CADMIUM BIOSORPTION RATE IN PROTONATED
SARGASSUM BIOMASS icon
Abbreviated version of a contribution shortly to be published in
ENVIRONMENTAL SCIENCE & TECHNOLOGY (1998)
Jinbai Yang and Bohumil Volesky1
Department of Chemical Engineering , McGill University,
3610 University Street, Montreal, Quebec, Canada H3A 2B2

Abstract 
        Dynamic biosorption rate of the heavy metal ion Cd2+ onto protonated non-living brown alga Sargassum fluitans biomass was determined at constant pH 4.0. An one dimensional intraparticle diffusion model, combined with Langmuir sorption isotherm assumption, was developed to describe the overall biosorption rate of cadmium ions in flat seaweed biomass particles. The model equations were solved numerically yielding the effective diffusion coefficient De about 3.5x10-6 cm2/sec, which is of the same order of magnitude as the molecular diffusion coefficient for cadmium ions in aqueous solution. 

Introduction 
        Biosorption of the non-living brown alga Sargassum fluitans has been found particularly effective in binding metal ions of cadmium. High sorption capacity (exceeding 100 mg/g), easy regeneration and low costs make this biomass of special interest for the purification of high volumes of low-concentration wastewater (1, 2, 3). For any practical applications, the sorption process rate and the dynamic behavior of the system are very important factors. While several mechanisms have been proposed to describe the rate of the biosorption process (4, 5, 6), the resulting diffusion coefficients often did not yield reasonable values. In our earlier work (7), an intraparticle diffusion model was proposed for the acidic desorption process for the Sargassum fluitans biomass. The effective diffusion coefficient of Cd2+ ions was determined in the range of 0.23 - 0.55 of the molecular diffusion coefficient. The present work investigated the sorption behavior of protonated Sargassum biomass at an optimum sorption pH 4.0 directly. A one-dimensional plate diffusion model could enable the prediction of the dynamic behavior of the metal ion binding process. 

Material and Methods 
        Dry Sargassum fluitans particles of the same thickness (0.1 mm) were cross-linked and protonated with formaldehyde and HCl according to Leusch et al. (1). Unless specified otherwise, the biomass particle size used was (1.0 - 1.4 ) mm. 
        An end-point titration process was used to measure the biosorption rate. A certain amount of biomass and Cd(NO3)2 solution were stirred while the pH of the solution was maintained (NaOH addition recorded) by a computer-driven autotitrator assembly in the end-point mode. The solution was sampled at pre-defined time intervals and analyzed for metal concentration (AAS). 
        The metal binding was determined by the simple mass balance q=(C0 - Cb) V / W

Experimental Results 
        Sorption rate.  As external mass transfer resistance was eliminated by proper agitation (3 Hz ), the biosorption rate of the Cd cation onto the (1.0-1.4 mm) biomass particles could be established from Figure 1. 

Figure 1: Dynamics of the cadmium metal uptake and proton release in time at pH4.0.

        The first stage of sorption featured a high rate, about 75% of the total cadmium adsorption took place in 15 min. The second stage was slower, taking approximately 3 hours to reach the sorption equilibrium. The rate of the proton released reflected the cadmium ion uptake rate well throughout the process. The proton release was calculated from the consumption of the NaOH added to the sorption system for maintaining the constant pH 4.0. Similar results were obtained for other sizes of biomass particles. 

        The effect of biosorbent particle size on the Cd sorption rate. The time profiles of the dimensionless Cd concentration for different sizes of Sargassum biosorbent particles were similar (Figure 2). 

Figure 2: The equilibrium Cd concentration in solution for different particle sizes.

        The solid curve is the model prediction (described later) and the scattered points are from the experiments. The concentration profiles for three different particle sizes of (0.5 - 0.7) mm, (0.84-1.00) mm and (1.0-1.4) mm agreed with each other within the deviation of about 5%. This indicates that the overall sorption rate of Cd by the biomass is actually practically independent of the biosorbent particle size used. 

        The effect of cross-linking on the Cd sorption rate. The sorption rate for the cross-linked biomass was significantly lower than that for native biomass (Figure 3). 

Figure 3: Cd concentration time profiles for cross-linked and not cross-linked biomass.

Mathematical Model 
        For quantitative description of the biosorption process dynamics, the similar assumptions as in our earlier work on cadmium desorption(7)are made here as follows: 

  1. The particle-to-liquid mass transfer resistance has been eliminated through adequate turbulence created by proper agitation. and the overall sorption rate is controlled by the diffusion of the Cd cation inside the biomass material.
  2. The intraparticle diffusion inside the biomass is one dimensional, i.e. in the thickwise direction. Because the thickness of the relatively flat seaweed Sargassum biomass particle is much smaller than the length and width, the biomass particle can be considered as a thin plate.
  3. The amount of metal ions adsorbed inside the biomass particle is in equilibrium with the metal concentration in the liquid phase and the Langmuir sorption isotherm relationship holds:
                                     (1)
        Based on the model assumptions, the mass conservation equations for metal ions in the biomass particle and bulk solution are as follows: 
                         (2)
                          (3)
        Please see the Glossary at the end of text for symbols. De represents the effective intraparticle diffusion coefficient. 
        The boundary and initial conditions for the sorption process are as follows: 
                        (4)
                      (5)
                                 (6)
                       (7)
        Equations (2) and (3) are he simultaneous non-linear partial differential equations (PDEs) with respect to Cr and Cb, respectively. The Galerkin Finite Element Method (GFEM) (8) and the Euler backward integration in time was applied to obtain the numerical solution. 
        The intraparticle diffusion coefficient De could be regressed from the comparison of the simulated profile curves and the experimental results by minimizing the following objective function: 
                (8)
where i is the ith experimental data point and N is the total number of experimental data points. 
        Equilibrium biosorption experiments were conducted at pH 4.0 for regression of the Langmuir parameters in the model equations. The regressed parameters are K = 0.035 mmol/L and qm = 0.994 mmol/g, respectively. The model-simulated concentration profile curve for protonated biomass and cross-linked biomass were plotted as a solid line in Figure 2 and Figure 3, respectively. The diffusion coefficient De values regressed from the corresponding experimental data are 3.5x10-6 cm2/sec and 1.0x10-6 cm2/sec, respectively. The fact that the simulation curve and the experimental data points are in a good agreement (within 10% average deviation) demonstrates that the model can describe the experimental data with an acceptable accuracy. 

Discussion 
        The metal uptake and the proton release rate.  Biosorption of Cd took place very fast during the initial stage of contact (Figure 1). The agreement between the cadmium metal uptake and the proton release during the sorption process indicates an equivalent ion exchange between Cd2+ and H+. With a fast pH probe response and titration speed, the computer-recorded titration volume of the NaOH vs. contact time correlation could be used to regress the effective diffusion coefficient directly. This method provides a useful alternative to the fast evaluation of the sorption rate, avoiding the physical difficulty of sampling the reaction solution at the early stage of the sorption process and the tedious procedure for metal concentration analysis. 
        As indicated in Figure 1, the sorption rate could be divided into two stages, the fast initial rate followed by a much slower sorption rate. This has often been reported by other researchers. Brassard et al. (9) attributed the fast initial metal sorption rate to the surface binding by natural particles and the following slower sorption to the interior penetration. In the case of Sargassum seaweed particles, the active binding groups reside in the cell wall and due to its large surface the initial sorption rate is accelerated. The actual mechanism of Cd sequestration has been studied only to a limited extent (10) and should be studied further. 

        Effect of particle size on the sorption rate. The experimental results indicated that the particle size does not affect the sorption rate. While this seems to be contradictory to the general idea of intraparticle diffusion controlling the process, it is necessary to point out that the grinding of biomass and particle size grading by standard sieves only work on the length and width dimensions. All sizes of the Sargassum biomass chip-like particles are actually of the same thickness which determines the diffusion distance. This is reflected in the present model which assumed a one-dimensional thin plate as the intraparticle diffusion field. A special care was taken in producing the biomass particles. The structure of the seaweed biomass is not homogeneous and different parts of the seaweed offer different resistance to grinding. Thus different sizes of the sieved biomass may differ in composition resulting in a dependence of the sorption rate on the particle size. 

        Evaluation of the diffusion coefficient. In general, the diffusion process inside a porous material is slower than that in a corresponding homogeneous system having the same liquid composition as in the pore phase (11, 12). In the brown alga Sargassum biomass, alginate is the main component responsible for the metal sorption (13). It is present in a gel form in the cell wall which appears very porous and easily permeable to small ionic species (14, 15). The actual mobility of the diffusing entity in the dense-phase gel may be somewhat reduced by mechanical friction or interaction with the cell wall molecules. As a result, the calculated intraparticle diffusion coefficient is an effective diffusion coefficient, i.e. De, and it is usually smaller than the molecular diffusion coefficient Dm considered in the absence of the sorbent material matrix. For Cd2+, Dm was assessed as 7.19x10-6 cm2/sec (16, 17) and the De /Dm calculated with the presently regressed value was 0.486 which is in a good agreement with the one determined for the desorption process (7). A smaller De /Dm ratio of 0.14, calculated from the results in Figure 3 for cross-linked biomass, correctly reflects the retarding effect of cross-linking of the sorbent framework on the sorption rate. 
        In summary, the end-point titration method is suitable for the determination of sorption rate at a constant pH value. The rate of Cd2+ biosorption on Sargassum fluitans biomass could be described properly by a simple one-dimensional intraparticle diffusion model. The diffusion coefficient of Cd2+ ion in the biomass regressed from the model at pH 4.0 was about 3.5 x 10 -6 cm2/sec, this being of the same order of magnitude as the corresponding molecular diffusion coefficient. 

Glossary 
C0 , Cb     initial and instant Cd concentration in bulk solution (mg/L) 
Cr    Cd concentration in bulk solution at position r and time t (mg/L) 
De    effective intraparticle diffusion coefficient (cm2/sec) 
Dm   molecular diffusion coefficient (cm2/sec) 
i     is the ith experimental data 
K    Langmuir equilibrium constant (mg/L) 
N    is the total number of experimental data points. 
qm   Langmuir maximum uptake (mg/g) 
q    uptake (mg/g) 
r    arbitrary position coordinate (cm) 
R    half thickness of the biomass particle (cm) 
St    total surface area of biomass particles (cm2
t     time (sec) 
V    solution volume (L) 
W   biomass weight (g) 
r    density of biomass g/(1000 cm3
j    objective function for curve fitting. 

Literature Cited 
(1) Leusch, A.; Holan, Z.R.; Volesky, B. J. Chem. Tech. Biotechnol.  
          1995, 62, 279-288. 
(2) Aldor, I.; Fourest, E.; Volesky, B. Can. J. Chem. Eng. 1995, 73, 516-522. 
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(4) Jang, L.K.; Brand, W.; Resong, M.; Mainieri, W.; Geesey, G.G. 
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(7) Yang, J.; Volesky, B. J. Chem. Technol. Biotechnol. 1996, 66, 355-364. 
(8) Lapidus, L.; Pinder, G.E. Numerical Solution of Partial Differential 
          Equations in Science and Engineering, Wiley: New York, 1982, pp 
(9) Brassard, P.; Macedo, E.; Fish, S. E.T.S. 1996, 30, 3216-3222. 
(10) Crist, R.H.; Oberholser, K.; Schwartz, D.; Marzoff, J.; Ryder, D.; Crist, D.R. 
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(11) Helfferich, F. Ion Exchange, McGraw-Hill: NY, 1962, pp 299-319. 
(12) Westrin, B.; Axelsson, A. Biotechnol. Bioeng. 1991, 38, 439-446. 
(13) Fourest, E.; Volesky, B. Appl Biochem Biotechnol 1997, 67, 33-44. 
(14) Percival, E.; McDowell, R.H. Chemistry and Enzymology of Marine Algal 
          Polysaccharides, Academic Press: London, U.K., 1967, pp 99-126. 
(15) Dodge, J.D. The Fine Structure of Algal Cells, Academic Press: 
            London, U.K., 1973, pp 14-45. 
(16) Horvath, A.L. Handbook of Aqueous Electrolyte Solutions
            Ellis Horwood: West Sussex, UK, 1985, pp 289. 
(17) Dobos, D. A Handbook for Electrochemists in Industry and Universities
            Elsevier Scientific: Amsterdam, The Netherlands, 1994, pp 88. 

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  By Jinbai Yang (E-mail: cyya@musica.mcgill.ca