Biomedical Engineering Reference
In-Depth Information
or molecules in the solution may, on collision, join into groups of two, three, four, or
more particles, forming dimers, trimers, tetramers, etc. The kinetics of nucleation is
described by the nucleation rate
J
, which is defined as the number of nuclei created
per unit volume-time, and determined by the nucleation barrier, kink integration
rate, transport, and other factors.
J
is an important characteristic of the process of
new phase formation.
2.2.2.1
Thermodynamic Driving Force
Nucleation is the process in which the first-order phase transitions begin. The
driving force for nucleation of new phases (e.g., crystals) , which is defined
as the difference between the chemical potentials of a growth unit in the mother and
the crystalline, and for ice crystallization, is given according to [
47
]:
h
m
T
T
e
D
;
(2.1)
T
D
.T
e
T/;
(2.2)
where
h
m
is the ice enthalpy of melting per molecule,
T
e
is the equilibrium
temperature (the melting temperature of ice), and
T
is supercooling.
2.2.2.2
Nucleation Barrier
A characteristic feature of the nucleation process is that the substance with the
properties of the new phase is fluctuating and localized in small nanoscale spatial
regions. These are occupied by various numbers of atoms or molecules in the form
of clusters. The clusters remaining at equilibrium with the surrounding mother
phase are the critical nuclei, and the smaller or the larger clusters are the subnuclei
or supernuclei, respectively. Only the supernuclei are the clusters that can grow
spontaneously to reach macroscopic sizes. For simplicity, we call hereafter the
subnuclei “clusters,” and the supernuclei “nuclei” (cf. Fig.
2.4
a).
The nucleation rate
J
describing the number of nuclei successfully generated
from the population of clusters per unit time, per unit volume is determined by the
height of the free energy barrier, the so-called nucleation barrier. The occurrence of
a nucleation barrier is attributed to the following two opposing effects:
1. Since the crystalline phase is a stable phase, the emergence of the new phase
from the mother phase will lead to a lowering of the (Gibbs) free energy of the
system.
