Homogeneous nucleation of a new phase near an Ising-type critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order parameter associated with the critical point. The total magnetization of the nucleus scales as the response function and so it diverges. Vapor–liquid critical points are in the Ising universality class and so our results imply that near such a critical point the number of molecules in a nucleus of another phase, such as a crystalline phase, diverges as the isothermal compressibility. The case where symmetry prevents coupling between the nucleus and the order parameter is also considered.
REFERENCES
1.
Here we consider only homogeneous nucleation, nucleation in the bulk, far from any interface. Heterogeneous nucleation, nucleation at an interface, either with a wall or an impurity, is in fact more common, and is not always an activated process.
2.
P. G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, 1996).
3.
L. P. Kadanoff, Statistical Physics (World Scientific, Singapore, 2000).
4.
P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995).
5.
6.
7.
8.
9.
N. M.
Dixit
and C. F.
Zukoski
, J. Colloid Interface Sci.
228
, 359
(2000
).10.
11.
M. L.
Broide
, C. R.
Berland
, J.
Pande
, O. O.
Ogun
, and G. B.
Benedek
, Proc. Natl. Acad. Sci. U.S.A.
88
, 5660
(1991
).12.
13.
S. D.
Durbin
and G.
Feher
, Annu. Rev. Phys. Chem.
47
, 171
(1996
).14.
15.
T. W.
Burkhardt
and E.
Eisenriegler
, Phys. Rev. Lett.
74
, 3189
(1995
).16.
17.
18.
Classical nucleation theory predicts that for reasonable values of the interfacial tension (here that between the and phases) the will be of the right order for nucleation to occur when the nucleus contains spins. As critical fluctuations change by an amount this conclusion still holds near a critical point.
19.
See Ref. 24 for a careful, thermodynamic, derivation of Eq. (11). It is Eq. (24) of this reference. Note that they use language appropriate to fluids, so our is their the excess number of molecules in the nucleus and the field is not h but μ the chemical potential of the molecules.
20.
21.
22.
Y.
Viisanen
, R.
Strey
, and H.
Reiss
, J. Chem. Phys.
99
, 4680
(1993
).23.
R. K.
Bowles
, R.
McGraw
, P.
Schaaf
, B.
Senger
, J.-C.
Voegel
, and H.
Reiss
, J. Chem. Phys.
113
, 4524
(2000
).24.
R. K.
Bowles
, D.
Reguera
, Y.
Djikaev
, and H.
Reiss
, J. Chem. Phys.
115
, 1853
(2001
).25.
26.
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