First-Order Phase Transitions in to Dimensional Systems (Adsorbed Layers)
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Date
1987-06
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Addis Ababa University
Abstract
Intercst III tllin films arIses both from a theoretical
point of view and from the wide range of applications they
can offer. All the advantages and applications of thi.n
fil ms a 1'e too many to men tion, But some of them are, their
use, as compact technological devices, corrosion protections,
optical instrulIlcnts and sensors of scientific research.
The aim of the present paper consists in the theoretical
investiga tion of firstĀ·~order phase transitions in physi ..
sOTbed monolayers. Hereby, mainly thermodynamic methods are
applied. Therefore, first a thermodynamic theory of homogeneous
aJld heterogeneous monolayers is developed. In parti ..
cular, general ('quations for the curvature dependence of the
J ine tension are obtained. It is shown tha t cm'va ture
dependence of 1. ine tension is of importance only for very
small 2-d clusters. A general thermodynamic analysis of
first-6rder phase transitiollS, starting from metastable
in:itial states, is given. It is shown that in real situations,
wilen depl etion effec ts are ta ken into accoun t, the trans i tion
proceeds via three main stages: a stage of nucleation and
possible simultolleous growth, n stage of independent growth
of the clusters, their number being nearly constant and a
third stage of cOlllpeti tive grO\'lth of Ostwald ripening. The
'j'esults are analogous to phase transitions in 3-d systems, as
was discussed by Schmelzer [19, 20], Ulbrich eLal [1]. Based
on the thermodynamic investiga tiOll, a kinetic desc ription of
the growth of single and ensemble of 2-d clusters is developed.
It is shown tha t in the s ta ge of independen t growth, the
mean radius of the ensemble of clusters grollls as, R" t for
kinetic limited growth and as R2.;, t for diffusion limited
grOlvth. Moreover, a kinetic theory of Ostwald ripening in
monolayer:> is developed which allol'ls i1 clesc ription of the who 1 e
course of the process 0 In the asymptotic region, the result5
coincide with the predictions obtained first by Lifshit.z and
51 yo zov [23].
The resu1t5 are used for a theoretical explilllct 1.ion of the
computer simulation of a first-order phase transition III a
physisorbed monolayer carried out by Kock eLaI. [4] 0 That
is, first the asymptotic resul t of R2", t for the case of Ostwald
ripening in kinetic-"l imited growth is reconfirmed. In
addition, the developed theory allows the interpretation for
the initial slo\'1 increase of the mean cluster size, R, in the
first stage of Ostwald ripening.
The analysis, carried out here, is for isothermal conditions
and one component systerns. A general iza tion to other
types of constraints, e.g" adiabatic conditions and multicomponent
systems is possible
Description
Keywords
Adsorbed Layers