Salt Separation by Charged Gel-Filled Microporous Membranes

Salt Separation by Charged Gel-Filled Microporous Membranes. Alicja M. Mika ... experiment over a wide range of the gel polymer volume fractions. For ...
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Ind. Eng. Chem. Res. 2003, 42, 3111-3117

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Salt Separation by Charged Gel-Filled Microporous Membranes Alicja M. Mika and Ronald F. Childs* Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada

A series of membranes composed of a microporous polypropylene substrate filled with a polyelectrolyte gel of poly(N-benzyl-4-vinylpyridinium chloride) of different gel polymer volume fractions has been used to study a pressure-driven separation of mono-monovalent salts from aqueous solutions. The experimental results are compared with that obtained from theoretical calculations based on the Teorell-Meyer-Sievers model of charged membranes combined with the Manning-Oosawa counterion condensation theory being used to estimate the membranes effective charge density. For counterions of low specific binding to the polyelectrolyte such as chloride and fluoride, the theoretical predictions were found to be in a good agreement with the experiment over a wide range of the gel polymer volume fractions. For strong binding counterions such as iodide, the separation is substantially lower than that predicted and is accompanied by an almost 3-fold increase in flux suggesting a microphase separation in the gel. The implications of this study on the design of gel-filled membranes are discussed. Introduction Microporous membranes containing pores filled with gels provide an interesting and versatile membrane platform. A wide variety of gels with little mechanical strength and no film-forming properties can be used in this construct to give robust membranes owing to the strength imparted by the porous support. Such membranes have recently been described by Anderson and co-workers1-3 and Childs and co-workers.4-15 In our exploratory studies of gel-filled membranes, we have shown that membranes composed of polyelectrolyte gels can function successfully as low-pressure water-softening membranes6,11 or diffusion dialysis membranes in acid recovery.5,12 While the inert microporous support provides mechanical strength and integrity to the membranes, both molecular and viscous transport occur through the gel phase. As such, the gel properties determine the separation properties of the membranes, with the basis of separation including molecular sieving (size exclusion), Donnan exclusion of co-ions, or both these mechanisms. The important consequence is that the gel network chemistry and the gel polymer concentration can be used, in principle, as tools in the membrane design and optimization. It is extremely important to understand the fundamental relationships between the gel structural parameters and the properties of the gel-filled membranes in order to select and optimize these membranes for various applications.14 Since the separation of salts with charged gel-filled membranes is based predominantly on the Donnan exclusion mechanism,9 the effective charge density is expected to play a critical role in separation. As the charge density is related to the polymer volume fraction of the pore-filling gel, a strong effect of gel density on the separation can be expected. An earlier study focused on the effect of gel-filling chemistry on membrane separation performance appeared to confirm this prediction in that the salt * To whom correspondence may be addressed. Tel.: +1-9055259140, ext. 24506. Fax: +1-905-5212773. E-mail: rchilds@ mcmaster.ca.

separation with the charged gel-filled membranes was predominantly affected by the gel concentration and not the gel chemistry.8 However, the results of this study seemed to suggest that a limiting salt rejection is reached beyond which increase in the gel polymer has a very little effect on salt rejection. In this work, we examine both theoretically and experimentally the effect of gel polymer volume fraction on ionic separation of positively charged gel-filled membranes by calculating and measuring the asymptotic rejection (reflection coefficient) of single salts as a function of the gel polymer concentration of the membranes. The theoretical calculations of the asymptotic rejections are based on the Hoffer-Kedem fixed charge model16 with the Manning-Oosawa counterion condensation theory17,18 being used to estimate the effective charge density. We will show that the theoretical calculations are in a very good agreement with experimental data for salts with no specific binding of counterions with the gel. However, presence of such binding, particularly strong in the case of sodium iodide, results in a substantially lower asymptotic rejection than that predicted from the model. The results of this study also explain the apparent limiting of the salt separations observed in our earlier work.8 Experimental Section The porous substrate used was a poly(propylene) microfiltration membrane (3M Company) produced by a thermally induced phase separation process. The substrate had a bubble point pore diameter of 0.57 µm, porosity of 84.5 vol %, and a thickness of 110 µm. The polymer used was poly(4-vinylpyridine) (P4VP), MW (1.5-2.0) × 105 (Polysciences, Inc.). R,R′-Dichloro-pxylene (DCX) (Aldrich) was used as a cross-linker and benzyl bromide (Aldrich) as a quaternization agent. All reagents were used without further purification. The gel-filled membranes were made by in situ crosslinking of poly(4-vinylpyridine) with R,R′-dichloro-pxylene in N,N-dimethylformamide (DMF), according to procedure described elsewhere.10 The ion-exchange capacities of the quaternized samples were measured

10.1021/ie021016w CCC: $25.00 © 2003 American Chemical Society Published on Web 05/31/2003

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according to the procedure described elsewhere.4 The degree of quaternization of poly(4-vinylpyridine) in the pore-filled gels exceeded 95% of the available nitrogen atoms estimated from the concentration of the polymer solutions used to prepare membranes. The mass of the incorporated gel was determined from a difference between the dry mass of a pore-filled membrane sample (dried in a vacuum at room temperature to a constant mass) and that of the substrate. The gel concentration (volume fraction), N, was calculated from the following equation (eq 1)

φ)

(mm,dry - ms)υ2 MuVss

(1)

where mm,dry is the mass of a pore-filled sample (in a dry state), ms is the mass of the substrate in the sample, υ2 is the partial molar volume of the gel polymer, Vs is the substrate volume in the sample, s is the substrate porosity, and Mu is the molar mass of the polymer repeating unit. The value of υ2 ()180 ( 2.5 cm3/mol) used was determined from the density measurement19,20 and the ab initio calculations.21 In the case of any change in the volume of the pore-filled sample compared to the original volume of the substrate sample, eq 1 was modified to

φ)

(mm,dry - ms)υ2 ms Vm M γPP u

(

)

(2)

where Vm is the volume of the swollen sample and γPP is the density of poly(propylene) (0.91 g/cm3). Salt separation experiments were carried out in a N2pressurized dead-end cell with the membrane active area of 38.50 cm2. The cell was equipped with a thermocouple, a pressure gauge, and a bleed valve to sample the feed. The feed solution was pressurized in the range of 100-500 kPa and stirred at the rate of 250-300 rpm. Under these conditions, the permeate flux remained proportional to the pressure with the deviations from linearity less than 8%. The concentration polarization effect on salt rejection was determined from the rejection measurements at different stirring rates followed by extrapolation to an infinite stirring rate. Under the applied conditions, the concentration polarization effect was reduced to less than 2%, thus allowing the observed rejections to be taken as real rejections. Permeate samples were collected for a defined period of time and weighed. The salt concentrations in feed and permeate were determined by ionexchange chromatography. The data were used to calculate permeate mass flux, Jm, at 25 °C and salt rejection, R, according to eqs 3 and 4, respectively

Jm ) mpR/At R)1-

cp cf

(3) (4)

where mp and cp are the permeate mass and concentration (mM), respectively, cf is the feed concentration (mM), A is the membrane surface area (m2), t is the sample collection time (h), and R is the empirical temperature correction factor (R ) -0.575 ln[temperature(°C)] + 2.85). The standard error in the measure-

Table 1. Properties of Ionic Components in the Pressure-Driven Salt Separations ion

diffusion coefficient40 ×109 (m2 s-1)

polarizability41 (au)

hydrated radius40 (nm)

Na+ K+ FClI-

1.33 1.95 1.47 2.03 2.05

1.002 5.339 8.8 25.4 50.0

0.358 0.331 0.352 0.332 0.331

ments of flux and rejection were less than 6.5% and less than 2.5%, respectively. The mass flux, Jm, was converted to the volume flux, Jv, assuming the permeate density to be equal to the pure water density at 25 °C. The error associated with this assumption was less than +0.1% for KCl and -0.1% for NaCl in the concentration range studied. Results and Discussion A series of membranes containing poly(N-benzyl-4vinylpyridinium) gels of different concentrations of the polyelectrolyte in the pores of porous poly(propylene support) were tested for the pressure-driven separation of 1,1-valent salts. The selected properties of the ionic components of the salts are given in Table 1. Asymptotic Rejection and Salt Permeability as a Function of Gel Polymer Volume Fraction. Asymptotic (infinite) rejection, σ, is a limiting value of rejection attainable by a membrane at the infinite flux. In the case of charged membranes, the asymptotic rejection of monovalent salts can be estimated based on the Teorell-Meyer-Sievers (TMS) model22-25 by assuming a uniform charge distribution in the membrane and using bulk diffusion coefficients to quantify ion transport in the membrane. The asymptotic rejection can be calculated from the following equation16

σ)1-

2 D1 X 2 -1 + D 1 + D2 cf

(

) [( ) ] X cf

2

+4

0.5

(5)

where D1 and D2 are the bulk diffusion coefficients of counterion and co-ion, respectively, X is the membrane effective charge density, and cf is the salt concentration in the feed solution. From this equation it follows that rejection of a given salt by a charge membrane depends on the ratio of the membrane charge density to the feed concentration, not on their absolute values. Effective charge density can be obtained from the membrane potential.26,27 In this work, however, we used a theoretical approach based on the counterion condensation theory in the form proposed by Manning28 and Oosawa.18 The theory postulates that the reduced linear charge density, ξ, defined as

ξ ) e2/1kTb

(6)

(where e is the proton charge, 1 is the solvent dielectric constant (electric permittivity), k is the Boltzmann constant, T is the absolute temperature, and b is the average distance between charges for the fully extended chain) has a limiting value ξ ) 1. If ξ is greater than 1, the system of a polyion, its counterion, and the solvent becomes unstable, causing a sufficient number of counterions to condense onto the chain to reduce its charge density to the level given by ξ ) 1. On the basis of this theory, the effective charge density of the pore-filling

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Figure 1. Sample data of reciprocal rejection (1/R) of KCl as a function of reciprocal volume flux (1/Jv) for membranes with the gel polymer volume fraction φ ) 0.08 (9) and φ ) 0.103 (0) at salt concentration 11.0 ( 0.25 mM. Asymptotic rejection, σ, is given by the intercept of the straight lines while the salt permeability is given by the slope of the lines. Correlation coefficient, R2 is 0.999 for φ ) 0.08 and 0.994 for φ ) 0.103.

gels (and membranes) was calculated as the density of the uncondensed counterions, neglecting the effect of ionic strength and polymer concentration. (These two effects are likely to counteract each other.29) The total charge density, Xtot, was calculated as a ratio of the polymer volume fraction, φ, to the partial molal volume of the polyelectrolyte repeat unit, ν2, which included the volume of the chloride counterion, assuming no volume change due to counterion condensation. The uncondensed counterion density was obtained by multiplying the total charge density, Xtot, by the condensation factor, f, equal to

f ) 1 for b/LB > 1

(7)

f ) b/LB for b/LB < 1

(8)

where b is the average contour distance between charges and LB is the Bjerrum length. For fully quaternized poly(4-vinylpyridiunium) salts b ) 0.252 nm; the Bjerrum length LB ) 0.713 nm for water as a solvent at 25 °C. The calculated effective charge density was subsequently used to obtain the asymptotic rejection from the eq 5. A series of membranes with different gel polymer volume fractions, N, of poly(N-benzyl-4-vinylpyridinium) gel was used in the salt rejection experiments. The range of the gel polymer volume fraction 0.07 < φ < 0.15 studied was selected to give membranes with stable and measurable fluxes in the applied pressure range 100-500 kPa. A potassium chloride solution with a concentration of 11.0 ( 0.5 mM was used to evaluate the effect of the gel density on the separation performance of the gel-filled membranes. The permeate flux and salt rejections obtained at different pressures were used to calculate asymptotic salt rejections and salt permeabilities of the membranes from the intercept and the slope, respectively, of a linear function relating the reciprocal rejection (1/R) to the reciprocal volume flux (1/Jv).30 Sample data from these measurements are presented in Figure 1, which shows the reciprocal rejection of KCl as a function of the reciprocal volume flux for two membrane samples with the gel polymer volume fraction φ ) 0.08 and φ ) 0.103. The correlation coefficients in the linear fits of the experimental data were 0.999 for φ ) 0.08 and 0.994 for φ ) 0.103. The standard errors in estimation of the slopes were less

Figure 2. Asymptotic rejection, σ, of KCl as a function of gel polymer volume fraction, φ: solid line (s) represents data calculated from eq 5 for KCl concentration 11 mM; points (O) represent experimental data obtained at KCl concentration of 11 ( 0.5 mM.

than (1% for φ ) 0.08 and less than (2% for φ ) 0.103. For the whole membrane series tested, the correlation factor was found to be always higher than 0.99 while the standard error in estimation of salt permeability was always less than (4.5%. The asymptotic rejection of KCl by the membranes at 11.0 mM feed concentration is shown as a function of the gel polymer volume fraction, φ, in Figure 2. The solid line represents the theoretical values calculated from the eq 5 while the points represent experimental data obtained with the membranes in the concentration range of 11.0 ( 0.5 mM KCl. Two general observations can be made based on the data in Figure 2. First, the experimental points are very close to the theoretical line except for the very high gel densities (φ > 0.1) and, second, the asymptotic rejection is little affected by the gel density in the range studied. The close proximity of the experimental data to the theoretical line at lower gel densities points to the validity of the assumptions underlying the eq 5. At higher gel densities, the steric hindrance may affect the results and the use of bulk diffusivities may become questionable. This may explain higher rejections obtained experimentally than these calculated values. The gel concentration range for which there is a good agreement between the experimental data and the theoretical calculations overlaps the range of practical importance (0.08-0.10) in which a good separation can be obtained at the reasonable fluxes. The small effect of gel density on asymptotic rejection can be understood on examination of the X/cf ratio, its effect on rejection, and the range of values of this parameter present in the experiments discussed. The graphs presented in Figure 3 illustrate this point. The asymptotic rejection of KCl as a function of the X/cf ratio (Figure 3a) shows a sharp change only at low values of the ratio (below 10). In the range between 10 and 20, the asymptotic rejection increases only by 0.1 and by about 0.08 in the rage between 20 and 100. As can be seen in Figure 3b, the ratio changes from 6 to 25 in the analyzed range of the polymer volume fraction (0.040.16) and exceeds 10 in the polymer volume range of 0.08-0.10. The charge effect becomes more visible at higher feed concentrations. The curves shown in Figure 4 were calculated from eq 5 for three different concentrations of potassium chloride: 10, 25, and 50 mM. In the case of 50 mM feed solution, the asymptotic rejections more than doubles in the analyzed gel polymer volume fraction range.

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Figure 5. Normalized KCl permeability, ks, as a function of gel polymer volume fraction at 11.0 ( 0.5 mM feed concentration.

Figure 3. Asymptotic rejection, σ, as a function of X/cs,feed ratio (a) and X/cs,feed ratio as a function of polymer volume fraction, φ (b).

these equations are related in the same way as the bulk diffusion coefficients of potassium ion and sodium ion, i.e., the ratio of these constants equal to 1.474 is the same (within an experimental error) as the ratio of diffusion coefficients of the respective co-ions equal to 1.466. Prediction of Salt Rejection. The extended NernstPlanck equation31 combined with the TMS model can be used to predict pressure-driven ionic rejection of charged membranes. An analytical solution of the equation has been obtained by Tsuru et al.32 for 1,1valent electrolytes in the form32,33

Jv ) -

[

Z(cp)2 - 2cpZ(cp) + A 1 Ds + ln 2 ∆x Z(cf)2 - 2cpZ(cf) + A

(

)]

Z(cp) - cp - B Z(cf) - cp + B cp ln B Z(cp) - cp + B Z(cf) - cp - B

(11)

where

A ) 2(1 - 2R)cpX - X2 B ) [(X - cp)2 + 4RXcp]0.5 Figure 4. Effect of KCl concentration on the asymptotic rejection, σ, calculated from eq 5 as a function of the gel polymer volume fraction, φ.

The salt permeabilities, ks, obtained from the slopes of the reciprocal salt rejection versus the reciprocal volume flux and normalized by the membrane thickness are shown in Figure 5. The solid line is a power law fit (R2 ) 0.976) to the experimental points and the empirical equation is obtained from the fit given as

ks ) (8.46 × 10-10)φ-3.41

(9)

A similar experiment with sodium chloride at the same concentration of 11.0 ( 0.5 mM as KCl resulted in the following empirical relationship

ks ) (5.74 × 10-10)φ-3.38

(10)

The exponents in both equations are identical within an experimental error. The values of the constants in

Z(c) ) (4c2 + X2)0.5 R)

D1 D1 + D 2

Ds )

2D1D2 D 1 + D2

c is the concentration with the subscripts p and f indicating permeate and bulk feed, respectively, and ∆x is the membrane effective thickness. In the application of eq 11 described in the literature,32-36 the effective charge density, X, and membrane thickness, ∆x, were used as fitting parameters. In this work, we have used the equation to calculate salt rejection (eq 4) as a function of volume flux using the physical (measured) membrane thickness as the effective thickness, ∆x, and the concentration of uncondensed counterions as the effective charge density, X. Two membranes of the polymer volume fraction φ ) 0.08 and 0.091 were selected from the series and tested

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Figure 6. NaCl rejection as a function of permeate volume flux for two membranes with the gel polymer volume fraction φ ) 0.08 (a, b, and c) and φ ) 0.091 (d, e, and f) obtained at three different salt concentrations: 3.2 mM (a and d), 6.0 mM (b), 6.1 mM (e), 11.1 mM (c), and 11.4 mM (f). The solid lines represent the rejection values calculated from eq 11 for the same salt concentrations.

with sodium chloride solutions at three different concentrations. The results obtained from these tests are presented in Figure 6 together with the curves calculated from eq 11. The data indicate a good agreement between the experimental and calculated values for both membranes at each concentration. The agreement is particularly good with a membrane of higher gel density (φ ) 0.091). As the gel density further increases, however, the calculated lines tend to underestimate the salt rejection by the gel-filled membranes, Figure 7. For the high gel densities, the assumptions of the TMS model, particularly, the application of the bulk diffusion coefficients, are not valid. Effect of Counterion on Salt Rejection. One of the assumptions of the Manning-Oosawa counterion condensation theory is the absence of specific interactions between a polyion and the counterion. A substantial body of literature exists, however, which indicates the existence of specific nonbonding interactions between polyelectrolytes and the counterions. For example,

Burkhardt et al.37 found remarkable counterion specificity in the concentrations of inorganic salts required to produce the thermodynamic θ condition for aqueous solutions of poly(1,2-dimethyl-5-vinylpyridinium chloride). This specificity resulted in a Hofmeister-type series of counterions in which the monovalent salt concentrations decreased in the following order: F- > HCO3- > Cl- > Br > NO3- > MnO4- > IO4- > I- > ClO4- > SCN-. The lower the salt concentration, the stronger is the affinity of the counterion to the polyelectrolyte. Another example of a similar counterion effect has been reported by Kawaguchi and Satoh38 who studied the swelling behavior of partially quaternized poly(4-vinylpyridine) gels. For counterions such as chloride and bromide, the gel swelling in water increased with the degree of quaternization. For iodide and thiocyanate, however, deswelling and gel collapse were observed at the higher degrees of quaternization. It is believed that the extent of counterion binding depends on two factors, namely, the counterion polar-

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Figure 8. Salt rejection, R, as a function of flux, Jv, for NaF (9), NaCl (b), and NaI (0). Solid lines represent polynomial fits of experimental data (R2 > 0.99). Salt concentration was 5.5 mM.

Figure 7. KCl rejection as a function of permeate volume flux for two membranes with the gel polymer volume fraction φ ) 0.122 (a) and φ ) 0.140 (b) obtained with 10.8 mM feed solution. The solid lines represent the rejection values calculated from eq 11 for the same salt concentration. Table 2. Effect of Counterion on Calculated, σcalcd, and Experimental, σexptl, Asymptotic Rejection of Sodium Salts with Different Counterions counterion

σcalcd

σexptl

F-

0.962 0.962 0.954

0.946 ( 0.018 0.955 ( 0.016 0.695 ( 0.010

ClI-

izability and the hydrated radius. The binding strength is reported to increase with the increased polarizability37 and to decrease with the increase in hydrated radius of the counterion.39 The data in Table 1 show that ionic polarizability increases and the hydrated radius decreases in the following order: F- < Cl- < I-. The higher propensity of some ions to form an ion pair with the polyelectrolyte would be expected to result in lower charge density than that predicted from the counterion condensation theory. This should lead to poorer separation properties. To study this effect, a poly(N-benzyl-4-vinylpyridinium salt)-filled membrane with a gel density of φ ) 0.088 was selected and tested with 5.5 mM solutions of sodium fluoride, sodium chloride, and sodium iodide. Prior to each test, the membrane was converted into given counterion by contacting it with 0.1 M solution of the salt for 24 or more hours followed by a thorough wash with deionized water. The results obtained are summarized in Table 2. For the two low binding ions, namely, fluoride and chloride, the calculated asymptotic salt rejections are very close to that obtained by experiment. This is not true, however, in the case of the strong binding iodide where the measured asymptotic salt rejection is nearly 30% lower than that calculated. At the same time, there

is dramatic increase in the permeate flux as compared to that obtained with sodium chloride or fluoride (Figure 8), suggesting a possible microphase separation in the pore-filling gel,9 thus invalidating the TMS model assumption of the homogeneous charge distribution. The estimation of the effective charge density based on the counterion condensation could also be invalid for ions such as iodide. It is worth noting that the iodide binding to the poly(vinylpyridinium) salts is completely reversible indicating that the binding is of an electrostatic, nonbonding nature. The membrane recovers both the flux and rejection when converted back into the chloride form. Conclusions The TMS model combined with the Manning-Oosawa counterion condensation theory can be used to predict the infinite salt rejection of gel-filled membranes over a wide range of gel densities for salts with counterions of low-binding affinity to the gel polyelectrolyte. The charge density of the gel-filled membranes, which is a function of the gel polymer volume fraction, affects the membrane separation properties through the ratio of the effective charge density to the feed concentration. At low salt concentrations, the parameter retains high values and the charge density effect on the separation is barely visible. The charge density comes to play, however, at higher salt concentrations and it may determine the recovery rate achievable for a given product (permeate) quality. High charge density will also play a crucial role in reducing the negative effect of strong binding counterions. The capability to predict the separation properties of the charged gel-filled membranes based on a low number of measurable parameters such as the gel polymer volume fraction, the support porosity, and the membrane thickness gives one an important tool in the design of potential practical applications. The most important and unique characteristics of the gel-filled type membranes is that these parameters can be easily changed and the effects of these changes predicted with a good accuracy. This creates a new paradigm in membrane design, one that practically eliminates the trial-and-error approach to achieving the desired membrane characteristics. Acknowledgment This research was supported by 3M Canada Company and the Natural Sciences Research and Engineering

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Received for review December 12, 2002 Revised manuscript received April 25, 2003 Accepted April 30, 2003 IE021016W