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HAL Id: jpa-00209517

https://hal.archives-ouvertes.fr/jpa-00209517

Submitted on 1 Jan 1982

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Two-dimensional films of discotic molecules at an air-water interface

F. Rondelez, D. Koppel, B.K. Sadashiva

To cite this version:

F. Rondelez, D. Koppel, B.K. Sadashiva. Two-dimensional films of discotic molecules at an air-water interface. Journal de Physique, 1982, 43 (9), pp.1371-1377. �10.1051/jphys:019820043090137100�.

�jpa-00209517�

(2)

Two-dimensional films of discotic molecules

at an

air-water interface

F. Rondelez, D.

Koppel

Laboratoire de Physique de la Matière Condensée, Collège de France, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France

and B. K. Sadashiva

Raman Research Institute - Bangalore, 560080 India

(Reçu le 11 mars 1982, accepté le 30 avril 1982)

Résumé. 2014 On montre pour la première fois que des molécules discotiques de benzène-hexa-alkanoates peuvent être étalées en monocouches à un interface eau-air. Les mesures de pression superficielles donnent des résultats

très analogues à ceux des films d’acides gras. Le noyau benzénique joue le rôle de la tête polaire grâce à six groupes

carboxyliques périphériques, et se met à plat sur l’interface. Les chaines alkanoates jouent le rôle des chaines aliphatiques. Les isothermes de pression permettent une estimation des dimensions moléculaires dans le plan de

l’interface. Ces dimensions sont pratiquement identiques à celles déduites des mesures de rayons X dans les phases

à colonnes formées par les benzène-hexa-alkanoates (cristaux liquides thermotropes). Ces expériences permettent de réfuter l’interprétation de la transition liquide expansé-liquide condensé comme une transition du second ordre

entre une phase isotrope et une phase cristal liquide nématique.

Abstract. 2014 The possibility of forming Langmuir monolayers with disc-like molecules of benzene-hexa-alkanoates has been investigated for the first time. Surface pressure measurements show that these monolayers behave in

many respects as the well-known films of fatty acids. The benzene ring plays the role of the polar head group while the alkanoates chains are the long aliphatic tails. Molecular dimensions can be derived from the surface pressure- concentration isotherms. The results indicate that the benzene rings lie flat at the interface. The projection of the

molecular diameter onto the interface is practically identical to the lattice spacing measured in the liquid-crystalline

columnar mesophases formed by benzene-hexa-alkanoates in bulk. These experiments allow to refute the inter- pretation of the liquid expanded-liquid condensed transition in terms of a second order isotropic ~ nematic phase transition, as recently proposed by several theoretical groups.

Classification

Physics Abstracts

68.15 - 64.70J - 61.30E

1.

Introduction. - Soaps

and

phospholipids

are

classical

examples

of

amphiphilic

molecules. Their molecular structure is

composed

of a

hydrophobic hydrocarbon

chain tail and of a

hydrophilic polar

head. As a consequence of this dual character,

they generally

lie at the interfaces of emulsions or foams,

forming

a

large variety

of structures : lamellar, hexa-

gonal,

etc...

[1].

The numerous molecules

forming thermotropic liquid crystalline phases

compose a

much less known class of

amphiphilic

molecules. It is clear however that the formation of smectic

phases

for instance is due to the

partial segregation

of the

aliphatic

flexible chains from the

rigid

aromatic cores.

To the best of our

knowledge,

there have been few attempts to check if such

compounds

could also be used as surfactants in aqueous solutions since

they

have no

prominent

water-soluble group. There is

only

one report

by

Dbrfler et al.

[2],

in which calamitic

(rod-

like)

molecules of 4-4’

azoxy-a-methyl

cinnamate,

forming

nematic

liquid crystalline phase

in bulk, have

been

spread in.monolayers

at an air-water interface.

Such observations are however very

interesting

since

they

could lead the way to the

discovery

of two-

dimensional nematic films with

quasi long

range orien-

tational order of the

long

molecular axes. This

possi- bility

is not ruled out

by theory

as first shown

by

de

Gennes as

early

as 1971

[3].

In this paper, we show for the first time that the discotic class of

thermotropic liquid crystalline

mate-

rials can also be

spread

as

Langmuir monolayers.

Preliminary

results are

presented

on the benzene- hexa-alkanoates molecules which possess six

aliphatic

chains attached to a central benzene group. From surface pressure measurements, the benzene

rings

are

observed to lie flat on the water due to the pressure of six

carboxyl water-attracting

groups. The

aliphatic

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043090137100

(3)

1372

chains are also, at least

partially, parallel

to the inter-

face but

they

do not

adopt

a

fully

extended

configura-

tion. The results will be

compared

with the average molecular diameters deduced from X-rays lattice

spacing

measurements in the columnar bulk

liquid crystalline phases.

2.

Experimental.

- Surface pressures were measur-

ed both

by

the

Wilhelmy hanging plate technique

and

by

the movable barrier method

[4].

The two methods

are indeed

complementary.

In the former, the total sur-

face area is fixed and the

amphiphilic

molecules are

added as

drops

of solution in a volative solvent until the

spreading

is no

longer

effective. In the latter, a fixed

number of

drops

is

spread

at the

beginning

of the

experiment

and the surface area of the

trough

is then

continuously

decreased up to the

collapse point

of the

monolayer.

2.1 WILHELMY PLATE METHOD. - The force trans-

ducer was a Hewlett-Packard 8805-B pressure

ampli-

fier. The system was calibrated with

precisely

known

weights.

The output

voltage

was

adjusted

so that 10 mV

corresponded

to 1.0 x 10-4 N m -1. The quartz

glass

cuvette

containing

the water

subphase

had a surface of

29.6 x 10-4 m2. It was

totally

enclosed in a massive,

temperature-controlled,

oven in which water from a

Haake F3-thermostat was

constantly circulating.

The temperature was varied between 4 OC and 60°C. The set temperature was constant to within ± 0.1 °C. This

was a necessary step since the

Wilhelmy technique

cannot compensate for the temperature variation of the surface tension of pure water

against

air. This

variation can indeed be

large, typically

1.5 x 10-4 N m - I OC - 1

[5].

The total drift

during

the course

of an

experiment,

after

allowing

for thermal

equili-

bration, was less than 0.4 x 10-4 N m-1.

2.2 MOVABLE BARRIER METHOD. - A commercial Lauda film balance was used. All

experiments

were

performed

at room temperature, T = 21 ± 5°C. A

rigorous

temperature control was not

employed

because the film balance

directly

measures the diffe-

rence between the surface pressure of pure water and that of the

monolayer.

Therefore thermal fluctuations in the water surface pressure are

automatically

can-

celled out The maximum drift was observed to be about 10- 5 N m - 1 per minute. The

speed

at which the

barrier was moved was 0.25 x 10- 2

m/min.

This

corresponds

to an average percentage variation in the total

monolayer

surface of 1-3

%, sufficiently

low to

always

allow for mechanical

equilibration

of the

monolayer,

while still

being compatible

with the

experi-

mental drift

during

the

measuring

time. The duration

of one

single

run was about one hour. The surface

pressure was monitored both upon

compression

and

expansion

to check for

possible hysteresis

effect.

2. 3 CHEMICALS. - The

synthesis

of the benzene- hexa-alkonates (BH for

short)

has

already

been des-

cribed elsewhere

[6, 7].

Five successive

homologs

were studied

starting

from n-pentanoate up to n-decanoate.

Small

quantities

(~ 10-3

g)

were

weighted

on a

Cahn electrobalance to an accuracy of 10-6 g and dissolved in 20 ml of

methylene

dichloride (Merck- spectro

grade).

This solvent had been checked pre-

viously

to be a

good spreading

solvent, non miscible

with water and

highly

volatile, and also to contain

only insignificant

fractions of surface-active

impuri-

ties

[8].

The surface pressure increase when pure solvent

was added and let evaporate was less than 5 x

10-6 N m-1 after 10

drops. (Up

to 60

drops

could be

added for a

complete experiment

with the

Wilhelmy plate

and up to 300

drops

with the Lauda

balance.)

3. Results. - For all

compounds,

the surface pres-

sure measurements have been

performed

at several

Fig. 1. 2013 Surface pressure isotherms of benzene-hexa-n- pentanoate (BH-5) using either Wilhelmy hanging plate or

movable barrier (Lauda) methods. Substrate is pure water.

temperatures between 5 and 60 OC

using

the

hanging plate,

and at room temperature,

using

the movable

barrier

techniques. Typical

results are shown on

figures

1 and 2 for

benzene-hexa-n-pentanoate (BH-5)

and on

figures

3 and 4 for benzene-hexa-n-nonanoate

(BH-9).

The curves obtained in these two

examples

are

somewhat different.

1)

For the lower

homolog,

the pressure 7c increases

regularly

when concentration C is increased

(Wilhelmy method)

or when film surface A is decreased

(Lauda balance).

At

relatively large

pressure values,

typically

between 6 x 10-3 N m -1 and 8 x 10-3 N m -1

depending

on temperature, there is a sudden

change

of

slope.

The

corresponding

concentration will be called

Ckink in

the

following.

Above

Ck;nk,

the 7T-C or n-A curves become

nearly

parallel

to the abscissa axis. This

region

of

slight

(4)

Fig. 2. - Continuously recorded surface pressure isotherms of benzene-hexa-n-pentanoate (BH-5). The monolayer is

first compressed (decreasing areas per molecule), then re- expanded (increasing areas). The data points have also

been reported in figure 1 for comparison with the Wilhelmy technique.

upward slope

has

only

a limited width.

Finally

the

slope

is observed to re-increase

sharply

until a state of

saturation is reached in the film. This saturation occurs

for different surface pressures values

according

to the

technique

of

investigation.

With the

hanging plate technique,

where

drops

are

successively deposited

onto a fixed surface area, the maximum surface pres-

sure attainable

corresponds

to the

equilibrium spread-

Fig. 3. - Surface pressure isotherms of benzene-hexa-n- nonanoate (BH-9) usmg Wilhelmy hanging plate technique.

Substrate is pure water.

Fig. 4. - Continuously recorded surface pressure isotherms of benzene-hexa-n-nonanoate (BH-9). The monolayer is

first compressed (decreasing areas per molecule), then re-expanded (increasing areas).

ing

pressure n,,. This is the surface pressure obtained when the

monolayer

is in

equilibrium

with the stable bulk

phase. Experimentally,

as n,, is

approached,

the

time

required

for

equilibration

after

deposition

of one

further

drop

increases

drastically.

The

corresponding

surface concentration and surface area per molecule

are called

Ce and Ae respectively.

For BH-5 at room temperature, ne = 11.6 x 10- 3 N

m-1, Ce

= 1.05 x 10-3 g m-2

and Ae

= 1.20 nm2. With the movable barrier

technique,

where the film area is

continuously

reduced while the total number of molecules in the

monolayer

is

kept

constant, the maximum surface pressure attainable

corresponds

to the

collapse

pres-

sure nr. This is the

highest

surface pressure to which the

monolayer

can be

compressed

without

expulsing

molecules into the third dimension. The

corresponding

surface area and surface concentration are called

Ac

and

Cc respectively.

Above nc, three-dimensional islands start to form, and if one tries to compress the film even more, the surface pressure is

actually

observ-

ed to decrease

(Fig.

2). For BH-5 at room temperature, nc = 15.2 x 10-3 N

m-’, Ac

= 1.10 nm2 and

Cc

1.15 x 10-3 g m-2. nc is

markedly higher

than ne.

However this

gives only

little difference between

Ae and Ac

because of the large pressure

slope

in that

domain of concentrations.

Experiments

at different

compression speeds yielded

similar values of nc to within 5 %. After compression to an area per molecule less than

A, large hysteresis

was observed upon

subsequent

film

re-expansion.

On the contrary there was no detectable

hysteresis

as

long

as the film surface pressure was

kept

below 7rc.

2) For the

higher homolog,

the overall pressure increase at room temperature is much less

gradual

than

in the lower

homolog

case. In

figure

3, the data

points

at 22°C stay on the zero pressure line until a concen-

tration of 5 x 10-3 g m-2 is reached, at which

point

the pressure increases so

rapidly

that the maximum pressure ne = 2.9 x 10- 3 N m-’ is

already

reached at

(5)

1374

Table I. - Characteristic

surface

concentrations and

surface

pressures observed in the

surface

pressure isotherms

of the benzene-hexa-n-alkanoates. Ck;nk corresponds to the

surface

concentration at the onset

of

the transition

between the

liquid expanded

and the

liquid

condensed states

of

the

monolayer. Ce corresponds

to the

surface

concen-

tration at the equilibrium

surface

pressure 7r,,.

Cc

corresponds to the

surface

concentration at the collapse

surface

pressure of the

film

7r,,.

a concentration of

Ce

= 0.68 x

10-3 gM-2 .

The same

features are observed on the Lauda curves. As film surface is decreased, the pressure increases first very

slowly

then much more

rapidly

until a maximum

Pressure 7rc = 3.2 x 10- 3 N m -1 is reached. The

corresponding

surface area per molecule is

A,, =

2.67 nm2. For still lower surface areas, a decrease in pressure is observed

indicating

that a

collapse

of the

film has taken

place.

In

figure

3, the results for a much

higher

temperature of 60°C have also been

plotted. Although

the measu-

rements are less accurate at this elevated temperature,

we observe that some of the features discussed for the lower

homolog

case start. to re-appear. A kink in the

curve can be detected for a concentration

Cki-k -

0.2 x 10-3 g m - 2 . At

larger

concentrations it is followed

by

a somewhat flat

region

until a very

sharp

rise in surface pressure occurs. At this temperature the

equilibrium spreading

pressure 7r,, is found to be 6.9 x 10-3 N m-1.

Unambiguous

evidence for the reappearances of three distinct domains in the surface pressure-concen- tration

plots

when the temperature is increased is also

yielded

from measurements on the BH-8 and BH-10

homologs.

The

important

data for all the

homologs

which have

been studied in the present

investigation

are summa-

rized in table I.

4. Discussion. - All our

experimental

curves can be understood

by analogy

with the

monolayer

behaviour

of the

simpler

chain

fatty

acid substances which have been

extensively

studied in the past. It is well reco-

gnized

that such

monolayers

can take at least three characteristic film states at an air-water interface. In order of

decreasing

surface concentration,

they

are

referred as condensed

(solid

or

liquid)

films,

liquid- expanded

films and

finally

gaseous films

[4].

For a

particular

substance, all the different states may or may not be observed

depending

on the

experi-

mental conditions

(e.g. temperature).

For instance, at

room temperature,

myristic

acid shows the three

phases

while

palmitic

acid shows

only

the condensed and the gaseous

phases.

It should also been

pointed

out that

the present discussion is

oversimplified.

Indeed, much

more intricate

phase diagrams, including

mesomor-

phic

states, have been described in the literature

[9].

However this crude level of

presentation

is

quite

suf-

ficient for our present purposes.

The existence of the three

phases

is

clearly

evident in

our

monolayers

of benzene-hexa-alkanoates. From table I, it is seen that BH-5 at 5 and 21 °C, BH-6 at

5 and 21 oC, BH-8 at 40 OC, BH-9 at 40 and 60 °C and

BH-10 at 40 OC, all show

expanded-liquid

films and

condensed-liquid

films

(no

attempts to observe the

always existing

gaseous film have been made since it

corresponds

to low surface pressures and

requires

very accurate measurements

[10]).

The transition between the

liquid-expanded

and

liquid-condensed phases

is very obvious in the surface pressure isotherm

plots.

In the transition

region

the

compressibility

of the

monolayer

becomes small and there is not much of a

surface pressure

change

when surface concentration is increased (see

Fig. 1).

This transition, called the main

transition, is

generally

assumed to be first-order

although

the isotherm shows a non-zero

slope

in the

(6)

transition

region.

The fact that the main transition does not behave as an

ordinary

three-dimensional

solid-liquid phase

change has been discussed

by

many authors

[11]. Recently,

Albrecht et al.

[9]

have

suggested

that this is due to the limited size of the

cooperatively transforming

units. For

phospholipid monolayers, they

have estimated that these domains

incorporates

about 150 molecules.

Our

experimental

data show a number of cases

where the transition between a

liquid-expanded

and a

liquid-condensed

film is not observed. The pressure isotherms stay very close to the horizontal axis until the concentration reaches a certain concentration at which the curves turn

upward

almost

vertically.

Here

the gaseous films are

directly

converted to condensed

films. BH-9 at 21°C

gives

a

good example

of such a

behaviour

(Figs.

3 and 4).

We thus observe here that the range of

stability

of

the different

phases

changes in a

regular

manner with temperature. This behaviour is also encountered with

single

chain

fatty

acids materials

[4].

For a

given compound

the occurrence of a

liquid expanded phase

becomes less and less

probable

as the temperature is lowered.

Reciprocally,

at fixed temperature, the

liquid- expanded

film becomes less and less

probable

as the

chain

length

is increased from five to ten carbon atoms.

It is often found in other

compounds

that the addition

of one carbon atom to the

length

of one

aliphatic

chain shifts the curves in

nearly

the very same fashion

as a decrease of 8-10 OC in temperature. The present

experiments

corroborate

roughly

that result.

Going

from BH-7 to BH-8, it is necessary to increase the temperature from 21°C to 40 OC to re-observe the

expanded-liquid

film.

The pressure isotherms

yield

information on the conformation of the benzene alkoanoates

spread

at an

air-water interface. We will see that the present data

are

only

consistent with a model where the benzene

rings

lie flat on the water while the chain

align

more or

less

horizontally, although

not

completely.

Such a

conformation is

intuitively

evident since the presence of the six

water-attracting carboxyl

groups forces the benzene to be in direct contact with the aqueous

subphase.

On the other hand, the

aliphatic

chains have

no reason to stay close to the water. However there is a

certain chain

rigidity

which prevents the first

methy-

lene groups to stand

directly upright.

This local

rigi- dity

has been

amply

demonstrated in fluid

bilayers by

measurements of the order parameter for each seg- ment,

using

EPR

[12]

or NMR

[13]

spectroscopy. For

typical aliphatic

chains, the first five or six

methylene

groups are in a stretched

configuration.

The average molecular dimensions can be estimated from the concentration at which the film reaches its

equilibrium spreading

pressure. Indeed at

Ce

the molecules can be considered as closed

packed

and therefore the average

area per molecule

Ae

is

easily

deduced

knowing

the

molecular

weight

of the

compound

under

investigation.

The measured

Ce

for the various benzene-alkanoates have been

reported

in table I and the

corresponding

calculated

Ae

values are

given

in table II. The maximum molecular

length d,,

can then be estimated

assuming

that there is no

interpenetration

of the

aliphatic

chains

between two

adjacent

molecules. Under these condi-

tions,

simple geometric

relations shows that

d,, c!e

1.24

A e ’I’

for molecules

having

a

hexagonal shape.

The different values for

d,,

are also

given

in

table II. The

subscript

n indicates that the

d,,

values

are derived from surface pressure

experiments.

It is

true that the choice of

Ae

to calculate the

d,,

values is

somewhat

arbitrary.

The average molecular areas at the

collapse point, A, ,,

could also have been chosen.

At any rate, the

Ae and Ac

values are very close and

certainly

within the uncertainties of the

experiments.

Therefore the

dx

values are

probably

correct to better than

10 %.

A

comparison

of these values with those derived from X-ray diffraction

photographs

in the

three-dimensional columnar

mesomorphic

state is

very

interesting.

In that latter case, Chandrasekhar

et al.

[7]

have

proposed

an

aligned, liquid crystalline

Table II. - Molecular dimensions

of

the benzene-hexa-n-alkanoates as derived

from

monolayer

surface

pressure

experiments

(dft)’ from

molecular models

assuming fully

extended chains

(dm) and from

X-ray lattice spacing bulk

measurements

(dx-ray)’ Ae

and

Ac

are the areas per molecule measured at the

equilibrium surface

pressure ne and at

the collapse pressure 7r,,,,

respectively.

All data

are for

T = 21 °C.

(7)

1376

structure of stacked discs

forming

columns with an

hexagonal close-packed

arrangement. Therefore an estimate of the disc molecular diameter can be derived

directly

from measurements of the lattice

spacing.

Unfortunately,

such

dx-,a,

data are

only

available for BH-7 and BH-8

[7-14],

since for the other benzene- hexa-alkanoates the columnar

mesomorphic

state does

not exist or is

highly

metastable. A

comparison

bet-

ween dn

and

dx -,ay in

these two

existing

cases show an

amazingly good

agreement between the two sets of data

(see

columns 3 and 5 of table II). It therefore

appears that the molecules

adopt nearly

the same

conformation when

they

are

spread

as a

monolayer

at an air-water interface or when

they

are

piled

on top of each other in fluid columns.

In neither case are the

aliphatic

chains

fully

extended

as evidenced

by

a

comparison

with the molecular diameter

dm

calculated for stretched chains from mole- cular

Dreiding

models

(see

column 4 of table

II).

The

dn

values are

consistently

lower than

dm

in all cases.

Lastly,

several other conformations can be

certainly rejected.

Were the

aliphatic

chains

fully

vertical

relative to the water surface, a much lower molecular surface area would be observed. From a

space-filling

model we can estimate that it should be in the order of 95

A2, independent

of the actual chain

length.

This is

clearly

not substantiated

by

our observations which show a variation in

Ae

from 110 up to 3 30 A’. Another

possibility

would be that the benzene nucleus is forced to take an

upright position

upon

compression.

Such a conformation has been indeed observed

by

Adam on benzene derivatives with various lateral substitutions

[15].

The

projected

molecular area

occupied by

one benzene is then of the order

of 24 A2,

much too low

again

to account for our

experimental

results, even when

considering

the additional area

occupied by

each of the six

aliphatic

chains. It should

be noted that the Adam

compounds

were not hexa-

substituted with

water-attracting

groups. Therefore it was much easier for the benzene to tilt away from the aqueous

subphase.

5. Conclusions. - The present

experiments

show

that benzene-hexa-alkanoates form stable

monolayers

when

spread

at an air-water interface. The pressure isotherms exibit the well-known three states charac- teristic of

liquid-condensed, liquid-expanded

and

gaseous films

according

to surface concentrations and temperatures. Benzene-hexa-alkanoates constitute therefore a new class of surfactant materials with

properties

as well defined as the classical

single long

chain

fatty

acids or

phospholipids.

The benzene nucleus is observed to lie in direct contact with the water,

probably

because of the existence of the six

carboxyl

«

pinning points

». The

aliphatic

chains are also, at least

partially,

parallel to the water. A certain

amount of randomness does exist however, as indi-

cated from a

comparison

between the measured mole-

cular

dimensions and that of

fully

extended chains.

In the two cases where the data are available in the literature, the measured molecular diameters are in close agreement, to better than 1

A,

with the diameters measured in the

mesomorphic

bulk

liquid

state where

these disc-like molecules are stacked in columns.

The

possibility

of

forming monolayers

with mole-

cules

having thermotropic mesomorphic

states in the

bulk open

interesting perspectives

to try and demons- trate the

theoretically predicted

existence of

quasi-

nematic order in two dimensions

[3].

In that case it is

true that calamitic molecules will have to be used rather than discotic molecules. However, the present work can

give

some hints on which type of molecules will be best suitable.

Monolayers

of disc-like benzene-hexa-alkanoates may prove

important

as new systems on which to test the current ideas on two-dimensional

melting.

Their

six-fold symmetry is well

adapted

to detect the occur-

rence of the defect-mediated hexatic

phase predicted by

Nelson and

Halperin [16].

This could

perhaps

be

done

through

surface

viscosity

measurements

although

such

experiments

are

always

very delicate in mono-

layers.

Finally,

the present

experiments

do not bear out

the recent

interpretation

of the kink observed in the surface pressure isotherms in terms of a second-order

phase

transition between the

liquid-expanded

and the

liquid-condensed

states

[11].

Indeed the associated theoretical models all suppose a

gradual

orientation of the

projection

of the

aliphatic

chains in the inter- facial

plane.

Such a

liquid crystalline,

uniaxial, nematic

ordering

is

clearly

not

possible

with molecules

having

six-fold symmetry. Therefore the more classical inter-

pretation

of a first-order

phase

transition seems more relevant here,

although

a true flat transition

region

with infinite

compressibility

is not observed.

Acknowledgments.

- We thank H. Gruler for many

helpful

discussions

during

his sabbatical stay at the

College

de France. This work has been

supported

under a

joint

program

by

the C.N.R.S.

(France)

and

the C.S.I.R.

(India).

References

[1] PERSHAN, P. S., J. Physique Colloq. 40 (1979) C3-423.

[2] DÖRFLER, H. D., KERSCHER, W. and SACKMANN, H., J. Phys. Chem. (Leipzig) 251 (1972) 314.

[3] DE GENNES, P. G., Farad. Symp. 5 (1971) 16.

[4] GAINES, G. L., Insoluble monolayers at liquid-gas inter- faces (Wiley, New York) 1966.

[5] Handbook of Physics (Chemical Rubber Company), Cleveland, Ohio.

(8)

[6] CHANDRASEKHAR, S., SADASHIVA, B. K. and SURESH, K.

A., Pramana 9 (1977) 471.

[7] CHANDRASEICHAR, S., SADASHIVA, B. K., SURESH, K. A., MADHUSUDANA, N. V., KUMAR, S., SHASHIDAR, R.

and VENKATESH, G., J. Physique Colloq. 40 (1979)

C3-120.

[8] VILANOVE, R. and RONDELEZ, F., Phys. Rev. Lett. 45

(1980) 1502.

[9] ALBRECHT, O., GRULER, H. and SACKMANN, E., J.

Physique 39 (1978) 301.

[10] HAWKINS, G. A. and BENEDEK, G. B., Phys. Rev. Lett.

32 (1974) 524.

KIM, M. W. and CANNELL, D. S., Phys. Rev. A 13 (1976) 411.

[11] For a recent review, see BARET, J. F., Progress in Surf.

and Memb. Sci. ed. by D. A. Cadenhead and J. F. Danielli (Academic Press, New York) 1981, Vol. 14, p. 291.

[12] SEELIG, J., J. Am. Chem. Soc. 92 (1970) 3881; 93 (1971)

5017.

[13] CHARVOLIN, J., MANNEVILLE, P. and DELOCHE, B.,

Chem. Phys. Lett. 23 (1973) 345.

[14] GOOZNER, R. E. and LABES, M. M., Mol. Cryst. Liq.

Cryst. Lett. 56 (1979) 75.

[15] ADAM, N. K., Proc. Roy. Soc. 119 (1928) 628.

[16] HALPERIN, B. I. and NELSON, D. R., Phys. Rev. Lett.

41 (1978) 121. Phys. Rev. B 19 (1979) 2457.

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