Local structures of the surfactant aggregates in dilute solutions deduced from small angle neutron scattering patterns

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Local structures of the surfactant aggregates in dilute

solutions deduced from small angle neutron scattering

patterns

J. Marignan, J. Appell, P. Bassereau, G. Porte, R.P. May

To cite this version:

Local

structures

of

the

surfactant

_aggregates

in dilute solutions

deduced

from small

_angle

neutron

_scattering

_patterns

J.

_Marignan

_(1),

J.

_Appell

_(1),

P. Bassereau

_(1),

G. Porte

₍₁₎

and R. P.

_May

₍₂₎

(1)

Groupe

de

_Dynamique

des Phases Condensées

_(associated

to the C.N.R.S. UA

_233),

Université des Sciences et

_Techniques

du

_Languedoc,

34060

_Montpellier,

France

(2)

Institut Max von Laue-Paul

Langevin,

BP _156X, 38042 Grenoble, France

(Reçu

le 5 mai _1989, révisé le 24

_juillet

1989,

accepté

le 31 août

₁₉₈₉₎

Résumé. 2014 Nous étudions par diffusion des neutrons aux

_{petits angles}

_(vecteur

de diffusion

compris

entre 2 x 10-3 et 5 x 10-1

Å-1)

les trois structures locales

_(sphère,

_cylindre,

_plan).

Nous avions

_{précédemment}

montré

_[1,

8,

9]

de

_façon

_{indirecte que les}

_agrégats

de surfactants

adoptaient

l’une ou l’autre de ces trois structures dans les

_phases

riche en eau

_(salée)

de

_systèmes

binaires

_{(surfactant/eau salée)}

ou ternaires

(surfactant/eau salée/hexanol).

Nous obtenons une

confirmation directe de ces structures et déterminons avec

_précision

leurs dimensions caractéristi-ques.

Abstract. 2014 The three local structures

(spherical,

cylindrical

and

_planar)

_previously

assumed

_[1,

8,

9]

to be that of the surfactant _aggregates in the brine rich

_phases

of

_binary

_{(surfactant-brine)}

or

ternary

(surfactant-alcohol-brine)

are studied

_by

small

_angle

neutron

_scattering

_(scattering

vectors

range from

2 10-3

to 5

10-1

_Å-1).

We confirm

entirely

the

_{previous assumptions}

and determine

precisely

the characteristic dimensions for these structures.

Classification

Physics

Abstracts 61.30 - 64.70 -

82.70

1. Introduction.

In the recent _years two of the

_phases

formed in solutions of surfactants have received

increasing

attention

_namely

the solutions of

_{large elongated}

micelles and the so-called anomalous

_{isotropic phase}

_(L3).

Large

elongated

micelles have been studied in dilute solutions where

_they

offer an

_example

of unidimensional

_growth

_{[1-3] :}

_they

are

_pictured

as

_long

flexible

_cylinders

and

_they

are thus

expected

to

_{display polymer-like}

behavior. In semi dilute

solutions,

Candau et al.

_[4]

indeed

found

_{typical scaling}

law behaviors

(for

scattered

_{light intensity,}

diffusion

coefficient,

etc.).

These

_polymer-like

micelles offer a further

opportunity namely they

exist with a

_large

distribution of

_lengths

in

_{dynamical equilibrium}

and are thus «

living polymers

»

[5]

which are

expected

to

_{display peculiar rheological properties.}

All these studies

_imply

a flexible

cylindrical

local structure characterized

_by

the radius of the

_cylinder

and

_by

a

_persistence

length

which is a measure of the

flexibility. Clearly

the relative

magnitude

of this

length

with

respect

to the radius is crucial for the

_validity

of the

_{polymer-like representation}

of

_elongated

micelles.

The anomalous

_{isotropic phase L3}

is _{encountered in many}

systems

(non-ionic

surfactant in water, ionic surfactant

plus

alcohol in

_brine...).

It is

_{optically isotropic}

at rest but exhibits

striking birefringence

upon

shaking.

Recent studies

[6, 7]

suggest

a bicontinuous

_phase

with

an infinite

_{bilayer separating}

two interwoven selfconnected brine domains. In this

_picture,

the

bilayer

is a film with the same

topology

as the

_monolayer

film

_separating

the oil and water

domains in a bicontinuous microemulsion. In the

L3 phase

the two disconnected domains are

identical and the film has a

_spontaneous

curvature

_equal

to zero ; this is not the case _anymore

in the bicontinuous microemulsion where the

asymmetry

of the domains can introduce a finite

spontaneous

curvature. The

_{L3 phase}

thus

_represents

a «

simplified

» model for bicontinuous

microemulsion,

to test different structural

_{descriptions.}

This

_implies

that the local structure of the surfactant

_aggregates

is a thin

_bilayer

(of

_{very small thickness}

_compared

to its

_extension).

For some

_time,

we have been

_engaged

in the detailed

_study

of the

_phases

formed in some

water

_{(or brine)}

rich

_binary

_{(surfactant/water)}

or

_ternary

_{(surfactant/alcohol/water)}

_systems.

We showed that the

_polymorphism

was rich in these

_systems

_[1,

_8,

_9]

in

_agreement

with other

groups’

work

_[3,

_10,

_11]

and tried to understand the

_phase

behavior in terms of the

morphological

transformations of the

_{elementary objects}

induced

_by

addition of salt to the

binary

systems

[2]

or

_by

the variation of the alcohol-to-surfactant ratio in the

_{ternary system}

[12].

The local structure of the

_{elementary objects}

was infered from the nature of the observed

_phases

_(micellar

_solutions,

lamellar

_{lyotropic liquid crystal La}

and anomalous

isotropic phase

L3)

and from more or less indirect

_experimental

evidences

_[1,

8,

9].

We found

the,

now

classical,

_{sequence for the local} structure of

_aggregates

due to the

_{self-assembly}

of surfactants

_plus

_(in

some

cases)

alcohol

_molecules,

_{namely spherical, cylindrical}

and

_planar

structures. A low

_spatial

resolution

_small-angle

neutron

_{scattering study}

_[9]

confirmed the

previous assumptions,

however an exact

_quantitative

assessment of characteristic dimensions is

_{impeded by}

the

_possible

existence of

_{interaggregates}

interactions

which,

although

weak,

can

_modify

the

_scattering

pattern.

The purpose of the

present

study

is to confirm our

_previous

results and to obtain exact

quantitative

values of the characteristic dimensions of the three local structures

_which,

as

stated

_above,

are

_{prerequisites}

to the use of the surfactant

_phases

as model

systems.

In order to reach our

_goal

we first choose

_{appropriate samples representative}

of the three local

structures amenable to a

_small-angle

neutron

_{scattering study}

on the

_{largest possible}

_q-range

and in

_particular

with the

_{highest spatial}

resolution. The

_scattering

_patterns

are then

_analysed

using

the well established

_procedures

for the structural studies of colloidal or micellar

aggregates

[13-15].

In the successive

_parts

_{of the paper} we discuss in turn the results on each local structure,

namely spherical,

cylindrical

or

_planar.

We indicate the nature of the chosen

_samples

and then describe and

_analyze

the

_scattering

_pattern.

2.

_{Experimental.}

2.1 SAMPLE PREPARATION. -

Cetylpyridinium

bromide

_{(CPBr), cetylpyridinium}

chloride

(CPCI),

hexanol and sodium bromide and chloride are the same as in

[8].

Deuterated brine were

_{prepared by}

dissolution of the salts in

D20

(99.8

%

D).

The

samples

were

_prepared

by

weight.

Institut Laue

_Langevin

in Grenoble. The

_samples

are contained in

_quartz

cells

_{(Hellma) (with}

a

_path

of 2

_mm).

An area of 1

CM2

is illuminated

_by

the neutron beam. Intensities relative to the incoherent

_scattering

of

_H20

in a cell with a

_path

of 1 mm are obtained from the measured

intensities after substraction of the solvent and

_empty

cell contributions. The data are then handled

_according

to standard

_procedures

_{[16, 17].}

_Only

one contrast factor is assumed : the contrast is

_mainly

between the

_hydrogen

atoms of the

_aggregates

and the deuterium atoms of the solvent

_[15].

The

_density

_{(p )}

of the surfactant in the

_aggregates

is derived from the evolution of the

_binary

surfactant brine mixture as a function of solvent volume fraction

(linear dependence)

giving

for CPCI

_(p

= 0.96

g/cm3)

and for CPBr

(p

= 1.07

g/cm3)

and the

density

of hexanol in the

_aggregates

is assumed to _{be that of the pure}

_liquid

hexanol

(p

= 0.82

g/CM3).

The fast

exchange

between the

initially protonated

OH

groups of the hexanol and the deuterium atoms of the brine solvent is taken into account

_(this

is

_certainly

important

in the estimation of the mass of the

_aggregates).

At

_D11,

_experiments

are

_performed

with low

_spatial

_{resolution ;}

the

_wavelength

= 10

Å

and the

_scattering

vectors

_{(q )}

_{range from 2} x

10- 3

Â-1

to 1.5 x

10-1

 -1.

In _this q-range interactions between

aggregates

can _{show up in the}

_scattering

_pattern,

however we

studied very diluted

samples

(

-- 1 %

aggregates)

and

_neglected

eventual interactions in our treatment of the data. The excellent

_agreement

found between the

_geometrical

characteristics derived from these measurements and from the measurements at D16 indicates that this

neglect

is reasonable.

At

_D16,

the

_experiments

are

_performed

with

_{high spatial}

resolution ;

the

_wavelength

= 4.52

Â

and the

_scattering

vectors

_{(q )}

_{range from 7} x

10- 2 Â -1

to 5 x

10-1 Â -1.

We

computed

the invariant

_Q

and the ratio of surface to volume

_{(s Iv)}

_{[13-15] :}

For a disordered material and in the

_large-q

limit the interactions between

_aggregates

have no influence on the

_scattering

_pattern

which reflects

_only

the local structure and we studied more concentrated

_samples

in order to increase the

_scattering

cross-sections. The values obtained for the invariants and the Porod limits are

_given,

in table

I,

for the three studied

samples.

Table I. 2013 The invariant

2.3 LIGHT SCATTERING. - In

one case we

_completed

the

scattering

_pattern

at

_{low q by}

measuring

the

_angular

distribution of scattered

_light

on the

_laboratory

set _{up : the}

_light

source

is an _{argon ion laser}

_working

at 4 880

_À,

the beam is focalised on the

_sample

contained in a

cylindrical

cell and the scattered

_photons

are collected on a

_{photon multiplier}

and counted as a function of

_scattering

_angle.

The

_scattering

_{vectors q}

_{range from}

3 x 10- 4 Â -

1 to

3 X 10-3 A-l.

3. Globular structure.

The studied

_samples

are two micellar solutions : 0.01

_g/cm3

CPCI

_(at

low

_q’s)

and 0.05

_g/CM3

CPCI

_(at

_larger

_q’s)

in 0.2 M NaCI brine. From

_previous

studies the micelles are

expected

to be

_globular

_{[18, 19].}

3.1 Low q SCATTERING PATTERN. - If the local structure is

globular

we

_expect

the scattered

intensity

to _vary as

_[13-15]

at

_{small q}

_(qRg

_{1 ).}

_Rg

is the radius of

_gyration

of the

_particle,

c is the concentration

(g/cm3),

M is the mass of the

_particle

(g),

and

(bm -

_vm

po) is

the contrast difference

_[20]

between the

_particle

and the solvent

_(cm/g).

In

_figure

1,

Ln

_{(1 (q»}

is

_plotted

as a function of

q 2.

From the linear

_part

at the lowest

_q’s,

we

_compute

_using

_{(2) :}

from the

_slope,

_Rg

= 20 ± 2

À

and from the

extapolated intensity

1 (0),

M =

(6.6 ± 0.5 )

_x 10- 20

g.

Assuming

the

_aggregates

to be

_{perfect spheres}

( 2 _ 5

_R2

and rm

m

3 M )

₄

we obtain two estimates of their radius : irp

Fig.

1. - Guinier

plot Log

(1 (q»

vs.

q 2

for the

_sample

1 % CPCI in 0.2 M NaCI brine

_{representative}

of

the

_{spherical local}

structure. The arrows indicate the limits :

_qRg

= 0.2 and 2 between which

₍₂₎

is found

to hold.

3.2

_{LARGE q}

SCATTERING PATTERN. - From the Porod limit

_using

₍₁₎

and

_assuming

the micelles to be

_{perfect monodisperse spheres}

we obtain another estimate of the radius of the

Fig.

2. - Form factor oscillations in the Porod

region.

The full line = calculation for

_spheres

with

r =

25 A;

dots =

experimental

result for the

sample :

5 % CPCI in 0.2 M NaCI brine.

As

usual,

oscillations

_reflecting

the form factor of the

_scattering

_objects

are observed in the

plot

of

_{q 4 I (q )}

versus _{q shown in}

_figure

2.

_Assuming,

as

_previously,

that the micelles are

spheres :

the form factors

_{corresponding}

to different radii r are

_computed

and

_compared

to the

experimentally

observed oscillations. We seek for the best

_agreement

for the

_position

of the extrema : this is found to _{be very sensitive} to the chosen radius. In

_figure

2 the curve

computed

with r =

25 Â

is

displayed,

the

agreement

is

_good

for the

_position

of the three first extrema and is the best we observed

_(trials

with the form factors for a

_cylinder

₍₄₎

or a

_plane

(9)

led to no

_agreement).

We thus obtain a fourth estimate of the radius of the

_{sphere :}

ro = 25 ± 1

Â.

The

_experimental

_damping

of the oscillations can be due to a size

_{polydispersity}

and/or to a small

_{shape anisometry}

of the micelles.

_{Looking carefully}

at

_figure

2 we note

_that,

although

the overall

agreement

between calculated and

_experimental

extrema is

_good,

the first

_experimental

maximum is on the left of the calculated one, the first

experimental

minimum is on the

_right

and the second maximum matches

_exactly.

If the

_damping

was due to

polydispersity

alone we would not

_expect

such deviations from the exact

_positions

of the

extrema, which would

_correspond

to a mean radius. On the

_contrary,

a

_{shape anisometry}

of

the micelles could

_explain

both the

_damping

and the deviation from exact coincidences of the extrema. These

_experimental

results are thus in favor of a small

_anisometry

of the

micelles,

too

_small,

however to be

_{quantitatively}

established.

The evidences obtained at all

_q’s

are in excellent

_agreement

with one another and confirm

that the small micelles have a

_{quasi-spherical}

form. The four estimates obtained for the radius of the

_globular

micelles are

_equal

within

_experimental

errors

_(cf.

Tab.

II)

r = 25 ± 1

Â.

It is

interesting

to _{compare the radius thus} obtained to _{the average}

_hydrodynamic

radius of the CPCI micelles

_previously

obtained

_{by quasi-elastic light scattering}

_{[18] :}

_Rh

= 29 :t 2

Â.

The

agreement

is

_good

if one recalls that

_Rh

measures the radius of the

_{equivalent diffusing sphere}

(micelle

+

_hydration

_layer)

while the r’s measured here are the radius of the

_{dry equivalent}

Table II. - The radius

_of

the

_{spherical local}

structure : the micelles

_of

CPCI in 0. 2 M NaCI

brine.

4.

_Cylindrical

structure.

The studied

_samples

are two micellar solutions : 0.01

_g/cm3

CPBr

_(at

low

_q’s)

and 0.05

_g/CM3

CPBr

_(at

_larger

_q’s)

in 0.8 M NaBr brine. From

_previous

studies the micelles are

expected

to be

_large

flexible

_cylinders

_[1,

18,

19].

4.1

_{LARGE q}

SCATTERING PATTERN. - From the Porod limit

_using

₍₁₎

and

_assuming

the micelles to be

_long

rods with a circular cross-section we obtain an estimate of the

cross-sectional radius :

Oscillations

_reflecting

the form factor of the

_{scattering objects}

are observed in the

_plot

of

q41 (q)

versus _{q shown in}

_figure

3.

_Assuming

that the micelles are

_{cylinders :}

Fig.

3. - Form factor oscillations in the Porod

_region.

The full line = calculation for

cylinders

with _a

circular cross section r = 19.5

À ;

dots =

experimental

result for the

sample :

5 % CPBr in 0.8 M NaBr

the form-factor for

_cylinders

of different radius r is

_computed

and

_compared

to the

experimentally

observed oscillations. We seek for the best

_agreement

for the

_position

of the extrema. In

_figure

3 we _compare our data with the curve

_computed

for r = 19.5

Â,

the

coincidence in

_position

of the three

_experimental

and

_computed

extrema is found to _{be very} sensitive to the chosen radius

_(the

_precision

is

probably

better than 0.5

_{À) ;}

here

_again

trials with the form-factors for other structures

_{(sphere (3)}

or

_plane

₍₉₎₎

led to no

_agreement.

We thus obtain another estimate of the radius of the

_{cylinder : ro}

= 19.5 ± 1

Â.

The observed

experimental damping

of the oscillations

_(see

_Fig.

₃₎

can be due to fluctuations of the radius of the

_cylindrical

micelles and/or to a small

_ellipticity

of their cross-section. We have no clue

allowing

to choose between these

_{possibilities.}

4.2

LOW q

SCATTERING PATTERN INCLUDING LIGHT SCATTERING DATA. - In

_figure

4 the neutron and

_{light scattering}

patterns

are

_{displayed illustrating}

the excellent

_overlap

between the two

_patterns

_(within

a

_scaling

_factor).

In this

_{log/log representation,}

two linear

_regions

can

clearly

be

_{distinguished}

the first one at the lowest

_q’s

has a zero

_slope

and

_corresponds

to the overall finite size of

_objects

and the second one in the intermediate q-range with a

_{slope equal}

to one is indicative of rod-like

_objects

[15].

Fig.

4. -

Log/Log display

of the low q-range

spectral

pattern.

(a)

=

light scattering

and

(0)

= _neutron

scattering

for the

_sample

1 % CPBr in 0.8 M NaBr brine

_{representative}

of the

cylindrical local

structure.

4.3 INTERMEDIATE

_{q-RANGE :}

THE RADIUS OF THE CYLINDER. - For a random distribution

of rod-like

_particles

we

_expect

_{qI (q )}

to _vary as

_{[13, 14] :}

in the range

qR,,

:: 1

and q f > --

1 where

R,

is the radius of

gyration

of the normal section of

the rod

_{and (f)}

is the

_{persistence length}

i.e. the average

length

below which the linear

_object

can be considered as

_straight

and

_{rigid ;}

in

_figure

4 a _{q-range where}

_{I (q )}

oc

q -1

is indeed

observed

_{(see above).}

In

₍₅₎

_ML

is the mass _{per unit}

_length

of the rod. Ln

_{(qI (q»}

as a

function of

_q’

is shown in

_figure

5. From the linear

_dependence

_{in the range}

3 x 10-2 À- 1 --q. 1.5 x 10-’À-1

we deduce

_using

_{(3) :}

_{Rc = 15.5:t2À}

and

_{ML =}

Fig.

5. -

Log (qI (q ) )

as a function of

q’

in the intermediate low q-range for the

_sample

1 % CPBr in 0.8 M NaBr brine. The arrows indicate the limits :

_qR,

= 0.4 and 1.5 between which

(5)

is found _to hold.

we obtain two estimates of its radius :

_rg

= 22 ±

2 Â

and

4.4 LOWER Cj-RANGE : EVIDENCE FOR THE FLEXIBILITY OF THE LONG CYLINDRICAL MICEL-LES. - We stated above that

(5)

is valid down to

_q’s

_{such (f)}

1 so that if the

_objects

are

infinite

_{rigid cylinders}

₍₅₎

will be valid down

_{to q}

= 0

while,

if

they

_are

rigid cylinders

of finite

length

L,

[qI (q) ]

will fall to zero

_{with q}

from

q (L - 1)

downwards. A

_plot

of

qI

(q )

versus _{q in the lowest q-range is shown in}

_figure

_{6 ;}

_clearly

instead of one of the two behaviors

_expected

for

_{rigid cylinders}

a third behavior is observed :

_going

downwards

_along

the

_q-axis

₍₅₎

is valid down

_{to q;:-}

1.5 x

10-2

Â- 1,

qI (q )

then increases before

_falling

down

to zero. This last behavior indicates that the

_{scattering objects}

have a finite size

(see below).

Let us first examine the

possible origin

of this

_bump

in the

qI(q)

_plot.

Such an

_upward

trend has

already

been

_previously

observed in the neutron

_scattering

_spectra

of another micellar

_system

_[21],

but was then

_interpreted

as the indication of a

_{secondary aggregation}

of the micelles. However we

_suspect

from our

_previous

studies

_{[18, 22]}

that the

_long

rod-like micelles are flexible

_cylinders

and we feel that the

_upward

trend in the

_qI

(q )

_plot

could be due

to this

_flexibility.

The

_asymptotic

limit of

_{I (q )}

_goes over from

q -

in

the case of a

_long

thin

rod

_{(cf. (5))}

to

q-z

for a Gaussian coil

[23] ;

in the intermediate case of a flexible

_rod,

the two

dependences

of

_{1 (q)}

_{with q}

must be observable in two

_adjacent

_ranges

_{of q provided they}

are

not obscured

_by

the

_exponential

_decays,

due to the finite radius of the cross section of the rods on the

_{highest q}

side and to the finite size of the flexible coil on the

_{lowest q}

side. Such a cross over from one

_dependence

to the other of

_{I (q )}

_{on q} occurs at

_[24]

_{qc .}

_{1.9/ (f),}

from

figure 6

we can estimate

q, %,% 1 X 10-2 Â- 1.

We thus obtain for the

persistence

length

(P)

= 190 ± 50

Á.

If _our attribution of the

upward

trend _to the influence of the

flexibility

_on

the

_scattering

pattern

is correct the

_following

relation

_[25]

should furthermore hold :

for

_{L - ’ « q .c R,}

with

_L,y,

the

_length

of the flexible

_cylinders.

The

_plot

of

_{qI (q )}

versus

q -

is

shown in

_figure

7 in the

_appropriate

_{q-range ; this}

_plot

is

_{approximately}

linear and from its

_slope

and

_origine

we can deduce another estimate of

(P )

= 180 ± 50

Â.

We had

Fig. 6.

Fig. 7.

Fig.

6. -

Manifestation of the

_flexibility

of the

_cylinders

in the

_{qI (q )}

plot

for the

sample

1 % CPBr in 0.8 M NaBr brine

_{(see text).}

Fig.

7. -

Approximately

linear part of

_{qI (q )}

as a function of

_q-1

which allows for the determination of the

_{persistence length}

characteristic of the

flexibility

of the

_cylinders

for the

_sample

1 % CPBr in 0.8 M NaBr brine

_{(see text).}

experiments

and

_{magnetic birefringence}

_{experiments) ;}

with these methods we had to take into account

_explicitly

the size distribution of the micelles in the

_experimental

situations so

that the estimates

_{of l>}

were somewhat

_dependent

on the model of micellar

_growth

assumed. The estimated

_(f)

-. 200 --t 50 Â

is however in excellent

_agreement

with the

present

values. In the

_present

_procedure,

we

_neglect

the interference effects due to interactions between

_{scattering objects}

which could

_modify

the

_scattering

pattern

due to the

«

single » object

in the

_present

_{q-range. The}

hight salinity

of the

sample

which insures an

efficient

_screening

of the

_long

_{range electrostatic interactions is} a

_{partial justification}

for this

neglect

which is further

_{justified by}

the

_good

_agreement

between the different estimates of

(f) .

4.5 THE LOWEST _q-RANGE.

_{- Drawing}

an

_analogy

between the

_long,

_flexible,

_cylindrical

micelles and

_polymers,

we

_expect

_{in this range,} to

_gain

information either on the overall size

reflected

_by

the radius of

_gyration

of the coil if the solution is dilute or on the correlation

length

f c

which is a measure of the mean distance between the

entanglements

of the

_polymer

chains if the solution is semi-dilute

_[26].

The situation is here

_{complicated by}

the fact that the

long

micelles are

_expected

_[1]

to have a very broad size distribution so that

_possibly

the

_largest

micelles form an

_entangled

network while the smallest ones are still free in the meshes of this

network. For free coils we

_expect

_{I (q )q o}

oc

_{exp (-}

q Rgl3 )

(with

_Rg

the mean radius of

gyration).

For

_entangled

coils the Ornstein-Zernicke

_expression

reduces to

I (q oc

exp (-

q 2 Q )

for

_{qîc «}

1. _{Our purpose here is} not to make a

_precise

measurement but to evaluate an order of

_magnitude

of a

_{length e}

which is

_possibly

some combination of

e =

_Rg/

w5

and 9

=

fc

and _{to compare this}

length

to the

previously

determined

persistence

Fig.

8. - Guinier

plot Log

I

_{(q )}

vs.

q 2

in the lowest _q-range

_{(light scattering)}

for the

_sample

1 % CPBr in 0.8 M NaBr brine.

§ is

deduced from the

_slope

at the

_origin

of the Guinier

_lot

shown in

_figure

8. We obtain

=

900 ± 100

Â.

If we

_interpret

this value

_{as §}

=

Rg/

y3

we obtain a

_fairly

small value of

Rg( ’" 500 Â);

in our

_{previous investigations}

_{[18, 22]}

on more dilute solutions of CPBr in 0.8 M NaBr brine we had evidence that the micelles had

_{already larger}

mean radius of

_gyration

so

that the

_{interpretation}

of e

as a correlation

_length

or

_eventually

as some mean between a

correlation

_length

and radiis of

_gyration

seems

_appropriate.

The results obtained on these

_elongated

micelles at all scales thus lead to the

_following

picture :

the micelles are

_long

flexible

_cylindrical

micelles,

the radius of the cross section of

the

_cylinders

is r = 19.5 ± 1

Â,

and the

persistence length,

characteristic of their

_flexibility,

is

equal

to 180 ± 50

Â.

We note that the radiis determined from the Guinier

_plot

in the intermediate q-range which reflects the

cylindrical

structure are

_larger

₍₂₂

Â)

than the radius

(19.5

Â)

deduced from the form factor oscillations at

_{large q}

_(cf.

Tab.

_{III) ;}

this can well be

due to the fact that the

_cylinders

are flexible on a scale which is not much

_larger

than their

diameter

_{(180 Â}

_compared

to 40

_Â)

and that the influence of this

_flexibility

on the

_scattering

pattern

can

_already

be

_perceptible

in the intermediate q-range. On the other hand the

persistence length

characteristic of the

_flexibility

is not _{very much smaller than the corrélation}

length e

deduced from _{the lowest q-range. This restricts}

_severely

_{the q-range where the}

influence of the

_flexibility

of the coils is

_perceptible

and from which we deduced the value of

this

_{persistence length.}

However as

_already

stated the

_good

_agreement

between values

obtained from very different

experiments

reinforces our

_{interpretation although}

it would be

preferable

to find tractable

_experimental

situations where the

_cylindrical

micelles would be

longer

and in a dilute solution.

5. Planar structure.

Two

_samples

of the

_{L3 phase}

_(anomalous

_isotropic

_phase)

of the CPCI-hexanol-0.2 M NaCI brine

_system

_[8]

have been studied with a ratio hexanol/CPCl = 1.1 in

weight

and 91 % brine

(large q’s)

and 97.7 % brine

_(at

lower

_q’s).

In

_previous

studies

_{[7, 9]}

we have obtained

_strong

evidence for a

_bilayer

structure on a local scale and no

_long

_{range order.}

5.1

_Low-q

SCATTERING PATTERN. - For

a random distribution of

_large

flat

_particles

we

expect

q2[ (q)

to _vary as

_{[13, 14]}

in the range

_qdg

-- 1

and q :::.

L -

where

dg

is the

_apparent

dry

thickness of the

bilayer

(as

derived

_{[13, 14]}

from the one dimensional radius of

_gyration

of the

_{scattering .length density}

along

the normal to the

_bilayer)

and L is a dimension characteristic of the lateral extension of the flat

_{bilayer ;}

_MA

is the mass _{per unit} area of the

_bilayer.

In

_figure

9 a

_{logarithmic plot}

of

q21 (q)

is shown : in the

_{lowest q}

_range a linear variation

_corresponds

to

₍₈₎

and we derive

from its

_slope

dg

= 24 ±

2 Â

and from its

extrapolation

_to

q =

0,

MA =

[2.1 ±

0.1

_{] x}

_{107g/cm 2}

from which

_assuming

a constant thickness of the

_bilayer

(dm

= MA/p )

we derive

_dm

= 23 ±

4 Â

in

_good

_agreement

with the value

_dg.

5.2

_LARGE-q

SCATTERING PATTERN. - From the Porod limit

using

(1)

and

_assuming

here

again

a flat local structure we obtain an other estimate of the thickness of the

_bilayer

dp = 22 -, 4 Â.

Oscillations

_reflecting

the form factor of the

_{scattering objects}

are observed in the

_plot

of

Fig.

9. -

Log (q 2 1 (q»

_vs.

q 2

in the low

q-range for the

sample

CPCI + hexanol in 0.2 M NaCI brine

(97.7

%

_Brine).

This

_sample

is

_{representative}

of the

_planar

local structure. The arrows indicate the limits

q’I(q)

versus _{q shown in}

_figure

10.

_Assuming

that the

_{scattering objects}

are

_{bilayers :}

the

_intensity

scattered

_by

_bilayers

of different thicknesses d is

_computed

and

_compared

to the

experimentally

observed oscillations. The best

_agreement

for the

_position

of the extrema in the calculated and

_experimental

curves is obtained for

_do

= 22 ± 1

Â.

The coincidence in

position

of the two

_experimental

and

_computed

extrema is found to _{be very sensitive} to the chosen

_{thickness ;}

here

_again

trials with the form factors for other structures

_{(sphere (3)}

or

cylinder

(4))

led to no

_agreement.

The fluctuations of the thickness of the

_bilayers

must be

responsible

for the observed

_{experimental damping}

of the oscillations

_(see

_Fig.

_10).

The evidences obtained at all

_q’s

in excellent

_agreement

with one another and

_{they totally}

confirm the assumed

_{[7, 9]}

local structure in the

_{L3 phase :}

a

_{planar bilayer.}

The four

estimates obtained for the thickness of the

_bilayer

are in reasonable

_agreement

(cf.

Tab.

IV) ;

Fig.

10. - Form factor oscillations in the Porod

_region.

The full line = calculation for flat

bilayers

with

d =

22 Â ;

dots =

experimental

result for the

sample :

CPCI ₊ hexanol in 0.2 M NaCl brine

(90

%

brine).

the somewhat

_larger

values _{obtained from the lower q-range}

_pattern

is

_possibly

due to the fact that the

_bilayers

are not

_{completely rigid}

at this scale

_(as

assumed in

₍₈₎₎

and that the influence of their

_flexibility

is

_perceptible

in the

_scattering

_pattern

_{in this q-range.}

6. Conclusion.

The

present

study

at

_{high spatial}

resolution

_brings

a direct

_experimental

evidence of the

existence of three different local structures observed in brine rich

_binary

_{(surfactant/brine)}

or

ternary

(surfactant/alcohol/brine)

phases

namely spherical,

cylindrical

or

_planar.

This confirms

_thoroughly

our

_{previous assumptions regarding}

these local structures which were

derived,

in

_particular,

from

_experiments

at low

spatial

resolution.

The best measure of the characteristic dimension

(the

radius of the

_sphere

of the

_cylinder

of

the thickness of the

_bilayer)

is obtained from the oscillations of the

_scattering

_pattern

in the

high

q-range as

_expected

[15].

The decrease of this characteristic dimension when

going

from

the

_spherical

to the

_planar

structure is similar to that observed in concentrated

_mesophases

in similar

_systems

_{[27, 28].}

This

_implies

that the characteristic dimension in a

_particular

local structure

_{depends essentially}

on the

_geometry

of the structure and not on the reasons which

drive the

_system

to

_adopt

a

_given

local structure

_(properties

of the surfactant

_layer

and/or interactions between

_aggregates).

The thickness of the

_bilayer

_(d

=

22 Â)

in the

L3 phase

(deduced

from the

high spatial

resolution

_{measurements)}

is

_{significantly}

different from that

_(d

=

26.5 À)

in the

adjacent

lamellar

_{phase La}

which was

_previously

deduced from the evolution of the

_position

of the

Bragg

peak

of the lamellar

_phase

with dilution

_[29].

This difference is

_possibly

real however

we feel that another

_explanation

is more

_{plausible namely}

that the thickness of the lamellae in

the

_La

_phase

_(deduced

in an indirect

way)

is

_{artificially larger}

than the real thickness as a

result of the

_large

ondulations of the lamellae :

_dapparent

=

(S/Sp ) d

with S,

the real surface of

the

lamella,

and

_Sp,

the

_projection

of this surface on a

_{plane perpendicular}

to the axis of the stack of lamellae. These ondulations have been evidenced

_by

Electron

_Spin

Resonance studies

_[30]

on the same

_{La phase.}

As noted

_above,

_{they probably}

exist in the

L3 phase

where

_they

lead to the determination of

_{apparently larger}

_{thicknesses in the low} q-range

(see above).

A definitive answer to the

_questions,

_namely

what is the real thickness in the

La

phase ?

and is it

_equal

to that of the

_{L3 phase ?,}

will be obtained from

_high

spatial-resolution SANS we

_plan

to make on

_{La samples.}

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