Polymer supported ultrafiltration as a technique for selective heavy metal separation and complex formation constants prediction

Separation and Purification Technology 73 (2010) 126–134

Contents lists available at ScienceDirect

Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur

Polymer supported ultrafiltration as a technique for selective heavy metal separation and complex formation constants prediction ˜ Javier Llanos ∗ , Rafael Camarillo, Ángel Pérez, Pablo Canizares Chemical Engineering Department, Faculty of Chemical Sciences, University of Castilla-La Mancha, Edificio Enrique Costa Novella, Avda. Camilo José Cela 12, 13005 Ciudad Real, Spain

a r t i c l e

i n f o

Article history: Received 5 February 2010 Received in revised form 16 March 2010 Accepted 17 March 2010 Keywords: Selective separation Heavy metal Ultrafiltration Rejection prediction Modelling

a b s t r a c t This work is aimed at evaluating the affinity of partially ethoxylated polyethyleneimine (PEPEI) towards industrially valuable metal ions (Cu2+ , Ni2+ , Cd2+ and Zn2+ ). To face this aim, a characterization of polymer and macromolecular complexes by acid–base potentiometry was carried out. Next, lab-scale total recirculation mode ultrafiltration experiments were performed, checking that the affinity order was the same as that calculated from acid–base potentiometric titrations. Moreover, the influence of pH and loading ratio (LR) on Cu2+ and Zn2+ selective separation was evaluated, obtaining a maximum Zn/Cu selectivity of 12.31 at the optimal working conditions: pH 6, T = 50 ◦ C, P = 3 bar, LR = 286.74 mmol Me2+ /mol PEPEI. Finally, a model based on the competitive reaction between polymer functional groups and the solution cations was proposed. This model accurately adjusts metal rejection coefficients when pH is close to neutrality. Moreover, in order to overcome the drawbacks of acid–base potentiometry method, this model was used to calculate new complex formation constants from metal rejection data. © 2010 Elsevier B.V. All rights reserved.

1. Introduction A great variety of industrial effluents, such as those produced in mining industry, metal processing and finishing, electrodeposition or batteries-manufacturing, are multi-component mixtures of heavy metal ions at variable concentration [1,2]. Thus, it is compulsory to face this effluents treatment to reduce its environmental hazard as well as to purify and to separate these metal ions, allowing its reuse. Polymer supported ultrafiltration (PSU) allows separating, concentrating [3–8] and recovering [9,10] very different metal ions from both industrial and natural effluents. The selectivity of this process depends mainly on both the affinity of the selected polymer to the target metals and the selected working conditions [11,12]. In this process, the development of new models that allow predicting rejection coefficient as a function of complex formation constants is a matter of great interest [12,13]. Furthermore, these models can be applied to predict what requirements must be fulfilled by polymers and metal ions to guarantee the technical viability of the separation process [14]. One of the first applications of ultrafiltration in conjunction with water-soluble polymers was as an analytical technique, used to calculate polymer–metal complex formation constants. Complex formation constants of the most used water-soluble polymers

∗ Corresponding author. Tel.: +34 926 29 53 00x3511; fax: +34 926 29 52 56. E-mail address: [email protected] (J. Llanos). 1383-5866/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2010.03.015

and different heavy metals have been calculated by this technique. Specifically, Juang and Chen used ultrafiltration to calculate complex formation constants between polyethyleneimine (PEI) and Cu2+ , Ni2+ and Zn2+ ions [15]. Rumeau et al. tested poly(acrylic acid) (PAA) and its complexes with Cu2+ , Ni2+ , Cd2+ and Ag+ [16]. In this latter work, constants obtained by ultrafiltration were compared with those calculated by acid–base potentiometry, obtaining similar values with both methods. Nevertheless, the lack of powerful computer tools made this process tedious as the error has to be minimized by a stepwise testing of the different constant values. Moreover, neither of these works has dealt with more complex polymers as partially ethoxylated polyethyleneimine (PEPEI). In the present work, the polymer PEPEI was evaluated as a selective binder to be used in a polymer supported ultrafiltration process. This polymer was selected because 80% of the most active functional groups of polyethyleneimine (primary and secondary amines) are substituted by hydroxyl groups. This substitution should slightly reduce the high activity of PEI towards heavy metal ions binding and, subsequently, should enhance polymer selectivity. In a first step, the selected polymer acid–base behaviour was characterized by potentiometric titrations using the Henderson–Hasselbach equation. Next, polymer–metal complexes formation constants were calculated for four different heavy metal ions of industrial interest: Cu2+ , Ni2+ , Zn2+ and Cd2+ . Both Ni2+ and Cd2+ appear together in effluents from batteriesmanufacturing plants, whereas Cu2+ and Zn2+ are common heavy

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

127

metal ions in different industries such as metal finishing processes or printed wiring board industry [17]. Secondly, the polymer affinity to bind these four metal ions was studied for single metal solutions in PSU experiments. Next, the selective separation of Cu–Zn bimetallic solutions was checked, studying the influence of both pH and loading ratio on the process selectivity. Finally, a model to predict rejection coefficients by PSU is proposed. This model is an improved version of one developed by our research group in previous works [12]. Here, this model has been applied to predict metal rejection coefficients for monometallic solutions, using the complex formation constants obtained by potentiometry. Moreover, this model has been integrated with an error minimization algorithm (Marquardt’s algorithm) using the Visual Basic programming language, in order to obtain new complex formation constants from experimental metal rejection data. 2. Experimental Fig. 1. Back titration curves for polymer PEPEI + HNO3 (0.1N) with NaOH (0.1N) and different initial volumes of HNO3 . [PEPEI] = 0.06 wt.%, [Na2 SO4 ] = 0.01 M.

2.1. Experimental set-up Ultrafiltration tests have been carried out at laboratory scale in an experimental set-up described elsewhere [10]. It works with a ceramic ultrafiltration membrane (Carbosep from Novasep® ), with an active area of 0.004 m2 and a MWCO of 10 kDa. This membrane presents an inner diameter of 6 mm, but it was used an internal stainless steel rod (5 mm of outer diameter) in order to reduce hydraulic diameter from 6 to 1 mm. The configuration with this internal rod increases system versatility as the same set-up can be applied to the treatment of more complex solutions (e.g. emulsions or solutions with small precipitates) just by working without the internal rod and avoiding problems of channel blocking. 2.2. Analytical techniques Polymer concentration was measured by a Total Organic Carbon (TOC) analyser Shimadzu 5050A. Metal ion concentration in monometallic solutions was measured by Atomic Absorption Spectrometry (Varian SpectrAA 220). When multi-component solutions were filtered, metal ions concentration was measured by Inductively Coupled Plasma-Atomic Emission Spectrometry (Varian Lyberty RL).

higher than 1 and usually near 2 [18,19]. Dissociation degree can be calculated by means of Eq. (2): ˛a =

[L]free CA

(2)

where CA is the analytical concentration of polyelectrolyte and [L]free is the concentration of dissociated polyelectrolyte. To calculate this concentration of dissociated polyelectrolyte, both mass and charge balances should be used. Firstly, different back titrations of PEPEI were developed. In these titrations, polymer was previously protonated by adding growing and known amounts of nitric acid 0.1N. Next, one titrates with sodium hydroxide 0.1N. In this way, a part of these functional groups of polymer are initially protonated to be analysed later as it were an acid. This has been the method most widely used in bibliography to analyse polyethyleneimine [20–22]. Fig. 1 depicts the titration curves for PEPEI. In all these titrations two inflection points are observed. The first one is due to the excess of acid added, and the second one is due to protonated functional groups of polymer. This behaviour can be clearly observed in Fig. 2, where the derivatives of curves in Fig. 1 are drawn. In this figure, we can observe two maximums in each plot, corresponding to the two inflection points. In the graph, NaOH

2.3. Materials Partially ethoxylated polyethyleneimine (Mw = 50,000 Da; 37 wt.%) was purchased from Aldrich. Metallic salts selected were sulphates, all of analytical grade from Panreac. All solutions were prepared by using ultrapure water. 3. Results and discussion 3.1. Calculation of polymer acidity constant and complex formation constants by potentiometry To characterize the acid–base behaviour of PEPEI, the experimental results of potentiometries were fitted to Henderson–Hasselbach equation (Eq. (1)): pH = pKa + n · log

˛a 1 − ˛a

(1)

where pKa is the cologarithm of the apparent dissociation constant of polymer (when ˛a = 0.5), ˛a is dissociation degree and n is an empirical constant taking into account the intramolecular electrostatic forces of the polyelectrolyte, the value of which is always

Fig. 2. Derivatives of back titration curves for polymer PEPEI + HNO3 (0.1N) with NaOH (0.1N) and different initial volumes of HNO3 . [PEPEI] = 0.06 wt.%, [Na2 SO4 ] = 0.01 M.

128

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

Table 1 Differences in NaOH volumes for the two maximums in each derivative of titration curves as a function of initial HNO3 volume added. VHNO3 initial (mL) VNaOH between maximums (mL)

2 1.11

4 1.35

6 2.05

8 2.05

volume added for each maximum in the derivative is marked. The difference between these two consecutive maximums will correspond to the amount of protonated functional groups of polymer. Thus, Table 1 shows the difference in volumes for the two maximums for each titration as a function of initial HNO3 volume added. In the case of a weak acid (as this polyelectrolyte), it does not possess an absolute acid constant, but an apparent dissociation constant (KaH ), which depends on pH. The value of this apparent dissociation constant increases with decreasing pH, and the polymer behaves as a stronger acid, that is to say, with a higher tendency to dissociate. According to this reasoning, the proportion of protonated functional groups will not indefinitely increase with decreasing pH, but it will reach a maximum. When pH value decreases, there is an interaction between charged groups that hinders a higher protonation of functional groups [23]. This is the result that can be observed from data in Table 1, where the amount of NaOH employed in the titration of the protonated groups of polymer increases until an initial HNO3 volume of 6 mL, but it keeps constant for higher volumes. Taking into account the volume of NaOH used to titrate the protonated functional groups, the proportion of these groups with regard to the total amount of groups can be calculated. If this calculation is performed, it is observed that the maximum proportion of protonated groups is 0.3096. This proportion is slightly lower than that obtained in bibliography for polyethyleneimine, with a value of 0.78 [21]. This result would imply that hydroxyl groups are not capable of protonation within the pH range studied, reducing the maximum protonation degree of polymer. The calculated maximum protonation degree corresponds to the proportion of active functional groups for the formation of complexes with cations in medium. For this reason, when calculating the analytical concentration of functional groups (CA ), necessary for both the Henderson–Hasselbach equation and modified Bjërrum method, we will make use of the concept of available analytical concentration of functional groups (CAA ). This concentration can be calculated with Eq. (3), where ˛p,max is the maximum protonation degree (0.3096): CAA = CA · ˛p,max = CA · (0.3096)

Fig. 3. Calculation of pKa for polymer PEPEI by means of Henderson–Hasselbalch equation. [PEPEI] = 0.06 wt.%, titrating agent: NaOH (0.1N), VHNO3 (0.1 N) = 6 mL.

Fig. 4. Back titration curves for polymer PEPEI + HNO3 and mixtures Titrating agent = NaOH (0.1N), [PEPEI] = 0.06 wt.%, PEPEI + Me2+ + HNO3 . [Me2+ ] = 1.97 mM, [Na2 SO4 ] = 0.01 M, VHNO3 (0.1 N) = 6 mL.

(3)

Moreover, added volume of acid in the titrations to calculate pKa for polymer and PEPEI–Me2+ (Me2+ : Cu2+ , Ni2+ , Zn2+ and Cd2+ ) complex formation constants will be the minimum to reach maximum protonation degree (6 mL of nitric acid 0.1N). Fig. 3 shows the fitting to Henderson–Hasselbach equation of the data obtained in the back titration of polymer (and 6 mL of nitric acid 0.1N). According to this fitting, the value of pKa for polymer is 7.267 and constant n is 1.920. The values of pKa in bibliography [21] are higher than the obtained in this study for PEPEI. There are values of 8.39 and 7.69 for protonation degrees lower/higher than 0.3. This result indicates that the substitution of amine groups by hydroxyl groups diminishes the basic character of PEPEI, which is to say, it increases acidic character of protonated polymer. Regarding constant n, indicative of intermolecular interactions between neighbour groups [24], the value obtained is similar to that one calculated in bibliography when the protonation degree is lower that 0.3 (n = 2) and markedly inferior to that for higher protonation degrees (n = 7). Next, PEPEI–Cu, PEPEI–Ni, PEPEI–Zn and PEPEI–Cd complex formation constants were calculated according to modified Bjërrum

method, just as it is explained in bibliography [18,19]. Fig. 4 gathers titration curves obtained for different PEPEI-metal systems. Table 2 summarizes the results obtained for complex formation constants. Furthermore, it gathers the pH values at which weighted average complex coordination values of 0.5 and 1.5 are reached and the polymer pKaH calculated at these values of pH. One can observe that polymer forms the most stable complexes with Cu2+ , with a differTable 2 Results of PEPEI-Me2+ (Me2+ = Cu, Ni, Zn, Cd) complex formation constants by acid–base potentiometry. Titrating agent = NaOH (0.1N); [PEPEI] = 0.06 wt.%; [Me2+ ] = 1.97 mM; VHNO3 (0.1 N) = 6 mL. PEPEI–Cu

PEPEI–Ni

PEPEI–Zn

PEPEI–Cd

log K1 (¯r = 0.5) pH pKaH

4.492 3.4 5.40

3.731 5.1 6.19

3.309 5.9 6.60

3.590 5.3 6.30

log K2 (¯r = 1.5) pH pKaH Log ˇ102

4.430 4.6 5.97 8.922

3.444 7.6 7.42 7.175

3.380 7.0 7.12 6.689

3.469 7.3 7.29 7.059

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

Fig. 5. Evolution of metal rejection coefficients with pH value. P = 3 bar, T = 50 ◦ C, loading ratio = 147.37 mmol Me2+ /mol PEPEI (Me2+ = Cu, Ni, Zn, Cd).

ence of almost two magnitude orders in constant ˇ102 with the rest of metal ions. The order of affinity of PEPEI with the different metal ions is the following: Cu2+  Ni2+ > Cd2+ > Zn2+ At this point, it is necessary to take into account the high pH values at which K2 constants (complexes of Me:L stoichometry 1:2) of Ni2+ , Cd2+ and Zn2+ are obtained. At this pH, insoluble hydroxides could be formed so complex formation constants could be slightly influenced by the formation of this kind of compounds. 3.2. Ultrafiltration tests 3.2.1. Ultrafiltration of single metal solutions The first part of this section consisted of several UF tests to check the differences in the polymer affinity to bind each one of the following metal ions: Cu2+ , Ni2+ , Cd2+ and Zn2+ . All the tests were carried out at the same transmembrane pressure (3 bar), temperature (50 ◦ C) and molar metal–polymer ratio (loading ratio) (147.37 mmol Me2+ /mol polymer). These conditions were selected based on a previous work on Cu2+ ultrafiltration [10], where the optimal loading ratio for a polymer concentration of 0.06 wt.% was found at a Cu2+ concentration of 125 ppm (1.97 mM). The presence of ionic strength causes the decrease in rejection of non-complexed ions [25] because the reduction in electrostatic repulsions with membrane active layer [26]. For this reason, a low concentration of sodium sulphate (0.01 M) was added to minimize non-complexed metal rejection and to assure that the entire rejections are only due to the macromolecular complex formation. At these conditions, pH was varied from 2 to 7 with monometallic solutions. Fig. 5 gathers metal rejection coefficient evolution with pH. In this figure there is an evident decreasing of rejection coefficient with lower pH values. This result is explained by the breaking of macromolecular complex after the addition of protons to the medium, which compete with metal cations to bind the functional groups of polymer. In the same way, it can be appreciated that Cu2+ rejection coefficients at pH ≥ 4 are higher than for the rest of metal ions. Taking into consideration the rejection coefficients at typical pH values for retention stage in a PSU process (4 < pH < 6), the order of affinity of polymer for the different metal ions would be: RCu  RNi > RCd > RZn The only result that does not coincide with this general tendency is Zn2+ rejection coefficient at pH 7, which could be explained by

129

Fig. 6. Evolution of metal rejection and selectivity coefficients with pH for aqueous solutions of polymer Cu2+ and Zn2+ (tendency lines are added). P = 3 bar, T = 50 ◦ C, [PEPEI] = 0.06 wt.%, [Cu] = [Zn] = 1 mM.

precipitation of zinc hydroxide. This precipitation can take place since the macromolecular complex for zinc is the weakest and as a result, free Zn2+ concentration will be the highest. This fact lacks of practical relevance because all the retention and selective separation tests in present work will be developed at pH ≤ 6, with the aim of preventing the formation of insoluble hydroxides. These results for rejection coefficients are in concordance with the order of affinity obtained by means of potentiometric measurements, if it is expressed as the value for constant ˇ102 appeared in Table 2. This concordance implies that the main mechanism of metal ions rejection (except for Zn2+ at pH 7) by membrane is the formation of macromolecular complexes and not other mechanisms with far lower selectivity, such as electrostatic repulsions with membrane active layer or the formation of insoluble hydroxides. Finally, as one can observe, Cu2+ and Zn2+ ions are those with the highest difference in affinity for PEPEI. Moreover, both metal ions usually appear together in acid baths for surface treatment [17]. For all these reasons, selective separation of both metal ions was tackled in this study. 3.2.2. Ultrafiltration of bimetallic Cu–Zn solutions With the aim of studying the polymer behaviour in bimetallic Cu2+ –Zn2+ solutions, some experiments were completed with the following procedure. In the first place, pH influence on rejection coefficient was analysed with constant polymer and metal ions concentrations. Next, once optimum operating pH value was selected, the influence of loading ratio on rejection coefficients was studied. All experiments in this section were performed with solutions that were equimolar in both metal ions. 3.2.2.1. Influence of pH value. Fig. 6 gathers rejection coefficients and selectivity coefficients for Cu2+ and Zn2+ at different pH values. The selectivity coefficient Zn/Cu (˛Zn/Cu ) can be calculated as follows: ˛Zn/Cu =

[Zn]p /[Cu]p [Zn]f /[Cu]f

(4)

where [Me]p and [Me]f are metal ion concentrations in permeate and feed stream, respectively. As a comparison, this selectivity constant has been calculated taking into account the rejection coefficients for bimetallic solutions (Section 3.2.2) but also for monometallic solutions (Section 3.2.1).

130

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

value for selectivity Zn/Cu (12.31) has been obtained at a loading ratio of 286.74 mmol Me2+ /mol PEPEI. Any additional tests at higher loading ratios were not developed in order not to endanger Cu2+ rejection coefficient and also to avoid the precipitation of insoluble hydroxides. 3.3. Rejection coefficients prediction

Fig. 7. Influence of loading ratio (LR = mmol Me2+ /mol PEPEI) on metal rejection and selectivity coefficients (tendency lines are added). P = 3 bar, T = 50 ◦ C, [PEPEI] = 0.06 wt.%, pH 6, [Cu] = [Zn].

This figure shows that rejection coefficients for Cu2+ are higher than Zn2+ , in the same way it happened when solutions of separated metal ions were studied. At pH 6 and 2, the values for selectivity coefficients for both kinds of solutions were alike. Nevertheless, selectivity coefficient at pH 4 is rather higher than that foreseen for monometallic solutions. The same behaviour was observed during the separation of Cd2+ and Pb2+ with poly(acrylic acid), in which a more selective separation for bimetallic solutions [14] was observed in contrast to monometallic solutions [12]. Furthermore, this separation was more pronounced at slightly acidic pH values. This difference is due to the amount of free macromolecular ligand available to form the weakest complex is smaller if a metal ion with higher preference for polymer is present. Because of that, the amount of macromolecular complex with Zn2+ will be smaller if Cu2+ is present and, therefore, the rejection coefficient for the first will decrease whereas selectivity coefficient ˛Zn/Cu will increase. The maximum selectivity (11.31) is attained at pH 6. This value is higher than that obtained in bibliography for Cu2+ /Ni2+ pair using PEI as water-soluble polymer [27] and for the Zn2+ /Ni2+ mixture with PAA [4]. On the other hand, it is similar to that obtained for Hg2+ /Cd2+ with PEI [1]. However, the selectivity coefficient obtained is rather smaller than that obtained for the Pb2+ /Ca2+ mixture using PAA as watersoluble polymer [13]. This lower selectivity is probably the result of the nature of polymer–metal bond. Poly(acrylic acid) shows a behaviour as weak polyelectrolyte and polyacrylate ion shows a pair of electrons that can be donated to form a coordination bond. This bond will be far more easily formed with Pb2+ , which possesses three empty p orbitals in its valence layer, than with Ca2+ , which only shows one empty s orbital in its valence layer. Thus, the smallest rejection coefficients in PSU technique are always obtained for alkaline and alkaline earth metal ions [7]. 3.2.2.2. Influence of loading ratio at pH 6. Keeping constant polymer concentration, temperature, transmembrane pressure and pH value, metal/polymer loading ratio was modified. Selected pH value was 6, since it led to the maximum selectivity. Fig. 7 gathers the influence of this parameter on rejection and selectivity coefficients of Cu2+ and Zn2+ . Fig. 7 shows evidence of the increase of selectivity Zn/Cu with loading ratio. This is a foreseen result since if the polymer shows a greater affinity for one of the metal ions in solution, the optimum for selectivity usually takes place when the amount of polymer is the exact to complex metal ion [8,28]. In this case, the maximum

Once the experimental data were obtained, a new and improved model based on previous works [12] was developed to predict metal rejection coefficients as a function of pH. The first step consisted of predicting metal rejection coefficients, using the complex formation constants obtained in Section 3.1. Although the model will be set out for multi-metallic solutions, it will be applied to rejection data of monometallic solutions (data gathered in Section 3.2.1), which means the most simple approach of the model. Metal rejection prediction, using complex formation constants obtained by potentiometry, could lead to inaccurate results due to the appearance of conformational changes or electrostatic interactions that are not considered by this method. In order to improve model prediction, it was used to calculate new polymer–metal complexes formation constants directly from experimental rejection data. Finally, model fitting to experimental data, when these new constants are used, will be compared to that reached when potentiometric constants are employed. To carry out this comparison, only metal rejection coefficients of monometallic solutions were also selected in order to simplify model formulation [14], although the same mathematical treatment could be applied to multi-component solutions. 3.3.1. Proposed model The proposed model is based on different competitive reactions between functional groups of polymer (L), protons (H) and metal ions (Me) in solutions. Eqs. (5)–(7) describe, omitting the charges of implied species, the different reactions to take into consideration, with their respective formation constants: HL ↔ H + L; Ka =

[H] · [L]free [HL]

Me + L ↔ MeL; Ki,1 =

(5)

[MeL] [Me]free · Lfree

Me + nL ↔ MeLn ; Ki,n =

(6)

[MeLn ]

(7)

[Me]free · [L]nfree

This initial approach makes use of the following simplifying hypotheses: (1) The equilibrium is instantaneously attained. (2) MeLn with stoichometries from 1:1 to 1:n are formed. (3) Neither hydroxides nor hydroxianions of metal ions are formed within operating pH interval. (4) The system behaves as a continuous stirred tank reactor. (5) The pH value is alike in the both sides of membrane. (6) The rejection coefficient of macromolecular complex is the same as that for polymer. Applying a mass balance, total concentration of each metal ion will be: [Me] = [Me]free +



n

(8)

[MeLn ]

Taking into account simplification number 6, the concentration of each metal ion in permeate stream will be:



[Me]p = [Me]free · (1 − RMe free ) + (1 − RL )

n

[MeLn ]

(9)

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

From Eqs. (8) and (9), rejection coefficient for each metal ion can be calculated as: RMe = 1 − = 1−

RMe =

[Me]p [Me]



[Me]free · (1 − RMe free ) + (1 − RL ) [Me]free +

[Me]free · RMe free + RL [Me]free +





n



n

[MeLn ]

RMe =

1+

[MeLn ]

(11)

n [MeLn ]



K · n n i,n [L]free



K n i,n

(12)

· [L]nfree

On the other hand, applying a mass balance to ligand, its total concentration could be determined from Eq. (13): [L] = [L]free + [HL] +

 i

n

n · [MeLn ]

(13)

Linking Eqs. (13), (5) and (7), we get: [L] = [L]free +

[L]free · [H]   + n · Ki,n [Me]free · [L]nfree Ka i n

(14)

Using Eq. (8) and equilibriums of complex formation (6 and 7), free metal concentration can be calculated as: [Me]free =

1+

 [Me]



[L]free · [H]  [Me] n n · Ki,n · [L]free  + [L] = [L]free + Ka i Ki,n · [L]nfree 1+ n

Zn2+

Rmod

Rexp

Rmod

Rexp

Rmod

Rexp

Rmod

Rexp

0.97 0.94 0.72 0.05

0.97 0.96 0.69 0.05

0.88 0.78 0.31 0.01

0.85 0.80 0.14 0.08

0.86 0.74 0.25 0.01

0.76 0.59 0.08 0.04

0.87 0.53 0.14 0.00

0.92 0.46 0.06 0.04

Putting together all these considerations, metal rejection coefficient from Eq. (12) takes the shape of Eq. (19) when there is insoluble hydroxides precipitation: RMe =



K · n + /[Me]free,max n i,n [L]free [Me(OH)2 ] n K · + /[Me] [L] [Me(OH) ] 2 free,max free n i,n

RMe free + RL

RMe =

(17)

The precipitation will take place if the product of free Me2+

ions by the square of the concentration of hydroxyl ions is higher than its solubility product (Kps ). From this equation, the maximum concentration of free Me2+ ions in solution in the absence of precipitation of insoluble hydroxides can be estimated: Kps

Cd2+

solution without hydroxide precipitation will be calculated. (3) If concentration from Eq. (15) is smaller than one from Eq. (18), the absence of hydroxide formation is confirmed. On the contrary, if it is bigger, we suppose that free Me2+ ions concentration is equal to the maximum permitted (Eq. (18)) and the rest until Eq. (15) is forming hydroxides. This calculated amount of metal in hydroxides is symbolized as [Me(OH)2 ]. (4) If hydroxide precipitation occurs, a hydroxide rejection coefficient of 1 will be considered.

(16)

The only unknown term in Eq. (16) is free ligand concentration ([L]free ). Since this equation is not easily solved with analytical tools, it is necessary to apply a numerical method (Newton’s method) to solve it. Once this concentration is obtained, metal rejection coefficient can be calculated by substitution of this value in Eq. (12). This initial approach considers insoluble hydroxides precipitation as negligible. Nevertheless, ultrafiltration data have been obtained up to pH 7, a value at which metal hydroxides precipitation could play its role. Consequently, this general model has been modified to consider the formation of insoluble metal hydroxides that can be rejected by membrane. Nevertheless, the formation of soluble Me(OH)+ hydroxianions is considered as negligible, since [Me2+ ]/[Me(OH)+ ] ratio is usually higher than 100 [29]. Both the reaction of hydroxides formation and their solubility product are expressed as: Me + 2OH ↔ Me(OH)2 ; Kps = [Me]free · [OH]2

Ni2+

1+



(19)

Next, introducing expression (18) in (19), Eq. (20) is obtained, which allows to calculate metal rejection coefficient when hydroxides precipitate.

n

[OH]2

7 6 4 2

(15)

K · n n i,n [L]free

Finally, introducing Eq. (15) in Eq. (14):

[Me]free,max =

Cu2+

(10)

Bearing in mind equilibrium (7), Eq. (11) turns into: RMe free + RL

Table 3 Experimental and predicted results for evolution of metal rejection coefficients with pH value for aqueous solutions of PEPEI–Me2+ using constants obtained by potentiometry. pH

n [MeLn ]

131

(18)

Thus, in order to include the formation of this kind of compounds in the model, this procedure will be followed: (1) All calculations will be made supposing there is not formation of insoluble hydroxides. In this way, the free Me2+ ions concentration will be calculated from Eq. (15). (2) With the aid of Eq. (18) and considering the concentration of hydroxyl ions, the maximum concentration of free Me2+ ions in

RMe free + RL 1+





K n i,n

· [L]nfree + [OH]2 · [Me(OH)2 ] /Kps

K · n n i,n [L]free

+ [OH]2 · [Me(OH)2 ] /Kps

(20)

Finally, in order to calculate free ligand concentration, Eq. (14) can be transformed into Eq. (21), when free Me2+ concentration is substituted by the maximum concentration of free Me2+ ions, Eq. (18). [L] = [L]free +

Kps  [L]free · [H] + n · Ki,n · [L]nfree Ka [OH]2 i

(21)

n

3.3.2. Verification and validation of proposed model In order to prove the validity of prediction model of rejection coefficients, evolution of this design parameter with pH value has been calculated using polymer acidity constant and complex formation constants previously measured by potentiometry. In this point, it is important to remark that Ki,2 constant of proposed model, Eq. (7), is equivalent to constant ˇ102 of modified Bjërrum method (Section 3.1). To carry out the fitting, values of 0.98 and 0 for polymer and free metal rejection coefficients have been considered. Table 3 summarizes experimental and predicted values. It can be observed that Cu2+ is the metal ion with the smallest differences between the predicted and experimental values of rejection coefficient. Moreover, the fitting of the model is of rather better quality at pH values near neutrality, that is to say, at typical pH values for retention stage. On the contrary, a biggest error in the prediction of rejection coefficient is associated at more acidic pH values. All these considerations induce the authors to suggest that linearity foreseen by Henderson–Hasselbalch equation may fail at acidic pH values, due to the increase in the charge density of polymer with higher protonation degree [21]. Furthermore, at these pH values, the assumption that conditional dissociation constants in the presence and in the absence of metal ion are alike (used for the calculation of complex formation constants) is not realistic. Finally,

132

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

Table 4 Values for PEPEI–Me2+ complex formation constants obtained from the fitting of ultrafiltration (UF) data to the model (Ki,n ) and comparison to those obtained by acid–base potentiometry (Pot., ˇ102 ). Cu2+

UF Pot.

Ni2+

Cd2+

Zn2+

K1

Ki,2 ≡ ˇ102

K1

Ki,2 ≡ ˇ102

K1

Ki,2 ≡ ˇ102

K1

Ki,2 ≡ ˇ102

3.11 × 104 3.11 × 104

4.96 × 108 8.34 × 108

4.11 × 103 5.39 × 103

2.78 × 107 1.50 × 107

2.01 × 103 3.89 × 103

2.25 × 106 1.15 × 107

4.80 × 102 2.04 × 103

2.54 × 106 4.90 × 106

effects like polymer concentration within the boundary layer over the membrane cannot be quantified from the present approach. On the other hand, the only experimental case for which the model predicts hydroxide formation is Zn2+ ion at pH 7 (Rmod = 0.87). For this value, the initial approach of our model (the absence of hydroxides) would predict a rejection coefficient of 0.7, far from the experimental value (0.92). All these calculations make clear that hypothesis in Section 3.2.1 about zinc hydroxide formation at pH 7 could be the answer to an abnormally high rejection coefficient.

3.4. Complex formation constants prediction by PSU As it has been previously remarked, complex formation of stoichometry 1:2 (K2 in Table 2) takes place at a pH value at which metal precipitation could be occurring. Moreover, when these constants are employed, error prediction is very high at acidic pH values when the model is fed with constants from potentiometry. In order to overcome these drawbacks, we propose to make use of the model to obtain complex formation constants by means of ultrafiltration tests. With this new approach, three main objectives are pursued. First of all, it is important to diminish the error associated to the fitting of experimental data (above all, at acidic pH values). Secondly, the contribution of hydroxides precipitation and complex formation can be clearly differentiated. Finally, the versatility of ultrafiltration technique both as an analytical tool and as a separation procedure could be checked.

Fig. 8. Experimental data and model prediction for the evolution of metal rejection coefficient with pH using complex constants obtained by UF. P = 3 bar, T = 50 ◦ C, [PEPEI] = 0.06 wt.%, LR = 143.37 mmol Me2+ /mol PEPEI, [Na2 SO4 ] = 0.01 M.

Thus, taking as a starting point the curves for the evolution of rejection coefficient with pH value, an algorithm of non-linear fitting of parameters (Marquardt’s algorithm) will be used to obtain the value of complex formation constants that minimizes the error in prediction. In this fitting, we start from the value for

Fig. 9. Comparison in percentage errors for predicted values of rejection coefficients when complex constants are obtained by potentiometric analysis and by UF: (a) Cu2+ , (b) Ni2+ , (c) Cd2+ , (d) Zn2+ . P = 3 bar, T = 50 ◦ C, [PEPEI] = 0.06 wt.%, LR = 143.37 mmol Me2+ /mol PEPEI, [Na2 SO4 ] = 0.01 M.

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

polymer dissociation constant measured via acid–base potentiometry, and formation constants will be used as fitting parameters. This approach demands the integration of diverse calculation algorithms (Marquardt and Newton) to develop the required optimization. This integration was performed by means of Visual Basic programming language. According to this procedure, formation constants for coordination indexes 1 and 2, for different metal ions, have been calculated (Table 4). Fig. 8 shows the fittings with the new model considering the new calculated constants. Finally, Fig. 9 compares prediction percentage errors when constants obtained by the two proposed methods (constants from potentiometric analysis vs. constants from PSU rejection data) are used. As one can observe by comparing errors gathered in Fig. 9, there is a decrease in error of predictions with the new model in most cases. Using the new formation constants obtained in this section, the biggest error in prediction of rejection coefficients at pH 6 and 7 is 5.4% (Zn2+ , pH 7). The improvement of the fitting for all metal ions at pH 4 is specially significant, above all for Cd2+ , with a decrease higher than 140%. Regarding the values for formation constants obtained, with the exception of constant ˇ102 for Ni2+ , the new values are smaller than those obtained by acid–base potentiometry. This result can be explained in the light of the polymer concentration within the boundary layer over the membrane increases faster than for the metal ion, since free metal ions in solution can penetrate the membrane. This increase in polymer–metal loading ratio provokes a slight decrease in complex formation constants [20]. Furthermore, as it can be derived from Eq. (16) and equilibriums (6) and (7), if the concentration of free metal ion diminishes with regard to polymer concentration, the concentration of free ligand becomes higher. Under these considerations and analysing Eq. (12), if the concentration of free ligand within the boundary layer increases, smaller values of successive complex formation constants are necessary to reach a determined rejection coefficient. In other words, if polymer–metal ratio is slightly higher within the boundary layer, slightly weaker complexes reach the same rejection coefficients. Lastly, it has to be remarked that all formation constants have the same magnitude order as the constants obtained by potentiometry. This result, together with the improvement in the prediction of rejection data, suggest that the calculated constants possess physical meaning and validate the proposed method as an alternative to the calculation of complex formation constants. 4. Conclusions The main conclusions that can be gathered from this work are summarized below: • The affinity order of PEPEI towards four industrially valuable metal ions, can be established as follows: Cu2+  Ni2+ > Cd2+ > Zn2+ . Global complex formation constant (ˇ102 ) between this polymer and Cu2+ is close to two orders of magnitude higher than the rest of formation constants. • Cu2+ and Zn2+ selective separation by PSU is technically feasible. Process selectivity increases with pH and loading ratio, reaching a selectivity coefficient of 12.31 at the optimum working conditions (pH 6, T = 50 ◦ C, P = 3 bar; LR = 286.74 mmol Me2+ /mol PEPEI). • The proposed model accurately adjusts rejection coefficients evolution for monometallic solutions, when pH is close to neutrality. Prediction error increases at lower pH values. • This model also allows calculating complex formation constants from metal rejection data. These constants are similar to those obtained by acid–base potentiometry, although constants pre-

133

dicted from UF data are slightly lower. Model prediction is improved when these constants are used, instead of those calculated by potentiometry, as prediction error is lower for all single experimental points. List of symbols

General symbols LR loading ratio (mmol Me2+ /mol PEPEI) [Me]p metal ion concentration in permeate stream [Me]f metal ion concentration in feed stream MWCO molecular weight cut off (Da) PAA poly(acrylic acid) PEI polyethyleneimine PEPEI partially ethoxylated polyethyleneimine RMe metal rejection coefficient T temperature (◦ C) TOC total organic carbon selectivity coefficient Zn/Cu ˛Zn/Cu P transmembrane pressure (bar) Analytical parameters for Henderson–Hasselbach and modified Bjërrum methods analytical concentration of polyelectrolyte (mol L−1 ) CA available concentration of functional groups (mol L−1 ) CAA apparent dissociation constant (mol L−1 ) KaH Kn successive complex formation constants in equilibrium: MeLn−1 + L ↔ MeLn (L mol−1 ) [L]free concentration of dissociated polyelectrolyte (mol L−1 ) n exponent of Henderson–Hasselbach equation cologarithm of the dissociation constant of polymer pKa r average value of complex coordination ˛a dissociation degree of polymer maximum protonation degree ˛p,max ˇ102 global complex formation constant (K1 , K2 ) (L2 mol−2 ) Model symbols [H] proton concentration (mol L−1 ) [HL] non-active polymer repeat unit concentration (mol L−1 ) Ka dissociation constant of polymer (mol L−1 ) Ki,n MeLn complex formation constant in equilibrium: Me + Ln ↔ MeLn (Ln mol−n ) Kps solubility product (mol3 L−3 ) [L] total polymer repeat unit concentration (mol L−1 ) [L]free concentration of dissociated polyelectrolyte (mol L−1 ) [Me] metal concentration (mol L−1 ) [Me]free free metal concentration (mol L−1 ) [Me]free,max maximum metal concentration when precipitation of insoluble hydroxides occurs (mol L−1 ) metal concentration in permeate stream [Me]p [MeLn ] MeLn macromolecular complex concentration (mol L−1 ) [Me(OH)2 ] Me(OH)2 concentration (mol L−1 ) n coordination index of ligand L with metal Me [OH] hydroxyl concentration (mol L−1 ) RL polymer rejection coefficient RMe free free metal rejection coefficient References [1] J. Müslehiddinoglu, Y. Uludag, H.Ö. Özbelge, Y. Yilmaz, Effect of operating parameters on selective separation of heavy metals from binary mixtures via polymer enhanced ultrafiltration, J. Membr. Sci. 140 (1998) 251–266. [2] I.S. Chang, B.H. Kim, Effect of sulphate reduction activity on biological treatment of hexavalent chromium [Cr(VI)] contaminated electroplating wastewater under sulphate-rich condition, Chemosphere 68 (2007) 218–226.

134

J. Llanos et al. / Separation and Purification Technology 73 (2010) 126–134

[3] K. Volchek, E. Krentsel, Y. Zhilin, G. Shtereva, Y. Dytnerky, Polymer binding/ultrafiltration as a method for concentration and separation of metals, J. Membr. Sci. 79 (1993) 253–272. [4] I. Korus, M. Bodzek, K. Loska, Removal of zinc and nickel ions from aqueous solutions by means of the hybrid complexation–ultrafiltration process, Sep. Purif. Technol. 17 (1999) 111–116. [5] P. Baticle, C. Kiefer, N. Lakhchaf, O. Leclerc, M. Persin, J. Sarrazin, Treatment of nickel containing industrial effluents with a hybrid process comprising of polymer complexation–ultrafiltration–electrolysis, Sep. Purif. Technol. 18 (2000) 195–207. [6] C. Mendiguchia, C. Moreno, M. Garcia-Vargas, Separation of heavy metals in seawater by liquid membranes: preconcentration of copper, Sep. Sci. Technol. 37 (2002) 2337–2351. [7] B.L. Rivas, E.D. Pereira, I. Moreno-Villoslada, Water-soluble polymer–metal ion interactions, Prog. Polym. Sci. 28 (2003) 173–208. [8] R. Molinari, T. Poerio, P. Argurio, Selective separation of copper(II) and nickel(II) from aqueous media using the complexation–ultrafiltration process, Chemosphere 70 (2008) 341–348. ˜ [9] R. Camarillo, J. Llanos, L. García-Fernández, Á. Pérez, P. Canizares, Treatment of copper(II)-loaded aqueous nitrate solutions by polymer enhanced ultrafiltration and electrodeposition, Sep. Purif. Technol. 70 (2010) 320–328. ˜ [10] J. Llanos, A. Pérez, P. Canizares, Copper recovery by polymer enhanced ultrafiltration (PEUF) and electrochemical regeneration, J. Membr. Sci. 323 (1) (2008) 28–36. [11] B.L. Rivas, I. Moreno-Villoslada, Prediction of the retention values associated to the ultrafiltration of mixtures of metal ions and high molecular weight watersoluble polymers as a function of the initial ionic strength, J. Membr. Sci. 178 (2000) 165–170. ˜ [12] P. Canizares, A. Pérez, R. Camarillo, J.J. Linares, A semi-continuous laboratoryscale polymer enhanced ultrafiltration process for the recovery of cadmium and lead from aqueous effluents, J. Membr. Sci. 240 (1–2) (2004) 197–209. ˜ [13] P. Canizares, A. Pérez, R. Camarillo, J. Llanos, M.L. López, Selective separation of Pb from hard water by a semi-continuous polymer enhanced ultrafiltration process (PEUF), Desalination 206 (2007) 602–613. ˜ [14] P. Canizares, A. Pérez, R. Camarillo, R. Mazarro, Simultaneous recovery of cadmium and lead from aqueous effluents by a semi-continuous laboratory-scale polymer enhanced ultrafiltration process, J. Membr. Sci. 320 (2008) 520–527. [15] R.S. Juang, M.N. Chen, Measurement of binding constants of poly(ethylenimine) with metal ions and metal chelates in aqueous media by ultrafiltration, Ind. Eng. Chem. Res. 35 (1996) 1935–1943.

[16] M. Rumeau, F. Persin, V. Sciers, M. Persin, J. Sarrazin, Separation by coupling ultrafiltration and complexation of metallic species with industrial water soluble polymers. Application for removal or concentration of metallic cations, J. Membr. Sci. 73 (1992) 313–322. [17] J.H. Chen, C.E. Huang, Selective Separation of Cu and Zn in the citric acid leachate of industrial printed wiring board sludge by D2EHPA-modified amberlite XAD4 resin, Ind. Eng. Chem. Res. 46 (2007) 7231–7238. [18] C. Morlay, M. Cromer, Y. Mouginot, O. Vittori, Potentiometric study of Cu(II) and Ni(II) with two high molecular weight poly(acrylic acid), Talanta 45 (1998) 1177–1188. [19] C. Morlay, M. Cromer, Y. Mouginot, O. Vittori, Potentiometric study of Cd(II) and Pb(II) with two high molecular weight poly(acrylic acid); comparison with Cu(II) and Ni(II), Talanta 48 (1999) 1159–1166. [20] S. Kobayashi, K. Hiroishi, M. Tokunoh, T. Saegusa, Chelating properties of linear and branched poly(ethylenimines), Macromolecules 20 (1987) 1496–1500. [21] A. von Zelewsky, L. Barbosa, C.W. Schläpfer, Poly(ethylenimines) as Brönsted metal ions bases and as ligands for metal ions, Coord. Chem. Rev. 123 (1993) 229–246. [22] P.L. Kuo, S.K. Ghosh, W.J. Liang, Y.T. Hsieh, Hyperbranched polyethyleneimine architecture onto poly(allylamine) by simple synthetic approach and chelating characters, J. Polym. Sci.: Polym. Chem. 39 (2001), 3018-3013. [23] A. Katchalsky, H. Eisenberg, S. Lifson, Hydrogen bonding and ionization of carboxylic acids in aqueous solutions, J. Am. Chem. Soc. 73 (12) (1951) 5889–5890. [24] F. Oosawa, Polyelectrolytes, Dekker, New York, 1971. ˜ [25] P. Canizares, Á. Pérez, J. Llanos, G. Rubio, Preliminary design and optimisation of a PEUF process for Cr (VI) removal, Desalination 223 (2008) 229–237. [26] S. Condom, S. Chemlal, A. Larbot, M. Persin, Behaviour of a cobalt spinel ultrafiltration membrane during salt filtration with different ionic strengths, J. Membr. Sci. 268 (2006) 175–180. [27] R. Molinari, P. Argurio, T. Poerio, G. Gullone, Selective separation of copper (II) and nickel (II) from aqueous systems by polymer assisted ultrafiltration, Desalination 200 (2006) 728–730. [28] J.X. Zeng, H.Q. Ye, N.D. Huang, J.F. Liu, L.F. Zheng, Selective separation of Hg(II) and Cd(II) from aqueous solutions by complexation–ultrafiltration process, Chemosphere 76 (2009) 706–710. [29] F.B. Martí, F.L. Conde, S.A. Jimeno, J.H. Méndez, Química Analítica Cualitativa, 15th ed., Paraninfo, Madrid, 1994.