742
Ind. Eng. Chem. Res. 1989,28, 742-756
pressure and at four levels of temperature from 973 to 1123 K. These data were found to be correlated with a quadratic equation, and the rate of reaction was obtained from the slope of these curves. A differential method of analysis was introduced to determine the empirical rate equation. The apparent activation energies were found to be 30.6 and 50.9 kJ/mol, while the reaction orders of aluminum hydroxide and magnesium hydroxide are 0.45 and 0.55, respectively. A reaction sequence for the decomposition reaction was proposed assuming that the dehydration reaction was a rate-limiting step, although other steps at equilibrium favored the forward direction of decomposition reactions. These products were identified as y-alumina and magnesia by using XRD. Nomenclature a , a’ = order of reaction A1,(OH)B, = aluminum hydroxide = [Al(OH)& Mg,(OH)2, = magnesium hydroxide = [Mg(OH),], [C], [C’] = weight fraction of hydroxides, wt % E , E’ = apparent activation energy, kJ/mol k,, k b = frequency factor k , k’, k,, kl’, k-l, k-l’, k”, k”’ = reaction rate constants
m , n = uncertain integer number R = ideal gas law constant r = rate of reaction, wt % / s T = absolute temperature, K t = time, s Registry No. Al(OH),, 21645-51-2; Mg(OH)2, 1309-42-8.
Literature Cited Hattori, H.; Tanaka, Y.; Tanabe, K. J. Am. Chem. SOC.1976, 98, 4652. Hightower, J. W. The Use of Heterogeneous Catalysts. Sections B and D, Houston Intensive Short Course, 1975. Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; Wiley & Sons: New York, 1978; Vol. 2, pp 218-240. Levenspiel, 0. Chemical Reaction Enguneering; Wiley & Sons: New York, 1983; pp 67-76. Miyahara, K.; Murata, Y.; Toyoshima, I.; Tanaka, Y.; Yokoyama, T. J . Catal. 1981, 68, 186. Windholz, M. The Merck Index, 10th ed.; Merck & Co.: Rahway, NJ, 1983; pp 52, 811.
Received for review September 2, 1987 Revised manuscript received September 8, 1988 Accepted January 13, 1989
MATERIALS AND INTERFACES Analysis and Construction of Multilayer Composite Membranes for the Separation of Gas Mixtures Kevin A. Lundy and Israel Cabasso* The Polymer Research Institute and Chemistry Department, College of Environmental Science and Forestry, State University of New York, Syracuse, New York 13210
Multilayer composite membranes suitable for separating gas mixtures have been synthesized and studied. Fundamental features associated with mass-transport phenomenon in three types of composite membrane structures are described. The structures studied are ultrathin rubbery layers (poly(aminosi1oxane)) deposited on anisotropic porous glassy support (polysulfone), and dense isotropic and anisotropic (asymmetric) glassy layers (poly(dimethylpheny1ene oxide)) deposited on the former. Electron microscopy techniques (SEM, TEM), gas permeation experiments (02, N2), and the resistance model analogue are used layer the determination of structure-permeability relationships. A correlation between the thickness of the deposited layers, surface porosity of the porous support, and the membrane’s permeability and selectivity is given. The results show that the available surface for transport depends largely on the thickness and permeability of the rubbery layer for both the two- and three-layered composites. In the latter, the thickness ratio of the glassy separating layer to the rubbery intermediate (channeling) layer can be adjusted to render maximum surface area (which is otherwise limited by the surface porosity of the support). Introduction Separation of gas mixtures by selective permeation through nonporous polymer membranes has attracted much attention during the past 2 decades. Although considerable progress has been made in the development of permselective membranes, the intrinsic parameters that control diffusivity and solubility of permeating species in polymer matrices impose inherent limitations for mem-
* To whom correspondence should be addressed. 0888-5885/89/2628-0742$01.50/0
brane separation processes, that is, insufficient permeability for dense, isotropic membranes. Membrane productivity, however, can be increased with a decrease in membrane thickness to a level that often jeopardizes the mechanical integrity of the membrane, especially when the driving force for permeation is a pressure gradient. In order to obviate this problem, anisotropic membranes have been developed (Loeb and Sourirajan, 1963; Cabasso, 1987). Such membranes consist of an ultrathin skin resting on a progressively porous structure which does not provide significant resistance to the mobility of the permeating 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 743 species. Thus, permselective layers of less than 0.1 pm, resting on a porous supporting structure of about 100 pm, have served successfully in a number of separation processes. Two families of membranes have evolvedasymmetric and thin film composites. In the first type, the dense layer and the supporting porous structure are comprised of the same polymer. This type of membrane is prepared through an anisotropic coagulation of a polymer solution yielding a densified permselective surface growing out of the porous matrix. The second family, the composite membrane, consists of a porous substrate coated by an ultrathin layer of another polymer(s) (Ward, 1981; Henis and Tripodi, 1980a,b). Permeability and selectivity of composite membranes depend on the properties of the permselective layer as well as the surface porosity of the support. The main thrust of the present work is focused on the chemical and physical parameters involved in the performance of composite membranes for gas permeation and separation. Some of the advantages and shortcomings of this type of membrane will also be discussed in the following text. Multilayered Membranes for Gas Separation. The introduction of composite polysulfone membranes for gas separation (Henis and Tripodi, 1980a,b, 1981,1983) by the Monsanto Company, designated Prism, has been a major breakthrough regarding the practicality of membrane technology for gas separation processes. The membrane unit employs an asymmetric hollow fiber membrane of which the skin is the separating entity. The membranes have been coated with ultrathin layers of rubbery polymers, eliminating the possibility of viscous flow of the permeant through the skin’s imperfections. This ultrathin coating is prepared from a highly permeable polymer such as cross-linked silicone rubber (Henis and Tripodi, 1981). Although treated (sealed) with a protective coating, these membranes are conceptually similar to the asymmetric membranes and differ significantly from the principles that have led to the successful development of thin-layer composite membranes for reverse osmosis (Riley et al., 1967; Caddotte, 1985; Cabasso, 1981). In the latter, a thin layer consisting of two principal zones is deposited on a highly porous support (Riley et al., 1967; Cabasso, 1985; Cabasso and Lundy, 1986). The first zone is the permselective layer which interfaces with the feed mixture. The second zone is an intermediate layer which channels the permeate into the surface pores, rendering the entire membrane surface area (and not only that defined by support surface porosity) available for transport. The principal advantages of these thin film composites over the asymmetric membranes are 2-fold: (i) The need to develop a rather complex casting or spinning method for the production of a defect-free asymmetric structure from polymers having a desired permselectivity is eliminated; in fact, many polymers cannot be cast and spun to yield this structure. (ii) A large variety of polymers can be feasibly employed because the quantity of the polymer required to deposit such a permselective layer (e1pm) is much lower than that used in the preparation of the porous supporting material. In most instances, readily available polysulfone, polypropylene, or glassy porous supports, ca. 100-200 pm thick (primarily in anisotropic configurations),can be adequately employed. The objective of this study was to provide experimental data from which quantitative analyses can be drawn, thus providing framework from which the principles of the composite membranes shown in Figure 1 can be extended to gas permeation and separation. This study identifies
PS P o r o u s S u p p o r t
PPO C o a t i n g PAS C o a t i n g
PS P o r o u s S u p p o r t
Figure 1. Illustration depicting cross sections of (a) polysulfone porous support, (b) two-layer composite membrane consisting of support coated by a single layer of poly(aminosiloxane), and (c) three-layer composite membrane consisting of PS/PAScoated by an additional layer of PPO.
two- and three-layer composite membrane systems (Figure 1). The first is comprised of a polysulfone porous substrate coated by an ultrathin layer of poly(aminosi1oxane)(PAS) with different degrees of cross-linking (Figure lb); in the second, the cross-linked poly(aminosi1oxane)layer is topped with poly(2,6-dimethyl-l,4-phenylene oxide) (PPO) (Figure IC). In the first, the poly(aminosi1oxane) serves as a permselective layer; in the second, it serves as an intermediate layer which channels the permeate to surface pores in the support. Preliminary Considerations Based on the Resistance Model. Membranes consisting of two (or more) layers laminated together are referred to as composite membranes. Analogous to the flow of current in an electrical circuit, Henis and Tripodi (1980a,b, 1981, 1983) showed that the ultimate properties of the composite membranes depend on the respective resistance of the component layers. In the case of the Prism membranes, the total resistance to gas flow depends on the resistances of the coating material, the substrate material, and the pores filled with coating material (Pinnau et al., 1988). This analogy is depicted in Figure 2a. The resistance (R’) of each component of the composite membrane to the gas flow is given by 1 R‘= PA
where 1 is the thickness of the component, P is the permeability coefficient of the penetrant in the material, and A is the relevant surface area. The total resistance (RT)of the composite membrane to the flow of a given gas is calculated in the same manner as the resistance of an analogous electrical circuit. For the case of a composite membrane consisting of two dense, defect-free layers la-
744 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 P o i o u ~ Gla%w
Coal
/
Plugged
._ __.
PPO L a y e r
-PAS
Layer
FS S u p p o r t
thickness ratio of the two layers determines the contribution of each to the overall separation. In the case of three-layer composite membranes, Figure IC,where the porous support shows no resistance to transport, the overall ideal separation factor, a*T(A/B), derived from eq 5 and 6 is given by
The presence of defects in the permselective layer (i.e., PPO in this study) can be quantified by using the resistance model (Figure 2b). When the resistance of the supporting layer is negligible, the total resistance, RT, to gas flow of the membrane shown in Figure 2b can be defined as
I" Ib)
(a)
Figure 2. Resistance model analogue for (a) Monsanto's Prism separator membrane and (b) PS/PAS/PPO composite membrane, taking into account the contribution of defects in the surface layer. RD is the resistance of the intermediate layer exposed by defects in the surface;R1and R2are the resistances of PPO and PAS, respectively.
minated together, R T is simply the sum of the resistances of the individual layers: IT
RT=--
- -I1
+- l 2
PTA PIA P2A where PTand ZT are the overall permeability and total thickness of the dense layers, respectively, and the subscripts 1and 2 refer to the separate layers comprising the composite membrane. The resistance of the porous support is considered marginal but can be added if necessary. For the Prism-type composite membranes, it may be shown that (Henis and Tripodi, 1981) (3)
where Rc is the resistance of the two layers (i.e., R1 and R2), and R D is the resistance of the PAS exposed by the defects in the top layer (Figure 2b). Here, Rc is merely the s u m of two resistances connected in series. Therefore,
where Zl and Z2 refer to the thicknesses of the layers and Al is the surface area of the top layer excluding the defects. The resistance of the intermediate layer exposed by defects is (Figure 2b) z2
RD
=-
where A D is the area of the defects. Note that the resistance of the defects within the top layer is considered negligible since it is only the area of the intermediate layer exposed by them that is taken into account in eq 8-10 and Figure 2b. Since Rc and R D are combined in parallel (Figure 2b), the total resistance for the three-layer composite membrane will be
where the subscripts refer to the segment of the membrane indicated in Figure 2a. Assuming the surface area of the defects to be small compared to the total surface area, it may be shown that the permeability factor ( p = P/Z) is given by
+-+PIAl
where AP is the surface area of the pores and AT is the total surface area of the membrane. Some of the conclusions derived from eq 2 concerning the two deposited layers (Figure 2b) are of primary interest in the present study. This equation suggests that the overall permeability, PT,depends on the ratio Z1/Z2, as shown from the rearrangement of eq 2:
where 8 = Z1/Z2. The ideal separation factor of a membrane toward a two-component gas mixture is defined as (6) a*(A/B) = P(A) /P(B) where P(A) and Pm)are the permeability coefficients of two pure gas components. Consequently, the ideal separation factor of three-layer composite membranes as depicted in Figure IC(i.e., porous support topped with two different polymer layers) will also be dependent on 8. That is, the
(10)
P2AD
P2A1
P2AD
Defining the term f = A D / A T as the defect ratio of the membrane, where AT is the total membrane area, RT becomes
(
I1 Pd1-f)
+ P , (l2l - f )
)" pzf
The total resistance, RT, can be calculated for a given membrane/penetrant system, and the resulting values can be used to calculate permselectivity of the membrane. This study verifies to a great extent the above considerations. Of special concern to this study were the ramifications drawn from eq 7 concerning the dependence of the permselectivity on the layer's thickness ratio.
Experimental Section Materials. The polysulfone membrane was kindly provided by Robert Riley, San Diego, CA, to whom we are in debt. The manufacturer's designation for this product
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 745 Table 1. Structure and Properties of Poly(aminosi1oxanes) (Tsai, 1985) designation PAS I1
structure CH3
CH3
CH3
I I I CH3SiO+SiO~SiO+ I CH3 I I CH3 CH2 I H3CCH
CH3
I SiCH3 I CH3
amine mol ?%
degree of polymerization
M""
10
300
13800
8
300
24OOOb
I
CH2NHCH2CH2NH2
PAS IV O
(same as PAS 11)
From intrinsic viscosity.
Extrapolated value.
Table 11. Permeabilities of Or and Nrand Permselectivity for Two-Layer Composite Membranes Prepared by Depositing PAS IV on Polysulfone Porous Support lOsP,cm3cm-? s-l (cmHg)-' P,barref PAS concn, PAS layer membrane w t ?% in hexane thickness, pm 0 2 N2 0 2 N2 a* 6.70 27.0 10.9 181.0 73.2 2.5 1025-3 8 1111-1 4 2.80 41.1 16.2 115.0 45.4 2.5 1111-2 4 2.22 55.5 22.6 122.0 50.1 2.4 1111-3 4 0.98 43.6 17.1 42.7 16.8 2.5 1129-2 2 0.27 103.0 43.0 27.8 11.6 2.4 1129-3b 2 0.44 41.1 14.4 18.1 6.34 2.9 "P(barrer) = 1OloP cms (STP) cm s" cm'* (cmHg)-'. bNote that this sample displays a much higher a* (probably due to excessive cross-linkingwithin the PAS layer).
was E-183, and it was reported to have a hydraulic permeability, Lp, of 95 X lo+ g of H20cm-2 s-' atm-' (note that Lp was incorrectly identified as the air permeability in Cabasso and Lundy (1986)). The polysulfone was supported by a backing fabric, and its cross section is shown in Figure 3. The total thickness of the polysulfone layer was ca. 80 pm. Poly(aminosi1oxanes)(PAS)used in preparing the composite membranes were experimental samples which were provided by Dr. Gordon Fearon of Dow Corning Corp., Midland, MI. The structure and properties of these materials are described in Table I (Tsai, 1985). Toluene diisocyanate (TDI) was used as the cross-linking agent for the poly(aminosi1oxanes). This reagent was obtained from Aldrich Chemical Co., Milwaukee, WI. Technical grade TDI (Lot 090697) was used. According to the manufacturer, the reagent contained 80% toluene 2,4-diisocyanate and 20% toluene 2,6-diisocyanate. Poly(2,6-dimethyl-l,4-phenyleneoxide) (PPO), M, of 23 400, was supplied by General Electric Co., Schenectady, NY. All solvents used were reagent grade. Preparation of Composite Membranes. (1) TwoLayer Composite Membrane, Poly(aminosi1oxane) on Polysulfone (PAS/PS), Figure 1b. Poly(aminosi1oxane) (PAS) was deposited on the surface of flat sheet polysulfone anisotropic porous supports by flooding the surface with a solution of the PAS. This was done in the following manner: A rectangular sheet (7 X 14 cm) of polysulfone membrane, secured in a frame with the top surface exposed, was flooded with PAS solution (2-8 wt % in hexane) and allowed a residence time of 10-30 s. The frame was then tilted in one direction and the solution flowed evenly over the surface; excess solution was collected through a groove in the frame, leaving behind an evenly coated surface. The solvent was allowed to evaporate from the coated surface for 5-10 min, a sufficient period of time for the removal of the hexane. Birefringence of the deposited layer could often be observed. The PAS was then crosslinked with a solution of TDI in hexanes (2 wt %), which was applied to the surface in a similar manner. Cross-
Figure 3. Scanning electron micrograph of three-layer composite membrane consisting of (a) poly(2,6-dimethyl-l,4-phenylene oxide), (b) poly(aminosiloxane), and (c) polysulfone anisotropic porous support.
linking of the poly(aminosi1oxane) layer proceeded, as depicted by the reaction scheme shown in Figure 4. Subsequent heat treatment was employed to complete the reaction by placing the membrane in an oven for 10-15 min a t 90-95 "C. There is a direct correlation between the concentration of the PAS coating solution and the thickness of the de-
746 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
7% s i-0-SCE3 i-0 I I
~ ~ ~ FE3 i - o - ~ i ~ o cE3 y 2 CE3-CE CE2-NE-CE2-CE2-NR-C-0
CR3 CR I 2 CE3-CE CR2-NR-CEz-CR2-NE2
+
0-C-N
Q H-C-0
+
-
R2N-CE2-CR2-NR-CRI 2
-
AC-CE3 E C CE
i i -'
o' i -o-
i
CE3
CE3
% NR
O-C-NE-CR2-CE2-NR-CE EC-CE3 I 2
E27 A 0-s
y 3 i
i-o-?
CE3
CE3
Figure 4. Schematic diagram of cross-linking reaction between poly(aminosi1oxanes) and toluene 2,4-diisocyanate.
posited layer, as shown in Table 11. A longer residence time for the PAS application solution yielded increases in the concentration due to solvent evaporation, resulting in thicker depositions from solutions of the same initial concentration. This can also be achieved by multiple applications of the PAS/hexane solution prior to the application of the cross-linking agent, as was done in the deposition of samples 1111-1, 1111-2, and 1111-3shown in Table 11, in all of which two applications were performed with an elapsed time of 2-3 min between applications. (2) Three-Layer Composite Membrane, PPO/ PAS/PS, Figures IC and 3. Two methods were employed for coating membrane surfaces with ultrathin layers of PPO. The first used the PAS/PS membranes described in the previous section employing a similar procedure; i.e., a dilute solution (1wt %) of PPO in carbon tetrachloride was introduced onto the surfaces of the PAS/PS membranes and allowed to flow across the surface of the membrane, resulting in a deposition of an ultrathin layer of PPO. In order to compare membrane performance before and after coating with PPO, a second method was employed for coating the already tested PAS/PS composite membranes. The PAS/PS composite membrane was affixed to a glass cylinder (diameter 10 cm) with the PAS surface exposed (Lundy, 1987). The cylinder was then rotated, while the membrane surface was interfaced with PPO solution (1wt %) and then removed. The solvent was allowed to evaporate from the surface of the membrane, leaving an ultrathin film of PPO resting on the surface of the cross-linked poly(aminosi1oxane)(Figure 3). (3) Two-Layer Composite Membrane, PPO/PS, Figure 5. Neither of the above methods were practical for depositing PPO directly on the surface of the anisotropic polysulfone. Problems associated with composite membranes in which two glassy layers are in contact with one another were discussed elsewhere (Lundy, 1987). The difficulties associated with such depositions become progressively greater when exceedingly thin layers are desired. This is especially true when the support surface contains blemishes such as those frequently found in the PS anisotropic substrate. For these reasons, a method similar to that previously developed (Ward, 1981; Browall and Salemme, 1975; Ward e t al., 1976; Lundstrom, 1973) was used to produce PPO/PS membranes. In this method, ca. 1 mL of PPO (4 wt %) solution in chloroform was deposited from a pipet held 1-2 cm above the surface of a rectangular water bath (45X 30 X 15 cm) at ambient temperature. Upon contact with the bath, the solution immediately spread to form an ultrathin layer floating on the water. The chloroform evaporated, forming a PPO film which was laminated to the surface of the polysulfone membrane. This was ac-
Figure 5. Scanning electron micrograph of PPO/PS composite membrane. The PPO consists of three layers cast on water surface and subsequently laminated on the surface of PS anisotropic support. (a) PPO; (b) PS.
complished by securing the PS support to the surface of a glass cylinder, which was immersed in the water bath beneath the floated PPO film and lifted in a way that allowed deposition of the film on the surface of the attached polysulfone support. All attempts to produce a defect-free singlecoating PPO/PS membrane by this method failed. The membrane shown in Figure 5 was produced by laminating three layers. These authors feel, however, that a defect-free PPO/PS coating can be prepared by a single deposition using PPO of much higher molecular weight ( M , >lOOO00). Membrane Evaluation. Membranes were evaluated for their permeability to pure oxygen and nitrogen from which the ideal separation factor was calculated. Actual separation of air delivered from a compressed air cylinder was measured from permeate compositions (oxygen and nitrogen) determined by gas chromatography. Permeability of gases through the membranes was measured by using the apparatus shown in Figure 6. The apparatus consists of a compressed gas supply, a permeation cell, and a soap bubble flowmeter. The permeation cell is a circular cell exposing membrane area of 10-40 cm2. Permeabilities were measured for pure oxygen and nitrogen and for air (i.e., 20.8% 02).Compressed gas from the cylinder was fed to the cell employing a regulator, which was used to vary the pressure of the feed. The permeate was routed to a soap bubble flowmeter to mecsure permeation rate or to a GC. A permeability factor, PT, was calculated from the following equation:
where PTis the permeability coefficient, t is the time required for a bubble to displace a volume, AV, of gas in the
Ind. Eng. Chem. Res., Vol. 28,No. 6, 1989 747
I
Figure 6. Schematic diagram of membrane testing apparatus. (a) Gas cylinder, (b, d) pressure gauges, (c) membrane testing cell, (e, g, j) valves, (h) GC sample collection ports, (1) vacuum pump, (m) gas chromatograph.
flowmeter, A is the surface area of membrane, and Ap is the pressure difference across the membrane. The thicknesses of PPO and PAS layers in the composite membrane were determined by scanning electron microscopy, SEM. The ideal separation factor was calculated from the ratio of the permeability coefficients of oxygen and nitrogen, Le., eq 6. Stage Separation Factor. The apparatus depicted in Figure 6 was also used for the determination of the stage separation factor (i.e., the ratio of the product to feed composition) by routing the permeated gas to a gas chromatograph equipped with a 183- X 0.64-cm column packed with molecular sieve 5A, 30-60 mesh. Two types of experiments were conducted to show the dependence of the stage separation factor (cy) on the pressure difference and pressure ratio across the membrane. In the first, the feed (air) pressure was increased from 69 to 690 kPa, in increments of 69 kPa, by adjusting the pressure regulator. The product collected a t each increment of pressure was analyzed by a gas chromatograph equipped with a gas sampler. The feed outlet valve was fully opened during operation, allowing separation to occur a t relatively low stage cut (less than 5 % ) . The maximum pressure ratio in this measurement was relatively low, less than 7. Higher pressure ratios were achieved by evacuating the downstream side by means of a vacuum pump connected to the product outlet of the sample valve. The downstream side was evacuated to a pressure of 0.69-0.069 kPa while maintaining the feed side of the membrane a t a constant 138 kPa. This method allowed for a greater pressure ratio, and consequently higher separation factors were reached. In both types of experiments, a t least three reproducible measurements were recorded after the membrane was allowed to equilibrate to operating conditions. Electron Microscopy Measurements. Membrane thickness as well as other aspects of membrane morphology was determined by employing scanning electron microscopy (SEM) techniques (Figure 3). Most of the membranes were evaluated subsequent to testing. The samples were freeze-fractured in liquid nitrogen and mounted edgewise on aluminum stubs. Two specimens approximately 1 X 0.5 cm were mounted on each stub and then spattered with gold/palladium coating using a Hummer I1 plating device. Three 30-9 pulses with a 90-9 cooling period between each were employed in order to avoid damage to the structure. Surface porosity and topology of the polysulfone were assessed by transmission electron microscopy (TEM) using
Figure 7. Transmission electron micrograph replicas of the surfaces of two commercial polysulfone anisotropic porous supports employed in construction of two- and three-layer composite membranes. (a) Membrane support used; (b) PS anisotropic support used in fabrication of thin-film composite membranes for reverse osmosis. This highly open structure failed to support the gas separating ultrathin layers reported herein. (Magnification, X64OOO). Note, the mounded structure reflects the assembly of nodules in the upper surface of the polysulfone.
a shadow replica technique conducted as follows: Specimens of the polysulfone membranes were placed on glass microslides with the surface facing up. Chromium or platinum was shadow cast on the specimens from a 30° angle followed by evaporation of carbon to the surface of the samples. A layer of paraffin was applied to the film surface, and specimens were cut into 3-mm squares and floated on concentrated sulfuric acid for a few hours to dissolve the polysulfone. The replica was then washed in freshwater and placed on a grid where excess paraffin was melted from it. The remaining paraffin was removed from the samples by heating in benzene under reflux. A Jeol 2000x TEM was used for examination of the specimens (Figure 7). Application of TEM techniques to analyze surface morphology of the porous membrane from this laboratory will be discussed in a separate paper.
Results and Discussion Composite membranes composed of poly(aminosi1oxane) deposited on polysulfone anisotropic supports were prepared. These membranes were fully characterized, as described below, before coating with an additional (third) layer of PPO.
748 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 ,
A
2xl.y-
c Nitrogen
0
d
PAS 1 V
, ; / '
I
/"
1
I
5C
I
'C: '56 23G Ppessu-e L j t ^ c z - e i c e
Figure 8. Flux versus pressure difference posite membrane (PS/PAS 11) 1
2::
30:
35:
I
43:
'
n3a
(AP)for two-layer com-
Cxyger
IbO
/So
3bo
i50
do0
Pressure Difference (kPB
3'50
4
Figure 10. Ideal separation factor versus pressure difference (AF') for two-layer composite membranes (PS/PAS 11, PS/PAS IV).
-
"
0 Nitrogei
h
b
0
/'
Oxygen Nitrogen
d / /
,./
, "
c
50
lloo
I50
200
$50
P r e s s u r e D i f f e r e n c e (itPo)
3b0
is0
400
Figure 9. Flux versus pressure difference (AP) for two-layer composite membrane (PS/PAS IV). Table 111. Flux and Ideal Separation Factor for Two-Layer Composite Membranes Consisting of Poly(aminosi1oxane) Deposited on Polysulfone 1035, 1035, cm3/(cm2-s), cm3/(cm2.s), for PAS IV for PAS I1 AD, kPa 0, N, a* 0, N, a* 2.137 0.862 2.45 69 1.360 0.556 2.48 4.608 1.927 2.44 2.739 1.210 2.39 138 7.184 3.005 2.48 207 4.231 1.706 2.39 9.797 4.126 2.47 5.641 2.288 2.37 276 5.408 2.49 7.081 2.844 2.31 12.49 345
Two-Layer Composite Membranes. Permeability to Pure Gases. The composite membranes prepared with poly(aminosi1oxanes) (PAS) are represented by Figure lb. Flux versus pressure plots, obtained with oxygen and nitrogen for PAS I1 and PAS IV, are shown in Figures 8 and 9. The plots are linear for both membranes, and the ideal separation factor is more or less constant at a pressure greater than 100 kPa (Figure 10 and Table 111). The permeability factor, PT, of the gases was calculated according to eq 13. The values of P(0,) for the two memcm3cm-, branes were found to be 4.56 X lod and 2.7 X s-* (cmHg)-', respectively. The flux measured with the uncoated polysulfone support was found to be several orders of magnitude higher than the coated membrane (Figures 8 and 9), confirming that the resistance of the support used in this study to gas permeation can be considered negligible. Therefore, the permeability coefficients ( P )of the gases permeating the PAS layer were calculated from P after obtaining the thickness ( I ) from scanning electron microscopy. The
n
1
I
2
5
I
4
I
5
PAS Layer Thickness (micrometers)
b
Figure 11. Permeability coefficients of oxygen and nitrogen (P) versus PAS layer thickness for PS/FAS IV composite membranes.
calculated values of P(0,) for these membranes (Table TI) were found to be lower than those generally reported for dense isotropic poly(dimethylsiloxane), PDMS, Le., 500-600 barrer. Comparison between PDMS- and PASbased membranes (Lundy, 1987) verifies these observations. Effect of Membrane Thickness on Permeability in PAS/Polysulfone Composite Membranes. A series of six composite membranes consisting of PAS IV deposited on porous polysulfone supports were prepared. Substantial differences in the chemical makeup of the layer would have significantly affected the ideal separation factor, as shown, for example, in comparing PAS I1 and PAS IV, Figure 10, Table 111. The membranes in this series all have the same ideal separation factor, a* = 2.46 f 0.025, suggesting a uniform degree of cross-linking for this series. The permeability coefficients (PT)were calculated for the deposited layer employing eq 13; the thickness was determined from SEM. The permeabilities of oxygen and nitrogen versus PAS thicknesses in this series are given in Table I1 and Figure 11. The data seem to indicate that PTis progressively decreasing with a reduction in the PAS thickness. The PT, in fact, is not expected to vary with effective membrane thickness, unlike PT,which is inversely proportional to the thickness. Plots of P(0,) and P ( N J versus thickness ( I ) for this series are shown and compared with the theoretical curves in Figures 12 and 13. Values for P(0,) and P(N,) (200 and 80 barrer) were extrapolated from the asymptotes of the curves in Figure 11 and used to plot the theoretical curve. The experimental and calculated curves appear to be within reasonable proximity for membranes containing thick PAS layers ( 1 p 2~ 2 gm). Below the 2-pm mark, the experimental results clearly
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 749 m A
Exporimto1 Doto
X
l e
-
m-
Figure 12. Oxygen permeability factor (P(02))versus PAS layer thickness for PS/PAS IV composite membranes. ( 0 )Corresponds to membrane 1129-3, for which the ideal separation factor was much higher than the other samples. (-) Theoretical curve, calculated by dividing the permeability coefficient (P)by the thickness of the PAS layer.
Figure 14. Permeation modes of penetrant in two-layer composite membranes. (a) Diffusion parallel to the pressure gradient; (b) radial diffusion.
0
< L 0 U 4 0
5
VI
o !
0
I
2
I
4
'6
PAS Layer Thickness (micrometers)
I
8
Figure 15. Effective surface area versus PAS layer thickness for permeation of O2 in PS/PAS IV composite membranes. (A) Corresponds to membrane 1129-3 (Table 11).
D i
I
O
I
5
I
I
3
4
Thickness (micrometers)
k
b
I
Figure 13. Nitrogen permeability factor (P(N2))versus PAS layer (see Figure 12).
indicate that the predicted augmentation of P is impeded. Considering that the chemical makeup of the layers is the same for all membranes, the apparent decrease in PT (Figure 11)and the results shown in Figures 12 and 13 can be explained by a loss of available surface area as the thickness of the PAS layer is reduced. In a one-dimensional mode of permeation, where the penetrants are viewed to diffuse perpendicular to the surface of the membrane, the area available for permeation would correspond to the cumulative area of surface pores in the supporting membrane (e.g., porous polysulfone). In this model, the area available for permeation should be independent of the coated layer thickness. This assumption was made in the development of the Resistance Model presented by Henis and Tripodi (1980a,b, 1981). Later, Lopez et al. (1986) proposed a two-dimensional model which takes into account the radial diffusion component. The driving force for radial diffusion is the concentration gradient established between the region immediately above a pore and the surrounding region (Figure 14). This concentration gradient arises as molecules diffuse rapidly through the membrane within the region above the pore, resulting in a lower concentration of penetrant than in the region between pores. Radial mass transport allows a greater fraction of the membrane surface area to be available for permeation in comparison with the one-dimensional model, for which permeation is confined to the area of the pores in the support's surface. However, the extent of increase in the
surface area is governed by the relative magnitudes of the concentration gradients, i.e., parallel to radial, and the distance over which the radial concentration gradient is allowed to prevail. Therefore, as the thickness of the surface layer is increased, the radial concentration gradient may extend further from the pore axis and the surface area available for permeation is increased. This increase results in augmentation of the apparent permeability coefficient (Figure 11)until the layer thickness is large enough and the entire surface area of the membrane is available for permeation, from which the permeability coefficient of the penetrant in the material comprising the layer can be obtained (e.g., the asymptotes of the curves in Figure 11 yield permeability coefficients for O2and N2 in PAS close to that obtained from independent measurements that yield -200 and -80 barrers, respectively). The fraction of surface area available for permeation may be calculated from the ratio of the apparent permeability coefficient (Papp = P1) and the permeability coefficient ( P ) of the material comprising the layer: A' = Papp/P (14) where A'is the effective surface area. Plots of A'versus the thickness of the PAS layer for this series are shown in Figures 15 and 16. Extrapolation of the data leads to intercepts which indicate ca. 8% available surface area of the polysulfone support. Note, however, that this extrapolated value should be taken cautiously since the number of data points is limited. Evaluation of the LMMQ Permeability Model. In addition to the thickness and intrinsic permeability of the polymer comprising the surface layer, the ultimate properties of the composite membrane also depend on the nature of the porous support, i.e., geometry, size, and distribution of pores, and the intrinsic permeability of the polymer comprising the supporting layer.
750 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
f
< 0 0 Lc
is
ln 0
.-
+I
0
4 W 4
-
1
i
0
b
I
I
PAS Loyer Thickness (micrometers)
‘e
lb
Figure 16. Effective surface area versus PAS layer thickness for permeation of N2in PS/PAS IV composite membranes. (A)Corresponds to membrane 1129-3(Table 11).
T
= - O T
x
-
-d
1 ,--I
2b
I
Figure 17. Schematic illustration of pore dimensions, for single pore unit, within a membrane represented by repeating pattern of right circular cylinders (such as those used in development of two-dimensional model of diffusion (Lopes e t al., 1986));2a is the pore diameter and 2b is the average distance between the center of two pores.
The model proposed by Lopez et al. (1986),henceforth the LMMQ model, portrays the porous support as a repeating pattern of right circular cylinders as depicted in Figure 17. By use of the two-dimensional model of diffusion, these investigators have proposed the following equation for P:
Figure 18. Scanning electron micrograph depicting cross section of PPO/PAS/PS composite membrane. The PPO layer is asymmetric and consists of a dense skin (a) connected to a porous region (b) which is comprised of an assembly of nodules 66 nm in diameter. This nodular region is similar to that of the polysulfone PS support which extends up to the interface with the intermediate PAS layer (c) (magnification, X17780).
ability of the penetrant in the unfilled pores, Pp, is assumed to be the sum of viscous and Knudsen flow contributions to transport of gases within the pores. The viscous flow (Pf)is given by the expression
310a2p Pf = IIT
where a is the radius of the pores (in micrometers), p is the pressure gradient, q is the viscosity of the penetrating gas (in micropoises), and 7’ is the absolute temperature. The Knudsen flow is calculated from the relation PK
P8(1- e)
+ Ppc+ -
where 1 is the coated layer thickness, Pcis the permeability coefficient of the penetrant in the coated layer, d is the depth of surface pores in the substrate layer (corresponding to the asymmetric membrane skin thickness), Pa is the permeability coefficient of the penetrant in the substrate (e.g., polysulfone), Ppis the effective permeability of the penetrant in the pores (in barrers), y2= PJP, y3.= Pp/Pc, e is the surface porosity (ratio of the cross-sectional area of the pores to area of the membrane), and F is a twodimensional factor represented by the following expression: 0.8(1 - 1//9) F= (16) 6(1 + 2/B3) where /9 = b/a and 6 = d / a (see Figure 17). The perme-
(17)
3.48~ =(MT ) 1/2
where M is the molecular weight of the gas. Equation 15 was rearranged to give an expression for the effective permeability of the penetrant in the composite membrane in terms of the poly(aminosi1oxane) layer thickness (IpAS): -1
4 1 + FIT3 + T2€/(1- 411 P*(1- €)
+ Pp€+ 1-€
In order to establish a plot of P versus !PAS from this equation, it was necessary to estimate the porosity, pore size, and thickness of the surface layer of the porous support. Analysis of the micrographs obtained’by SEM and TEM (Figures 7,18,and 19)suggests that the surface
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 751
I "
919s
ilm
2lm
3100
tlm
s!m
PAS Layer Thickness (microaetws)
dm
Figure 20. Permeability coefficient ( P ( 0 2 ) )versus PAS layer thickness for PS/PAS IV composite membranes. The experimental data are shown against several curves computed according to eq 19 employing the data given in Table IV.
............ ......... .......
-
I)-
........
........_..... ........
......... .............
........ ...
I
P
al h
U E
E 0
Figure 19. Scanning electron micrograph of PS anisotropic support surface. Several of the larger pores (indicated by arrows) are a p parent (Magnification, X50750).
of the porous support consists of a layer of partially fused nodules. The porosity, and hence the flux of the uncoated support, will depend on the size, packing arrangement, and the extent to which the nodules are fused during the membrane casting procedure. The average size of the nodules, which are virtually monodispersed spheres in polysulfone membranes, has been measured as 66 nm in diameter (Cabasso, 1981) (Figure 18). For a hypothetical membrane with a surface consisting of nodules of this size, packed in a regular hexagonal order with each sphere tangent to those surrounding it, it can be shown by simple geometrical computation that the idealized membrane porosity is 9% and the pore radius is 7.5 nm (Lundy, 1987). This may closely characterize "high-flux" membranes with surfaces containing closely packed, well-defined spheres. In reality, considerable fusion of nodules in and near the surface layer may occur during membrane casting, resulting in a reduction of porosity and pore size and consequently the membrane flux (Lundy, 1987). This is illustrated in Figures 7, 18, and 19, showing micrographs of the "low-flux" membrane used as a support in these experiments. The actual number of pores per unit area was estimated from the micrographs by mapping and counting the number of pores. This was used to approximate the actual porosity, yielding a pore radius of 7.5 nm and porosity of ca. 2 % . The pore diameter cannot, however, be measured properly from a direct observation of the surface and in this instance has to be speculated. However, partial fusion of nodules results in smaller radii as well as a diminished number of pores; thus, for example, for a reduced pore radius, 5 nm, a surface porosity of 0.86% is obtained. A series of plots of P versus I calculated from eq 19 for oxygen and nitrogen are shown in Figures 20 and 21. In
u E 0
-
b
1.h
1.h
3.h
b.h
5.h
PAS Layer Thickness (micrometers)
6 . h
Figure 21. Permeability coefficient (P(N2)) versus PAS layer thickness for PS/PAS IV composite membranes. The experimental data are shown against the computed curve predicted by eq 19. Table IV. Parameters Used in Calculating Theoretical Curves Displayed in Figures 20 and 21 Figure 20 (02) Figure 21 (N2) curve d, A a,A t, ?% d, A a. A t, % 1 330 75 2.00 660 75 2.00 2 660 75 2.00 660 75 0.86 3 660 50 0.86 660 21 0.10 4 660 15 0.10 660 31 0.10 5 660 31 0.10
both figures, curves 1 and 2 were calculated using the estimated surface porosities described above (Q = 7.5 nm and c = 2% for curve 1 and Q = 5 nm and c = 0.86% for curve 2), and the surface layer thickness ( d ) was taken as equal to the diameter of a nodule (66 nm). The remaining curves, 3-5, were fit to the experimentaldata by arbitrarily selecting pore radius and surface porosity values. Table IV summarizes the parameters used in calculating the cu'rves depicted in Figures 20 and 21. The porosity and pore size corresponding to the experimental data are significantly lower than the values estimated from the electron microscopy measurements. There are a t least two factors that may account for this difference: (1)Further fusion of nodules during the coating procedure (i.e., exposure to hexane and heat) will result in lower porosity and smaller pore size and consequently lower values of Pew (2) Partial filling of pores during the coating procedure will result in lower permeability for the composite mem-
752
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
Table V. F l u x a n d Ideal Separation Factors for Oxygen a n d Nitrogen Permeating through Three-Layer Composite Membranes (PS/PAS/PPO) 1035,
1035,
cm3/(cm2*s), for PAS I1 Ap, kPa 69 138 207 276 345
O2
N2
0.979 2.024 3.074 4.106 5.161
0.315 0.655 0.937 1.247 1.565
a* 3.12 3.09 3.28 3.29 3.30
cm3/(cm*d, for PAS IV O2 N, 0.636 0.174 1.271 0.346 1.939 0.524 2.485 0.711 3.131 0.892
a*
3.65 3.67 3.71 3.50 3.51 0 ;
I
I
0
10
I
I
I
20 30 40 Pressure Difference ( k P d
I
50
Figure 23. Flux versus pressure difference for three-layer PS/PAS IV/PPO composite membrane (see Figure 9).
U VI N t
U
'C
IJC
200 25C 2 ~ e s s u r e ' ~C-^erence o (kPd
300
350
400
Figure 22. Flux versus pressure difference for three-layer PS/PAS II/PPO composite membrane (see Figure 8).
X L
brane; this factor should be more significantly pronounced for the thinner layers. While no apparent gross intrusion of PAS into the surface pores was observed, the data points (Figures 20 and 21) indeed show higher P values for membranes with thicker PAS coatings (which, however, should not be considered a t this stage, as evidence for intrusion of the polymer into the surface pores). The LMMQ model may be refined using data obtained from membranes composed of ceramic anisotropic porous support. The latter obviates the possibility of surface alteration of the support; this work is in progress in this laboratory. Three-Layer Composite Membranes. An ultrathin layer of PPO was deposited on the surface of the PAS/PS membranes described in Table I1 subsequent to evaluation in the permeability cell. Thus, it was possible to compare the properties of the membranes before and after the deposition of PPO layers. Scanning electron micrographs (Figure 3) illustrate the presence of three distinct layers after coating. In this morphology (Figure IC),the PAS layer serves as a "gutter layer," channeling the permeate from the permselective layer to the surface pores in the polysulfone support. The intermediate rubbery layer also provides a resilient support for the glassy permselective ultrathin PPO layer. The three-layer composite membranes were tested for their permeability to pure oxygen and nitrogen as described earlier for the two-layer PAS/PS composite membranes. The experimental results are presented in Table V. Plots of oxygen and nitrogen fluxes versus the pressure difference across the membrane are shown in Figures 22 and 23 for membranes containing PAS I1 and PAS IV. (Note that the membranes shown in these figures are the three-layer modification of those shown in Figures 8 and 9, which were coated with the PPO layer after testing.) The plots are linear within the range of pressures employed. A comparison with Figures 8 and 9 shows lower fluxes, about half the values measured for the corre-
-
1
o
olr
ole
112
11.6
Thickness R a t i o PPOIPAS
'2
i.4
2.0
Figure 24. Permeability coefficients of 0,and N, in three-layer membranes versus thickness ratio (PPO/PAS IV). The theoretical plots were drawn according to eq 5 using Pp*s(O2) = 200, P p u ( N Z ) = 80, Pppo(02) = 16.9, and PPPO(NB) = 3.8 barrer for the solid line (see also Figure l l ) , and Ppm values of 250 and 100 barrer for 0, and N,, respectively. The actual thickness ratio for asymmetric PPO layers is indicated by arrows for the two relevant data points. Table VI. Permeability a n d Ideal Separation Factors for Oxygen a n d Nitrogen i n Three-Layer Composite Membranes (PPO/PAS/PS) layer thickness, P, barrer" Irm membrane PAS PPO 6 (PPO/PAS) 0, N, a* 1025-3a 6.70 0.95 0.14 91.9 26.30 3.82 1111-la 2.80 1.26 0.45 53.8 13.20 4.06 1111-2a 2.22 1.64 0.74 61.7 16.60 3.72 1111-3a 0.98 1.53 1.56 32.0 9.12 3.51 1129-2a 7.51 4.31 0.27 0.69 2.56 32.4 5.57 4.20 2.00 23.4 1129-3a 0.44 0.88 "Barrer =
cm3 (STP) cm s-l cm-, (cmHg)-'.
sponding PAS/PS membranes. Permeability coefficients calculated from the measured flux and total thickness of the PAS and PPO layers for this series of membranes are listed in Table VI. Although the data in Tables I1 and VI indicate a reduction in the permeability factor ( P ) subsequent to the application of the PPO layer, the apparent permeability coefficient (P,,,) is shown to increase for after such treatment in two of the samples. The Papp PAS/PS membranes was shown above to depend upon the effective surface area of the membrane, which was, in turn, dependent on the thickness of the PAS layer. The experimental data were analyzed, using the resistance model to determine whether a similar relationship exists between
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 753
-
..
\
..%
- * . - -.. ..
.'y
Figure 25. Scanning electron micrograph showing cross section of membrane 1111-la. A dense isotropic PPO layer (a) is shown residing on the surface of a two-layer composite membrane consisting of PAS (b) deposited on a polysulfone anisotropic support (c) (magnification, X3600).
the permeabilities and layer thicknesses for the three-layer composite membranes. Thus, plots of PTfor O2 and N2 versus 8 for the series of composite membranes described in Table VI are shown in Figure 24, together with the curves predicted by eq 5. The experimental data are in close agreement with the predicted values of PT, which were calculated based on the availability of the entire membrane surface area for permeation. Note that the experimentaldata points in the figure that fall significantly above the calculated curve are due to the PPO layer with anisotropic morphology, as depicted in Figure 18. Therefore, the reduced barrier thickness resulting from this morphology yields higher permeability values than that of an isotropic dense PPO layer (such as those shown in Figures 25 and 26) of an equal overall thickness. The corresponding data points of the latter are closest to the calculated curve and appear to depict dense layers of PPO. The outcome shown in Figure 24 is quite different from that observed for the corresponding two-layer composite membranes. The close fit of the data to the calculated curve (eq 5 ) suggests that the entire surface area is available for permeation for three-layer composite membranes, in contrast to the corresponding composite twolayered membranes presented in Figures 15 and 16. These results also strongly support the validity of the "gutter layer" concept, which infers that the PAS intermediate layer channel permeates from the permselective layer to pores in the support. A plot of the ideal separation factor versus the thickness ratio (0 = l p p o / I p ~ for ) this series of membranes is shown in Figure 27. The experimental data are shown to fit the curve calculated from eq 7. The upper and lower limits of this equation yield ideal separation factors correspondingto those for single layers of PPO (a* = -4.3) and PAS (a* = 2.5), respectively. There are insufficient experimental data to demonstrate the downward trend a t 8 < 0.2 as predicted by the equation. Nevertheless, the two data points that correspond to the asymmetric layer of PPO clearly reflect this trend. Problems inherent in the construction of defect-free ultrathin membranes by conventional casting methods were discussed in the Introduction. The close agreement of the experimental data with the predicted separation factors indicates that these membranes contain no significant defects. Only two of the data points in Figure 27 fall below the calculated curve. These points correspond
I
Figure 26. Scanning electron micrograph showing cross section of membrane 1129-3a. A dense isotropic PPO layer (a) is shown residing on the surface of a two-layer composite membrane consisting of PAS (b) deposited on a polysulfone anisotropic support (c) (magnification X8550). S 0
Expalmmtol Dot0
b
4J L0 L
C .e
4J L
a
vr
0
D
' I
0
I
.5
1
1
I
1.5
Thickness Rat 1o PPOIPAS
I
2
c5
1
Figure 27. Ideal separation factor versus thickness ratio (PPO/ PAS) for PS/PAS IV/PPO composite membranes,plotted against a*theoretical curves calculated for (-) a* (02/N2) = 4.3 and (02/N2)= 4.15. Arrows indicate actual thickness ratio for data taken with two asymmetric PPO layers. (-0)
to membranes with anisotropic PPO layers. Therefore, the actual thickness ratio (IppO/lp& is lower for these samples than that computed from the overall thickness of PPO. The dense skin of 0.1-0.2 pm that was measured for these membranes fits well in the calculated plot shown in Figure 27. Effect of Surface Layer Defects. The total resistance of the membrane, RT,was calculated for the PPO/PAS/PS membranes, and the resulting values were used to calculate permselectivity of the membrane. Figure 28 shows the ideal separation factor computed from eq 12 for the defect ratio (f value) a t the range 104-1. Accordingly, as the surface defects increase above ca.1% of the total surface area, there is a dramatic decrease in the separation factor. However, viscous flow is prevented, and for the case described here, some permselectivity is retained even when defects of greater magnitude are
754 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
,
' I
15 0 i
?, \
Table VII. Effect of Pressure Ratio on Stage Separation Factor for Composite Membranes (PPO/PAS/PS) Ap, kPa
PwlPr
n
138 276 414
2.36 3.72 5.08
552
6.44
690
7.80
1.97 2.39 2.57 2.77 2.76
"This is a high flux asymmetric PPO layered membrane that was chosen for this experiment.
Figure 28. Ideal separation factor versus fraction of PPO surface exposed by defects for PS/PAS/PPO composite membrane for which the following parameters were used: PpAs(Op)= 200, PPAs(NP) = 80, Pppo(Op) = 16.9, Ppp0(NZ)= 3.8 barrer; thickness ratio 8 (PPO/PAS) = 0.1 for a membrane with 0.1 and 1.0 pm of PPO and PAS, respectively.
present in the PPO layer, due to the presence of the underlying layer of PAS. In comparison, damage to the outer layer of Prism-type membranes (Henis and Tripodi, 1980a,b) is much more likely to result in a total collapse of permselectivity, since the exposure of the porous substrate to the gas feed mixture may lead to nonsegregative viscous flow through the porous support. Stage Separation Factor. The ideal separation factor, as defined by eq 6, is a useful measure of the relative permeation rates of the permeants of a binary gas mixture and thus is a measure for the permselectivity of a membrane. Another way of defining the separation factor can be done by comparing the compositions of gas mixtures before and after permeating a membrane. Referred to as the stage separation factor (a),this quantity is defined by X ( 0 J /X(Nz) a= (20) W,)/VN,) where X(Oz) and X(Nz) are the mole fractions of oxygen and nitrogen in the product and Y(0,) and Y(N& are the mole fractions of oxygen and nitrogen in the feed. The stage separation factor depends on a number of parameters, such as flow pattern, stage cut, feed composition, and pressure ratio between both sides of the membrane. However, when the stage cut is very low (e.g., less than ca. 0.051, the stage separation factor may be assumed to depend only on the pressure ratio and the composition of the feed. Stern and Wallawender (1969) derived an equation for a in terms of these two parameters and the ideal separation factor (a*):
(21) where r is the pressure ratio (i.e., feed to product side) and XA is the mole fraction of the more highly permeable component in the feed. According to this equation, and the reported experimental values as well, as the pressure ratio reaches infinity, the stage separation factor approaches the ideal separation factor. Figure 29 and Table VI1 depict the experimentally determined stage separation factors over a range of pressures
Figure 29. Stage separation factor versus pressure ratio for twolayer (PS/PAS 11) and three-layer (PS/PAS II/PPO) composite membranes. The data are plotted against the theoretical curve (solid lines) derived from eq 21.
from 69 to 690 kPa for two- and three-layer composite membranes (i.e., PAS/PS and PPO/PAS/PS). The data in Figure 29 are plotted against the theoretical curve calculated from eq 21 using the experimentally determined values for a*. The two-layer composite membrane (PAS/PS) yielded a stage separation factor of 1.97 at a pressure ratio of 7.8 (pressure difference = 690 kPa, Table VII). The stage separation factor increased to 2.25 at a pressure ratio of ca. 30, which was attained by employing partial vacuum at the downstream side of the membrane. The data indicate that the experimentally determined stage separation factor and that predicted by eq 21 are in close agreement. The slight departure of the data points from the calculated curve at a high pressure ratio (Figure 29) may be due to the fact that at these pressures the flux through the membrane is rather high-to the extent that the porous matrix may interfere with the pattern of gas flow at the downstream side. The increase in a after coating this membrane with an isotropic PPO layer is clearly demonstrated (Figure 29). The maximum stage separation factor observed for this asymmetric PPO/PAS/PS membrane (which was randomly chosen) at the pressure range shown in Figure 29 was 2.77. Increasing the pressure ratio to ca. 20 (by applying vacuum method at the membrane's downstream side) resulted in a stage separation factor of nearly 2.9. Comparison of Two- a n d Three-Layer Composite Membranes. The principal factors that influence the properties of the composite membranes described above are associated with the intrinsic properties of the materials comprising the layers and the morphology of the membrane. The permselectivity of the two-layer composite membranes discussed above is based on a rubbery polymer, poly(aminosiloxane), characterized by high permeability and low selectivity. In the case of the three-layer mem-
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 755 branes,the permselective layer consists of a glassy polymer, PPO, characterized by lower permeability and higher selectivity. These differences in intrinsic properties were reflected in the mass-transport properties through these two types of membranes. A refined assessment of the membranes could be made had the PPO been deposited directly on the PS support, yielding PPO/PS composite membranes that could be compared to those given in Table I1 and VII. However, a layer of PPO could not be deposited from solution because all the appropriate solvents for PPO attack or dissolve the delicate porous polysulfone surface. Lamination of a single ultrathin film (
