분자 모델링을 이용한 생물흡착 공정의 해석

박재연, 전충, 유영제*

서울대학교 응용화학부

Molecular Analysis of Biosorption between Alginic Acid and Metals

Jae Yeon Park, Choong Jeon, and Young Je Yoo*

School of Chemical Engineering, Seoul National University

Molecular modeling of the reaction between alginic acid and metal was performed to understand the mechanism of biosorption. Molecular analysis was used to understand factors, mainly geometrical factors, affecting the biosorption process and to predict equilibrium constants and selectivity constants. COSMO (Conductor-like Screening Model) model was introduced to include the solvent effect. The structures were stabilized and equilibrium constants estimated by molecular analysis were similar with those obtained by experiment. Selectivity order was the order of uptake capacity when the same initial concentration of metals existed in the same system. Selectivity was similar to the reaction governed by kinetic control and could be predicted by the comparison of activation energy between competing reactions. Activation energy was obtained by the energy difference between transition state and reactants or products. Selectivity order predicted from the activation energy was Cd>Zn>Mg which was consistent with experimental order.

Introduction

Theoretically, biosorption and ion exchange of metals have been studied extensively, regarding their selectivity. Analyses by mathematical model were studied by many researchers, but their approaches were black box models[1,2,3]. Most studies about selectivity of metal were about the qualitative understanding and relationship between a functional group and metal, as well as metal affinity change of the calixarene in the viewpoint of the affect of changing their functional group, structure and class[4,5]. The main reasons for this uncertainty were our ignorance of the atom itself and complexity effect of factors on selectivity (i.e. the kind of functional groups, size of adsorption site, heavy metal hydraulic radius, coordination number of metal, and electro-negativity of metal etc)[4].

Many mechanisms were included in the biosorption of metals, and it was too complicated to analyze biosorption reaction using an arithmetic equation. Also, limited sources for stability constant and selectivity constant of specific reaction were available, especially in biosorption.	Biosorption reaction was analyzed by molecular modeling because it contained several selectivity factors and interaction between molecule and metal.

Alginic acid was used as a model material. Alginic acid is polysaccharide which is the component of the cellular wall and plays a key role in biosorption of marine algae[6]. It had high uptake capacities, and many researchers have studied its structure and characteristics. Because its structure was known, it could be built and used in the computer simulation.

Materials and Methods

The molecule was constructed using graphical tools in MOPAC and 1SCF (Self Consistent Field) calculation. Then, geometry optimization was executed to obtain heat of formation. When optimization failed due to the incorrect Z-matrix or 3 atom linearization during the calculation, the other initial geometry was placed in the calculation.

After obtaining optimized geometry, force and thermodynamic calculation were performed to calculate enthalpy and entropy. The force calculation could indicate whether the geometry was in a stationary or transient state.     Then, Gibbs free energy of reaction and equilibrium constant were obtained using the equation of (1). The same calculations were repeated in considering the solvent effect to obtain the geometry in water.

□G = □H - T□S = -RT ln K (at const. T and P)	(1)

,where □G : Gibbs free energy change,  □H : enthalpy change, □S : entropy change, T : absolute temperature, R : gas constant, and K : equilibrium constant.

Reaction coordinate was the path on which one reactant approached the other reactant. During the approach, the energy was calculated to see the potential energy surface. First, geometry similar to the transition state was obtained, and then optimization to the real transition state was performed. At the transition state, the energy was lower to the two point: one was reactant and the other was product. The calculation started from transition state to reactant and product to until it reached a stationary energy surface which meant there was enough space not to interact between products.

Results and Discussion

Prediction of equilibrium constants

Fig. 1 modeling of alginic acid;

gluronic acid and metal complex.

For the calculation of geometry optimization, the monomer of alginic acid was modelled using an MOPAC drawer. The model of alginic acid was referred to a schematic diagram obtaining from x-ray crystallography[7]. A rough initial sketch was rendered by 1SCF calculation. Vibrational analysis was made to verify whether the calculation result was in the equilibrium state or not.

When there was no solvent effects in molecular modeling, a very large discrepancy occurred between the modeling calculation and the experimental value. The entropy and enthalpy value of metal was that of gas phase because alginic acid and the complexes of metal and alginic acid were calculated in the gas state.

The reason for the large discrepancy was that the solvent effect was not introduced, and the data of metal ions in the gas phase were used. Metal ion in the gas phase needed much energy when it existed in ionic state. Thus, the enthalpy of the formation of metal ion in the gas phase was so large that it caused big discrepancy in calculations. Another important reason for the error was the solvent effect. As mentioned before, the biosorption process occurred in the liquid phase. Therefore, enthalpy of formation and entropy in the gas phase had to include enthalpy and entropy of solvation. Solvent model was applied to this biosorption process.

The result of molecular modeling with the solvent model of COSMO is shown in Table 1. When the solvent model was calculated, the bond lengths between metal ion and oxygen of carboxylic acid were extended, and the overall geometry was stabilized which appeared by lowered energy of geometry. The bond length before and after the COSMO model is shown in Table 2. As shown in Table 1, the discrepancy of equilibrium constant between the calculated value and experimental value decreased within order of magnitude, and the sequence of adsorption capacity was the same as the experimental order.

Prediction of selectivity

Table 1 The results of thermodynamic calculation in MOPAC for the reaction between alginic acid and heavy metals when COSMO model was considered. The alginic acid was modelled as monomeric form

	Heat of formation (kcal/mol)	Entropy (cal/K·mol)	Gibbs free energy (kJ/mol)	Equilibrium constant of reaction (lnK) modeling	Equilibrium constant of reaction (lnK) experiment
alginic acid	-336.5	101.0	-1539.6
complex of alginic acid and Cd2+	-708.6	140.0	-3151.5	-2.1	-4.3
complex of alginic acid and Mg2+	-794.6	135.6	-3507.0	-10.8	-7.7
complex of alginic acid and Zn2+	-722.5	138.7	-3207.9	-7.4	-5.2

The transition state of reaction was obtained by TS calculation which was proved by force calculation in which only one negative frequency existed. The structure of the transition state was generally an ionic state and was affected very much by the near solvent molecules. Calculations, including solvent effects, were performed so that the parameters used were the same as those used in the calculation of equilibrium constant. The calculation was performed using a reaction path calculation which varied bond length between oxygen of carboxylic acid in alginic acid and metal. After each metal was changed from the location of transition state geometry, the complex was stabilized and ran to the geometry of product or reactant. Fig 2 shows the result. The activation energies when Cd approached the Zn was 42.32 kcal/mol, and the Mg was 48.84 kcal/mol. Other results are; The activation energies when Zn approached the Cd was 64.02 kcal/mol, and the Mg was 81.14 kcal/mol. The activation energies when Mg approached the Zn was 85.90 kcal/mol, and the Cd was 69.76 kcal/mol. Metals, which followed the reaction path and had large activation energy, had low selectivity order and vice versa. The experimental selectivity order was Cd > Zn >> Mg. Direct comparison between these energies could predict the easiest way which reaction proceeded, but the exact value of activation energy for each reaction was not known so that direct comparison was impossible. This activation energy could first give selection parameter of what kinds of metals were the main metal that must be considered first in mixed metal system. After the first selection was done, analysis on the selected metal system could be done more precisely. Though the activation energy could not be compared directly with the experimental value, the selectivity of metals itself could be interpreted as the order of activation energy.

References

[1] Crist, R. H., J. R. Martin,  P. W. Guptill, and J. M. Eslinger, Interaction of Metals and Protons with Algae. 2. Ion Exchange in Adsorption and Metal Displacement by Protons, Environ. Sci. Technol., 24, 337-342, 1990.

[2] Tsezos, M., S. H. Noh, and M, H. I. Baird,  A Batch Reactor Mass Transfer Kinitic Model for Immobilized Biomass Biosorption, Biotechnol, Bioeng. 32, 545-553, 1988.

[3] Tsezos, M. and A. A. Deutschmann, An  Investigation of Engineering Parameters for the Use of Immobilized Biomass Particles in Biosorption, J. Chem. Tech. Biotechnol. 48, 29-39, 1990.

[4] Jun, H. B., Separation and behavior of Co, Ni, Cu and Zn using Crown Ether, Thesis of Ph. D., Chungnam Univ., 1989.

[5] Sung, H. M., An NMR study on  Complexation of o-Xylyl-17-Crown-5 and Bis-o-Xylyl-17-Crown-5 whth Alkali Metal Ions, Thesis of Ph. D., Seoul Nat. Univ., 1993.

[6] Fourest, E. and B. Volesky, Contribution of Sulfonate Groups and Alginate to Heavy Metal Biosorption by the Dry Biomass of Sargassum Fluitans, Environ. Sci. Technol., 30, 277-282, 1996.

[7] Yalpani, M., Polysaccharide : Syntheses, Modifications and Structure / Property Realtionships, Elsevier, New York, USA, 8-49, 1988.

Table 2 Bond length between metal and oxygen of the carboxylic acid, heat of formation for complex between metal and alginic acid, and atomic charge of metal before and after the solvent effect was considered

	Magnesium	Cadmium	Zinc
bond length (Å) before considering solvent model	2.104	2.288	2.160
bond length (Å) after considering solvent model	2.153	2.859	2.509
atomic charge of metal before considering solvent model	0.844	1.410	0.625
atomic charge of metal after considering solvent model	1.336	1.689	1.434
Heat of formation (kcal/mol) before considering solvent model	-678	-558	-543
Heat of formation (kcal/mol) after considering solvent model	-795	-708	-722

Fig. 2 Reaction coordinate when Cd and Zn complex was formed. Ea was activation energy. The name of metal before the activation energy was approaching metal.