Persistence length measurements in middle phase microemulsions

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Submitted on 1 Jan 1985

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Persistence length measurements in middle phase

microemulsions

D. Guest, L. Auvray, D. Langevin

To cite this version:

Persistence

_length

measurements

in

middle

_phase

microemulsions

D. Guest

_(1),

L.

_Auvray

₍₂₎

and D.

_Langevin

₍₁₎

(1)

Laboratoire de

_{Spectroscopie}

Hertzienne de l’E.N.S., 24, rue _Lhomond, 75231 Paris Cedex 05, France

(2)

Laboratoire de

_Physique

de la Matière Condensée,

Collège

de _{France, 11, place} Marcelin Berthelot, 75231 Paris Cedex 05, France

and Laboratoire Léon Brillouin, CEA-CEN

_Saclay,

91191 Gif-sur-Yvette Cedex, France

(Re.Cu

le

_{29 juillet}

1985, accepte le 27

_septembre

1985)

Résumé. 2014 Nous avons effectué une étude _{par rayon X de} microémulsions médianes _(en

_équilibre

avec de l’eau et de

_l’huile)

réalisées avec un tensioactif

_alkyl

benzene sulfonate _(SHBS). Les tailles caractéristiques de la

_dispersion

sont notablement

_supérieures

à celles trouvées dans un autre _système modèle dans

_{lequel le}

tensioactif était un

_alkyl

sulfate _(SDS). La différence est

_analysée

en termes de

rigidité

des films de tensioactif et de coefficient de _partage de l’alcool entre les films et les domaines eau et huile. Les conclusions sont en faveur du modèle de De Gennes, où l’échelle de la

_dispersion

est identifiée avec la

_longueur

de _persistance du film de tensioactif. Abstract. 2014 An

X-ray

study

of middle

_phase

microemulsions has been

_performed

on a model _system

where the surfactant is an

_alkyl

benzene sulfonate _(SHBS). The characteristic

_dispersion

sizes were found to be

_{significantly}

_larger than in an earlier work on a model _system where the surfactant was an

_alkyl

sulfate

_(SDS).

The difference is discussed in terms of

_rigidity

of surfactant

_layers

and of alcohol

_partitioning

between the

_layers

and the oil and water domains. The conclusions _support

the

_picture

in which the

_dispersion

scale is identified with the

_{persistence length}

of the surfactant

layers.

Classification

Physics

Abstracts 61.10 - 61.25 - 64.70 - 82.70 1. Introduction.

Microemulsions are

_dispersions

of oil and water stabilized

_by

surfactants. In some

_interesting

situations

_(first

discovered

_by

Winsor

_[1]),

_they

are in

_equilibrium

with both excess of oil and water ; the

_{corresponding}

interfacial tensions are then ultralow

(

10 - 2

dyn/cm)

and the microemulsion

phase

cosolubilizes

_comparable

and

_large

amounts of oil and water. As these microemulsions

(made

with ionic

_surfactants)

are intermediate

_(when

the water ionic

_strength

is

_varied)

between oil in water and water in oil

_{microemulsions,}

it is

_currently

admitted that

_they

are not

_simple

dispersions

of either oil

_{(or water)}

in water

_{(or oil).}

Scriven first

_proposed

that their structure could he hicontinuous, the oil and water

microdomains,

separated by

a dense

_monolayer

of

surfactant,

being

both interconnected over

_macroscopic

distances

_[2].

Several models were elaborated

_recently

to describe these structures

_{[3-5] :}

the microemulsion volume is divided into

_elementary

_cells,

_randomly

filled

_by

oil and water and the surfactant is distributed at the oil-water interface. In the

_{Talmon-Prager}

_model,

the cells are

_polygonal

and

L-1056 JOURNAL DE _{PHYSIQUE -} LETTRES

defined

by

a random Voronoi

tesselation;

their size distribution is

_large.

It was later

_{argued by}

De Gennes and

_{Taupin [6]}

that when the curvature

_elasticity

of the surfactant film is

_explicitely

taken into account, the stiffness of the film forbids the curvature fluctuations of the oil-water interface at scales smaller than the

_{persistence length}

of the film

_{ÇK. ~K}

is the basic size of the

_cells,

which are taken identical and cubic

[4-5].

If K is the

bending

elastic modulus of the surfactant

layer,

which is smaller than kT in disordered flexible microemulsions

_[6],

one has :

where a is a molecular

length.

In both

_models,

the cells mean

_{size, ~}

_(~K

in Ref.

_[6]),

which is the scale

length

of the random structure, is related to the microemulsion

_composition

_by

the relation:

(00

and

_ow

are the oil and water volume

fraction,

Cg,

the surfactant concentration and Z the area

per surfactant

polar

head in the

film).

Although

the Winsor middle

_phases

remain much less known than the classical

_droplets

microemulsions,

the main features of their structure

_begin

to be

_{distinguished experimentally.}

The

_{scattering techniques}

have thus

_recently

exhibited different evidences for the existence of random bicontinuous structures in the Winsor microemulsions. It was first shown that

[7-8]

the characteristic

_length

of the

microemulsion ~,

drawn from the

_spectra

in the intermediate range

of

_scattering

_{vector q}

_(qç

>

₃₎

and defined as a

_{pseudo-radius}

of

_gyration

in reference

_[7]

or as

a mean radius of curvature in reference

_[8],

follows

_{prediction [2].}

It was also demonstrated

_[9]

that the mean curvature of the film was zero on _{average when the Winsor microemulsions contain}

exactly

as much oil as water.

_Finally,

it has been deduced from the observation of a correlation

peak

in the

_scattering

_spectra

_[8-11]

that the size of the

_elementary

volumes of oil and water is well defined and does not fluctuate _very much as was assumed in the De Gennes model. This

provides

an indirect

indication

that

_rigidity

effects are

_important

in microemulsions.

In _{this paper,} we

investigate

further this

_{point by comparing}

two

_already

studied

_systems

[12, 7, 13], trying

to understand the

_origin

of the similarities and differences which

_they

exhibit The first

_system

was made with sodium

_{dodecyl-sulfate (SDS) [12],}

the second one

_{[7, 13]}

with

sodium

_hexadecyl

benzene sulfonate

(SHBS

or Texas *

1). Contrarily

to

SDS,

the SHBS molecule has a double

_aliphatic

_tail;

as it can be

_expected

from the

_geometry

of the molecules

_[14],

the first

surfactant forms micelles in pure water whereas the second

_only

builds lamellar

_phases.

These differences

_suggest

that the

_rigidity

coefficient K is

_larger

in the SHBS

layers.

From

_{equation (2)}

this could lead to

_{larger dispersion}

_{scales, ~.}

Our interfacial tensions measurements on the two microemulsion

_systems

showed that the tensions y are about 5 times smaller in the SHBS microemulsions

_[13].

As _y is

_expected

to be

inversely proportional

to ç2

[13],

this was indeed an indication that the

_dispersion

scales were

larger

on the SHBS

_system.

To check

this,

we have measured the characteristic

size ~

of the middle

phase

microemulsion in the

SHBS

_system

_by

small

_{angle X-ray scattering.}

These data will be discussed in

_comparison

with the earlier ones on both

_systems

_[7-10].

2.

_Experiments.

2.1 THE SYSTEMS.

N The first

_system,

referred as « SDS

_{system »}

is a mixture of

brine,

(47

wt

_%),

toluene

₍₄₇

wt

_%),

butanol

(4

wt

_%)

and SDS

₍₂

wt

_%).

The brine is an _{aqueous sodium} chloride solution of

concen-tration S

(wt

%).

The middle

_phase

microemulsions

coexisting

with both excess oil and water are

equilibrium

with excess brine

_(S

>

_7.4).

The structural

light [12],

neutron and

_X-ray

_{[8, 10]}

scattering

data

_concerning

this _system are summarized in

figure

1 and its

caption.

Fig. 1. - Product

LCs

I/6

plotted

versus oil volume fraction

_~o.

The characteristic

_length

L is _equal to

ÇK

in the _three-phase domain and to twice the core radius of the

_droplets

in the

_two-phase

domains.

Accord-ing

to the _{Talmon-Prager-de} Gennes model

_LCg

I/6 =

00 ow (parabola).

In the

droplets

models

LC.

I/6 =

2

₀₀

or 2

_q5,

_(lines).

_{Experimental points}

for the SDS _{system : (0)}

_{light scattering}

data

_{[12] ; (A)}

_X-ray

scattering

data

_{[8] ;}

_{( x )} neutron _scattering data

_{[10] ;}

we have taken Z = 60 A2.

Experimental points

for

the SHBS _{system : (8) light}

_scattering

data

_{[17] ;}

_(A)

_{X-rays scattering}

_data, this

_study;

we have taken

f = 100 A2.

00

and

_Cs

values have been taken from Refs.

_[32]

and _[17].

N The second _{system, referred} as « SHBS _{system »} is a mixture of brine

_(56.8

wt

_%),

dodecane

(38.2

wt

_%),

n-butanol

_(3.3

wt

_%)

and SHBS

_(1.7

wt

_{%) purchased}

from IRCHA France. The

weight

ratio have been chosen to have

_equivalent

volumes of oil and water rather than

_equivalent

weights

as in the first

_system.

Such a

_composition

had been

_adopted

in an earlier

_study

of SHBS microemulsions

_[7],

in which middle

_phases

were observed. between S = 0.6 and 0.8.

Here,

the

middle

phases

are obtained in the narrow _{range : 0.52} S 0.6. We think that the

_origin

of this

shift arises from three differences :

-temperature

differences : here T = 20 ~C and in the earlier work T =

25 ~C ;

the alcohol is different : we have chosen the same alcohol

(n-butanol)

for the SHBS and

the SDS

_system.

In the

_precedent

work on

_SHBS,

the alcohol was

_isobutanol;

the surfactant

_purity

_may be different.

The

_composition

of the middle

_phase

microemulsions has been determined

_by

gas

com-L-1058 JOURNAL DE PHYSIQUE - LETTRES

Table I. - Oil and water volume

_{fractions ~o}

and

_ow

and

_surfactant

concentration

_{Cs for}

the studied microemulsions. Characteristic distances 2

_{n lql}

and

_R’GIO.55

as

deduced -f orm

the

X-rays

experiments.

The

_{corresponding data for}

the SDS microemulsions S = 6.5 _are also

given.

Mean

cell

_{size ~}

_{calculated from Eq. (2)}

with

_ESHBS

= 100

A2

and

~sDS

= 60

A 2.

The _{accuracy on} distances

are about 10

%.

position

of the middle

_phase

with that of the oil and brine

_phases

in _excess, we have also measured

the number of alcohol _{molecules per surfactant molecule in the} interfacial film

_(1).

Two

_features,

which will be

_important

in the

_following,

_emerge from these data :

i)

As it was the case for the SDS

salinity

scan, the

product 00

_~w/Cs

is

approximately

constant in the middle

_phase

of the SHBS

_salinity

scan.

ii)

The number of alcohol

molecules

per surfactant molecule adsorbed in the SHBS interfacial film is about

3,

three times

_larger

than in the SDS

_system

where it was about 1

(1).

2.2 SCATTERING EXPERIMENTS. 2013 The small

_{angle X-rays scattering experiments}

were

_performed

on a

_set-up

located at Laboratoire de

_Physique

de la Matiere

Condensee,

College

de France. The

_X-ray

source was a

_{Rigaku rotating}

_{copper anode}

_generator.

The

_{X-ray wavelength}

was

À = 1.54

A

and the collimation _was

quasi-ponctual.

The

scattering

_vector is

given by

the relation

~ = 2013r-

₍

sin 0

₍₂

_0,

~

_scattering

g

_angle).

g )

° The

_{observed q}

q _{range is} g

10 - 2

q q 0.2

A

The

_spectra,

p measured with a

position

sensitive

proportional

detector

(Elphyse),

are not dismeared.

_They

are

normalized

_by

the

_sample

transmission and the monitor of the incident beam. For each

_sample,

the contribution to the

_scattering

of an

_empty

_capillary

has been subtracted.

(1)

We have assumed that the amount of alcohol in the oil and brine microdomains of the microemulsion

was the same than in the excess

_phases.

This seemed reasonable as the _composition of the microemulsions continuous

_phases

in the two

_phase

domains

_extrapolated

towards the

_composition

of the excess

_phases

3. Results-discussion.

We have

_analysed

the

_spectra

_following

the same

_procedure

than in reference

_[8].

If the

_middle-phase

microemulsions are not molecular

_mixtures,

as it could be inferred from

the

_high

self-diffusion coefficients of the constituents

_[15],

i.e.,

if it exists a well defmed surfactant

interfacial film between oil and water, the scattered

_intensity

follows

_asymptotic

laws characteristic of the electron

_{density profile through}

the interfacial film

_[16].

In the case of the SHBS

_system

where the electron

_density

of the surfactant

_polar

head

_{(n f)}

is

_larger

than the electron

_density

of brine

_(nw)

and dodecane

_{no(no nw),}

the absolute

_{intensity i(q)}

scattered _per unit volume of the

_sample

is

_expected

to

_obey

the

_following

relation

(observed

in the SDS

_system

where the contrast conditions are

similar) :

valid in the

_{range ~ ~>}

_{1, qd}

1,

where d is thickness of the

_polar

head

_layer.

Experimentally,

we observed that the

_quantity

q41 (q) (I(q)

is the measured normalized

inten-sity)

was linear in

qz

in the range 2 x

10-2

_q 0.15

Å -1

_{(Fig. 2) :}

Fig. 2. -

X-rays

scattered _intensity times

_q4

versus q for the SHBS microemulsion S = 0.6, and the SDS

microemulsion S = 6.5. The

_position

of the

_{minimum q}

is

_represented.

Up

to the

_{experimental uncertainty,}

A and B are constant in the

SHBS

_{middle-phases,}

which is in accordance with the observation that the variations of the surfactant concentration

_Cs

in this

L-1060 JOURNAL DE PHYSIQUE - LETTRES

This

_{surprisingly high}

value of ~ is in excellent agreement with the values deduced from the

light scattering

measurement of the radius R of the

_droplets

of the dilutable

_biphasic

micro-emulsions S 0.52 and S > 0.6

_{(cf. Figs.}

1 and

3) (for

this last case of water in oil

_droplets,

one

has the well known

_{equation :}

r = 3

~w/Cs

R) [17].

Thus,

_as in the SDS

system,

ESHBS

does not

depend

very much on the

salinity

and the

_large

value of

_ESHBS

_compared

to

_ESDS

is

_certainly

due to the

_larger

dimension of the SHBS

_polar

head and

_particularly

to the

_larger

amount of alcohol in the film.

Fig.

3. - Characteristic sizes for the SHBS

system as measured from

_{light scattering experiments}

after

dilution

_{[ 17]}

and _X-rays

_experiments

_(data from Table _1). R is the microemulsion

_droplets

radius as deter-mined from static

_{light scattering.}

R * _is

a radius determined from

_{angular disymmetry. RH}

is the

hydrodyna-mic radius as determined from _{quasielastic light scattering.} The differences between the different radius arise from oil

_penetration

in _W/O microemulsions _(S >

_S2)

and from

_{droplets elongation}

in _O/W microemulsions

(S

~).

The studies of the

_asymptotic

behaviour of the scattered

_intensity

do not

_{only provide}

a

measure-ment _{of the surface per}

_polar

head in concentrated

microemulsions,

but also a measurement of the mean radius of curvature of the film. As shown

_by

Kirste and Porod

_[18]

for a two

_phase

contrast

_{(for example,}

_{no =1=}

_nw =

nf),

the

asymptotic

behaviour is observed as soon as the

interface appears flat at the scale

_{q -1;}

on the

low q

side,

there is

always

a deviation

_(shown

to be

always positive)

from the

_{q - 4}

Porod’s

_law,

which leads to a characteristic

bump

on the curve

q41 (q)

function of q

(Fig. 4).

This deviation

only depends

on a certain

quadratic

_average of the

curvature of the interface. This

_justifies

the definition used in reference

_[8],

of a characteristic

scattering

vector _{q 1, abscissa of the minimum of the}

q4

I(q)

versus _{q curve,} which

_points

the cross-over between the

_asymptotic

Porod’s _q-range and the intermediate Kirste-Porod q-range, and

Fig. 4. -

q41

versus

q2

for the same microemulsions than in

_figure

2. The line is a tentative fit to _theory

(modified Porod’s _law).

Experimentally, q 1

is found constant in the middle

_phases

range of the

salinity

scan of the SHBS

_system

_(Table

_{1). This}

confirms that the structure cannot be described

_by

a

_droplet

model

and shows that the

predictions

of the random structure models

_[3-4]

_{ql1 ’" ç ’"}

_{00 cPw/Cs E}

is well verified.

At this

_stage,

a

question

arises;

why

do the Winsor

_systems

demix at

constant ~

(given

by

Eq.

(2))

in the middle

_{phase salinity range ?}

This

fact,

already

observed

_{[7, 10]}

but never

empha-sized,

is not

_interpreted.

It

_suggests

that,

in

_spite

of the chemical

_complexity

of the Winsor

_systems,

it is

_possible

in a

salinity

scan to

_separate

the

_parameters

_controlling

the

_dispersion

scale

(surfac-tant and

_alcohol,

related in the

_picture

of De Gennes to the film

_rigidity)

from the

_parameters

governing

the film curvature

_(e.g.

water ionic

_strength).

Further information can be obtained from the data on the SHBS

_system

_{by comparison}

with the SDS

_system.

It was observed in reference

_[8]

_{that, if ~}

is defined

by equation (2),

one had the

experimental

relation,

valid in the microemulsion inversion zone :

Assuming

that the same relation is valid in the SHBS

_system,

one obtains

(within

10

_%

uncer-tainty

due to the low resolution of the _spectra in the _very

_{low q}

_range

_{where q 1}

is

_measured)

~ ~

390

_A,

which is in

_good

_agreement with the direct calculation based on

_{equation (2),}

(ç = 6 cPo

~w/Cs

E),

the microemulsion

composition (Table I)

and the

_large

value of E

_(E

=

100 A~)

measured from the

_asymptotic

behaviour.

In the intermediate Kirste-Porod q-range, it was noticed in the SDS

_system

that In

I(q)

is

linear in

_q2.

This was also observed for the SHBS _system

_{(Fig. 5).}

This

_although

the

_spectra

are

not recorded at _very

_{low q (q~ 1)}

where one knows that the Guinier laws is not

_{experimentally}

observed

_[8-10],

it is

_possible

in the intermediate q-range

(q

ql)

to define a

_{pseudo-radius}

of

gyration R’ G through

the relation In I

_{= - q2 (R~)2/3}

+

Cte,

which

_gives

in

_principle

the same

information on the microemulsion mean radius of curvature as _{ql. Such} a defmition is useful to

compare the data first with the

Talmon-Prager

model which

predicts [19]

that at _very

_{low q}

the scattered

intensity

should follow Guinier’s law with

_R~

=

0.55 ~

and also with earlier

reports

L-1062 JOURNAL DE _{PHYSIQUE -} LETTRES

Fig.

5. -

Log

I versus

q2

for the same microemulsions. The domain of

_{linearity corresponds}

to the same range of reduced wave vectors

_q/ql.

In the

_previous

_study

on the SDS

system,

it was shown that

_R~

was _very close to

_{0.55 ~}

indeed. For the SHBS

_system,

we observed that

_RG

was constant _{as q 1 in the}

_{middle-phases}

and that the

precedent

relation between

_{R~ (=}

_{220 )}

and

(~

400 Á)

was also well verified and consistent

with the value E = 100

A2

(cf.

Table

I).

Thus these

_{procedures provides}

_convergent

estimations of the absolute value of the

_dispersion

scale ~

in the microemulsions. In this

_respect,

we note that the

_R~

measured here

_(RG

= 220

A)

significantly

differs from the «

_apparent

radius of

_{gyration »}

measurements made

_{previously [7]}

on the SHBS isobutanol-dodecane-brine Winsor microemulsions

_{(RG ^_r 180}

A).

We attribute

this difference to the different

_experimental

conditions. In

_particular,

it is

_possible

that a

_larger

temperature

(25 ~C),

a branched cosurfactant

_(isobutanol)

and

_impurities

in the surfactant

playing

the role of the cosurfactant decrease the value of the

_dispersion

scale.

The essential result of the

_experiments

is

_{that ~}

is much

_larger

in the SHBS

_system

than in the SDS

_system

_{(ÇSDS ’"}

250

_A).

From

_{equation (1),}

this could indicate that the film stiffness K is

larger

in the SHBS

_system

than in the SDS

_system.

_{By assuming a -}

10

_A,

one

_get

from

equa-tion

_{(1) :}

The value of K has been

_recently

measured in the SDS

_system

_{[20] : Kgps = (3}

±

1).10-14

erg in the middle

_phase

domain. The

estimated

value is very close to the measured one.

We note that

_contrarily

to what one could

_expect

from the

_geometry

of the two surfactants and from their behaviour in pure water, the differences between

KSDS

and

_KSHBs

remain small

(if a

is different for the two

surfactant,

the difference may still be

_smaller)

and that K determined in that way remains of the order of kT.

An

_{important point}

is however the much

_larger

amount of alcohol molecules in the SHBS film than in the SDS film. It has been

_{proposed recently [6]}

and confirmed

_{experimentally}

on

bire-fringent

lamellar microemulsions

[21]

that the

_important

role of the cosurfactant

_(and

_possibly

of _any

_impurities

adsorbed on the interfacial

film)

is to reduce the film

_{rigidity sufficiently}

so that

The

_comparison

which we have made between two Winsor microemulsions

_systems

whose structure is random and bicontinuous

_{(~ ~ 00}

_cPw/Cs

₀

and where the

_rigidity

effects of the film are not biased

_by

effects

_giving

a

_spontaneous

curvature to the film

_(ç

_independent

of

_salinity)

confirms this

_hypothesis.

_{The very}

_rigid

_pure SHBS films

need

to

_incorporate

a

large

number of

alcohol molecules to form

_{microemulsions,}

much

larger

than the less

_rigid

SDS films. The exact

reasons

_why

these

_particular

ratio surfactant-cosurfactant are achieved remains to be elucidated We

_conjecture

that

_they

have

_probably

to do with a detailed _energy balance between small

curvature

_{energies (small K)}

and small interfacial

energies (small

y, i.e.

large ~

and

large K).

This would lead to a critical value of K to form a microemulsion.

Acknowledgments.

This work has received

_partial

financial

_support

from PIRSEM

_(GRECO

Microemulsions of the

_C.N.R.S.).

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