Heterogeneous Cross-Linking of Chitosan Gel Beads: Kinetics

Sep 2, 1997 - The rate processes of the heterogeneous cross-linking reaction and the effect of cross-linking on the cadmium ion adsorption capacity we...
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Ind. Eng. Chem. Res. 1997, 36, 3631-3638

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Heterogeneous Cross-Linking of Chitosan Gel Beads: Kinetics, Modeling, and Influence on Cadmium Ion Adsorption Capacity Tzu-Yang Hsien and Gregory L. Rorrer* Department of Chemical Engineering, Oregon State University, Corvallis, Oregon 97331

Chitosan, a linear biopolymer of glucosamine residues, selectively adsorbs transition-metal ions such as cadmium from dilute solution. In order to process chitosan into a more durable form, a 5 wt % chitosan solution was cast into spherical gel beads of 3 mm diameter and then reacted with glutaraldehyde at free amine sites to form imine cross-links between linear chitosan chains. The rate processes of the heterogeneous cross-linking reaction and the effect of cross-linking on the cadmium ion adsorption capacity were determined. The cross-linking reaction was complete within 48 h at 27 °C, and the final extent of cross-linking ranged from 0.07 to 2.40 mol of glutaraldehyde consumed/mol of amine. Heterogeneous cross-linking was modeled as a shrinking core process where the molecular diffusion of glutaraldehyde through the cross-linked shell of the gel bead limited the overall rate of glutaraldehyde consumption. The effective diffusion coefficient of glutaraldehyde through the cross-linked layer was 4.7 × 10-8 cm2/s. The saturation adsorption capacity of cadmium ions on the cross-linked gel beads exponentially decreased from 250 to 100 mg of Cd/g of chitosan as the extent of cross-linking increased from 0 to 1.3 mol of glutaraldehyde consumed/mol of amine. At higher extents of cross-linking, the saturation adsorption capacity remained at 100 mg of Cd/g of chitosan. Highly porous chitosan beads formed by freeze-drying of cross-linked gel beads had the same cadmium ion adsorption capacity as the cross-linked gel beads over the same extents of cross-linking. Introduction Biopolymers are a promising new class of low-cost adsorbents for removal of heavy-metal ions from aqueous waste streams (Volesky and Holan, 1996). Of particular interest is chitosan, a linear polysaccharide of β-1,4-O-glycosyl-linked glucosamine residues (Figure 1). Chitosan is derived from chitin, a major component of the shells of crustacean organisms and the second most abundant biopolymer in nature next to cellulose (Muzzarelli, 1977). The amine group on each glucosamine unit within the chitosan biopolymer chain serves as a selective binding site for group III transitionmetal ions. The adsorption of heavy-metal ions on chitosan, including adsorption isotherms, and the selectivity of group III transition-metal ions over groups I and II alkali/alkaline earth metal ions are well documented (Inoue et al., 1988; Jha et al., 1988; McKay et al., 1989; Udaybhaskar et al., 1990; Kawamura et al., 1993; Rorrer et al., 1993; Hsien and Rorrer, 1995). Chemical modifications of chitosan have been reported to enhance transition-metal ion adsorption capacity (Tong et al., 1991; Kawamura et al., 1993; Inoue et al., 1995; Guibal et al., 1995). In the attempt to improve the material properties of chitosan for engineering and biotechnological applications, several investigators have developed porous, chemically cross-linked chitosan beads for the removal of heavy-metal ions from wastewater (Kawamura et al., 1993; Rorrer et al., 1993, Hsien and Rorrer, 1995), enzyme recovery (Yoshida et al., 1994), and drug delivery (Nishimura et al., 1986; Bodmeier et al., 1989). The amine group on each glucosamine residue within the chitosan chain can serve a reactive site for two attractive chemical modifications. First, N-acylation with nonanyl chloride adds a hydrocarbon side chain to the amine group (Figure 1) and imparts a hydropho* Corresponding author. Telephone: 541-737-3370. Fax: 541-737-4600. E-mail: [email protected]. S0888-5885(97)00157-7 CCC: $14.00

Figure 1. Acylation and glutaraldehyde cross-linking of amine groups on chitosan.

bic substructure to the biopolymer (Hirano et al., 1976, 1977; Fuji et al., 1980). This reduces interchain hydrogen bonding between chitosan chains and modestly improves the adsorption capacity for heavy metal ions at low extents of N-acylation (Kurita et al., 1988; Hsien and Rorrer, 1995). Second, reductive animation with glutaraldehyde forms an imine (-CdN-) cross-link between linear chitosan chains (Figure 1). cross-linking reduces the solubility of chitosan in aqueous solvents © 1997 American Chemical Society

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at low pH and can improve resistance to chemical degradation or long-term biological degradation. The properties of homogeneously cross-linked chitosan have been studied (Roberts and Taylor, 1989; Thacharodi and Rao, 1993). However, no quantitative relationship between the extent of cross-linking and adsorption capacity for transition-metal ions has been established. The limited previous work is incomplete and conflicting: Kurita et al. (1986) and Koyama and Taniguchi (1986) claimed that homogeneous cross-linking of a chitosan solution optimized copper ion removal at low extents of cross-linking, whereas Masri et al. (1978) claimed that heterogenous cross-linking of chitosan powder reduced heavy-metal ion adsorption capacity. Our previous work showed that cross-linking of chitosan gel beads with glutaraldehyde followed by freezedrying significantly enhanced final material properties. For example, cross-linking of 3 mm, 7% N-C9 acylated chitosan gel beads with 250 mM glutaraldehyde followed by freeze-drying resulted in a mesoporous material with an internal surface area of 224 m2/g. The cross-linked, freeze-dried chitosan beads were also insoluble in low-pH environments (Hsien and Rorrer, 1995). Unlike freeze-drying, the cross-linking process has many variables associated with it. However, no studies have considered how cross-linking bath parameters affect the heterogeneous cross-linking kinetics and the final extent of cross-linking. Furthermore, although cross-linking combined with freeze-drying may produce highly porous beads, it is not known if the freeze-drying step improves the adsorption capacity for transitionmetal ions. To address these research needs, this study has four objectives. The first objective is to determine the kinetics of the heterogeneous cross-linking of glutaraldehyde with the chitosan gel beads by measuring the glutaraldehyde consumption as a function of time and process parameters, most importantly the initial molar ratio of glutaraldehyde in the cross-linking bath to the amine groups in the chitosan gel bead. The second objective is to develop a physical and mathematical model for the heterogeneous cross-linking process in order to predict the extent of cross-linking as a function of time, bead properties, and cross-linking bath parameters. The third objective is to determine how the extent of cross-linking affects the saturation adsorption capacity of cadmium ions on both chitosan gel beads and freeze-dried beads. The fourth objective is to determine if the high internal surface area of the freeze-dried beads is required for high adsorption capacity of cadmium ions. In all studies, both chitosan beads and 7% N-C9 acylated chitosan beads are compared. Materials and Methods Chitosan Gel Bead Synthesis. Chitosan solution was prepared by dissolving 3.75 g of chitosan powder (94% deacetylation; Vanson Chemical Co., Redmond, WA) into 70 mL of a 0.68 M acetic acid solution. The 5 wt % chitosan solution was mixed at 500 rpm with a 4.5 cm marine blade impeller for 30 min and then mixed on an orbital shaker at 120 rpm and 25 °C for an additional 72 h to lower the solution viscosity. The chitosan solution was cast into spherical beads using the spinnerette system described by Rorrer et al. (1993). The newly formed beads were dropped into a precipitation bath containing 400 mL of 2 M NaOH, which neutralized the acetic acid within the chitosan bead and thereby coagulated the chitosan to a uniform gel. The gel beads were mixed in the sodium hydroxide solution

for an additional 4 h to ensure complete coagulation. The residual acetate concentration in the gel bead was not measured. However, only 70 g of gel beads were made per 400 mL of a 2 M NaOH solution so that no more than 6% of the NaOH in the precipitation bath was neutralized. The total amine and residual acetamide group content was estimated to be 6.13 mmol/g, assuming that the chitosan initially consisted only of 94% glucosamine residues (mol wt 161.2) and 6% residual N-acetylglucosamine residues (mol wt 203.2). For simplicity, both groups are referred to as unreacted amine groups. To prepare chitosan with 7% of the amine groups acylated as N-C9 amides, 70 mL of a 5 wt % chitosan solution was acylated with 0.28 g of nonanoyl chloride, CH3(CH2)7COCl (Aldrich Chemical No. 15,683-3, mol wt 176.7), and then recovered in pyridine and purified as described by Hsien and Rorrer (1995). The same gel bead casting procedures were followed, using a 1.0 M aqueous methanolic sodium hydroxide solution (50% v/v) as the precipitation bath. The free amine and acetamide group content (YB) of the 7% N-C9 acylated chitosan was taken as 5.77 mmol/g. Heterogeneous Cross-Linking of Chitosan Gel Beads. The chitosan gel beads were cross-linked with aqueous glutaraldehyde (GA), HOC(CH2)3COH (Aldrich Chemical No. G400-4, 25 wt % in aqueous solution, bp 101 °C). Gel beads (6.40 g) were mixed with an aqueous glutaraldehyde dialdehyde solution (9.60 g) within a sealed 125 mL Erlenmeyer flask on an incubated orbital shaker at 120 rpm and 27 °C. The initial glutaraldehyde concentration in the cross-linking bath ranged from 12.5 to 500 mM. The cross-linking bath was sampled periodically after 48 h. The pH of the crosslinking bath was measured periodically with a pH electrode. The glutaraldehyde concentration in the cross-linking bath was determined by a gas chromatograph (GC). Specifically, a 1.0 µL aliquot of solution sampled from the cross-linking bath was injected into a HewlettPackard 5890 GC system equipped with a HewlettPackard HP-FFAP column (10 m × 0.53 mm × 1.0 µm) and FID detector. The analysis conditions were set at the following: 150 °C injector, 100 °C column, 155 °C detector, He carrier gas at 10 mL/min. The retention time of glutaraldehyde was 2.7 min under these analysis conditions. The concentration of glutaraldehyde was quantified by the external standard method. The extent of glutaraldehyde consumption by cross-linking (XT), defined as the moles of glutaraldehyde consumed per mole of amine groups initially available in the chitosan gel bead, was estimated by

XT ) moles of GA monomer consumed by the gel bead ) moles of -NH2 initially in the gel bead (CA0 - CA)VC (1) mbxBYB where CA0 is the initial concentration of glutaraldehyde in the cross-linking bath, CA is the current concentration of glutaraldehyde in the cross-linking bath, mb is the mass of beads in the cross-linking bath, VC is volume of glutaraldehyde solution in the cross-linking bath, xB is the weight fraction of chitosan in the gel bead, and YB is free amine group content of the chitosan before crosslinking. As a control experiment, 9.6 mL of a 250 mM glutaraldehyde solution containing no gel beads were mixed on an orbital shaker at 120 rpm and 27 °C for 48

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h. The glutaraldehyde concentration assayed by GC was constant over the 48 h of incubation time, demonstrating that the aqueous glutaraldehyde solution was stable. The extent of cross-linking was also estimated gravimetrically. The glutaraldehyde solution in the crosslinking bath was filtered from the gel beads. The filtered gel beads were air-dried at room temperature for 24 h, weighed, and then oven-dried at 85 °C for 4 h and weighed again to make sure that the final weight of the cross-linked product was obtained. The weight of the un-cross-linked gel beads was also determined by soaking 6.4 g of gel beads in 9.6 mL of distilled water for 48 h, followed by filtration and drying as described above. The retention of cross-linked reagent in the bead after air drying (XR), expressed as mole of glutaraldehyde cross-linked per total mole of amine groups in the gel bead, was estimated by

XR )

wB - wB0 mbxBYBMA

(2)

where wB0 is the mass of the air-dried gel beads before cross-linking, wB is the mass of the air-dried cross-linked beads, and MA is the average molecular weight of a monomeric unit within the cross-link assembly, which was assumed equal to 64 g of cross-link/mol of glutaraldehyde consumed. Cadmium Ion Adsorption Capacity. Batch isotherm adsorption measurements for cadmium ions on chitosan beads are described by Hsien and Rorrer (1995). In the present experiments, 0.79 g of the gel beads were mixed with 40 mL of a cadmium nitrate (Cd(NO3)2) solution within a sealed 125 mL Erlenmeyer flask at 120 rpm on an orbital shaker at 25 °C for 60 h. The solution was filtered from the gel beads and analyzed for cadmium ion concentration by ion chromatography (IC) using a Dionex CS-5 column as described by Hsien and Rorrer (1995). The final cadmium loading in the beads was determined by

Qf )

(C0 - Cf)V mbxB

(3)

where C0 is the initial cadmium ion concentration, Cf is the final cadmium concentration, Qf is the final cadmium loading in the beads (mg of Cd+2/g of adsorbent), and V is the volume of the cadmium solution. For all saturation adsorption capacity measurements, C0 was at least 2000 mg of Cd+2/L. Cadmium adsorption capacity measurements for the cross-linked freeze-dried chitosan beads (40 mg/40 mL of a cadmium nitrate solution) were also obtained by the same methods. All Qf values were corrected to mg of Cd+2/g of chitosan to facilitate comparison at different extents of crosslinking. Other Measurements. The density for the 7% N-C9 acylated gel beads was 1.06 ( 0.03 (one standard deviation, 1s) g/cm3 as determined by volumetric displacement. The diameter of the beads was measured with a digital caliper, and average diameters were 3.3 ( 0.2 (1s) and 3.2 ( 0.2 (1s) mm, respectively, for chitosan beads and 7% N-C9 acylated chitosan beads. Selected cross-linked chitosan gel bead and 7% N-C9 acylated chitosan gel bead preparations were also freeze-dried as described by Rorrer et al. (1993). The diameter of the cross-linked freeze-dried beads was the same as that of the cross-linked gel beads. The weight fraction chitosan in the gel beads before cross-linking

was determined gravimetrically by oven-drying 6.4 g of gel beads at 85 °C for 24 h. The pH within the chitosan gel beads before cross-linking was measured by crushing 6.4 g of gel beads down to a pulp with a mortar and pestle and then immersing a pH electrode directly into the crushed gel. The pH was typically between 10 and 12. The alkaline gel beads readily dissolved in a 1 M acetic acid solution at pH 2.4, but cross-linked gel beads were insoluble in this solution at 27 °C for at least 24 h. Modeling of Heterogeneous Cross-Linking Kinetics The heterogeneous cross-linking of the spherical chitosan gel beads with glutaraldehyde is carried out in a well-mixed batch isothermal reactor at constant volume. The depletion of glutaraldehyde in the crosslinking bath is balanced by the formation of cross-linked chitosan as the glutaraldehyde monomer diffuses into the chitosan gel and reacts between available amine groups on adjacent chitosan chains to form the crosslink assembly. Relevant to this process are two stoichiometric parameters, R and β:

R)

CA0VC initial moles of GA ) initial moles of -NH2 mbxBYB

(4)

moles of GA reacted moles of -NH2 reacted

(5)

β)

The fraction of cross-linked amine groups X h is related to β and the extent of glutaraldehyde consumption XT by

X h ) XT/β

(6)

The diffusion-controlled model assumes that (1) the cross-linked chitosan is found in an outer shell of the gel bead bounded by r ) R to r ) rC, where r is the radial position within the bead, R is the outer radius of the bead, and rC is the moving boundary between the crosslinked zone and the uncross-linked zone; (2) the thickness of cross-linked layer R - rC increases with time; (3) the flux of glutaraldehyde into the gel bead is limited by molecular diffusion of the glutaraldehyde monomer through the cross-linked shell; (4) the glutaraldehyde flux approximates the dilute solution diffusion process; (5) the glutaraldehyde flux at a given value for rC is at a nominal steady state, even though the glutaraldehyde concentration in the cross-linking bath decreases with time; and (6) the glutaraldehyde monomer completely and rapidly reacts so that its concentration is zero at rC. Under these six assumptions, the modified shrinking core model (Rao and Gupta, 1982) can be applied to the heterogeneous cross-linking process. Major steps in the mathematical development are overviewed below. According to the shrinking core model approach, X h given by eq 6 is represented as

X h ) 1 - [rC/R]3

(7)

Rearrangement and differentiation of eqs 1 and 7 with respect to time yields

dCA dX h mbxBYBβ )dt dt VC

(8)

drC 3 dX h ) - 3rC2 dt dt R

(9)

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The glutaraldehyde flux into the gel beads is balanced by the rate of depletion of glutaraldehyde in the crosslinking bath

VC

dCA dC′A 2 3mb ) -4πNA,RR2n ) DAe r 3 dt dr RF

(10)

b

where CA′ is the glutaraldehyde concentration within the gel bead, DAe is the effective diffusion coefficient of glutaraldehyde through the cross-linked layer of the gel bead, and NA is the molecular diffusion flux of glutaraldehyde with continuity condition NA,rR2 ) NA,rr2. The number of beads in the cross-linking bath (n) is estimated as 3mb/4πR3Fb, where Fb is the density of the gel bead. If external mass-transfer resistances are negligible and the rate of cross-linking is limited by the molecular diffusion of glutaraldehyde through the crosslinked layer to reaction boundary rC, then it can be shown that the combination of eqs 8-10 followed by integration of CA′ over r from r ) R (CA′ ) CA) to r ) rC (CA′ ) 0) yields

rC2

drC )dt

DAeCA 1 1 xBFbYBβ rC R

[

]

(11)

Figure 2. Extent of glutaraldehyde consumption (XT) and pH vs time at CA0 equal to 75 mM for the heterogeneous cross-linking of the 7% N-C9 acylated chitosan gel beads. The solid line represents the calculated profile by the diffusion-limited modified shrinking core model as described in the text.

Figure 3. Extent of glutaraldehyde consumption (XT) and pH vs time at CA0 equal to 250 mM for the heterogeneous cross-linking of the 7% N-C9 acylated chitosan gel beads. The solid line represents the calculated profile by the modified shrinking core model.

Separation of variables rC and t followed by integration gives

[] []

1-3

rC R

2

+2

rC R

6DAe

3

) xBFbYB

t CA dt ∫ βR 2 0

(12)

In terms of X h , eq 12 becomes

h) ) F(X h ) ) 1 - 3(1 - X h )2/3 + 2(1 - X 6DAe

∫0 CA dt t

xBFbYBβR2

(13)

which is a modified shrinking core model for the heterogeneous cross-linking of the chitosan gel beads in a well-mixed batch reactor. Alternatively, combination of eqs 1, 6,7, and 11 yields a differential equation explicitly in terms of rC

drC )dt

[

[ ( ) ]]

rC βmbxBYB 1VC R 1 2 1 xBFbYBβ - r rC R C

DAe CA0 -

[

]

3

(14)

If DAe and all other constant parameters are known, then the kinetics of the cross-linking process can be obtained by numerical integration of eq 14 to obtain rC vs time. With rC vs time known, predicted values for X h , XT, and CA vs time can then be backed out in order by eqs 7, 6, and 1, respectively. Results and Discussion Heterogeneous Cross-Linking of Chitosan Gel Beads. Representative kinetic data for the heterogeneous cross-linking of 3 mm 7% N-C9 acylated chitosan gel beads at initial concentrations of 75 and 250 mM glutaraldehyde in the cross-linking bath are shown in Figures 2 and 3 respectively. In both experiments, the concentration of glutaraldehyde in the cross-linking bath went to zero within 48 h, and the pH in the bath leveled off between 7 and 8. Final values for XT after

Figure 4. Effect of mixing speed on the XT vs time profile at CA0 equal to 250 mM.

48 h were 0.399 ( 0.025 (1s) and 1.26 ( 0.097 (1s) mol of GA/mol of -NH2 at CA0 equal to 75 and 250 mM, respectively. Increasing the orbital shaker speed from 120 to 240 rpm had no effect on the cross-linking kinetics, as shown in Figure 4. Therefore, the heterogeneous cross-linking process was not subject to external mass-transfer resistances. The effects of the initial glutaraldehyde concentration on the final extent of glutaraldehyde cross-linking for the chitosan gel beads and 7% N-C9 acylated chitosan gel beads are shown in parts a and b of Figure 5, respectively. The initial glutaraldehyde concentration values in terms of R as defined by eq 4 are shown in Table 1. The extent of cross-linking was estimated as XT by eq 1 using the measured glutaraldehyde concentration in the cross-linking bath and as XR by eq 2 using gravimetric data from air-dried gel beads before and after cross-linking. In all experiments, maximum values for both XT and XR were obtained within 48 h of cross-linking. If one glutaraldehyde molecule crosslinks with two amine groups as schematically illustrated in Figure 6, then an R value equal to 0.5 mol of GA/mol of -NH2 is required for stoichiometric conversion. At low extents of cross-linking below this R value, XT and XR were comparable. However, at higher R values, both XT and XR continued to increase. Furthermore, XT was now higher than XR. The reason for this last result is not clear. However, when the gel beads were dried prior to measurement of XR, any glutaraldehyde not chemically bonded to amine groups may have volatilized along with the water.

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Figure 5. Effect of initial glutaraldehyde concentration (CA0) on the final extent of glutaraldehyde consumption, measured as both XT and XR: (a) 7% N-C9 acylated chitosan gel beads; (b) chitosan gel beads. Error bars are not shown, as the standard for all points shown was within 10% of the average value from duplicate samples.

Figure 6. Proposed cross-link assemblies for monomeric and oligomeric forms of glutaraldehyde, based on the literature citations given in the text. Table 1. Initial pH and GA/-NH2 Ratio in the Cross-Linking Bath for Data Shown in Figure 5 initial GA/-NH2 ratio, R ) CA0VC/mbxBYB

CA0 (mM) initial pH 12.5 25.0 75.0 250.0 500.0

4.16 4.07 3.68 3.40 3.25

chitosan beads (xB ) 0.068)

7% N-C9 acylated chitosan beads (xB ) 0.0453)

0.044 0.088 0.265 0.885 1.77

0.072 0.143 0.430 1.434 2.87

The above results suggest that not all of the glutaraldehyde consumed by the gel bead was directly crosslinked to -NH2 groups on chitosan. One possibility is that the glutaraldehyde polymerized into short-chain oligomers before cross-linking. Another possibility is that unreacted glutaraldehyde was trapped within the gel bead. To determine if any unreacted glutaraldehyde was freely absorbed within the gel, cross-linked gel beads were mixed with distilled water at 27 °C and 120 rpm within an orbital shaker. After 48 h, less than 0.1% of the glutaraldehyde originally taken up by the gel bead was found in the distilled water, suggesting that the glutaraldehyde was irreversibly retained within the cross-linked bead.

Homogeneous Cross-Linking of a Chitosan Solution. In the homogeneous cross-linking experiment, 6.4 g of a 5.0 wt % chitosan solution was vigorously stirred into 9.6 g of a 250 mM glutaraldehyde solution for 10 s, and then mixed on an orbital shaker at 120 rpm and 27 °C. At these conditions, R was equal to 1.2 mol of GA/mol of -NH2. The mixture formed a uniformly textured, rigid gel within 1 min. In the homogeneous cross-linking reaction, the mixture was acidic with about pH 2.7, whereas in the heterogeneous crosslinking reaction, the pH environment was neutral to basic. Despite the difference in pH environments, this experiment showed that the homogeneous cross-linking reaction was very rapid relative to the heterogeneous reaction and further supported the premise that the heterogeneous cross-linking process was subject to mass-transfer resistances associated with the diffusion of glutaraldehyde through the cross-linked layer of the bead. Modeling of the Heterogeneous Cross-Linking Process. Although glutaraldehyde is a common protein cross-linking reagent, the cross-link assembly resulting from the reaction of aldehyde groups on glutaraldehyde with the amine groups on the substrate to be crosslinked is still under debate. Although glutaraldehyde exists only as a monomer in aqueous solution at acidic or near neutral pH (Hardy et al., 1969; Kawahara et al., 1992), glutaraldehyde can polymerize to short-chain oligomers in alkaline environments. Specifically, several investigators (Richards and Knowles, 1968; Peters and Richards, 1977; Margel and Rembaum, 1980; Gorman and Scott, 1980; Kawahara et al., 1992) have verified that glutaraldehyde polymerizes by aldol condensation to form R,β-unsaturated aldehydes. During cross-linking, an available amine group reacts with the terminal unsaturated aldehyde moieties on each side of the glutaraldehyde oligomer to yield a Schiff’s base with a conjugated double bond (-NdC-Cd), as schematically illustrated in Figure 6 (Peters and Richards, 1977; Gorman and Scott, 1980). Although the size of the oligomers appears to be dependent on pH, temperature, and time, two protein cross-linking studies (Korn et al., 1972; Monsan et al., 1975) showed that the dominant stable oligomer consisted of 8 glutaraldehyde residues per cross-link assembly or 4 glutaraldehyde residues per -NH2 group. According to Figure 6, if β is equal to 0.5, then the cross-link assembly consists of one glutaraldehyde residue with a molecular weight of 64; if β is equal to 4, the molecular weight of the crosslink assembly is 640, and MA is equivalent to 80. In this present study, the cross-linking bath is slightly acidic to neutral with a final pH between 7 and 8. Consequently, glutaraldehyde assumes a monomeric form in the cross-linking bath. However, the chitosan gel bead is alkaline with an nominal pH of 10-12 before cross-linking, because a high stoichiometric excess of 2 M NaOH is used in the casting bath to precipitate the chitosan during the gel bead casting process. Consequently, the alkaline environment inside the gel bead could promote the polymerization of glutaraldehyde to higher oligomers. Previous work strongly suggests that the oligomer has a putative chain length of 8 glutaraldehyde residues, or a β value of 4. Therefore, the proposed physical model for the heterogeneous crosslinking process of glutaraldehyde with the chitosan gel bead consists of three steps: (1) molecular diffusion of the glutaraldehyde monomer through the cross-linked shell of the gel bead to the moving reaction boundary rC; (2) rapid polymerization of the glutaraldehyde monomer to glutaraldehyde oligomers; (3) rapid reaction

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Figure 7. F(X h ) vs ∫CA dt plot for the estimation of the effective diffusion coefficient DAe for glutaraldehyde in the 7% N-C9 acylated chitosan gel beads. The solid line represents the leastsquares linear fit to eq 13. Input parameters: CA0 ) 250 mM, R ) 0.16 cm, xB ) 0.055, YB ) 5.77 mmol of -NH2/g of chitosan, β ) 4 mol of GA reacted/mol of -NH2 reacted, Fb ) 1.06 g/cm3. From the least-squares slope, DAe ) 4.7 × 10-8 ( 9.3 × 10-10 cm2/s (r2 ) 0.990).

Figure 8. Comparison of representative cadmium ion (Cd2+) adsorption isotherms for both gel and freeze-dried 7% N-C9 acylated chitosan beads prepared at an extent of cross-linking equivalent to 0.4 mol of GA/mol of -NH2.

Table 2. Effect of β on DAe for the Data Shown in Figure 7 effective diffusion coefficient β

DAe ( 1s (r2), cm2/s

DAe/DA°

0.5 1.0 2.0 4.0

( 5.5 × (0.918) 6.3 × 3.4 × 10-7 ( 1.4 × 10-8 (0.950) 9.9 × 10-8 ( 1.6 × 10-9 (0.993) 4.7 × 10-8 ( 9.3 × 10-10 (0.990)

0.070 0.038 0.011 0.0052

10-7

10-8

of the terminal, conjugated -CHO groups on glutaraldehyde oligomer with available -NH2 sites to form the imine (-NdC-) cross-link. The process is mathematically modeled according to the modified shrinking core model described earlier. Using the modified shrinking core model in the form of eq 13, the effective diffusion coefficient of monomeric glutaraldehyde through the cross-linked shell of the 3 mm 7% N-C9 acylated gel bead was estimated. A plot of F(X h ) vs ∫CA dt at β equal to 4 and CA0 equal to 250 mM yielded a straight line with a regression coefficient of 0.990, demonstrating that the modified shrinking core model was appropriate for data analysis (Figure 7). From the least-squares slope, DAe was estimated to be 4.7 × 10-8 ( 9.3 × 10-10 (1s) cm2/s. Since the value of β could not be determined absolutely, DAe was reestimated for different values of β (Table 2). As β increased, DAe decreased. The regression coefficient for the data fit was optimal at β equal to 2 and 4. The molecular diffusion coefficient of monomeric glutaraldehyde in water at infinite dilution (DA°) is 9.0 × 10-6 cm2/s at 27 °C by the Wilke-Chang correlation. All DAe values were 1-2 orders of magnitude lower than the molecular diffusion coefficient, showing that the cross-linked layer provides a significant barrier to diffusion. If the assumption that glutaraldehyde polymerization only occurs at the reaction boundary is not valid, then DAe could represent a composite diffusivity of glutaraldehyde monomers, dimers, trimers, and higher oligomers in the gel bead during the cross-linking process. In comparing Figures 2 and 3, the time required for cross-linking to achieve completion cross-linking decreased as CA0 decreased. This observation was also predicted by the diffusion-limited modified shrinking core model. The calculated XT vs time curves using DAe equal to 4.7 × 10-8 cm2/s at β equal to 4 were consistent with the measured curves, except at very short crosslinking times at the lower initial glutaraldehyde concentration of 75 mM. Although the heterogeneous crosslinking reaction was modeled as diffusion controlled, at very short times or low values of R the process could be reaction rate controlled, leading to cross-linking rates

Figure 9. Effect of cross-linking on the saturation cadmium ion (Cd2+) adsorption capacity for chitosan beads: (a) 7% N-C9 acylated gel and freeze-dried chitosan beads; (b) chitosan gel beads. The solid line is the nonlinear least-squares fit of the gel bead data to eq 16.

that could be higher than those proposed by a diffusionlimited model. Effect of Cross-Linking on Cadmium Ion Adsorption Capacity. Representative cadmium ion adsorption isotherms at pH 6.5 for cross-linked gel chitosan beads and freeze-dried, cross-linked chitosan beads are provided in Figure 8. Both gel beads and freezedried beads possess a stepped isotherm. The physical processes underlying the shape of this two-step isotherm are described by Rorrer et al. (1993) and Hsien and Rorrer (1995). Figure 8 shows that both gel and freezedried beads have comparable maximum cadmium ion adsorption capacities. However, for the gel beads, the location of the second step on the isotherm occurs at a significantly lower cadmium ion concentration than that for the freeze-dried beads, suggesting that the cadmium ions penetrate more readily into the gel bead. Furthermore, although the freeze-dried, cross-linked chitosan beads have high internal surface areas exceeding 150 m2/g (Hsien and Rorrer, 1995), the highly-porous structure of the freeze-dried beads did not improve the saturation cadmium ion adsorption capacity relative to the cross-linked chitosan gel beads. The effect of cross-linking on the saturation cadmium ion adsorption capacity at pH 6.5 for both chitosan beads and 7% N-C9 acylated gel beads is shown in Figure 9. The saturation cadmium ion adsorption capacities were obtained from the last plateau of the two-step isotherm. The cadmium ion adsorption capacities of the gel beads decreased exponentially as the extent of cross-linking increased, leveling off at XT values greater than 1.0 mol of GA/mol of -NH2. The freeze-dried 7% N-C9 acylated chitosan beads showed a similar trend.

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3637

The theoretical maximum loading of cadmium ions in the un-cross-linked chitosan gel bead is estimated by

Qe ) YBMCd/ν

(15)

where MCd is the molecular weight of cadmium (112 mg of Cd/mmol of Cd), and ν is the chelation coordination number for cadmium (2 mol of -NH2/mol of Cd2+). From eq 15, the value of Qe is 347 mg of Cd/g of chitosan. The cadmium ion chelation site for the cross-linked outer shell is an imine group (-NdC-), whereas the chelation site for the un-cross-linked core is an amine group (-NH2). Both N-containing moieties are strong transition-metal ion chelators (Kantipuly et al., 1990). However, even the un-cross-linked gel bead had a saturation adsorption capacity of only 257 mg of Cd/g of chitosan, suggesting that the metal was not uniformly loaded in the bead, a phenomena described by Nestle and Kimmich (1996) for transition-metal ion adsorption into biopolymer gel beads. At higher extents of crosslinking where the cadmium adsorption capacity levels off, the adsorbed cadmium may be localized in the crosslinked layer of the bead. This behavior further suggests the empirical correlation

Qf ) Qf,c + (Qf,o - Qf,c)e-XT/KX

(16)

where Qf,o is the cadmium loading for the un-crosslinked chitosan gel bead, Qf,c is the cadmium loading within the cross-linked zone of the gel bead, and KX is a proportionality constant. The adsorption data for the 7% N-C9 acylated chitosan gel beads given in Figure 9a were fitted to eq 16 with Qf,o equal to 257 mg of Cd/g of chitosan. Best-fit values of Qf,c equal to 100 ( 13.5 (1s) mg of Cd/g of chitosan and KX equal to 0.325 ( 0.094 (1s) mol of GA/mol of -NH2 were obtained by nonlinear regression with a regression coefficient of 0.94. When the homogeneously cross-linked chitosan described earlier was used for cadmium ion adsorption measurements, the saturation cadmium ion adsorption capacity was 75 mg of Cd/g of powdered air-dried material, or 50 mg of Cd/g of chitosan, assuming MA equal to 64 g/mol of GA reacted. This value was comparable to the heterogeneously cross-linked chitosan gel beads. Conclusions Chitosan, a linear biopolymer of glucosamine residues, is a highly selective biosorbent material for heavymetal ions such as cadmium. Chemical cross-linking of amine (-NH2) groups on chitosan gel beads with glutaraldehyde (GA) renders the bead insoluble in acid solution and imparts other desirable material properties, including high internal surface areas upon freezedrying. The overall goals of this study were to experimentally and mathematically describe the kinetics of heterogeneous cross-linking of chitosan gel beads with glutaraldehyde and to determine how the extent of cross-linking affects the saturation cadmium ion adsorption capacity. The kinetics of the heterogeneous cross-linking process for 3 mm chitosan gel beads were measured at initial glutaraldehyde concentrations ranging from 12.5 to 500 mM at 27 °C and pH 7-8. Final extents of crosslinking ranged from 0.07 to 2.40 mol of GA consumed/ mol of amine (-NH2). Glutaraldehyde consumption was considerably higher than the theoretical value of 0.5 mol of GA/mol of -NH2. This information, combined with considerable literature precedence for glutaraldehyde

polymerization at high pH, suggested that glutaraldehyde polymerized to an oligomeric cross-link assembly within the alkaline gel bead. Furthermore, the heterogeneous cross-linking of chitosan gel beads was modeled as a “shrinking core process” where the molecular diffusion of glutaraldehyde through the cross-linked layer of the gel bead limits the overall rate of crosslinking. The diffusion-limited modified shrinking core model adequately described the kinetics of the heterogeneous cross-linking process as a function of gel bead properties, cross-linking reagent properties, and crosslinking bath reaction parameters. The effective diffusion coefficient of glutaraldehyde cross-linking reagent through the cross-linked layer of the gel bead was 4.7 × 10-8 cm2/s, 2 orders of magnitude lower than the molecular diffusion coefficient for glutaraldehyde in water. The saturation adsorption capacity of cadmium ions onto cross-linked chitosan gel beads exponentially decreased from 250 to 100 mg of Cd/g of chitosan as the extent of cross-linking increased from 0 to 1.3 mol of GA/mol of -NH2. At higher extents of cross-linking, the saturation adsorption capacity remained at 100 mg of Cd/g of chitosan. Highly porous 7% N-C9 acylated chitosan beads formed by freeze-drying of cross-linked gel beads had the same saturation cadmium ion adsorption capacity as the cross-linked gel beads over the same extents of cross-linking. Consequently, it the crosslinking process which determines both the material properties and the maximum cadmium ion adsorption capacity of the chitosan beads. However, the rates of cadmium ion uptake may still be different for each bead preparation. This question will be addressed in future work. Notation CA ) glutaraldehyde concentration (GA) in the crosslinking bath, mmol/L (mM) CA0 ) initial glutaraldehyde concentration in the crosslinking bath, mmol/L (mM) CA′ ) unreacted glutaraldehyde concentration within the gel bead, mmol/L (mM) Co ) initial concentration of cadmium ions in the batch adsorption experiment, mg of Cd2+/L Cf ) final concentration of cadmium ions in batch adsorption experiment, mg Cd+2/L DAe ) effective diffusion coefficient of glutaraldehyde through the cross-linked layer of the gel bead, cm2/s DA° ) molecular diffusion coefficient of glutaraldehyde in water at infinite dilution, cm2/s KX ) proportionality constant in eq 16, mol of GA/mol of -NH2 MA ) average molecular weight of a monomeric glutaraldehyde residue within the cross-link assembly, g of crosslink/mol of glutaraldehyde reacted mb ) total mass of the gel beads within the cross-linking bath, g MCd ) molecular weight of cadmium, 112 mg/mmol NA ) flux of the glutaraldehyde monomer through the gel bead, mol/cm2 s Qe ) theoretical maximum loading of adsorbed cadmium on uncross-linked chitosan, mg of Cd2+/g of chitosan Qf ) loading of adsorbed cadmium on the chitosan bead, mg of Cd2+/g of chitosan Qf,o ) loading of adsorbed cadmium on the un-cross-linked chitosan gel bead, mg of Cd2+/g of chitosan Qf,c ) loading of adsorbed cadmium on the cross-linked layer of the chitosan gel bead, mg of Cd2+/g of chitosan r ) radial position within the gel bead, cm R ) outer radius of the gel bead, cm

3638 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 rC ) radial position within the gel bead defining the boundary between the outer cross-linked layer and the inner un-cross-linked core, cm t ) cross-linking time, h V ) volume of cadmium ion solution in the batch adsorption experiment, cm3 VC ) volume of glutaraldehyde solution in the cross-linking bath, cm3 wB ) mass of dried cross-linked beads after cross-linking, g wBO ) mass of chitosan in gel beads before cross-linking, g xB ) weight fraction of chitosan in the gel bead, g of chitosan/g of gel X h ) extent of cross-linking defined by eq 6, mol of -NH2 reacted/mole of -NH2 before reaction XR ) extent of cross-linking defined by eq 4 XT ) extent of cross-linking defined by eq 1, mol of glutaraldehyde consumed by the gel bead/total mol of -NH2 groups within the gel bead YB ) amine group content of chitosan, mol of -NH2/g of chitosan before cross-linking R ) initial molar ratio of glutaraldehyde to amine groups in the cross-linking bath, mol of GA/mol of -NH2 β ) mol of GA consumed to form a cross-link assembly/ mol of -NH2 cross-linked Fb ) density of the gel bead, g/cm3 ν ) chelation coordination number for cadmium, 2 mol of -NH2/mol of Cd2+

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Received for review February 17, 1997 Revised manuscript received June 9, 1997 Accepted June 11, 1997X IE9701579

X Abstract published in Advance ACS Abstracts, August 1, 1997.