Environmental Engineering Reference
In-Depth Information
configuration of minimum energy. Thus, the work required for cleavage or surface stretching
is the same when the adsorption is not taken into account, namely, γ
lv
=
f
lv
. [5]. Second,
because the liquid fails the elastic deformation resistance, γ
lv0
(
T
) called as surface tension
equals surface stress when surface adsorption is not taken into account, which is defined as
the reversible work per unit area involved in forming a new surface of a substance plastically
[5]. Although early measurement methods of γ
lv0
(
T
) are sufficiently precise, there is still
uncertainty regarding its absolute values and particularly regarding γ′
lv0
(
T
) function mainly
due to the effect of impurities, which strongly changes the measured results. Therefore,
considerable efforts have recently been directed towards the experimental determinations of
γ
lv0
(
T
) and γ′
lv0
(
T
) of metals, and progress has been achieved with the advent of levitation
processing and oscillating drop techniques [168-170]. However, such an experiment often
suffers from the ambiguities in the interpretation of the resulting frequency spectra [168], it is
also unlikely that experimental measurements will ever encompass all possible temperature
ranges of interest and for all metals.
In contrast to the determination of γ
lv0
(
T
m
) value, γ′
lv0
(
T
m
) value is not well known
experimentally even for elemental metallic liquids [171]. A recent analysis of existing data
shows that this quantity is known with accuracy better than 50% for only 19 metals; For 28
metals, the accuracy is worse; For 18 metals (mainly refractory metals) there are no
experimental results [171].
Computer stimulations with Monte Carlo or molecular dynamics methods are considered
to be one of the reliable methods [172], in which γ
lv0
can be calculated either using the
mechanical expression for the surface stress, or from the viewpoint of the surface energy.
Unfortunately, the former approach suffers from rather high fluctuation and statistical
uncertainty, while the latter introduces additional complexity into performance. Thus, the
demand of developing reliable prediction methods has never declined.
Semi-empirical predictions based on the correlation between the surface and bulk
thermodynamic properties are always active [123,173-176]. Stephan firstly links γ
lv0
to the
heat of evaporation
H
v
′ at
T
= 0 K [173],
γ
lv0
(
T
m
) =
c
5
′
H
v
′/
V
2/3
(5.1)
with
c
5
′ being an unknown constant. Since there is no suitable theoretical determination of
c
5
′,
Eq. (5.1) seems to be apparent only for transition metals [171,173]. Although Eq. (5.1) exists
more than hundred years, the attempt to determine
c
5
′ value theoretically is scarce.
On the other hand, γ
lv0
(
T
) of pure substances may be evaluated from values of the critical
temperature
T
c
by the Eötvos or Guggenheim empirical equations [177],
γ
lv0
(
T
)
V
2/3
= A+B
T
;
T
c
= -A/B
(5.2-a)
or
γ
lv0
(
T
)/γ
lv0
(
T
m
) = (1-
T
/
T
c
)
α
(5.2-b)
where the exponent α is system dependent, e.g. 4/5 for strongly hydrogen bonded substances
or 11/9 for H
2
, N
2
and CO, etc [177]. However, α value for liquid metals is not known to our
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