Environmental Engineering Reference
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sample is small compared to this length parameter, then the object is two-dimensional.
Similar definitions can be given for one-dimensional and zero-dimensional.
Although an increasing body of excellent computational materials science, the computer
simulations remain many uncertainties in nanosize range. Thus, the classic thermodynamics
still remain importance to model the above phenomena since the history of science
demonstrate a belief in the universal nature of thermodynamics.
The laws of thermodynamics were formulated as phenomenological laws about
observable and operationally defined quantities. One of the main points of classical
thermodynamics is that the thermodynamic approach is applicable to macroscopic systems
only, i.e. to systems containing great number of molecules, atoms, ions, or to black holes and
the entire Universe [6]. From this point of view, a single small object, including a nanosized
droplet and a nanocrystal, does not satisfy the definition of the macroscopic thermodynamic
system. At the same time, an ensemble of many small objects will be a macroscopic system.
Such an ensemble may be rather speculative or correspond to a real dispersed system
(aerosol, micro-emulsion, composed material etc). However, if the system is monodispersed
(a contemporary example is an ensemble of the same, in a well-defined approximation,
working elements in micro- or nanoelectronics), the treatment may be reduced to the
investigation of a single modeling ensemble element. Introducing adequately defined
distribution functions, the polydispersed systems may be also replaced (at least in a first
approximation) by a modeling monodispersed one. Thus, extension of thermodynamic
methods to very small objects, including nanoparticles seems possible but faces many
principal difficulties.
It is also noteworthy that, in the context of some modern experimental techniques such as
the atomic force microscopy, the thermodynamic method is equally promising as a theoretical
and empirical description of the experimentally investigated nanosystems. Indeed in many
cases, experimental data on nanoparticle properties are rather scanty and contradictory. Thus
if the particle is not entirely rigid, the experimental arrangement can have an effect on the
object under investigation. It was demonstrated by Monte Carlo computer experiments [7]
that the tip of the atomic force microscopy could have a noticeable effect on a nanodroplet in
the space between the tip and the solid substrate. Hence difficulties of principle inevitably
occur not only at the thermodynamic treatment but also at the experimental study of very
small objects. However, no comprehensive overview of that field exists. This contribution
aims to fill that gap, which is essentially based on the author′s own recent works. It gives a
review of modern approaches how the traditional thermodynamics treats these interface
amounts. Particular emphasis is placed on the size dependence of these quantities at the
nanometer size range.
Solid-Liquid Interface Energy
The Bulk Solid-Liquid Interface Energy γ sl0
The solid-liquid interface free energy γ sl0 , which is defined as the reversible work
required to form or to extend a unit area of interface between a crystal and its coexisting
fluid plastically [8-13], is one of the fundamental materials properties. Many practically
important processes and phenomena like crystal growth, homogeneous nucleation, surface
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