Metal Binding Stoichiometry and Isotherm Choice in Biosorption

Sep 18, 1999 - General properties of these stoichiometric assumptions are pointed out, and tools are provided to facilitate the choice of the most app...
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Environ. Sci. Technol. 1999, 33, 3821-3828

Metal Binding Stoichiometry and Isotherm Choice in Biosorption SILKE SCHIEWER* AND MING HUNG WONG Institute for Natural Resources and Waste Management and Department of Biology, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People’s Republic of China

Seaweeds that possess a high metal binding capacity may be used as biosorbents for the removal of toxic heavy metals from wastewater. The binding of Cu and Ni by three brown algae (Sargassum, Colpomenia, Petalonia) and one green alga (Ulva) was investigated at pH 4.0 and pH 3.0. The greater binding strength of Cu is reflected in a binding constant that is about 10 times as high as that of Ni. The extent of metal binding followed the order Petalonia ∼ Sargassum > Colpomenia > Ulva. This was caused by a decreasing number of binding sites and by much lower metal binding constants for Ulva as compared to the brown algae. Three different stoichiometric assumptions are compared for describing the metal binding, which assume either that each metal ion M binds to one binding site B forming a BM complex or that a divalent metal ion M binds to two monovalent sites B forming BM0.5 or B2M complexes, respectively. Stoichiometry plots are proposed as tools to discern the relevant binding stoichiometry. The pH effect in metal binding and the change in proton binding were well predicted for the B2M or BM0.5 stoichiometries with the former being better for Cu and the latter preferable for Ni. Overall, the BM0.5 model is recommended because it avoids iterations.

Introduction Biosorption, the passive binding of metals by living or dead biomass, can be used to remove toxic heavy metals from industrial wastewaters, e.g., of the electroplating industry. High effluent quality can be reached at low cost because cheap raw materials may be used as biosorbents, making biosorption a potentially attractive alternative to conventional metal removal processes such as ion exchange resins (1). One type of biomass particularly suited for biosorption are seaweeds, which display a large metal binding capacity, occur abundantly, and can be harvested at low cost. To have a quantitative means of comparing metal binding strength and to design biosorption processes effectively, it is useful to employ mathematical models predicting the metal binding. Although Langmuir and Freundlich sorption isotherms have been widely used to describe biosorption data (1-4), it has now been recognized that these simple isotherm models have severe shortcomings. The Freundlich isotherm cannot be easily interpreted in mechanistic terms. Both Langmuir and Freundlich models do not incorporate pH effects. Since pH is one of the key parameters in biosorption (3, 5), it is desirable to use isotherm equations that can accommodate pH as one model variable. * Corresponding author e-mail: [email protected]; telephone: 852-2339 7050; fax: 852-2339 5995. 10.1021/es981288j CCC: $18.00 Published on Web 09/18/1999

 1999 American Chemical Society

Second, simple Langmuir and Freundlich models assume that the sorbate, e.g., metal, is bound to free binding sites and do not take into account that biosorption is often an ion exchange process (6, 7). It has therefore been recommended to use ion exchange constants that reflect the fact that the biosorbent is initially saturated with some ions that have to be released when the metal ion is taken up (8). Ion exchange constants do, however, not take into account that the degree of binding site occupation may change. Therefore, multicomponent isotherm models have been proposed that can account for ion exchange and pH effects (7, 9, 10). Third, simple Langmuir and Freundlich models assume a 1:1 stoichiometry whereby one metal ion binds to one binding site. Divalent metal ions, however, are known to form bidentate complexes in many biomaterials such as alginate and pectin (11). It will therefore be more appropriate to use a model based on a 1:2 binding stoichiometry whereby one divalent metal ion M binds to two binding sites B. Two different approaches have been proposed in this respect: i.e., to use ion exchange constants that assume the formation of B2M complexes (2, 8, 12) or a multicomponent isotherm assuming the formation of BM0.5 complexes (7, 10). In the past, little attention has been paid to choosing the most appropriate metal binding model. For Zn-Ca exchange, the difference between ion exchange constants and Langmuir isotherms was elucidated in a linearized Langmuir plot and in a Scatchard plot (8). For exchange between two divalent metal ions at constant pH, a stoichiometry plot of the ratio of metal uptakes (q1/q2) as a function of the concentration ratio ([M1]/[M2]) has been used. The observed behavior fell between the ones expected for assumption of either BM0.5 or B2M complexes (10). For Cd proton ion exchange in Sargassum, plotting qM/qH or qM0.5/qH, respectively, versus [M]0.5/[H] for BM0.5 and B2M complexes indicated that both assumptions were similarly appropriate (13). The first main objective of this study is to compare three possible metal binding stoichiometries, namely, the formation of BM complexes (Langmuir model), B2M complexes, or BM0.5 complexes in a more systematic way than in previous studies. To enable a fair comparison, the same level of model complexity will be considered for all stoichiometries. General properties of these stoichiometric assumptions are pointed out, and tools are provided to facilitate the choice of the most appropriate one to be used in future biosorption studies. The use of two types of stoichiometry plots is recommended to discern which stoichiometric assumption holds in a given situation. The second main objective is to clarify how many constants are necessary to describe metal binding for different types of biomass, metals, and pH values. Should, for example, the number of binding sites be determined for each isotherm or should the same number of binding sites be assumed for any metal ion and pH value? Is it preferable to use lumped constants for metal proton exchange or one constant each for metal and proton binding? Can the same proton binding constant or pKa value be used for all data or does it have to vary with the metal, pH value, or biomass? Furthermore, this work provides a comparison of metal binding for four seaweeds and two metals, Cu and Ni.

Materials and Methods Biomass. Three brown seaweeds (Sargassum hemiphyllum, Colpomenia sinuosa, and Petalonia fascia) as well as one green seaweed (Ulva fascia) were employed as biosorbents. Ulva and Sargassum are the most abundant green and brown seaweeds in Hong Kong, respectively. They occur globally in VOL. 33, NO. 21, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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large quantities. U. fascia and P. fascia were collected in March 1998 on Big Wave Bay (Hong Kong Island), C. sinuosa and S. hemiphyllum were harvested in April 1998 in Saikung and in January 1998 on High Island, respectively (both located at the eastern coast of the New Territories). All samples were collected from life stocks. The seaweed was dried in an oven and ground in a blender. About 20 g of the size fraction 1-2 mm (∼average size after blending) was washed in 1 L of DI water to remove the major part of salt from the seaweed. Then each biomass was washed in 1 L of 0.1 M HNO3 for protonation, washed subsequently 20 times in 1 L of DI water (to remove excess acid), and finally oven-dried at 50 °C. The protonation was performed in order to remove unknown quantities of light metal ions from the seaweed and to ensure that all binding sites were converted to their acidic form, i.e., saturated with protons. Metal Binding Experiments. The nitrate salts Cu(NO3)2‚ 2.5H2O and Ni(NO3)2‚6H2O (Riedel de Haen) were dissolved in DI water. Nitrate was chosen as the anion because of its low tendency for complex formation with most metals. A 0.1 g of biomass was contacted with 40 mL of metal solution in 100-mL Erlenmeyer flasks on a Labline orbit shaker at 150 rpm. Known amounts of 0.1 M NaOH or HNO3 were added (∼10 additions were necessary) till the pH value, measured on an Orion 290A pH meter, was stable at the desired value (3.0 or 4.0). The amount of base added increased with increasing metal concentration, yielding total Na concentrations of 0.5-6.5 mM for pH 4.0 and 0-2 mM for pH 3, respectively. The samples were then left shaking overnight for complete equilibration, and the final pH was recorded. Initial and final metal concentrations [M]i and [M] were measured by an atomic absorption spectrometer (AAS) (Varian AA-20). The initial concentrations ranged from 0.2 to ∼20 mM. Determination of the Equilibrium Cation Binding. The mass balance for protons is

qH,i m + [H]addVH,add - [OH]addVOH,add + [H]iVi ) qH m + [H]V (mM) (1) where [H] is the concentration of protons in solution, qH is the amount of protons bound to the biomass, m is the mass of biosorbent, and V is the solution volume. The subscript i denotes initial values, otherwise final values are referred to. [H]add and [OH]add are the concentrations of added acid or base, respectively, with their solution volumes being VH,add and VOH,add. The amount of protons bound at equilibrium can be obtained by solving eq 1 for qH:

qH ) qH,i + ([H]addVH,add - [OH]addVOH,add + [H]iVi - [H]V)/m (mequiv/g) (2) For protonated biomass, the initial proton binding qH,i equaled the total number of binding sites Bt except for Ulva, which contained 0.4 mequiv/g of excess acid (which led to pH ∼3 when 0.1 g of Ulva was equilibrated in 40 mL of DI water) so that qH,i ) Bt + 0.4 mequiv/g. The mass balance for a divalent metal ion M is

0.5 qM,i m + [M]iVi ) 0.5 qM m + [M]V (mM)

(3)

whereby qM is the amount of metal bound to the biomass (mequiv/g) and [M] is the metal concentration in solution. The factor 0.5 is required to convert from equivalent to molar concentration. Solving this equation for qM and assuming that no metal is bound initially (i.e., qM,i ) 0) yields

qM ) 2([M]iVi - [M]V)/m (mequiv/g) 3822

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Since this equation may lead to large errors in the calculation of qM if the difference between [M]i and [M] is small (14), the metal binding qM was determined by desorption if [M] was larger than 50% of [M]i. For desorption, the solution after sorption was decanted or filtered off, and the wet metalladen biomass was blotted on a dry filter paper to remove excess liquid. The biomass (without the filter paper) was then transferred onto a weighing tray of a known mass and weighed immediately (to avoid evaporation). The biomass on the weighing tray was dried in an oven at 50 °C and weighed again after being equilibrated at room atmosphere to regain the “normal” moisture content. The biomass was then transferred into 40 mL of ∼0.1 M (or 0.9%) HNO3 in a 100-mL Erlenmeyer flask and equilibrated overnight on a Labline orbit shaker at 150 rpm. The liquid after desorption was then analyzed by AAS to determine the desorbed metal concentration [M]des. The metal binding after sorption (and before desorption) was calculated as

qM ) 2([M]desVdes/mdes - [M]Vm) (mequiv/g)

(5)

whereby Vdes is the volume of the desorbing solution, mdes is the dry weight of the biomass to be desorbed, and Vm is the specific volume of the wet biomass after sorption (L/g), i.e., its wet weight (assuming a density of one) after sorption divided by the dry weight. The term [M]Vm is subtracted in order to account for metals that are not bound to binding sites but contained in the absorbed or adhering water. For an accurate determination of qM, it is desirable that the term [M]Vm is kept as small as possible. This is the reason for blotting the biomass dry before desorbing it and for not drying and desorbing it together with the filter paper.

Modeling Metal Binding. For simplicity’s sake, all models considered here involved only one type of binding site and one type of metal ion. They can however easily be modified to account for multimetal, multisite biosorption (10, 15). The binding sites are assumed to be uniform (no affinity distribution), and secondary interactions are neglected. For any of the three models, the reaction for the binding of protons is

B + H h BH

KH ) BH/(B[H]) (1/mM)

(6)

Three models that assume different metal binding stoichiometries (heading of Table 1) are compared: (a) the BM model (Langmuir isotherm), which assumes that one metal ion M binds to one binding site B, forming a BM complex; (b) the BM0.5 model, which was introduced by Schiewer and Volesky (7); and (c) the commonly (8, 16, 17) used B2M model. The latter two assume that one divalent metal M binds to two binding sites B. The total number of binding sites is given by eq 8 (model eqs 5-12 are listed in Table 1). For the first two models, explicit pH-sensitive isotherm equations for calculating the proton and metal binding as a function of metal concentration and pH (eqs 9a,b and 10a,b) can be derived from eqs 6-8. For the B2M stoichiometry, it is unfortunately impossible to derive explicit isotherm equations. The proton and metal binding, respectively, are obtained from eqs 6 and 7c, rearranged as eqs 9c and 10c. Since the number of free sites, B, is unknown, iterative calculation of B, qH, and qM is required using eqs 8c, 9c, and 10c, which renders this model rather tedious and inconvenient to use. Lumped Parameter Isotherm Model. For constant pH, eq 10a,b can be simplified by dividing the enumerator and the denominator by (1 + KH[H]), yielding a lumped parameter isotherm (eq 11a,b) whereby the lumped binding constant K* is given in eq 12a,b (Table 1). Equation 11a is the well-

TABLE 1. Model Equations for Three Stoichiometric Assumptions

a Units are g mequiv-1 mM-1 for column c. b Units are mM0.5 g mequiv-1 for column b and mM0.5 g0.5 mequiv-0.5 for column c. c Units are mM for column b and mM g mequiv-1 for column c. d Units are g mequiv-1 for column c.

known Langmuir isotherm. For the B2M model, the apparently free number of sites B* is defined as

B* ) Bt - 2B2M ) B + BH ) B(1 + KH[H]) (mequiv/g) (13) Inserting eq 13 into eq 10c yields eq 11c. The metal binding (eq 11c) and B* (eq 13) can be calculated iteratively (using the lumped constant K*). When eq 13 is inserted into eq 11c to eliminate B*, and the equation is then solved for B2M, qM can be calculated more conveniently, without iterations, as

qM ) 2B2M ) (1 + 4BtK*[M] (1 + 8BtK*[M])0.5)/(8K*M) (mequiv/g) (14) Stoichiometry Plots for Constant pH. The linearized isotherm eqs 15a-c can be derived from eqs 11a-c and 13. Equations 15a-c are rewritten as eqs 16a-c (Table 1) for graphical determination of Bt, which is the inverse of the slope when [M]/qM, [M]0.5/qM, or ([M]/qM)0.5 are plotted versus [M], [M]0.5, or ([M]qM)0.5, respectively, for the three stoichiometries. The linearity of the data indicates how appropriate the model is for the data. For the BM0.5 model, this linearization has been recommended by Fogler (18) as a means of confirming this stoichiometric assumption. Stoichiometry Plots for Proton-Metal Ion Exchange. The exchange constant Kx (eqs 17a-c) is obtained by dividing KM according to eqs 7a-c over KH (eq 6) or its square, respectively, for the latter two stoichiometries. Rearranging eqs 17a-c yields eqs 18a-c (Table 1) on which the stoichiometry plot is based. If the respective stoichiometric assumption is correct, plotting qM/qH, qM2/qH2, or qM/qH2 versus [M]/[H], [M]/[H]2, or [M]/[H]2, respectively, for the three stoichiometries should yield a straight line with the slope Kx (or 2 Kx for the B2M stoichiometry). For the BM0.5 model, this type of plot was previously used (13).

Results and Discussion Stoichiometry Plot for Proton-Cu Ion Exchange. The proton-metal ion exchange stoichiometry plot (eqs 18a-c) for Cu binding by all four algae at pH 4 is shown in Figure 1. Since both the x and y values range over about 4 orders of magnitude, a log/log scale was chosen. A linear representation would only do justice to the highest data points (within about 1 order of magnitude). A linear correlation on the linear scale (eqs 18a-c) translates into a linear correlation with the slope 1.0 on the log/log scale, i.e., for the correct stoichiometric assumption the data in the log/log plot should fall on a straight line with the slope of 1.0. The upper right side of Table 2 lists the slope of the regression lines fitting the data for each biomass for log/log representation. Only data points with qH > 0.1 mequiv/g were used for the regressions, since the relative error in determining lower proton binding values is large. For any biomass, the slopes are highest for the BM0.5 stoichiometry plot, intermediate for the B2M stoichiometry plot, and lowest for the BM plot. The predictions of each model would yield straight lines with a slope of 1.0 in the respective stoichiometry plot. For the B2M representation, the slope of the experimental data (Figure 1) is closest to 1.0, deviating from this value by an average of 17% (upper right side of Table 2). This indicates that the B2M model may be the most appropriate one to use because it corresponds well to the data. Since the regression coefficients R 2 are high (g0.90) in most cases, the slope is the decisive factor in which the B2M model excels. On a linear scale, the ion exchange constant Kx would be equal to the slope of the regression lines. On the log scale this translates into the position of the regression lines. The exchange constant can be read from the graphs conveniently as the y value for x ) 1 or better as the inverse of the x value which yields y ) 1 (except for the B2M stoichiometry where the factor 2 in eq 18c has to be taken into account). For the VOL. 33, NO. 21, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Stoichiometry plot for proton-Cu ion exchange: (a) for BM complex formation; (b) for BM0.5 complex formation; (c) for B2M complex formation. B2M and BM0.5 plots (Figure 1b,c), the exchange constants are around 1/10 for Sargassum, Colpomenia, and Petalonia. For Ulva, the exchange constants for any stoichiometry are 1 order of magnitude lower than for the other algae. That means Cu can displace protons more easily from the other biosorbents than from Ulva. Ulva is therefore less suitable for Cu biosorption because it shows comparatively less affinity for Cu. The stoichiometry plots for constant pH (eq 16, Figures 4 and 5 and discussion in the Supporting Information) show that the number of binding sites Bt decreases in the order Sargassum = Petalonia > Colpomenia > Ulva (left side of Table 2). One can conclude that Sargassum and Petalonia are superior biosorbents as compared to Colpomenia and Ulva because the former feature both a higher number of binding sites (i.e., a higher metal binding capacity) and a higher proton metal exchange constant (i.e., a higher affinity of Cu). Consequently, the following experiments for Ni 3824

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binding were performed for Sargassum and Petalonia as the best biosorbents. Stoichiometry Plot for Proton-Ni Ion Exchange. The proton-metal exchange stoichiometry plot for Ni binding by Sargassum and Petalonia at pH 4.0 and pH 3.0 is depicted in Figure 2. The slope of the regression lines is very close to 1.0 for the BM0.5 model, deviating only an average 6% from 1.0. For the B2M and BM models, the slopes are consistently much too low, deviating an average of 33 and 44%, respectively, from the expected value of 1.0 (lower right part of Table 2). Consequently, the BM0.5 model is the most adequate one in this case. All stoichiometric assumptions yield average regression coefficients R 2 > 0.90. The data for the BM stoichiometry (Figure 2a) are however considerably more scattered. This is due to the fact that, unlike for the other two models, the data obtained for different pH values do not ”line up” but are clearly higher for pH 4.0. This means the BM model does not reflect pH effects adequately. For a correct stoichiometric assumption, the data for any pH value should yield the same exchange constant, i.e., all assemble along one straight line. It is not surprising that the BM stoichiometry fails to model pH effects adequately: it is based on the assumption that metal ions bind to one binding site only, i.e., that one divalent metal ion exchanges with one proton. This is however not the case: it has been shown in various instances that divalent metals bind to two binding sites each, which means they can displace two protons (6, 7, 17). The values of the Ni-proton exchange constants for the B2M and BM0.5 models range between 1/30 and 1/100 (Figure 2b,c) which is almost 1 order of magnitude lower than for Cu. That means Cu is more strongly bound than Ni. pH-Sensitive Models. Although it is possible to use simple lumped parameter models (eqs 11a-c) that cannot predict pH effects so that each set of constants is only valid for one pH value (Supporting Information, Figures 6 and 7, Table 4, and relating text), it is desirable to use pH-sensitive models such as eqs 9 and 10. These models offer the advantage of predicting not only proton binding but also the effect of pH on metal binding. They require, however, the determination of a proton binding constant as an additional parameter. For all pH-sensitive models, the total number of binding sites Bt that had previously been determined in pH titrations (Sargassum, 2.6 mequiv/g; Colpomenia, 1.5 mequiv/g; Petalonia, 2.9 mequiv/g; Ulva, 1.1 mequiv/g) (19) was used. These values were valid for different metals and at different pH values. Only when the same Bt is used for different pH values is it possible to predict pH effects. Though the total metal binding capacity (or number of binding sites) may seem to be reduced at low pH (Supporting Information, Table 4, section on lumped parameter models), it is rather the case that the availability (not number) of the binding sites is reduced because they are occupied by protons. As shown below, pH effects can be predicted using the same number of binding sites at different pH values. For the BM model, two cases (a and b) are distinguished. The BMa model assumes that one divalent metal ion exchanges with one proton. The maximum amounts of metal ions and protons bound qM,max and qH,max both in molar terms are equal. This is, however, not confirmed by observations: the maximum amount of divalent metals bound usually equals the maximum amount of protons bound in equivalent terms, i.e., one divalent metal ion exchanges with two protons, such as predicted by the BM0.5 and B2M models. The BMa model therefore fits very badly when both metal and proton binding are to be modeled (Tables 3 and 5). The BM model can however be “salvaged” by the following empirical modification yielding the BMb model. The term 2Bt in eq 10a is replaced by Bt, i.e., it is assumed that the total number of proton binding sites is twice the total number of metal binding sites: qH,max (mequiv/g) ) Bt (mequiv/g) ) 2qM,max (mmol/g)

TABLE 2. Stoichiometry Plot Parameters stoichiometry plot for metal proton ion exchange

stoichiometry plot for constant pH BM

R2 (-)

BM0.5

Bt Bt/Bt,tita (mequiv/g) (-)

R2 (-)

B2M

Bt Bt/Bt,tita (mequiv/g) (-)

R2 (-)

BM

Bt Bt/Bt,tita (mequiv/g) (-)

R2 (-)

BM0.5

slope (-)

R2 (-)

slope (-)

B2M

R2 (-)

slope (-)

Copper Sargassum Colpomenia Petalonia Ulva average

0.99 1.00 0.99 1.00 1.00

2.7 1.8 2.7 1.0

1.02 1.18 0.93 0.91 9b

0.96 0.98 0.98 0.34 0.82

3.1 2.2 2.9 2.9

1.18 1.43 1.01 2.63 56b

Sargassum, pH 4 Sargassum, pH 3 Petalonia, pH 4 Petalonia, pH 3 average

0.99 0.98 0.99 0.98 0.99

2.4 1.1 2.1 1.3

0.93 0.41 0.72 0.44 38b

0.95 0.90 0.99 0.87 0.93

3.1 1.6 2.4 2.9

average for all

1.00

24b

0.88

0.99 1.00 0.99 1.00 1.00

2.8 1.9 2.8 1.2

1.08 1.25 0.97 1.10 12b

1.21 0.59 0.83 0.99 20b

0.98 0.98 0.99 0.96 0.98

2.6 1.2 2.2 1.6

1.00 0.46 0.74 0.54 32b

38b

0.99

0.95 0.84 0.94 0.73 0.88 0.56 0.99 0.72 0.94 29c

0.87 1.76 0.87 1.52 0.86 1.09 0.97 1.41 0.89 45c

0.91 1.34 0.92 1.12 0.89 0.82 0.98 0.96 0.93 17c

Nickel

22b

0.92

0.58 0.92

0.95 0.94

0.68

0.89

0.54 0.97

0.94 0.98

0.66

0.91 44c

0.95

6c

0.96 33c

0.93 37c

0.92 26c

0.95 25c

a

Number of binding sites determined from the stoichiometry plot divided by number of binding sites determined in pH titrations (19). b Average deviation of the number of binding sites determined in the stoichiometry plot from the one obtained in pH titrations (19), expressed in percent. c Average deviation of the slope in the stoichiometry plot from the expected value of 1.0, expressed in percent.

) qM,max (mequiv/g). This means that maximum proton and metal binding are equal in equivalent terms. The fit of the BMb model is much better than that of the BMa model (Tables 3 and 5). For each of the stoichiometries, two cases will be distinguished: either the proton binding constant will be individually optimized for each set of data at fixed pH or the same proton binding constant is used for all data. Table 5 (Supporting Information) lists the optimum pKa value (log (KH × 1000 mM/M)), metal binding constant KM, and mean square error ∆q for each series as determined by individual fitting with MATLAB 4.2b. The optimum apparent pKa values range from 4.1 to 7.2 with an average around 5.1. Even though a better fit may be obtained if a separate pKa value is determined for each series, it is desirable to use a common pKa value for different pH values, different metals, different models, and if possible, even for different types of biomass. This reduces the number of parameters to be determined and makes it possible to predict how the metal binding changes with pH (within about ( 2 pH units of the pKa value, i.e., where the presence of other groups with different pKa values can be neglected). The pKa value 5.1 was chosen as a common value for the modeling of all data since it is the average of the optimized pKa values (Table 5, Supporting Information) and yields a good fit. The left half of Table 3 shows the metal binding constants optimized by MATLAB for the common pKa value of 5.1 and the respective average errors for metal and proton binding. The model deviations are very similar to the ones obtained with the optimum pKa values for each data series (Table 5, Supporting Information). That means it is possible to use the same pKa value for all data, irrespective of the metal ion, pH, model, and biomass with a negligible increase in the error. For an average of both Cu and Ni, the BM0.5 model is the best (average error: 0.18 mequiv/g), closely followed by the B2M (0.19 mequiv/g) and BMb (0.24 mequiv/g) models (left side of Table 3). Similarly good fits can even be achieved if the same (averaged) metal binding constant KM is used for all three brown algae as indicated in the right half of Table 3. These results are similar to those of the lumped parameter model in that the B2M stoichiometry was best for Cu and the BM0.5 stoichiometry was best for Ni while all models were overall (for Cu and Ni) similarly accurate (Supporting Information, section on lumped parameter model, Figures 6 and 7, Tables 4 and 6).

An example of the predictions of the BMb and BM0.5 model predictions is shown in Figure 3 where the Ni and proton binding at pH 3.0 and pH 4.0 by Petalonia are depicted. To render the model predictions more smooth, the average pH values of 4.04 and 3.07 were used. The average absolute deviation of individual pH values from these mean values was 0.11 and 0.02, respectively. The increase of metal binding with increasing pH is well predicted, even though the same number of binding sites is used to model both pH values. The corresponding decrease of the proton binding with an increase in the metal binding illustrates the ion exchange behavior. Predictions of the BM0.5 model were better than those of the BMb model. While the latter shows a comparatively abrupt change in cation binding with metal concentration, the former predicts a rather gradual increase that matches the experimental data. The B2M model (not shown) shows an intermediate shape. The different isotherm shapes, which are characteristic for the respective stoichiometries, are further discussed in the Supporting Information (Figures 6 and 7, section on lumped parameter models). Overall Comparison of Stoichiometric Assumptions. The regression coefficients of the stoichiometry plots are of little use to distinguish among the stoichiometries because they were mostly high. R 2 > 0.9 can even be obtained for obviously very unsuitable models, like the BM assumption in the Niproton exchange plot (Figure 2a), which was not able to describe the pH effects adequately. The main advantage of the BM0.5 and B2M models is that they adequately represent the fact that divalent metals usually occupy two binding sites. Therefore these stoichiometric assumptions are better suited to model the exchange between metals and protons. The BM0.5 and B2M models yield slightly lower deviations from the experimental data than the BMb model, but all are of similar magnitude. For Cu binding, the B2M model was better than the BM0.5 stoichiometry while the reverse was the case for Ni. This was the case because of different isotherm shapes, whereby the BM0.5 model showed rather gradual changes of ion binding with metal concentration. In either case, the stoichiometric assumption that yielded the better fit displayed a slope in the exchange plot much closer to 1.0 than for the other model. It can be concluded that the slope in the log/log plot for metal proton ion exchange (Figures 1 and 2) is the best indicator of the appropriateness of the stoichiometric assumptions. This plot, unlike the stoichiometry plot for constant pH (Figures 4 and 5 in the Supporting VOL. 33, NO. 21, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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0.21

0.20 0.25 0.23

0.26

0.30 0.33 0.32 0.54 0.58 0.56

0.18 0.24 0.64

Absolute mean square deviations of the model predictions from the data for qM and qH. a

average for all

2.2 1.7

Sargassum Petalonia average

0.54 0.57 0.56

12 7.5

0.29 0.32 0.31

410 230

0.15 0.14 0.15

240 130

0.19

2.0 2.0

0.85

Nickel 0.19 0.23 0.21

0.71

10 10

0.20

320 320

0.21

0.26

0.16 0.16 0.16

190 190

0.19

0.22 0.15 0.21 1400 1400 1400 0.32 0.23 0.23 2900 2900 2900 0.15 0.13 0.32 380 380 380 8.9 8.9 8.9

1.00 0.49 1.07

Copper 0.21 0.15 0.21 0.07 0.16 1800 1300 1200 130 0.30 0.21 0.23 0.08 0.21 4200 1600 2800 130 0.14 0.11 0.31 0.10 0.17 440 270 430 11 0.98 0.49 1.03 0.33 0.71 13 8.4 5.3 1.3

B2M BM0.5

∆qa ∆qa

BMb

optimized KM for each alga

∆ qa

∆q a 9

Sargassum Colpomenia Petalonia Ulva average

B2M BM0.5

KM KM KM KM KM KM KM KM ∆ qa ∆qa ∆qa (1/mM) (mequiv/g) (1/mM) (mequiv/g) (1/mM) (mequiv/g) (g mequiv-1 mM-1) (mequiv/g) (1/mM) (mequiv/g) (1/mM) (mequiv/g) (1/mM) (mequiv/g) (g mequiv-1 mM-1) (mequiv/g)

BMb

∆qa

average KM for all brown algae

BMa 3826

BMa

Information), gives due importance to the data points at low concentrations, and it is easily possible to distinguish whether a given stoichiometric assumption yields a straight line with a slope near 1.0, which indicates the appropriateness of the assumption. The use of this stoichiometry plot is therefore recommended as a tool for the choice of the stoichiometric assumption to be used in further modeling. The ultimate test, of course, is how the model predicts the data (Figures 3, 6, and 7 partially in the Supporting Information). This, however, requires time-consuming programming of model equations and fitting of constants (especially for the B2M model, which requires iterations). The B2M model can be advantageous at very low metal concentrations where the BM0.5 model sometimes tends to overpredict the metal binding. Since however both stoichiometric assumptions fit in average equally well and since the BM0.5 model offers the additional advantage of being much more easy to use (no iterations are required), it is recommended to use the BM0.5 model unless further considerations

TABLE 3. Parameters and Errors for the pH-Sensitive Models with Common pKa Value of 5.1

FIGURE 2. Stoichiometry plot for proton-Ni ion exchange: (a) for BM complex formation; (b) for BM0.5 complex formation; (c) for B2M complex formation.

binding sites at suitable distance in order to form a stable complex, the lesser affinity in Ulva may be caused by a lack of a suitably spaced sites, i.e., the individual carboxyl sites may be too far apart to allow bidentate binding. The higher metal binding selectivity of guluronic acid as compared to mannuronic acid (which both have similar pKa values) (12, 22) has been explained as being due to similar steric effects (23). Even though the brown algae in this study might differ in their ratios of mannuronic acid to guluronic acid and therefore display different metal binding constants, their affinity for the metals is similar enough that the same metal binding constants can be used for all three algae (Table 3).

Supporting Information Available Text plus three tables (Tables 4-6) and four figures (Figures 4-7) (12 pages). This material is available free of charge via the Internet at http://pubs.acs.org.

Glossary B BH BM,BM0.5, B2M Bt H KH KM Kx K* FIGURE 3. Proton and Ni binding by Petalonia. Experimental data and pH-sensitive BMb and BM0.5 models with common pKa: (a) at pH 4.0 and (b) at pH 3.0. advise against it. Overall Comparison of the Metals and Biosorbents. Cu has a higher affinity to all types of biomass when compared to Ni, leading to an exchange constant or metal binding constant that is 1 order of magnitude higher than that for Ni (Tables 3-5). This corresponds to the higher tendency of Cu to form covalent bonds since it is a “softer” metal than Ni (20). The best biosorbents (high Bt and high Kx or KM) are Sargassum and Petalonia. Colpomenia displays intermediate (medium Bt and high Kx or KM), and Ulva by far displays the worst (low Bt and low Kx or KM) performance. The much lower metal binding constant in Ulva as compared to the other biosorbents might be related to the fact that Ulva is the only green alga among the seaweeds studied. Carboxyl groups are probably the main binding site in all four seaweeds since the number of weakly acidic carboxyl groups determined in pH titrations (19) corresponds well to the metal binding capacity Bt (Tables 2 and 4). One might therefore at first suspect that these should display the same metal binding constants. However, there is a marked difference in the molecular environment of the carboxyl groups in green and brown algae, respectively. In brown algae, carboxyl groups occur mainly in alginate, a polysaccharide composed of mannuronic and guluronic acids. Green algae, on the other hand, do not contain alginate. Their carboxyl groups will therefore rather be present in either protein or complex hetero-polysaccharides of the cell wall containing some uronic acids (21). Since divalent metals often need two

M m pKa qH qM V []

amount of free binding sites (mequiv/g) amount of protonated binding sites (mequiv/ g) amount of metal-binding site complexes (mequiv/g) total amount of binding sites (mequiv/g) proton equilibrium constant for the binding of proton (L/mmol) equilibrium constant for the binding of metal ion (L/mmol) or (g mequiv-1 mM-1) equilibrium constant for metal-proton ion exchange (mmol/L) or (-) lumped equilibrium constant for the metal binding (L/mmol) metal ion dry weight of biomass (g) -log of acid dissociation constant ) log (1000KH) (-) amount of protons bound to the biosorbent (mequiv/g) amount of metal bound to the biosorbent (mequiv/g) volume of solution (L) concentration of molecular species (mmol/ L)

Indices add des i

added desorbed initial

Literature Cited (1) Biosorption of Heavy Metals; Volesky, B., Ed.; CRC Press: Boca Raton, FL, 1990; pp 7-43. (2) Chen, X. H.; Gosset, T.; Thevenot, D. R. Water Res. 1990, 24, 1463. (3) Ferguson, J.; Bubela, B. Chem. Geol. 1974, 13, 163. (4) Tsezos, M.; Volesky, B. Biotechnol. Bioeng. 1981, 23, 583. (5) Greene, B.; McPherson, R.; Darnall, D. In Metals Speciation, Separation and Recovery; Patterson, J. W., Pasino, R., Eds.; Lewis: Chelsea, MI, 1987; p 315. (6) Crist, R. H.; Martin, J. R.; Guptill, P. W.; Eslinger, J. M.; Crist, D. R. Environ. Sci. Technol. 1990, 24, 337. VOL. 33, NO. 21, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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(7) Schiewer, S.; Volesky, B. Environ. Sci. Technol. 1995, 29, 3049. (8) Crist, R. H.; Martin, J. R.; Carr, D.; Watson, J. R.; Clarke, H. J.; Crist, D. R. Environ. Sci. Technol. 1994, 28, 1859. (9) Huang, C.; Huang, C. P.; Morehart, A. L. Water Res. 1991, 25, 1365. (10) Schiewer, S.; Volesky, B. Environ. Sci. Technol. 1996, 30, 2921. (11) Kohn, R. Pure Appl. Chem. 1975, 42, 371. (12) Haug, A.; Smidsrod, O. Acta Chem. Scand. 1970, 24, 843. (13) Schiewer, S.; Volesky, B. Environ. Sci. Technol. 1997, 31, 2478. (14) Schiewer, S.; Volesky, B. Biotechnol. Tech. 1995, 9, 843. (15) Chong, K. H.; Volesky, B. Biotechnol. Bioeng. 1995, 47, 451. (16) Haug, A.; Smidsrod, O. Acta Chem. Scand. 1965, 19, 341. (17) Jang, L. K.; Nguyen, D.; Geesey, G. G. Water Res. 1995, 29, 315. (18) Fogler, H. S. Elements of Chemical Reaction Engineering; Prentice Hall: Englewood Cliffs, NJ, 1986; pp 238-244.

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(19) Schiewer, S.; Wong, M. H. Chemosphere In press. (20) Nieboer, E.; Richardson, D. H. S. Environ. Pollut. 1980, 1B, 3. (21) Lee, R. E. Phycology; Cambridge University Press: Cambridge, U.K., 1980; p 7. (22) Haug, A. Acta Chem. Scand. 1961, 15, 950. (23) Lobban, C. S.; Harrison, P. J.; Duncan, M. J. The physiological ecology of seaweeds; Cambridge University Press: Cambridge, U.K., 1985; pp 123-128.

Received for review December 11, 1998. Revised manuscript received May 14, 1999. Accepted July 22, 1999. ES981288J