Concentrated Winsor microemulsions : a small angle X-ray scattering study

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Concentrated Winsor microemulsions : a small angle

X-ray scattering study

L. Auvray, J.-P. Cotton, R. Ober, C. Taupin

To cite this version:

Concentrated Winsor microemulsions :

a

small

angle

X-ray

scattering

_study

L.

_Auvray

_(1,2),

J.-P. Cotton

_(2),

R. Ober

₍₁₎

and C.

_Taupin

₍₁₎

(1)

Laboratoire de

_Physique

de la Matière _Condensée,

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

(2)

Laboratoire Léon _Brillouin, C.E.A.-C.E.N. _Saclay, 91191 Gif-sur-Yvette Cedex, France

(Reçu le 11 août 1983, révisé le 18 novembre, accepte le _{6 junvier 1984)}

Résumé. 2014 Nous

avons étudié par diffusion centrale des rayons X la structure de microémulsions de Winsor dont les

_proportions

de saumure et d’huile _(toluène) sont

_comparables

et _grandes devant les

_proportions

de tensio-actif _(sodium

_dodécyl

sulfate, SdS) et cotensioactif _{(butanol 1).} Trois

_systèmes

ont été

_fabriqués.

Dans le

_premier

(déjà

très étudié) les microémulsions sont en

_équilibre

avec une

_phase

eau _et/ou huile en _excès, la

_composition

des microémulsions varie en fonction de la salinité. Les deux autres

_systèmes

sont des

_monophases

faites avec une saumure de salinité _6,5 %. Dans le second

_système,

nous faisons varier la fraction

_volumique

en _huile,

_03A60,

de 20 à 90

_%

à concentration constante en _{tensioactif (5} x 10-2

_g/ml).

Dans le _troisième, nous avons choisi les

proportions

des constituants de telle sorte que la

quantité

03A6003A6w/CS

(03A6w :

fraction

_volumique

en _{saumure, cs :} concen-tration de _SdS) reste constante quand

03A6o

varie de 20 à 80

_%.

On fixe ainsi la

_{longueur caractéristique théorique}

des microémulsions, selon

_{l’expression 03BE}

= 603A6003A6w/cs03A3

_prédite

par

Talmon-Prager

et de Gennes _(03A3 est la surface

par tête

polaire

de _{tensioactif).}

1) La contribution des têtes

_polaires

au contraste et à l’intensité diffusée aux _grands

_angles

dans le domaine

asymptotique est substantielle. Nous en déduisons une _{preuve directe de l’existence d’un film interfacial de} savon

séparant les _parties eau et huile de la microémulsion et une méthode de mesure de la surface par tête polaire

(03A3 ~ 60

_Å2);

2) Nous mesurons la taille

_{caractéristique}

des _{microémulsions 03BE} en fonction de

_03A6o

et _{cs. Les différents balayages}

suggèrent que, pour les systèmes de

_Winsor,

à _partir du

_point

d’inversion

_(03A6o

= 0,5),

quand

la proportion d’eau

ou de toluène _augmente, on _passe

progressivement

d’une structure aléatoire bicontinue d’eau et d’huile

(0,3

03A6o

0,7, 03BE ~ 03A6o03A6w/CS 03A3)

à une

_dispersion

faite de

_gouttelettes

distinctes d’eau dans l’huile ou d’huile dans

l’eau

(03A6o

0,3 ou

_03A6o

> _{0,7, 03BE ~}

03A6o/cs03A3

ou

03A6w/cs03A3);

3) Nous observons aux très

_petits

_{angles (q ~} 10-2

Å-1)

des effets de corrélations ou d’interactions non

_prédits

par les modèles existants de microémulsions bicontinues.

Abstract 2014

By small _{angle X-ray scattering,} we have studied the structure of Winsor microemulsions, with brine

and oil (toluene)

proportions

comparable and much _larger than the surfactant _{(sodium dodecyl} sulfate, SdS) and co-surfactant (butanol 1)

proportions.

Three _systems were made. In the first

_(already

studied in detail), the microemul-sions are in _equilibrium with an oil _and/or water

_phase

in excess, the microemulsion composition varies as a

fonction of the brine

_salinity.

The two other systems are _monophases made with a brine of

salinity

6.5

_%.

In the

second _system, we vary the oil volume fraction

03A6o

from 20 to 90 _% at constant SdS concentration ₍₅ x 10-2 _g/ml).

In the _third, we chose the component

proportions

such that the

quantity 03A6o03A6w/cs

_{(03A6w :}

brine volume fraction, cs : SdS _{concentration)} remains constant as

_03A6o

varies from 20 to 80 _%. Thus one fixes the theoretical microemulsion

characteristic _length

_according

to the _expression

$$

predicted

_{by Talmon-Prager} and de Gennes _(03A3 is the area _{per SdS polar head).}

1) The SdS _polar head contribution to the contrast and to the _intensity scattered at _{large angle} in the _asymptotic domain is _large. From this, we deduce a direct _proof of the existence of a _{soap film between the oil and} water

parts of the microemulsion and also a method of measurement of the area _per

_polar

head _{(03A3 ~} 60

Å2);

2) We measure the characteristic microemulsion size as a _{function of cs and}

_03A6o.

The various scans _{suggest that,} for Winsor _{microemulsions, starting} from the inversion _point

_(03A6o

= 0.5) and increasing the water _or oil proportion,

Classification

Physics Abstracts

61.10 - 61.25 - 82.70

a _{progressive change} occurs from a random bicontinuous water and oil structure

$$ to

a

_dispersion

made of distinct oil in water or water in oil

_{droplets (03A6o}

0.3

_{or 03A6o}

> _{0.7, 03BE ~}

$$

or

$$;

3) At very small

angles

(q ~

10-2 Å-1),

we observe correlations or interaction effects not

_predicted

_by the

existing

bicontinuous microemulsion models.

Introduction.

Microemulsions are

_fluid,

_transparent,

_isotropic

mix-tures of water

_(or

_brine)

and

_hydrocarbon

_(o

oil

_»)

stabilized

_{by amphiphilic}

substances

_(a

surfactant and often a cosurfactant : _e.g. a short

alcohol) [1].

They

exist as

_{single phase}

or coexist with either an excess of _water, or an excess of oil

(Winsor

II

phases),

or both

(Winsor

III

phases)

[2],

(sometimes

they

also coexist with an

_{oil-water-amphiphiles}

_liquid

cristalline

_phase

_[3]).

With

_lipophilic

surfactants,

one solubilizes water

in

_oil;

with

_hydrophilic

_surfactants,

it is the reverse.

Depending

on the choice and

_quantities

of surfactant and

cosurfactant,

and

_depending

on the

_temperature

and

_salinity,

the oil and water

_proportions

in a micro-emulsion can be

_practically

fixed at will.

At low water

_{(or oil)}

concentration,

the structure of these

_phases

is

_precisely

known : the microemul-sion is a

_dispersion

of water in oil

_(or

oil in

_water)

spherical droplets (the

radius is ~ 100

A) ;

the

oil-water interface is saturated

_by

a dense mixed film of surfactant and cosurfactant.

When the oil and water

_proportions

are

_comparable

(this

corresponds

to the «inversion zone » of the

phase

diagram)

the structure

_question

becomes more

puzzling :

i)

In certain cases, well defined

spheres

still exist : models of hard

spheres

in interaction

_successfully

interpret

the neutron and

_{light scattering}

data

_[4].

This _{type of} microemulsions has been

_particularly

studied

_along

_{dilution-paths}

in the

_{phase-diagram}

_{[5] :}

for a water in oil

microemulsion,

the molar ratio

water/soap,

the

_composition

of the continuous oil-alcohol

_phase

and the structure of the water

_droplets

are

_kept

constant as the water-concentration is increased until an _upper bound is reached. This bound

corresponds

either to a

_solubility

limit or to an oil in water microemulsion

_(inversion).

It often coin-cides with the random

_{sphere-close-packing}

con-centration

_[5].

ii)

In some other cases, the oil or water

_objects

are less well defined :

_sphere

_aggregates are evidenced

_[6].

iii) Finally

it may

happen

that there are no

longer

any defined

objects,

but

only

a bicontinuous random

partition

of oil and water

_[7].

This would

explain

that :

- In

some

phase diagrams,

one can _pass

conti-nuously

from an oil in water to a water in oil struc-ture.

- Non dilutable microemulsions exist

(in

parti-cular Winsor III

microemulsions).

Recently

de Gennes and one of us have

_interpreted

part

of these various features

_{by considering}

the curvature

_elasticity

of the interfacial film

_{[8] :}

When the film exhibits a _{strong spontaneous} curvature due to a _strong

dissymmetry

between the

polar

and

_aliphatic

_part

of the

film,

well defined

objects (oil

in water or water in

_oil)

are

_preferred

When there is no

preferred

curvature but a

_large

rigidity

of the

film,

the _system tends to build well

organized

lamellar

_phases.

An

_interesting

case

corresponds

to a weak sponta-neous curvature and a flexible interfacial film. In this case, a bicontinuous random structure exists at

_sufficiently

_high

water and oil concentrations. The characteristic size of this structure is the per-sistence

_length

of the film

_{c;k (the}

interfacial film is

rigid

and flat at scales smaller

_{than c;k}

and wrinkled at

_{larger scales) :}

the volume is divided into domains of size

_c;k’

these domains

_{being randomly}

filled either

by

oil or water.

This structure

_model,

derived from the

Talmon-Prager

model

_[9]

also allows an initial discussion of the Winsor

_type

_phase

_equilibria

to be

_given

in terms of the surface _energy, the film _entropy and the curvature _energy

_[10].

The main results are : :

i)

the model

_only

_generates Winsor II _systems

ii)

the

_compositions

of the

_phases

in

_equilibria

fall on the line :

where cs is the surfactant concentration

(in

molecules number _per

_{Å 3),}

E is the area _per surfactant

_polar

head

_(in

_A2),

₀₀

and

_0,

are

_respectively

the oil and water volume fractions in the

_phases.

The Winsor microemulsions have been much studied because their solubilization

_capabilities

are

high

and the interfacial tension between the micro-emulsion

_phase

and the

_phase(s)

in excess are ultra-low

_(-

10 - 3

_dyne/cm)

_[11].

But their structures have been less studied and we do not know _yet if

_they

enter in the above framework :

- Their

phase

behaviour

_depends

_practically

on

pumerous

parameters

(salinity,

alcohol,

tempera-ture)

whose roles are

_poorly

identified.

- In Winsor III

- The critical behaviour often observed at the

transition Winsor II-Winsor III when one of the

parameters is

_varied,

still raises

_problems.

In order to test in these microemulsions the existence of a bicontinuous structure and the model

predic-tion

_(1),

we have studied their structure

_by

small

angle X-ray scattering.

The microemulsion are made of

_brine,

_toluene,

sodium

_dodecyl

sulfate

_(SdS)

and butanol 1.

We obtained three _{systems :}

The first one

_(A)

has been studied in detail

_[13-15].

Starting

from a mixture whose

_{proportions (by}

weight)

are : brine

_{47.95 % ;}

toluene

_{46.35 % ;}

SdS

1.95 % ;

butanol

_{3.75 %}

and

_varying

the

_salinity

of brine

_(S

= NaCI

weight-percentage

of

brine),

_one

obtains a series of Winsor

_{phases :}

At low

_{salinity (S}

5.5

_%),

an oil in water micro-emulsion coexists with

_nearly

_pure

_toluene;

at

_high

salinity

(S

> 7.5

_%)

the role of oil and water are

inverted;

in between Winsor III microemulsion coexists with brine and toluene excesses.

In this _system, the

_composition

of the micro-emulsion

_phases

is not controlled. Thus we have also worked on

_monophasic

microemulsions

(called

B and

_C)

located in the same

_region

of the

phase diagram.

The amount of

SdS, toluene,

and brine was a

_priori

chosen. It was then examined if a

_given

mixture could be titrated

_by

butanol to form a

_monophasic

micro-emulsion.

This

_procedure

has allowed us :

i)

To

_perform

a toluene volume fraction

₍₀₀₎

scan

_(from

_qlo

= 20

%

to 90

%)

at fixed

salinity

(S

= 6.5

%)

and

approximatively

constant SdS

con-centration

_(system

_B).

Thus one

_separates

as much as

possible

the effects of salt

_(which

seems to

_modify

the curvature of the interfacial

film)

and the effects of butanol.

ii)

To make a

_{00-scan (0.2}

_qlo

_0.8)

_{at Çk}

(expressed

by

formula

₍₁₎₎

_{approximatively}

constant

(system

C).

1.

_Experiment

1.1 SAMPLE PREPARATION. - We used commercial

products

without further

_{purification.}

Toluene was

purchased

from Merck

_{(Uvasol, spectroscopic}

_grade),

n-butanol from SDS

_(puran),

SdS was from Serlabo and sodium chloride from Prolabo.

1.1.1

_{A-system (salinity scan).}

- After

mixing

the constituants in a tube and

_stirring

on a vortex _system, the tube was

equilibrated

in a thermostated bath

(T

= 20 _± 0.5

°C).

The stable demixtion

equilibrium

was reached after about one

day.

Approximate

microemulsion

_compositions

were deduced from the measurement of the

phase

volumes

assuming

that the

_phases

in excess were _pure toluene

and/or

pure brine

(Table

I).

(The

relative

precision

on the oil and water volume fraction and SdS concen-tration is about 5

_%.)

Table I. -

Composition

of system

A,

S :

_{salinity (% by}

weight

of

salt in

_brine);

_{00 :}

toluene volume

_fraction;

cs :

surfactant

concentration

(A-3)

multiplied by

104.

1.1.2

_B-system.

- The

samples

were made with a constant

_salinity

brine

_prepared

in advance

₍₃

series were tested : S = 5.5

% ; S

= 6.5

% ; S

= 7.5

%).

The

_{predetermined}

volumes of brine

_(Vw),

toluene,

Vo

(V,

+

_Vo

= 10

ml)

and the _mass of

SdS,

ms were mixed Then the

_samples

were « titrated »

_by

repeated

addition of small amounts of butanol and stirred We

_stopped

when the

_monophasic

micro-emulsion was obtained at

_equilibrium

in a thermo-stated bath

_(T

= 23 ± 0.5

°C) ;

_or, in the

opposite

case, when there was more than 1 ml of butanol in the tube.

Before

_{complete titration,}

either we could not solubilize all the

_SdS,

or we obtained a Winsor II microemulsion

_coexisting

with an excess of toluene. As in

_{system A,}

the

_B-samples

of the inversion zone and of the water rich side are very sensitive to

tempe-rature

_{change :}

a shift of one

_degree

_may lead to a demixtion.

Compositions

are

_given

in tables II and

_figure

1. When the titration was

performed,

the volume of butanol was less than 8

%

of the oil and brine volume.

_Ignoring

the butanol

_partition

coefficient between

toluene,

brine and

film,

we

_neglect

butanol

volume in the evaluation of the aqueous and oleus volume fractions of the microemulsion

_(0,

and

_00).

We _express

_’

_as

Yw

_as

V°

and the

Vo +

w

’

Vo + w

surfactant concentration cs

(in

Å - 3)

as the ratio of the SdS molecule number to

_Vo

+

V,,,-1.1.3

_C-system.

- The

preparation procedure

was the same as for the _system B. The volumes of brine

Table II. -

Composition of ’ system

B and

C,

_{00 :}

toluene

_{volume fraction}

_ddined

as

_{V o/(V o}

+

V w)

(ml) ;

VB :

volume

_{of butanol}

in the microemulsion

_{(in ml) ;}

_{ms :} mass

qf*SdS

in the

microemulsion ;

cs :

surf actant

concentration

(A-3)

multiplied by

104.

Table IIa. - S

= 6.5

%, m.,

= 0.5 _g

(this corresponds

to a volume

_{of’ surfactant, V}

= 0.431 ml and _a number

of SdS

molecules

_N.

= 1.046 x

1021 ;

_cs = 1.046 x

10-4

Å -3.

Fig. 1. - Volume of butanol

(Vb) in

the B _system

micro-emulsions. 0 S = 6.5 %; + S = 7.5 _%; * S = 5.5 _{% ;}

mr = 0.5 g; El S = 6.5 %; m. = 0.4 g;

* S =-, 6.5 %; mg = 0.35 g. Table lib. Table He. -

System C,

ms = 0.5 _{g; S} = 6.5

%.

chosen so

_that,

with ms = 0.5 g and the above

defi-nitions of

_{00, (p,}

_{and cs,} one has :

Çk = 6 l/lo iw = 150 A

(with 2:=6o

A ,

cf. §

2.2. 1).

CS 2:

The

_C-samples

₀₀

> 0.4 were

_prepared

at T = 23 °C.

They

were insensitive to _temperature

_change

between 23 °C and 30 °C. Their

_X-ray

_spectra

were recorded at T = 23 °C.

After a few

_days,

the two

_C-samples

₀₀

= 0.2 and

0.3

_appeared

to be not stable at T = 23 °C. Their

X-ray

spectra were recorded at T = 27

_OC,

where

they

were stable without

_ambiguity.

1.2 ELECTRICAL CONDUCTIVITY MEASUREMENTS.

-They

were

_performed

on

_system

B

_{samples (S}

= 6.5

%)

1. 3 X-RAY SCATTERING EXPERIMENTS. - Two

diffe-rent

_X-ray

sources were used

The first one was an Elliot

_rotating

_copper anode

generator

(located

at the « Centre de

_G6n6tique

Moléculaire»,

Gif-sur-Yvette), giving

after mono-chromation and collimation a _very fine beam

_(thickness

150

_gm)

about 3 mm wide. The detector was a

_position

sensitive

_proportional

counter

_[16].

The

_X-ray

wave

length

was A = 1.54

A.

The second source was the

synchrotron

radiations of L.U.R.E. at

_Orsay.

The collimation there was

ponctual (beam

dimensions 0.5 mm x 1

_mm).

The used wave

_length

was : A = 1.61

A

[17].

All the

_samples

were examined in thin sealed

_glass

capillaries,

which diameters had been

_previously

measured The

_sample

holder was thermostated at the

_temperature

of

_{sample preparation.}

Empty

capillaries

were used to measure the back

ground intensity

which was subtracted from the

sample signal.

In a

_given

series of

_experiments,

the intensities were normalized

_{by dividing}

the

_counting

rate

_by

the

sample

thickness,

by

the

_sample

transmission coeffi-cient and

_by

a

_{quantity proportional}

to _{the energy} of the incident beam. This defines the

experimental

intensity

L

Experiments

which were done with

_synchrotron

radiation will be denoted

_by

L,

those with the

_rotating

anode

_generator

_by

G.

By varying

the

_sample

detector distance between 50 cm and

_{1 m,}

we

_explored

the _q-range

10-2-0.25

Å - 1.

Collimation effects affect the first 50

_{points (among}

200)

of the G

_experiment

_{spectra :}

compared

to L

spectra the intensities are lowered but the

_general

shape

is not

_changed

As in the _very low _q-range our

_analysis

is

_{only qualitative,}

the G

_spectra

were not desmeared

2. Results and discussion.

2. 1 REMARKS ON THE PHASE BEHAVIOUR OF B MICRO-EMULSIONS. - In

system A, oil rich microemulsions are associated with

_high

salinities

(S

> 6.5

_%)

and brine rich microemulsions to low salinities. The

highest

oil and brine

_uptakes

are reached at the inversion

_point

for an «

_optimal

_salinity

» S = 6.5

%.

To obtain a toluene volume fraction scan as wide as

_{possible (following}

the constraint of constant SdS concentration and

_salinity),

we tried different sali-nities around the

_{optimal salinity (S}

= 5.5

%,

S = 6.5

%,

S = 7.5

%)

and different SdS

concentra-tions

_(see

_Fig.

1 and Table

_II).

2 .1.1 Salt

effect

on

_phase

equilibria.

- As in

system A,

the salt effect on the _aqueous or oleus character of the microemulsions

_(ms

= 0.5 _g,

Yo + V,,,

= 10

ml)

is

_striking.

For S = 7.5

%

_we could

only

make oil rich

micro-emulsions.

For S = 5.5

%,

it _was the _{reverse : we} made brine

rich microemulsions however with much

_larger

amount of

butanol,

it was also

_possible

to inverse the structure

_(Vo

> 7.5

_ml).

Only

with the S = 6.5

%

brine _was it

possible

_to

realize microemulsions in the inversion zone and to cover a wide oil volume fraction _range

(0.2

00

0.9).

Thus,

the

_{optimal salinity}

not

_{only corresponds}

to the maximum oil and .water

_uptakes,

but also to the

_largest

existence domain of the microemulsions. 2.1.2 SdS concentration

_influence

on

_phase

equili-bria. - At S = 6.5

%,

_we

systematically

decreased

the surfactant amount

_keeping

the oil and brine volumes constant

_(Vo

_{+ VW}

=

10 ml).

For each

toluene volume

_fraction,

a minimum amount of

surfactant is

_always

necessary to

_disperse

toluene and

brine;

below this amount, a demixtion occurs whatever the butanol amount,

showing

that butanol alone does not

_replace

the surfactant The smallest is the initial

₀₀

_{(or symmetrically}

_),

the smallest is this lower bound

2.1.3 Conclusions. - In

our

_systems,

the oil and water

_{uptakes (a}

_priori

_imposed)

are

_mainly

deter-mined

_by

SdS and salt

The Talmon

_Prager

model

_{explains qualitatively}

why

a minimum surfactant amount is _necessary. The SdS amount fixes the oil water interfacial area and the size scale of the

_dispersion;

at

_given

oil and water

contents, a small

_specific

area

_corresponds

to a

_large

characteristic size

_(see

formula

₍₁₎₎

and a small

entropy. If the _entropy becomes too

small,

the sur-face energy term becomes

_predominant

and the microemulsion demixts.

The

_salt,

in the

_picture

of de

_Gennes,

screens the electrostatic

_repulsion

between SdS

_polar

heads and

_determines

the

_spontaneous

curvature of the interfacial film. It then

_imposes

the

_dissymmetry

of the oil and water contents. At the

_{optimal salinity,}

the oil and water contents can be varied in the widest

proportions showing

that the _spontaneous curvature of the film is the weakest

Butanol also influences the

_uptake,

but in a more versatile _{way. It} modulates the film _curvature,

_(very

efficiently

when at a certain

salinity,

the film has no

preferential

curvature towards the oil or water

side);

however its main role is

_certainly

not limited to that

_{Quite surprisingly,}

the butanol volume necessary to make a microemulsion of

_given

_00,

0,,

does not

_{apparently depend}

on the SdS concen-tration

_(Fig.

1 and Table

_IIb).

This could mean that the cosurfactant role is not

_only

interfacial in Winsor microemulsions.

2.2 ELECTRICAL CONDUCTIVITY OF B MICROEMULSIONS.

- As

a first test of the

_phase

inversion in the toluene volume fraction scan

(S

= 6.5

%,

ms = 0.5 _g,

These microemulsions are

conducting

as soon as

0,

is _greater than 12

_%.

The

_conductivity

6 increases

as

_0,

increases,

in a _{way very} similar to that observed

on _system A

_[15]

and on other Winsor

phases [18]

(see Fig.

2,

a is normalized

by

the brine

conductivity

(Jw = 90.7 mS

cm-’).

In the linear _part of the

_plot,

.!!-

_{1.3(0,, -}

_0.3).

QW

Thus this

_expression

can be

_compared

to an effective

medium

_{approximation}

_{[19] :}

: w I N

(§ -

N),

W

where N is the

_{demagnetization}

coefficient of

con-ducting objects

whose volume fraction is

_0.

This

_gives

N =

0. 3 -- I

which is the result for _a

sphere.

3

We conclude that :

i)

The

_exchange

_{possibilities}

between brine domains are

_large.

ii)

These domains are not

_anisotropic.

2.3 STRUCTURE OF WINSOR MICROEMULSIONS. ANA-LYSIS OF THE X-RAY SPECTRA. - When

a

_point

colli-mation of the

_X-ray

beam is

used,

the

_experimental

intensity

I(q)

is

_proportional

to

_{[20, 21] :}

i(q)

= 4 r

(

n2

r

r2 sin qr

dr

(2)

Jo

Y( )

q r

( )

i(q)

is the scattered

_intensity

_per unit volume in electronic

_{units. q}

is the

_scattering

vector related to the

4 7r

scattering

angle

2 0

_{by q}

=

4;..1t

sin 0.

If

_n(r)

is the electron

_density

at

_point

_{r, n >}

its average

value,

q(r)

=

n(r) - n >

is the local

elec-tron-density-fluctuation ;

its _mean-square value is

(

tl’ >

and

_y(r)

is the correlation fonction defined

by :

Fig. 2. - Conductivity of microemulsions

_(system

B, S = 6.5

%, m.

= 0.5 g) versus brine volume fraction

_0,,,.

The

straight line corresponds to

_a/c,,

=

1.3(o, -

0.3).

where the brackets mean that the average has been taken.

In our

_{experiments, depending}

on the

_{series, q}

varies between

10-2

and 0.25

A-’ :

we

_explore

the micro-emulsions structure between

_(roughly)

15 and 300

A.

Because the characteristic

_{sizes j}

of the micro-emulsions are

_large

_{(j a}

100

A),

we found that one can observe and define

precisely

three _{q-ranges :}

i)

A

_«large

_{q-range »}

_(q

> 0.1

_{Á -1,}

small

_spatial

scale,

30

_A),

also called

_asymptotic

_range, since in this domain the

_{X-ray scattering}

follows

_general

laws

_(presented

_below)

which are

_independent

of the

large

scale structure. These laws enable the existence of an interfacial film in our _systems to be discussed.

ii)

A « medium _{q-range »}

(2-5 qj

_5),

where the

_spectra

_depend

_only

on the size of the water

and/or

oil domains.

iii)

A very small _q-range

_(qç

₁₎

which describes the

_large

scale structure of the microemulsions.

Only

in the last

_q-domain

do the

_spectra

exhibit a _very

qualitative

different behaviour from one

sample

to another.

In the

_analysis,

we will follow this distinction between the three _q-ranges.

2.3.1 The

_interfacial

_film.

- At

large

q

(say

0.3 > q > 0.1

Á - 1),

the

_signal

is due to electron

density

variations at small

_spatial

scales

_(~

15-30

_A),

smaller than the dimensions of oil and water

domains,

but

_larger

than the atom sizes. At these

scales,

if

-

as it seems -

a narrow interfacial film does exist in the

microemulsion,

one can

distinguish

three

parts :

the oil

_phase

and the brine

_phase,

where the erectron

_density

is

uniform,

and the interfacial

_layer,

where the variations of electron

_density

are loca-lized The

_intensity

then

_only

_depends

on the local structure of the interface and on the amount of inter-face.

In

_particular,

if the variations of electron

density

simply

were a

_jump

_through

the

_{supposed infinitely}

thin interface from a

_{value nl}

in brine to _{n3 in}

toluene,

one would have :

A/Y

is the area _per unit volume between oil and water. However the intensities of the

_samples

do not

obey

Porod’s law

_(3),

but

_they

exhibit a definite

asymptotic

behaviour.

i)

This behaviour

_only

_depends

on the surfactant

concentration,

cs

(we

checked in

particular

that it was identical for all B

samples

of the toluene scan, at constant

_cs).

Fig. 3.

_{- q41}

versus

q2.

_{A-system (L experiment).} From the

100th point, the data are _averaged on five consecutive channels. S = 3

%, S

= 6.5 %, S = 9 %.

axis,

Y are both

_proportional

to the SdS concentra-tion

_(see

Table

_III).

This behaviour is at variance with that

_expected

with a critical molecular

_mixture,

where the

Omstein-Zemike law

_{predicts i(q) -}

_Ijq2

without a

Ijq4

term. In contrast, the existence of a well defined

interfacial surfactant film between oil and water enables all the above

facts,

to be

_interpreted

if one takes into account the

_polar

heads electron

_density

contribution to the contrast

With the electron

_{density profile}

of

_figure

4,

for a

locally flat

interface,

Porod’s law takes the form

(Appendix

1) :

where d is the thickness of the

polar

part

of the inter-facial film nt, n2 and n3

respectively

are the electron densities of

brine,

film and toluene.

The first term is Porod’s term

₍₃₎

due to the diffe-rence of electron

_density

between oil and _water; the second is the contribution of the thin

_polar

heads sheet

_{(i(q) - I Iq 2}

is characteristic of the

scatter-ing

by

thin disks

_[20]).

Both terms are surface _terms,

proportional

to the

_specific

area, which is fixed

by

the surfactant amount If all the SdS is at the

_oil/water

interface,

A/Y

=

cs E

(Z

is the _{area per} SdS

polar

head),

and the two coefficients P and Y of the law

q4

I = Y ₊

Pq2

_are

proportional

to

cs E.

Up

to the

experimental uncertainty,

this is indeed the case and Z is constant.

Table III. - Parameters

of

the

_asymptotic

behaviour

of

I(q)

(defined

in

_text).

_(a)

_L1

_experiment.

_A-system

and two

_samples

_of

the

_B-system

_(S

= 6.5

%,

ms =

0.5 _g,

_cPo

= 0.5 and

4Jo

=

0.75) ; (b)

G3

experiment.

System

C.

a

Fig. 4. - Electron

density

profile through the interfacial

layer.

The measured value of I does not _vary from a

_sample

to another

If one

_{knows 4}

one deduces from I the electron excess in the

_polar

_part

of the interfacial film and the area _per SdS

_polar

head E

(in

A2)

(Appendix

II).

As a

_reference,

we chose a brine in

cyclohexane-pentanol

microemulsion,

whose structure has been

already

studied

_by

neutron

_scattering

₍₆₎

_(it

is called 5 B 1 M in this reference : the

_{NaCl -brine molarity}

is 1M

_(S

= 5.5

%),

the

weight

ratio of water to SdS

is

_2.5,

the

_{cyclohexane-brine}

volume ratio is

_5).

This microemulsion is of the hard

_sphere

_type

_[6].

We measured its

_X-ray

_spectrum and observed that

q4

I was also linear in

q2

in the

asymptotic

_range as in our brine-toluene microemulsions.

Certainly 4

the thickness of the SdS

polar

heads

layer

is not _very different in the two

_systems.

_Knowing

E for the BIM _system from the neutron

_scattering

experiments,

we deduce the value of d in this _system from the

_X-ray

_experiments,

and use the obtained value to evaluate Z in our brine-toluene

_system.

The

_expression

of I calculated from the electron

density

of brine and

_cyclohexane

is

_(Appendix

_II)

Experimentally,

we found I = 11

A.

The f value

deduced from the water

_droplets

radius measure-ments is 52

A2

_[6].

This is

_compatible

with a thickness d = 5

A,

comparable

_to both the

Debye

screening

length

and

_polar

heads size.

Returning

to the brine-toluene

microemulsions,

with

d=5A,l= 12 + 1.5A,l 2 =

E

_E

595 2 1 + Ed (at

(

)

salinity

S = 6.5

%),

_we

deduce,

E = 61 _±

8 A ,

in

accordance with the known results

[15].

Thus,

the oil-water interface in our _systems is narrow and well

defined,

even in the critical behaviour zone of the

_{phase diagram.}

Our

_study

_proves that the determination of the

asymptotic

behaviour of the

intensity

scattered

_by

microemulsions is _very useful to discriminate between the two

_possible

situations :

microemulsion,

molecular solubilized mixture or

microemulsion,

dispersed

com-posite

liquid Apparently,

this mean was not used

before,

because the

_X-ray

or neutron

_scattering

mea-surements

_(which

can offer

_{simpler two-phases}

contrasts)

were not extended to

_sufficiently

_large

_q. To our

knowledge,

such a

_type

of

_asymptotic

behaviour -

q" I

linear in

_{q2 -}

is observed here for the first time in colloidal surfactant _systems. In the

X-ray

experiments,

this is due to the

_high

contrast of SdS

_polar

heads

(relatively

to water and

_toluene)

associated with

large

sizes

_{(much larger}

than the thickness of the interfacial

film).

This enables the

asymptotic

regime

to be observed at

_relatively

small values

_{of q (q}

> 0.1

_A-1).

Such a

_type

of contrast allows a

_practical

deter-mination of E which is :

i)

independent

of the structure model of

micro-emulsions,

ii)

independent

of the normalization of the inten-sities.

_(Notice

that one cannot normalize

_I(q)

with the usual invariant

q2

_{I(q) dq}

_[21],

which in this case

0

diverges).

2.3.2 Semi-local scale : characteristic

_length.

-Expressions (3)

and

₍₄₎

of Porod’s law are valid as

long

as the interface is

_flat

on the scale defined

_by

the

_{scattering angle (~}

_nq-l).

In the absence of a detailed structural model

_adapted

to our contrast

conditions,

our idea is that the location of

_{the q}

crossover zone between the _very small

_angle

behaviour and the

_asymptotic

behaviour

_gives

the size scale where the film becomes

_curved,

i.e. an estimation of the

_{persistence length}

of the

film,

C;k.

In the

_paragraph

_{(a) below,}

we define the cross-over

scattering

vector q,

and

_point

out the

_practical

and theoretical limitations of this definition. In

paragraph (b),

we show

_that,

for all the

samples,

the intensities in the medium _q-range can be written as

I(q)’

=

Io

f (qlq 1),

thus q 1

is _a

good

choice to

determine a characteristic

_length.

In

_{paragraph (c),}

we

_report

the observed

dependence

of ql

on the

composition

of the microemulsions.

a)

The definition of a characteristic

scattering

vector _ql. - We have chosen

as a definition of the cross-over

scattering

vector _{ql, the abscissa of the} minimum of the

_q’

I versus _q

_{plot (see}

_Fig.

5 and Table

IVa,

b,

c,

d).

Let us first

_point

out the

_practical

limitations of this _{choice. The determination of q,}

_{mainly depends}

on the

precision

on

q 4

bq _

2

_%

and

2%

q

1

lead to

bq 4 1-

10

_%).

. We found that the

measure-q

I

)

Table IV. - Structural data

of

A,

B,

C

_samples,

_{q1 i} is

defined

in

text, Z

= 6 _x

101

A2, 4>

is

0,,

in the oil

rich side and

₀₀

in the water rich side.

Table IVa. -

Fig. 5. -

q41

versus _{q. System} B

_(L2

_{experiment) ; S} = 6.5

%, m.

= 0.5 g; **

_0,

= 0.5, ** _0.7, + + 0.8, x x _0.85, oo 0.9.

Table IVb. -

System

B,

oil volume

_fraction

scan

(S

= 6.5

%,

ms = 0.5

g), first

column : G

_experiment;

second column : L

experiment.

Table IVc. -

System

B,

SdS concentration scan

(S

=

6.5

_%,

_-00

=

0.8)

(L

experiment).

Table IVd -

_System

C.«

_{constant ç}

» scan

(S

= 6.5

%).

6 00 Ov =

150 Á.

Cg Z

50

ment _{of q,} was more

_precise

in L

experiments

than in G

_{experiments :}

the statistics are better and the

smaller statistical uncertainties on the

_intensities,

we estimate the

_precision

_ðql/ql

to be about 5

_%

in L

_experiments

and 10

_%

in G

_experiments.

_By

comparing

the results obtained on the two _set-up

(Table

IV and

_Fig.

_6),

we find that the

_systematic

error introduced in the G

experiments by

the colli-mations corrections are within the above uncer-tainties.

Fig. 6. - The

product cs

-Fql ’

is

plotted

versus the toluene volume fraction

_0,.

0 system A

_{(L1 experiment); 0}

system B

(L2

experiment);

+ system B

_(G1

_experiment);

* _system B

(G2

experiment); A system C

_(G3

_experiment). The straight

line

_corresponds

to _cs

_fql

1 = 0.65

_(0,,

or

_l/Jo).

The _parabola

corresponds to _cs

_Zql

1 = 0.9

§o 0,.

There is also a theoretical limitation in our choice : q 1 is located in a _q-range where the

volume-scattering

contribution

(dominated

at

_{low q}

_by

oil and water

correlations) a

priori

becomes of the same order of

magnitude

as the surface contribution

(dominated

at

_{high q by}

the

_film).

A

_{priori qi}

_may be a

compli-cated function of the characteristic size

ç,

the

oil,

water, SdS volume fractions and electron densities. However there are very

interesting

particular

cases where the relation between _q,

_{and ç}

is

_simple.

If there is

_only

one

_length

in the structure

_description

and if one can write the intensities as

_i(q)

_{= io}

_f(qç),

then

_{ql 1}

is

_proportional

to

_ç.

This occurs :

i)

If the film contribution is

_negligible.

Then Porod’s law

(3)

imposes

and

ii)

If the film contribution is dominant.

Then,

Porod’s law

₍₄₎

_imposes

and

b)

Behaviour of the intensities in the medium q-range

(q -

?i).

i) Similarity

of

the _spectra. - As the relation

between q 1

and

_thç,

characteristic

_length

could be not

_simple,

we looked for the existence of a

_scaling

law

_{by plotting}

Ln I as a function of

(q/qi)2.

For 0.5

_qlql

1

_(domain

of the

_q’

I versus _q

peak),

the

_logarithms

of the intensities

_only

differ

_by

a constant

_(Fig.

7

_concerning

_system

_B),

the _spectra are similar. The

similarity

domain is even more extended towards

_{smaller q}

for the dilutest

_samples

(l/Jo

0.8).

Thus

_{experimentally ql}

is a

good

scatter-ing

vector unit in the medium _{q-range. For} 0.5

q/q

1

1,

we write

I(q)

=

10 f(q/ql).

ii)

Variations

_of

the intensities. - The formulae

(5)

and

_{(6) predict}

the variations of

_{Io, prefactor}

of the

scaling law,

as a function of the surfactant concentra-tion cs and the characteristic

length ç,

in the two extreme cases : the film contribution either dominant or

_negligible.

_Assuming

ql 1 we

found that the measured

_Io

decreases with

_increasing

_ql, buts

in a _way which is not so

simple

as that stated

_by

formulae

₍₅₎

and

_(6).

The mean

_slope

of a

plot

In

_Io

versus _{In ql is about}

- 3.3 for the

scan

₀₀

variable at constant surfactant

concentration,

i.e. intermediate between the pre-diction - 4

_(film

contribution

_negligible)

and - 2

(film

contribution

dominant).

At cs variable

(serie

00

=

0.8),

the _same

slope

is about -

2.6;

with the

_assumption

_{that ç}

is

_inversely

proportional

to _{cs, the}

_predictions

of formulae

₍₅₎

and

₍₆₎

are in this case,

_{respectively, Io}

( 1 /) - 3

or

(1/ ç) -

1.

Thus,

we are not

_strictly

in one of the two _pure cases of formulae

₍₅₎

and

_(6),

however the evolution of

_Io

is better described

_by

formula

(5)

than

_by

for-mula

_(6).

We conclude that the oil-water contri-bution to the

_scattering

is the most

_important

_{at q} less than ql, and

that,

in a first

approximation,

ql1

fulfills the conditions to be the characteristic size of our microemulsions.

iii)

Remark. - A remarkable feature of the

plots

In I versus

(q/ql)2

is

that,

the curves are

approxi-mately

linear in the _range 0.2

_(q/ql)2

0.65

_{(Fig. 7),}

although

it is not the _very

_{low q}

Guinier _range

_[20]

q2

o2B

Fig. 7. -

Intensity in reduced unit

_(q/ql)

_(In

I vs.

_(q/qy2)

system B

_(L2

_experiment).

particles,

which have a radius of

gyration

RG).

A

possible

explanation

of this fact is that the

_expression

q4

exp q 3 L

well

_reproduces

the

_peak

of the

_{q4 I}

versus q

plot

This can serve as another means to estimate the

_typical

size in the

_systems.

On

_figure

_7,

the

straight

line

_parallel

to the

_experimental

curves

corresponds

to the

_expression

I N

exp q 3 L

with

_{L = 3.8 ql1.}

c)

Behaviour

_{of q 1 : interpretation.}

- At

constant

salinity

(S

= 6.5

%)

and oil volume fraction

(00

=

0.8),

we have varied the SdS concentration. In this series _ql varies

_linearly

as a function of SdS concentration _cs

(Table

IVc).

In system

C,

where the theoretical

_length

6 Po Pw

_Å

Çk = Cs I

was

_purposely

held constant

₍

= 150

A

cs E

with Z’ = 60

A2).

ql 1 is found to be constant

(q,

1 =

0.046

_{Å - 1)}

in the inversion zone

_(0.4

₀₀

_0.6).

To

_study

the behaviour

_{of q1}

as a function

_{of 00,}

we have

_plotted

for all

_samples

of

_system

A

_(salinity

_scan)

and

_systems

B and C

_(00-scans),

the

_product

_cs

_{fql 1}

versus

₀₀

_(Fig.

_6).

The

_resulting

curve is

_symmetric

in

00

and maximum at the inversion

_{point (00}

=

0.5).

On the water rich side

₍₀₀

_0.3),

_cs

_Eql1

is linear in

00.

On the oil rich side

₍₀₀

>

0.7),

_cs

Eql1

is linear in

_{(1 -}

_00).

Our

_{interpretation}

is the

_{following :}

At low water or oil concentrations

_{(Oo oro,}

0.3),

q 11

is

_proportional

to the size of distinct

_isotropic

objects.

Using

the low water concentration data

_(0,,,

_0.3)

(Table

lVb and

c)

the

_{proportionality}

factor between

-1

and

00 -

is experimentally : q 1 and

s-_y

s is

experimentally :

(we

neglect

the

_slight

_dissymmetry

between the oil rich and water rich

_side).

In a s here model

R -

3 W

th s the h In a

_sphere

model

_S,W

=

thus

the

phenome-Cs

nological

relation between

_P,

_{and q 1}

is

_Rs,w

=4.6

_ql1.

Surprisingly

the

_experimental

relation between L

(defined

in the

_{precedent paragraph)}

and

_{RS :}

L = 3.8

qi 1

= 0.8

Rs,

is akin to the

_expression

of the radius of

_{gyration RG}

of a

sphere

of radius R :

_RG

-0.77 R.

We

also

have checked the

_procedure

of size measure-ment

_{by q1}

on the known microemulsion 5B 1M of reference

_[6].

We

_{found q 1}

= 0.063

A -1

and 4.6

_{ql1 =}

73

A.

The radius of the water core _{r w deduced from} neutron

_scattering

is 66.5

_{A. Again}

the _agreement is

good

As our results are consistent at low oil or water

concentration,

we infer that a

_{proportionality}

relation between

_{ql 1}

and the characteristic

_length

of the micro-emulsions is also valid in the inversion zone.

. In the inversion zone

(0.3

00

0.7),

as

_directly

demonstrated

_by

the results on

_system

C

_{(constant Çk}

scan)

which confirm the evolution on

_system

B

₍₀₀

scan),

ql1

follows -

up to a numerical factor - the

prediction (1)

(we

do not know if the deviations observed on _system A

_(salinity

_scan)

_{- figure}

6 -are

_significant

because of the much

_larger

_uncertainty

on the

_phase

_{composition).}

_{Experimentally,}

one appro-ximately has q1 -1

=

0 9 Po

ow

In the inverso _{n z n}

Cs E

the

_experimental

relation between

_ql1

_{and Çk}

_(defined

by

(1))

is then

_{qi 1}

_{= 0.15 Çk or Çk}

= 6.5

_{ql 1.}

Then

L = 3.8 ql1

= 0.6 Çk’

Thus,

although

not a direct

_proof,

the observed relation

_{between q 1}

and

_{Çk’ showing}

that in our sys-tems the inversion is a smooth _process

culminating

at

00

=

0.5,

may be the first

experimental

evidence from

scattering

experiments

that as

₀₀

_increases,

one _passes

progressively

from a structure made of distinct oil in water

_spheres

to the bicontinuous structure described

by

the

_{Talmon-Prager}

or de Gennes

model;

the curva-ture of the film is inverted at

₀₀

=

0.5, and,

_as

00

again

increases,

the reverse _{process takes}

_place.

2. 3. 3 CORRELATIONS OR INTERACTIONS IN MICROEMUL-SIONS. - The

structures of our microemulsion are very similar

(up

to a scale

_factor)

at scales which are of the same order of

_magnitude

or smaller than the cha-racteristic size. The differences between the

_samples

appear at

larger

scales

(smaller scattering

vector

q -

10-2 A-’).

We have noticed three different types

of behaviour :

i)

The B

_samples

in the inversion zone

_(0.4

_{00 ,}

0.65) exhibits a diffuse band centred around

q*

(q*

= 0.011

_A-1,

the

_{corresponding}

_Bragg

_spacing

d *

_{2 nq* -’}

is 590

_A)

_[23].

This

_peak

is

broadened,

but does not move as one _goes far _away from the inver-sion

_point

and it

_disappears

at

₀₀

= 0.7

(oil

rich

side)

and

₀₀

= 0.35

(water

rich

side).

The _same features

were observed in the C

_system

(q*

= 0.02

A-1,

d* = 310

A)

revealing

a _strong correlation between the

_place

of the

_peak

and q,.

ii)

The B

_samples

outside the inversion zone

(00

0.3,

00 >,

0.75)

do not follow the « Guinier » law

_[20]

in the Guinier _range

_qR

1

_{(Fig. 7).}

In

parti-cular,

the intensities

_rapidly

increase _{as q goes} to zero.

iii)

The two

_samples

most dilute in oil of system A

(S

= 3

%

and S = 4

%)

also exhibit _a diffuse

peak.

(g*

(S = 3

(),,)

= 0.25

Á -1, d*

(3

0,’’)

= 250

A,

q* (S

=

4 %)

= 0.019

Á -1, d*

(4 %)

= 330

A).

These three different behaviours indicate that the interactions or correlations between oil or water domains are

_{quite complex.}

i)

In the inversion zone, the

intensity

scattered

_by

a two

_phase

random oil and water

_partition

in Voronoi

polyhedra

has been calculated

_by

Kaler and Pra-ger

[24].

As this

_partition

is

_random,

_{they predict}

that at low q, one sees the structure factor of -

say -

a water domain

_(in

the oil rich

_side),

and the intensities

appro-ximately

follow a Guinier law

(the

«

_equivalent

radius of

_{gyration R. >>}

is

_equal

to 0.572 c-

1/3’1

where C- l,3 is the characteristic

_length

of the microemulsion related to the

_specific

surface in the microemulsion

_{cs -Y by :}

[9] cs f

= 5 . 82

el/3

4J 0 (p"",

thus

C- 113

=

5.82 cs 00 0,,,,

0.97

_Çk;

within this model

_RG

= 0.55

Çk)’

This

_prediction

does not _agree with the

_experimental

results at _very

_{low q (the}

intensities exhibit a

_peak).

But

again,

we note a remarkable coincidence : the

experi-mental relation found in the inversion zone between L = 3.8

qi 1

and Çk

(L

= 0.6

Çk)

is _very close of the

Kaler-Prager

theoretical

_{prediction RG}

= 0.55

Çk’

The

_peak

existence is

_puzzling

within the frame of the random

models,

however it is not

_by

itself a

_proof

in favour of a model of - _say - hard

spheres.

It is

mainly

a

proof

in favour of a model less random than that of Kaler and

Prager.

Considering

the results of the

_preceding

section,

it is worthwhile to _try to understand how a

_peak

can arise within the frame of the random models :

Probably,

the correlations between

neighbouring

oil and water domains linked

_by

the interfacial film are not

_negligible

as was

_{supposed by}

Kaler and

Prager.

The situation could be

_analogous

to that observed in

_hydrogenated

and deuterated diblock

copolymer

melts : the double

constraint,

global

incompressibility

and link between the two distinct