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On the solid-liquid surface tension and the nature of the liquid state
CHEMICAL
PHYSICS
LETTERS
1
(1967)
446.
NORTH-HOLLAND
PUBLISHING
COMPANY,
AMSTERDAM
ON THE SOLID-LIQUID SURFACE TENSION AND THE NATURE OF THE LIQUID STATE M.PRIGGGINE FacuM des Sciences Appliqules. Univevsit& Libre de Bmzelles, Belgiml Received
27 November
The experimental determination of the surface tension between the solid and the liquid phases of the same substance would be of a great interest for an understanding of the nature of the difference between these two states of matter. As well known Cl], we have v =ea-Tsa
,
+=_da
dT -
(1)
For the liquid/vapo L interface the surface tension csdecreases with a temperature and therefore surface entropy sa>O. In this case, the surface tension can be understood as resulting from a decrease of the molecular field when a molecule is transferred from the bosom to the sn&-face of a iiquid with a corresponding increase of an entrqpy. Et has been suggested by many authors (see especially Turnbull 123) that the difference betileen a solid and a liquid is essentiaily related to the difference in the molecular order. As a result, when a molecule of the liquid is transferred near the boundary of a solid phase, there would be an increase in order and s” would be negative. Unfortunately, data on do/dT for the solidliquid interface exist a$ present only for water. They have been obtained by studying the freezing temperature of liquid droplets as a function of their radius [3,4]. The method applied is very crude. Indeed it is based on the theory of nucleation which mixes in a somewhat arbitrary way macroscopic and microscopic concepts. StiR it seems the only at present avaiIable method giving the possibilities of calculation of du/dT for the solid-liquid interface. The data obtained by Jacobi and Carte have
December
1967
1967
been carefully analyzed by Dufour and Defay [S]. They concluded that in the case of water
da
Z’O
do do = 0.102 dyn/cm oK
namely
with u = 20.24 d&cm
(2)
at -350C; saco.
(3)
The object of this note is to draw attention to the fact that these data confirm Turnbull’s view. Indeed not only sac 0 but even u=
Tdo
dT .
(4)
Of course,
the case of water may be rather this reason, we have eIaborated the program of adaptation of Jacobi’s method to the study of do/dT for the liquified rare gases such as Kr and Xe. The results will be reported in due time. peculiar.
For
We thank Prof. Defay and Prof. Thomaes for their kind interest and help. This investigation has been supported by the F.R.F.C. (Fonds de la Recherche Fondamentale Collective).
References [l] R. Defay.
1. Prigogine, A. Bellemans ett, Surface Tension and Adsorption
Green, 1966).
and D. H. Ever(Longmans
[Z] D. Turnbull.. Liquids, in: General Motors Research Laboratories Symposium, 1963, ed. ‘I’. J. Hughel (Elsevier. New York, 1965) p. 6. [3] W.Jacobi. 2. Naturforsch. 1Oa (1958) 322. [4] A. E. Carte, Proc. Phys. Sot. (London) B 69 (1956) 1028. [5] L. Dufour and R. Defay, Thermodynamics of Clouds (Academic Press, New York- London, 1963) p. 226.
PHYSICS
LETTERS
1
(1967)
446.
NORTH-HOLLAND
PUBLISHING
COMPANY,
AMSTERDAM
ON THE SOLID-LIQUID SURFACE TENSION AND THE NATURE OF THE LIQUID STATE M.PRIGGGINE FacuM des Sciences Appliqules. Univevsit& Libre de Bmzelles, Belgiml Received
27 November
The experimental determination of the surface tension between the solid and the liquid phases of the same substance would be of a great interest for an understanding of the nature of the difference between these two states of matter. As well known Cl], we have v =ea-Tsa
,
+=_da
dT -
(1)
For the liquid/vapo L interface the surface tension csdecreases with a temperature and therefore surface entropy sa>O. In this case, the surface tension can be understood as resulting from a decrease of the molecular field when a molecule is transferred from the bosom to the sn&-face of a iiquid with a corresponding increase of an entrqpy. Et has been suggested by many authors (see especially Turnbull 123) that the difference betileen a solid and a liquid is essentiaily related to the difference in the molecular order. As a result, when a molecule of the liquid is transferred near the boundary of a solid phase, there would be an increase in order and s” would be negative. Unfortunately, data on do/dT for the solidliquid interface exist a$ present only for water. They have been obtained by studying the freezing temperature of liquid droplets as a function of their radius [3,4]. The method applied is very crude. Indeed it is based on the theory of nucleation which mixes in a somewhat arbitrary way macroscopic and microscopic concepts. StiR it seems the only at present avaiIable method giving the possibilities of calculation of du/dT for the solid-liquid interface. The data obtained by Jacobi and Carte have
December
1967
1967
been carefully analyzed by Dufour and Defay [S]. They concluded that in the case of water
da
Z’O
do do = 0.102 dyn/cm oK
namely
with u = 20.24 d&cm
(2)
at -350C; saco.
(3)
The object of this note is to draw attention to the fact that these data confirm Turnbull’s view. Indeed not only sac 0 but even u=
Tdo
dT .
(4)
Of course,
the case of water may be rather this reason, we have eIaborated the program of adaptation of Jacobi’s method to the study of do/dT for the liquified rare gases such as Kr and Xe. The results will be reported in due time. peculiar.
For
We thank Prof. Defay and Prof. Thomaes for their kind interest and help. This investigation has been supported by the F.R.F.C. (Fonds de la Recherche Fondamentale Collective).
References [l] R. Defay.
1. Prigogine, A. Bellemans ett, Surface Tension and Adsorption
Green, 1966).
and D. H. Ever(Longmans
[Z] D. Turnbull.. Liquids, in: General Motors Research Laboratories Symposium, 1963, ed. ‘I’. J. Hughel (Elsevier. New York, 1965) p. 6. [3] W.Jacobi. 2. Naturforsch. 1Oa (1958) 322. [4] A. E. Carte, Proc. Phys. Sot. (London) B 69 (1956) 1028. [5] L. Dufour and R. Defay, Thermodynamics of Clouds (Academic Press, New York- London, 1963) p. 226.