Abstract- In order to understand the physics behind the extreme behavior of materials in nano-scale, one of the most important factors is to know the activity of nano-scale materials in different environments. This information comes directly from the surface cohesion binding energy of materials. We first review a simple thermodynamic-based theory for size dependence feature of surface binding energy of metallic nano-particles. Then a hypothesis for activity of metallic nano-particles through the modified classical physico chemical formalism of activity in a reactive medium will be presented. Qualitative computations for Al, Ag, Ga and W metallic nano-particles in a reactive solution shows that by decreasing the size of particles less than 100 nm, the reaction equilibrium constant and consequently the activity of particles increases.

THE STATE OF ART

In nano-application areas the charge, activity and stability of surface of nano-materials are the most important characteristics, for which there is still no exact formulation in literature, and our knowledge is yet based on experimental observations. The term activity in classical thermodynamic represents the active portion of concentration. Experimental observations show that respect to micro- or macro-scale, the activity of nano-materials increases [1]-[2] and this tendency increases by decreasing the size. In addition, some metallic nano-particles such as Ag show antibacterial effect [2], but others shows toxic feature [3]. These unpredicted features of nano-particles can be interrelated to their instable surface structures and extreme activity.

MODEL OF SURFACE INSTABILITY ENERGY

Cohesion energy represents how strongly atoms or molecules stick together to hold the structure [4] and at nano-scale by decreasing the size of particle, the bulk and surface cohesion energy decrease [5]. Binding energy of atoms at surface determines the ability of surface for reaction, thus, the decrease of surface cohesion energy represents the surface instability

1 Plasma Physics and Engineering Group, Laser and Plasma Research Institute, Shahid Beheshti University, Tehran, Iran.

2 Materials and Energy Research Center, Tehran, Iran. 3 Institute for Studies in Theoretical Physics and Mathematics, School of

Physics, Tehran, Iran. * Contacting Author: Maziar S Yaghmaee is with Plasma Physics and

Engineering Group, Shahid Beheshti University, Tehran, Iran. (phone: 0098-21-22431773; fax: 0098-21-22431775; email: fkmsahba@uni-miskolc.hu and yaghmaee@sbu.ac.ir).

feature or in other words the reaction tendency. Figure. 1 shows the mono-layer surface model and different energy terms considered in our hypothesis. Regarding the authors’ previous theory [5], a new formulation for inner and surface instability of metallic nano-particles will be presented respectively by Eq. (1) and Eq. (2), as:

,1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

pv

acohb

cohp Df

dGG (1)

where cohpG is cohesion energy in kJ with subscript bp,

respectively standing for particle and bulk value, ad is diameter of atom in neutral state in nm, pD is diameter of the particle in nm, vf is the volume packing factor, and

,)81210(6

7322

2

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−+−=

xDxxDfDd

DfdGG

pps

pa

pv

acohb

cohs (2)

where here s stands for surface value, sf is the surface packing factor, and x is the actual atomic thickness of mono surface layer in nm as illustrated in Fig. 1.

EFFECT OF SIZE ON ACTIVITY OF NANO-PARTICLES

In nano-scales by reducing the size of particles, the reaction rate and the reaction efficiently increase [6]. Here we reformulate the classical kinetics of reaction considering the size dependency of activity of metallic nano-particles in a reactive medium. Regarding Eqs. (1-2), previous results [5] and Fig. 1, in nano-scales by neglecting the entropy change, it is believed that the Gibbs free energy change is due to enthalpy (cohesion) differences [4]. This difference can be written as:

,0)(:,* ≤−≈∆−∆=− p

cohNPB

cohB

NPBf

macroBf DFGGHHH (3)

where macroBf

NPBf HH ∆∆ , are respectively the enthalpy formation

of B type particle in nano- and macro-scale in kJ/mol, *H is the enthalpy difference value between the nano- and macro-scale and )( pDF represents the size dependency function.

The reaction of a metallic nano-particle with atoms/molecules of a medium leads the formation of either a surface layer or

Thermodynamic Based Theory for Extreme Activity of Metallic Nano-Particles

Maziar S Yaghmaee1-2,*, Babak Shokri1,3 and Mohammad R Rahimipour2

Oral

TNT2007 03-07 September, 2007 San Sebastian-Spain

Poster

release of ions/atoms from particle. Thus, the extended classical physics of reactions, considering the increase of equilibrium constant due to surface instability and higher activity of particle in nano-scale respect to macro-scale, can be formulated as:

,expexp*

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅=⇒⎟⎠⎞

⎜⎝⎛

⋅∆−

=TR

HbKKTRGKas NPr (4)

where NPKK , are the reaction constant for macro- and nano-scale respectively; Gr∆ is the change of Gibbs free energy change of reaction in kJ/mol, R is the universal gas constant, T is the temperature in absolute scale, and b is stoichiometric number related to nano-particle of B type in our reaction.

Using the results of Eq. (3), we rewrite the Eq. (4), as:

.1)(expexp*

≥⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅

≈⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

=TR

GGbTR

HbK

K cohcohNP

NP

(4)

Figure. 2 shows computation simulation for Al, Ag, Ga and W

metallic nano-particles for 1=b . One can see that for example at 50 nm Al, Ag, Ga and W metallic nano-particles respectively the

rate of increase of K (represented by NPKK / ) is 1.280, 1.279, 1.424 and 1.295 respect to macro-scale. It should be noticed that this value increases by decreasing the nano-particle size due to activity increase, which conforms experiential observations.

REFERENCES [1] G. M. Whitesides, “The ‘right’ size in nanobiotechnology,” Nature Biotechnology, No. 10, Vol. 21, pp. 1161-1165, Oct. 2003 [2] S. Y. Yeo and S. H. Jeong, “Preparation and characterization of polypropylene/silver nanocomposite fibers,” Polymer International, 52, pp. 1053-1057, 2003 [3] P. HM Hoet, I. Brüske-Hohlfeld and O. V. Salata, “Nanoparticles – known and unknown health risks,” J. Nanobiotechnology, 2:12, pp. 1-15, 2004 [4] G. Kaptay, G. Csicsovszki and M. S. Yaghmaee, “An absolute scale for the cohesion energy of pure metals,” Mater.Sci. Forum, Vols. 414-415, pp. 235-240, 2003 [5] M. S. Yaghmaee and B. Shokri, “Effect of size on bulk and surface cohesion energy of metallic nano-particles,” Smart Mater. Struct. 16, pp. 349-354, 2007 [6] A. Zaluska, L. Zaluski and J. O. Ström-Olsen, “Structure, catalysis and atomic reactions on the nano-scale: a systematic approach to metal hydrides for hydrogen storage,” Applied Physics, A 72, pp. 157-165, 2001

Fig. 1 Schematic representation of bulk and surface of metallic nano-particles considering different binding energies.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100Dp [nm]

K/K

NP [1

/b m

ole

of B

]

for Al nanoparticlefor Ag nanoparticlefor Ga nanoparticlefor W nanoparticle

towards micro/meso/macro scale the relative activity coefficient tends to unity

by decreasing the size, particle becomes relatively more active

Fig. 2 Relative representations of size dependency effect on activity of Al, Ag, Ga and W nano-particles in a reactive medium.

Oral

TNT2007 03-07 September, 2007 San Sebastian-Spain

Poster