Symmetry transition in the cubic phase of a ternary surfactant system

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Symmetry transition in the cubic phase of a ternary

surfactant system

S. Radiman, C. Toprakcioglu, A.R. Faruqi

To cite this version:

1501

LE JOURNAL DE

PHYSIQUE

Short Communication

Symmetry

transition

in

the cubic

_phase

of

a

_ternary

surfactant

system

S. Radiman

_(1),

C.

_Toprakcioglu

_(1,2)

and A.R.

_Faruqi

₍₃₎

(1) Cavendish

Laboratory,

University

of

_{Cambridge, Madingley}

Road,

Cambridge

CB3

OHE,

G.B.

(2) AFRC

Institute of Food

_Research,

_Colney

_Lane,

Norwich NR4

7UA,

G.B.

(3) MRC

Laboratory

of Molecular

_Biology,

Hills

Road,

Cambridge

CB2

2QH,

G.B.

(Reçu

le 3

_{ai7il 1990,}

_accepté

le 23 mai

₁₉₉₀₎

Abstract. - We

report a

_small-angle

_X-ray

and neutron

_{scattering investigation}

in the cubic

_phase

of the

_ternary

_system

_{water/didodecyldimethyl}

ammonium bromide

_{(DDAB)/octane.}

We have observed

a

_systematic

variation in the lattice

_parameter

as a function of water content, which can be related to

the

_change

in interfacial area _per unit cell with the _aqueous volume fraction. Our results are consistent with a bicontinuous

_periodic

constant mean curvature structure, and show a transition from diamond

to

_body-centred

cubic _symmetry on

_increasing

the water content of the _system. 1

_Phys

France 51

_{( 1990)}

1501-1508 . 15 JUILLET _1990, Classification

Physics Abstracts

61.12E - 61.10L- 61.30E Introduction.

The existence of cubic

_phases

in

_{binary lipid-water}

_systems

has been

_firmly

established

_by

the

pioneering

work of Luzzati et aL

_[1].

More

_recently,

cubic

_phases

of

_{ternary systems}

have received

much attention

_[2-5].

These

_systems

can be described in terms

_{of periodic}

constant mean curvaturé

(CMC)

surfaces which are solutions to the

_problem

of area minimization under the constraint of

constant enclosed volume fraction

_[3,6,7].

The

_resulting

structure consists of bicontinuous

_{periodic labyrinths}

of water and oil

_conforming

to a cubic

_symmetry.

In recent _years, several authors have

_reported

transitions between cubic

structures of different

_symmetry

in the

_{phase diagrams}

of certain

_binary

_systems

_{[8, 9].}

Theoretical

models have been

_proposed

to account for such transitions

_[9-11].

It is thus of interest to

_explore

the

_possibility

of a

_symmetry

transition in a

_ternary

cubic

_system,

where the additional

_degrees

of freedom afforded

_by

the introduction of the third

_component

are

likely

to lead to a richer

_variety

of microstructures.

_Furthermore,

the

transition

from a cubic

_phase

to a

_neighbouring

microemulsion merits closer

_attention,

since it is

_possible

to

_regard

the latter

1502

as a molten

_{liquid crystal.}

In the

_present

_paper

we

_report

a structural

_study

of the cubic

_phase

of the

_system

_{D20/didodecyldimethylammonium}

bromide

_{(DDAB)/octane. Ternary}

mixtures of

DDAB,

water and oil are characterized

_by

an extensive cubic domain and a

_large

microemulsion

phase,

which has been the

_subject

of much work

_recently

_{[12, 13].}

Experimental.

The

_samples

were

_{prepared by thorough mixing}

of the three

_components

in a closed container at

~100

_°C,

and were then allowed to cool to room

_temperature.

The

_{small-angle X-ray scattering (SAXS)}

measurements were carried out with a

_{point-collimated}

beam from a Cu-Ka line of À = 1.54

Á

A two-dimensional

position

sensitive detector

[14]

was

used at a distance of 75cm from the

_sample,

which was

_placed

between two mica sheets and rotated

in the beam at about 1

_r.p.m..

A

_sample

thickness of ca. 0.7mm was maintained

_by

means of a

Thflon

_0-ring.

The

_temperature

of the

_sample

was 22 ± 1° C. The

_samples

were

_subjected

to

several

_cycles

of

_heating

and

_quenching

_prior

to the measurements as this reduces the size of

large crystallites

and

_gives

rise to much

_{improved powder}

diffraction

_patterns.

The

_small-angle

neutron

_scattering

_(SANS)

_experiments

were carried out on D17 at the

ILL,

Grenoble with a monochromatic

_wavelength

of 12

Â

and a variable

_{sample-detector}

distance 1.4-2.8 m. The

_samples

were contained in lmm

_{path length}

_quartz

cells and

_subjected

to

_heating

and

_{cooling cycles}

before each measurement. The

_spacings

obtained from the SAXS and SANS

measurements on a

_{given sample}

were

_equal

to

v4thin +3À

Results and discussion.

The

_phase

_diagram

of the

_{system D20/DDAB/octane}

exhibits a

_large

cubic domain

_extending

from ca. 35% to 77%

D20

_(Fig.l).

The

_high-octane

side of this cubic

_region

faces the

L2

mi-croemulsion

_phase,

while the low-octane side is

_opposite

a lamellar

_region.

Within the cubic

_phase

itself,

there is considerable variation in the

_{physical properties}

of the

_system

as a function of

com-position. Notably,

the

_rheological

_properties

_{change significantly,}

with increased

_{rigidity being}

observed at low water content.

_Moreover,

the

_"melting

_point"

of the cubic

_{samples (i.e.}

the

tem-perature

at which

_long-range

order is lost and the cubic

_{liquid crystal}

"melts" into a

microemul-sion)

varies

_dramatically

with

_{composition, being}

lowest

_(ca.

_{40° C)}

in the low-water extreme of the cubic

_region.

These cubic

_phases

are further characterised

_by

the

_property

of

_{"ringing" (i.e.}

they ring

like a bell when

_{tapped gently). Rheological}

data associated with this

_interesting

effect

will be

_reported

elsewhere. The

_frequency

of

_ringing

also

_depends

on

_composition

and decreases

at

_high

water content.

_Furthermore,

some of these

_properties

_appear

to

_change

_rapidly

with

com-position

in certain

_regions

of the cubic domain. These observations

_strongly

_suggest

the

_possibility

of structural

_changes

within the cubic

_region

as a function of

_composition.

Measurements of

spe-cific heat in a similar

_{ternary system}

were

_{recently reported by}

Radlinska et aL

_[15],

which also

suggested

a transition between two cubic

_phases.

We have used SAXS and SANS to

_investigate

the microstructure of the cubic

_{phase along}

a water dilution

_{path (Fig.l).}

The results

_clearly

indicate a

_symmetry

transition at an

_aqueous

volume

fraction close to 0.5

_(Fig.2).

At low water content the SAXS

_profiles

can be indexed to a diamond

(D)

structure(l).

As the water content is

_increased,

there is a transition to a structure of

Fig.

1. - Phase

diagram

of the _ternary

_system

_{D20/DDAB/octane}

at 22° C

_showing

the cubic

_region.

The dashed line is a

_D20

dilution

_path.

’Me

_{sample compositions}

are

_{given by}

the

_points

within the cubic domain:

(e)

diamond

_symmetry,

and

_(*)

_body-centred

cubic

_symmetry.

The

_point

indicated

_by

an arrow

_corresponds

to a

_sample

for which SANS data

_suggest

an I-WP

_monolayer

structure.

If e

is the lattice constant of the cubic structure with an interfacial area A

_per

unit

_cell,

it is useful to define a dimensionless area A* =

Ae-2@

with

where 0

is the volume

_fraction,

cs is the surfactant concentration in molecules

_per

unit

volume,

and as is the area

_per

surfactant at the interface. The value of

_{A* (0)}

_depends

on the

_symmetry

and

_topology

of a

_given

CMC

surface,

and has been

_computed

for various surfaces

_by

Anderson

[3].

For bicontinuous

_periodic

CMC surfaces of cubic

_symmetry,

he found

where

Po,

A*

_(Po),

and c are

_{symmetry-dependent}

constants. The lattice

_constante

is related to

1504

Fig.

2. - SAXS

profile of samples with composition by weight

(A)D20 :51.7%,

DDA-B:40.1%,

octane:8.2%

and

_{(B)D20 :56.36%,}

_{DDAB :36.22%,}

octane:7.42%

_showing

diamond and bcc

_symmetry

_{respectively. (The}

feature at _very low

_Q

is due to the

_beam-stop,

and is not a

_{Bragg reflection).}

It follows from

_{(1), (2)}

and

₍₃₎

that a

_plot

of

_{cs/Qmax against 0}

should be sensitive to

_changes

of

symmetry

and

_topology,

as these would manifest themselves in the

_0-dependence

of A*.

_Figure

3 shows such a

_plot,

and the transition from a D to a bcc structure is

_clearly

indicated. There is also

some evidence of a further transition above ca.68%

_D20,

but more measurements are

_required

before this can be shown

_{conclusively.}

Fig.

3. - Plot of

cg/Qmax

against

the volume fraction of the _aqueous

_phase

_(including

the surfactant

head-group).

cs has the units of mol 1

-1.

Qmax

corresponds

to the

_position

of the

_principal

reflection and has the units

of A -1.

The

_symmetry

of each

_sample

is indicated

_by

different

_symbols:

diamond

_(o)

and bcc

_{( ).}

The arrow indicates the transition between the two

_symmetries.

The dashed lines are theoretical fits to the diamond

_{bilayer (Pn3m)}

and

_P-bilayer

_(Im3m).

The

_only

_adjustable

_parameter is _as,

_yielding

a value of 65 z 2

Â2

for both

_{symmetries (see Eqs. (1) - (3)).}

Since A* values for the bcc and diamond

_symmetry

have been

_computed

_[3,6]

it is

_possible

to extract values for as for the two

_regimes

described in

_figure

3.

_(Conversely,

if one assumes a value

for as, an A* value follows which can be

_compared

to

_theory

for various

_symmetries

and

topolo-gies).

In

_determining

as,

however,

the

question

arises whether one should assume a

_monolayer

or

bilayer

arrangement.

This issue can

_only

be resolved

_{conclusively by}

careful measurement of

_peak

intensities in a

_scattering

_experiment

with "bulk" contrast

_(e.g.

a SANS measurement with

_D20

and the other

_components

_unlabelled)

as

_opposed

to the combination of the "bulk" and "film"

scattering

that is

_normally

observed with

_X-rays.

At

_present,

we have insufficient SANS data to

address the

_{problem directly.}

_However,

the tansition shown in

_figure

3 indicates a

_change

of ca.

17% in

_{cs/ Qmax}

which is _very close to the theoretical difference in A* between the

_D-bilayer

and the

_{P-bilayer(3).}

We have thus assumed a transition from a diamond

_{bilayer (space}

_group

_Pn3m)

to a

_{P-bilayer (space}

_group

Im3m) (4 )

and the dashed curves in

_figure

3 are based on A * values for these

_topologies.

This allows determination

_{of as}

which is found to be 65 ± 2

Â2

both for the D and P

_bilayers.

While these values are reasonable and in

_good

_agreement

with those obtained in the

(3)

It follows from

_{equations (1), (2)}

and

₍₃₎

that

_{cs/ Qmax f’J}

A*. Since the A* values for the D and P

bilayers

at 0

= 0.55 are ca. 3.4 and 4.1

_{respectively,}

a transition between these structures

_implies

a

_change

of about 20% in

_cs/Qmax

at constant as.

1506

L2

microemulsion

_phase

_[3,12,13J,

it should be noted that there is no

_{a priori}

reason

_why

_{as must}

have the same value in the cubic

_phase

as in the

_{microemulsion.}

It

_might

be reasonable to

_expect

somewhat

_tighter

_packing

of the surfactant molecules in

the

cubic

_phases

in

_comparison

with the microemulsion. Anderson

_[3]

found as to vary with water content from ca.40

Â2

to ca.60

Â2

in the

water/DDAB/decane

microemulsion

_system.

A similar variation

_might

occur in the cubic

_phase,

and it _may thus be

_misleading

to assume a constant as over the entire

_{compositional}

_range of the cubic

_phase.

_{Nevertheless,}

our data are in

_good

_agreement

with a

_D-bilayer

to

_P-bilayer

transi-tion at an as value of ca.65

Â2.

If

_monolayers

were

_assumed,

the as values

corresponding

to the diamond and bcc

_symmetries

would be 35

Â2

and 55

Â2

_{respectively.}

The as for the

D-monolayer

would seem

_unreasonably

low(5).

Thble I. z D ₌

diamond,

bcc =

body-centred

cubic

_(see

notes

_(1),

(2)

and

_(4),

d =

21r/Qmax

is the

spacing of

the

_first

observed

_{Bragg reflection.}

The

_{composition of}

each

_sample

is

_given

in %

_weight:

DDAB/D20/octane.

Finally,

it is

_appropriate

to comment on the

_possible

mechanism of the

observed

transition. In

recent _years

_Hyde

et al.

_[9,10]

have

_propounded

the

_interesting

_argument

that transitions

re-lated

_by

the Bonnet transformation

_(a

_{conformal, isometric,}

and curvature-invariant

_topological

transformation that can occur between certain

_{surfaces) might play}

an

_important

role in cubic

phases,

since Bonnet-related transitions would occur

_smoothly,

without _any

_change

in _curvature, and would thus

_require

a

_{negligible enthalpy.}

Our

_{results, however,}

are consistent with a

first-order

transition,

and our data

_suggest

that in a certain

_region

within the cubic

domain,

samples

can be

_prepared

which

_appear

to contain two

_coexisting

cubic

_phases.

This observation seems to be

supported

by

the results of Radlinska et aL

_[15].

In addition to the transition between the diamond and bcc

_{symetries, assuming}

this to occur within a

_bilayer

_topology,

there _{may be} a

_monolayer

to

bilayer

transition within the bcc

domain,

for SANS data

_[5]

from a

_sample

at the

_{high-octane edge}

(5)

We _note,

_however,

that the SAXS

_pattern

of

_sample

_5(o

=

0.53)

is

compatible

with a

_D-monolayer

structure.

_{At 0}

= 0.5 in the

_D-monolayer

the bulk

_amplitudes

vanish,

and

_only

film

scattering

is observed

(see

ref.[3]).

The

_amplitudes

extracted from the SAXS

_spectrum

_{of sample}

5,

for the first three reflections are

1, 1.12, 0.47

(normalized

to the first

_reflection),

in

_good

_agreement

with the theoretical values of

1, 1.02, 0.55

for a

_{monolayer decorating}

a D-minimal surface.

_However,

this

_might

be due to a fortuitous combination of

of the cubic

_{phase (see Fig.1)}

are in much better

_agreement

with the I-WP

_monolayer

than the

P-bilayer.

This would further

_support

our view that

_symmetry

transitions between

_ternary

cubic

phases

need not be confined to the Bonnet

transformation,

and _may involve

_{topologically}

more

disruptive

processes.

In

fact,

many

lyotropic

transitions occur without _any

_possibility

of a

topolog-ically

smooth

transformation,

and the mechanism of surface deformations

_responsible

for these

transitions remains an

_open

_question.

In

conclusion,

our

_analysis

shows that the structure of

_ternary

cubic

_phases

is well-described

_by

a

_periodic

minimal or CMC surface

model,

and that the

_dependence

of lattice

_spacing

on

aque-ous volume fraction is a useful indicator of structural

_changes

in such

_{systems. Furthermore,}

our

results

_clearly

confirm the existence of more than one

_symmetry

within the cubic domain of a

ternary system.

The transformation mechanism between the observed

_symmetries,

and the

tran-sition from the cubic

_phase

to the

neighbouring

microemulsion are not well-understood. More work is in

_progress

to address these issues.

Acknowledgments.

The authors are

_grateful

to Dr. D.M.

Anderson,

University

of

_Lund,

for

_helpful

_discussions,

and

to Dr. M.E.

Cates,

and Dr. C.

_{Marques, University}

of

_Cambridge

for

_helpful

comments. The authors are also indebted to the

ILL,

Grenoble for the allocation of beam time.

Note added.

The cubic

_phase

of a similar

_{ternary system}

has been

_{investigated by}

Barois et

_aL,

_Langmuir,

in

press,

using small-angle

X-ray scattering.

These authors have used the same surfactant

_(DDAB),

but a different oil

_(cyclohexane

as

_opposed

to octane

_employed

in our

_study).

In

_agreement

with

our

_results,

_they

also find a

_symmetry

transition from a diamond to a bcc structure as a function

of water content.

_Assuming

a value of 68

Â2

for the area

_per

_surfactant,

Barois et aL calculate the

expected topology

of the diamond and bcc structure, and find in favour of a

_bilayer

cubic

_phase

for both

_{symmetries. Contrary}

to the calorimetric data of Radlinska et al.

_(see

_Ref.[15]),

_they

find

no evidence of a further

_topological

transformation within the bcc

_regime

in their

_system.

_They

point

out,

however,

that in the bcc

_region

their data are

_subject

to some scatter which

_precludes

a more definite conclusion.

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_V,

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