Properties–performance of thin film composites membrane: study on trimesoyl chloride content and polymerization time

Journal of Membrane Science 255 (2005) 67–77

Properties–performance of thin film composites membrane: study on trimesoyl chloride content and polymerization time A.L. Ahmad ∗ , B.S. Ooi School of Chemical Engineering, Engineering Campus, Universiti Sains Malaysia, Seri Ampangan, 14300 Nibong Tebal, S.P.S., Penang, Malaysia Received 4 December 2004; received in revised form 19 January 2005; accepted 23 January 2005 Available online 16 February 2005

Abstract The characteristics of polyamide membranes with respect to interfacial polymerization of diamine mixtures with trimesoyl chloride (TMC) are investigated. This study provides the information about the effect of TMC content and reaction time on membrane properties like pore size, effective thickness/porosity and charge density. The membrane properties were determined based on the charged and uncharged solute permeation test and the hypothetical mechanistic structure (pore size, effective thickness/porosity, fixed charged density) was determined using Donnan steric pore flow model (DSPM). It was found that the membrane pore size was reduced at higher TMC content whereas the effective thickness/porosity shows a minimum value at 0.10% TMC content. Besides, the membrane effective charge density achieved its highest absolute value at 0.10% TMC content. The TMC content and reaction time could be optimized for CuSO4 removal. It was concluded from the experimental results that the optimum rejection of CuSO4 could be achieved at low reaction time (5 s) with TMC content around 0.10%. At this optimum condition, the rejection of CuSO4 was more than 95% without compensating for the flux loss. © 2005 Elsevier B.V. All rights reserved. Keywords: Trimesoyl chloride; Reaction time; Thin film composite; Polyamide; Nanofiltration

1. Introduction The composition and morphology of composite membranes prepared by interfacial polymerization (IP) method depends on several variables, such as concentration of reactants, partition coefficients of the reactants, reactivity ratios where blends of reactants are employed, solubility of nascent polymer in the solvent phase, the overall kinetics and diffusion rates of the reactants, presence of by products, hydrolysis, cross-linking and post-treatment [1]. Research works had been carried out to find out the optimum conditions to produce optimized and high performance membrane. Basically, the works could be categorized into three areas, which included preparation condition, material selection and kinetic control. Numerous studies have been carried out to find out the effect of preparation condition on ∗

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membrane performance. These parameters did play an important role in determining the structure of the interfacially polymerized film and subsequently the membrane performance. Rao et al. [2] found a method using attenuated total reflectance infrared (ATR-IR) spectroscopy to study the structural–performance correlation of polyamide thin film composite membranes. They found out that the critical parameters for thin film coating were reaction time, relative humidity and coating temperature. The membrane flux could be improved by optimizing the time of contact between the discriminating layer, the temperature of contact and the pH of the amine solution [3]. In terms of material selection, it was believed that several factors could influence the polyamide film thickness, such as monomer size, solubility, shape and reactivity [4]. Mickols, for example patented the works on flux enhancement by varying the type of amine employed [3]. Moreover, Chen et al. [5] found that wetting agent, monomer concentration as well as swelling agent played a great impact on membrane properties.

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In the case of reaction kinetic control, Lu et al. [6] pointed out that, the key of the IP method was to select the right partition coefficient of the reactants in the two-phase solution and to set the appropriate diffusion speed of the reactants to achieve the ideal degree of densification of the membrane surface. Moreover, the concentration of the diamine is an important factor, which can affect the performance of the resulting composite, since it may control the uniformity and thickness of the ultimate polyamide support on the substrate. If the coating is non-uniform, it can lead to develop small holes, which may adversely affect salt rejection property of the membrane [7]. Since the IP process is diffusion controlled in the organic layer [8], the effect of organic phase reactant is likely to have a great impact on membrane performance. In the discovery by Cadotte and Rozelle of the NS100 membrane at Northstar Research Institute, several monomeric amines had been tried as well as piperazine [9]. High rejection composite membranes could be made by interfacial reaction of piperazine with isophthaloyl chloride. Conditions necessary for obtaining good composite membranes of poly(piperazineamide) included concentrations of 1–2% piperazine, use of an acid acceptor and use of a surfactant in the amine recipe [10]. From 1978 to 1988, an intensive research has been carried out to modify the membrane flux and salt rejection with variety of acid acceptor and replacement of a portion of the isophthaloyl chloride with trimesoyl chloride. It was found that the maximum water flux was obtained at roughly 50:50 (w/w) diacyl:triacyl chloride content. The membrane produced could reject 99.9% MgSO4 and 64% NaCl at the flux of 96 gfd (salt flux) under 1500 psig operating pressure and 3.5% synthetic wastewater [11]. NF-40, NTR-7250, UTC-20 and UTC-60 are some of the membranes developed based on the poly(piperazineamide) technology. In this paper, the effect of TMC on the membrane properties was studied based on the piperazine/3,5-diaminobenzoic acid (PIP/BA) system. It was expected that by incorporating the BA into the membrane poly(piperazineamide) backbone, the membrane will be more hydrophilic due to the carboxylic group of benzoic acid. Subsequently, the hydrophilic nature of the membrane would enhance the membrane performance in terms of water flux. The membrane prepared under different PIP/BA ratio has been studied in our previous paper [12], it was found that the diamine content with 0.05% BA was proved to improve the membrane in terms of flux. However, the excessive incorporation of BA into the membrane skin layer will reduce its flux as well as rejection. In the case of nanofiltration membrane or membrane with higher porosity compared to reverse osmosis, it was speculated that the TMC content has an high impact on the rate and degree of reaction which eventually affect the final performance of the membrane. The relationship between PIP/BA and TMC system were studied throughout this paper and its performance in terms of flux and rejection were evaluated.

2. Experimental 2.1. Preparation of microporous polysulfone support membrane The polysulfone support was prepared by dissolving 15% Udel P-1700 polysulfone (supplied by Solvay Advanced Polymers, L.L.C.) in N-methylpyrrolidone (NMP, Fluka) with 18% polyvinylpyrrolidone (PVP-10, Sigma) as the poreformer. The solution was cast onto a tightly woven polyester fabric with a nominal thickness of 100 ␮m using a labdeveloped auto-casting machine. The entire casting machine was kept in an air-conditioned room and the temperature was maintained between 24 and 26 ◦ C with a relative humidity of 59–61% during the casting process. After coating, the membrane was immersed into water bath for at least 24 h until most of the solvent and water-soluble polymer was removed [13]. 2.2. Fabrication of thin film composite membranes The support layer, which was taped onto a glass plate, was immediately dipped into an aqueous diamine solution containing 1.95% (w/w) piperazine (PIP, Merck) and 0.05% (w/w) 3,5-diaminobenzoic acid (BA, Merck) for 5 min at ambient temperature. The excess solution from the impregnated membrane surface was removed using a rubber roller. The membrane was then dipped into n-hexane solution containing 0.05–0.20% (w/v) trimesoyl chloride (TMC, Fluka) for predetermined time of 5, 10 and 30 s, which resulted in in situ formation of active skin layer over the surface of the polysulfone support. 2.3. Morphology checking Membrane morphology was examined under Variable Pressure Field Emissions Scanning Electron Microscope, VP FESEM (Leo Supra 50VP, German). The membranes were prepared under different TMC content of 0.05, 0.10, 0.15 and 0.20% (w/v) with reaction times of 5 s. The membranes were fractured cryogenically in liquid nitrogen, gold coated and the cross-sectional view was observed under 10,000× magnification. 2.4. Analytical technique for bonding confirmation Bonding confirmation of the membrane active layer was carried out using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy instrument (PerkinElmer Series II) with a ATR accessory fixed at the angle of 45◦ , which caused a 5 ␮m depth penetration of the IR beam into the surface of the membrane. 2.5. Membrane performance test The membrane permeation test was carried out using the Amicon 8200 stirred cell (Amicon, Inc.) at five different pres-

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sures: 150, 250, 350, 400 and 450 kPa. The membrane was cut into a 5.5 cm diameter disc (effective area of 28.27 cm2 ) and then mounted at the bottom of the stirred cell. The separation ability was tested using the feed solution of monovalent ions of 0.01 M NaCl (Merck) and divalent ions of 100 ppm CuSO4 anhydrous (Merck), which were dissolved in deionised water of 18.2 M
resistivity. For each operating pressure, fresh solution was used as a feed. Bulk feed concentration was calculated based on the average of initial and final feed concentration. Nitrogen gas was used to pressurize the water flux through the membrane. The NaCl in feed and permeate solutions were measured using a conductivity meter (Hanna Instruments, Model: HI8633), while copper ion concentration for the feed and permeate solutions were analyzed using Hanna copper ion specific meter (Hanna Instruments, Model: HI 93702) which is an adaptation of the EPA approved method. Each membrane was subjected to pressure pre-treatment at 500 kPa for 1 h before the permeation experiment. The flux was equilibrated for the passage of the first 20 ml permeate whilst the following 10 ml permeate was collected for concentration analysis. All the results presented were an average data obtained from three membrane samples with a variation of ±10%. 2.6. Determination of rp and x/Ak using uncharged solute (glucose) For determination of the pore size and effective thickness/porosity, the permeation test was carried out using deionised water and 300 ppm glucose solution. The flux and rejection data of the solution was fitted using the DSPM

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model and the Hagen–Poiseuille equation as described elsewhere [14–16] to get the optimized mechanistic structure. The DSPM model and its background are briefed in Appendix A. 2.7. Determination of charge density (X) using charged solute (NaCl) The charge density, X were found by best fit the Jv –Rreal curve of 0.01 M NaCl solution using an analytical equation derived from the basic principles of Donnan steric pore flow model [14–16]. The rp and x/Ak value were obtained from the previous fitting of glucose solution rejection. The fitting of the rejection curves to obtain X was done using curve fitting software (Sigma Plot 2000), which utilizes the Levenberg–Marquardt method.

3. Results and discussion 3.1. Membrane cross-sectional morphology under SEM Fig. 1 shows the composite membranes that are prepared under 5 s reaction time and at 0.05 and 0.20% TMC, respectively. The SEM pictures under 10,000× magnification shows that the composite membrane consists of two distinctive layers with a dense layer coated on top of the porous layer. At 0.05% TMC content, a very thin, non-perfect layer is found to be pore filled on top of the porous structure whereas at higher TMC content (0.20%), the skin layer becomes bulky and a distinctive solid layer is observed to be coated on the porous support with the thickness around 0.4 ␮m. Higher TMC con-

Fig. 1. SEM pictures of membranes fabricated under (a) 0.05%, (b) 0.10%, (c) 0.15% and (d) 0.20% TMC with 5 s reaction time (10,000× magnification).

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tent implies that the rate of polymerization is higher which produced a thicker skin layer at the predetermined reaction time. 3.2. Effect of trimesoyl chloride on membrane properties (pore size (rp ) and effective thickness/porosity (x/Ak ) and charge density (X)) Fig. 2 shows the effect of TMC concentration on membrane pore size. It was found that as the concentration of TMC content is increased, the pore size is reduced. The pore size change is drastic from 0.05 to 0.10% TMC content especially for membrane reacted under short time (5 and 10 s). However, for 30 s reaction time, the pore size is reduced steadily from 0.65 to 0.49 nm. A total of 36.8% reduction in pore size is observed for 5 s reaction time. It is followed by 10 s reaction time (21.9%) and 30 s reaction time (12.3%) from 0.05 to 0.10% TMC content. However, the extent of pore size changes become less significant after 0.10% TMC content. The other phenomenon observed here is that at high-TMC content (0.20%), the pore size seems to be independent of the reaction time and the value is about 0.50 nm. TMC content plays an important role in determining the rate of reaction while the reaction time will determine the extent of reaction. For short reaction time (5 s), the extent of cross-linking is low, as a result, the pore size produced is larger (0.74 nm). However, when the concentration of TMC content is increased, the rate of reaction is increased tremendously. Since this interfacial polymerization is an instantaneous process, further cross-linking process takes place immediately to reduce the pore size [17]. It is note that, the membrane properties is determined to a great extent by the partitioning coefficient [18] of aqueous phase reactant (PIP/BA) into the polymer film to reach the reaction zone. Densification of the polymeric film will result in a low diffusion of both reactant. In other words, it suggests that the polymerization is diffusion controlled which is independent of the organic phase concentration (TMC).

Fig. 2. Effect of TMC content on membrane pore size.

However, the reaction time carried out throughout this study was constricted to less than 30 s, in which the membrane can be considered less dense to restrict the diffusion of PIP/BA. This assumption was also made by Ji et al. [19] in which the diffusion coefficient of A in the newly formed polymer film is constant. This phenomenon is more prevalence in the case of PIP/BA mixtures because of its reduced reactivity that produced a more porous structure. It can be proved from our previous paper [12] on the PIP/BA content study, which found that at higher BA ratio to PIP, the pore size produced is bigger. Under this constricted time, the effect of TMC content on membrane morphology should not be neglected. With respect to the effect on x/Ak , Fig. 3 shows that the value of x/Ak reduced drastically when the TMC content increased from 0.05 to 0.10% TMC. x/Ak reached the minimum value at 0.10% TMC content irrespective to the reaction time and increased beyond 0.15% and become plateau at higher TMC content. Membrane reacted under different time shows the same x/Ak profile, however, the magnitude of x/Ak is increased with the increase in reaction time. It is unexpected that x/Ak obtains its highest value at 0.05% TMC content because membrane reacted under this concentration most probably produced a very thin effective layer. Furthermore, the pore size is larger at low TMC content, which would result in higher porosity that reduces the x/Ak value. Therefore, it is deduced that the higher value of x/Ak observed at 0.05% TMC content must be resulted from the low surface porosity. Since porosity is a function of pore size and pores number, it is postulated that the number of pores should be less compared to the membrane prepared at higher TMC content. At low TMC content, the rate of reaction is very low which produced polymer aggregates with low molecular weight. The small polymer aggregates are closely packed to give a denser surface structure. This phenomenon agrees well with the finding of Ozaki et al. [20] in which the more porous structure of membrane has been evolved from large

Fig. 3. Effect of TMC content on membrane x/Ak .

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loosely packed aggregates while the denser structure consists of small closely packed polymer aggregates. The degree of polymerization, which is an indication of the molecular weight, can be related to the conversion and the reactant ratio as outlined by Kumar and Gupta [21]. They derived the relationship between number-average chain length, µn (degree of polymerization) with the conversion and reactant ratio of two bifunctional reactant. However, in this case, the relationship was re-derived for the reaction involves trifunctional group trimesoyl chloride (TMC) and bifunctional group piperazine (PIP). In order to determine the molecular weight, we need to determine the total number of molecules at time t when the conversion of TMC functional groups is PTMC : PTMC =

2NTMC0 − 2NTMC 2NTMC0

(1)

The total number of moles of unreacted TMC functional group at time t is equal to 2NTMC0 (1 − PTMC ) while the total number of moles of unreacted PIP functional group at time t is equal to (3NPIP0 − 2NTMC0 PTMC ). The total number of moles of polymer is simply half of the unreacted piperazine functional group and one-third of the unreacted TMC functional group. In other words, the total number of moles of polymer, N, at time t is equal to 1 1 3 (3NTMC0 (1 − PTMC )) + 2 (2NPIP0 − 3NTMC0 PTMC ). Similarly, the total number of moles of polymer initially, N0 , is equal to NTMC0 + NPIP0 : µn =

N0 NTMC0 + NPIP0 = N NPIP0 + NTMC0 − 53 NTMC0 PTMC =

1+r 1 + r − 25 PTMC r

(2)

where µn is defined as the number-average chain length or degree of polymerization and r=

NTMC0 NPIP0

Fig. 4. Effect of conversion and reactant ratio on degree of polymerisation.

molecular weight of the polymer is expected to increase about 10% from 0.05% TMC (r = 0.01) to 0.20% TMC (r = 0.04). Besides that, the increase of x/Ak value from 0.10 to 0.15% is a result of the increased effective thickness because the experimental data shows that the pore size is quite constant between 0.10 and 0.15%. On the other hand, the small changes of x/Ak at 0.20% indicate that the rate of reaction is slowing down due to the diffusional barrier of the layer developed. As presented in Fig. 5, the membrane charge density is altered significantly by changing the TMC content. In overall, the charge density of membrane is higher for membrane reacted at lower reaction time. For example, at 0.10%, the charge density of membrane reacted at 30, 10 and 5 s are −269, −392 and −564 mol m−3 , respectively. The charge density decreased drastically from 0.05 to 0.10% TMC content, marking significant property changes within this 0.05 to 0.10% TMC differences. This phenomenon may be due to: (i) at low TMC content, majority of the functional group

(3)

It is observed that when 100% conversion of TMC functional groups (PTMC = 1) is achieved, the average chain length has a limiting value of 1+r3 . It is thus seen that an r value of 2/3 1− 2 r is desirable for the formation of polymer with high molecular weight. However, in this reaction system, the concentration of TMC compared to PIP is far smaller. The ratio of TMC to PIP is around 0.01–0.04. Thus, it is expected that the degree of polymerization is very low due to the limiting concentration of TMC. Nonetheless, it can be seen from Fig. 4 that the degree of polymerization is higher for higher ratio of TMC content to PIP. In other words, the higher the ratio of TMC, the higher molecular weight of skin layer will be formed. It could be deduced from Fig. 4 that the molecular weight also increased with higher conversion. Since higher conversion of reactant could be achieved at longer reaction time, the

Fig. 5. Effect of TMC content on membrane charge density.

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is reacted which reduce the opportunity of the acyl chloride group to be hydrolysed; (ii) the decrease of pore size from 0.05 to 0.10% TMC content increase the charged density due to the higher extent of electrostatic double-layer overlap in narrow pores [22]. By assuming the NF membrane with pore radius (rp ) and constant surface charge density (qw ), the fixed 2πr q w charge density, X can be expressed as X = πr2pFw = 2q rp F [23]. p

The relationship between X and rp implies that as the pore size is reduced, fixed charge density will be increased. This phenomenon is validated in Figs. 2 and 5, in which a drastic decrease of pore size from 0.75 to 0.45 nm, result in the sudden increase of charge density from −100 to −550 mol m−3 . On the other hand, at higher TMC content (>0.10%), it is found that the charge density is decreased. Since the pore size changes beyond 0.15% TMC is not significant, this phenomenon may be due to the hydrolysis process. The hydrolysis process increases the membrane positive charge because of protonation of the amine group [24]. 3.3. Effect of TMC content on NaCl rejection and flux Fig. 6 shows the NaCl flux at 0.05, 0.10, 0.15 and 0.20% TMC content and different reaction time. The flux for 0.05% TMC content is reduced from (2.1 to 1.1 × 10−5 ) m s−1 when the reaction time is increased from 5 to 30 s. However, the effect of reaction time on flux becomes less significant at higher TMC content. Extended degree of reaction (which is a function of reaction time) cause extensive cross-linking and film-growth that reduced the membrane flux at higher reaction time. There are distinct drops in flux when the TMC content is increased but the flux is leveled-off at higher TMC content (>0.15%). At higher TMC content, the rate of reaction is high, which do rapidly build up the film layer and exert diffusional resistance for further monomer reaction to occur. This explains why the flux is reduced tremendously from 0.05 to 0.15% TMC content. However, for 30 s reaction time, the

Fig. 6. Effect of TMC content and reaction time on flux of NaCl solution.

Fig. 7. ATR-FTIR spectrum of membrane prepared with 0.05% and 0.10% TMC at 5 s.

flux seems not much affected by the TMC content compared to 5 and 10 s reaction time. Since flux is a function of membrane thickness [25], the reduction of flux is an indication of increasing film thickness. While the film increased at the expenses of some flux loss, the carboxylic acid group incorporated through 3,5-diaminobenzoic acid increases water flux due to its hydrophilic properties [26]. The incorporation of the hydrophilic group can be seen from the IR spectrum of 0.05 and 0.10% TMC as shown in Fig. 7 in which the carboxylic group (the OH and C O group) of the 0.10% TMC is found higher than the 0.05% TMC. This explains why the flux did not drop at 0.10% TMC content although the skin layer thickness is increased. On the other hand, the leveled-off flux after 0.15% TMC content as observed in Fig. 6 indicates that the diffusional barrier for the organic and aqueous phase reactant formed instantaneously at 0.15% TMC content and the barrier thickness reach its limit at 30 s reaction time. Fig. 8 shows the rejection profile of NaCl under different TMC content and reaction time. For 5 and 10 s reaction time, rejection is increased at low TMC content and vice versa. For 30 s reaction time, a steady increase in rejection is observed within the TMC range, however, the overall rejection performance of 30 s reaction time is not satisfactory compared to 5 and 10 s reaction time. The increased in rejection at 0.10% TMC (10 s) and 0.15% TMC (5 s) are due to the decreasing pore size as a result of cross-linking as shown in Fig. 2. However, it is observed that the rejection performance dropped at high-TMC content (0.20% TMC). It is postulated that the pore loosening starts to occur at this high-TMC content that the contribution of convective flow again become significant. At this TMC content, the reaction rate is so high that excessive 3,5-diaminobenzoic acid is introduced. Skin layer with higher BA content produces membrane with loose structure. Same finding was outlined by Konagaya and Tokai [27] in which copolyamides from diaminobenzoic acid could not be

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Fig. 10. Effect of TMC content and reaction time on Rejection of Cu2+ ion. Fig. 8. Effect of TMC content and reaction time on real rejection of sodium chloride solution.

The effect of TMC content on the CuSO4 solution flux is shown in Fig. 9. The flux profile is following the same trend as the flux profile of NaCl in Fig. 6. It is found that the flux at lowest reaction time is higher than the flux at higher reaction

time and basically the flux at lower TMC content is higher than the flux at higher TMC content. The effect of TMC content and reaction time on Cu2+ rejection is shown in Fig. 10. It is found that for the 5 and 10 s reaction time, the rejection is drastically increased when the concentration of TMC is increased from 0.05 to 0.10%. The rejection is immediately leveled-off after 0.10% TMC and maintained constant around 95%. On the other hand, for 30 s reaction time, the CuSO4 rejection is found to be continuously increased with the TMC content. At low reaction time (5 and 10 s), the membrane rejection characteristic is controlled by reaction time whereas for high reaction time, the membrane rejection characteristic becomes concentration controlling. Since the rate of reaction is comparatively lower at low-TMC content, the extended cross-linking is only allowed at longer reaction time. At longer reaction time and higher rate of reaction, the membrane rejection is higher due to the cross-linking process that enhanced the tortuosity of CuSO4 to transport through the membrane.

Fig. 9. Effect of TMC content on the volume flux of CuSO4 .

Fig. 11. Separation ratio of membrane at different TMC content.

achieved at high temperature because of higher reaction rate. The membrane prepared is defective if BA was incorporated extensively at higher reaction rate. In overall, rejection is poorer at higher polymerization time (30 s) because the skin layer tends to create channeling (defect) at prolonged reaction time. However, a continuous increase in rejection is noticed for higher TMC content at 30 s reaction. This behavior is due to the continuous pore size reduction as a result of continuous cross-linking process at high-TMC content. 3.4. Effect of TMC content on CuSO4 rejection and flux

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3.5. Effect of TMC content on relative selectivity between NaCl and CuSO4 Membranes fabricated under different TMC content and reaction time is compared for its relative selectivity (γ). Relative selectivity (γ) is the ratio of copper ions rejection to R 2+ sodium ion rejection γ = RCu + on the basic of single solute Na system. Since both the concentration of CuSO4 and NaCl are different, relative selectivity is only suitable to compare the properties of membrane tested under the same salt system. Fig. 11 shows that the changes of γ value within the TMC content is significant for both 5 and 10 s reaction time whereas for 30 s reaction time, only a small change of γ is observed. A drastic drop of γ from 0.05 to 0.10% TMC content is at-

tributed to the sudden increase of diffusional barrier because of instantaneous film growth. This effect can be seen in Fig. 2 that the membrane encounters a sudden decrease of pore size from 0.05 to 0.10% TMC content. During this concentration change, the solute transport mechanism will be immediately changed from diffusional flow to a more convective flow. At larger pore size, NaCl is exclusively transported through the membrane while the CuSO4 is still sterically hindered. For 30 s reaction time, it seems that the relative selectivity do not change much because at this high reaction time, the membrane morphology is close to each other due to similar degree of reaction. At higher TMC content, the selectivity is slightly improved due to the increase in polymer free volume. The increase in polymer free volume is most likely caused by the bigger aggregates formed under higher rate of reaction. 3.6. Optimization of CuSO4 removal by varying TMC content Membrane properties such as pore size, thickness, porosity as well as charge density could be optimized for CuSO4 removal by means of controlling TMC content and reaction time. The optimum condition allows maximum separation of metal salt at lowest possible operating pressure. Fig. 12(a) and (b) are plotted using Sigma Plot 2000 to show the optimum rejection and flux under the effect of reaction time and TMC content. The 3D surface view is smoothened using quadratic negative exponential method. It is found that the optimum rejection occur at medium TMC content and short reaction time (5 s) while the optimum flux is marked at low-TMC content and short reaction time (5 s). Fig. 13 shows that the optimum membrane for divalent ion (Cu2+ ) removal could be prepared under 0.10% TMC and 5 s of reaction time. Under this fabrication condition, membrane rejection and flux value are noted to be the highest under the operating pressure of 450 kPa. It is due to the higher charge density that enhanced the rejection ability and increased porosity. Beyond 0.10%, the membrane shows a

Fig. 12. 3D view of the effect of reaction time and TMC content on (a) real rejection of CuSO4 , (b) volume flux.

Fig. 13. Optimization of Cu2+ ion removal (reaction time: 5 s).

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level-off rejection profile and a gradual loss in flux is observed. This phenomenon is not favored for the process that requires low operating pressure because of low water permeability. On the other hand, membrane prepared under 0.05% TMC and 5 s reaction time is not properly cross-linked that a defective skin layer is produced. The defective membrane resulted in poor rejection to NaCl and CuSO4 . 4. Conclusion Membrane reacted under different TMC content and reaction time produces skin layer with different characteristics. It is found that the membrane pore size is reduced with the increase of TMC content because of extensive cross-linking process. However, a minimum effective thickness/porosity is observed at 0.10% TMC content, which indicates that within 0.05–0.20% TMC content, the polymer subjected to the changes in thickness as well as porosity due to the packing of polymer aggregates. It is also noted that the charge density marked the highest value at 0.10% TMC content, which is a result of sudden decrease in pore size. On the other hand, the charge density is reduced at higher TMC content and higher reaction time due the hydrolysis process. An optimum membrane could be produced at lowest possible reaction time (5 s) and at 0.10% TMC content. The optimum membrane shows improved rejection of CuSO4 at reasonably high water flux. Acknowledgements The authors wish to thank the Fundamental Research Grant (FRGS) and IRPA EA Grant by MOSTI for giving financial support in this project.

Nomenclature Ak ci Ci,m Ci,p Di,p Di,∞ F ji Jv Jw k K−1 Ki,c

porosity of the membrane concentration in the membrane (mol m−3 ) concentration on the feed side of membrane (mol m−3 ) concentration in permeate (mol m−3 ) hindered diffusivity (m2 s−1 ) bulk diffusivity (m2 s−1 ) Faraday constant (= 96 487) (C/mol) ion flux (based on membrane area) (mol m−2 s−1 ) volume flux (based on membrane area) (m3 m−2 s−1 ) water flux (based on membrane area) (m3 m−2 s−1 ) mass transfer constant (m s−1 ) the hydrodynamic enhanced drag coefficient hindrance factor for convection

Ki,d N N0 NPIP NPIP0 NTMC NTMC0 Pem PTMC qw r rp rr rs Robs Rreal T V x Xd zi

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hindrance factor for diffusion total number of moles of polymer at time t (g mol/l) initial total number of moles of polymer (g mol/l) PIP concentration at predetermined time, t (g mol/l) initial PIP concentration (g mol/l) TMC concentration at predetermined time, t (g mol/l) initial TMC concentration (g mol/l) Peclet number conversion of TMC functional group surface charge density (C/m2 ) ratio of TMC and PIP concentration as defined in Eq. (3) effective pore radius (m) radius of stirrer stokes radius of solutes or ions (m) observed rejection real rejection absolute temperature (K) solute velocity effective membrane thickness (m) effective membrane volume charge (mol m−3 ) valence of component i

Greek letters λ ratio of solute radius/pore radius µn number-average chain length (degree of polymerization) ω stirring speed ψ electric potential in axial direction (V) ψD Donnan potential (V) Φ steric partition term

Appendix A The Donnan steric pore model (DSPM) is first proposed by Bowen et al. [14] based on the extended Nernst-Planck equation (ENP). ENP which was proposed by Schlogl and Dresner [28] forms the basis description of ions transport through the membranes. The equation can be expressed as ji = −Di,p

dci F dψ − zi ci Di,p + Ki,c ci v dx RT dx

(A.1)

where Di,p = Ki,d Di,∞

(A.2)

ji is the flux of ion i and the terms on the right-hand side of Eq. (A.1) represent the transport due to diffusion, electromigration and convection, respectively.

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Ki,d and Ki,c are related to the hydrodynamic coefficients as Ki,d = K−1 (λ, 0) = 1.0 − 2.30λ + 1.154λ2 + 0.224λ3 (A.3) Ki,c = G(λ, 0) = (2 − Φ)(1.0 + 0.054λ − 0.988λ2 +0.441λ3 )

(A.4)

For uncharged solute (glucose), the electrical potential gradient in the axial direction could be eliminated, thus Eq. (A.1) could be reduced to Eq. (A.5): dci ji = −Di,p + Ki,c ci v dx

(A.5)

For purely steric interactions between the solute and the pore wall, the notation, Ф is the steric terms relate the finite size of the solute and pore size. Φ = (1 − λ)2

(A.6)

where λ is a ratio of solute radius (rs ) to pore size (rp ). In terms of real rejection, Eq. (A.5) becomes Rreal = 1 −

Ci,p Ki,c Φ =1− Ci,m 1 − exp(−Pem )[1 − ΦKi,c ]

Ki,c Jv x Ki,d Di,∞ Ak

(A.7)

(A.8)

where Di,∞ is the bulk diffusivity (m2 s−1 ), Jv is the volume flux (based on membrane area) (m s−1 ), x is the effective thickness (m) and Ak refer to the porosity of the membrane. The Hagen–Poiseuille equation gives the relationship between the pure water flux and the applied pressure across the membrane [29]: Jw =

rp2 P 8µ(x/Ak )

r2 k = 0.23 r v

0.567


v D∞

0.33

D∞ rr

(A.12)

For charged solutes the basic equation that governs the transport of ions inside the membrane is given in Eq. (A.1). The conditions of electroneutrality in the bulk solution and inside the membrane are expressed respectively as n 

zi Ci = 0

(A.13a)

zi ci,m = −Xd

(A.13b)

i=1 n  i=1

where Ci is the bulk concentration of ion, ci is the concentration of ion i inside the membrane and Xd is the effective volumetric membrane charge density. Xd is assumed to be constant at all points in the active part of the membrane. Since the electric potential gradient is common for every ion inside the membrane, the electric potential and concentration gradients can be derived from Eq. (A.1): (A.14)

where the flux of ion ji is expressed as ji = Jv Ci,p

(A.15)

By assuming constant Xd throughout the membrane, for binary salt such as NaCl, Eq. (A.14) can be written as z1

dc1 dc2 + z2 =0 dx dx

(A.16)

By solving Eqs. (A.14)–(A.16), the following potential gradient could be obtained n 

dψ = dx

(zi Jv /Di,p )(Ki,c ci − Ci,p )

i=1

(F/RT )

n 

(A.17) (z2i ci )

i=1

(A.9)

where Jw is the water flux (m3 m−2 s−1 ), P is the applied transmembrane pressure (kPa) and µ is viscosity of the solution (kPa s). To find the film layer concentration, the concentration polarization equation was employed. For a stirred cell configuration, the observed rejection was related to the real rejection by volume flux, Jv and mass transfer coefficient, k as follows [14]: 

1 − Rreal Jv 1 − Robs = ln + (A.10) ln Robs Rreal k k = k ω0.567






dci zi ci dψ Jv (Ki,c ci − Ci,p ) − = F dx Di,p RT dx

where Ci,m and Ci,p refer to the concentration on the feed side of membrane (mol m−3 ) and concentration in permeate (mol m−3 ), respectively. The Peclet Number, Pem is defined as Pem =

where

(A.11)

Eq. (A.17) is integrated across the membrane thickness with the solute concentration in the membrane at the upper (x = 0) and lower (x = x) expressed in terms of the external concentrations (Ci,m and Ci,p ) using the Donnan steric equilibrium partition as follows [16]:
 zi F ci = Φ exp − ψD (A.18) Ci RT References [1] R.J. Petersen, Composite reverse osmosis and nanofiltration membranes, J. Membr. Sci. 83 (1991) 81–150.

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