The problem of orientational order in tilted smectic phases : a high resolution neutron quasi-elastic scattering study

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The problem of orientational order in tilted smectic phases : a high resolution neutron quasi-elastic

scattering study

A.J. Dianoux, H. Hervet, F. Volino

To cite this version:

A.J. Dianoux, H. Hervet, F. Volino. The problem of orientational order in tilted smectic phases : a high resolution neutron quasi-elastic scattering study. Journal de Physique, 1977, 38 (7), pp.809-816.

�10.1051/jphys:01977003807080900�. �jpa-00208642�

THE PROBLEM OF ORIENTATIONAL ORDER

IN TILTED SMECTIC PHASES :

A HIGH RESOLUTION NEUTRON QUASI-ELASTIC SCATTERING STUDY

A. J. DIANOUX

Institut

Laue-Langevin, 156X,

38042 Grenoble

Cedex,

^France

H. HERVET

Laboratoire de la Matière

Condensée, Collège

^de

France, place Marcelin-Berthelot,

⁷⁵²³¹ Paris Cedex

05,

^France

and F. VOLINO

Institut

Laue-Langevin, 156X,

38042 Grenoble

Cedex,

^France

and

Groupe

^de

Dynamique

des Phases

Condensées,

Laboratoire de

Cristallographie (*) U.S.T.L., place

^E.

Bataillon,

³⁴⁰⁶⁰

Montpellier ^Cedex,

^France

(Reçu

^le

20 janvier 1977, accepté

^{le 30 mars}

1977)

Résumé. ²⁰¹⁴ On présente des résultats de diffusion incohérente quasi

élastique

^{de neutrons, à}

haute résolution, ^{dans les}

phases

smectiques ^H surfondue, ^{VI et VII du}

téréphtal-bis-butyl-aniline

(TBBA). ^{Le facteur de structure}

elastique

incohérent ²⁰¹⁴ EISF 2014 et la forme des raies sont

analysés

^à

l’aide de modèles qui incluent la

possibilité

^{d’un ordre} orientationnel autour du

grand

^{axe. Les conclu-}

sions sont les suivantes :

(i) ^{Dans la}

phase

H, les molécules toument uniformément autour de leur

grand

axe, ^{sur une} échelle de temps ^de 10-11 s, ^ce qui

n’implique

^aucun ordre orientationnel des

dipôles.

(ii) ^{Dans la}

phase

VI, les molécules se réorientent, ^{sur la même} échelle de temps,

probablement

par sauts de 03C0 autour du

grand

^{axe, ce} qui, ^comme

précédemment n’implique

^aucun ordre orientationnel des

dipôles.

(iii) ^{Dans la} phase VII, ^il n’y ^a

plus

^de mouvements rotationnels de

grande amplitude

^{sur une}

échelle de temps ^de 10-11 s.

De (i) ^et (ii), ^on conclut que les

phases smectiques

^{inclinées ou non inclinées doivent} être caracté- risées par ^un critère autre que l’existence ^ou l’absence d’une forte interaction

dipolaire

^{entre les}

molécules.

Abstract. ²⁰¹⁴

High

resolution neutron

quasi-elastic

scattering data in the

supercooled

^smectic H, smectic VI and smectic VII

phases

^of

terephtal-bis-butyl-aniline

^{2014 TBBA - are} presented. ^The elastic incoherent structure factor ²⁰¹⁴ EISF 2014 and the line

shapes

^are

analyzed

^{in terms of models}

permitting

orientational

ordering

around the

long

axis. The conclusions are :

(i) ^{In the H}

phase,

^{the molecules rotate}

uniformly

around their

long

axis, ^{on a} time scale of 10-11

s, implying

^no orientational order of the

dipoles.

(ii) ^{In the VI} phase, the molecules

probably

reorient, ^{on the same time} scale,

by jumps

^{of 03C0 around}

the long axis, again

implying

^no orientational order of the

dipoles.

(iii) ^{In the VII} phase,

large amplitude

rotational motions on a time scale of 10-11 s do not exist any ^more.

From (i) ^and (ii), ^{it is concluded} that the tilted or non-tilted smectic

phases

should be characterized

by ^a criterion other than the existence or non-existence of a strong intermolecular

dipole-dipole

interaction.

Classification

Physics ^Abstracts

7.130 ^- 7.114

(*) ^{Associe au (’.N.R.S.} (La 233).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01977003807080900

810

1. Introduction. - The

problem

^{of the nature of}

molecular

ordering

^{in the} tilted smectic

phases

^has

been,

^{in the}

past

^few years, the

subject

of conside- rable

work,

^both

theoretically

^and

experimentally,

and the answer is still controversial. The former

microscopic

^mean field theories

of Meyer

^{and McMil-}

lan

[1]

for the smectic C and H

phases

and that of

Meyer [2]

for the smectic H and VI

phases

^contain

orientational

ordering

of the molecules around their

long

^{axis as a} fundamental feature. This

ordering

^is

linked to the existence of a

strong

intermolecular

dipole-dipole interaction,

^which

plays

^{an essential}

role in these

theories,

^as

being responsible

^{for the}

tilted character of these

phases. Although

^{some authors}

have claimed to have observed some

ordering,

^the

published X-ray [3],

^NMR

[4, 5, 6],

^ESR

[7],

^Raman

[8]

and neutron

[9, 10, 11]

results do not support ^the existence of such an

order,

^{at least in some C and H}

phases. Consequently,

other theories have been deve-

loped

^{which do not} contain this feature

[12, 13].

However,

^this

negative

^{result is not}

yet

^well

accepted,

as could be noticed at the VIth International

Liquid Crystal Conference, Kent,

^Ohio

(1976).

For

studying

^this

problem,

incoherent neutron

quasi-elastic scattering (NQES)

^is

certainly

^{one of}

the most

powerful

tools since it can

probe

^{both the}

geometry

^{and the}

dynamics

^{of the molecular}

^motions, provided

^{these are}

sufficiently rapid (- ^lO-11 s) [14].

This is the ^case for the

typical

mesogen

terephtal-bis- butyl-aniline (TBBA).

^{In a series of} papers, ^we have

presented NQES

results in the

crystalline [15]

^{and the}

various smectic

phases

^{of TBBA}

[9-11, 14, 16].

Analysis

^{in terms} of the elastic incoherent structure factor

(EISF)

^have

suggested

^{that :}

(i)

^In the C and H

phases,

^{the molecules rotate}

rapidly

around their

long axis,

^{with some}

additional, rapid

fluctuations of this axis about its

equilibrium position.

(ii)

^{In the VI}

phase, rapid

rotational motion still

exists,

^{but it} should be less

uniform

than rotational diffusion ^- or

jump

motion among six

equivalent positions

around the

long

axis. The existence of an

orientational

ordering

around the

long

^axis may

explain

this feature.

In this _paper, we present ^{a more detailed}

NQES study

^{of the}

supercooled ^H,

VI and VII

phases [3]

of

TBBA,

^{aimed at the}

problem

^{of the} orientational order.

Here,

^not

only

the EISF but also the line

shapes

are

analyzed

^{in terms of models}

permitting

^orienta-

tional

ordering

around the

long

axis. The results

essentially

^{confirm our}

previous conclusions; namely,

no

ordering

^{in the H}

phase

^and

possible,

^but

weak,

order in the VI

phase.

Because of this

weakness,

^we

propose ^an alternative

(and

^{in our}

opinion

^more

realistic)

model for the VI

phase,

where the molecules

are allowed to

flip by x

around their

long axis,

^{as has}

been

suggested

^{for a} non-tilted smectic E

phase [17].

In section

2,

^we present theoretical models which

are used to describe the

possible physical

^situations

and write down the

corresponding

incoherent neutron

scattering

^{laws. In section}

3,

^the

experimental

^results

are

presented

^{and some results are} extracted from an

analysis

^{in terms of the}

experimental

^{EISF. In sec-}

tion

4,

^{the same data are}

analysed

^{in terms of the}

complete scattering

^{laws. In section}

5,

conclusions are

drawn and discussed in terms of other

experimental

results.

2. Theoretical models and incoherent neutron

scattering

^{laws. - In these}

models,

^{we assume that}

(i)

the molecules are fixed in a three-dimensional

lattice, (ii)

^{that a}

body

^{axis can} be defined and

(iii)

^{that the}

molecules can rotate about it.

Any

translational motion of the centre of mass is assumed to occur on a different time scale to rotation

(much longer

^for

self-diffusion,

much shorter for

vibrations). According

to the

microscopic

^theories

[1, 2],

the molecules are

submitted to a

potential

of the form

where _T is the azimuthal

angle

around the

long

^axis.

This

potential

describes the

dipole-dipole

interaction which tends to

align

^the

dipoles

^{towards a fixed}

direction,

^{taken as}

origin (T

⁼

0).

^{In a}

NQES

expe-

riment,

^{one follows the}

protons

^{which are attached}

to the molecules. These protons ^are

generally

^not

situated on the

long

^{axis but at a distance a. To}

analyse

the

NQES data,

^we should thus calculate the incohe- rent

scattering

^{law for a}

particle undergoing

^random

motion on a circle of radius a and submitted to the

potential given by

eq.

(1).

^{In a}

previous

paper

[18],

FIG. 1. - The first non-zero order parameter yN ⁼ (cos Ncp >

versus yg, ^{for a} circular random motion in an N-fold cosine poten- tial : eq. (5) ^{of the text.}

we have solved this

problem

^{in the case of a more}

general potential

of the form

In what

follows,

^we

give

the results relevant to our present

problem.

^{The rate}

equation governing

the

probability

^function

Gs(lp,

lpo,

t)

^{which is the}

probability

^of

finding

^the

particle

at 9 at time t if it was at To ^{at t =}

0,

^{was chosen to be of the}

Debye

type,

namely

where

Dr

^{is a} rotational diffusion coefficient and 2

yN

the relative barrier

height

^defined

by

The

first

^{non-zero order} parameter yN is defined

as the _average value of cos

N(p

^{and we have}

where the I are modified Bessel functions of first kind.

Figure

¹ shows the curve yN ^versus

yN

^calculated

from _eq.

(5).

The neutron incoherent

scattering

^{law can be} calculated. The result

is,

^{for a}

powder

^form

sample

with

and

where

jo

^{is the}

spherical

Bessel function of order zero.

In these

expressions :

(i) Ap

^and

Vnp

^{are the}

eigenvalues

^and

eigenvectors

^{of the}

(infinite)

^{matrix M whose terms are}

(m, n >, 1)

(ii)

_P, ^and

Wnp

^{are the}

eigenvalues

^and

eigenvectors

^{of the}

(infinite)

matrix N whose terms are

(m, n >, 1)

(iii) T pn

^{are the elements} of the matrix T such that

where the elements of the matrix 0’ are

(m, n >, 1)

(iv) U pn

^{are the} elements of the matrix U such that

812

where the elements of the matrix Q’ are

(m, n > 1)

In items

(iii)

^and

(iv),

^the

argument

of the Bessel functions I is

yfv.

^{It is}

interesting

^to consider the two limit-

ing

^cases

y%

^{= oo and}

y%

^{= 0. For}

y%

⁼ oo we recover the

jump

^model among N

equidistant

^{sites on a circle}

[19, 20].

^The

scattering

^function

is,

^{in this case}

with

and

For yN

⁼

0,

^{we recover} the rotational diffusion model on a

circle,

^which

clearly,

^is

independant

^{of N.}

This case is in fact identical to the case

y%

^{= oo and N = oo so that we have :}

In other

words,

when the number of wells is

large,

^the

scattering

law is almost

independant

of this number and of the barrier

height.

^In

practice,

for TBBA in the Sm H

phase,

^a

jump

model between six sites and the rotational diffusion model are indiscernable from one another for

Q

^1.2

A-1 [9].

^{For N =1 or}

2,

^{this is}

no

longer

^{the case} and this fact will be used to

analyse

^the

present NQES

data. This is

why

^we

give

^{a few more}

results

concerning

^{these two cases. For N =}

1,

^whatever

y’,

^no

approximate expression

^{for the}

scattering

^law

(eq. (6))

^exists.

^However,

^{in this case it} is clear that the two matrices M and N are identical

(since

^{m - N is}

never

negative). Hence,

eq.

(6)

^can be written in a

slightly

^more compact ^{form. For N} >

1,

^{on the} _contrary,

an

approximate

^{form for} eq.

(6)

^can be written as soon as

yN

^is

sufficiently large.

^{For N =}

2, when y2

> 1.2

(corresponding

^{to an order} parameter Y2

= (

^{cos 2}

qY ) = 0.5), only

the lorentzian

corresponding

^to

À1

^can

be retained in _eq.

(6)

since all the other ones are much broader

(at

^{least 10}

times)

^{and can} thus be considered

as

contributing

^{to a flat}

background.

^{We can} then write :

with

The functional form of _eq.

(20)

is identical to that of _eq.

(15)

^{for N = 2. The}

quantity D, A,

^{can thus be}

identified for

large y2,

^{to the}

jump

^rate between the two

equilibrium positions.

^{For the}

proofs

of all the statements made in this

section,

the reader is referred to ref.

[18].

3.

Experimental

results and

analysis

^{in terms of the}

EISF. ^- As in our

previous

^work

[9 -11],

^the

sample

studied was the

partially

deuterated derivative of TBBA ^we called DTBBA

(completely

deuterated ^on

the

butyl ^chains,

^{in order to} render their motion invisible to

neutrons),

ⁱⁿ

powder

^{form. The}

sample

environment is described in ref.

[9].

^The

NQES

expe-

riments

^were

performed using

^the

time-of-flight

spec-

trometer IN 5 installed at the cold source of the reactor of the Institute

Laue-Langevin.

The incident

wavelength

^{used was 11.0}

A, yielding

^{an elastic}

energy resolution function of Aco 20.0

J.l.e V (1 J.l.eV

^{= 1.52 x}

¹⁰⁹ rad . s-’)

^FWHM

(compared

to Aco 33

J.l.eV

^{in ref.}

[9-11]).

Two kinds of ^run

were

performed

^{for 24} temperatures between 102 and 68 OC in the

supercooled

^Sm

H,

^{Sm VI and}

Sm VII

phases.

^In the first kind of _run, the spectra

were recorded for six

scattering angles corresponding

to

(elastic) Q

values between 0.5 and 1.05

A-l.

Such

runs needed rather

large counting

times and were

performed only

^{for a few} temperatures. ^{In the second} kind of run,

only

^two spectra ^were

recorded, using

many ^counters for

each, corresponding

^{to average}

Q

values of 0.78 and 1.03

A-1 (AQ

⁼ ± ^0.03

A-1).

In all _cases, care was taken in

changing

^the tempe-

rature between two runs. Indeed it turned out that the Sm VI

phase

could be missed if the

temperature

was

changed

^too

rapidly.

^In

particular,

^{we found it}

important

^to

stay

^a

relatively long

^time

(-

¹

hour) just

above the normal

crystal-Sm

^H transition tem-

perature

( x 114 C)

^before

gently cooling

^the

sample further,

first in the

supercooled

^{Sm H}

phase

^{and then}

into the Sm VI

phase. Figure

^{2 shows a}

typical NQES spectrum

^obtained in the Sm VI

phase

^at

78°C, together

with the instrumental resolution function. It

clearly

^{shows a}

sharp peak reproducing

the

resolution

^function

superimposed

^{on a broad}

component, ^as

expected [9-11].

Since these two

components

^{are well}

separated,

^the

experimental

^EISF

(i.e.

the relative

intensity

^{of the}

sharp peak

^{to the total}

(quasi-elastic) intensity)

^{can be} deduced. This was

done

using

^the computer method described in ref.

[11].

The results of this

analysis

^are summarized in

figure

³

FIG. 2. ^- Typical NQES spectrum for DTBBA in the smectic VI

phase. Temperature ^{T = 78} °C, ^{momentum transfer} Q ^{= 1.03} A - 1.

The corresponding instrumental _energy resolution function is also shown.

FIG. 3. ^- Experimental EISF of DTBBA B’ersus temperature deduced from NQES spectra ^{taken at} Q ^{= 1.03 A-1. The error}

bars depict ^the uncertainty ^{inherent to} the method for extracting

the EISF. The limits correspond ^{to a} pessimistic ^{and an} optimistic evaluation of the intensity ^{in the} wings ^{of the} spectra. On the left hand side of the figure ^{is indicated} the theoretical value of the EISF for the jump model among ^N sites on a circle (yg ⁼ oo) : eq. (16) of the text, averaged ^{over the five kinds of} protons of the DTBBA molecule, calculated for Q ^{= 1.03} A-’. Point D : N 1, point ^{C :}

N ⁼ 2, point ^{B : N = 3 and} point ^{A : NN} 4, ⁵ ..., oo. Point A also corresponds ^{to the} rotational diffusion model (yN = 0). Varying yN, ^the theoretical EISF should vary between : ^D and A for N ⁼ 1,

C and A for N ⁼ 2, ^{B and A for N =} 3, ^etc...

where we have

plotted the, experimental

^{EISF for}

the spectra ^{taken at}

Q

^{= 1.03}

A-1,

^versus

tempe-

rature. It is seen that the EISF increases as the tem-

perature

^is

decreased,

with definite

jumps

^{between 90}

and 89 °C and between 70 and 68 °C. Let us

analyse

these data in terms of the models

presented

in section 2.

Since the DTBBA molecule contains

only

^{five kinds}

of proton, ^{all located on the}

body,

^the theoretical

expressions (6)

^to

(8),

^and

(15)

^to

(21)

^{should be}

averaged

^{over the}

corresponding

^five

gyration

^radii ai.

These _are,

assuming

^{that the}

body

^is

rigid,

^{in its trans-}

conformation, 2.33, 1.90, 1.52,

^{2.33 and 1.90}

A [11].

In what

follows,

^when

referring

^{to these}

expressions,

we shall

always

^{assume that such an} average has been

performed.

^{On the left hand side of}

figure ^3,

^{we have}

indicated,

^{for a} few values of

N,

the range in which the theoretical EISF

(eq. (7))

^{can vary with}

^yg,

^for

the value

Q

^{= 1.03}

A- 1.

^{The limit}

yg

^{= 0 is the same}

for all N

(point A).

^{The limits}

yN -

^{oo are calculated}

from _eq.

(16).

^{It is seen that for} N >-

4,

all are

practi- cally

^{the same and}

correspond

^to

point A,

^{N = 3}

corresponds

^to

point ^B,

^{N = 2 to}

point

^{C and N = 1}

to

point

D. With these

indications,

^some conclusions

can

immediately

^{be drawn :}

(i)

^{Down to 90 OC - the}

supercooled

^H

phase

^-

we have N

large, suggesting

uniaxial rotational

motion,

^but no, ^or very

weak,

orientational

ordering

814

in the sense of the theories of ref.

[1]

^and

[2].

^The

lowest value of the EISF ^at 102 °C

compared

^{to that}

at 90 °C can be attributed to a kind of motion other than rotation around the

long

^{axis. In ref.}

[11],

^we

assumed that the effect was due to fluctuations of this axis.

(ii)

Between 89° and 70 OC - the Sm VI

phase

^-

since the

experimental points

lie between A and D

(case

^{N =}

1),

^{some finite} orientational order in the

sense of the theories of ref.

[1]

^and

[2]

may exist.

However,

^the

points

also lie between A and C

(case

N ⁼

2),

^{so that a}

symmetrical

model where the mole- cules

jump by 7r

around the

long

^{axis is also}

possible.

(iii)

^{Below 70} OC - the Sm VII

phase

^-

only

^the

case N ⁼ 1 is

possible, although

it is difficult to conclude in this case whether the measured EISF is

meaningful (the

broadened contribution in the spectra is in fact _very

weak).

4.

Analysis

^{in terms of the}

complete scattering

^{laws :}

order parameters and correlation times. ^- In this

section,

^{we take}

advantage

of the fact that

(i)

^for

each temperature, many spectra ^are available for

different Q

^{values and}

(ii)

that formal

expressions

^for

the incoherent

scattering

^{laws are}

available,

^to

confirm the above

conclusions,

deduce order _parame- ters and correlation times and try ^to discriminate between the two

possible

models for the Sm VI

phase.

We shall thus discuss the cases N ⁼ 1 and N ⁼ 2 for the smectic H and VI

phases.

4.1 CASE N ⁼ 1. ^- This case

corresponds

^{to the}

microscopic

theories of ref.

[1]

^and

[2],

^{where the}

molecules are allowed to

perform large

^{and over-}

damped

oscillations around the

long

axis about the

direction qJ

^{= 0. We} have fitted the

scattering

^law

given by

eq.

(6)

^{for N = 1}

simultaneously

^{to all the}

spectra obtained in one run, for all temperatures.

The fitted parameters ^are

y’, 1 Dr,

^{a flat}

background

and a

Debye-Waller

factor. The

fitting procedure

^is

described in ref.

[15].

^The computer time turned out to be rather

large

^{due to} the fact that the

large

^matrices

M and N

(truncated

^{at a} dimension s -

20, typically)

have to be

diagonalized

many times.

Figure

^{4 shows}

the results for the order

parameter

yi

= (

^cos T

>,

related to

T’ by

eq.

(5) (or Fig. 1).

^{It is seen that this}

model

yields :

(i)

^cos

o > --

^{0 in the}

supercooled

^H

phase, (it) ( cos T > varying

^{from 0.2 to 0.5} in the Sm VI

phase.

^This

corresponds

^to average

angular

^fluctua-

tions

of ±

^{80 to} ± 60° about the

equilibrium position.

Figure

⁵ shows the

corresponding

values found

for

the correlation time

Dr 1.

4.2 CASE N ⁼ 2. ^- This case

corresponds

^{to a}

model in which the

dipoles play

^no

^role,

^{as in the}

non-tilted Sm B and Sm E

phases.

^{The molecules are}

FIG. 4. ^- Values of the order parameters y for the models N ⁼ 1 and N ⁼ 2, ^versus temperature, ^obtained by fitting eq. (6) ^or eq. (20), according ^{to the} case, simultaneously ^{to all the} spectra ^obtained in a run at a given temperature. ^{The white} symbols correspond ^to

runs with two spectra, ^{the black} symbols ^{to runs with six} spectra.

The circles stand for the model with N ⁼ 1, the squares for the model with N ⁼ 2. The corresponding ^mean angular fluctuation

amplitude Acp is also indicated for each case.

FIG. 5. ^- Values of the correlation time of the motion for models N ⁼ 1 and N ⁼ 2, ^versus temperature, ^obtained by fitting eq. (6)

or eq. (20), according ^{to the} case, simultaneously ^{to all the} spectra obtained in a run at a given temperature. The circles stand for the

quantity Di ^{of the model N =} 1, ^the squares stand for the quan-

tity (Dr A 1) of the model N ⁼ 2. It is seen that whatever the model, the correlation times are roughly ^{the same} within 50 %

and that no discontinuity ^is apparent ^at the Sm H-Sm VI transition.

allowed to oscillate about two

opposite equilibrium positions (T

^{= 0 and} T ⁼

a)

^{and to}

jump

^between

these two

positions.

^We have fitted _eq.

(6)

^{for N = 2}

to the same data. The result for the order parameter Y 2

= (

^{cos 2} cp

B

^{related to}

y2 by

eq.

(5) (or Fig. 1),

is also shown in

figure

^{4. It is seen that :}

(i) (

^{cos 2}

T > --

^{0 in the}

supercooled

^H

phase.

This result was

expected

^{from the case N =}

1,

^since all the models are identical for

yg

^{= 0.}

(ii) (

^{cos 2}

T >

^{varies from 0.7 to - 1.0 in the}

Sm VI

phase.

^This

corresponds

^to average

angular

fluctuations of z ± ^{200 to}

nearly

⁰ about each

equi-

librium

position.

^In

fact,

^to obtain these

results,

^we used the

approximate scattering

^law

given by

eq.

(20) since

^{cos 2}

T >

^was

expected

^{to be}

high.

On

figure

^{5 are} also shown the

corresponding

^corre-

lation times

(Dr Â.1)-1.

In both _cases, N ⁼ 1 and N ⁼

2,

^the

quality

^{of the}

fit was found to be

equally good,

^{as can be seen on}

figure

^6.

FIG. 6. ^- Example ^{of the} quality of the fit obtained. The crosses are

experimental corresponding ^{to a} temperature of 73°C. The full line is either the best fit of _eq. (6) ^{for N =} 1, corresponding ^to

yl ⁼ 0.44, Dr ^{= 3.3 x 10-11} s, ^or to eq. (20) (N ⁼ 2), ^corres- ponding ^to Y2 = 0.97 and (Dr A 1) ^{= 2.0 x 10-11 s. The number}

of counts has been normalized so that it makes sense to compare the amplitudes of the four spectra.

5. Discussion.

2013 1)

^{For the smectic H}

phase,

^we

confirm,

^{in the}

supercooled

state, ^our

previous

^conclu-

sions obtained in the normal ^state

[9, 10], namely

that

(i)

the molecules rotate around their

long. axis,

in contradiction to the arguments

against

rotation of de Vries

[21]

^and

(ii)

no, ^or very

weak,

orientational

ordering exists,

^{in the sense of the}

Meyer-McMillan [1] ]

and

Meyer [2]

theories for this

phase.

^{On the} contrary,

they

agree with most of the conclusions deduced from results obtained with other

spectroscopic

^tech-

niques [3-8].

^In

particular,

^{we wish to} mention the

X-ray

^results

[3]

which indicate the existence of three

equivalent

orientations for the molecules around their

long

^axis

(X-ray

^{data cannot}

distinguish

^between

static and

dynamic disorder),

^{and a} theoretical cal- culation

[22],

^{which can}

reproduce

^rather

accurately

the

X-ray

patterns

using

^{a model}

assuming only

steric hindrance between the

phenyl rings.

^{In other}

words,

the molecular order in the tilted smectic H

phase

^{of TBBA} appear ^to be the same as that

expected

for a non-tilted Sm B

phase.

2)

^For the smectic VI

phase,

the existence of a

broadened

component

^{in the}

NQES

spectra

is,

ⁱⁿ

our

opinion,

^a

proof

^{that some} rotational random motion similar to that

existing

^{in the H}

phase,

^still

exists. In that _sense, we are at variance with the conclusions drawn from DMR

[6]

^{and Raman}

[8]

works where it is

suggested

^that the motion freezes

on

cooling

^{to the}

phase

^{VI. On the} contrary, ^{we are}

not in contradiction

(i)

^{with the}

picture suggested by X-ray

diffraction ^-

only

^the average orientation of the molecules is seen

there; (ii)

with the weak entropy

change

^{AS = 0.34}

Ro

^{measured at the}

Sm H - Sm VI transition

[2]

^{- one would}

expect

S >

Ro Log 1.1 Ro

^{if a}

complete freezing

^occur-

ed

(although

^this argument may be

questioned) ; (iii)

^with proton

spin-lattice

relaxation measure- ments

[23]

which show

only

^a very weak

change

^at

the H-VI transition

indicating

^{that no}

major change

in the nature and the time scale of the motions occur.

The

question

left is thus to discuss

which,

^{of the two}

possible

^{models we} propose and which are consistent with our present

NQES data,

^{is the more realistic.}

Since the fit of both models is

equally good,

^we

should look to other results to answer this

question.

In our

opinion,

^{there are}

(at least)

^{two reasons for}

believing

that the model

corresponding

^{to N = 2 is}

the correct one. The first reason is theoretical.

Although

^{our data do not}

disagree

with the existence of an orientational order as

predicted by

^the

Meyer theory [2],

^this

theory

^also

predicts

^{a similar}

(but weaker)

order in the

higher

temperature ^{Sm H}

phase.

However,

^{we have seen} that such order does not seem to exist in the H

phase,

i.e. that the

dipole-dipole

interaction is not dominant in this

phase.

^{If so, there}

is no strong ^{reason to} believe that it becomes a

leading

term in the Sm VI

phase.

The second reason is related to the structure of the VI

phase.

^The

X-ray

^results

suggest

^a

herring-bone

arrangement ^{for the}

molecules,

where at the two kinds of sites in the _a, b

plane

^the

two mean orientations are at + 300 and - 300 with respect ^{to the b direction}

[3]. Consequently,

^{an ave-}

rage

angular fluctuation

^{of ± 80 to} ± 60° around each

equilibrium position,

^as

predicted by

^{the model}

with N ⁼ 1 would

imply

^{that the two} kinds of sites

are

continuously exchanging

^{on a} time scale of

-

10-11

s

(a

fluctuation

just

greater ^than + ³⁰⁰ would have

implied

^{the same}

result).

^{Such a motion}

is

necessarily

collective

and,

^{in our}

opinion, unlikely

on this time scale. On the contrary, with the model N ⁼

2,

where the molecules are allowed to

flip by

n around their

long axis,

the maximum

angular

fluctuation is

only

^{± 200.} This result _agrees with the

symmetry

^{and the}

jump by

^{n will}

only

^{involve a}

(more reasonable)

mononiolecular motion. If thus we

adopt

the model N ⁼ 2 for the VI

phase,

the molecular order in the Sm VI

phase

^{of TBBA} appears ^to be the same as in the non-tilted Sm E

phase,

^{for which a similar}

type of motion has been

suggested,

^{based on}

NQES

results

[17].

This result

is,

ⁱⁿ

addition,

^{more reasonable}

when

regarding

the conclusion for the Sm H

phase.

816

3)

^{For the Sm VII}

phase,

^no

large amplitude

^rota-

tional

motions,

^{on a} time scale of

10- 11

_s, are detected any ^more. The Sm VI-Sm VII transition thus _appears

as a

freezing

^{of the}

jump by

ⁿ around the

long

^axis.

This result is in

agreement

^with proton

spin-lattice

relaxation measurements which exhibit a

large jump

at the Sm VI-Sm VII transition. The nature of the

remaining

^motions

compared

^{to the}

crystalline phase

cannot be inferred from the present

experimental

results.

6. Conclusion. ^- From

high resolution,

^incoherent

NQES

^on

TBBA, making

^the

(weak) assumptions

that

(i)

the molecular

body

^is

mainly

^{in its transcon-}

formation on a time scale of

10-11.

s and

(ii)

^{that the} observed

broadening

^{of the}

spectra

^{is due to rota-} tional motion

only,

^we have shown

that,

^{at least for}

TBBA,

^{there is no} orientational

ordering

^{around the}

long axis,

^as

predicted by

^the

microscopic

theories in which the

dipole-dipole

interaction

play

^{an essential}

role,

in the tilted Sm H and Sm VI

phases.

^{It thus}

seems that the tilted and non-tilted smectic

phases

should be characterized

by

^a criterion other than the existence or non-existence of a strong

dipolar

^inter-

action between the molecules. This result has received

recently

^{a chemical}

confirmation,

^{where a} mesogen, whose molecules have no

dipole

^{moment on the}

body,

has been

synthetized,

^and

which,

ⁱⁿ

spite

^of

this,

presents ^{a smectic C}

phase [241

Finally

^we want to comment on the conclusions Note added in

proof :

^{In a recent letter}

(SELIGER, J., OSMDKAR,

R.,

2AGAR,

^{V. and}

BLINC,

R.,

Phys.

^Rev.

Lett. 38

(1977) 411),

^{14N nuclear}

quadrupole

^reso-

nance data in TBBA have been

presented and,

^for the H

phase,

^{it was} concluded that the results may be

interpreted

within the

Meyer-McMillan

^{model. In}

we drew in ref.

[16].

That reference

corresponds

ⁱⁿ

fact to results

preliminary

^{to those}

presented

^here.

The

interpretation

^was however somewhat different.

In

particular

for the increase of the EISF as the tem-

perature ^was lowered in the

supercooled

^H

phase,

it was

suggested

that this could

correspond

^{to some}

kind of orientational

ordering announcing

^{the Sm VI}

phase.

^{In this}

analysis

^{we had}

only

considered a

simple

uniaxial rotation of the molecules around the

long

molecular axis. In fact the DTBBA molecule contains five kinds of

protons

^and

using

^a

unique gyration

radius is

certainly

^an

oversimplification.

^The

good

agreement ^{at 119 °C with a}

simple

uniaxial rotational model was obtained with a

gyration

radius of 2.5

A

which is much

larger

^{than the} average of the

gyration

radii we have used in the

present

work. The rise of the EISF with

decreasing temperature

^{in the} super- cooled H

phase

^{can thus be}

interpreted

^{as due to}

the

freezing

^{out of} the fluctuations of the

long

^mole-

cular axis. On the view of the new results of ref.

[11]

and of this _paper, based on a more realistic theore- tical treatment

(in particular,

^it

clearly

appears ^now that the

gyration

radius should not be taken as an

adjustable

parameter, ^{as was} done in ref.

[16]),

^one

should

replace

^the conclusions of ref.

[16] by

^those

presented

^here.

Acknowledgments.

^{- VVe are indebted to Pr.}

P. G. de Gennes for

stimulating

discussions and

reading

^the

manuscript.

a

subsequent

paper

(to

^be

published)

^{we have shown}

that these data _may also be

interpreted

^{in terms of}

a model which is consistent with the

NQES

^results.

The reverse however is not true

[10, 11].

^{For the}

VI

phase,

^we have shown that both methods lead to

remarkably

consistent conclusions.

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