0% found this document useful (0 votes)
58 views6 pages

Effect of Salt Concentration On Interfacial Behavior in The Surfactant System Water+noctadecane+diethylene Glycol Monohexyl Ether

Materiais

Uploaded by

Souza Tchar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
0% found this document useful (0 votes)
58 views6 pages

Effect of Salt Concentration On Interfacial Behavior in The Surfactant System Water+noctadecane+diethylene Glycol Monohexyl Ether

Materiais

Uploaded by

Souza Tchar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 6

Effect of salt concentration on interfacial behavior in the surfactant system

water+noctadecane+diethylene glycol monohexyl ether


L.J. Chen and M.C. Hsu

Citation: The Journal of Chemical Physics 97, 690 (1992); doi: 10.1063/1.463563
View online: http://dx.doi.org/10.1063/1.463563
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/97/1?ver=pdfcov
Published by the AIP Publishing

Articles you may be interested in


Critical fluctuations of the micellar triethylene glycol monoheptyl ether-water system
J. Chem. Phys. 124, 124910 (2006); 10.1063/1.2179424

Surface phase behavior in Langmuir monolayers of diethylene glycol mono- n -hexadecyl ether at the air-
water interface
J. Chem. Phys. 121, 10217 (2004); 10.1063/1.1806818

Critical behavior of ionic micellar systems at different salt concentrations


J. Chem. Phys. 101, 6874 (1994); 10.1063/1.468499

Anionic surfactant–water systems: Influence of lecithin addition on the rheological behavior


J. Rheol. 34, 1121 (1990); 10.1122/1.550076

Critical Solution Phenomenon in TwoComponent Liquid Systems. The System WaterEthylene Glycol
MonoIsobutyl Ether
J. Chem. Phys. 33, 1816 (1960); 10.1063/1.1731510

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14
Effect of salt concentration on interfacial behavior in the surfactant system
water + n-octadecane + diethylene glycol monohexyl ether
L.-J. Chen and M.-C. Hsu
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10764,
Republic of China
(Received 29 January 1992; accepted 17 March 1992)
We study the phase behavior and observe wetting and nonwetting behaviors, as well as the
wetting transition which occurs in the four-component surfactant system water + n-
octadecane + diethylene glycol monohexyl ether + NaCl. All experiments are performed at
constant weight ratio of water:n-octadecane (1: 1) and constant temperature 35.0 ± 0.05 ·C,
with varying NaCI concentration. It is found that the system water + n-octadecane + C 6 E2
exhibits a wetting transition lying at 17.1 wt. % of NaCI in water. This observation is further
confirmed by interfacial tension measurements. In addition to that of lyotropic salt (NaCI),
the effect of hydrotropic saIt on the interfacial wetting transition is also discussed.

I. INTRODUCTION Type-III phase equilibria consist of three phases with a


middle phase containing most of the surfactant and sig-
In general, when any three fluid phases a, p, and coex- r nificant amounts of water and oil, which coexists with a
ist at equilibrium with only a small amount of the middle p
water-rich phase and an oil-rich phase.
phase, as illustrated in Fig. 1, there are three interfacial ten-
Type-IV phase equilibria have only a single homoge-
sions 0"a(3' 0"ar' and 0"(3r between the coexisting phases, where
neous phase in which water, oil, and surfactant are mu-
0"ij denotes the interfacial tension of the interface between
tually solubilized.
the i and j phases. If these tensions satisfy the Neumann's
inequality I O"ar < O"a(3 + O"(3r' the middle p phase only par- Within a certain range of temperature and pressure,
tially wets the ar interface and forms a lenticular drop float- these four types (I, II, III, and IV) of phase equilibria can all
ing on the ar interface, as shown in Fig. 1 (a). If the Anton- be observed in three-component surfactant systems. Figure
ow's rule2 0"ar = 0"a(3 + U (3r holds, the middle p phase 2 shows a schematic "fish"-shape phase diagram, a plot of
completely spreads across the ar interface and forms a thin temperature vs weight fraction of surfactant at constant wa-
r
film separating the a and phases, as shown in Fig. 1 (b). ter:oil weight ratio, of these ternary systems at constant pres-
For some systems, the middle p phase can exhibit both sure. In Fig. 2, obviously, the phase behavior between Win-
types of interfacial behavior (wetting and nonwetting) at sor types I-Ill-II can be simply monitored by varying the
different thermodynamic conditions. The interfacial phase system temperature if a proper composition is chosen, for
transition from a wetting regime to a non wetting regime, or example, the surfactant composition c in Fig. 2. One finds
vice versa, is called a wetting transition. 3 Such a transition Winsor type-I phase equilibria at low temperatures and
has been observed at vapor-liquid interfaces,4.5 solid-liquid Winsor type-II phase equilibria at high temperatures. At in-
interfaces, 6 and liquid-liquid interfaces. 7- 10 termediate temperatures, one may find Winsor type-III
Recently, a wetting transition at the liquid-liquid inter- phase equilibria. As the temperature rises, the surfactant
face was found by Robert and co-workers 7 in three ternary transfers continuously from the water-rich phase to the oil-
surfactant systems: water + n-tetradecane + C 6 E 2, wa- rich phase, i.e., the mutual solubility between surfactant and
ter + n-hexadecane + C 6 E 2, and water + n- water decreases and the surfactant becomes more lyotropic.
octadecane + C 6 E 2, where C 6 E2 denotes the nonionic sur- Apart from temperature, there are other system param-
factant diethylene glycol monohexyl ether, eters that can be used to monitor the phase behavior between
CH 3 (CH 2 )5 (OCH 2CH 2 )20H. These three ternary sys-
tems of the type water + n-alkane + C 6 E2 separate into
three coexisting liquid phases within a certain temperature
range. The phase behavior of such systems depends on tem-
perature, pressure, and the nature of the components. II Ac-
cording to Winsor's classification,t2 the various phase equi- a
libria of such systems can be grouped into four types: fj-I-----1
Type-I phase equilibria consist of two phases with most r
of the surfactant dissolved in the aqueous phase and a
small amount of oil dispersed in the aqueous phase.
(s) (b)
Type-II phase equilibria consist of two phases with most
of the surfactant dissolved in the oil-rich phase and a FIG. 1. Schematic illustration of three coexisting phases: (a) nonwetting
small amount of water dispersed in the oil-rich phase. middle phase; (b) wetting middle phase.

690 J. Chem. Phys. 97 (1).1 July 1992 0021-9606/92/130690-05$06.00 ® 1992 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14
L. -J. Chen and M. -C. Hsu: Effect of salt on interfacial behavior 691

II. EXPERIMENT
A. Materials
n-octadecane of 99% purity is a product of Sigma
i 2 r/J
Chemical Co. The nonionic amphiphile diethylene glycol
monohexyl ether (C6 E 2 ) of99% purity is purchased from
T
Aldrich Chemical Co., and the salt NaCI of99.5 + % purity
from Fluka Chemical Co. All these chemicals are used as
1 r/J
received without any further purification, and water is puri-
fied by a Barnstead NAPOpure II System.
1
C 1
",I B. Procedure
o Surfactant % ~ 1. Phase diagram
Water:Oil= 1:1
First, we prepare the brine at different concentrations of
NaCl. The samples are prepared in a clean glass test tube at
FIG. 2. Schematic "fish" -shape phase diagram of constant water:oil weight fixed water:oil weight ratio (I: I) with varying surfactant
ratio, for example, 1: 1. concentration. The samples are then placed in a water bath
at a temperature of35.0 ± 0.05 'c for several hours to allow
the system to reach equilibrium. Before and during the equi-
libration process, the samples are shaken vigorously several
times to ensure a thorough mixing. After equilibrium is
reached, the number of liquid phases for each sample is re-
types I-III-II. These system parameters are the alkyl chain corded at different salt NaCI concentrations. The phase
length of the surfactant, the aromaticity of the oil, and the boundary is systematically searched for each brine concen-
salt concentration. 13 For example, if the salt concentration tration by locating the surfactant concentration at which the
is chosen as the system parameter for a system of the type number of the liquid phases changes.
water + n-alkane + C 6 E 2 , the phase behavior of such a sys-
tem at constant temperature can be schematically described
by a fish-shape phase diagram with salt concentration, as a 2. Wetting transition
coordinate instead of temperature, in Fig. 2. The samples are prepared at the composition in a weight
It is well understood that both temperature and salt con- ratio of water:oil:C 6 E2 equal to 2:2: I with varying salt
centration have the same effect on phase behaviors of wa- (NaCl) concentration. The samples are placed in a water
ter + n-alkane + C 6 E2 systems as described above. How- bath which is set at a temperature lying within the three-
ever, there is no literature, at least to our knowledge, stating phase region: 35.0 ± 0.05'C. The equilibration procedure
that these two parameters also have the same effect on inter- described above is followed. After equilibrium is reached, all
facial behaviors of water + n-alkane + C 6 E2 systems. three phases are transparent with sharp, mirrorlike inter-
In the study of Robert and co-workers,7 the tempera- faces.
ture was used as the system parameter to locate the wetting Following equilibration, the upper and lower phases are
transition temperature in systems of the type water + n- carefully removed and put into a second test tube by using
alkane + C 6 E 2 • It is believed that the properties of interface pipettes. Next, one or two drops of the middle phase are
are directly related to those of the coexisting bulk phases. added to the second test tube containing only the upper and
Since temperature and salt concentration have the same ef- lower phases. The wetting and non wetting regimes can be
fect on the phase behavior of these systems, it is natural for us distinguished from the shape of the middle phase by direct
to conjecture that both temperature and salt concentration eye observation. When the middle phase forms a lenticular
also have the same effects on their interfacial behavior. If so, drop floating on the interface between the upper and lower
there should also exist a wetting transition in the systems of phases, this indicates nonwetting behavior; while when the
the type water + n-alkane + C 6 E2 at constant temperature middle phase spreads across the interface and forms a very
by varying salt concentration. It is the purpose of this study thin layer between the upper and lower phases, this indicates
to verify this point. wetting behavior.
In this manuscript, we present experimental results on Consequently, the wetting transition concentration C w
wetting transitions in the four-component water + n- can be determined by direct eye observation of the wetting
octadecane + C 6E2 + NaCI system at constant tempera- and nonwetting behaviors of the middle phase at different
ture, in which the salt concentration is varied. The experi- NaCI concentrations. When the NaCI concentration lies be-
mental procedures for determining the phase behavior and low C w , the middle phase exhibits nonwetting behavior,
locating the wetting transition in the four-component system while when it lies above C w , the middle phase exhibits wet-
water + NaCl + n-octadecane + C 6 E2 at constant tem- ting behavior.
perature 35 'c are described in the next section. The experi- In order to confirm our eye observations, a spinning-
mental results and further discussion are given in Sec. III. drop tensiometer (Kruss SITE 04) is used to measure the

This article is copyrighted as indicated in the article. ReuseJ.of AIP content


Chern. is subject
Phys .• Vol. to the
97. No.1. terms
1 July at: http://scitation.aip.org/termsconditions. Downloaded to IP:
1992
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14
692 L. -J. Chen and M. -C. Hsu: Effect of salt on interfacial behavior

4.0
interfacial tensions, while density measurements are made
by using a vibrating-tube densiometer (Paar DAM 45). 35

~
3¢<-:->2¢
I
30
III. RESULTS AND DISCUSSION I

25
Figure 3 shows the experimental result for the phase
diagram at constant temperature 35.0·C and constant S 20
weight ratio of water:n-octadecane ( = 1:1). As expected, "-
:z: 15
the phase diagram does exhibit a fish shape, except that the !
lower half is not a closed loop due to no Winsor type-I phase b 1.0

equilibria existing for this particular temperature 35.0·C : we~hng transition


0.5
and water/n-octadecane weight ratio. At constant weight I
,
p0l1 t
ratio of water:n-octadecane:C6 E2 ( = 2:2: 1), the three liq- 0.0
0 8 10 12 14 16 18 20 22 24 26
uid-phase coexistence region ranges from 0% to 18.7% Salinity (%)
NaCI weight percentage in brine, which is the region where
we search for a wetting transition. FIG. 4. Variation ofinterfacial tensions as a function of NaCl concentration
It is found from eye observations that the water + n- for the water + n-octadecane + C. E2 + NaCl system at constant tempera-
octadecane + C 6 E:z system does exhibit a wetting transition ture 35·C.
lying at 17.1 wt. % of NaCI (in brine). The concentration
C w at which the wetting transition occurs is known as the
wetting transition concentration. Note that the phase
boundary of Winsor type II and type III is found, in Fig. 3, to
be at 18.7 wt. % ofNaCI (in brine). This result is consistent not exactly the same as the salt effect. In the ternary wa-
with that resulting from interfacial tension measurements. ter + n-octadecane + C 6 E2 system, there exists an unique
The variation of the interfacial tensions is illustrated in Fig. wetting transition temperature (62 ·C). While in the quater-
4. The wetting transition occurs when the three interfacial nary water + NaCI + n-octadecane + C 6 E2 system at con-
tensions «(J'af3' (J'ay' and (J'f3y) change from satisfying Anton- stant temperature, the wetting transition concentration is,
ow's rule to Neumann's inequality, or vice versa. It is clear in instead of an unique value, a function of mean composition,
Fig. 4 that at a particular concentration (wetting transition e.g., the wetting transition concentrations at three different
concentration Cw ), the sum of (J'af3 and (J'f3y becomes equal to mean compositions, water:n-octadecane:C6 E2 = I: I: 1,
(J'ay' i.e., a wetting transition occurs at the concentration 2:2:1, and 3:3:1, are found to be, respectively, 16.0 wt. %,
where the curves of (J'af3 + (J'f3y and (J'ay coincide in Fig. 4. 16.6 wt. %, and 17.1 wt. %. Consequently, these wetting
The wetting transition concentration Cw is found to be transition concentrations at different mean compositions
16.6%, which is sightly smaller than the value obtained from will form a wetting transition concentration surface inside a
eye observations due to experimental uncertainty. tetrahedron phase diagram of the quaternary NaCI + wa-
It should be pointed out that the temperature effect on ter + n-octadecane + C 6 E2 system at constant tempera-
interfacial behaviors of water + alkane + C 6 E2 systems is ture.
According to the force balance at interfaces,14 these in-
terfacial tension data can be used to calculate the contact
angle e, defined in Fig. 5(a), by applying the relation
(J' 2 22
ay - (J' af3 - (J' f3y
e
cos =--~----~--~~
2(J'af3 (J'f3y
24
22
When the middle {3 phase spreads across the interface
20
between the upper and lower phases and forms a thin film,
18
the contact angle becomes zero. As a consequence, when a
16
wetting transition from nonwetting to wetting occurs, the
14
contact angle e vanishes.
~
~
12 For the water + n-octadecane + C 6 E2 system, the vari-
.e- 10 ation of the contact angle e as a function of salinity is shown
:§ 8 in Fig. 5. Within the accuracy of our experiments, the deriva-
a;
UJ 6 tive of the contact angle ewith respect to salinity, in Fig. 5, is
4 discontinuous at the wetting transition concentration C w ,
2 i.e., the wetting transition is first order. In the study of Rob-
0 ert and co-workers,7(b) the wetting transition for the wa-
ter + n-hexadecane + C6 E2 system is also found to be first
0 60 80 100
[C.E2/( C.E..-H,o+c,.,H,.,l ]
order by using the temperature as the system parameter.
FIG. 3. Fish-shape phase diagram of the water + n·octadecane Our experimental results of phase behavior and wetting!
+ C.E2 + NaCl system at constant temperature 35·C and constant wa- nonwetting behaviors confirm that increasing the NaCI con-
ter:n-octadecane weight ratio ( I: I) with varying NaCl concentration. centration in the water + n-octadecane + C 6 E2 system

J. Chem. Phys., Vol. 97, No.1, 1 July 1992


This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14
L. -J. Chen and M. -C. Hsu: Effect of salt on interfacial behavior 693

Figure 6 schematically shows both the upper and lower


critical solution temperatures of a system of the type wa-
ter + n-alkane + C;Ej' between which three liquid phases
(a) coexist, as a function of salt concentration. 13 (b) Obviously,
increasing the salinity in systems of the type water + n-
alkane + C;Ej will lower the critical temperatures of the sys-
tem. As a consequence, increasing the salinity in the wa-
ter + n-octadecane + C 6 E2 system at constant temperature
is, in a sense, approaching a critical point, and the occur-
90
rence of a wetting transition is expected by critical wetting
0
80 theory. However, the effect of salt concentration on the sys-
~ 0
0
0 tem is not unique and depends on the nature of the salt.
70 J
0
0
0 ----- 1'\ According to the effect of anions, 13(a) inorganic electro-
0 60 0
lytes are classified into two different groups: (i) lyotropic
v
S0
0
,\ salts which decrease the mutual solubility between water
be and surfactant, for example, NaCI; (ii) hydrotropic salts
s:: 40
CO
...
tJ
30
...s::
CO
20
0
tJ
10

o
o 2 6 8 10 12 14 16 18 20
Salinity (%)
(b)

e
FIG. 5. (a) Contact angle for three coexisting liquid phases. (b) Variation t
of contact angle e as a function of NaCI concentration for the water + n-
octadecane + C.E, + NaCI system at constant temperature 35"C. T

re'

does have the same effects on phase behaviors, as well as on


interfacial behaviors, as raising the temperature.
o
The occurrence of a wetting transition in the water + n- Salt% ~

octadecane + C6 E2 system by adding NaCI can be ex- (a)


plained by the phenomenological arguments of Cahn 15 and
by the critical wetting theory of Ebner and Saam. 16 Accord-
ing to these theories, when a three-phase system with a non-
wetting middle phase approaches a critical end point, the
middle phase should completely wet the interface between
the upper and the lower phases. This argument suggests that
re U

a wetting transition can be induced by adding a new compo-


nent to a three-phase system of complete wetting middle
t
phase to drive the system away from its critical point. Mol- r
dover and Cahn 4 have applied this idea to find the wetting
transition in the liquid-liquid-vapor system of cyc10hexane rei
and methanol by adding water.
On the other hand, this argument directly suggests that
by tuning a system parameter of a three-phase system with
an incomplete wetting middle phase to drive the system close
to its critical point can induce a wetting transition. In the
o
region of three liquid-phase coexistence of the water + n- Salt% ~

octadecane + C6 E2 system, Robert and co-workers 7 suc- (b)


cessfully observed the wetting transition by raising the tem-
perature to drive the system to approach its upper critical
end point. Instead of raising the temperature, we increase the FIG. 6. Schematic variation of upper and lower critical temperatures as a
salinity to bring the system close to its critical point, more function of salt concentration for a system of the type water + oil + C,E,
precisely, the upper critical solution point. with two different types of salt: (a) lyotropic salt; (b) hydrotropic salt.

This article is copyrighted as indicated in the article. ReuseJ.ofChern.


AIP content is subject
Phys., Vol. to the
97, No.1, terms
1 July at: http://scitation.aip.org/termsconditions. Downloaded to IP:
1992
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14
694 L. -J. Chen and M. -C. Hsu: Effect of salt on interfacial behavior

which increase the mutual solubility between water and sur- able to us his experimental facilities. This work was support-
factant, for example, NaCI04 • Therefore, adding lyotropic ed by the National Science Council of Taiwan, Republic of
salt to a three-component surfactant system will force the China (Grant No. NSC81-0402-EOO2-15).
surfactant to move continuously from the water-rich to the
oil-rich phase, which is exactly the same effect as increasing
the temperature; while adding hydrotropic salt to a three-
component surfactant system has the same effect on phase
behavior as decreasing the temperature.
According to critical wetting theory,15.16 we should be
able to find another wetting transition from non wetting mid- I F. Neumann. Vorlesungen uber die Theorie der Capillaritat. edited by A.
Wangerin (Teubner, Leipzig, 1894), Chap. 6, Sec. 1, especially pp. 161
dle phase to wetting in the water + n-octadecane + C 6E2 and 162; F. P. Buffand H. Saltsburg, J. Chem. Phys. 26, 23 (1957); F. P.
system by decreasing the system temperature to bring the Buff, Encyclopedia of Physics, edited by S. Flugge (Springer, Berlin,
system close to its lower critical solution temperature. 7 1960), Vol. 10, Sec. 7, pp. 298 and 299.
2G. N. Antonow, J. Chim. Phys. 5, 372 (1907); Kolloid-Z. 59, 7 (1932);
However, before any wetting transition is reached, the sys- 64,336 (1933); N. K. Adam, The Physics and ChemistryofSurjaces, 3rd
tem freezes (the melting point of n-octadecane is around ed. (Oxford University, Oxford, 1941), pp. 7, 214, and 215.
28 ·C). Therefore, we have added the hydrotropic salt 3Fora review, see D. E. Sullivan and M. M. Telo da Gama, in Fluid Interfa-
NaCI04 to the system to bring it close to its lower critical cial Phenomena, edited by C. A. Croxton (Wiley, New York, 1985).
4M. R. Moldover and J. W. Cahn. Science 207,1073 (1980).
point and expect a wetting transition to occur before the S J. W. Schmidt and M. R. Moldover, J. Chem. Phys. 79, 379 (1983).
system's lower critical point is reached. "D. W. Pohl and W. 1. Goldburg, Phys. Rev. Lett. 48, 1111 (1982).
At constant weight ratio of water:n-octadecane:C6E2 7 (a) M. Robert and J. F. Jeng, J. Phys. (Paris) 49, 1821 (1988); (b) L.-J.

( = 2:2: 1) and constant temperature 35 ·C, the three liquid- Chen, J.-F. Jeng, M. Robert, and K. P. Shukla, Phys. Rev. A 42,4716
(1990).
phase coexistence region ranges from 0% to 9.0% NaCI04 3D. H. Smith and G. L. Covatch, J. Chem. Phys. 93, 6870 (1990).
weight percentage in water, which is the region where we 9 A. Estrada-Alexanders, A. Garcia-Valenzuela, and F. Guzman, J. Phys.
search for a wetting transition. The middle phase is found to Chem. 95, 219 (1991).
exhibit nonwetting behavior for the NaCI04 weight percen- 10M. Kahlweit, R. Strey, M. Aratono, G, Busse, J. Jen, and K. V. Schubert,
J. Chern. Phys. 95, 2842 (1991); M. Aratono and M. Kahlweit, ibid. 95,
tage ranging from 0% to 7.80%. For the systems of the 8578 (1991).
NaCI0 4 weight percentage higher than 7.80%, the amount II M. Kahlweit and R. Strey, Angew. Chem. Int. Ed. Engl. 24, 654 (1985);

oflower (aqueous) phase becomes very small. It is hard for P. K. Kilpatrick, C. A. Gorman, H. T. Davis, L. E. Scriven, and W. G.
Miller, J. Phys. Chem. 90, 5292 (1986); H. Kunieda and S. E. Friberg,
us to experimentally observe whether the middle phase wets
Bull. Chem. Soc. Jpn. 54,1010 (1981); M. Kahlweit, R. Strey, and D.
the interface between the upper and lower phases or not. Haase, J. Phys. Chem. 89, 163 (1985); M. Kahlweit, E. Lessner, and R.
However, there should exist a wetting transition in this sys- Strey, ibid. 87, 5032 (1983).
tem somewhere between the NaCI04 weight percentage I2P. A. Winsor, Trans. Faraday Soc. 44, 376 (1948).
13 (a) M. Kahlweit, E. Lessner, and R. Strey, J. Phys. Chem. 88, 1937
7.80% and 9.0% according to the critical wetting theo- (1984); (b) M. Kahlweit, R. Strey, and D. Haase, ibid. 89,163 (1985);
ry.15.16 (c) M Kahlweit, R. Strey, P. Firman, D. Haase, J. Jen, and R. Scho-
macker, Langmuir 4,499 (1988).
ACKNOWLEDGMENTS 14 J. S. Rowlinson and B. Widom, Molecular Theory ofCapillarity (Claren-
don, Oxford, 1982), Chap. 8.
One of us (L. J. C.) is grateful to M. Robert for fruitful IS J. W. Cahn, J. Chem. Phys. 66, 3667 (1977).

discussions. We are indebted to C.-Y. Mou for making avail- I"C. Ebner and W. F. Saam, Phys. Rev. Lett. 38, 1486 (1977).

J. AIP
This article is copyrighted as indicated in the article. Reuse of Chem. Phys.,isVol.
content 97, No.1,
subject to the1terms
July 1992
at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.160.4.77 On: Fri, 19 Dec 2014 19:21:14

You might also like