Simulation of the Growth Process of a Silicium Nanotubes Structure as Biomaterial in the Porozity of Zeolite AFI

Ana Ioanid University of Bucharest, Romania

ana_ioanid@yahoo.com

Radu Mircea Ciuceanu University Politehnica of Bucharest, Romania

raduciuceanu@yahoo.com

Abstract Hydroxyapatite (HA,Ca10(PO4)6(OH)2), that the principal mineral component of the bone

tissue, has remarkable precursor of growth properties in the porous structure sort with strongly interconnected pores. The interconnection of the pores is an essential condition assuring high quality of bone implants. We suggest the experimentation of a silicon nanotubes structure (SiNT) as support to enhance the growth of a high quality HA. We propose a model obtaining a silicon nanotubes structure, by silicon atoms adsorption, from vapour phase, in the pores of AlPO4 (AFI) zeolite. A collection of 3D interconnected nanotubes of the deposited silicium can be obtained after matrix removal.

Keywords: biomaterials, zeolite, interconnected pores, adsorption, nanotube structure. 1. Introduction

Biomedical used materials must correspond to the goal requests. Thus, a different and very complex variety of the performance criterion is need.Their selection for specific applications (prothesis, grafts) is made as function on chemical, morphological, biological needs for a suitable structure-properties-biological effects relation.

Knowledge of the mechanism of this relation demands an integrate interdisciplinary study of the chemical and physical properties, of the biological effects and of the clinical evolution.

Synthetic biomaterials are preferred those natural because can be obtained into large variety, in inspected conditions, having predicable, reproducible, uniform properties and also with safe immunity. Anticipating the genetic therapy with the new materials as genetic support, the simulation of process to obtain this materials, is more than need.

Biomaterials used as support for repair and growth of the bone tissue, must be precursors of growth follow up by osseoconversion, osseointegration and osseoconduction.

Hydroxyapatite (HA, Ca10(PO4)6(OH)2) is the principal mineral component of the bone tissue. HA has remarkable above properties in the porous structure sort with strongly interconnected pores. The interconnection of the pores is an essential condition assuring high quality of bone implants. An unidimensional pores structure or 2D interconnected pores only, restricts the support for bone tissue growth and the implant is inefficient [1, 2].

We suggest the experimentation of a silicon nanotubes structure (SiNT) as support to enhance the growth of a high quality HA. We propose a model obtaining a silicon nanotubes structure, strongly 3D interconnected, by silicium atoms adsorption, from vapour phase, in the

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DOI 10.1109/CANS.2008.34

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2008 First International Conference on Complexity and Intelligence of the Artificial and Natural Complex Systems. Medical Applications of the Complex Systems. Biomedical Computing

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DOI 10.1109/CANS.2008.34

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2008 First International Conference on Complexity and Intelligence of the Artificial and Natural Complex Systems. Medical Applications of the Complex Systems. Biomedical Computing

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pores of various zeolites: AlPO4 (AFI), silicalite, siliceous form of faujasite and others porous glass-ceramics [3]. A collection of 3D interconnected nanotubes of the deposited silicon can be obtained after matrix removal (using acid leaching for exemple).The paper presents a simulation of silicon adsorption in the porozity of AFI zeolite single crystals.

1. Arguments for using a SiNT 3D interconnected pores structure as biomaterial support

The sanguine fluid (or simulated body fluid) facilitates the formation of the Si-OH groups on the surface of nanotubes walls, stabilizing the structure by terminating certain dangling bonds with OH- ion. The hydrophilic group OH- may belong to the water molecule or to others functional groups as PO(OH)2 [4]. It is known that the pore surfaces of the nanoporous silicas as MCM-41 and SBA-15, are hydrophilic due to silanol groups attaching onto the pore wall when the mesoporous silica is synthesized; the hydrophobicity of the pore wall can be modified by the functional groups that can be used ranges from non-polar to polar or ionic group [5].

The Si-OH groups have a catalytic rôle in the HA nucleation process, following by a rapid process of HA growth in the presence of the Ca2+ and PO4

3- ions from the sanguine fluid [6]; HA grows directly in the 3D interconnected pores structure, with performances in the

repair process of bone. The SiNT structure as support, assures a great mechanical durability for HA extending the

applications area to the great stress zones of the body. It is known that smallest carbon nanotubes are possible in the channels of porous zeolite

AlPO4-5 (AFI) single crystals [7]. The carbon nanotubular structure shows efficient sp2 hybridization and π bonding, thus

allowing a high stability of the carbon nanotube structure. In contrast, silicon prefers sp3

hybridization and favors the tetrahedral diamond-like structures, thereby forming the commonly observed nanowires. Nevertheless, when the dangling bonds are properly terminated, SiNT can in principle be formed. The resulting energy minimized SiNT, however, adopts a severely puckered structure, with a corrugated surface, with Si---Si distances ranging from 1.85 to 2.25 Å.

On this structure a great number of silan Si-OH groups is possible, by fixing of the dangling bonds with OH- ions from the sanguin fluid.

3. The silicon adsorbate-zeolite adsorbante potential energy

The AFI zeolite has an orthorhombic with centered basis unit cell containing a molecule AlPO4: Al3+ ions are placed at the corners of the unit cell and the PO4

3+ tetrahedral groups on middle points of basis, Fig.1.In an (0,2,0) plan the P5+ ions and the projections of the 1,2,3,4 O2- ions, form a deformed hexagon. An anodization treatment along of the perpendicular to plan, may be produce a hexagonal channel. AFI is a type of transparent microporous crystal containing onedimensional channels packed in hexagonal arrays, with an inner diameter of 0.73±0.01 nm.The starting material for deposition can be an silicon vapour beam along this direction. The interaction adsorbate-adsorbante, e.g., silicon atom with Al,P,O atoms participating to AFI structure, may be described by a potential function that restricts the adsorbtion atomic energy to two body terms only.

3.1. Hypotesis

1. It is take into account only the silicon interaction with Al, P, O atoms from the unit cell, e.g., from a molecule AlPO4;

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2. Adsorbate-adsorbante interaction is two-body only, thus the total interaction energy is sum of all distinct pair interactions;

3. Adsorbate-energetically heterogeneous adsorbante interaction is one-to-one type: at first preferable to strongest energy sites then progressively occurring before interaction with weaker energy sites [8]. After primary adsorbate-adsorbante interaction, in each of these cases, one has to take into account the lateral adsorbate-adsorbate interaction that tend to increase as the number of adsorbed silicon atoms increases;

4. The chemical interaction between adsorbate and all the adsorbante atoms is neglected for any coverage.

43

21

Al3+

P5+O2-,.

.

.

.

. .O

.O.O.O.O

.O .O.O.O

Figure.1 Orthorombic unit cell of AlPO4 zeolite

Thus, the interaction energy of a silicon atom adsorbed at position i on the zeolite adsorbante surface with the zeolite framework species, may be written:

[ ]∑ −−−= −

jiiijijijijiji ERC)Rbexp(Au 266

21 α (1)

where j =Al, P, O species from a molecule AlPO4 . The first term is the Born- Mayer energy for the short-range repulsive interaction due to finite compressibility of electron clouds of the partners of ij pair. The repulsive parameters ijA and ijb for the ij pair are obtained mixing rules of like-atoms pairs [9] ijRijb

ijij eAu −= where 50.jiij )AA(A = and )bb(b jiij +=

21 .

One consider iA and ib constants, for maxijmin RRR ≤≤ , where 051 a.Rmin ≈ , 053 a.Rmax ≈ , 25900 .a = Ǻ. The second term is the dipolar interaction from the multipolar

expansion serie form of the long-range attractive dispersion interaction energy. The Van der Waals coefficients 6

ijC for ij pair are given by the Casimir-Polder form [10].

∫∞−=0

16 3 ωωαωαπ d)()(C jiij (2)

where )(),( ji ωαωα is the dynamic polarizabilitiy of imaginary argument for i,j atom, respectively. They can be evaluated with the approximate formula (3):

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[ ] 21666 50 /jijijjiiij )E)(E()EE(CC.C −+≈ ΔΔΔΔ (3)

where ji E,E ΔΔ are the energy separations of the principal transitions of i and j atoms. The multipole interactions are neglected, because the implicated atoms have not multipole moment. The last term is the attactive polarization energy of the adsorbate atom in the electrical field of the all others existing or induced dipoles.This term is neglected because brings an insignificant contribution.The equilibrium conditions as energy and position of the minimum are showns in Figure 2. The silicium adsorbate-zeolite adsorbante evaluated energy interaction is shown in Figure 3, comparatively with the silicon atom-silicon atom energy interaction (in 529021127 0 .a,eV.Eh == Ǻ units).

0.8 1.0 1.2 1.4 1.6 1.8

-30

-25

-20

-15

-10

-5

0

543

2

1

54

3

2

1

Si at-Al ionSi at-Si ion

Si at-P ion

Si-at-O ion

Si at-Si at

u 0[Eh]

R0[a0]

Figure.2 Equilibrium energy and position for Si-zeolite Interactions

-4 -2 0 2 4

-20

0

20

40

Si-atom - zeolite

Si-atom - Si-atom

u[Eh]

R[a0]

Figure.3 Energy of Siatom -zeolite and Siatom -Siatom interactions

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4. Model of nanotube growth We show a model for growth into a full channel realized through a step-by-step mechanism

on the surface of the pore walls, starting with the atom sites from the (0,2,0) plane in unit cell. With above hypothesis and taking into account the evaluated energies in Fig.2, it is possible a step-by-step growth mechanism sketchily shown in Fig.4. The steps are 1 → Siatom-O2-, 1’ → Siatom-Siatom, 2 → Siatom-P5+

, 2’ → Siatom-Siatom, 3 → Siatom-Al3+, 3’ → Siatom-Siatom, 4 → Siatom-Siatom pair interactions.

The average number of adsorbed silicon atoms depends on vapour beam pressure and temperature conditions. The sanguine fluid presence facilities the termination of certain dangling bonds with hydrogen and with oxydril group, stabilizing the structure and keeps the the inside of channel open for fluid.

1

Siatom

Al3+P5+O2+

Ο

atom beamsilicium.

4Ο

4Ο

4Ο

4Ο

3'Ο

3'Ο

3'Ο

3'Ο

3Ο

3Ο

3Ο

3Ο4Ο

4Ο3'Ο

3'Ο2'Ο2'Ο1'Ο

1'Ο 1Ο1Ο

2'Ο

2'Ο4Ο

4Ο

3'Ο

3'Ο2Ο

2Ο

4Ο4Ο

3'Ο3'Ο

2'Ο2'Ο1'Ο1'Ο

1ΟΟ

.

..

.

Figure.4 Growth model of silicon nanotube in zeolite

5. Conclusions

We propose a model obtaining a silicon nanotubes structure, strongly 3D interconnected, by silicon atoms adsorption, from vapour phase, in the pores of AlPO4 zeolite. Any supplementary stability conditions of this structure and the hydrophobicity of silanol group also, must be seeked in the chemical bonding and physical interactions theories. It remains a challenge to produce silicon nanochannels experimentally.

6. References [1] Hulbert S.F., Young F.A., “Potential ceramics materials as permanently implantable skeletal prosthesis”, J.Biomed. Mater. Res., 4, 433, 1970. [2] Klawitter J.J., Bawell J.G., “An evolution of bone ingrowth into porous high density polyethylene”, J.Biomed. Mater. Res., 10, 311, 1976. [3] Hideo Hosono, Yasuhiro Sakai and Yoshihiro Abe, J.of Non-Cryst. Solids, 139, 1992, pp. 90-92. [4] Fekkar-Nemmiche N., Devautour-Vinot S., Coasne B., Henn F., Mehdi A., Reye C., Corriu R., and Collet A., Eur.Phys. J. Special Topics 141, 2007, pp.45-48. [5] Naoki Aoyama, Tsukasa Yoshihara, Shin-ichi Furukawa, Tomoshige Nitta, Hideaki Takahashi, Masayoshi Nakano, Fluid Phase Equilibria 257, 2007, pp.212-216.

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[6] Tanahashi M., Matsuda T., “Surface functional groups dependence assembled monolayers in a simulated body fluid”, J.Biomed. Mater. Res., 34, 1997, pp.305-315. [7] Wang N., Tang Z.K., Li G.D., J.S.Li, “Single-walled 4 Å nanotube arrays”, Nature, 408, 2000, pp.50-51. [8] Philip L. Llewellyn, Guillaume Maurin, Thomas Poyet, Nathalie Dufau, Renaud Denoyel and Fran oise Rouquerol, Adsorption 11, 2005, pp.73-78. [9] Adolf A. Abrahamson, Phys.Rev., 178(1), 1968, pp.76-79. [10] A. Derevianko, J.F. Babb, and A. Dalgarno, Phys. Rev. A, 63, 052704-1—052704-4, 2001.

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