4236
Ind. Eng. Chem. Res. 2008, 47, 4236–4250
Synthesis and Modeling of Charged Ultrafiltration Membranes of Poly(styrene-co-divinyl benzene) for the Separation of Chromium(VI) Sonny Sachdeva and Anil Kumar* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, India 208016
A ceramic supported cross-linked polystyrene (PS) composite membrane has been prepared from its monomers using a dual initiator system, and it has been chemically modified by gas-phase nitration (using NOx), amination using hydrazine hydrate, and quaternization using dichloroethane and triethylamine. The membranes (unmodified, aminated, and quaternized) have been used to study the rejection of chromium(VI) as a function of pressure, concentration, and pH of the feed solution, which was observed to be >90%. The experimental results have been fitted using a space charge model (SCM) to obtain the membrane wall potential and membrane surface concentration. The transport through the membrane capillaries has been described by a two-dimensional model, using the Nernst-Planck equation for ion transport, the Navier-Stokes equation to describe the flow, and the Poisson-Boltzmann equation for the radial distribution of potential. A semianalytical series solution to the highly nonlinear Poisson-Boltzmann equation has been developed, to reduce the computational time required to solve the set of coupled differential equations. The effective wall potential was determined to be 85.95 and 78.7 mV for the quaternized and aminated membranes, respectively. 1. Introduction Ultrafiltration membranes have been put to many applications, such as purification, concentration, and fractionation of highmolecular-weight materials, because of their large pore size and high solvent fluxes at low pressure drop. These membranes have limited selectivity of separation, because of the uneven pore size distribution, and literature1 reports indicate that separation can be improved by introducing specific functional groups on the membrane surface. These functional groups can be introduced to the base monomer or by surface modification of the polymer using chemical methods.1 The surface modification of the polymer suggested in this work allows the membrane to have better specificity, a uniform distribution of functional groups, and resistance to fouling. Many composite membranes reported in the literature 2,3 have been prepared via the surface modification of the polymer film supported on another polymer film2 or a ceramic support,3 with the support providing the necessary mechanical, thermal, and chemical resistance. The surface modification of the membranes is done using various methods, such as classical organic reactions,4–6 plasma treatment,7 polymer grafting,8 photochemical modification,9 and surfactant modification.10 Of all these methods, classical organic reactions such as nitration,4 sulfonation,5 and acid-base treatment in liquid phases6 are the most common, because these can be easily performed and the ion exchange capacity can be tuned according to the type of separation to be performed, as has been also illustrated in this work. Chromium is an essential nutrient for plant and animal metabolism, but when accumulated at high levels (>0.1 mg/g body weight), it can cause serious diseases such as nausea, skin ulcerations, and lung cancer.11 Chromium(VI), which is a highly toxic, carcinogenic oxidizing agent, is a major effluent from leather tanning, chromium electroplating, and chemical manufacturing industries,12 and its recovery is one of the major environmental problems. The method currently used for the treatment of the effluent is the chemical reduction of chromi* To whom correspondence should be addressed. Tel.: +91 512 2597195. Fax: +91 512 2590104. E-mail address:
[email protected].
um(VI) to chromium(III) and neutralization and precipitation at pH 7-9, followed by sedimentation and separation of metal hydroxides.13 This method produces a large amount of sludge that contains chemicals and cannot be used for the recycling of either chromium(VI) or water. Various other technologies for removal of pollutant and recycling the water are ion exchange,14–17 evaporation,18 adsorption,19 liquid-liquid extraction13,20,21 and membrane separation processes.22–28 Membrane separation processes are preferred over all the other processes, because they do not require any addition of chemicals, they require less energy, they are selective, and almost total recovery of the chromates is possible. Several membrane processes have been reported in the literature for the removal of chromium(VI).22–28 Recently, chromic acid separation, using charged ultrafiltration membranes, has been studied using inorganic zeolite membranes,26 polymeric PMMA membranes,27 and phenol formaldehyde-based carbon membranes.28 These membranes have been prepared such that they have fixed charges to membrane pores, giving a high intrinsic rejection of chromic acid. Membranes made from polystyrene and its copolymers are noncellulosic materials that have high chemical stability and mechanical strength. These are generally dense and are used for gas separation requiring high operating pressures,29,30 and the literature 8,5,33–41 also suggests an extensive use of styrenebased membranes as ion-exchange membranes. The sulfonated8,31 and the aminated32 membranes have been in electrodialysis,33 as proton exchange membranes34,35 in fuel cells and as bipolar membranes.36,37 Styrene can be copolymerized with many monomers, such as acrylonitrile and butadiene (ABS), acrylonitrile (SAN), and divinyl benzene (DVB).38 In this paper, a ceramic-supported poly(styrene/DVB) (PS) composite membrane using a dual initiator (azo-bis-isobutyronitrile (AIBN), benzoyl peroxide (BPO)) system catalyzed by N,N-dimethyl aniline (DMA), which gives a stable polymer syrup in its own monomer, has been prepared. Membranes prepared in such a manner are modified by gas-phase nitration, followed by amination using hydrazine hydrate, and they are further quaternized to make them strong anion exchange
10.1021/ie070730g CCC: $40.75 2008 American Chemical Society Published on Web 05/20/2008
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4237 Table 1. Compostion of Clay Supports sample number
clay raw material
chemical formula
composition (wt %)
1 2 3 4 5 6
kaolin ball clay feldspar quartz pyrophyllite calcium carbonate
Al2(Si2O5)(OH)4 3SiO2 · Al2O3 (Na,Ca)(AlSi3O8) SiO2 Al2(Si2O5)2(OH)2 CaCO3
13.28 16.15 5.15 24.44 13.54 27.44
membranes. These have high flux at very low pressure drop without much loss in regard to rejection of the solute (chromium(VI)). The membranes have been fully characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), atomic force microscopy (AFM), contact angle measurements, water content, and molecular-weight cutoff experiments. Here, the separation performance of the membrane so prepared has been evaluated by utilizing it for the removal of harmful chromium(VI) for a range of feed concentrations as a function of pressure and pH. Because the separation is performed using charged membranes, the real rejection of chromium(VI) obtained is >90%, even for very low feed concentrations. The space charge model (SCM) has been used to fit the experimental results to determine membrane wall potential and surface concentration. In the experimental data fitting, it was observedthatthenumericalsolutionofthenonlinearPoisson-Boltzmann equation (PBE) had to be integrated several times, which required a large amount of computation time (on the order of 15 h). To overcome this problem, a series solution of the nonlinear Poisson-Boltzmann differential equation has been developed, which leads to considerable savings of computation time. 2. Experimental Section 2.1. Materials. Styrene and divinyl benzene (DVB) (obtained from Merck, Philadelphia, PA) are distilled to remove the inhibitors. The LR-grade calcium carbonate, ferrous sulfate, sulfuric acid, hydrochloric acid, chromium trioxide, sodium nitrite, hydrazine hydrate, triethylamine, benzyol peroxide (BPO), azobisisobutyronitrile (AIBN) are procured from SD. Fine Chemicals (Bombay, India), and tetraethylorthosilicate (TEOS), dimethyl aniline (DMA), dichloroethane, toluene, ethanol, methanol, nitric acid, polyethylene glycol (PEG), and calcium chloride (fused) were obtained from Qualigens (Bombay, India). 2.2. Preparation of Clay Supports. Microporous ceramic membrane supports have been prepared from a mixture of clays (kaolin, ball clay, pyrophyllite, calcium carbonate, feldspar, and quartz) in water; the composition is given in Table 1.39 A paste of all these clays is made in water and cast on a gypsum surface in the form of a circular disk, using an aluminum ring with an internal diameter (ID) of 76 mm and a thickness of 4 mm. These supports are dried for 24 h at ambient temperature on the gypsum surface, then for 24 h at 100 °C, and, finally, for 24 h at 250 °C, to ensure the slow removal of water. The dried supports are then calcined at 1000 °C for 8 h. The hard, rigid, and porous supports prepared in this way are finally polished using a silicon carbide (SiC) abrasive paper (No. C-220) to get smooth and flat ceramic discs 64 mm in diameter and 2-3 mm thick. 2.3. Preparation of PS Membrane. The first step in preparing the composite polystyrene membrane is the synthesis of a stable polystyrene/divinyl benzene copolymer solution. The copolymer syrup is prepared from its monomer (styrene) using
a dual initiator (BPO and AIBN) system, dimethyl aniline (DMA) as an accelerator, and divinyl benzene (DVB) as the cross-linking agent. The initiators BPO and AIBN are recrystallized in methanol before being used, and styrene monomer is washed with caustic (5% NaOH solution) and distilled water to get rid of the inhibitor pyrocatechol. A mixture of styrene (5.0 g, 0.048 mol), BPO (0.0675 g, 2.78 × 10-4 mol), AIBN (0.037 g, 2.25 × 10-4 mol), DMA (0.0205 g, 1.69 × 10-4 mol), and DVB (0.15 g, 1.15 × 10-3 mol),40 in the presence of N2, is heated for 1 h at 70 °C in the water bath and then cooled quickly to room temperature. The reaction mass, which is a homogeneous solution of the copolymer, is diluted with toluene and is further used for membrane casting. The clay support is placed over wet polyurethane foam, so that the air present inside the pores of the supports is displaced by water. Moreover, water, being a nonsolvent for the polymer mixture to be cast on the support, does not allow the foam to penetrate inside the pores of the clay support, forming a distinct thin layer on the surface. A known amount of this polymer solution (∼2 g) in toluene is spread uniformly over the wet clay support and dried at room temperature until all the solvent evaporates. The polymer coated clay support is further dried and cross-linked at 70 °C for 24 h. 2.4. Modification of PS Clay Composite Membrane. The composite membrane is further chemically modified in a series of four steps to make it anionic in nature. 2.4.1. Gas-Phase Nitration of the PS Composite Membrane. The gas-phase nitration reaction of the composite polymer membrane is performed by a gaseous mixture of NO and NO2 (called NOx) that is generated by the reaction of sodium nitrite (10 g, 0.14 mol) with sulfuric acid (36 N, sp. gr. 1.18, 25 mL) and ferrous sulfate (5 g, 0.072 mol), following a procedure reported in the literature.41 The membrane is placed inside a glass reactor that has a stainless steel lid, with a rubber septum in the center, through which the vacuum is created and NOx is injected in the reactor using a needle. The reactor is filled with 500 cm3 of NOx (a mixture of NO and NO2) gas and kept at a temperature of 110 °C for 6 h for the complete nitration of the polymer layer. After the nitration reaction, the membrane is kept in distilled water to remove the NOx gas adsorbed by the clay support. The overall nitration reaction scheme is shown as Figure 1. 2.4.2. Amination of the PS Composite Membrane. The nitrated membrane is further refluxed with a 50% hydrazine hydrate/50% water mixture for 6 h at 50 °C in a water bath, to reduce the NO2 groups to amine (NH2) groups. A membrane prepared in this manner has primary ammonium groups on its surface, which make it more hydrophilic, as well as charged, as shown in Figure 1.2.4.3. Quaternization of the PS Composite Membrane. The aminated membrane is further modified by refluxing it with 2% (v/v) 1,2-dichloroethane solution in ethanol for 4 h at 50 °C. The modified membrane is quaternized by refluxing it with a 5% solution of triethylamine (TEA) in ethanol for 4 h at 50 °C. This modified membrane is a strong anion exchange membrane, with quaternary ammonium groups (see Figure 1) on its surface. 2.5. Characterization of Modified PS Membranes. The structural morphology of the top surface and the cross section of the composite PS membrane has been analyzed using a JeolJSM (Model 840 A) SEM system at an acceleration voltage of 3 keV. Pore sizes of membranes have been measured by visual inspection of the line profiles of various AFM images, corresponding to different areas of the same membrane. All the samples are scanned using AFM equipment from Molecular
4238 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
Figure 1. Reaction scheme of the polystyrene membrane modification.
Imaging (MI) (USA) in Acoustic AC (AAC) mode. Cantilevers used for AAC mode NSC 12I were obtained from Mikro Masch with a force constant of ∼4.5 N/m and a frequency of ∼150 kHz. The scan speed is maintained at 2 lines/s, and the imaging is done in air at room temperature. About 35 pores are obtained by visually inspecting the line profiles of different pores on the AFM images of the different areas of the same membrane and arranged in ascending order to which median ranks are assigned. Median ranks are calculated from the following formula: j - 0.3 × 100 (1) n + 0.4 where j is the order number of the pore, when arranged in ascending order, and n is total number of pores measured.42 To obtain a cumulative distribution function graph, these median ranks are plotted on the ordinate axis against pore sizes arranged in increasing order on the abscissa. This plot yields a straight line on log-normal probability paper if the pore sizes have a log-normal distribution. From this graph, values of the mean pore size (µp) and the geometric standard deviation (σp) can be calculated. The pore size of the unmodified and the modified membranes has been determined by analyzing the retention of aqueous solution (1000 ppm) of polyethylene glycol (PEG) of different molecular weight (200-35000 Da), using the following relation:42 median )
a ) 16.73 × 10-10M 0.557 (2) where a is the pore radius of the membrane and M is the molecular weight of PEG taken. All the experiments are conducted at room temperature and 40 psi. To determine the PEG retention as a function of molecular weight, the PEG concentration in feed and permeate is estimated using refractive index (RI) measurements. To confirm the presence of amine and nitro groups on the membrane surface, FTIR spectra of the unmodified, nitrated, aminated, and quaternized membrane samples have been obtained using a Bruker model VERTEX 22 spectrometer. The static contact angles of the unmodified and modified membrane
Figure 2. Schematic diagram of the unstirred batch ultrafiltration setup.
surface with water are measured using the sessible drop method, using a goniometer (Model 100-00-230) that was supplied by R’ame-Hart, Inc., USA with RH1 2001 Imaging software. Water uptake of the unsupported films was measured by calculating the difference in weight of the dry and wet membrane sample: Water Uptake (%) )
Wwet - Wdry × 100 Wdry
(3)
2.6. Experimental Setup and Ultrafiltration Experiments. The experimental setup used for the ultrafiltration experiments is a dead-end-type batch cell. The batch cell (Figure 2) consists of two parts: the cylindrical top part and a base plate that is made of SS316 stainless steel with a height of 240 mm and an outer diameter of 76 mm. This cylindrical cell has a volume of 800 mL, and the base plate has a circular groove 4 mm deep, which houses the membrane. The PS ceramic composite
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4239 Table 2. Reflection Coefficient, Solute Permeability, and Pure Water Permeability of the Membranes type of membrane
reflection coefficient, σ
solute permeability, Pm (m/s)
pure water permeability, Lp (m s-1 kPa-1)
unmodified PS aminated PS quarternized PS
0.916 0.868 0.807
1.246 × 10-6 6.71 × 10-5 2.44 × 10-5
2.5 × 10-8 1.4 × 10-7 6.43 × 10-7
membrane is placed inside a perforated stainless steel casing, which has an inner diameter of 60 mm and grooves 2-3 mm deep. The membrane, which is cast in a casing and sealed with a fast-setting epoxy resin, is placed inside the cylindrical groove of the base plate. The upper half of the cell is fixed to the base plate by a nut and bolt and an O-ring is kept on the membrane, thus making the entire setup leakproof. The membrane crosssectional area available for flux and retention measurements is 28.4 cm2. The membrane is compacted with doubly distilled water at a pressure (70 psi) higher than the maximum operating pressure until a constant water flux is obtained. Pure water flux and permeate flux are obtained by measuring the time interval corresponding to a permeate volume of 25 mL. Before each run, the membrane is cleaned with distilled water at higher pressure (70 psi) and water flux is determined to ensure that there is no flux decline due to partial plugging. For each run, the cell is filled with 500 mL of salt feed solution and the permeate flux is measured after 50 mL of permeate has passed through the membrane. The separation of chromium(VI) salt solution has been performed, and its concentration is measured using a conductivity cell (Century CMK 731, µP-based water analysis kit) with 0.1 µΩ accuracy and a UV spectrophotometer (Elico) at 372 nm. The separation experiments are conducted at five different pressures (in the range of 68-300 KPa) and three different concentrations of chromium(VI) (in the range of 100-1000 ppm) and at different pH values (pH ) 2-8.5). The pH of the feed solution is varied by adding HCl or NaOH solutions in required amounts. 2.7. Permeate Flux and Rejection. The pure water flux through an ultrafiltration membrane can be described by Darcy’s law, which states that volumetric flux is directly proportional to the applied pressure gradient: Jw ) K∆Papplied
(4)
where K ) 1/(Rm µw), Rm is the intrinsic hydraulic resistance, Jm is the water flux, and µw is the viscosity of water. In ultrafiltration experiments, the rejection factors are defined as follows: observed rejection factor :
real rejection factor :
( )
Robs(%) ) 1 -
Csol p
Csol R
( )
Rreal(%) ) 1 -
Csol R
Cmsol
× 100 (5)
× 100 (6)
where Cpsol is the solute concentration in the permeate, CRsol the solute concentration in the retentate (in bulk), and Cmsol, the solute concentration at the membrane interface. Rreal is an inherent property of the membrane, whereas Robs is strongly dependent on the operating conditions. Therefore, it is desirable to report separation performance of a membrane in terms of Rreal, although the determination of Cm is difficult. The
Figure 3. Schematic view of the membrane showing the concentration profile of the solute in the bulk, concentration polarization layer, and membrane.
value of Cm can be determined by either following of the two techniques:(1)directmeasurementofCm throughinteroferometric43,44 and optical shadow measurements,45 and (2) determination of Cm by solving transport equations in the polarization layer (the accuracy of the estimated value of Cm is dependent on the validity of the hydrodynamic model used). In the second technique, the following equations are used to determine the value of Cm. The membrane surface concentration is calculated using the osmotic pressure model:44 JV ) Lp(∆P - σ∆π)
(7)
where JV is the permeate flux, ∆P the applied pressure difference, σ the membrane reflection coefficient, and ∆π the osmotic pressure difference. The osmotic pressure difference is calculated using the van’t Hoff equation for electrolytes: ∆π ) νRT∆C (8) The reflection coefficient is related to the real rejection of the membrane through the equation given by Spiegler and Kedem:46 Rreal )
σ(1 - F) 1 - σF
(9)
where F is given by
[
F ) exp -(1 - σ)
JV Pm
]
(10)
The values of Cm, σ, and Pm (solute permeability) are calculated using eqs 7–10, following the iterative technique given by Ghose et al.,47 with the convergence criterion being a change of 7) and the latter at acidic pH (2-5). It may be observed that, under acidic experimental conditions (pH ∼3), the chromium is present in the form of acid chromate ions (HCrO4-). Because the membranes are positively charged, the retention of monovalent HCrO4- is expected to be more than that for the divalent CrO42at lower pH. It has been found that the retention of chromium(VI) acid decreases as the pH of the solution increases, as shown in Figure 16. This is because, as the pH increases, the ratio of HCrO4- to CrO42- decreases, as does the retention of HCrO4- ions. At pH 6.5, the HCrO4- and CrO42- are present in almost equal amounts. Therefore, the rejection curve shows
Figure 16. Effect of pH on the rejection of chromium(VI) solution at a feed concentration of 100 ppm and a pressure drop of 40 psi.
40% rejection for the monovalent ion (HCrO4-), as compared to the divalent ion (CrO42-). As the pH increases further, the divalent species is dominant and, hence, the retention falls to 20% for the aminated membrane and to 5% for the quaternized membrane. Because of the fact that the aminated membrane is weakly charged, its decrease in retention is slightly less, in comparison to the strongly anionic quaternized membrane. 4.6. Space Charge Model (SCM). The experimental data (Pepexp and Peexp) has been fitted to calculate the concentration at the interface of the membrane (including the rise in bulk concentration due to concentration polarization) and the wall potential. The model requires characteristic membrane structural (pore diameter, effective membrane area, and pore length) parameters for fitting of the experimental results. The pore diameter, effective membrane area, and pore length (which is the same as membrane thickness) are experimentally known to be 7.8 (aminated) and 8.6 nm (quaternized), 28 cm2, and 30 µm, respectively. The SCM is known to work in the region of large pore size and low concentrations and is consistent with the fact that our membrane is the charged ultrafiltration type. In this model, it has been assumed that the entire system is divided into two regions where, in the first region (Region I), increase in concentration occurs from cb to cI, because of the unstirred polarization layer and the interfacial resistance of the membrane. In Region II (which corresponds to the membrane capillaries), the SCM holds well and describes the effect of wall potential on the movement of ions (Figure 3). To check the efficiency of the procedure developed here, the simulation has been performed on a Pentium IV personal computer (PC), using MATLAB 7.1 software. The tolerance value for the numerical calculation of the solution of PoissonBoltzmann equation is kept at 10-6. The analysis presented in this work determines the wall potential of this region (Region II) and the concentration at the membrane surface. To show that the series solution reduces the computational load drastically, the CPU time required as a function of wall potential and λ has been determined. For a typical simulation with the same initial values of pore size and wall potential, the time taken for series solution method is 15 min, as compared to 15 h taken for the MATLAB 7.1 ordinary differential equation (ODE) solver for the numerical integration. A semianalytical series solution for the Poisson-Boltzmann equation has been presented and in Figure 4, it is shown that the series solution used is this work matches completely with the numerical solution of Poisson-Boltzmann equation. Using the SCM, the wall potential of the aminated and quaternized membrane corresponding to each pressure at which the experimental data is obtained has been determined. The wall potential obtained for each value of pressure and pH is given in Table 4. The average wall potential for the quaternized and the aminated
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4247 Table 4. Wall Potential Values Obtained for Various Pressures and pH for the Aminated and Quaternized Membranes Using the Space Charge Model Wall potential, FΨ/RT pressure (kPa) quaternized 68.94 137.89 206.84 275.79 344.73
3.47 3.46 3.49 3.41 2.91
Wall potential, FΨ/RT
aminated
pH
quaternized
aminated
3.23 3.35 3.33 3.14 2.86
2 3 6.5 8 8.5
4.23 4.04 3.27 2.79 2.76
3.47 3.38 3.10 2.80 2.75
membrane has been found to be 85.95 and 78.7 mV, respectively. The value of wall potential obtained shows that the quaternized membrane has a high charge density, confirming the effect of modification to make the membrane highly charged. The zeta potential of the similarly modified polystyrene particles has been determined experimentally to be 107 mV (at pH of 8.5), which is similar to the optimal fit value of the wall charge (85.95 mV). The effect of pH has also been investigated, and the results show that, with increasing pH, the wall potential decreases. This could possibly be due to counterion adsorption, and this also supports the experimental results obtained for the effect of pH. The pressure Peclet number (Pep) and the dimensionless Peclet number (Pe) obtained from the experimental data have been compared to those calculated using SCM in Figures 17 and 18, respectively. All the data points lie on the 45° line, confirming a good match between the experimental and the simulated results. In Figures 19 and 20, the rejection of chromium(VI) obtained using the concentration polarization model of Ghose et al.47 has been compared to that calculated from the SCM, as a function of pressure at a feed concentration of 1000 ppm. The concentration at the membrane surface is calculated in the SCM, taking into account the membrane charge, whereas the Ghose et al. model calculates the same for
Figure 19. Variation of the real rejection calculated from SCM and the Ghose et al.47 model for the aminated membrane, as a function of pressure (1000 ppm, pH 3).
Figure 20. Variation of the real rejection calculated from SCM and the Ghose et al.47 model for the quaternized membrane, as a function of pressure (1000 ppm, pH 3).
uncharged solutes and a neutral membrane. The former model considers osmotic pressure as well as the electrical body force for the calculation of rejection of solute, whereas the latter model takes only osmotic pressure into account for the estimation of rejection. Therefore, as is evident, a higher rejection is obtained by the SCM, because it includes the membrane charge effects. 5. Conclusion
Figure 17. Comparison of the pressure Peclet number obtained from simulation (SCM) with the experimental value for the aminated and quaternized membranes.
Figure 18. Comparison of the nondimensional Peclet number obtained from simulation (SCM) with the experimental value for the aminated and quaternized membranes.
In this work, a modified cross-linked ultrafiltration poly(styreneco-divinyl benzene) composite membrane has been prepared and used for the separation of Cr6+ ions. This composite membrane has been prepared by first preparing a polymer syrup of styrene/DVB, using a dual initiator system (AIBN, BPO, and DMA) and subsequently spreading it on a clay support. A membrane prepared in such a manner is homogeneously charged by the nitration reaction, followed by amination and quaternization. The real retention coefficient of the membrane has been studied to determine the effect of pressure, concentration, and pH of feed solution. It has been found that, after modification, the membrane becomes highly hydrophilic and a very high water flux could be obtained for low values of pressure drop and without much loss of retention of chromium(VI). The real retention always increased with pressure, even though the trends obtained for observed rejection were much different. Observed and real rejection data for different concentrations of chromic acid has been obtained, which showed that, with increasing concentration, the rejection of the solute decreased. The membrane works best at lower concentration as the effect of membrane charge becomes effective and, hence, a higher retention of the electrolyte is obtained. The experiments conducted at different values of pH showed that the retention of chromium(VI) decreased with an increase in the pH of the solution. Finally, the space charge model (SCM) has been used to determine the effective wall potential for the effect of pressure and pH. The average wall potentials for the quaternized and
4248 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
aminated membranes have been determined to be 85.95 and 78.7 mV, respectively, and the wall potential decreased as the pH was reduced. Therefore, it is concluded that the membrane gives a high separation performance at low concentrations of chromium(VI) salt solution and at a low pH of the feed solution.
x 4a2RTc(x) c(x) Fφ j) ξ) , c) , ω) , φ l cII RT µD+ 2 J l s a (P - π), J s/ ) Y)8µD+ D+cII
( )
L1 ) k5 + ωk7 -
Appendix A
∂ci Di ∂Φ zcF ∂x RT i i ∂x
∂P 0=- ∂r
( ( ) )
(∑ )
2 ∂Φ 1 ∂ ∂ux ∂ ux +µ Fzici r + 2 ∂x r ∂r ∂r ∂x
i
( ( ) )
(∑ )
( )
( )∑ c
( )
i
ψ)
r a
λ)
k a
(A.4)
RT 2F2c(x) The various a values are given in Table A-1. The boundary conditions of the equation are κ)
∂ψ ∂η
|
)0
(A.5a)
ψη)1 ) ψw
(A.5b)
|
(A.5c)
η)0
or ∂ψ ∂η
η)1
)q)
()
Fqa εRT
L3 dc Ul dY + L4 )D+ dξ c dξ
J s/ ) -L1
dc dY + cL2 dξ dξ
k5 - ωλ2k6
)
(A.8c)
4ωλ2k0k2
(A.8d)
k5 - ωλ2k6
-
( )
∫
L2L3 - L1L4
c(ξ)1)
c(ξ)0)
(J s/ ⁄ Pe)L4 - cL2
dc
(A.9)
a2 [(P - Π)ξ)1 - (P - Π)ξ)0] ) 8µD+
∫
c(ξ)1)
c(ξ)0)
(J s/ ⁄ Pe)L3 - cL1 dc (J s/ ⁄ Pe)L4 - cL2 c
(A.10)
Nomenclature
Fψ RT
η)
k4 + ωk3
(A.8b)
(A.3)
where
where
L4 ) 1 +
Pe )
i
1 ∂ ∂ψ 1 η ) 2 sinh(ψ) η ∂η ∂η λ
(
)
and
(A.2a)
The relation between electrical potential and the charge density is given by the Poisson equation: F ∂Φ F 1 ∂ ∂Φ r + 2 )- )r ∂r ∂r ε ε ∂x
k5 - ωλ2k6
L3 ) ωk1 - ωλ2k0
2
2
k4 - ωλ2k8
where the ki values are given in Table A-2.
(A.2b)
Pe }
L2 ) 4k9 - 4k2
∂Φ 1 ∂ ∂ur ∂ ur +µ Fzici r + 2 ∂r r ∂r ∂r ∂x
i
k5 - ωλ2k6
(A.1a)
∂ci Di ∂Φ ji,r ) urci - Di zcF (A.1b) ∂r RT i i ∂r The steady-state fluid velocity is given by the Navier-Stokes equation: ∂P 0=- ∂x
(k4 - ωλ k8)(k4 + ωk3)
(
A.1. Physical Model and Governing Equations. The ion flux density are given by the Nernst-Planck equation as ji,x ) uxci - Di
(A.8a)
2
(A.6) (A.7)
a ) pore radius (m) l ) length of pore (m) A ) cross-sectional area of the pore (m2) c ) concentration of the electrolyte (mol/m3) cI ) concentration in the polarization layer (mol/m3) cp ) concentration in the permeate (mol/m3) jc ) dimensionless concentration of the electrolyte; jc ) c/cII Di ) diffusion coefficient of the ith ion (m2/s) d ) ratio of diffusion coefficients I ) electrical current through the pore (A) I* ) dimensionless current through the pores F ) Faraday constant (C/mol) j+,x ) flux of the ith ion in the axial direction (mol/m2/s) j+,r ) flux of the ith ion in the radial direction (mol/m2/s) J ) total solute flux rate across the pore (mol/s) Jw ) pure water flux (m/s) Js ) average solute flux across the pore (mol/s) Js* ) dimensionless solute flux ki ) integral defined by Table A.2 Li ) coefficients defined by eq A.8 P ) pressure (N/m2) Pe ) Peclet number, defined as the dimensionless average velocity through the pore Pep ) pressure Peclet number Peπ ) osmotic pressure Peclet number R ) gas constant T ) absolute temperature (K) U ) average velocity (m/s) ux ) axial velocity (m/s) ur ) radial velocity (m/s) Q ) volumetric flow rate (m3/s) Y ) dimensionless solvent pressure
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4249 zi ) valency of the ith ion Rm ) intrinsic hydraulic resistance
Greek Letters ) dielectric constant µ ) viscosity of the medium (poise) µw ) viscosity of water (poise) λD ) Debye length (cm) σ ) surface charge density of the pores of the wall (C/m2) ξ ) dimensionless axial position; ξ ) x/l ω ) dimensionless parameter defined as ω ) 4a2RTc(x)/µD+ λ ) dimensionless Debye length; λ ) λD/a Φ ) total electrostatic potential (V) φ ) axial component of potential (V) φ j ) dimensionless potential; φ j ) Fφ/(RT) ψ ) electric potential due to double layer (V) j ) dimensionless double layer potential; ψ j ) Fψ/(RT) ψ Ψw ) wall potential
Subscripts I ) denotes Region I II ) denotes Region II i ) denotes the ith ion; “+” means cation, and “-” means anion s ) solute w ) wall
Literature Cited (1) Ulbricht, M. Advanced Functional Polymer Membranes. Polymer 2006, 47, 2217. (2) Zhang, S.; Jian, X.; Dai, Y. Preparation of Sulfonated Poly(phathalazinone ether sulfone ketone) Composite Nanofiltration Membrane. J. Membr. Sci. 2005, 246, 121. (3) Castro, R. P.; Cohen, Y.; Monbouquette, H. G. Silica-Supported Polyvinylpyrrolidone Filtration Membranes. J. Membr. Sci. 1996, 115, 179. (4) Chowdhury, S. R.; Kumar, P.; Bhattacharya, P. K.; Kumar, A. Separation Characteristics of Modified Polysulfone Ultrafiltration Membrane Using NOx. Sep. Purif. Technol. 2001, 24, 217. (5) Shin, J. P.; Chang, B. J.; Kim, J. H.; Lee, S. B.; Suh, D. H. Sulfonated Polystyrene/PTFE Composite Membranes. J. Membr. Sci. 2005, 251, 247. (6) Bryak, M.; Hodge, H.; Dach, B. Modification of Porous Polyacrylonitrile Membrane. Angew. Makromol. Chem. 1998, 260, 25. (7) Zhao, Z. P.; Li, J.; Chen, J.; Chen, C. X. Nanofiltration Membrane Prepared from Polyacrylonitrile Ultrafiltration Membrane by Low-Temperature Plasma 2. Grafting of Styrene in Vapor Phase. J. Membr. Sci. 2005, 251, 239. (8) Nasef, M. M.; Saidi, H. Preparation of Crosslinked Cation Exchange Membranes by Radiation Grafting of Styrene/Divinylbenzene Mixtures onto PFA Films. J. Membr. Sci. 2003, 216, 27. (9) Bequet, S.; Remigy, J. C.; Rouch, J. C.; Espenan, J. M.; Clifton, M.; Aptel, P. From Ultrafiltration to Nanofiltration Hollow Fiber Membranes; A Continuous UV-Photografting Process. Desalination 2002, 144, 9. (10) Yoon, J.; Yoon, Y.; Amy, G.; Cho, J.; Foss, D.; Kim, T. H. Use of Surfactant Modified Ultrafiltration for Perchlorate (ClO4-) Removal. Water Res. 2003, 37, 2001. (11) Richard, F. C.; Bourg, A. C. M. Aqueous Geochemistry of Chromium: A Review. Water Res. 1991, 25, 807. (12) Kroschwitz J. L. Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, 1991. (13) Silva, P. T. S.; Mello, N. T.; Duarte, M. M. M.; Montenegro, M. C. B. S. M.; Araujo, A. N.; Silva, B. B. V. L. Extraction and Recovery of Chromium from Electroplating Sludge. J. Hazard. Mater. 2006, B128, 39. (14) Rengaraj, S.; Yeon, K. H.; Moon, S. H. Removal of Chromium from Water and Wastewater by Ion Exchange Resins. J. Hazard. Mater. 2001, B87, 273. (15) Tenorio, J. A. S.; Espinosa, D. C. R. Treatment of Chromium Plating Process Effluents with Ion Exchange Resins. Waste Manage. 2001, 21, 637. (16) Chmielewski, A. G.; Urbanski, T. S.; Migdal, W. Separation Technologies for Metals Recovery from Industrial Wastes. Hydrometallurgy 1997, 45, 333. (17) Lin, S. H.; Kiang, C. D. Chromic Acid Recovery from Waste Acid Solution by an Ion Exchange Process: Equilibrium and Column Ion Exchange Modeling. Chem. Eng. J. 2003, 92, 193.
(18) Frenzel, I.; Stamatialis, D. F.; Wessling, M. Water Recycling from Mixed Chromic Acid Waste Effluents by Membrane Technology. Sep. Purif. Technol. 2006, 49, 76. (19) Baral, S. S.; Das, S. N.; Rath, P. Hexavalent Chromium Removal from Aqueous Solution by Adsorption on Treated Sawdust. Biochem. Eng. J. 2006, 31, 216. (20) Noro, J.; Maruyana, K.; Komatsu, Y. Separation of Chromium(III) and Chromium(VI) by Combination of Solvent and Ion Exchange Methods. Anal. Sci. 2001, 17, 1333. (21) Lanagan, M. D.; Ibana, D. C. The Solvent Extraction and Stripping of Chromium with Cyanex 272. Miner. Eng. 2003, 16, 237. (22) Schaffer, A. I.; Fane, A. G.; Waite, T. D. Nanofiltration-Principles and Applications; Elsevier Science Publishers: New York, 2005. (23) Cassano, A.; Drioli, E.; Molinari, R.; Bertolutti, C. Quality Improvement of Recycled Chromium in Tanning Operation by Membrane Processes. Desalination 1996, 108, 193. (24) Hafez, A. I.; Manharawy, M. S. El. Design and Performance of the Two-Stage/Two-Pass RO Membrane System for Chromium Removal from Tannery Wastewater. Part 3. Desalination 2004, 165, 141. (25) Hafiane, A.; Lemordant, D.; Dhahbi, M. Removal of Hexavalent Chromium by Nanofiltration. Desalination 2000, 130, 305. (26) Shukla, A.; Kumar, A. Analysis of Separation of Chromic Acid by Zeolite-Clay Composite Membrane Using Space-Charge Model. J. Membr. Sci. 2004, 237, 119. (27) Neelakandan, C.; Pugazhenthi, G.; Kumar, A. Preparation of Nox Modified PMMA-EGDM Composite Membrane for the Recovery of Chromium(VI). Eur. Polym. J. 2003, 39, 2383. (28) Pugazhenthi, G.; Sachan, S.; Kishore, N.; Kumar, A. Separation of Chromium(VI) using Modified Ultrafiltration Charged Carbon Membrane and its Mathematical Modeling. J. Membr. Sci. 2005, 254, 229. (29) Kesting, R. E. Synthetic Polymeric Membranes; Wiley: New York, 1985. (30) Dominguez, H. R.; Trevino, F. A. R.; Reyes, R. C.; Montiel, A. G. Synthesis and Evaluation of Gas Transport Properties in Polystyrene-POSS Membranes. J. Membr. Sci. 2006, 271, 94. (31) Choi, Y. J.; Kang, M. S.; Kim, S. H.; Cho, J.; Moon, S. H. Characterization of LDPE/Polystyrene Cation Exchange Membranes Prepared by Monomer Sorption and UV Radiation Polymerization. J. Membr. Sci. 2003, 223, 201. (32) Gohil, G. S.; Shahi, V. K.; Rangarajan, R. Comparative Studies on Electrochemical Characterization of Homogeneous and Heterogeneous Type of Ion-Exchange Membranes. J. Membr. Sci. 2004, 240, 211. (33) Amado, F. D. R.; Gondran, E.; Ferreira, J. Z.; Rodrigues, M. A. S.; Ferreira, C. A. Synthesis and Characterization of High Impact Polystyrene/ Polyaniline Composite Membranes for Electrodialysis. J. Membr. Sci. 2004, 234, 139. (34) Smitha, B.; Sridhar, S.; Khan, A. A. Synthesis and Characterization of Proton Conducting Polymer Membranes for Fuel Cells. J. Membr. Sci. 2003, 225, 63. (35) Kim, J.; Kim, B.; Jung, B. Proton Conductivities and Methanol Permeabilities of Membranes made from Partially Sulfonated PolystyreneBlock-Poly(Ethylene-Ran Butylene)-Block-Polystyrene Copolymers. J. Membr. Sci. 2002, 207, 129. (36) Hosono, T.; Tanioka, A. Effect of Polymer Composition in Intermediate Layer on Water Splitting in Bipolar Membranes. Polymer 1998, 39, 4199. (37) Eto, R.; Tanioka, A. Characteristic Proton Transport through Composite Membrane Composed of Quaternary-Amino Poly(Sulfone) and Sulfonated Co-Poly(Styrene and Divinylbenzene). J. Colloid Interface Sci. 1998, 200, 59. (38) Brighton, C. A.; Pritchard, G.; Skinner, G. A. Styrene Polymers: Technology and EnVironmental Aspects; Applied Science Publishers Ltd.: London, 1979. (39) Gues, E. R.; Exter, M. J.; Bekkum, H. V. Synthesis and Characterization of Zeolite (MFI) Membranes on Porous Ceramic Support. J. Chem. Soc. Faraday Trans. 1992, 88, 3101. (40) Elvy, S. B.; Dennis, G. R.; Ng, L.-T. Catalyst-Accelerator Method for Preparation of Wood-Polymer Composite at Ambient Temperature. J. Appl. Polym. Sci. 1995, 56, 591. (41) Sinha, S.; Kumar, A. Preparation of High Capacity Chloromethylated Strong Base Anion Exchange Resin Using NOx. Sep. Sci. Technol. 2002, 37, 895. (42) Singh, S.; Khulbe, K. C.; Matsuura, T.; Ramamurthy, P. T. Membrane Characterization by Solute Transport and Atomic Force Microscopy. J. Membr. Sci. 1998, 142, 111. (43) Mahlab, D.; Yosef, N. B.; Belfort, G. Interferometric Measurement of Concentration Polarization Profile for Dissolved Species in Unstirred Batch Hyperfilteration (Reverse Osmosis). Chem. Eng. Commun. 1980, 6, 225.
4250 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 (44) Clifton, M. Polarization de Concentration Dans DiVers Procedes de Separation A Membrane;. These, Universite Paul Sabatier: Toulhouse, France, 1982. (45) (a) Vilker, V. L.; Colton, C. K.; Smith, K. A. Concentration polarization in protein ultrafiltration. Part I: An Optical Shadow Technique for Measuring Concentration Profiles near Solution-Membrane Interface. AIChE J. 1981, 27, 632. (b) Vilker, V. L.; Colton, C. K.; Smith, K. A. Concentration polarization in protein ultrafiltration. Part 2: Theoretical and Experimental Studies of Albumin Ultrafiltered in an Unstirred Cell. AIChE J. 1981, 27, 637. (46) Spiegler, K. S.; Kedem, O. Thermodynamics of Hyperfiltration (Reverse Osmosis): Criteria for Efficient Membranes. Desalination 1966, 1, 311. (47) Ghose, S.; Bhattacharjee, C.; Datta, S. Simulation of Unstirred Batch Ultrafiltration Process Based on Reversible Pore-Plugging Model. J. Membr. Sci. 2000, 169, 29.
(48) Sasidhar, V.; Ruckenstein, E. Electrolyte Osmosis through Capillaries. J. Colloid Interface Sci. 1981, 82, 439. (49) Coury, L. Conductance Measurements Part I: Theory. Curr. Sep. 1999, 18, 91. (50) Moresi, M.; Ceccantoni, B.; Presti, S. L. Modeling of Ammonium Fumarate Recovery from Model Solutions by Nanofiltration and Reverse Osmosis. J. Membr. Sci. 2002, 209, 405. (51) Peeters, J. M. M.; Boom, J. P.; Mulder, M. H. V.; Strathmann, H. Retention Measurements of Nanofiltration Membranes with Electrolyte Solutions. J. Membr. Sci. 1998, 145, 199.
ReceiVed for reView May 23, 2007 ReVised manuscript receiVed March 3, 2008 Accepted March 4, 2008 IE070730G
