Spiral textures in lyotropic liquid crystals : first order transition between normal hexagonal and lamellar gel phases

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Spiral textures in lyotropic liquid crystals : first order transition between normal hexagonal and lamellar gel

phases

K. Mcgrath, P. Kékicheff, M. Kléman

To cite this version:

K. Mcgrath, P. Kékicheff, M. Kléman. Spiral textures in lyotropic liquid crystals : first order transition

between normal hexagonal and lamellar gel phases. Journal de Physique II, EDP Sciences, 1993, 3

(6), pp.903-926. �10.1051/jp2:1993174�. �jpa-00247878�

Classification

Physics

Abstracts

61.30E 61.30J 64.70M 68.55

Spiral textures in lyotropic liquid crystals

_:

first order

transition between normal hexagonal and lamellar gel phases

K. M. McGrath

(I),

P. Kdkicheff

(')

and M. Kldman

(2)

(') Department

of

Applied

Mathematics, Research School of

Physical

Sciences and

Engineering,

Australian National

University,

Canberra, ACT 0200, Australia

(2) Laboratoire de

Physique

des Solides (*), Bitiments10, Universit6 Paris-Sud

Orsay,

91405

Orsay

Cedex, France

(Received 2

September

1992,

accepted

in

final for.m

12

Febt.ua>.j,

1993)

Abstract. The first order transition between the normal

hexagonal

phase (H~ and lamellar

gel

phase

(Lp, Lg., Ls, type)

in

lyotropic liquid crystals

of

binary

surfactant/water systems is

investigated.

Structural transformations and

epitaxial

relations _are

investigated by small-angle

X- ray

scattering

on

powdered

and oriented

samples. By

slow

evaporation

of water, growth of the

gel

layered structure from the two-dimensional

packing

of surfactant

cylinders

of the hexagonal

mesophase in the presence of _a solid wall reveals _a spectacular new texture

composed

of interwoven

spirals.

It is demonstrated that the

layers

_grow from the rods of the

hexagonal phase,

in

planes coplanar

with the

hexagonal packing

and

perpendicular

to the wall. The

configuration

is such that line

wedge

disclinations of

strength

_{s +} 1/2 of the

hexagonal

phase are

preserved

through ^the

phase

transition. Estimates of the radii for the

developable

domain and _cores, and also for the bending ^elastic constant are obtained. A mechanism for the phase transformation is discussed in view of topological structural transformations and _a modification of the short-range order associated to the disorder/order transition of the

configuration

of the paraffinic chains.

1. Introduction.

Lyotropic liquid crystals

exhibit _a rich

polymorphism [1-4],

due _to the

variety

of surfactant

headgroup

types, ^the nature of the

paraffinic

chain

(length,

frozen _or

liquid-like

state,

etc.),

and the _vast array of solvents available. The almost endless array of structures that these

amphiphilic

molecules _can

yield,

_may be

periodic along

_{one-, two-, or} three-dimensions

[1, 5, 6]. Despite

_a substantial _amount of information which has been

gathered

_on the

equilibrium

properties

of these

mesophases,

details of the mechanism of the structural transformations

remain _scant. Some 30 years ago a

good understanding

_was established

[7-11] conceming

structures that do not

undergo

_a

topology change through

a

phase

transition. Two schemes

(*) URA 002, associd _au C-N-R-S-

exist.

Firstly

a

change

in the

short-range

order

(that

of the

paraffinic chains)

is

affected,

_as in the transformation of two lamellar

phases,

_one with frozen chains

(the

so-called lamellar

gel)

and the other with

paraffinic

chains in _a

liquid-like

state

(L~ [9-13]. Secondly,

when the

long-

range order is affected

during

the transition (as ^well as a

phase

symmetry

change),

a

satisfying

and consistent

description

_was obtained for the _case where _a

slight

modification of the

shape

of the aggregates ^is

implicated.

This _was well described

by

Luzzati and collaborators who

showed for instance how circular

cylinders

of the two-dimensional

hexagonal phase

H~

tum into

anisotropic

ribbons of the deformed

hexagonal (two-dimensional

monoclinic _or

rectangular phase) [7].

In the _case where _a

topological change

is involved in the structural

transformation,

the mechanism is less understood.

Only recently

^{have studies} dealt with this

problem,

and most

reported

observations _{are as a} function of temperature

[14-16],

rather than

as a function of

composition [17, 18]. Epitaxial

relations

occurring

at the transition have been evidenced

[14,

16, 17,

19], indicating

that two

adjacent mesophases

are

strongly

related _; that is the _new

phase

grows with _a fixed orientation relative to the former _one.

Furthermore,

dense reticular

planes

of the _new structure

develop

from the dense

planes

^of the former _one

[14,

16,

17, 19].

For

instance,

in non-ionic surfactant/water

systems,

^clear relations _were established

between the dense

planes

of the two-dimensional

hexagonal packing

of

cylinders (planes (10)),

those of the three-dimensional bicontinuous cubic structure Ia3d

(planes (211)),

and the

planes

of the one-dimensional

layered

stack of the lamellar

mesophase [14, 16].

In the latter _cases, the

long-range

order of the

mesophase

is affected

during

the transitions, but _not the

short-range

^order associated to the translational and orientational order of the

paraffinic

chains within the aggregates. Transitions

involving

_a

change

in both the

long-range

and

short-range

order parameters are of great

interest,

_as

they

are often encountered in

lipidic

systems

[1,

2,

6].

This

problem

is addressed here,

namely

^the transition between _a normal

hexagonal phase (H~

^and a lamellar

gel phase

is examined for

binary

systems ^{of surfactant in}

water.

In

addition,

the effect of _a solid wall _on this transformation is

investigated.

It has indeed been known for

nearly

_a

century

^{that solid surfaces have} an

orienting

action on

liquid crystals [20, 21]. Textures,

seen

by

_means of

optical microscopy

are characteristic of the

phase they

represent

[22-25]

but also

depend

_upon the nature of the substrate. The orientation _or

anchoring

direction taken

by

such

anisotropic

materials at the surface of _a substrate

depends

on a set of

competing

parameters

[26-28]. Anisotropic

interactions between the

liquid crystal

molecules and the molecules of the solid _{are a}

major

contribution in the orientation process, where the

symmetry ^{of the surface and several}

nonsuperficial layers

of the substrate may

play

_an

important

^role

[29].

In

lyotropic liquid crystals,

_a classical

example

is the build up of

homeotropic

lamellar

mesophases,

where the

layers

^{of the} stack lie

parallel

to the flat surfaces of the walls. The _nature of the first

layer

built is

mainly governed by

electric interactions

between the substrate and the surfactant molecules. If this interaction is

favourable,

the adsorbed

layer

will be

hydrophobic, (the polar

heads _are adsorbed _onto the solid

[30]),

otherwise _a thin _water

layer

will remain between the substrate and the altemate stack of

bilayers/water layers

of the lamellar

mesophase [31].

The terraced _nature of the substrate

surface,

_{or more}

generally

its

roughness

_may

drastically change

the

anchoring

directions

[32].

If _some of the parameters

determining

the structure of the substrate _or

liquid crystal

_are

changed, anchoring

transitions _{can occur,} for

example

when the chemical

potential

of the

system is varied

[33, 34].

In

addition,

the

history

of the system

plays

an

important

role.

Depending

_on the way the contact between the _two

phases

is made

(for

instance

during

the

wetting

of the substrate

by

the

liquid crystal),

the first selection of _one

anchoring

direction may be switched to another _one when _an external

change

_occurs

(flow inducing

shear

[35],

_{or an}

applied

electric field in

liquid crystal displays).

columnar

phases

in

thermotropic liquid crystals,

_can orientate either in _a

planar

_or in _a

homeotropic configuration [36],

the latter

being

_not

usually

observed in the

hexagonal phase

of

lyotropic

systems.

Indeed,

it is often observed that the director of the

mesophase (along

the

cylinders)

is

parallel

to the walls

[15, 16, 19, 36]

and that the dense

planes (10)

_are next to them

[19].

Note that _a

mesophase

does _not

necessarily

orient itself with its _most dense reticular

planes along

_a solid wall,

although

this is _common

(see

for

example

the cubic

phase

of the space group in the class

Im3m,

which orients with

planes (I

I

I) along

the walls

[19]).

The orientation of

mesophases

with

complex

structures seems to result from _a

compromise

betwedn the interactions of the substrate with the first closest

plane

of

aggregates

^{which will be built}

next to

it,

and the

required

structure of the

mesophase

which is _to be

preserved.

Such observations have

already

been made for instance

anisotropic

ribbons _can lie with their flat parts ^{tilted relative} to solid flat walls

[19].

As _a consequence,

growth

of _one

phase

from _a former _one in the presence of _a solid

wall,

is

a result of

epitaxial

relations between the _{two structures as} well _as with the substrate. We

shop

here,

that unusual

growth

_{can occur} under certain conditions in

particular bilayers

of _a lamellar

gel liquid crystal

_can be grown

perpendicular

to flat

walls, by

slow

evaporation

of

water from _a normal

hexagonal mesophase.

This

growth yields

a

spectacular

texture,

composed

of interwoven

spirals.

This _new texture, which has not

previously

been

reported

for

lyotropic liquid crystals,

arises due to a combination

of,

defects inherent in the system,

anchoring,

and nucleation effects

[37-41].

The

departure

from the

perfectly

ideal

crystallogra- phic packing

of the aggregates can take the form of

twists, splays

_or

bending

of the aggregates

[42].

A detailed

investigation

of the nature of the defects is

presented, enabling

_us to extract an

estimate of the

bending

modulus for these

phases.

2.

Experimental.

2.I MATERIALS.- Sodium 10-undecenoate

(Na-10)

_was

prepared by reacting equimolar

amounts of 10-undecenoic acid

(~

99 % pure,

purchased

from

Tokyo

Kasei

Kogyo Co.,

Ltd

and _vacuum distilled before

use)

and 50 % NaOH solution. The

precipitate

was filtered and

washed with

ethanol,

redissolved in water, washed with ether _{to remove} any traces of the parent ^{acid and}

finally

freeze dried. Further

purification

_was obtained

by repeated recrystallis-

ation from absolute ethanol

[43, 44].

The

resulting product begins

to

decompose

at 220 °C and

melts at 280 °C. Elemental

Analysis

Calculated for

CijHj~o~Na

: C 64.08

%,

H 9.22

%,

O 15.53

%,

Na I I.17 %. Found C 64.16 % and H 9.38 %. NMR

Analysis

Proton

(CH2)4-

(CH~)~-C=O

1.31&;

CH~-CH~-CH=C 1.38&; CH~-CH~-C=O

1.56&;

CH2-CH=C

2.05 _;

CH~-C=O

2.18 &;

CH2~C

doublet of doublets centred at 5.01 &; CH=C 5.87 &.

Carbon13

CH~-C=O

25.78 _;

(CH2)5-CH2-C=O

28.64 _;

CH2-CH2-C=O

33.12 &;

CH2-

CH=C 37.36

=CH~

113.83 =CH 139.67 C=O 183.55 &.

Hexadecyltrimethylammonium

chloride

(CTAC,

99 %

pure), dodecyltrimethylammonium

chloride

(DTAC,

99 %

pure)

^and

hexadecyltrimethylammonium

bromide

(CTAB,

99 ₊ %

pure)

_were

purchased

from Kodak. Sodium tetradecanoate

(C14Na, purity 99%)

_was

purchased

from

Sigma

Chemical Co.

potassium

oleate

(KO)

and sodium

di(2-ethylhexyl)

sulfosuccinate

(AOT,

~95 %

pure)

were

purchased

from

Tokyo

Kasei

Kogyo

Co., Ltd.

Octaethyleneglycol

_mono

n-hexadecyl

^ether

(Cj5E08,

⁹⁸ %

pure), octaethyleneglycol

mono

n-dodecyl

ether

(Cj2E08,

98%

pure)

and

hexaethyleneglycol

_mono

n-dodecyl

ether

(Cj2E05,

98%

pure)

were

purchased

^from Nikko Chemicals

Co.,

Ltd. Sodium

Dodecyl

Sulfate

(SDS, special purity

99%

pure)

was

purchased

from BDH chemicals Ltd. All

surfactants _were used _as received.

2.2

TECHNIQUES.

-Bulk

samples

of the surfactant

(Na-10, CTAC)/water

_{systems were}

prepared by adding weighed

amounts of the surfactant and

purified

water into _a

glass ampoule

which _was flame sealed. The

samples

_were

homogenized by

continual

heating (at

90

°C)

and

centrifugation

_{over a}

period

of several weeks.

All

phase

^behaviour _was

investigated

first

by polarising optical microscopy using

the concentration

gradient

method

[45].

A small amount of the

powder

or melt _was

placed

on a

slide with _{a cover}

slip,

water was allowed to

penetrate completely.

The

phases

_were observed

as bands of variable

birefringence

as the _water evaporates. An

Olympus

BH-2

polarising

optical microscope

with _a Mettler FPB2HT hot stage ^attached to _a Mettler FPBOHT Central Processor

capable

of temperature ^control to ± 0. I °C was used. For each

given

temperature a new concentration

gradient

_was

performed.

The temperature range was between 25 and 80 °C for the various

surfactant/water systems.

The thickness _was controlled

by using

calibrated

mylar

sheets _as spacers from 5 _to 400 _~m. Bulk

samples

of _a

given composition

were also viewed under crossed

polarising

filters and the temperature was varied between 25 and 100 °C.

Photographic

work _was done

using

an

Olympus

C-35 _camera fitted _onto the

microscope.

The _structure of the

phases

was checked

by small-angle X-ray scattering (SAXS)

measurements

using

a

Kiessig

_camera. The _camera is

capable

of

recording simultaneously

both

small-angle (sample

to film distance of 200

mm)

and

wide-angle (film placed

in the range of 40 to 70

mm) scattering

^detection. The _{camera was} attached to a

Philips

_generator I120/00

with _a 6°Co

(K~

^{line with} A

=

1.79285

h)

fine focus

high intensity

_source

PW2216/20.

Bulk

hexagonal

^and lamellar

gel phase samples

used for the

X-ray analysis

_were

prepared

in thin walled

capillaries

of intemal diameter 0.7 _or 1.0 _mm which _were sealed. Bulk

samples

were also sealed between _two

mylar

or mica

windows, resulting

in _an

approximate sample

thickness of I _mm. Powder diffraction pattems ^obtained

using

all four of the different methods

to house the

sample

_were identical. An oriented

sample,

in the lamellar

gel phase,

was

prepared by placing

a micellar solution of Na- lo _or CTAC either between _two concentric X- ray

capillaries

of diameter 1.0 and 0.7 _{mm, or} in _a flattened

X-ray capillary (obtained

in-house

by

slow

melting)

of about 0.I _mm thick. The _{water was} then allowed to evaporate

slowly.

After _a

period

of _{two to} four weeks the

spiral

texture was

clearly

visible when viewed

using

the

optical microscope

at which time the

capillaries

_were sealed. An oriented

sample,

contained

between _two mica windows

spaced approximately

0.5 _mm apart was also formed

by

evaporation

of water from the

hexagonal phase.

3. Results.

For the

binary

_system Na-10 in water,

only

two

liquid crystalline phases

_are formed between 0 and loo °C. A

hexagonal phase (H~,

two dimensional structure of

hexagonal

_symmetry with

liquid-like chains)

forms between 42.6 % and 55.5 %

by weight

and _a lamellar

gel phase (Ls, layered

structure with frozen chains in _a helical

conformation)

between 69.8 % and 80.8 % _at 25 °C. Between 55.5 and 69. 8 % the two

phases

coexist. The

partial phase diagram

for this system ^is shown in

figure1.

3.I OPTICAL MIcRoscoPY.-

Figure

2 shows _a

typical optical

texture observed

through

crossed

polarising

filters of _a

sample

within the Na-10

hexagonal phase region

of the

phase diagram.

This texture, a classic

example

of the sometimes called fan texture

[22, 23],

in _reason of its

similarity

with the well-known SmA fan _texture of Friedel

[46],

is _{common to}

samples

prepared by

concentration

gradients

and those obtained from the bulk. The observance of the

fan _texture has been shown _to arise when the director of the

cylinders

is

aligned parallel

to the

wall

[36].

Each fan is

composed

^of two

pairs

of brushes, these brushes _are not coincident with the directions of the

polariser

and

analyser

but rather lie _{at an}

angle

of between 15 and 20°

90

so

g

~s 70

j

60

(

~ ₅₀

g

~ ₄₀

Li

_~ ^L8

E

Li

+

Ha +"

_L8 *

g

³⁰

20

io

o

0 10 20 30 40 50 60 70 80 90 100

wt % Na-10

Fig.

I. Schematic Binary Phase diagram of sodium 10-undecenoate and water.

Lj

_: micellar solution,

H~.

normal

hexagonal phase, Ls.

lamellar

gel

phase with frozen

hydrocarbon

chains in _a helical conformation

perpendicular

to the plane of the

bilayers

and A _:

hydrated

Na- lo crystals. The horizontally shaded _area indicates _a

region

where two

phases

coexist.

'£

Fig.

2. Fan texture of the Na- lo

hexagonal phase

(crossed

polarising

filters,

magnification

200). The

cylinders

lie

parallel

to the glass slide and the brushes

correspond

to line disclinations of

strength

s = + 1/2, The brushes do _not lie coincident _to the

polariser

and

analyser

but make _an

angle

of between 15 and 20°. Note that _even under this low

magnification

the central ends of the two brushes of _one fan _are

seen not to converge to the _same

point.

(indicating

a non-uniaxial

hexagonal phase,

^similar to the _case found in tilted columnar

phases

of

thermotropic liquid crystalline phases (C~ [47]),

however

they

rotate

along

^with rotations of the

polariser

and

analyser

in the _{same sense.} The

topological

nature of the

singularity (line

defect of

strength, s)

which is

responsible

for the formation of _the brushes has been studied

previously [36, 48-50].

The

strength,

_s, is

equal

to the number of brushes divided

by

^four and is

positive

if the brushes _rotate in the _{same sense as} the

polariser

and

analyser

and

negative

JOURNAL DE PHYS<QUE II -T 3. N'6, JUNE <993 36

otherwise.

Hence,

line disclinations of

strength

_s

=

+1/2 _are

responsible

for the brushes observed in

figure

2, these disclinations _are

paired

for all thicknesses used

[361.

Note that the central ends of the two brushes of _one fan have been observed not to converge ^to the _same

point indicating

that the molecular

cylinders

have the

shape

of

developable

domains

[36,

51,

52],

As water is allowed _to evaporate ^{from the}

hexagonal phase

on a

glass

slide the texture

obtained after _{one or two}

days,

is shown in

figure

3.

Although

the _texture resembles the smectic

fan,

it is _not

composed

of classic focal conic domains

[46]

with

layers parallel

to the

glass

^slide. The texture is forced _to form

by

the presence of the disclinations inherent in the

hexagonal phase.

The

layers

remain

parallel

and _at

equal

distances

(except

in the

fractures),

but do not have the

shape

of

Dupin cyclides. They

rather have the

shape

^of

cylinders

whose cross-sections _are evolutes of circles. As far _{as we}

know,

this

striking

texture has _not been

previously reported

for

lyotropic

_systems. It

corresponds

to the

development

of _{a new}

phase

as

evidenced

by

the occurrence of _a

boundary

and _an enhanced

opacity

of the _new band. However the line disclinations within the

hexagonal phase

_are maintained

through

the

phase

transition _;

note also that the

angle

of the brushes with respect to the

polariser

and

analyser

remains

constant

throughout

the transition (15 to

20°).

Further evidence for the

phase change

_was

obtained from SAXS which will be discussed later.

X-ray

measurements

performed

_on this

new

phase

showed that it consists of

bilayers

of surfactant molecules with frozen

hydrophobic

chains indicative of _a lamellar

gel phase.

Fig. 3. Spiral texture for the Na- lo lamellar gel phase formed by slow evaporation of water from the

hexagonal

phase when grown on a flat surface (crossed polarising filters, magnification 200). Note the brushes do not lie coincident _to the

polariser

and

analyser, maintaining

the _same

angle

observed in the hexagonal

phase.

Figures

4a and 5 show

enlargements

of the

spiral

_texture when viewed under crossed

polars

and

plane polarised light respectively.

The interwoven

spirals

^which are observed in both _cases indicate that their

origin

is

physical

and _not due _{to an} interference mechanism, whereas the brushes _{are no}

longer

evident under

plane polarised light.

More than _one

spiral

_may

originate

from the _{same core} of the line disclination

(s

=

+1/2).

When _more than _one

spiral

does

originate

from a

single

_core these

spirals

have the _same

period (the

distance measured between two consecutive arms of the same

spiral along

^their common

normal).

Therefore these

spirals

are evolutes of circles

[53]. Furthermore,

because

they

can be

formally superimposed

on one

another

(I.e.

if the

spirals

_were to have the _same

origin they

would be

indistinguishable) they

are evolutes of the _same circle

(see

Sect.

4.2).

On the other hand

spirals originating

from different _cores have _no

relationship.

The

periodicity

is different for

spirals originating

from

a) b)

Fig.

4. Details of the domains in the Na- lo

spiral

texture

(magnification

800). Note the _occurrence of

multiple

fractures

originating

from the _{same core} and different

periodicities

for the interwoven

spirals

(the periodicity ^{of all} spirals

originating

from _{one core} is about I. I ~m and those from the second _core about 0.9 ~m). a) Crossed

polarising

filters. b)

Circularly polarised

light the _core radius

(>.~ is estimated _to be 0,2 and 0,16 _~m

respectively.

Note the presence of single _core striations in conjunction with the spirals,

which arise when the _{cores are no}

longer paired,

Fig- ^{5, Na-10}

spiral

texture viewed under plane polarised

lighI (magnification

800),

Fig, 7. Striations obtained for the oriented lamellar

gel

phase ^{of Na- lo} grown by ^slow

evaporation

of

water from the

hexagonal phase

on mica (crossed

polarising

filters,

magnification

400),

FJg.

6. - _Mosaic texture

obtained from the Na-10 bulk lamellar

different _cores and

totally independent

of the distance between the _cores.

Nevertheless, spirals

can

only

be formed in the presence of

paired

line

disclinations,

where the second _core influences the

growth originating

from the first. If the two cores are

sufficiently separated, spirals

no

longer

form but instead striations _are observed

(Figs.

4a and

b)

which is _a

consequence of the

density

of the _cores

being

too low. Formation of

spirals

_was monitored _{as a} function of time. As the _water evaporates ^{it is observed that the number of} tums increases and the

spirals

_grow

larger,

I.e. outwards. The

helicity

of the

spirals

is

statistically

random

throughout

^the texture.

The

spiral

texture can be obtained

only by evaporation

of _water from the

hexagonal phase.

Indeed when _a

sample

of the bulk lamellar

gel phase

is viewed

through

crossed

polarising

filters the

resulting

texture,

figure

6, contrasts

strikingly

to the _{texture seen} in

figure

3, this feature will be discussed later

(Sect. 4.2).

The _nature of the substrate is also _a determinant in the formation of the

spiral

texture.

Attempts

to form _a uniform

spiral

texture on a

piece

of

mylar

or mica _were unsuccessful.

Mylar

cannot be used because concentration

gradients

cannot be

successfully performed

due to its

hydrophobicity.

The texture shown in

figure

7 is that obtained for _a micellar solution _on mica after slow

evaporation

of _{water to} form first the

hexagonal

and then the

gel phase.

This texture

which consists of

long

striations is characteristic for _a mica surface and it resembles

closely

the texture seen on

glass

when the _{cores are no}

longer paired.

Mica is

molecularly

smooth upon

cleaving

and the absence of _a uniform

spiral

texture on this substrate may be due to the absence of

large

nucleation sites _on mica, in _{contrast to} the

glass

surface.

Remarkably

the

spiral

texture can be grown on a

glass

slide with _{no cover}

slip,

if the concentration

gradient

is

performed

in _a close _to saturated _water vapour

atmosphere.

This

implies

that the formation of such _a texture is related _{to an}

anchoring

_{process on} a

simple

substrate and _not induced

by

a confinement

problem.

Note that

usually

_a free surface _can induce features other than

anchoring

for instance the

Grandjean

terraces

[39].

Similar features have been found in other

binary

surfactant/water systems. ^A concentration

gradient performed

at 25 °C for CTAC gave

initially

_a

_hexagonal phase (Fig. 8),

_as

expected (binary phase diagram

^shown in

Fig. 9)

which _was followed

by

^{the formation} of the

spiral

texture

(Fig. lo).

As in the _case of the Na- lo

hexagonal phase,

the

hexagonal phase

fomled in the

CTAC/water

_system is non-uniaxial with the brushes of the fan texture

lying

at an

angle

of between 5 and 10° relative _to the

polariser

^and

analyser.

^This

angle

^{is conserved}

during

the transition from the

hexagonal

to the lamellar

gel phase.

The texture tends to that of concentric

Fig.

8, Fan texture of CTAC

hexagonal phase

(crossed

polarising

filters,

magnification

200). The brushes do not lie coincident to the

polariser

and analyser but make _an

angle

of between 5 and lo". Note that _even under this low

magnification

the central ends of the _two brushes of _one fan _{are seen not to}

converge to the _same

point.

Qu

~

lnti

f ^~~~2

f

40

B

j

~~ L

H~

^G.I

1

0

40 50 60 70 80 90

wt°ACTAC

Fig.

9.

-Hexadecyltrimethylammonium

chloride and

2H20 binary phase diagram

(courtesy of Henriksson _et al. [54]).

Lj

micellar solution,

H~.

normal

hexagonal phase,

L~. lamellar

phase, gel

lamellar

gel phase

of type

Lp

or

Lg., Qa

bicontinuous cubic phase, Int-I and Int-2 _are intermediate

phases

and A

hydrated

CTAC crystals.

circles rather than

spirals

when all four brushes converge almost to a

single point,

this is _true for both CTAC and Na-10 systems. ^The

stability

of the

spiral

texture for CTAC is

generally

much reduced

compared

with Na-10. This relative

instability

is reflected in the _more

rapid crystallisation

of pure CTAC from the

gel phase

which takes

only

a

couple

of

days

as

compared

^{with months in} the Na-10 _case.

Again,

there is little in _common between the bulk

Fig.

lo. CTAC

spiral

texture for the

gel phase

grown on a flat surface (crossed

polarising

filters,

magnification

200), Note the brushes do _not lie coincident _to the

polariser

and

analyser, maintaining

the

same angle observed in the hexagonal phase,

Fig.

ll.-Mosaic _texture obtained from the CTAC bulk

gel

phase (crossed

polarising

filters,

magnification

200), where the layers are

parallel

to the

glass

slide,

lamellar

gel

texture

(Fig.

I

I)

and the _texture of the lamellar

gel phase

grown on the

glass

slide

(Fig. lo).

CTAC is _an ideal system to

study

because it is believed that formation of the

spiral

_texture

arising

from the

gel phase

grown on a flat

glass surface, requires

_a direct

phase

transition between the

hexagonal

and

gel phases.

At

higher

temperatures ^CTAC no

longer

has _a first order

phase

transition and the

spiral

texture should _not be observed. Indeed, at 56 °C _no

spiral

texture could be

prepared by

the concentration

gradient

method, _as

expected

due to the

formation of _a cubic

phase

in agreement ^{with the} observations of Henriksson et al.

([54]

_;

Fig. 9). However,

the

spiral

texture was still observed at any temperature

prior

to the formation of the cubic

phase.

In addition _no intermediate

phase

_was observed in contradiction to the

reported phase diagram ([54]

_;

Fig. 9).

To further illustrate the

requirement

of _a direct first order

hexagonal-gel phase transition, C14Na

_was

investigated.

The

spiral

texture is observed _{over a narrow} temperature _range

only

(55-67 °C),

in agreement ^{with the}

reported phase diagram [45, 55, 56].

The

rarity

of this

texture arises from the fact that the

majority

of

binary

surfactant/water system ^have

intermediary phases

between the

hexagonal

and

gel phases

and _so do _not

undergo

_a direct

two

not been

previously reported.

^Some characteristic

examples

were chosen _to illustrate this statement.

Three

polyalkyl(ethylene oxides)

surfactants _were chosen _as characteristic of non-ionic systems.

According

to Mitchell et al.

[57],

_a bicontinuous cubic

phase

is located between the

hexagonal

and the lamellar

phases

for

C12E06, C12E08

and

Cj6E08.

In addition the two latter form _a micelle close

packed

cubic _at

high

water content. Concentration

gradients performed

on these surfactants at

varying

temperatures gave no evidence for the formation of _a

spiral

texture.

Anionic surfactants _can have different head groups and

hydrocarbon

chain character~ and hence it is difficult to

predict

their

phase

behaviour.

SDS,

_a

single

chained surfactant with _a sulfate

headgroup

and _a sodium _counter ion exhibits six

liquid crystalline phases,

_a

hexagonal,

a two-dimensional

monoclinic,

_a rhombohedral, a bicontinuous

cubic,

_a

tetragonal

and _a

lamellar

phase [17,

19,

58-60]. AOT,

_a branched chain surfactant with _a sulfonate

headgroup

and sodium counter ion forms _a

lamellar,

a cubic and _a reversed

hexagonal phase [61, 62].

KO is _a

fatty

acid with _a

potassium

counter ion and _a double bond in the middle of the

hydrocarbon

chain. Unlike SDS and

AOT,

^KO does _not form _a cubic

phase

but instead two intermediate

phases

^between the

hexagonal

and

lamellar,

the

rectangular

and the

complex hexagonal phase [56, 63-66].

For the three anionic systems ^{studied there} was no evidence for formation of _a

spiral

texture.

DTAC and CTAB _were chosen _to represent ^{the class of cationic} surfactants, because of their different chain

lengths

and counterions. DTAC forms _a micelle

packed

cubic,

hexagonal,

bicontinuous cubic and lamellar

phases [67],

whereas CTAB has the _same

phase progression

without the micelle

packed

cubic

[68, 69].

These _two surfactants like all those above have _no first order

phase

transition between a

hexagonal

and _a

gel phase

^and a

spiral

texture was never

observed.

3.2 X-RAY SCATTERING.

Assignments

of the

regions

in the

phase diagram

were established

by

determination of the structures with SAXS. Diffraction

patterns

were obtained for

powdered

bulk

samples

in the

hexagonal

and lamellar

gel phases

for Na- lo. In addition, the

reciprocal

space of oriented

samples

in the

gel phase (which gives

rise to the

spiral texture)

of Na- lo and CTAC was

fully

determined.

For bulk

samples,

the diffraction patterns come out as

Debye-Scherer rings produced by

all domains in the irradiated volume. The Na-10

hexagona phase

^is characterized

by

four

sharp rings

at small

angles

with

spacing

in the ratios 1:, 3 _:

/ :,I

as

expected

for

parallel cylinders packed

ⁱⁿ a two-dimensional

hexagonal

_array

(Tab. I).

The wide

angle scattering

shows one diffuse

ring

^located at 2 ar/4.4 =1.4

h~ indicating

a

liquid-like

state for the

paraffinic

chains

[I].

The diffraction

pattern

^{of the bulk}

gel phase

^of Na-10 is

comprised

at small

angles by

^three

sharp rings

ⁱⁿ the ratio _: 2 _: 3 characteristic of a

layered

structure and _a diffuse central

ring

located at

0.1181-' _(for

a 75.02 _wt %

sample) (Tab. I).

This diffuse

scattering

reflects the existence of correlations _{over a} range of 53.

h.

The wide

angle

pattern ^is characterized

by

_a

set of two

sharp

reflections _at

Q

=

1.337

l~

'

(strong)

and at

,fi _{Qi (weak),}

_and

two diffuse

rings

at

Qo

₌ ^0.945

h~

' and _at 2

Qo,

all

positions

_are

independent

of concentration. The

sharpness

of the

reflections,

whose

ratio,

relative _to

Qo,

is

(I :,,fi:,j:,I),

_{has been}

analysed by

^Tardieu et al.

[12].

The diffuse

rings

_are ascribed to the

polar

_groups

organised according

to _a two-dimensional _square lattice of

edge equal

to 2

ar/Qo

₌

6.71.

_The

_sharp

reflections

correspond

to stiff chains

organised

with rotational disorder in another two-

dimensional square lattice where the

diagonal

is the side of the

polar

_group lattice

Table I. Structural

pat.ametet.s for

Na-10/water

mesophases

at 27 °C.

Na-10 % Unit Cell Volume Surfactant Water Mean Area

Q length (a)

Fraction

Aggregate

Thickness per Polar

Thi cknes _s

(dw

Head

(A

(ds)

(W/w) (h-') (h)

_4S

(h) (h) (h2)

44.18

H~

o,162 44.8. 0.39 29.5 15.3 38.3

0.278 0.321 0.427

51.39

H~

_o,160 45.4 0.46 32.5 12.9 34.8

0.278 0.323 0.427

55.50

H~

o,158 46.0 0.51 34.3 1.6 32.9

0.267a 0.323a

69. 80

H~

0. 105*

+ 0.158 46.0 0.65 39.0b 6.9b 28.9b

Ls

0.201 31.2 0.64 20.0 11.2 26.5

0.405

74.40

L~

o_105*

0.210 29.9 0.69 20.7 9.2 25.6

0.418 0.640

75.02

Ls

o,l18*

0.219 28.7 0.70 20.0 8.7 26.4

0.440 0.661

80.16

Ls

o,123*

0.223 28.2 0.76 21.3 6.9 24.8

0.440 0.640

* Diffuse ring.

a

Very

weak.

b Structural parameters ^{calculated with m} = 0.65 _as if the

H~

phase were

extending

up to 69.8 %.

(Qi

=

/ _Qo).

_The

hydrocarbon

chains _are

perpendicular

to the

plane

of the lamellae and in _a helical conformation

(L~) [12]. X-ray

diffraction

experiments performed

_{on a}

sample

of the Na-10 system ^which

produced

the

spiral

texture between _two

capillaries

and the

equivalent

texture of

long

striations on mica gave diffraction data, both at small and wide

angles,

^identical

to that of the bulk

gel phase.

^{It follows that the}

crystallographic

structure associated with all the

textures

(Figs. 3-7)

is the same and hence

corresponds

to the _same

thermodynamic

lamellar

gel

texture obtained in

CTAC,

where the lamellar

gel

is of the type

L~

or

L~, (I.e.

the

paraffinic

chains, in _an all-trans

conformation, adopt

_a

close-packed hexagonal

_or

quasi-hexagonal

arrangement, ^and can be either normal _or tilted with

respect

to the

plane

of the

bilayers [9-13])

as indicated

by

the observation _at wide

angles

of

only

_one

sharp

reflection at

2 WM. I

= 1.53

l~ '.

In order to determine

fully

the

reciprocal

_space of the lamellar

gel phase,

oriented

samples

were used

(Sect. 2.2). Figure12

shows _a film obtained with the incident

X-ray

beam

28

Fig.

12. X-ray scatIering pattem of the Na-10 lamellar gel phase oriented by slow evaporation of

water from the

hexagonal

phase. The incident beam is

perpendicular

to the mica windows of the cell

(inset)

the

Bragg

diffraction spots located _on the vertical axis indicate that the

layers

have grown

perpendicular

to the walls

(periodicity

28.7

1).

_{Note the diffuse}

_scattering

_{spot located}

_along

_{the vertical}

IQ ₌ 0.118

h- ').

JOURNAL DE PHYSIQUE II -T 3. N' 6. JUNE 1993 "

perpendicular

to the mica windows of the cell. Three

Bragg

spots are detected

along

the

vertical, indicating

that the

layers

have grown

parallel

to the

equatorial plane.

These spots appear with _{a crescent}

shape

due _{to a}

slight mosaicity

of the

sample.

The former diffuse

ring

of the

powdered sample

_now lies

along

the _same axis _as the

Bragg

_spots.

Rotating

the

sample along

the vertical axis does _not

change

this pattem ^{which indicates} a full symmetry ^of revolution

along

the normal _to the

layers.

No other

scattering

has been detected in other

geometries

of the

sample

^relative to the incident beam.

From the locations of the

Bragg peaks

the unit cell dimensions _can be calculated. The

number of surfactant molecules per unit cell

(N~)

can be determined from the known

composition

of the

mesophase, assuming complete segregation

of

paraffin

and

polar regions

V~PN~10~~~

~~ jl)

M~(

where V is the volume of the unit cell

(h3), _M~

is the molecular

weight

of the surfactant

(M~

₌ ^{206 for}

Na-10), (

the

specific

volume of the surfactant

(cm3 g-I),

and ~P the volume fraction of the two component

mesophase

of surfactant concentration

c(g/g ), ((

is the

specific

volume for _~A,ater

=

1.004399 cm3

g~'

_at 27

°C)

:

~P=

1+)(~-l)1(2)

v~ ^c

The

specific

volume of _a

dry

^surfactant can be deduced from

Ms

_~s

"

Mpol

_~pol ⁺

Mpar

_~par

(3)

where M~~j ^and M~~~ ^are the molecular

weights

and

)

and

~

_are the

specific

volumes of the

polar

head group and

paraffinic

chains

respectively.

The

specific

^volume of the

paraffinic

chains is calculated from _:

where_nc~~, and

nc~ _are

the number

of

methene ^{and methine} groups in

the

b

(cm3

^g~') can ^be obtained from v (molar) for which tables of data

at

varying

temperatures

are available

[7,

_8, 12, 70]. The

volume

of the sodium ^rboxylate group

was

estimated at

27

_°C

by a

linear

extrapolation using the _specific volume

values

_{for sodium}

tetradecanoate _and odium decanoate

at

₇₀ and

loo °C

[1,

70].

From this, the specific

volume of Na-10 at ₂₇ °C, _where the

chains

are in

the

a

onfiguration,

was

0.825 _cm3 g~' _and

0.772 cm3 g~' for the _&

We assume here that the ^ggregates

of

the exagonal _hase

can

cylinders, and the _bilayers of the ^amellar phase

are _infinite

_and flat (this _will be

Sect.

4. I).

Within

thisramework, the

radius

_of the

cylinders is

r~

= a (/

qS/2

hexagonal ^haseand the

thickness of the bilayer is d~

=

_{aqs in}

the phase, where a ^s

the unit

^cell _length. ^The _mean ^area

per

olar ead

on the

interface

is A

=

2 for

exagonal phase and

A

= _{2/N~ for} the lamellar phase,

where N~ is the umber of

molecules per

unit _ength

of cylinders and per unit

area

of ilayers Table I _gives

the

structural parametersobtained. All

equations

were

calculated

for T =

27 °C.

In the

lamellar

gel the

bilayer

_thickness (Tab. I) is _{with frozen}

in the helical nfiguration of

3.4

monomers (the H2 _roups) per tum [71].

A

bilayer

nsisting of chains

in

an _all-trans conformation which

are not

interdigited

would

have

a

presence of _a double bond _at the end of the

hydrocarbon

chain of Na-10 is

equivalent

_to

reducing

the chain

length by approximately

one

CH~ group).

The observed contraction of this thickness is consistent with the ratio of 1.145

[12]

between this extended form and the helix

configuration

for the chains in the

L~ phase.

The cross-sectional _area per chain _can be calculated from the

wide-angle spacing by assuming

_a two-dimensional square chain

packing

which for

Qj

= 2 ar/4.7

h~

'

corresponds

to A~ = 22. I

h~.

4. Discussion.

4. I STRUCTURAL TRANSFORMATION AND EPITAXIAL RELATION. To describe the structures

and _to understand the

physical

_reasons for the

phase changes (in

this _case from _a normal

hexagonal phase

to a lamellar

gel phase),

a

precise picture

of the

shapes

and the

packing

of the aggregates must be

obtained,

since the geometry ^of

self-assembly

is

directly

controlled

by

the intermolecular forces

[73-76].

In

principle

this information _can be extracted from the relative intensities of the diffraction lines for the observed patterns

[7, 77-79],

often

though

due _to the

complexity

ⁱⁿ the aggregate ^{form factors these} intensities _are difficult _to

analyse [5].

Furthermore,

the

exploitation

of the limited number of reflections

gives only

_{an average}

structure, which reflects the _nature and symmetry of the

long

_range order

displayed by

the

mesophase.

The real _structure may

depart

from this _mean

picture,

when diffuse

scattering

occurs due _to various types ^of fluctuations of lower symmetry

extending

over a short range.

To _ease the task of structure

determination,

chemical constraints

pertaining

_to the _nature of the molecules and their geometry can be introduced _to

produce

a choice of

possible

structures

which have the _correct

symmetry [7].

The main constraint is the

segregation

of _water from the

hydrocarbon

chains of the

amphiphilic

molecules.

Using

this well

accepted assumption,

which is demonstrated in several different _cases

[5,

7,

9-11, 13, 80, 81],

the relative volumes of the

aggregates ^and

interaggregate

water are obtained

(Tab. I)

from the known

composition

of the

mesophase, according

to the

analysis

recalled in section 3.2. Note

that,

_as the water content

decreases,

the _area per

polar

head _at the water-surfactant interface _never

increases,

_even when

phase

boundaries _are crossed, in agreement ^{with the work of Luzzati and} collaborators

[7].

The above

procedure

has enabled _{us to}

analyse

the so-called lamellar

gel phase

for Na- lo in

water

(Sect.

3.2 and Tab.

I).

The one-dimensional

periodic

structure is _an alternate stack of

water

layers separated by bilayers,

where the

hydrocarbon

chains _are

perpendicular

to the

plane

of the lamellae and in _a helical conformation

(Ls ) [12].

The

paraffinic

chains maintain rotational motion

along

^the

long

axis of the molecule

[82]

and lateral motion in the

plane

of the

bilayer

is believed _to be slow

[83, 84].

In the normal

hexagonal phase H~,

the aggregates ^of

amphiphilic

molecules, whose

paraffinic

chains _are in a

liquid-like

state, are

generally

described _as indefinite

cylinders

of circular _cross section. As these sections have

symmetries higher

than

six,

this

description

is

compatible

with the

p6m

_symmetry of the lattice. For systems ^{of surfactant in} water

(I.e. binary

systems or mixture of different

amphiphilic

molecules in the absence of any alkanes which _can swell the interior of the

aggregates),

the radius of such

cylinders

_must be smaller _{or at}

maximum

equal

to the

length

of _an extended surfactant molecule

(as

there is _no water within the

hydrophobic region

of the

aggregates).

Hence when the surfactant concentration

increases,

the aggregates grow and the

hexagonal phase

is

preserved

as

long

as the section of the

cylinders

does _not become

larger

than this critical

width,

otherwise _a

phase

transition

usually

occurs. This is

exactly

what _occurs for Na-10 in water

(see

Tab.

I). However,

in certain

lyotropic liquid crystals [19, 85, 86],

it has been observed that the

hexagonal mesophase

can

remain stable and the

p6m

symmetry ^of the lattice

preserved, although

its aggregates

accommodate _a

higher

number of surfactant molecules than

expected.