Some Design Aspects of Aromatic Polyamide Reverse-Osmosis Membranes Hal Wood'. and S. Sourirajan2 ' Industrial Membrane Research Institute, Department of Chemical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, Canada K1N 6N5 Department of Chemical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 05 1 7 , Singapore Linear-polymer solutions are comparable to a suspension of macromolecule spheres. Macromolecules concentrate at the interface during the membrane-forming procedure. They coalesce with each other suficiently for the su$ace to become a sheet of interconnected macromolecules. Interstitial voids are formed whose magnitude is dependent on the size and packing arrangement of the macromolecules, and is also influenced by the extent of coalescence occurring in the interstitial voids. A subsequent gelation procedure renders the macromolecules paracrystalline. During operation, the membrane allows permeation of solution components primarily through the interstitial voids.Membrane design requires the ability to predict membrane pe~ormancefrom the precursor casting conditions. This paper illustrates the practical utility of the interstitial void modelfor membrane design purposes. Some design aspects are presented for various reverse-osmosis membranes made from an aromatic polyamide polymer. Review of Polymer Membranes Reverse osmosis (RO) and ultrafiltration (UF)membranes are made by gelling a film of polymer solution. The resultant membrane is a dense skin-layer supported by a more porous substrate. Changes in the casting conditions influence the performance of the final membrane product. For a given polymer, membrane performance is dependent primarily on the morphology of the skin layer. A polymeric membrane skin layer generally contains a bimodal distribution of pores. They originate from t h e interstitial void spaces in the surface layer of paracrystalline macromolecules. The porous structure is dependent on the size, geometric disposition, and degree of coalescence of the surface macromolecules. The following section contains a short review of linear polymer solutions and membrane films, including a summary of the equations that are used to determine * To whom correspondence should be addressed. Developments in Chemical Englneering and Mineral Processlng, Val. 1, No. 4, page 238 Design Aspects of Aromatic Polyamide Membranes 239 polymer-solution structure and membrane skin-layer morphology. The interstitial void model is then presented, and some established membrane design principles are reviewed. In the Evaluation section to follow, additional design aspects of some aromatic polyamide (PA) membranes are established. The emphasis is on large pores in skin layers of membranes made from PA/DMAc/CaC12 solutions. Design aspects of other surface morphological constants are also discussed. The interstitial void model is shown to be useful for determining an effective skin layer thickness and the number of pores per membrane area, which are valuable tools for transport analysis. Linear polymer solutions and their resultant films A typical linear polymer molecule occupies its own domain in the solution space. In most RO/UF casting solutions, accurate estimates of macromolecule dimensions can be determined from the equation:' 4xRs = VE -- 0.507 MIyN, (1) where Rs (cm) is the hydrodynamic radius occupied by the macromolecule M is the polymer molecular sphere; g is the polymer concentration (g weight (g gmol-'); and No is Avogadro's number. The quantity v (cm3) is the volume occupied by one polymer molecule in its crystal state, and E is an expansion factor to account for swelling of the macromolecule when in an appropriate solvent. A modification to equation ( 1 ) may be required if an additive is present in the casting solution.24 The quantity M is substituted in equation (1) by Map,,, the apparent polymer molecular weight (g gmol-'), as determined from: [TI)= m,,, 01 (2) The polymer-solvent-additive intrinsic viscosity, [TI' (cm3 g-'), is compared to the Mark-Houwink constants K (cm3 g-') and a,as determined for the polymer in pure solvent only. Then Mapp is equal to M, unless the additive causes an intrinsic viscosity change. From equations (1) and (2), Rs increases with either an increase in M, or decrease in g, or an increase in intrinsic viscosity caused by the additive. Surface tension and/or solvent evaporation effects during the membraneforming procedure cause polymeric particles to concentrate at the interface. Due to crowding, solvent evaporation or other effects, the polymeric particles form permanent contacts with each other. The interfacial layer becomes an interconnected sheet of partially coagulated macromolecules. The extent of coalescence amongst adjacent macromolecules is dependent on the casting composition, solution structure and membrane-forming procedure. It is unlikely that coalescence proceeds to such an extent that the interstitial gaps become completely closed. Eventually, the macromolecules are rendered paracrystalline, and the resultant membrane can be used as a separation film.5 The magnitude of an interstitial void in a monolayer of spheres can be determined from geometry considerations, and depends upon the size and packing disposition of the spheres. The geometric values of the interstitial voids in a macromolecule monolayer can also be determined for given values of Rs. Note that Rs and the geometric void spaces are inherent in the casting solution structure. However, the magnitude of an interstitial void i n a gelated macromolecule monolayer is also dependent on the degree of coalescence amongst the macromolecules. H, Wood and S. Sourirajan 240 From Poiseuille's equation: Q = AP n ~t~ ~ / p(. ~ 8) (3) where the flux Q (cm3 cm-'s-') of solvent, of viscosity p (g cm-' s-') through a sheet containing n (cm-') non-interacting pores of radius R (cm) and length L (cm) is proportional to the applied pressure gradient AP (g cm-' s-'). Experimental RO/UF membrane performance data may be applied to a modified Poiseuille transport equation in order to characterize the skin layer morphology in terms of a porous structure. The Poiseuille equation is modified to account for friction when the solute bumps along the pore wall, and for interfacial interactions that can cause the solute to be attracted or repelled from the membrane material. With ROKJF membranes, even under high operating pressures, separation can occur even if the solute is appreciably smaller than the pore diameter. The modified Poiseuille equation also accounts for the possibility there may be more than one mean pore size and pore size distribution on the membrane surface. The experimental data indicate that there are usually two average pore sizes. There are small pores of mean radius Rbl and standard deviation 01; there also are larger pores of mean radius Rb2 and standard deviation 62. The ratio of the number of large to small pores (h2) can be determined. Once the membrane surface is characterized by these constants, performance can be predicted for most solute-solvent combinations and operating conditions. 6 The interstitial void model of membrane surfaces It is assumed that all permeate transport occurs through the interstitial voids in the skin layer of an RO/UF membrane. The skin layer morphological constants are then a reflection of the size, disposition and degree of coalescence of the surface macromolecules. For each membrane, the surface morphological constants can be compared to the geometric interstitial void spaces, so that the disposition and degree of coalescence of the surface macromolecules can be determined. Since membrane performance can be predicted if the surface constants are known, then the interstitial void model is a link that connects casting conditions to the final membrane performance. Salt-separation ability is possible if the channels through the membrane skin layer are sufficiently small. According to the interstitial model, Rs must be small and the surface macromolecules be predominantly close-packed in order to produce the minimum possible geometric void space. Also, some coalescence occurs amongst the surface macromolecules, which further decreases the magnitude of the interstitial channels. The surface morphological constants Rbl and 01 result from interstitial voids formed by close packing of surface macromolecules. The constant h2 indicates there are also voids of size Rb2 and standard deviation 02, formed by other packing arrangements of the surface macromolecules. Solute-separation ability decreases if either Rs increases, or interstitial coalescence amongst surface macromolecules decreases, or if h2 increases. The interstitial void model is supported by data for casting solution and surface structure for RO and UF membranes made from cellulose acetate, polyethersulfone and aromatic polyamide polymer^.^ Design Aspects of Aromatic Polyamide Membranes 241 Evaluation of Membrane Formation and Performance The effect of casting conditions on PA membrane surface formation has previously been reported by the author^.^^^** In general, interstitial coalescence within close-packed voids increases with any change in casting composition that causes an increase in Rs. For any value of Rs, the degree of coalescence within close-packed voids is relatively independent of the type and/or quantity of additive used in the casting solution. A minimum macromolecule radius may be reached where permanent contacts between adjacent close-packed macromolecules do not occur, and this is relatively independent of the membrane-forming procedure. Deviations from close packing depend on the polymer type, the polymer molecular weight, and the type or concentration of additive in the solution. Large pores in RO membranes are formed by the square packing and subsequent partial coalescence of surface macromolecules. Membrane desalination ability decreases if the macromolecules rise into, but do not coalesce with, the surface monolayer. ' h o UF membranes made from polyethersulfone (PES) polymer have also been analysed according to the interstitial void model.7 Although Rs is small, many surface PES macromolecules do not pack closely together. Also, relatively large voids are formed because macromolecules are missing from the surface array. These factors contribute to the substantial decrease in selectivity of a PES membrane compared to those made from PA. For a cellulose acetate (CA) RO me~nbrane,~ the macromolecules are small and predominantly close-packed, and the CA polymer repulses salt ions more strongly than does PA, Therefore, for CA membranes, the degree of coalescence need not be so high, and some large pores may be formed by macromolecules missing from the array without greatly reducing overall desalination ability. In summary, membrane performance can be linked to the casting composition by comparing the surface morphological constants to Rs and the geometric void spaces. The interstitial void model is a useful tool for membrane design purposes. The effect of casting conditions can be related to the porous structure of the resultant membrane, and the structure and performance can be predicted without first making the membrane. The design of PA/DMAc/CaC12 membranes The following example illustrates the practical utility of the interstitial void model for design purposes. Membranes of various surface morphologies and ROAJF performance abilities are made by changing the concentration of PA polymer (M = 31,300 g gmol-') and/or CaC12 additive, in dimethylacetamide (DMAc) ~ o l v e n t .In~ all solutions to be analysed for design considerations, the CaC12 concentration is below the critical ~ a l u e . The ~ , ~ membranes are made by evaporating DMAc from a thin film of polymer solution at 95°C for 15 minutes, then immersing in ice-cold water for at least an hour. The macromolecule dimensions are calculated for each casting solution, and the porous structure of each resultant membrane is determined from experimental performance data.3 Casting composition, solution structure and the surface morphological data for the PA/DMAc/CaC12 system are contained in Table 1. The values of Rbl, 61, 6 2 and hz are not included in Table 1 since they remain relatively constant, and independent of the casting composition. Rbl ranges from 6.5 to 6.6 A and is independent of Rs. this indicates that interstitial coalescence in close-packed voids increases with an increase in Rs. The standard deviation (61) of Rbl is H,Wood and S. Sourirajan 242 Table 1 Casting solution and surface morphological data for some PA membranes3 7.0 9.0 10.5 12.5 14.0 0.1 0.1 0.1 0.1 0.1 64.6 59.1 55.6 52.5 50.4 31 27 23 22 20 2.8 3.9 6.1 5.4 6.3 31 27 24 21 20 7 .O 9.0 10.5 12.5 14.0 0.2 0.2 0.2 0.2 0.2 71.0 64.2 60.7 57 .O 54.6 43 34 30 29 25 -5.9 -0.4 1.7 0.8 3.5 43 35 31 27 25 7.0 9.0 10.5 12.5 14.0 0.3 0.3 0.3 0.3 0.3 72.3 66.1 62.5 58.6 56.1 50 44 36 31 29 -12.2 -9.4 -3.3 -0.4 0.3 51 42 37 32 28 * estimated from equation (8). usually negligibly small (about 0.01 A). This shows that for a particular membrane sample, the degree of interstitial coalescence in each close-packed void is constant throughout the membrane surface. The ratio of the number of large to small pores per membrane surface area is approximately 0.001. Changes in the casting composition mainly influence the magnitude of the large pores (Rb2) on the resultant membrane surface, while 0 2 is close to zero. The cross-sectional (xs) void area between square (s) packed spheres can be compared to a pore opening of equal area of radius rs xs. From geometry: Rs/rs xs = [(4 - T C ) / T C ] - ~=’ ~ 1.913 (4) Table 1 includes values of ARb2 (= rs xs - Rbz), and values close to, or greater than zero, indicate that the large pores are comparable in size to voids formed by the surrounding and partial coalescence of four surface macromolecules. The variation (02) in the average size of these large pores is approximately zero. Therefore, for each membrane, the degree of coalescence in each void formed by the square packing of surface macromolecules is relatively constant throughout the membrane surface. Some casting solutions made of low PA and high CaC12 content produce large pores which are much greater in magnitude than rs xs. These voids are formed by macromolecules that migrate towards the surface during membrane formation, but do not coalesce with the monolayer. In these Design Aspects of Aromatic Polyamide Membranes 243 Table 2 The slope and intercept of Rs versus ARb2 data Cfrom Table I ) . D1 g CaClz /g PA (A) 0.1 0.2 0.3 -3.43 -1.70 -1.12 Dz 73.28 61.41 57.53 Correlation coefficient 0.93 0.94 0.97 membranes, the standard deviation 0 2 can be quite large, and may be estimated in relation to the magnitude of ARbz.8 Membrane design for this PA/DMAc/CaC12 system is possible if the average large-pore radius can be predicted from the casting composition. Data from Table 1 are useful for this purpose, and show that there is a linear relationship between Rs and ARbz as given by: (5) Rs = Dimb2 + D2 if the CaClZIPA mass ratio is constant. The values of D1 and Dz, and corresponding correlation coefficients, are given in Table 2. The correlation coefficients are slightly smaller than 1, possibly because Rb2 is estimated to the closest Angstrom (A), but Rs and rs xs are calculated to a higher decimal place. From the data of Table 2, there is a direct relation between D1 and the CaC12/PA weight ratio in the casting solution, namely: D, = -(gPA/gCaClz)/3 (6) There is also a linear relation between D1 and D2, as given by: D1 = -0.1465Dz + 7.300 (7) The correlation coefficients for equations (6) and (7) are approximately one. By combining equation (6) with equation (7), and substituting into equation ( 5 ) , upon rearrangement: ARb2 = 3(49.8 - RS)(gCaCl2/gPA)+ 6.826 (8) Equation (8), in combination with equations (1) and (4), may be used to predict Rb2 from the casting composition. Values of Rb2 estimated from equation (8) are contained in Table 1. The critical CaClZ/PA ratio (CaC12*) is 0.33 g of CaC12 er g of PA.4 From equations (6) and (7), Dl equals -1 and D2 equals 56.7 at CaC12*. From equation (8), ARb2 equals zero at CaC12* when Rs equals 56.7 A. Equation (8) shows that when the CaClz concentration is at or above CaC12*, Rb2 is greater than rs xs when Rs is greater than 56.7 A. It is interesting to note that the minimum calculated Rs [equations (1) and ( 2 ) ] in this PA/DMAc/CaClZ system at CaC12* is 55.8 A. This indicates that membranes with large pores formed only by square packing are made from solutions below CaC12*. The origin, and ultimately the size of a large pore, is minimised if the casting composition is below CaC12*. Consider the possibility that no CaC12 is added to the casting solution. From equation (8): Rbz = Ts xs - 6.826 (9) s: H, Wood and S. Sourirajan 244 which indicates that large pores occur, even if no CaC12 is present in the casting solution. Since the minimum possible Rs in this PA/DMAc system is about 30 A, then Rb2 remains relatively large, and the close-packed voids become essentially closed when no CaC12 is present in the casting solution. Since h2 is small, low flux nanofiltration membranes are produced.' Flux Analysis Macromolecules in the surface PA monolayer are predominantly close-packed. There are two interstitial voids per close-packed macromolecule. From geometry considerations: = 3-112~ 2 S where n is the number of close-packed voids per membrane area. Equation (10) shows that n is maximised when Rs is minimised. Neglecting deviations from close packing, for typical data in Table 1 if Rs equals 60 A and Rbl is 6.6 A, then interstitial pores occupy about 2.2% of the total membrane surface area. This value agrees well with published data for CA UF membranes." Some modifications can be made to Poiseuille's equation in order to estimate an effective pore length (skin layer thickness) for RO membranes: a) The flux Q (cm3 s-') is substituted b the experimentally-determinedpure water permeation rate, PWP (g cm- 2 h- 7). b) According to Poiseuille's equation: PWP a R4. However, due to interfacial and/or pore size distribution effects, PWP for RO membranes is trongly affected by the pore radius, but to less than the fourth power.""' It is estimated that PWP a R'.' for CA RO membranes.13Therefore, PWP a R'.' is assumed to be applicable to PA RO membranes, since the dielectric constants of PA and CA are similar, at least in comparison to that of water. c) Since h2 for RO membranes is small, data from Table 1 and refs 2 to 4 show that Rbi is much greater than h2Rb2 1'5.Because salt-separating membranes are under consideration, the effect of the large pores on flux must be minimal. Therefore R is replaced by Rbl in the modified Poiseuille equation. d) Since h2 for RO membranes is small, then n can be estimated from equation (10). In a previous study,3 and for the data of Table 1, 13.2-cm2 membrane coupons were tested with 25°C water at an operating pressure of 250 psig. By substituting the above factors into the Poiseuille equation, upon rearrangement: L -2.0773~10~ X Rbl '.'/(RS X PWP) (1 1) where L is an effective skin-layer thickness. The units of Rbl, Rs and L for equation (11) are in Angstroms, and PWP in gl(13.2 cm2 h). An effective pore length may be estimated if Rs, Rbl and PWP are known. For example, Rs for a casting solution made from 10.5 wt% PA and 0.1 g CaC12/g PA is 55.6 8, cm2 h)3. From (Table l), and the resultant Rbl is 6.5 8, and PWP is 1.87 equation (1 l), the effective skin-layer thickness is about skin layer thicknesses observed by electron microscopy.' Design Aspects of Aromatic Polyamide Membranes 245 Example problem Assuming that an Rbl value of about 3.5 A is required to achieve excellent desalination ability with a PA membrane, estimate the optimum PWP for a membrane made from a PA-solvent-additive solution. Compare the performance to that of some existing PA membranes. (a) A small Rs value is desirable to maximise n [equation (lo)]. The minimum macromolecule radius5 for coalescence to occur within a close-packed void is approximately 30 A. With proper choice and quantity of additive, close-packed macromolecules (Rs approximately 35 A) can coalesce together sufficiently to produce interstitial voids that are 3.5 A in radius.2 Then from '~ equation (lo), if Rs equals 35 A, there are approximately 4 . 7 ~ 1 0 small pores per square centimetre of membrane surface. (b) The flux is maximised when the effective skin layer thickness is minimised. Assume the casting conditions can be controlled so that the skin consists of one monolayer of macromolecules, Then L is approximately equal to 2Rs, or 70 A, i.e. the diameter of a solution macromolecule. From equation (1 l), for 25°C water at an operating pressure of 250 psig, the optimal PWP is approximately 1.2 g cm-2 h. The optimal PWP can be compared to values for some PA/DMAc/additive membranes of ref.2. Note that the Rbl values for these membranes vary from about 3.0 to 4.0 A. From equation (1 l), the effect of this difference in the membrane Rbl-value, compared to the design value of 3.5 A, on the PWP is small. The PWP values for these membranes2 varies from h, which is significantly lower than the optimum PWP. 0.07 to 0.33 g %o major factors contribute to the decrease in the actual membrane PWP below the optimal value. From equations (1) and (lo), the polymer concentration is too low and/or the additive effect on swelling is too high to produce a small R s and large n. From equations (1) and (1 l), the polymer and additive concentrations are too low so the effective skin layer thickness is much greater than 2Rs, i.e. the skin layer is composed of more than a monolayer thickness of macromolecules. Conclusions Linear polymeric RO/UF membranes have been analysed according to the interstitial void model. Casting solution macromolecules that constitute the surface monolayer are predominantly close-packed. Variations in the casting conditions cause changes in the size, distribution and degree of coalescence of the surface macromolecules, thereby affecting the overall porosity and performance of the resultant membrane. This paper shows that the interstitial void model can be used for membrane design purposes. The large pores in PA/DMAc/CaC12 membranes have been examined in detail. The flux through an RONF membrane is determined by the interstitial model, and estimates of the number of pores per membrane area and effective skin layer thickness can be made. Using the interstitial model, membrane performance can be related to the casting conditions. The performance of a membrane can be predicted, without first having to make the membrane and test it. Membrane design is possible, regardless of the validity of the assumptions involved in determining casting solution structure and resultant membrane surface morphological constants. 246 H, Wood and S. Sourirajan Acknowledgements Hal Wood wishes t o thank the NSERC for partial support of this work. Special thanks to T.D. Nguyen for his helpful comments and suggestions. References I . Wood, H. and Sourirajan, S. 1991. The effect of additives, solvent type, and polymer concentration on macromolecule dimensions. J. Appl. Polymer Sci., 43( l), 21 3-217. 2. Nguyen, T.D., Matsuura, T. and Sourirajan, S. 1987. Effect of nonsolvent additives on the pore size and pore size distribution of aromatic polyamide RO membranes. Chem. Eng. Commun., 54, 17~ . 3. Nguyen, T.D., Matsuura, T. and Sourirajan, S. 1987. Effect of the casting solution on the pore size and pore size distribution of resulting aromatic polyiunide membranes. Chem. Eng. Commun., 57,351-369. 4. Nguyen, T.D., Chan, K., Matsuura, T. and Sourirajan, S. 1985. Viscoelastic and statistical thermodynamic approach to the study of the structure of polymer film casting solutions for making ROAJF membranes. Ind. Eng. Chem. Prod. Res. Dev., 24(4), 655665. 5 . Wood, H., and Sourirajan, S. 1992. The effect of polymer solution composition and film-forming procedure on aromatic polyamide membrane skin layer structure. J. Colloid Inte$ace Sci., 149(1), 105-1 13. 6. Sourirajan, S. and Matsuura, T. 1985. Reverse Osmosis/Ultrafiitration Process Principles, Chap.4. Available from Division of Chemistry, National Research Council, Ottawa, Canada, KIA OR6; NRCC No. 24188. 7. Wood, H. and Sourirajan, S. 1993. The nature of pores in the skin layer of polymeric reverse osmosis/ultrafiltration membranes. Dev. Chem. Eng. Min. Proc. 8. Wood, H. and Sourirajan, S. 1992. The origin of large pores on aromatic polyamide membrane surfaces. J. Colloid Inte$ace Sci. (accepted for publication). 9. McKinney, R. 1972. Reverse osmosis separations with aromatic polyamide films and hollow fibres. Sep. Purq Methods, 1(1), 31-115. 10. Ohya, H., Imura, Y.,Moriyama, T.and Kitaoka, M. 1974. A study on the pore size distribution of modified ultrathin membranes. J. Appl. Polymer Sci., 18, 1855-1867. 11. Matsuura, T., Taketani, Y.and Sourirajan, S. 1983. Interfacial parameters governing reverse osmosis for different polymer material - solution systems through gas and liquid chromatography data. J. Colloid Interface Sci., 95(1), 10-22. 12. Matsuura, T. and Sourirajan, S. 1981. Reverse osmosis transport through capillary pores under the influence of surface forces. Ind. Eng. Chem. Prod. Des. Dev., 20, 273-282. 13. Glueckauf, E. and Russell, P.J. 1970. The equivalent pore radius of dense cellulose acetate membranes. Desalination, 8(3), 351-357. Received: 16 September 1992; Accepted afier revision: 18 February 1993.