction order with respect to either precursor, deposition of solid in the substrate pores could reduce the average pore size. When CVD experiments were performed under conditions with an excessive amount of one precursor (usually oxidant), a quasi-zero reaction order could be assumed for that precursor. Under such conditions, the location of maximum deposition is at the
2616 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
substrate surface exposed to the other precursor (usually metal chloride) and deposition could result in an initial increase in the average pore size of a substrate with a pore size distribution.
Acknowledgment This work was supported by the National Science Foundation (CTS-9216164). One of the authors (G.X.) would like to acknowledge the financial support from Quantum Chemical Co. in the form of a graduate fellowship.
Nomenclature ah
= effective mean molecular velocity of i, m/s
A = metal chloride precursor in CVD reaction B = oxidant precursor in CVD reaction Bo = pore closure rate constant, see Table 1, s-l C," = concentration of reactant i in bulk vapor phase, mol/m3 Cio(eq) = concentration of reactant i based on equilibrium vapor pressure, m0Ym3 F = Knudsen permeation flow rate of membrane pore, molsl K = reaction rate constant, mo11-N-M.m3(N+~-2.s-1 KL = Knudsen flow constant, see eq 9, m~l*m-~*s-l L = thickness of membrane substrate, see Figure 1, m LB = thickness of solid deposit inside membrane pore, see Figure 1,m M = reaction rate order for oxidant (B)in CVD reaction Mi = molecular weight of reactant i, kg/mol M s = molecular weight of solid product, kg/mol ni = stoichiometric coefficients of reactants and products in CVD reaction nO(r0) = number pore size distribution of membrane N = reaction rate order for metal chloride (A) in CVD reaction p , q = exponents defined in Xomeritakis and Lin (1994) P"(r0)= pore size distribution of membrane, based on pore cross-sectional area AP = pressure drop across membrane during single gas permeation, Pa r(ro,z,t) = pore radius of substrate pore with initial size ro after deposition time t rav = average pore radius of modified zone, m ro = radius of substrate pore before deposition, m R , = gas constant, J*mol-l*K-l Ram = average pore radius at the location of maximum deposition, m Rkv = flow-averaged pore radius of porous substrate, see eq 15, m Rkvo= initial flow-averaged pore radius of ceramic membrane, m t = deposition time, s t,l = pore closure time of membrane pore, s T = temperature, K z = axial position of pore, see Figure 1, m ZA, ZB = edges of modification zone, see Figure 1,m 2, = location of maximum deposition inside membrane pore, see Figure 1, m Greek Letters a = permeability reduction ratio of substrate, see eq 11 5' = transformation variable defined in Table 4 or the
Appendix
Qs = density of solid deposit, kg/m3 t = tortuosity factor of membrane substrate #(lj,t) = dimensionless pore radius of membrane substrate (=rho) #cr = critical dimensionless pore radius for transition of diffusion mechanism #rn= dimensionless pore radius at maximum deposition location @i = thiele modulus of reactant i, see Table 1
Appendix. Semianalytical Solution of CVD Model with Quasi-Zero Reaction Kinetics with Respect to One Reactant For the special case where one CVD precursor (here reactant B) is in excess compared to the other (reactant A), the CVD model is reduced to two ordinary differential equations representing the conservation of mass equation for precursor A and the evolution of the pore radius profile:
64-21 Assuming N = 1, M = 2 and introducing the dimensionless variables (see Table 1for definition of @A and
BO),
+=-,r r0
y --C A A - ,Ao'
5=
A
''2 8 =Bot (A-3) L'
it is possible to obtain the model equations in a similarity form as shown below:
(A-4)
(A-5) with boundary and initial conditions:
at 5 = 0, YA= 1; at 5 -
03,
0; at 8 = 0,
YA=
+ = 1(A-6)
Equations A-4 and A-5 need to be solved only once in order to obtain the evolution of 4 and YAwith 5 and 8, independent of @A and Bo. Semi-analyticalsolutions of eqs A-4 and A-5 are proposed here based on intuition. For 8 = 0 the solution for YAis:
As time progresses, pore narrows near 5 = 0 which results in increasing mass transfer resistance for precursor A and hence a steeper concentration profile. A reasonable approximation for 0 > 0 is
e = dimensionless deposition time, (=t/t,l)
5 = dimensionless axial pore position (=zfL)
b, (B
= dimensionless edges of reaction zone in porous substrate Ern = dimensionless location of maximum deposition
On the basis of this profile, the pore radius profile can be obtained by solving eq A-5. The result is eq 2 in the
Ind.Eng. Chem. Res., Vol. 33, No. 11, 1994 2617 1 .oo
0.75
dl
0.50
0.25
------
Numerical solution Approximate solution
0.00
0
3
2
1
5 Figure 9. Numerical and semianalytical dimensionless pore radius, 9, vs dimensionless axial pore distance, 5, for three different values of dimensionless deposition time, 0.
main text. Figure 9 provides a comparison of the pore radius 4(f,8) profile as obtained from numerical solution of eqs A-4 to A-6 and as predicted by eq A-8. Note that the CVD process terminates when 8 1.
-
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Kitao, S.; Asaeda, M. Gas separation performance of thin porous silica membrane prepared by sol-gel and CVD methods. Key Eng. Mater. 1991, 61&62, 267-272. Lin, Y. S. A theoretical analysis on pore size change of porous ceramic membranes after modification. J . Membr. Sci. 1993, 79, 55-64. Lin, Y. S.;Burggraaf, A. J. CVD of solid oxides in porous substrates for ceramic membrane modification. AZChE J . 1992, 38, 445454. Lin, Y. S.; Burggraaf, A. J. Experimental studies of pore size change of porous ceramic membranes after modification. J . Membr. Sci. 1993, 79, 65-82. Lin, Y. S.; de Vries, K. J.; Brinkman, H. W.; Burggraaf, A. J. Oxygen semipermeable solid oxide membrane composites prepared by electrochemical vapor deposition. J . Memb;. Sci. 1992, 66, 211-226. Megins, C. E.; Glezer, J. H. E. Synthesis of Hz-permselective membranes by Modified Chemical Vapor Deposition. Microstructure and permselectivity of SiOdCNycor membranes. Ind. Eng. Chem. Res. 1992,31,1293-1299. Miller, J. R.; Koros, W. J. The formation of chemically modified alumina microporous membranes. Sep. Sci. Technol. 1990,25, 1257- 1280. Okubo, T.; Inoue, H. Introduction of specific gas selectivity to porous glass membranes by treatment with tetraethoxysilane. J . Membr. Sci. 1989, 42, 109-117. Rao, M. B.; Sircar, S. Nanoporous carbon membranes for separation of gas mixtures by selective surface flow. J . Membr. Sci. 1993,85, 253-264. Tsapatsis, M.; Gavalas, G. R. A kinetic model of membrane formation by CVD of Si02 and Al203. AChE J. 1992,38,847856. Tsapatsis, M.; Kim S.; Nam S.-W.; Gavalas, G. Synthesis of hydrogen permselective SiOz, TiOz,A 1 2 0 3 and Bz03 membranes from the chloride precursors. Ind. Eng. Chem. Res. 1991, 30, 2152-2159. Uemiya, S.; Sato, N.; Ando, H.; Kude, Y.; Matsuda, T.; Kikuchi, E. Separation of hydrogen through palladium thin film supported on a porous glass tube. J . Membr. Sci. 1991,56, 303313. Xomeritakis, G.; Lin, Y. S. CVD of solid oxides in porous media for ceramic membrane preparation and/or modification. Explicit solutions for deposition characteristcs. Chem. Eng. Sci. 1994, in press.
Received for review February 17, 1994 Revised manuscript received June 22, 1994 Accepted July 6, 1994@ Abstract published in Advance ACS Abstracts, September 15, 1994. @
