Microscopic ordering in smectic phases of liquid crystals

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Submitted on 1 Jan 1990

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Microscopic ordering in smectic phases of liquid crystals

M. Zgonik, M. Rey-Lafon, C. Destrade, C. Leon, H.T. Nguyen

To cite this version:

Short Communication

Microscopic

ordering

in smectic

_phases

of

_{liquid crystals}

M.

Zgonik(1,*),

M.

_{Rey-Lafon(1),}

C.

Destrade(2),

C.

_Leon(2)

and H.T

Nguyen(2)

(1)

L.S.M.C.

_{(URA 124),}

Université de Bordeaux

I,

351 Cours de la

Libération,

33405

Talence,

France

(2)

Centre de Recherche Paul

Pascal,

Chateau

_Brivazac,

33600

Pessac,

France

(Received

on

_May

_16,1990,

accepted

on

lllly

2,1990)

Résumé. 2014 On a étudié _par

_{spectroscopie d’absorption infrarouge}

l’ordre orientationel dans les

phases

smectiques

d’un matériau cristal

_liquide

_{ferroélectrique,}

le

_{décyloxy-4-thiobenzoate}

de

_[(2S,

3S)-chloro-2-méthyl-3-pentanoyloxy]-4’-phényle,

en

_abrégé

10.S.C1Isoleu. Deux

_types

d’échantillons

orientés,

l’un

_homéotrope,

l’autre en

_{configuration Clark-Lagerwall,}

ont été

_préparés

et

_plusieurs

bandes intenses en

_{infrarouge, caractéristiques}

des différentes

_parties

et orientations des

_molécules,

ont été choisies. Les résultats montrent _que l’inclinaison

_{des parties}

centrales

_(c0153urs)

des molécules varie très _peu de la

_{phase SA à}

la

_phase

_S*C,

ce

_{qui implique}

_que les c0153urs des molécules sont

_déjà

inclinés dans la

_phase

_SA.

Leurs axes,

qui

sont désordonnés sur un cône dans la

_phase

_SA,

_s’alignent

mais restent sur ce cône

quand

on _passe en

_phase

S*Cen

abaissant la

_{température.}

Ce modèle est en

accord avec

_quelques

résultats antérieurs.

Abstract. 2014 Orientational order in smectic

phases

of a ferroelectric

_{liquid-crystalline material}

4’-(2S, 3S)-2"-chloro-3"-methylpentanoyloxyphenyl-4-decyloxy

thiobenzoate,

abbreviated

10.S.C1Iso-leu,

was examined

_by

IR

_absorption

_{spectroscopy.}

Oriented

_samples

were

_prepared

in both bookshelf and

_{homeotropic alignment}

_geometry.

Several

_stronger

IR vibrations were selected

_{characterizing}

different _parts and orientations of the molecules. Results show that the molecular tilt of the core

parts

of the molecules

_changes

_very little from the

_SA

to the

_S*C

_phase

_implying

that the core _parts of the molecules are

already

tilted in the

SA phase.

Axes of the core

_parts,

that are disordered on a cone

in the

_SA

_phase,

start to

_align

with each other but remain on this cone on

_lowering

the _temperature into the

_S*C

_phase.

The model _agrees with some

_previous

results.

Classification

Physics A bstracts

61.30

1. Introduction.

Molecular

_ordering

in

_{liquid crystal}

_(LC)

_phases

is the basic

_{phenomenon leading}

to a

_great

va-riety

of different LC structures

[1].

As

_such,

it has been

_widely

studied

_by

several

_{spectroscopic}

techniques

and main features of the different

_phases

are indeed

understood,

but much remains

2016

to be done.

_Important

details in orientational distribution functions are still

_missing

as well as

knowledge regarding

the

_shape

of the molecules and the relative

_ordering

of different atomic

groups.

In this letter we

_present

new results on the molecular

_ordering

in the smectic A

_(SA)

and fer-roelectric smectic

_{Q (Sz)}

_phases

of 4’-

_(2S,

_{3S)-2"-chloro-3"-methylpentyloxyphenyl-4-decyloxy}

thiobenzoate,

abbreviated 10.S.ClIsoleu

_[2].

The material

_belongs

to the

_{recently synthesized}

family

of LCs which are

chemically

stable,

have

relatively

broad

Sè

phase

and have

_high

spon-taneous

_{polarization.}

The structure of the material is shown in

_figure

1. As the

_S*

_phase

is an

interesting phase

from a fundamental and an

application

point

of

view,

a better

understanding

of molecular form and

_{functionality}

of different molecular

_parts

is

_necessary

to allow the use of

molecular

_engineering

to

_improve

the

_properties

of materials.

Fig.

1. - Molecule of the

10.S.ClIsoleu liquid crystal.

2. Molecular order.

A

_typical

_mesogenic

molecule is

_composed

of a

quasi

rigid

central

_part

and one or two more flexi-ble

_aliphatic

chains or end

_groups.

A

_{commonly accepted}

_picture

of a smectic

_phase

shows

orien-tationally

ordered molecules

_arranged

in

_layers,

_changing

their orientational order at the

SA -

_S*c

phase

transition

_[1].

In the

_SA

_{phase long}

molecular axes are

_{suppposedly orthogonal}

to

smec-tic

_layers

and

_begin

to tilt

_away

from this direction on

_crossing

the

_phase

transition

_temperature.

The

_long

molecular axis

_usually

refer to

_average

axis of all of the molecule. As most

_{spectroscopic}

techniques

measure the orientation of the axes of the central molecular

_parts

one must be careful in

_{interpretation}

of the results. A well established fact is that the LC order is

_mostly

connected with

_ordering

of the central molecular

_parts

while

_aliphatic

chains are

quite

disordered

[3,4].

The orientational order in a smectic

_layer

can be described

by

an orientational distribution

function,

which-taking

molecules as

rigid

bodies-is a function of

all

three Euler

angles

[5].

Any

spectroscopic

technique applied

to measure this function can

give only

certain

approximations.

The IR

_absorption

due to a

single

molecule is

proportional

to

_(E.

Pi)2

where E is the

_optical

elec-tric field and

aM

is the

_change

of the molecular

_dipole

moment M due to a vibrational mode

p=- aQ

g

characterized

_by

the normal coordinate

_Q;.

Instead of the orientation of the whole

_molecule,

we

will

_study

the orientational distribution of

_dipoles

_pi that characterize the molecular

_parts

at which

some molecular vibration is localized. The distribution of pi is a function of

just

two Euler

_angles

,Q and y

defined in

_figure

2. The

_laboratory

coordinate

_system

is defined with the z axis normal

to the smectic

_layer

and the x axis normal to z and to the direction of

_spontaneous

_polarization

in the ferroelectric

_{S* phase.}

In the uniaxial

_SA

_phase

the distribution

_{depends just}

on ,Q,

but in

Di ({3,

y)

of a

_{particular vibrating}

_dipole

_pi in a series of

spherical

harmonics,

consistent with the

local

_symmetry

of the

_S*c

_phase.

where

_{Ai, Bi, Ci, Di, Ei,}

_{and Fi}

are the

expansion

coefficients and serve as order

_parameters

with the maximum value of 1 in

_completely

ordered

_systems.

_Ai

measures the

_polar

order and

can be nonzero in the ferroelectric

_phase.

If the

_dipole

pi is chosen so that it is

_{aligned along}

the molecular

_major

_{axix, Bai}

is the usual order

_parameter

_{(P2 (cosfl»}

in the

_SA

_phase

with

_P2(cos/?)

being

the

_{Legendre polynomial.}

In

_general,

coefhcients

Bi

measure the order relative to the z axis. A maximum value of 1 means that all of the

dipoles

are

parallel

to the z axis and minimum value of -0.5 shows the

_dipoles

are

_orthogonal

to z and _may be disordered otherwise.

Cs, Di,

Ei

and Fi

are four other

_parameters

_measuring

the

_quadrupolar

order.

Fig.

2. -

_(a)

shows orientation of the induced molecular

_dipole

moment _{pi in the}

_laboratory

frame with

z axis normal to the smectic

_layers

and _y axis

_parallel

to ferroelectric

_polarization

in the

_S*

_phase.

_(b)

de fines the

_{angles b}

and 0 that measure the orientation of the

_optical

electric field in

_{the x-y}

and x-z

_planes

respectively.

Let us first calculate the contribution to

_absorption

coefficient for the

_arbitrarily

oriented

_dipole

pi and the incident field E in

experimentally

accessible

principal

planes

of the

laboratory

coor-dinate

_system.

We write the

_components

of pi as

I pi

1 (sinfl

_cos-y,

_sin,8

_sin"

_cos,B)

and the

com-ponents

of the incident electric field

_polarized

in the x-z

_plane

_{as 1 E 1 (sino,}

_0,

_coso)

where 0 is the

angle

between the z axis and the electric field

direction,

as seen in

_figure

2. The contribution

pi)2

then

_equals:

An

_{analogous expression}

for the case

with

the electric field in the _x-y

_plane,

where it is written as

2018

’Ib calculate the measured

_absorption

coefficient we then

multiply

the

absorption

of a

single

molecule

₍₍₂₎

or

₍₃₎₎

with the distribution function

₍₁₎

and

_integrate

over

dy

and

d(cos/3).

The

resultant

_absorption

coefficients normalized to the

_absorption

in the

_{isotropic phase,}

where the distribution is

_isotropic,

are :

and

As seen,

_only

second order coefhcients can be deduced from IR

_absorption

measurements. No information is obtained on the

Ai

coefficients which are the ones that

_distinguish

the ferroelectric from the nonferroelectric

_Sc

_phase.

In an IR

absorption experiment

for a

birefringent

medium,

the incident beam should be

po-larized in one of the two

_{eigen polarization}

direction for the selected direction of

_propagation.

Therefore ,

only

two

_{angles corresponding}

to the

_{eigen polarizations}

are allowed for à and 0 in

the

_previous

_expressions.

3.

_{Experimental.}

The

_phase

transition

_temperatures

of

10 S Cllsoleu

measured on

_heating

are

_Txc

=

54° C,

TcA

=

6ô° C,

and

_TA,

= 74° C

corresponding

to transitions between the

crystal,

S*,

SA,

and

isotropic

phases respectively.

Disordered

_samples

for the IR

_spectroscopy

were

_{prepared by heating}

the

_powder

in vacuum

between two

_rough

Csl

_plates

until it melted and formed a film

approximately

5 _{pm thick. A}

homeotropically

oriented

_sample

of a thickness of around

5pm

was

_prepared

between two ZnSe

optically polished

plates

coated with lecithin. The cell was also filled in vacuum and

_good

align-ment in

SA

phase

was obtained

by

slowly cooling

the

sample

from the

isotropic phase.

The

align-ment was checked under a

polarizing microscope.

The transition to the

_S*

_phase

was

clearly

detected

_{by noting}

the reduction of

_optical

extinction between crossed

_polarizers.

The low

bire-fringence

observed

_proved

that the direction of the

_pitch

was normal to the ZnSe

_plates

and that the smectic

_layers

were not

_{perturbed by crossing}

the

_{SA -}

_S*c

_phase

transition.

Homogeneously aligned samples

were

_prepared

between Si

_polished

_plates

with indium-tin-oxide electrodes and

_poly-vinyl

alcohol

_{alignment coating.}

One of the

_plates

was mounted in a slide to allow

_shearing

the two

_plates.

This

_proved

to be

_necessary

in order to obtain

_good

alignment

in the

SA

_phase.

In the ferroelectric

_phase

an electric field was needed in order to

produce good

bookshelf orientation. A

_typical

_voltage

of 5 to 10 V was

applied

to the electrodes when the

_sample

thickness was around 5 rem. The

sample

could not be checked

_optically

but similar cells were

prepared using glass plates

and

procedure

was devised

_leading

_{unequivocally}

to

well-oriented

_samples.

Cells with

_glass

_plates

were used also for Raman measurements. Different cells for

_temperature

_regulation

were used in the

study

with an

_accuracy

and

stability

of better than

1 K.

The first measurements were directed toward band

assignments

in the IR and Raman

_spectra.

Infrared

_absorption

_spectra

were

taken,

depending

on the

availlability

of the

instruments,

with a

,Nicolet

740 and Brucker 113 Fourier transform

_{spectrometers.}

Some intermediate

_products

in the

synthesis

and Br-Cl substituted chiral chain

_samples

were

investigated,

the results for which will

could be observed. The

_aliphatic

C-H

_stretching

domain

_presents

a

_complex

_group

of bands as

well in the IR as in the Raman

_spectrum.

Besides C=0

stretching

vibrations at

_frequencies

1762

cm-1

_{(IR only)}

and 1672

cm-1

and C-S

_stretching

at 900

_{cm-1 ,}

all other

_stronger

bands are

associated with

_{para-substituted}

_benzene-ring

vibrations.

Seven characteristic

_dipoles

were selected for the determination of the molecular orientation.

The choice was made

_upon

a

compromise

between

following

criteria : the

respective

vibration

should be well localized with

_{predictable direction}

of the induced

_dipole

_moment,

their IR

ab-sorption

bands should be

_strong

_enough

and well isolated from the

_neighbouring

bands. Four of the

_dipoles

are directed

predominantly along

the

long

axis of the molecular core. These are

the bands around 1600

_cm-1,

1163

cm-1

and 1015

cm-1

that are all

_complex

bands with

compli-cated substructure and

_correspond

to benzene

_ring

C-C

_stretching

and C-H

_{bending in-plane}

vibrations and the 900

cm-1

C-S

_stretching

vibration. Three of the studied bands characterize

vi-brating dipoles making large angles

with the molecular

_major

axis. These are two C=0 vibrations

at around 1762

cm-’

and 1672

_cm-’,

and a

complex

band at about 839

cm-1

connected with the

ring

C-H out-of

_{-plane bending.}

For all the bands the

_integral

of the absorbance was taken over

the relevant

_{spectral region.}

The ratios

_Rixy

were calculated as :

and

_analogously

Rxz

too.

The measurements in

_{homeotropically}

oriented

_samples

were used to determine

_parameters

B=.

The

_layer

structure was not

_perturbed

at the

_{SA -}

_S*

_phase

transition as mentioned

previ-ously

but the helical structure with

_{approximately}

ten

_pitch

_periods

was

_present

in the

sample.

The

_polarized

IR beam was directed

normally

to the cell. Different incident

_{polarizations}

_gave

identical

_absorption

_spectra

and therefore the

_average

of the

_absorption

₍₅₎

over à was obtained.

The

_{parameters Bi}

were calculated from the

absorption

_spectra

as

Bi

=1-

Rixy.

Figure

3 shows

the

_temperature

_dependence

of the seven

_parameters.

As seen in the

figure

these

_parameters

do not

_change

much at

_TAC

and

_stay

_nearly

constant

_throughout

the

_S*

_phase.

’Ib determine the other two coefhcients

Ci

and

_Ds,

measurements in a cell with bookshelf

ori-entation were

performed.

In the

SA

phase

the results confirmed

previously

obtained values for

Bi.

Their absolute values were few

_percent

smaller and the différence was attributed to a

_poorer

sample

orientation. In the

_S*

_phase

the IR

_absorption

_spectra

were taken at several

_angles

0. The

extrema in the absorbances were found when 0 coincided with the

_optical

tilt

_{angle showing}

no

measurable

_dispersion

of the

_optical

indicatrix orientation from the visible into the IR

_region.

Due

to a less reliable

quality

of the

sample

orientation

only

the

_{strongest band,}

centered at 1600

_cm-1,

was

_investigated

and no

_precise

_temperature

dependence

was measured. The

_{corresponding}

sat-urated value

₍₁₀

K below

_TAO)

of the

_{parameter Ci}

was found to be 0.4 ±0.1 and the absolute value of

_Di

is smaller than 0.05.

4. Discussion.

We

_explain

the

_continuity

of

_{parameters Bi}

_by

a

specific ordering

of molécules at the

_{SA -}

_S*

2020

Fig.

3. -

Température dependence

of the order _parameters

_Bi

for the seven molecular

dipole

moments

associated with different molecular vibrations. Center

_frequencies

are marked in the

_figure.

Phase transition

temperatures

on

_cooling

are

_TA,

= 74° C and

TCA

= 66° C.

significantly

at this

_phase

transition. We can claim this for the core

_part

of the molécules which

was characterized

_by

the studied IR vibrations. The

long

axes of the core

_parts

of the molecules are disordered on a cone in the

SA

phase

and start to

_align

with each other on

passing

the

_phase

transition

_temperature.

The tilt

_angle

of the molecules therefore does not

_change

at the

_phase

transition. In this

_picture

the

_{parameter Ci}

associated with the induced

_dipole

moment _pi

_aligned

along

the molecular axis is the

_primary

_microscopic

order

_parameter

which characterizes the

non-ferroelectric

_Sc

_phase.

This is also valid for the ferroelectric

_S*

_phase

where the

_{parameter A%}

measuring

the

_polar

order of a

_permanent

_dipole

transverse to the

_long

molecular axis is

propor-tional to the

_spontaneous

_{polarization.}

It is

_{generally accepted}

that the

_spontaneous

_polarization

is

_only

a

_secondary

order

_parameter

_[4]

and so

_A;

is a

_secondary

_microscopic

order

_parameter

of the

_S*

_phase.

Parameters

_Bi

_{characterizing}

the orientation of the

_long

molecular axis are

_gradualy

dimin-ishing

in the

_S*

_phase.

The molecular tilt therefore

_slowly

increases when

_cooling

this

_phase.

1Y¡>ical

tilt

_angle,6i

calculated from

Bi =

(3cos2,Bi - 1)

/2

for the

_{dipole vibrating}

at 1600

cm-’

is

_increasing

from 27° at

_TAC

to 29°.

The idea of a tilted orientation in the

_SA

_phase

is not new. To our

knowledge

the first indication

of this kind of

_ordering

is the work

_by

Loesche and Grande

_[6].

Their conclusion was based on the

measurements of the

_{angular dependence}

of the

_proton

NMR linewidth in the smectic

_phases.

In Raman

_scattering

one is also

_measuring

the orientational order of the molecular core

_part

as all

studied vibrations are

modulating

the

polarizability

of benzene

rings.

In addition to

_{(P2 (cos,B))}

the

_technique

also

_permits

the determination of

_{(P4(cos,B)) .}

The results on

(P4(cos,B))

obtained

by

Jen et al.

_[5]

and also others

_[7]

in the

_SA

_phase

were considered to be

_anomalously

low in

comparison

with

_predictions

obtained from Maier

_Saupe

mean field

theory.

In the

picture

of

the

_average

molecular orientation

_orthogonal

to smectic

_layers

this would mean a

_{relatively large}

tilted _away from the

_layer

normal. If we then

_suppose

that the tilt distribution function is rather

narrowly

centred around the _average molecular

tilt,

that is around an

_angle

of

_30°,

it is not

surpris-ing

to find a

relatively

low contribution of

(P4 (cosQ))

to the series

_expansion

of the orientational distribution

_function,

since

_P4(cos,8)

is zero at 30.5°.

In

_support

of this model we should also

_repeat

that the tilt

angle

of the core

_part

and of the

aliphatic

chains not need to be the same. Evidence was

_presented

that this difference in tilt is

important

in

_explaining

the

_appearance

and

_sign

of the

_spontaneous

_polarization

in the

_S*

_phase

[8,9].

In most cases it seems that the tilt

_angle

of the core

_part

is

larger.

Judging

from the Ra-man and IR

_spectra

the molecular conformation does not

_change

on

going

from

SA

to

_S*

_phase

therefore the tilt of the core

_part

in

_SA

is also

_expected.

The

_strongest

evidence mentioned

_usually

_against

such a

_picture

of molecular

_ordering

is the

dependence

on

_temperature

of the smectic

_layer

thickness d. In materials where no association

of molecules is observed d is

_usually

constant in the

SA

_phase

and start to diminish on

crossing

TAC.

Such a behaviour is also measured in our LC. The

diminishing

of d in the

S*

phase

is

usu-ally

attributed to the

_appearance

of tilted molecular orientation. But in _many cases of smectic

phases

the value of d is

_{significantly}

shorter than that estimated for the most extended molecular

configuration

1

_[10].

The différence is

_typically

a little less than 10% . In our material the

_layer

thickness in the

_SA

_phase

was measured to be 3.072 _{nm, and is} 2.845 nm 10 K below

TAC.

The

length

of the extended molecule was estimated to be 1 = 3.3 nm. Various

interpretations

of this

mismatch include

_{interpenetration}

of

_liquid-like

_hydrocarbon

chains in the

_{neighbouring layers}

or the

_departure

of the

_{configuration}

of the terminal

_alkyl

chains from their

_fully

extended trans

conformation.

_{Nevertheless,}

the most obvious

_explanation

is the tilted molecular orientation

_[11].

Thking

the steric tilt

_angle

as

arccos(d/1)

we

_get

21.5° in the

SA

phase

and 30.5° 10 K below the

transition. Even if the steric tilt

_angle

defined in this _{way may} not be

_accepted

with

_great

confi-dence the values for the tilt

_angle

in the

_S*

_phase

_agree

_quite

well with our IR results

_(29°

for the 1600

cm-’

_vibration).

If we then take the molecular tilt to be around 30° in both smectic

_phases

we can attribute the increased

layer

thickness in the

SA

_{phase solely}

to increased disorder of the molecular

_{positions along}

the direction of the

_layer

normal.

5.

_{Acknowledgements.}

The authors would like to thank E Hardouin for the

_X-ray

measurements. One of the authors

_(M.

Zgonik)

would like to thank M.

_Copic

for extensive

_helpful

discussions

_during

the

_preparation

of this

_paper.

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