салон красоты Ларисы Румянцевой

Size Influence on Cohesion Energy of Nano-Materials

M.S.Yaghmaee a, B.Shokri b,*
Plasma Group, Laser-Plasma Research Institute, SBU, Teh. Iran
a fkmsahba@gold.uni-miskolc.hu, b b-shokri@cc.sbu.ac.ir, * correspondent author
Abstract. For theoretical and experimental analysis of nano-materials via plasma or any other production methods, and in
order to optimize the production technologies, we need to understand the fundamental properties of such small scale nanomaterials
and know how they differ from the expected properties of bulk materials. Among them the cohesion energy of
materials as fundamental materials property describes the most behaviors of mater in different environment [1-2]. When the
size decreases the surface to volume ratio of atoms/molecules increases which leads to domination effect of surface energy
on the most behaviors and cohesion structure change. Consequently through this, especially the surface cohesion energy all
other properties may change by size in small scale materials which mostly observe experimentally under 100 nm. This work
discusses this fundamental property through a nano-thermodynamical approach via two algorithms: one as a simple size
dependency of inner cohesion energy, and the second which considers also the surface cohesion energy too. Results will be
presented through a computational demonstration compared with experimental values.
Keywords: nano-materials, cohesion energy, nano-thermodynamics, plasma technology, surface property, thermodynamical
PACS: 61.30.Hn, 61.43.Bn, 61.46.Df, 61.46.Hk, 61.82.Rx, 64.10.+h, 67.40.Kh, 51.90.+r, 52.77.-j,
As the cohesion energy describes the inner structural energy of materials which shows how strongly particles
holds together the materials in bulk and surface which traditionally has been written through sublimation energy and
only in absolute value without considering the negative thermodynamic sign of it. Although for bulk materials we
already know that the sublimation energy is not a proper estimation and as there is no direct experimental or theoretical
method to obtain the exact value of it, we mostly make relative scaling but we are able to estimate this energy quite well
at least for bulk macroscopic materials “for a thermodynamical discussion of subject check the previous works [1,2]”. In
following briefly we present two approaches for describing the cohesion energy of nano-materials by introduction of size
into algorithms; the first method as a pure inside energy phenomena and the second method which considers the surface
cohesion energy too.
First Approach: bulk cohesion energy
One of the first, simple and well stabilized hypothesis yet in literature which recently published as short paper
in 2002 was the work of W.H.Qi, et al, [3] about the size dependency of cohesion energy. The main consequence of this
paper from our view point is Eq(1), showing how the size-effect appears in bulk cohesion energy in nano-scale world.
Such algorithm stands on the following assumptions:

The fundamental hypothesis behind Eq(1) are;
i. when a spherical particle is separated into its atoms/molecules by applying the cohesion energy, if the volume remains
constant, then we may wite: 3 / 3a p n = d D ;
ii. by defining the surface area change during applying the given energy for separation of a particle into n atoms which
apparently equals to surface energy of solid materials multiplying by the total surface area, then we may

For spherical free standing particles of Al, Ga, W and Ag metals, one can see in Fig.2. “to be checked in
poster” the surface cohesion energy not only change the slope of change of inside cohesion as function of size, but also
it explains interesting phenomena. It seems that there is a critical size for each material under which the surface cohesion
energy overlaps the bulk values respectively for Al, Ga, W and Ag under 8, 3, 6 and 8 nm. A simple explanation would
be that at least for sphere shape by decreasing the size under critical size there is a limit under which the surface atoms
are in attraction filed force of all others and this would mean increase of stability of atoms at surface more than the rate
of their decrease and a kind of surface reconstruction. Anyhow the general tendency of decreases of cohesion energy at
surface means for example the pre-melting phenomena which will be explain better in next reports, but under such
critical size the surface becomes more stable then a kind of reconstruction or rearrangement could occur leads to
stabilizing the surface more than bulk which is quite un-common in first look, but this could be the fundamental reason
of strange behavior of nano-materials under some sizes like increase of their melting points under certain size. Fig.3. “to
be checked in poster” shows the cohesion energy of W metal which compared with experimental values with a good
agreement. The bulk macroscopical value of cohesion energy of W was set to be -822.57 [kJ/mol] from [4] for sake of
comparison but one is referred to check the new scale of materials in [1-2].
Regarding the fact that cohesion energy control almost all physico-chemical properties of nano-materials, then
these results not only could explain the already found strange behaviors but also open a new window to search for
interesting new scale of properties of nano-materials. The results could be summarized as: i. introduction of bulk (inside)
cohesion energy of nano-materials, ii. development of a thermodynamical model for surface cohesion energy of nanomaterials,
iii. series of computational analysis for comparing the materials like: Al, Ga, W and Ag metals, iv. discussion
the critical size and its relation to surface cohesion energy domination, v. comparison the experimental values of W
metal with computational simulation. For further researches the following categorical steps are under construction: i.
introduction the shape effect in nano-materials properties specially in cohesion energy, ii. cohesion energy of liquid
phases in nano-scale materials, iii. inter-relation between the cohesion energy and other properties of nano-materials.
Such results help to understand the nature of nano-materials and give a tool to analyze the phenomena behind their
behaviors under different condition which also help to design better functionalized nano-materials and optimize the
production conditions.
“to be checked in poster”
“to be checked in poster”

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