Measurements are presented of the state of wetting of a binary liquid mixture on heavily silylated glass, which are believed to probe a new region of the wetting phase diagram. We find unusual temperature dependence and the first experimental evidence of a possible  partial drying  transition recently predicted by Ebner and Saam for the case of strong short-range substrate-liquid forces opposed by a weak long-range force

Durian, Douglas J

Franck, Carl

English

Kosmopolis

University of Pennsylvania
ScholarlyCommons
Department of Physics Papers Department of Physics
11-1-1987
Continued Exploration of the Wetting Phase
Diagram
Douglas J. Durian
University of Pennsylvania, djdurian@physics.upenn.edu
Carl Franck
Cornell University
Follow this and additional works at: https://repository.upenn.edu/physics_papers
Part of the Physics Commons
At the time of publication, author Douglas J. Durian was affiliated with Cornell University. Currently, he is a faculty member at the Physics Department
at the University of Pennsylvania.
This paper is posted at ScholarlyCommons. https://repository.upenn.edu/physics_papers/638
For more information, please contact repository@pobox.upenn.edu.
Recommended Citation
Durian, D. J., & Franck, C. (1987). Continued Exploration of the Wetting Phase Diagram. Physical Review B, 36 (13), 7307-7310.
http://dx.doi.org/10.1103/PhysRevB.36.7307
Continued Exploration of the Wetting Phase Diagram
Abstract
Measurements are presented of the state of wetting of a binary liquid mixture on heavily silylated glass, which
are believed to probe a new region of the wetting phase diagram. We find unusual temperature dependence
and the first experimental evidence of a possible "partial drying" transition recently predicted by Ebner and
Saam for the case of strong short-range substrate-liquid forces opposed by a weak long-range force.
Disciplines
Physical Sciences and Mathematics | Physics
Comments
At the time of publication, author Douglas J. Durian was affiliated with Cornell University. Currently, he is a
faculty member at the Physics Department at the University of Pennsylvania.
This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/638
PHYSICAL REVIEW B VOLUME 36, NUMBER 13
Continued exploration of the wetting phase diagram
1 NOVEMBER 1987
Douglas J. Durian and Carl Franck
Laboratory of Atomic and Solid State Physics and Materials Science Center,
Cornell University, Ithaca, New York 14853-2501
(Received 11 August 1987)
Measurements are presented of the state of wetting of a binary liquid mixture on heavily
silylated glass, which are believed to probe a new region of the wetting phase diagram. We find
unusual temperature dependence and the first experimental evidence of a possible "partial drying"
transition recently predicted by Ebner and Saam for the case of strong short-range substrate-
liquid forces opposed by a weak long-range force.
INTRODUCTION
In a recent paper by Durian and Franck' (DF), we re-
port capillary-rise measurements of the state of wetting of
the carbon disulfide+nitromethane binary liquid mixture
at coexistence on chemically altered borosilicate glass sub-
strates. We find that hydroxylated substrates are always
completely wet by the nitromethane-rich (N ) phase;
capillaries lightly silylated with hexamethyldisilazane
(HMDS) are less attractive to N* and exhibit a transition
from partial to complete wetting, by N*, as the tempera-
ture is increased toward the liquid-liquid critical demixing
point T, . In the course of the experiment several sub-
strates were produced with such heavy silylation as to be-
come attractive to the carbon disulfide-rich (C*) phase.
These substrates gave data with unusual temperature
dependence but were not included in DF because of unac-
ceptable errors arising from bulk-meniscus mislocation.
In this report we present data on similar heavily silylated
capillaries which have been corrected for this systematic
error. It should be noted that Abeysuriya, Wu, and
Franck (AWF) have published observations for similar
substrates; however, improved sample-preparation tech-
nique permits great enough precision that previously un-
noticed features are now observed.
aff'ected. 5 If this is true, our heavily silylated substrates
can be used to test the theoretical predictions of
Nightingale and Indekeu, and Ebner and Saam for the
wetting behavior of surfaces with a short-range force
weakly opposed by a long-range force. The predictions
are, briefly, that complete drying will occur continuously
at T„and that if the short-range surface field h ~ is strong
enough there will be a "partial drying" transition between
two states of incomplete drying. We follow Ebner and
Saam in referring to wetting by N* as "wetting, " and
wetting by C* as "drying. "
PROCEDURE
All sample cells used were similar to those of AWF and
DF. They were filled in an Ar atmosphere to have
0.601 ~ 0.01S volume fraction carbon disulfide, approxi-
mately the critical composition. The initial critical tem-
peratures were within T, =(63.052 ~0.011) C and were
found to drift, typically, by +5 mK/day. The positive
drift and T, )T, indicate increasing presence of impuri-
ties which are preferentially dissolved in one of the two
liquid phases.
The starting point of the work to be reported here is the
data shown in Fig. 1 for heavily silylated tubes with a net
attraction to the opposite phase from the hydroxylated
control. It is believed that hydroxylated surfaces produce
both short-range and long-range forces attractive to N*.
Furthermore, one can hypothesize that by changing the
glass surface chemistry only the short-range force is
I
C3
0
—2.5 —2.0 —1.0
log ~ o[T —T/T ]
FIG. 1. Preliminary capillary parameter (rise times inner ra-
dius) vs reduced temperature. In each of the three data sets
(displaced vertically for clarity) the solid symbols represent
completely wet, hydroxylated, capillaries. The open symbols,
having error bars comparable to the hydroxylated data,
represent heavily silylated capillaries which are incompletely
dry. From top to bottom, the HMDS exposures were 48 h at 8
mm Hg, then 67, 707, 226, and 130 h at 2.4 mm Hg. Vertical-
axis tick marks indicate successive decades.
7307 Oc 1987 The American Physical Society
7308 DOUGLAS J. DURIAN AND CARL FRANCK
(r;+x;, )a;=(r, + ; x)a,J. (2)
The correction x =&x; j) is then added to the measured
Three sets of preliminary data are shown in Fig. 1. The
open symbols denote the capillary parameter (rise times
inner radius) of heavily silylated capillaries; the solid sym-
bols (fit by power law) denote the absolute capillary pa-
rameter of completely wet hydroxylated capillaries. All
capillaries have identical radii, 0.188 mm. The capillary-
rise formula,
2 (x~p
a = cosO,
~pg
predicts that the capillary parameter will have the same
(maximum) magnitude for both complete wetting,
cosO= —1, and complete drying, cosO=1. Here a is the
capillary parameter, a,& is the interfacial surface tension,
hp is the liquid-liquid mass density difference, g is the
gravitational accelation, and O is the contact angle coex-
isting liquid phases made with the substrate. Equation
(1) is valid only for rise much greater than radius; this
condition is satisfied by all observations presented in this
report. Note that large systematic errors are present in
these data: The silylated capillary of the middle data set
in Fig. 1 attains a rise near T, greater than the depression
of the completely wet hydroxylated capillary. This behav-
ior corresponds to cosO& 1 and is unphysical; our ex-
planation is that mislocation of the bulk meniscus is re-
sponsible. Nevertheless, the following statements can be
made with certainty. Far from T, all silylated capillaries
are incompletely dry. Even near T, the two least heavily
silylated capillaries of the bottom data set are incomplete-
ly dry because their rises are less than that of the most
heavily silylated capillary in the sample cell. All data
show evidence of a possible discontinuity in slope which
could be interpreted as either a first-order drying transi-
tion or a partial-drying transition. To determine which,
we need to understand and eliminate the bulk-meniscus
location error in further experiments; this we now present.
Due to the curvature of the bulk meniscus at the sample
cell walls and around the capillary tubes, it is not possible
to measure capillary rise relative to the bulk without sys-
tematic error. This is especially troublesome for heavily
silylated capillaries because their menisci lie on the oppo-
site side of the bulk meniscus thereby preventing direct
comparison with the completely wet hydroxylated control.
In particular, there is little systematic error in calculating
the contact angle by cos8=(silylated rise)/(hydroxylated
rise) for lightly silylated tubes near complete wetting, but
there would be an unacceptably large error in doing the
same for heavily silylated capillaries near complete drying
(as we have just seen in Fig. I).
We attempt to eliminate the bulk-meniscus location er-
ror by using data from three hydroxylated capillaries of
diA'erent inner radii (0.134, 0.188, and 0.300 mm) to esti-
mate the eA'ective position of the bulk meniscus. To do
this, we rely on the property that capillary rise is inversely
proportional to radius. For each position of the capillaries
through the bulk meniscus, we measure the rise rk in the
hydroxylated tubes, radii ak, and for each distinct pair
compute x; J such that
rises of all capillary tubes. As expected, this correction
becomes smaller as T T, due to decreasing bulk-
meniscus curvature. As a mild check on our correction,
we plot the average corrected hydroxylated capillary pa-
rameter versus reduced temperature, t = (T —T, )/T, with
T and T, in K, as solid symbols in Fig. 2 for the two sam-
ple cells studied. The error bars represent both statistical
variation from values at diff'erent positions through the
bulk meniscus and variation in x. Based on the capillary-
rise formula, the predicted behavior is a =ao r
~
"
with9 p —p =0 935+.0.015. We find p —p =0.943
+ 0.010 and a0 =50+ 1 mm and include this fit in Fig.
2 for both data sets. We observe the correlation
X0.134,0.188 + x0.300,0.134 + X0.188,0.300 at all temperatures in
both sample cells; this indicates an unknown systematic
error and is reAected in the indicated uncertainties.
In each of the two sample cells there were three silylat-
ed capillaries with identical radii, 0.188 mm, in addition
to the hydroxylated capillaries discussed above. All capil-
laries were cleaned together according to the procedures
described in DF. Degrees of silylation were varied, as in
DF, by length of exposure to hexamethyldisilazane vapor
at 2.4 mm Hg.
After liquid equilibration, the capillary rises were mea-
sured with a cathetometer at four diferent positions of the
tubes through the bulk meniscus. By "equilibration" we
mean allowing the temperature to stabilize while mixing
the liquids, giving the liquids a final thorough mixing,
then waiting for the upper and lower phases to become en-
tirely clear. As in DF, the capillaries were raised so that
the silylated tubes, being partially wet by the lower (C*)
G
G I
/o
log ) g[T —T jT ]
FIG. 2. Corrected capillary parameter vs reduced tempera-
ture. The correction eliminates systematic error due to bulk-
mensicus mislocation. From top to bottom, the HMDS expo-
sures were 573, 227, 2733, 573, and 227 h at 2.4 mm Hg.
Vertical-axis tick marks indicate successive decades.
CONTINUED EXPLORATION OF THE WE'l lING PHASE DIAGRAM 7309
phase, had receding menisci. ' Consequently, the hy-
droxylated tubes, being completely wet by the upper (N )
phase, had advancing menisci; however, we measure the
hydroxylated rises to be identical for advancing and reced-
ing menisci. No systematic dependence of rise on position
indicates that the capillary tube surface chemistry was
uniform over its length.
A possible source of systematic error that must be noted
is an aging effect in which the silylated surface is attacked
by the liquid mixture. As pointed out in DF, the HMDS
silyl coatings can be entirely removed by our liquids, given
sufficient time. To minimize this effect, all data presented
here were taken within a 16-h period. Also, data for the
first sample cell were taken at a monotonically decreasing
sequence of temperatures; data for the second were taken
at a monotonically increasing sequence of temperatures.
No difference is seen in the resulting data sets. We feel
that negligible error was introduced by this aging effect
for two other reasons. In DF data were obtained on in-
completely wet silylated substrates by similar manner
which gave an understandable power law without notice-
able systematic error. Secondly, no position dependence
of capillary rise was observed to develop during the exper-
iment (as might be expected from different parts of the
tube being exposed to different liquid composition as it is
raised and held through the bulk meniscus). We believe,
however, that the next generation of experiments on
chemically altered substrates must squarely face this is-
sue.
227 h. (Data from a 419-h silylated capillary are omitted
due to their unusually large random scatter. This tube
was prepared identically with others; we speculate that a
piece of Tefion became lodged in the tube during insertion
into the holder. ) The lower data set shows tubes exposed
to HMDS for 2733, 573, and 227 h. The data of Fig. 2
share many features with the preliminary data of Fig. 1;
the main difference being that now we can compute the
contact angle and make statements about the state of dry-
ing.
All silylated tubes remain incompletely dry at the tem-
peratures studied. This assertion may be questioned for
the most heavily silylated capillary of the lower data set
because its error bars strongly overlap those of the hy-
droxylated capillaries as T T, . All others are definitely
incompletely dry either because there is no such overlap or
because there is a silylated capillary in the same sample
cell which shows a greater rise. In Fig. 3 we present the
contact angles for both the upper and lower data sets
(solid and open symbols, respectively). This is the most
informative way of presenting our data; unfortunately,
however, it magnifies the error bars, especially near T,
where the rises are small.
The temperature dependence of the incompletely dry
state is different from that of the incompletely wet state
reported in DF. There we observe that the incompletely
wet rise is proportional to ) t ~ ', or equivalently cos8
RESULTS
The bulk-meniscus correction was applied and the re-
sults are shown in Fig. 2. Frror bars for silylated tubes
are again comparable to the hydroxylated error bars. The
upper data set shows tubes exposed to HMDS for 573 and
0.8
a 0.6
u 0.4
0.2
—16
T —Tc in K
FIG. 3. Contact angle vs temperature computed from the
corrected capillary parameter data of Fig. 2. Note that capil-
laries appear incompletely dry at all temperatures studied and
cannot be described by a power law with exponent P& —p
(dashed curves). Indicated uncertainties are typical for all data.
FIG. 4. Wetting phase diagram of Ebner and Saam. W is the
locus of first-order transition to complete wetting (by "liquid",
e.g. , N ), D is the locus of continuous drying transitions (i.e., to
complete wetting by "vapor", e.g. C*). They meet as the so-
called ordinary point O. PD is the locus of first-order partial-
drying transitions. This is for the case of negative surface
enhancement and a weak long-range force which favors the wet-
ting phase N independently of the short-range force h &. Tra-
jectory 1 is for hydroxylated capillaries which are completely
wet at all temperatures studied. Trajectories 2 and 3 summarize
possible predicted behavior of the heavily silylated capillaries of
this report.
7310 DOUGLAS J. DURIAN AND CARL FRANCK
a:
i t )
' ", as predicted from short-range force scaling ar-
guments. The two examples of this power law, included as
dashed lines in Fig. 3, clearly show that the temperature
dependence of the incompletely dry state is not of this
form. If a long-range substrate attraction to N* is indeed
responsible for preventing a drying transition below T,
then the expected behavior is as follows. The free energy
per unit area to have the P phase at infinity with a layer of
the a phase, I, thick, adjacent to the wall is
crttw =cr,w+cr tt+&V(i, ), where AV(l, ) is the work done
by the long-range force in attracting the a-P interface
from infinity to I . If the long-range force can be modeled
by a contribution to the free-energy density of—hLtt(z)m(z), where hLR(z) =A/z and m(z) is the
bulk order parameter at distance z from the wall, then
d V(l, ) a:(m, mit)l, ' "—. According to Nightingale and
Indekeu, the long-range force will thin the drying layer
to thickness I = g at which the attraction is balanced by
the repulsion due to the interface fluctuations; ( is the
bulk correlation length. The predicted temperature
dependence of the state of partial drying for this case is
therefore
It is, in principle, possible to test this formula by
capillary-rise experiments. However, the large uncertain-
ty in our data prevents quantitative comparison. It should
be noted that Fig. 3 is consistent with the prediction
cos0 1 as T T„whereas the data of AWF on related
substrates are not.
A qualitative trend suggested by both Figs. 2 and 3 is
that there is a difference in the temperature dependence
near and far from T, . Our data are consistent with there
being either a discontinuity in slope or a rounding between
these two regions. A discontinuity would be interpreted as
the "partial drying" transition of Ebner and Saam in
which the partial-drying layer thickness jumps discontinu-
ously. This case corresponds to trajectory 3 of our repro-
duction of Ebner and Saam's wetting phase diagram, Fig.
4. A rounding would be interpreted as corresponding to
trajectory 2, which does not intersect the partial-drying
transition line. Stable surfaces are needed to obtain
enough data in the region of interest if the existence of the
partial-drying transition is to be addressed further by the
capillary rise method.
CONCLUSIONS
Heavily silylated capillary tubes have been produced
and used in experiments which are the first to confidently
explore a new region of the wetting phase diagram. The
capillaries remain incompletely dry at all temperatures
studied but do not have temperature dependences arising
from weak short-range force scaling only, as was seen in
DF for incomplete wetting. In contrast with the work of
AWF, our data are consistent with there being complete
drying only at T, . We notice a possible discontinuity in
the slope of capillary rise versus temperature. This is the
first experimental evidence of the "partial-drying" transi-
tion predicted by Ebner and Saam for the case of short-
range substrate-liquid attraction weakly opposed by a
long-range force.
ACKNOWLEDGMENTS
We have benefited from discussions with B. Widom and
W. F. Saam. This work was supported by the National
Science Foundation through the Materials Science Center
at Cornell University and under Low Temperature Phys-
ics Program Grant No. DMR-86-11350.
tD. J. Durian and C. Franck, Phys. Rev. Lett. 59, 555 (1987).
K. Abeysuriya, X.-1. Wu, and C. Franck, Phys. Rev. B 35, 6771
(1987).
E. S. R. Gopal, R. Ramachandra, P. Chandra Sekhar,
K. Govindarajan, and S. V. Subramanyam, Phys. Rev. Lett.
32, 284 (1974), find that p, 0.6014~0.0004 volume frac-
tion CS2 and T, (61.982+' 0.005)'C are the critical compo-
sition and temperature.
4J. L. Tveekrem and D. T. Jacobs, Phys. Rev. A 27, 2773
(1983).
5See Ref. 2 for discussion of these points.
6M. P. Nightingale and J. O. Indekeu, Phys. Rev. B 32, 3364
(1985).
7C. Ebner and W. F. Saam, Phys. Rev. Lett. 58, 587 (1987);
Phys. Rev. B 35, 1822 (1987).
sSee, for example, A. W. Adamson, Physical Chemistry of Sur
faces (Wiley, New York, 1982)
9See, e.g. , J. S. Rowlinson and B. Widom, Molecular Theory of
Capillarity (Clarendon, Oxford, 1982), p. 265, for values of
bulk critical exponents.
As recommended by W. A. Zisman, in Contact Angle, 8'etta-
bility, and Adhesionedited by, F. M. Fowkes (American
Chemical Society, Washington, DC, 1964), p.8.


Continued Exploration of the Wetting Phase Diagram

ScholarlyCommons@Penn

University of PennsylvaniaScholarlyCommonsDepartment of Physics Papers Department of Physics11-1-1987Continued Exploration of the Wetting PhaseDiagramDouglas J. DurianUniversity of Pennsylvania, djdurian@physics.upenn.eduCarl FranckCornell UniversityFollow this and additional works at: https://repository.upenn.edu/physics_papersPart of the Physics CommonsAt the time of publication, author Douglas J. Durian was affiliated with Cornell University. Currently, he is a faculty member at the Physics Departmentat the University of Pennsylvania.This paper is posted at ScholarlyCommons. https://repository.upenn.edu/physics_papers/638For more information, please contact repository@pobox.upenn.edu.Recommended CitationDurian, D. J., & Franck, C. (1987). Continued Exploration of the Wetting Phase Diagram. Physical Review B, 36 (13), 7307-7310.http://dx.doi.org/10.1103/PhysRevB.36.7307Continued Exploration of the Wetting Phase DiagramAbstractMeasurements are presented of the state of wetting of a binary liquid mixture on heavily silylated glass, whichare believed to probe a new region of the wetting phase diagram. We find unusual temperature dependenceand the first experimental evidence of a possible "partial drying" transition recently predicted by Ebner andSaam for the case of strong short-range substrate-liquid forces opposed by a weak long-range force.DisciplinesPhysical Sciences and Mathematics | PhysicsCommentsAt the time of publication, author Douglas J. Durian was affiliated with Cornell University. Currently, he is afaculty member at the Physics Department at the University of Pennsylvania.This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/638PHYSICAL REVIEW B VOLUME 36, NUMBER 13Continued exploration of the wetting phase diagram1 NOVEMBER 1987Douglas J. Durian and Carl FranckLaboratory of Atomic and Solid State Physics and Materials Science Center,Cornell University, Ithaca, New York 14853-2501(Received 11 August 1987)Measurements are presented of the state of wetting of a binary liquid mixture on heavilysilylated glass, which are believed to probe a new region of the wetting phase diagram. We findunusual temperature dependence and the first experimental evidence of a possible "partial drying"transition recently predicted by Ebner and Saam for the case of strong short-range substrate-liquid forces opposed by a weak long-range force.INTRODUCTIONIn a recent paper by Durian and Franck' (DF), we re-port capillary-rise measurements of the state of wetting ofthe carbon disulfide+nitromethane binary liquid mixtureat coexistence on chemically altered borosilicate glass sub-strates. We find that hydroxylated substrates are alwayscompletely wet by the nitromethane-rich (N ) phase;capillaries lightly silylated with hexamethyldisilazane(HMDS) are less attractive to N* and exhibit a transitionfrom partial to complete wetting, by N*, as the tempera-ture is increased toward the liquid-liquid critical demixingpoint T, . In the course of the experiment several sub-strates were produced with such heavy silylation as to be-come attractive to the carbon disulfide-rich (C*) phase.These substrates gave data with unusual temperaturedependence but were not included in DF because of unac-ceptable errors arising from bulk-meniscus mislocation.In this report we present data on similar heavily silylatedcapillaries which have been corrected for this systematicerror. It should be noted that Abeysuriya, Wu, andFranck (AWF) have published observations for similarsubstrates; however, improved sample-preparation tech-nique permits great enough precision that previously un-noticed features are now observed.aff'ected. 5 If this is true, our heavily silylated substratescan be used to test the theoretical predictions ofNightingale and Indekeu, and Ebner and Saam for thewetting behavior of surfaces with a short-range forceweakly opposed by a long-range force. The predictionsare, briefly, that complete drying will occur continuouslyat T„and that if the short-range surface field h~is strongenough there will be a "partial drying" transition betweentwo states of incomplete drying. We follow Ebner andSaam in referring to wetting by N* as "wetting, " andwetting by C* as "drying. "PROCEDUREAll sample cells used were similar to those of AWF andDF. They were filled in an Ar atmosphere to have0.601 ~ 0.01S volume fraction carbon disulfide, approxi-mately the critical composition. The initial critical tem-peratures were within T, =(63.052 ~0.011) C and werefound to drift, typically, by +5 mK/day. The positivedrift and T, )T, indicate increasing presence of impuri-ties which are preferentially dissolved in one of the twoliquid phases.The starting point of the work to be reported here is thedata shown in Fig. 1 for heavily silylated tubes with a netattraction to the opposite phase from the hydroxylatedcontrol. It is believed that hydroxylated surfaces produceboth short-range and long-range forces attractive to N*.Furthermore, one can hypothesize that by changing theglass surface chemistry only the short-range force isIC30—2.5 —2.0 —1.0log~o[T —T/T ]FIG. 1. Preliminary capillary parameter (rise times inner ra-dius) vs reduced temperature. In each of the three data sets(displaced vertically for clarity) the solid symbols representcompletely wet, hydroxylated, capillaries. The open symbols,having error bars comparable to the hydroxylated data,represent heavily silylated capillaries which are incompletelydry. From top to bottom, the HMDS exposures were 48 h at 8mm Hg, then 67, 707, 226, and 130 h at 2.4 mm Hg. Vertical-axis tick marks indicate successive decades.7307 Oc 1987 The American Physical Society7308 DOUGLAS J. DURIAN AND CARL FRANCK(r;+x;, )a;=(r, + ; x)a,J. (2)The correction x =&x; j) is then added to the measuredThree sets of preliminary data are shown in Fig. 1. Theopen symbols denote the capillary parameter (rise timesinner radius) of heavily silylated capillaries; the solid sym-bols (fit by power law) denote the absolute capillary pa-rameter of completely wet hydroxylated capillaries. Allcapillaries have identical radii, 0.188 mm. The capillary-rise formula,2 (x~pa = cosO,~pgpredicts that the capillary parameter will have the same(maximum) magnitude for both complete wetting,cosO= —1, and complete drying, cosO=1. Here a is thecapillary parameter, a,& is the interfacial surface tension,hp is the liquid-liquid mass density difference, g is thegravitational accelation, and O is the contact angle coex-isting liquid phases made with the substrate. Equation(1) is valid only for rise much greater than radius; thiscondition is satisfied by all observations presented in thisreport. Note that large systematic errors are present inthese data: The silylated capillary of the middle data setin Fig. 1 attains a rise near T, greater than the depressionof the completely wet hydroxylated capillary. This behav-ior corresponds to cosO& 1 and is unphysical; our ex-planation is that mislocation of the bulk meniscus is re-sponsible. Nevertheless, the following statements can bemade with certainty. Far from T, all silylated capillariesare incompletely dry. Even near T, the two least heavilysilylated capillaries of the bottom data set are incomplete-ly dry because their rises are less than that of the mostheavily silylated capillary in the sample cell. All datashow evidence of a possible discontinuity in slope whichcould be interpreted as either a first-order drying transi-tion or a partial-drying transition. To determine which,we need to understand and eliminate the bulk-meniscuslocation error in further experiments; this we now present.Due to the curvature of the bulk meniscus at the samplecell walls and around the capillary tubes, it is not possibleto measure capillary rise relative to the bulk without sys-tematic error. This is especially troublesome for heavilysilylated capillaries because their menisci lie on the oppo-site side of the bulk meniscus thereby preventing directcomparison with the completely wet hydroxylated control.In particular, there is little systematic error in calculatingthe contact angle by cos8=(silylated rise)/(hydroxylatedrise) for lightly silylated tubes near complete wetting, butthere would be an unacceptably large error in doing thesame for heavily silylated capillaries near complete drying(as we have just seen in Fig. I).We attempt to eliminate the bulk-meniscus location er-ror by using data from three hydroxylated capillaries ofdiA'erent inner radii (0.134, 0.188, and 0.300 mm) to esti-mate the eA'ective position of the bulk meniscus. To dothis, we rely on the property that capillary rise is inverselyproportional to radius. For each position of the capillariesthrough the bulk meniscus, we measure the rise rk in thehydroxylated tubes, radii ak, and for each distinct paircompute x; J such thatrises of all capillary tubes. As expected, this correctionbecomes smaller as T T, due to decreasing bulk-meniscus curvature. As a mild check on our correction,we plot the average corrected hydroxylated capillary pa-rameter versus reduced temperature, t = (T —T, )/T, withT and T, in K, as solid symbols in Fig. 2 for the two sam-ple cells studied. The error bars represent both statisticalvariation from values at diff'erent positions through thebulk meniscus and variation in x. Based on the capillary-rise formula, the predicted behavior is a =ao r~"with9 p —p =0 935+.0.015. We find p —p =0.943+ 0.010 and a0 =50+ 1 mm and include this fit in Fig.2 for both data sets. We observe the correlationX0.134,0.188 + x0.300,0.134 + X0.188,0.300 at all temperatures inboth sample cells; this indicates an unknown systematicerror and is reAected in the indicated uncertainties.In each of the two sample cells there were three silylat-ed capillaries with identical radii, 0.188 mm, in additionto the hydroxylated capillaries discussed above. All capil-laries were cleaned together according to the proceduresdescribed in DF. Degrees of silylation were varied, as inDF, by length of exposure to hexamethyldisilazane vaporat 2.4 mm Hg.After liquid equilibration, the capillary rises were mea-sured with a cathetometer at four diferent positions of thetubes through the bulk meniscus. By "equilibration" wemean allowing the temperature to stabilize while mixingthe liquids, giving the liquids a final thorough mixing,then waiting for the upper and lower phases to become en-tirely clear. As in DF, the capillaries were raised so thatthe silylated tubes, being partially wet by the lower (C*)GG I/olog ) g[T —T jT ]FIG. 2. Corrected capillary parameter vs reduced tempera-ture. The correction eliminates systematic error due to bulk-mensicus mislocation. From top to bottom, the HMDS expo-sures were 573, 227, 2733, 573, and 227 h at 2.4 mm Hg.Vertical-axis tick marks indicate successive decades.CONTINUED EXPLORATION OF THE WE'l lING PHASE DIAGRAM 7309phase, had receding menisci. ' Consequently, the hy-droxylated tubes, being completely wet by the upper (N )phase, had advancing menisci; however, we measure thehydroxylated rises to be identical for advancing and reced-ing menisci. No systematic dependence of rise on positionindicates that the capillary tube surface chemistry wasuniform over its length.A possible source of systematic error that must be notedis an aging effect in which the silylated surface is attackedby the liquid mixture. As pointed out in DF, the HMDSsilyl coatings can be entirely removed by our liquids, givensufficient time. To minimize this effect, all data presentedhere were taken within a 16-h period. Also, data for thefirst sample cell were taken at a monotonically decreasingsequence of temperatures; data for the second were takenat a monotonically increasing sequence of temperatures.No difference is seen in the resulting data sets. We feelthat negligible error was introduced by this aging effectfor two other reasons. In DF data were obtained on in-completely wet silylated substrates by similar mannerwhich gave an understandable power law without notice-able systematic error. Secondly, no position dependenceof capillary rise was observed to develop during the exper-iment (as might be expected from different parts of thetube being exposed to different liquid composition as it israised and held through the bulk meniscus). We believe,however, that the next generation of experiments onchemically altered substrates must squarely face this is-sue.227 h. (Data from a 419-h silylated capillary are omitteddue to their unusually large random scatter. This tubewas prepared identically with others; we speculate that apiece of Tefion became lodged in the tube during insertioninto the holder. ) The lower data set shows tubes exposedto HMDS for 2733, 573, and 227 h. The data of Fig. 2share many features with the preliminary data of Fig. 1;the main difference being that now we can compute thecontact angle and make statements about the state of dry-ing.All silylated tubes remain incompletely dry at the tem-peratures studied. This assertion may be questioned forthe most heavily silylated capillary of the lower data setbecause its error bars strongly overlap those of the hy-droxylated capillaries as T T, . All others are definitelyincompletely dry either because there is no such overlap orbecause there is a silylated capillary in the same samplecell which shows a greater rise. In Fig. 3 we present thecontact angles for both the upper and lower data sets(solid and open symbols, respectively). This is the mostinformative way of presenting our data; unfortunately,however, it magnifies the error bars, especially near T,where the rises are small.The temperature dependence of the incompletely drystate is different from that of the incompletely wet statereported in DF. There we observe that the incompletelywet rise is proportional to ) t ~ ', or equivalently cos8RESULTSThe bulk-meniscus correction was applied and the re-sults are shown in Fig. 2. Frror bars for silylated tubesare again comparable to the hydroxylated error bars. Theupper data set shows tubes exposed to HMDS for 573 and0.8a 0.6u 0.40.2—16T —Tc in KFIG. 3. Contact angle vs temperature computed from thecorrected capillary parameter data of Fig. 2. Note that capil-laries appear incompletely dry at all temperatures studied andcannot be described by a power law with exponent P& —p(dashed curves). Indicated uncertainties are typical for all data.FIG. 4. Wetting phase diagram of Ebner and Saam. W is thelocus of first-order transition to complete wetting (by "liquid",e.g. , N ), D is the locus of continuous drying transitions (i.e., tocomplete wetting by "vapor", e.g. C*). They meet as the so-called ordinary point O. PD is the locus of first-order partial-drying transitions. This is for the case of negative surfaceenhancement and a weak long-range force which favors the wet-ting phase N independently of the short-range force h &. Tra-jectory 1 is for hydroxylated capillaries which are completelywet at all temperatures studied. Trajectories 2 and 3 summarizepossible predicted behavior of the heavily silylated capillaries ofthis report.7310 DOUGLAS J. DURIAN AND CARL FRANCKa:i t )' ", as predicted from short-range force scaling ar-guments. The two examples of this power law, included asdashed lines in Fig. 3, clearly show that the temperaturedependence of the incompletely dry state is not of thisform. If a long-range substrate attraction to N* is indeedresponsible for preventing a drying transition below T,then the expected behavior is as follows. The free energyper unit area to have the P phase at infinity with a layer ofthe a phase, I, thick, adjacent to the wall iscrttw =cr,w+cr tt+&V(i, ), where AV(l, ) is the work doneby the long-range force in attracting the a-P interfacefrom infinity to I . If the long-range force can be modeledby a contribution to the free-energy density of—hLtt(z)m(z), where hLR(z) =A/z and m(z) is thebulk order parameter at distance z from the wall, thend V(l, ) a:(m, mit)l, ' "—. According to Nightingale andIndekeu, the long-range force will thin the drying layerto thickness I = g at which the attraction is balanced bythe repulsion due to the interface fluctuations; ( is thebulk correlation length. The predicted temperaturedependence of the state of partial drying for this case isthereforeIt is, in principle, possible to test this formula bycapillary-rise experiments. However, the large uncertain-ty in our data prevents quantitative comparison. It shouldbe noted that Fig. 3 is consistent with the predictioncos0 1 as T T„whereas the data of AWF on relatedsubstrates are not.A qualitative trend suggested by both Figs. 2 and 3 isthat there is a difference in the temperature dependencenear and far from T, . Our data are consistent with therebeing either a discontinuity in slope or a rounding betweenthese two regions. A discontinuity would be interpreted asthe "partial drying" transition of Ebner and Saam inwhich the partial-drying layer thickness jumps discontinu-ously. This case corresponds to trajectory 3 of our repro-duction of Ebner and Saam's wetting phase diagram, Fig.4. A rounding would be interpreted as corresponding totrajectory 2, which does not intersect the partial-dryingtransition line. Stable surfaces are needed to obtainenough data in the region of interest if the existence of thepartial-drying transition is to be addressed further by thecapillary rise method.CONCLUSIONSHeavily silylated capillary tubes have been producedand used in experiments which are the first to confidentlyexplore a new region of the wetting phase diagram. Thecapillaries remain incompletely dry at all temperaturesstudied but do not have temperature dependences arisingfrom weak short-range force scaling only, as was seen inDF for incomplete wetting. In contrast with the work ofAWF, our data are consistent with there being completedrying only at T, . We notice a possible discontinuity inthe slope of capillary rise versus temperature. This is thefirst experimental evidence of the "partial-drying" transi-tion predicted by Ebner and Saam for the case of short-range substrate-liquid attraction weakly opposed by along-range force.ACKNOWLEDGMENTSWe have benefited from discussions with B. Widom andW. F. Saam. This work was supported by the NationalScience Foundation through the Materials Science Centerat Cornell University and under Low Temperature Phys-ics Program Grant No. DMR-86-11350.tD. J. Durian and C. Franck, Phys. Rev. Lett. 59, 555 (1987).K. Abeysuriya, X.-1. Wu, and C. Franck, Phys. Rev. B 35, 6771(1987).E. S. R. Gopal, R. Ramachandra, P. Chandra Sekhar,K. Govindarajan, and S. V. Subramanyam, Phys. Rev. Lett.32, 284 (1974), find that p, 0.6014~0.0004 volume frac-tion CS2 and T, (61.982+' 0.005)'C are the critical compo-sition and temperature.4J. L. Tveekrem and D. T. Jacobs, Phys. Rev. A 27, 2773(1983).5See Ref. 2 for discussion of these points.6M. P. Nightingale and J. O. Indekeu, Phys. Rev. B 32, 3364(1985).7C. Ebner and W. F. Saam, Phys. Rev. Lett. 58, 587 (1987);Phys. Rev. B 35, 1822 (1987).sSee, for example, A. W. Adamson, Physical Chemistry of Surfaces (Wiley, New York, 1982)9See, e.g. , J. S. Rowlinson and B. Widom, Molecular Theory ofCapillarity (Clarendon, Oxford, 1982), p. 265, for values ofbulk critical exponents.As recommended by W. A. Zisman, in Contact Angle, 8'etta-bility, and Adhesionedited by, F. M. Fowkes (AmericanChemical Society, Washington, DC, 1964), p.8.

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Continued Exploration of the Wetting Phase Diagram

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