**3.2 Modified material three-metal sequential study**

Total amounts of metal bound to the native and modified materials at each stage of the sequence are listed in Table 2. Although the average amount of the fist metal ion bound was 24.5 µmol g-1, the average total metal ion bound after exposure to the second and third metals was 31.0 µmol g-1. This increase in the amount of metal captured by the biomass could be indicative of either the presence of metal ion-specific binding sites, or some degree of competitive metal ion binding.

Simultaneous exposure of the biosorbent material to an equimolar solution of all three metal-ions (0.2 mM) was undertaken. Figure 2A shows the resulting effluent concentration profile. Even with a total metal ion concentration of 0.6 mM, the effluent concentration maximized at only 94% of the influent concentration (i.e., 0.19 mM). The modified biomaterial average capacity with simultaneous exposure was 41.72 mol g-1 biomaterial. Specifically, total amounts of metal ion bound were 13.24, 14.17, and 14.31 mol g-1 for Ni2+ Zn2+ Cd2+, respectively. This suggests no significant binding preference of the *D. innoxia* cell material for these ions.

Figure 2B shows the effluent concentration profile of the subsequent 1.0 M HCl metal-ion recovery/strip step. Total metal ion recovered from the two acid washes was 27.48 mol g-1.

Comparative Metal Ion Binding to Native

**3.3.1 Influent and total metal bound comparison** 

decreased by only 42% and 40% respectively.

and position with no apparent pattern.

one two three Total Number Metals Exposed

smallest capacity on the native biomaterial (20.3 mol g-1).

metal bound.

Metal Bound

and Chemically Modified *Datura innoxia* Immobilized Biomaterials 147

By taking the ratio of metal bound for the modified and native biomaterials at each position in the sequence and averaging those ratios for both the influent metal bound and the total metal bound, the average effect of the esterification procedure on metal binding can be quantified. On average, the influent metal-ion bound decreased by 43% while the total metal bound decreased by 54%. Figure 3 illustrates a further breakdown these comparisons by metal-ion position within the sequence. For total metal bound to the biomaterial, metal ion position had only a small effect in the percentage decrease in binding capacity observed in the modified biomaterial. With the first metal ion capacity dropping 52%, the second decreased to 54% and the third decreased to 55%. However, the influent metal ion capacity seems to be more effected by its position in the sequence. The first metal ion exposed demonstrated a decrease in its capacity of 52%, while the second and third ions exposed

Figure 4 shows additional data regarding the influent metal bound by examining both position and specific metal ion exposed in the sequence. For nickel and zinc there was a steady decrease in the observed effect of the modification as their position in the sequence moved from first to third. Nickel was most pronounced, as the effect of the modification was decreased in capacity by 54% when nickel was the first ion exposed, 41% when it is the second, and 35% when the third. Zinc was similar as it drops from a 51% decreased in binding capacity when it was the first metal exposed, a 47% decrease when it was second, to a 41% decrease when it was third. Cadmium did not follow this pattern of decreasing effect based on position. When cadmium was the first metal exposed a decrease in binding capacity of 49% is observed, a decrease in capacity of 38% was observed when it was second, and a decrease of 44% when it metal on the column. The modified biomaterial total metal bound decreased between 49 – 57% depending on influent metal

**A B** 

Metal Bound

Fig. 3. Average total (A) and influent (B) metal-ion bound for native (shaded) and modified biomaterial based on number of metals exposed in series. Metal bound given in percentage

Simultaneous exposure of the three metal-ions showed an overall decrease of 43.7% for total metal bound for the modified biomaterial. Zinc showed the largest decrease showing a 50.2% decrease in binding capacity. The modified biomaterial exhibited a loss of 43.5% for cadmium. Nickel showed the smallest effect from the modification losing 34.8% of its capacity. It should be noted that zinc, which lost the most, had the largest capacity (28.5 mol g-1), while nickel, which demonstrated the smallest effect of modification, had the

one two three Total Number Metals Exposed



Table 2. Influent metal bound at each stage of the sequential exposure study. Values presented are given in moles metal per gram of modified biomaterial.

Fig. 2. Simultaneous exposure of 0.2mM Ni2+(□), Cd2+(), and Zn2+() to modified *D. innoxia* column (A) and is subsequent striping using 1.0 M HCl (B).

#### **3.3 Comparison of native and modified biomaterials**

By examining the results from the native and modified *D. innoxia* studies together, a hypothesis regarding the carboxyl sites contribution to the metal-ion binding process can be formulated. It was proposed, in previous studies of *D. innoxia*, that esterification of carboxylate sites can decrease metal uptake by as much as 40% (Drake, et al., 1996), depending on the metal.

### **3.3.1 Influent and total metal bound comparison**

146 Biomaterials – Physics and Chemistry

This included 7.68, 10.21, and 9.59 mol g-1 for Ni2+ Zn2+ Cd2+, respectively. Nickel recovery was lowest among the three ions (58.0%), while cadmium and zinc recovered 67.0% and 72.1%, respectively. This suggests the affinity of some of the Ni2+ binding sites were higher

Sequence Column a Column b Column c Average Std. Dev. %RSD Cd 28.26 22.63 25.49 25.46 2.56 10.05 Ni 23.57 20.79 23.35 22.57 1.84 8.16 Zn 24.56 24.88 26.76 25.40 1.57 6.16 Cd Ni 27.14 27.14 24.29 26.19 1.64 6.28 Cd Zn 30.33 24.57 24.51 26.47 3.34 12.62 Ni Cd 28.39 26.04 29.95 28.13 1.97 7.01 Ni Zn 29.72 25.95 25.57 27.08 2.29 8.47 Zn Cd 27.53 24.49 31.49 27.84 3.51 12.61 Zn Ni 25.99 26.09 27.66 26.58 0.94 3.52 Cd Ni Zn 30.83 27.00 30.06 29.30 2.02 6.91 Cd Zn Ni 27.89 24.21 27.54 26.55 2.03 7.64 Ni Cd Zn 32.89 26.00 25.42 28.10 4.15 14.78 Ni Zn Cd 21.63 24.57 27.69 24.63 3.03 12.29 Zn Cd Ni 27.45 27.45 40.95 31.95 7.80 24.40 Zn Ni Cd 26.27 23.75 23.62 24.55 1.49 6.09

Table 2. Influent metal bound at each stage of the sequential exposure study. Values

**A**

0.00E+00 1.00E-07 2.00E-07 3.00E-07 4.00E-07 5.00E-07 6.00E-07

Moles Metal in Effluent

Fig. 2. Simultaneous exposure of 0.2mM Ni2+(□), Cd2+(), and Zn2+() to modified *D. innoxia*

By examining the results from the native and modified *D. innoxia* studies together, a hypothesis regarding the carboxyl sites contribution to the metal-ion binding process can be formulated. It was proposed, in previous studies of *D. innoxia*, that esterification of carboxylate sites can decrease metal uptake by as much as 40% (Drake, et al., 1996),

0 0.5 1 1.5 2 2.5 Effluent Volume (mL)

**B** 

presented are given in moles metal per gram of modified biomaterial.

0 10 20 30 40 50 Effluent Volume (mL)

column (A) and is subsequent striping using 1.0 M HCl (B).

**3.3 Comparison of native and modified biomaterials** 

than those for each of the other two metal ions.

0.00E+00 2.00E-07 4.00E-07 6.00E-07 8.00E-07 1.00E-06

depending on the metal.

Moles Metal in Effluent

By taking the ratio of metal bound for the modified and native biomaterials at each position in the sequence and averaging those ratios for both the influent metal bound and the total metal bound, the average effect of the esterification procedure on metal binding can be quantified. On average, the influent metal-ion bound decreased by 43% while the total metal bound decreased by 54%. Figure 3 illustrates a further breakdown these comparisons by metal-ion position within the sequence. For total metal bound to the biomaterial, metal ion position had only a small effect in the percentage decrease in binding capacity observed in the modified biomaterial. With the first metal ion capacity dropping 52%, the second decreased to 54% and the third decreased to 55%. However, the influent metal ion capacity seems to be more effected by its position in the sequence. The first metal ion exposed demonstrated a decrease in its capacity of 52%, while the second and third ions exposed decreased by only 42% and 40% respectively.

Figure 4 shows additional data regarding the influent metal bound by examining both position and specific metal ion exposed in the sequence. For nickel and zinc there was a steady decrease in the observed effect of the modification as their position in the sequence moved from first to third. Nickel was most pronounced, as the effect of the modification was decreased in capacity by 54% when nickel was the first ion exposed, 41% when it is the second, and 35% when the third. Zinc was similar as it drops from a 51% decreased in binding capacity when it was the first metal exposed, a 47% decrease when it was second, to a 41% decrease when it was third. Cadmium did not follow this pattern of decreasing effect based on position. When cadmium was the first metal exposed a decrease in binding capacity of 49% is observed, a decrease in capacity of 38% was observed when it was second, and a decrease of 44% when it metal on the column. The modified biomaterial total metal bound decreased between 49 – 57% depending on influent metal and position with no apparent pattern.

Fig. 3. Average total (A) and influent (B) metal-ion bound for native (shaded) and modified biomaterial based on number of metals exposed in series. Metal bound given in percentage metal bound.

Simultaneous exposure of the three metal-ions showed an overall decrease of 43.7% for total metal bound for the modified biomaterial. Zinc showed the largest decrease showing a 50.2% decrease in binding capacity. The modified biomaterial exhibited a loss of 43.5% for cadmium. Nickel showed the smallest effect from the modification losing 34.8% of its capacity. It should be noted that zinc, which lost the most, had the largest capacity (28.5 mol g-1), while nickel, which demonstrated the smallest effect of modification, had the smallest capacity on the native biomaterial (20.3 mol g-1).

Comparative Metal Ion Binding to Native

modification (i.e., esterification ) reaction.

that the variances of the two means are the same.

ion to a (presumably) nearby site.

and Chemically Modified *Datura innoxia* Immobilized Biomaterials 149

calculations. A confidence limit for each was 95% ( = 0.05). The t-values presented indicate the respective probabilities that the amounts of the influent metal bound at each position were the same for both the native and modified materials. The results indicated that modification of the biomaterial did significantly decrease the binding capacities of the *D.* 

The F-values listed in Table 3 indicated the respective probabilities that the variances of the mean values between the native and modified biomaterials were statistically different. There were two cases a clear (>95%) difference in the variances was indicated; 1) the conditions when cadmium was the first metal exposed to the column and 2) when nickel was the third metal introduced to the biosorbent material. In both cases, larger variances were observed for cadmium binding to the chemically modified material, with a percent relative standard deviation (%RSD) of 27.22% compared to 4.86% for the native material. The binding of nickel showed similar behavior with a 25.97% RSD for its binding to the modified material in comparison to an RSD of 4.50% for the native biosorbent. This suggested sites involved in the binding of Cd2+ initially exposed to the material and those pertaining to Ni2+ binding as the third exposure metal ion were the least homogeneously affected by the chemical

P T ≤ t (two tail) 1.01E-04 3.72E-05 3.18E-07 P F ≤ f (one tail) 0.024 0.258 0.261

P T ≤ t (two tail) 1.58E-03 2.73E-03 2.86E-03 P F ≤ f (one tail) 0.119 0.419 0.006

P T ≤ t (two tail) 3.14E-07 1.66E-06 8.53E-07 P F ≤ f (one tail) 0.390 0.484 0.492 Table 3. Comparing influent metal bound at each position for the native and modified biomaterials. The P T ≤ t value indicated the statistical probability that the mean values for the native and modified *D. innoxia* are the same. The P F ≤ f value indicated the probability

One question that arose with regard to the sequential exposure of the sorbent to chemically similar metal ions is whether there is a statistically significant difference in the binding capacities as a function of the position of the metal in the exposure sequence (i.e., first, second, or third). This is related to the possible presence of cooperativity in the formation (or elimination) of binding sites for one metal because of the earlier binding of another metal

Table 4 summarizes a comparison of influent metal binding capacities within each of the studies based on metal position in the sequence using a Student t-test at 95% confidence. The t-values listed suggest there is no statistical difference in the amount of influent metal bound for either the native or modified biomaterials based on the position of each metal in the exposure sequence. Conversely, the F-values suggested statistical differences in the

Cd position 1 Cd position 2 Cd position 3

Ni position 1 Ni position 2 Ni position 3

Zn position 1 Zn position 2 Zn position 3

*innoxia* for each metal at each position in the sequential exposure sequence.

#### **3.3.2 Statistical analysis**

Because of the numerous variables studied pertaining to the ability of this adsorbent to remove each of these metal ions from a flowing influent, it became imperative that statistical tools be employed to ascertain differences (and similarities) in metal binding. Variables that were tested include the esterification of carboxylate functionalities, the identity of the metal bond, the identity of the metal ion(s) displaced or removed, and the general history of a column of the biosorbent. The Student-t test was employed to test the hypothesis that the measured means of binding capacities between any two conditions were statistically the same. The criteria used for these test were a 95% confidence level with 2 - 5 degrees of freedom.

Fig. 4. Comparison of native (shaded) and modified *D. innoxia* columns influent-metal bound capacities. Metal bound is reported in micromoles per gram biomaterial.

To statistically treat the results presented above in the comparison of the native and esterified biomaterial, two methods of statistical analysis were used. The Student-t test was used to test the statistical difference between the amounts of metal bound to the biomaterial at each stage in the studies at each stage for the native and modified biomaterials. This would also reinforce the position that by undertaking a simple chemical modification, the binding properties of a biomaterial could be altered significantly. Also, the Student-t test was used to examine the impact of exposure order and history (e.g., whether the amount of cadmium bound to the biomaterial is statistically different for the series Ni2+ Zn2+ Cd2+ and Zn2+ Ni2+ Cd2+). Differences in the variances calculated for each stage were similarly evaluated using an F-test (again considering both the order of metal ion exposure and the exposure history of the material).

Table 3 summarizes the resulting statistical comparisons of the native and chemically modified *D. innoxia* materials using the software package 'Analysis ToolPak' within Microsoft® Excel™. Mass balance values of the influent metal bound were used in these

Because of the numerous variables studied pertaining to the ability of this adsorbent to remove each of these metal ions from a flowing influent, it became imperative that statistical tools be employed to ascertain differences (and similarities) in metal binding. Variables that were tested include the esterification of carboxylate functionalities, the identity of the metal bond, the identity of the metal ion(s) displaced or removed, and the general history of a column of the biosorbent. The Student-t test was employed to test the hypothesis that the measured means of binding capacities between any two conditions were statistically the same. The criteria used for these test were a 95% confidence level with 2 - 5 degrees of

> Cd1st Cd2nd Cd3rd Ni1st Ni2nd Ni3rd Zn1st Zn2nd Zn3rd Metal & Position

Fig. 4. Comparison of native (shaded) and modified *D. innoxia* columns influent-metal bound capacities. Metal bound is reported in micromoles per gram biomaterial.

To statistically treat the results presented above in the comparison of the native and esterified biomaterial, two methods of statistical analysis were used. The Student-t test was used to test the statistical difference between the amounts of metal bound to the biomaterial at each stage in the studies at each stage for the native and modified biomaterials. This would also reinforce the position that by undertaking a simple chemical modification, the binding properties of a biomaterial could be altered significantly. Also, the Student-t test was used to examine the impact of exposure order and history (e.g., whether the amount of cadmium bound to the biomaterial is statistically different for the series Ni2+ Zn2+ Cd2+ and Zn2+ Ni2+ Cd2+). Differences in the variances calculated for each stage were similarly evaluated using an F-test (again considering both the order of metal ion exposure

Table 3 summarizes the resulting statistical comparisons of the native and chemically modified *D. innoxia* materials using the software package 'Analysis ToolPak' within Microsoft® Excel™. Mass balance values of the influent metal bound were used in these

**3.3.2 Statistical analysis** 

0

and the exposure history of the material).

10

20

30

Metal Bound

40

50

60

freedom.

calculations. A confidence limit for each was 95% ( = 0.05). The t-values presented indicate the respective probabilities that the amounts of the influent metal bound at each position were the same for both the native and modified materials. The results indicated that modification of the biomaterial did significantly decrease the binding capacities of the *D. innoxia* for each metal at each position in the sequential exposure sequence.

The F-values listed in Table 3 indicated the respective probabilities that the variances of the mean values between the native and modified biomaterials were statistically different. There were two cases a clear (>95%) difference in the variances was indicated; 1) the conditions when cadmium was the first metal exposed to the column and 2) when nickel was the third metal introduced to the biosorbent material. In both cases, larger variances were observed for cadmium binding to the chemically modified material, with a percent relative standard deviation (%RSD) of 27.22% compared to 4.86% for the native material. The binding of nickel showed similar behavior with a 25.97% RSD for its binding to the modified material in comparison to an RSD of 4.50% for the native biosorbent. This suggested sites involved in the binding of Cd2+ initially exposed to the material and those pertaining to Ni2+ binding as the third exposure metal ion were the least homogeneously affected by the chemical modification (i.e., esterification ) reaction.


Table 3. Comparing influent metal bound at each position for the native and modified biomaterials. The P T ≤ t value indicated the statistical probability that the mean values for the native and modified *D. innoxia* are the same. The P F ≤ f value indicated the probability that the variances of the two means are the same.

One question that arose with regard to the sequential exposure of the sorbent to chemically similar metal ions is whether there is a statistically significant difference in the binding capacities as a function of the position of the metal in the exposure sequence (i.e., first, second, or third). This is related to the possible presence of cooperativity in the formation (or elimination) of binding sites for one metal because of the earlier binding of another metal ion to a (presumably) nearby site.

Table 4 summarizes a comparison of influent metal binding capacities within each of the studies based on metal position in the sequence using a Student t-test at 95% confidence. The t-values listed suggest there is no statistical difference in the amount of influent metal bound for either the native or modified biomaterials based on the position of each metal in the exposure sequence. Conversely, the F-values suggested statistical differences in the

Comparative Metal Ion Binding to Native

three-metal system:

and Chemically Modified *Datura innoxia* Immobilized Biomaterials 151

 2a vs. 2b 3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b T Native 0.955 0.471 0.607 0.710 0.830 0.784 F Native 0.105 0.384 0.345 0.247 0.183 0.264 T Modified 0.328 0.969 0.401 0.326 0.621 0.623 F Modified 0.268 0.196 0.416 0.148 0.207 0.060 Table 5a. Effect of column history on influent cadmium bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a NiCd, 2b ZnCd, 3a NiZnCd, 3b ZnNiCd.

 2a vs. 2b 3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b T Native 0.483 0.104 0.326 0.557 0.345 0.665 F Native 0.093 0.454 0.036 0.043 0.267 0.304 T Modified 0.760 0.183 0.310 0.536 0.427 0.377 F Modified 0.459 0.034 0.047 0.413 0.055 0.374 Table 5b. Effect of column history on influent nickel bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a CdNi, 2b ZnNi, 3a CdZnNi, 3b ZnCdNi.

 2a vs. 2b 3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b T Native 0.214 0.515 0.193 0.542 0.959 0.274 F Native 0.939 0.953 0.736 0.691 0.553 0.221 T Modified 0.412 0.327 0.383 0.440 0.470 0.354 F Modified 0.094 0.392 0.357 0.264 0.157 0.224 Table 5c. Effect of column history on influent zinc bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a CdZn, 2b NiZn, 3a CdNiZn, 3b NiCdZn.

Three assumptions were made in pursuing this avenue of exploration. 1) There exist common binding sites shared between all three of the metal ions (δ0). 2) For each metal ion, there exist ion-specific binding sites available only to that particular ion (α, β, γ). 3) For each stage in the influent solution exposure sequence, there may be enhancement or inhibition of binding due to the history of metal exposure, i.e., some level of cooperativity between sites. Making these assumptions allows for the construction of an overall binding equation for the

MBound = [ αCd XCd + αNi XNi + αZn XZn ] + { βCdNi XCdNi + βCdZn XCdZn + βNiCd XNiCd + βNiZn XNiZn + βZnCd XZnCd + βZnNi XZnNi } + ( γCdNiZn XCdNiZn + (1) γCdZnNi XCdZnNi + γNiCdZn XNiCdZn + γNiZnCd XNiZnCd + γZnCdNi XZnCdNi + γZnNiCd XZnNiCd ) + δ0 Xcommon From the sequential experiments, the amount of total metal bound is known for each of the above situations except for metal binding to the common binding sites, XCommon. While the site-type XCommon is available for each condition, the degree to which it is available may be limited by the metal exposure history on the column and the comparative affinities of each metal for those sites. To account for this, a secondary set of data was incorporated into the

variances based on position in the sequence for each of four cases: For nickel, binding to the native column comparing positions 1 and 3, and positions 2 and 3;. Also for cadmium exposed to the modified column comparing positions 1 and 3, and positions 2 and 3. These values again suggested greater inhomogeneity in the impact of the chemical modification procedure on the sites involved in the binding of these metal ions.


Table 4. Comparing influent metal bound at each position. T values are statistical probability that the mean metal bound at each position in sequence are the same. F values are statistical probability that their variances are the same.

Tables 5a-c provide a closer look at metal position by considering the history of metal exposure as well as position of each metal ion in the sequence. The t-values for all three metals indicated no statistical difference as a result of metal exposure history to the influent metal bound for either the native or modified biomaterial. The F-values again suggest statistical differences in the variances in Ni2+ binding based on exposure history. The modified biomaterial showed a difference in the variances for the comparison of the sequences CdZnNi with ZnCdNi, and CdNi with CdZnNi. Comparatively larger relative standard deviations (RSDs) were calculated for the sequences CdNi and ZnCdNi relative to that for the CdZnNi exposure sequence. A probable difference in variances for the comparison of CdNi with CdZnNi, and CdNi with ZnCdNi was also observed for the native material. Under these conditions, CdNi exhibited comparatively large standard deviation relative to those of the other two conditions.

#### **3.3.3 Binding site matrix analysis**

Traditional statistical analysis of the metal ion binding data suggested that the chemical modification of the *D. innoxia* material decreased the number of binding sites significantly, thus reducing metal binding capacities for the esterified biomaterial. Additionally, statistically significant changes in the Ni2+ binding variability suggested non-uniform changes in metal-specific sites that resulted from the esterification reaction. In an effort to extract more information about the binding behavior of the biomaterial towards these three metals, a secondary method of data analysis was undertaken.

variances based on position in the sequence for each of four cases: For nickel, binding to the native column comparing positions 1 and 3, and positions 2 and 3;. Also for cadmium exposed to the modified column comparing positions 1 and 3, and positions 2 and 3. These values again suggested greater inhomogeneity in the impact of the chemical modification

T Cd native 0.739 0.671 0.985 T Ni native 0.196 0.462 0.338 T Zn native 0.380 0.707 0.596 T Cd modified 0.241 0.195 0.912 T Ni modified 0.699 0.686 0.955 T Zn modified 0.567 0.182 0.428 F Cd native 0.119 0.253 0.296 F Ni native 0.407 0.035 0.022 F Zn native 0.399 0.485 0.413 F Cd modified 0.400 0.025 0.041 F Ni modified 0.223 0.382 0.320 F Zn modified 0.476 0.397 0.421 Table 4. Comparing influent metal bound at each position. T values are statistical probability that the mean metal bound at each position in sequence are the same. F values are statistical

Tables 5a-c provide a closer look at metal position by considering the history of metal exposure as well as position of each metal ion in the sequence. The t-values for all three metals indicated no statistical difference as a result of metal exposure history to the influent metal bound for either the native or modified biomaterial. The F-values again suggest statistical differences in the variances in Ni2+ binding based on exposure history. The modified biomaterial showed a difference in the variances for the comparison of the sequences CdZnNi with ZnCdNi, and CdNi with CdZnNi. Comparatively larger relative standard deviations (RSDs) were calculated for the sequences CdNi and ZnCdNi relative to that for the CdZnNi exposure sequence. A probable difference in variances for the comparison of CdNi with CdZnNi, and CdNi with ZnCdNi was also observed for the native material. Under these conditions, CdNi exhibited comparatively large standard deviation

Traditional statistical analysis of the metal ion binding data suggested that the chemical modification of the *D. innoxia* material decreased the number of binding sites significantly, thus reducing metal binding capacities for the esterified biomaterial. Additionally, statistically significant changes in the Ni2+ binding variability suggested non-uniform changes in metal-specific sites that resulted from the esterification reaction. In an effort to extract more information about the binding behavior of the biomaterial towards these three

1 vs. 2 1 vs. 3 2 vs. 3

procedure on the sites involved in the binding of these metal ions.

probability that their variances are the same.

relative to those of the other two conditions.

metals, a secondary method of data analysis was undertaken.

**3.3.3 Binding site matrix analysis** 


Table 5a. Effect of column history on influent cadmium bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a NiCd, 2b ZnCd, 3a NiZnCd, 3b ZnNiCd.


Table 5b. Effect of column history on influent nickel bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a CdNi, 2b ZnNi, 3a CdZnNi, 3b ZnCdNi.


Table 5c. Effect of column history on influent zinc bound. T values are probability that the two compared means are statistically equivalent. F values are statistical probability that their variances are equivalent. 2a CdZn, 2b NiZn, 3a CdNiZn, 3b NiCdZn.

Three assumptions were made in pursuing this avenue of exploration. 1) There exist common binding sites shared between all three of the metal ions (δ0). 2) For each metal ion, there exist ion-specific binding sites available only to that particular ion (α, β, γ). 3) For each stage in the influent solution exposure sequence, there may be enhancement or inhibition of binding due to the history of metal exposure, i.e., some level of cooperativity between sites. Making these assumptions allows for the construction of an overall binding equation for the three-metal system:

$$\begin{aligned} \mathbf{M}\_{\text{Bound}} &= \left\{ \mathbf{z}\_{\text{Cd}} \mathbf{X}\_{\text{Cd}} + \mathbf{z}\_{\text{Ni}} \mathbf{X}\_{\text{Ni}} + \mathbf{z}\_{\text{Zn}} \mathbf{X}\_{\text{Zn}} \right\} + \left\{ \left\{ \mathbf{\beta}\_{\text{CdNi}} \mathbf{X}\_{\text{CdNi}} + \mathbf{\beta}\_{\text{CdZn}} \mathbf{X}\_{\text{CdZn}} \right\} \\ &+ \left\{ \mathbf{\beta}\_{\text{NiCd}} \mathbf{X}\_{\text{NiCd}} + \mathbf{\beta}\_{\text{NiZn}} \mathbf{X}\_{\text{NiZn}} + \mathbf{\beta}\_{\text{ZnCd}} \mathbf{X}\_{\text{ZnCd}} + \mathbf{\beta}\_{\text{ZnNi}} \mathbf{X}\_{\text{ZnNi}} \right\} + \left\{ \mathbf{\gamma}\_{\text{CdNiZn}} \mathbf{X}\_{\text{CdNiZn}} + \mathbf{\gamma}\_{\text{CdNiZn}} \mathbf{X}\_{\text{CdZn}} \right\} \\ &\mathbf{\chi}\_{\text{C2ZnNi}} \mathbf{X}\_{\text{CdZnNi}} + \mathbf{\gamma}\_{\text{NiCdZn}} \mathbf{X}\_{\text{NiCdZn}} + \mathbf{\gamma}\_{\text{NiZnCu}} \mathbf{X}\_{\text{N2ZnCd}} + \mathbf{\gamma}\_{\text{ZnNiZn}} \mathbf{X}\_{\text{ZnCdNi}} + \mathbf{\gamma}\_{\text{ZnNiCd}} \mathbf{X}\_{\text{ZnNiCd}} \end{aligned} \tag{1}$$

From the sequential experiments, the amount of total metal bound is known for each of the above situations except for metal binding to the common binding sites, XCommon. While the site-type XCommon is available for each condition, the degree to which it is available may be limited by the metal exposure history on the column and the comparative affinities of each metal for those sites. To account for this, a secondary set of data was incorporated into the

Comparative Metal Ion Binding to Native

metal on the column

and Chemically Modified *Datura innoxia* Immobilized Biomaterials 153

**ZnCd** 31.69 38.20 112.00 48.16 1.00

**ZnNi** 32.07 56.72 120.30 66.68 14.49 **CdNiZn** 31.27 31.87 167.60 -78.40 0.30 **CdZnNi** 28.80 32.57 162.60 -77.70 -0.96 **NiCdZn** 30.93 44.71 193.60 -65.50 13.17 **NiZnCd** 28.80 24.26 156.20 -86.00 -4.68 **ZnCdNi** 38.10 31.82 169.70 -78.40 2.56 **ZnNiCd** 28.69 30.96 167.30 -79.30 6.26 **Simultaneous** 41.72 36.41 191.70 410.20 -30.40

(B) Coefficient | Case Exp. mole/gram 1 2 3 4

Table 7. Modified (A) and Native (B) columns experimental and calculated total metals bound, Case 1: All unique single metal bonds are included when appropriate in the sequential case and only all three unique sites along with the common site for the

simultaneous case. Case 2: Same as case 1 except for the simultaneous all three, three metal binding site types are active along with the unique sites and common site. Case 3: The unique metal coefficients are not included in the simultaneous portion of the matrix calculation. Case 4: The unique metal coefficients are only included when they are the first

Cd 50.35 45.60 756.48 334.45 -16.11 Ni 49.42 38.00 268.98 326.85 -11.68 Zn 52.27 46.14 -202.78 334.99 -7.64 CdNi 70.31 50.81 557.30 90.26 -8.63 CdZn 69.39 55.57 82.16 95.02 -3.49 NiCd 61.10 46.83 553.32 86.28 -8.19 NiZn 67.60 50.40 76.99 89.85 6.78 ZnCd 59.34 54.47 560.96 93.92 3.00 ZnNi 69.16 52.05 78.64 91.50 8.20 CdNiZn 74.07 39.35 -102.89 -128.61 -4.86 CdZnNi 73.12 40.19 -102.05 -127.77 0.24 NiCdZn 67.28 37.77 -104.47 -130.19 -2.02 NiZnCd 66.05 37.36 -104.88 -130.60 1.84 ZnCdNi 64.08 40.10 -102.14 -127.86 4.35 ZnNiCd 68.13 39.51 -102.73 -128.45 3.77 Simultaneous 72.87 40.68 -1505.70 673.19 -50.24

(A) Coefficient | Case **Exp. mole/gram 1 2 3 4 Cd** 25.53 29.58 62.68 187.30 -6.53 **Ni** 22.57 43.73 67.24 201.40 -1.94 **Zn** 25.40 53.4 65.29 211.10 0.36 **CdNi** 30.59 32.75 116.00 42.71 0.02 **CdZn** 31.03 47.59 112.80 57.55 1.28 **NiCd** 30.39 45.32 128.80 55.28 12.62 **NiZn** 29.94 47.78 113.60 57.74 -3.17

ensuing analysis. The total metal-bound data from the simultaneous exposure of all three metals to the biomaterial were indicative of situations in which all three unique metal binding sites (XCd, XNi, and XZn) are used along with only the common site, XCommon. This enabled the isolation of the common site from any binding enhancement or inhibition that could be attributed to metal history. By using the total amounts of each metal bound for each stage in the sequences and the amount of metal bound during the simultaneous exposure of the material to the three metals, 16 equations for metal binding can be written. The variables XCd through Xcommon can have values of either 1 (the site-type is involved) or 0 (the site-type is not involved). These can then be combined into a single, 16 by 16 matrix (**X** in Table 6) with the corresponding coefficients comprising the contents of 1 by 16 vector (**c**). For each stage in the sequences the common site, the individual metal-ion sites, and the corresponding sequential site will make contributions to the total metal bound. For example, the total metal bound at the sequence stage Ni2+ Zn2+ can be represented by the equation:

$$\mathbf{M}\_{\text{Total}} = \mathbf{a}\_{\text{Ni}} + \mathbf{a}\_{\text{Zn}} + \boldsymbol{\beta}\_{\text{NiZn}} + \boldsymbol{\mathcal{S}}\_0 \tag{2}$$

And the simultaneous exposure of all three metals can be represented by:

$$\mathbf{M}\_{\text{Total}} = \mathbf{q}\_{\text{C:d}} + \mathbf{q}\_{\text{Ni}} + \mathbf{q}\_{\text{Zn}} + \mathbf{\mathcal{S}}\_0 \tag{3}$$

Where MTotal is the total metal bound and the coefficients (α, β, γ, and δ) indicate the contribution of each site-type to the total metal bound.


Table 6. Matrix representing the contributions to total metal ion bound to the immobilized D. innoxia at each stage of influent metal ion exposure in the sequential experiments. A '1' indicates a contribution to total metal binding at the particular stage, a '0' indicates the site is not involved.


ensuing analysis. The total metal-bound data from the simultaneous exposure of all three metals to the biomaterial were indicative of situations in which all three unique metal binding sites (XCd, XNi, and XZn) are used along with only the common site, XCommon. This enabled the isolation of the common site from any binding enhancement or inhibition that could be attributed to metal history. By using the total amounts of each metal bound for each stage in the sequences and the amount of metal bound during the simultaneous exposure of the material to the three metals, 16 equations for metal binding can be written. The variables XCd through Xcommon can have values of either 1 (the site-type is involved) or 0 (the site-type is not involved). These can then be combined into a single, 16 by 16 matrix (**X** in Table 6) with the corresponding coefficients comprising the contents of 1 by 16 vector (**c**). For each stage in the sequences the common site, the individual metal-ion sites, and the corresponding sequential site will make contributions to the total metal bound. For example, the total metal bound at the sequence stage Ni2+ Zn2+ can be represented by the equation:

MTotal = αNi + αZn + βNiZn + δ0 (2)

 MTotal = αCd + αNi + αZn + δ0 (3) Where MTotal is the total metal bound and the coefficients (α, β, γ, and δ) indicate the

> **β Cd Ni**

Cd 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 **Ni** 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 **Zn** 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 **CdNi** 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 **CdZn** 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 **NiCd** 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 **NiZn** 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 **ZnCd** 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 **ZnNi** 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 **CdNiZn** 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 **CdZnNi** 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 **NiCdZn** 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 **NiZnCd** 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 **ZnCdNi** 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 **ZnNiCd** 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 Simultaneous 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 Table 6. Matrix representing the contributions to total metal ion bound to the immobilized D. innoxia at each stage of influent metal ion exposure in the sequential experiments. A '1' indicates a contribution to total metal binding at the particular stage, a '0' indicates the site

**β Cd Ni**

**β Cd Ni**

**γ Cd Ni Zn** 

**γ CdZn Ni**

**γ NiCd Zn**

**γ NiZn Cd**

**γ ZnCd Ni**

**γ ZnNi Cd**

**δ0**

And the simultaneous exposure of all three metals can be represented by:

**β Cd Ni** 

**β Cd Ni**

contribution of each site-type to the total metal bound.

**β Cd Ni** 

**α Zn**

**α Cd**

is not involved.

**α Ni** 


Table 7. Modified (A) and Native (B) columns experimental and calculated total metals bound, Case 1: All unique single metal bonds are included when appropriate in the sequential case and only all three unique sites along with the common site for the simultaneous case. Case 2: Same as case 1 except for the simultaneous all three, three metal binding site types are active along with the unique sites and common site. Case 3: The unique metal coefficients are not included in the simultaneous portion of the matrix calculation. Case 4: The unique metal coefficients are only included when they are the first metal on the column

Comparative Metal Ion Binding to Native

**-20.00**

sequences.

**Cd**

**Ni**

**Zn**

**CdNi**

**CdZn**

**NiCd**

**NiZn**

Fig. 5. Comparison of native and modified (shaded) *D. innoxia* matrix coefficients.

**ZnCd**

Binding Sites Coefficient Native Material Modified Material Cd αCd 1.07 -15.57 Ni αNi -6.53 -1.42 Zn αZn 1.61 8.25 CdNi βCdNi 11.74 4.59 CdZn βCdNi 8.36 9.76 NiCd βCdNi 7.76 17.16 NiZn βCdNi 10.79 -4.20 ZnCd βCdNi 7.26 0.37 ZnNi βCdNi 12.44 4.74 CdNiZn γCdNiZn -13.07 -9.13 CdZnNi γCdZnNi -8.85 -13.60 NiCdZn γNiCdZn -10.67 -8.86 NiZnCd γNiZnCd -14.11 -7.95 ZnCdNi γZnCdNi -7.84 -4.96 ZnNiCd γCdNiZn -13.61 -10.19 Common δ0 44.53 45.15 Table 8. Coefficient values for both the native and modified D. innoxia metal ion binding

The modified biomaterial's coefficients behaved in a similar manner as the native. The single metal coefficients for Cd2+ and Ni2+ were both negative (Ni2+slightly, Cd2+ moderately)

**ZnNi**

**Position**

**CdNiZn**

**CdZnNi**

**NiCdZn**

**NiZnCd**

**ZnCdNi**

**ZnNiCd**

**Common**

**-10.00**

**0.00**

**10.00**

**20.00**

**Coeffiecient**

**30.00**

**40.00**

**50.00**

and Chemically Modified *Datura innoxia* Immobilized Biomaterials 155

The system can then be represented by the matrix equation:

$$\begin{bmatrix} \mathbf{M} \end{bmatrix} = \begin{bmatrix} \mathbf{c} \end{bmatrix} \begin{bmatrix} \mathbf{X} \end{bmatrix} \tag{4}$$

with [**A**] is a 1 by 16 vector containing the total amount of metal bound for each situation, [**c**] is a 1 by 16 vector containing the contribution coefficients for each site type, and [**X**] is the 16 by 16 matrix describing the types of binding that may be taking place. For example, the row in the matrix [**X**] corresponding to the previous example (Ni →Zn) would be [ 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 ]. Both [**M**] and [**X**] are therefore known or determined experimentally. The contribution coefficient matrix, [**c**], can then be calculated by solving the multivariate equation.

$$\begin{bmatrix} \mathbf{M} \end{bmatrix} \begin{bmatrix} \mathbf{X} \end{bmatrix}^{\mathrm{T}} \begin{ (\mathbf{X})} \begin{bmatrix} \mathbf{X} \end{bmatrix} \begin{bmatrix} \mathbf{X} \end{bmatrix}^{\mathrm{I}} \end{bmatrix} \begin{bmatrix} \mathbf{1} \end{bmatrix} = \begin{bmatrix} \mathbf{c} \end{bmatrix} \tag{5}$$

The superscripts T and -1 designate the corresponding transposed and inverted matrices, respectively.

Four matrices were examined using this methodology. The matrix presented in Table 6 includes all of the unique single metal bonds, where appropriate, in the sequential case, and only the three unique sites plus the common site for the simultaneous case. Tables 7a and b list the experimentally determined total amounts of metal bound with the predicted amounts from four separate theoretical calculations. Case 1 shows the results from the calculations using the matrix shown in Table 6. Case 2 is the same matrix as case 1 except for the simultaneous row, which now includes all three, three-metal binding sites (coefficients γNiZnCd, γZnCdNi, and γZnNiCd) along with the unique and common sites. Case 3 differs from case 2 by eliminating the unique sites from the simultaneous portion of the matrix. Case 4 is distinguished by only including the unique metal site type when the metal is the first metal introduced to the column.

Upon examining the results presented in Tables 7 a and b, it was evident that case 1 best approximated the experimental results. Figure 5 illustrates the values of the contribution coefficients for both the native and the modified (shaded) *D. innoxia* total metal bound studies.

The most striking and least surprising result of this analysis was the contribution the common site (δ0) made to overall binding for both the native and the modified biomaterial. Also noteworthy, was the series of positive coefficients present in the two metal ion systems. For both the native and modified biomaterials, it appears that the presence of a metal ion enhanced the biomaterial's binding capacity. The lone exception to this was the impact of the NiZn sequence on the modified material.

The native biomaterial exhibited slight positive coefficients for the unique Cd2+ and Zn2+ sites and a moderate apparent inhibition for Ni2+. All binary combinations of metal ions exposed to the native biomass resulted in moderate positive coefficient values. The tertiary combinations all yielded moderately negative values. This does not necessarily indicate an absolute inhibition of binding, but can be interpreted in terms of relative inhibition effects. Review of the experimental data listed in Table 7 b reveals single metal values as all near 50 mol g-1 (average 50.68). Comparatively, binary combinations ranged from 60 – 70 mol g-1 (average 66.15), an increase of 15 while tertiary combinations ranged from 65 –75 mol g-1 (average 68.78), an increase which may not be statistically significant. This suggests some degree of cooperativity in metal-ion binding while the primary mechanism of metal ion binding is simple electrostatic (i.e., the dominance of the common sites).

 [**M**] = [**c**] [**X**] (4) with [**A**] is a 1 by 16 vector containing the total amount of metal bound for each situation, [**c**] is a 1 by 16 vector containing the contribution coefficients for each site type, and [**X**] is the 16 by 16 matrix describing the types of binding that may be taking place. For example, the row in the matrix [**X**] corresponding to the previous example (Ni →Zn) would be [ 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 ]. Both [**M**] and [**X**] are therefore known or determined experimentally. The contribution coefficient matrix, [**c**], can then be calculated by solving the multivariate

 [**M**] [**X**]T ([**X**] [**X**]T)-1 = [**c**] (5) The superscripts T and -1 designate the corresponding transposed and inverted matrices,

Four matrices were examined using this methodology. The matrix presented in Table 6 includes all of the unique single metal bonds, where appropriate, in the sequential case, and only the three unique sites plus the common site for the simultaneous case. Tables 7a and b list the experimentally determined total amounts of metal bound with the predicted amounts from four separate theoretical calculations. Case 1 shows the results from the calculations using the matrix shown in Table 6. Case 2 is the same matrix as case 1 except for the simultaneous row, which now includes all three, three-metal binding sites (coefficients γNiZnCd, γZnCdNi, and γZnNiCd) along with the unique and common sites. Case 3 differs from case 2 by eliminating the unique sites from the simultaneous portion of the matrix. Case 4 is distinguished by only including the unique metal site type when the metal is the first metal

Upon examining the results presented in Tables 7 a and b, it was evident that case 1 best approximated the experimental results. Figure 5 illustrates the values of the contribution coefficients for both the native and the modified (shaded) *D. innoxia* total metal bound

The most striking and least surprising result of this analysis was the contribution the common site (δ0) made to overall binding for both the native and the modified biomaterial. Also noteworthy, was the series of positive coefficients present in the two metal ion systems. For both the native and modified biomaterials, it appears that the presence of a metal ion enhanced the biomaterial's binding capacity. The lone exception to this was the impact of

The native biomaterial exhibited slight positive coefficients for the unique Cd2+ and Zn2+ sites and a moderate apparent inhibition for Ni2+. All binary combinations of metal ions exposed to the native biomass resulted in moderate positive coefficient values. The tertiary combinations all yielded moderately negative values. This does not necessarily indicate an absolute inhibition of binding, but can be interpreted in terms of relative inhibition effects. Review of the experimental data listed in Table 7 b reveals single metal values as all near 50 mol g-1 (average 50.68). Comparatively, binary combinations ranged from 60 – 70 mol g-1 (average 66.15), an increase of 15 while tertiary combinations ranged from 65 –75 mol g-1 (average 68.78), an increase which may not be statistically significant. This suggests some degree of cooperativity in metal-ion binding while the primary mechanism of metal ion

binding is simple electrostatic (i.e., the dominance of the common sites).

The system can then be represented by the matrix equation:

equation.

respectively.

studies.

introduced to the column.

the NiZn sequence on the modified material.

Fig. 5. Comparison of native and modified (shaded) *D. innoxia* matrix coefficients.


Table 8. Coefficient values for both the native and modified D. innoxia metal ion binding sequences.

The modified biomaterial's coefficients behaved in a similar manner as the native. The single metal coefficients for Cd2+ and Ni2+ were both negative (Ni2+slightly, Cd2+ moderately)

Comparative Metal Ion Binding to Native

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while Zn2+ was moderately positive. All of the binary combinations were moderately positive except for NiZn, which was moderately negative, and ZnCd, which was only slightly positive. The tertiary combinations were as on the native biomaterial, all moderately negative. Again, this only reflects relative inhibition of metal ion binding. The data listed in Table 7a reveals single metal bound values were all about 25 mol g-1 (average 24.5). These are compared to those for the binary combinations which ranged from 30 – 32 mol g-1 (average 31.0), an increase of 6. Similarly to the native material, the tertiary combinations ranged from 29 – 39 mol g-1 (average 31.1), a slight increase which may not be statistically significant. This again suggested that some degree of cooperativity in binding with the primary binding mechanism involving electrostatic attractions.
