Simulation on the Orthophosphates Adsorption on Titanium Dioxide Surface by Monte Carlo Method

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Simulation on the Orthophosphates Adsorption on Titanium Dioxide Surface by Monte Carlo Method

Moon-Sun Kim and Jaygwan G. Chung^†

Department of Chemical Engineering, Sungkyunkwan University, Suwon 440-746, Republic of Korea (Received 30 June 1999; accepted 9 September 1999)

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Abstract−Computer simulations of the orthophosphates adsorption on titanium dioxide surface were carried out by Monte Carlo method. On computer simulations, considered variables were adsorbed plane properties, atoms distribution of titanium dioxide(adsorbent) and charges, lengths between atoms, and angles of orthophosphates(adsorbate). The result showed that in terms of adsorbability, rutile type of titanium dioxide was superior to anatase type and the adsorbability of Miller index (110)plane was especially better than any other plane in rutile type of titanium dioxide. Therefore, it is reasonable to select the titanium dioxide of which surface range of Miller index (110)plane is large in order to improve the adsorbability of titanium dioxide. Electrostatic interaction energy is the main force which affects the adsorbability of orthophosphates on titanium dioxide. It is necessary for the enhancement of electrostatic interaction energy to control the adsorption conditions, that is, pH, agi- tating speed, temperature, concentration, and so on in aqueous solutions.

Key words: Simulation, Adsorption, Orthophosphates, Titanium Dioxide, Monte Carlo Method

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†E-mail: jgchung@yurim.skku.ac.kr

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Fig. 1. Crystal structure of anatase type(a) and rutile type(b) of tita- nium dioxide.

Table 1. Comparison of structure of two kinds of titanium dioxide Structure Length(Å) Angle(deg.) Volume

(Å³)

Density (g/cm³)

a b c α β γ

Rutile type 4.492 4.492 2.283 90 90 90 058.382 4.54840 Anatase type 3.776 3.776 9.486 90 90 90 135.253 3.92381

Fig. 2. Structure of potassium phosphate.

Table 2. Charges and lengths of potassium phosphate structure (a) Charges

Atom Unit Value Remarks

H

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+0.25 O-H

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K +0.8 -

(b) Lengths

Structure Unit Value Remarks

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Å

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Table 3. Angles for main chain of potassium phosphate structure

Item Unit Value Remarks

O-P-O

deg.

113.6 H-O-P-O-H

O-P=O 110.0 -

H-O-P 102.8 -

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A : any quality to calculate in system Table 4. Difference of total energy as adsorption of orthophosphates on titanium dioxide crystal planes

Item(kcal/mol) Anatase (001)plane Rutile (110)plane Rutile (101)plane Rutile (100)plane

Initial time Final time Initial time Final time Initial time Final time Initial time Final time

Bond stretch energy 6,105 5,984 2,980 3,037 2,795 2,805 2,256 2,245

Angle bending energy 0 0 0 0 0 0 0 0

Torsion energy 0 0 0 0 0 0 0 0

Inversion energy 0 0 0 0 0 0 0 0

Van der Waals energy 1,652 1,538 2,464 2,492 2,250 2,259 2,375 2,310

Electrostatic interaction energy −179,140 −178,684 −104,977 −105,237 −41,280 −41,314 −65,229 −69,660

Difference of total energy(∆E) 221 −175 −15 5

Fig. 3. Model of adsorption of orthophosphates on titanium dioxide in simulation.

Fig. 4. Change of potential energy by adsorption of orthophosphates on various crystal plane; (a): anatase(001), (b): rutile(110), (c):

rutile(101), and (d): rutile(100).

Fig. 5. Comparison of change curve of potential energy as adsorption process for crystal plane titanium dioxide[þþ: anatase(001), ùù: rutile(110), : rutile(101), and üü: rutile(100)].

Table 5. Comparison of change of total potential energy by adsorption of orthophosphates on titanium dioxide crystal planes

Item Anatase type Rutile type

(001)plane (110)plane (101)plane (100)plane

∆E(kcal/mol) 221 −175 −15 5

Designed plane Total number of atoms : 1026 Ti : O = 342 : 684(1 : 2)

(5)

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<A> : ensemble average of A

C_n : coefficient chosen to satisfy appropriate boundary conditions including that the function has a minimum of the natural bond angle θ₀[-]

D_IJ : energy parameter [kcal/mol]

E : potential energy [kcal/mol]

E_el : electrostatic interacion energy [kcal/mol]

E_R : bond stretch energy [kcal/mol]

E_vdW : van der Waals energy [kcal/mol]

E_θ : angle bending energy [kcal/mol]

E_ϕ : torsion energy [kcal/mol]

E_ω : inversion energy [kcal/mol]

H(x) : Hamilton function

k : Boltzmann constant [erg/molÁK]

K_IJ : harmonic oscillator parameter [J/molÁç]

K_IJK : parameter [J/molÁdeg.]

K_IJKL: parameter decided by rotational barrier, the periodicity of the potential, and the equilibrium angle [J/molÁdeg.]

N : simulation iteration [-]

P() : probability density function [-]

Q_I, Q_J:partial charge in electron units [coulomb]

R_IJ : distance [ç]

r_IJ : harmonic oscillator parameter [ç]

T : absolute temperature [K]

x_IJ : length parameter [ç]

Z : partition function

ÒÊ ^¶

ε : 1 (dielectric constant)

θ_IJKL : angle of two bonds IJ and KL connected via a common bond JK [deg.]

χ : randomly selected one point in phase space

Ω : canonical ensemble state

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and Rogers, Jr., J. W.: J. Am. Chem. Soc., 115(25), 12096(1993).

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12. Moore, W. J.: “Basic Physical Chemistry,” Prentice-Hall Inc., Engle- wood Cliffs, New Jersey(1983).

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16. Wu, M. C. and Moller, P. J.: Chem. Phys. Letters, 171(1), 136(1990).

17. Fuga, S.: “New Technology of Functional Filler,” Research Center of International Industrial Information, Tokyo(1993).

Simulation on the Orthophosphates Adsorption on Titanium Dioxide Surface by Monte Carlo Method

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Simulation on the Orthophosphates Adsorption on Titanium Dioxide Surface by Monte Carlo Method

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