VOLUME 79, NUMBER 3 PHYSICAL REVIEW LETTERS 21 JULY 1997
What Drives the Surface Freezing in Alkanes?
In a recent letter [1] Tkachenko and Rabin (TR) sug-
gested that the crystalline monolayer observed [2] to form
at the surface of molten alkanes at a temperature T
m
1
DT , of up to a few
±
C above bulk melting T
m
, is en-
tropically stabilized by fluctuations along the axis of the
molecules. Such fluctuations are indeed significant in the
bulk rotator phases [3], and probably represent the entropic
component of its interfacial tensions neglected by TR. We
show here that some of TR’s assumptions are incorrect
and surface crystallization is expected purely on the basis
of the interfacial tensions (g, in units of mNm) of semi-
infinite bulk.
Formation of a solid layer at the surface of a liquid
entails creation of solid-liquid and solid-vapor interfaces,
with energy cost g
sl
1g
sy
, and the elimination of a
liquid-vapor interface with an energy gain of g
l y
. This
will occur only if a net energy gain is realized, i.e., g
l y
2
g
sl
1g
sy
2D
N
. 0. The g, which include an en-
tropic component, are defined for surfaces of semi-infinite
bulk. Therefore, for the above condition to be rigorously
correct, the finite thickness (N layers) of the surface crys-
tal requires that a term D
N
be included to account for
any enthalpic or entropic interactions of the two interfaces
D
N
! 0 as N ! `. As pointed out by TR, the observa-
tion [2] of only a single monolayer N 1 implies that
D
1
$ 0. In the simple approximation of surface-localized
interactions, D 0. While not all of these surface ener-
gies may be easily accessible experimentally, they are, in
principle, “experimental observables.”
From Wu’s data [2] one can obtain g
sy
1g
sl
g
l y
2
DT DS 1 S
l
, where DS is the surface entropy reduc-
tion from that of the bulk liquid upon surface freezing
and S
l
is the liquid surface-excess entropy. Zisman [4]
finds g
sy
2g
sl
19.2 for a liquid C
16
drop on a single
crystal C
36
, whose surface is 2CH
3
terminated, i.e., the
same geometry as the surface-crystal / melt interface of Wu
[2]. This is important, since Zisman [4] finds a CH
2
-
terminated surface to have a significantly higher g
sy
. Ap-
proximating Zisman’s value to apply for pure C
16
C
36
and using the corresponding g
sy
1g
sl
26.93 23.19
from Wu [2], we obtain g
sy
23.07 21.20 and g
sl
3.87 2.00. Since [2,5] g
l y
T
m
28 for all relevant n,
we have g
sy
T
m
,g
l y
T
m
. It is this lower surface ten-
sion of the solid, which is a necessary condition for sur-
face crystallization. Mitchell and Elton [6] also measure
g
sy
,g
l y
for C
16
and C
18
. Mach [7] measures g
sy
20
for smectic-A, CH
3
-terminated films of liquid crystals.
Hoffman [8] claims an extremely small g
sl
0.3 for C
94
in his growth rate study. These data, while not for the ex-
act conditions under consideration, should nevertheless be
very close and are the best available. These obviously con-
flict with TR’s assumptions that g
sy
.g
l y
, g
sy
35, and
g
sl
8. Their assumptions are not based on experiment,
but on a model where g~r
2
( r is the electron density),
a relation found to correlate nicely with the Hamaker con-
stant for various small molecule liquids [9]. However, this
has never been shown to hold for the ordered phases of the
alkanes and, in fact, the electron-poor “depletion region”
between the layers [3] should reduce the Van der Waals at-
traction in the crystal phases relative to the uniform-density
liquid state. Furthermore, even g
l y
T does not scale with
r
2
, since its significant entropic component is comparable
to its enthalpic component [5].
The finite thickness correction D
1
is the difference be-
tween two quantities: (1) the disorder of a single mono-
layer in contact with vapor and liquid and (2) the sum of
the disorder of an outermost layer of a semi-infinite crys-
tal in contact with the vapor phase and one in contact with
the liquid phase. TR computed only the first, thus overes-
timating D
1
. Much of their calculated D
1
is therefore the
surface excess entropy for the solid-liquid and solid-vapor
interfaces which are already included in g
sl
and g
sy
. This,
combined with unrealistically high values of g
sy
and g
sl
,
coincidentally predict the surface crystallization.
We have shown that the low energies of the CH
3
-
terminated crystal face can cause surface crystallization,
and demonstrated a need, and a new method, for a more
complete chain-length and temperature determination of
the individual g
sy
, g
sl
, and D
1
. The recognition by
TR of the importance of longitudinal freedom and their
calculation is an important step along that road.
E. B. Sirota,
1
X. Z. Wu,
2
B. M. Ocko,
3
and M. Deutsch
4
1
Exxon Research and Engineering Company
Route 22 East, Annandale, New Jersey 08801
2
Physics Department, Northern Illinois University
DeKalb, Illinois 60115
3
Physics Department, Brookhaven National Laboratory
Upton, New York 11973
4
Physics Department, Bar Ilan University
Ramat Gan 52900, Israel
Received 15 January 1997 [S0031-9007(97)03344-9]
PACS numbers: 68.10. – m, 61.25.Em, 64.70.Dv
[1] A. V. Tkachenko and Y. Rabin, Phys. Rev. Lett. 76, 2527
(1996).
[2] X. Z. Wu et al., Phys. Rev. Lett. 70, 958 (1993); Science
261, 1018 (1993); B. M. Ocko et al., Phys. Rev. E 55,
3164 (1997).
[3] A. Craievich et al., Phys. Rev. B 30, 4782 (1984).
[4] W. A. Zisman, in Contact Angle, Wettability and Adhe-
sion, edited by F. M. Fowkes (ACS, Washington, DC.,
1994).
[5] D. M. Small, The Physical Chemistry of Lipids ( Plenum,
New York, 1986).
[6] J. W. Mitchell and G. A. H. Elton, J. Chem. Soc. London
1953, 839.
[7] P. Mach et al., J. Phys. II (France) 5, 217 (1995).
[8] J. D. Hoffman, Macromolecules 18, 772 (1985).
[9] J. N. Israelachvili, Intermolecular and Surface Forces
(Academic, New York, 1992).
0031-9007 97 79(3) 531(1)$10.00 © 1997 The American Physical Society 531