X-ray structural study of the mesophases of some cone-shaped molecules

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X-ray structural study of the mesophases of some cone-shaped molecules

A.M. Levelut, J. Malthête, A. Collet

To cite this version:

A.M. Levelut, J. Malthête, A. Collet. X-ray structural study of the mesophases of some cone-shaped

molecules. Journal de Physique, 1986, 47 (2), pp.351-357. �10.1051/jphys:01986004702035100�. �jpa-

00210212�

X-ray structural study of the mesophases of

^some

cone-shaped molecules

A. M. Levelut

(*),

^{J. Malthête}

(+)

^{and A. Collet}

(+)

(*)

Laboratoire de

Physique

^{des Solides}

(**),

Université Paris-Sud, ⁹¹⁴⁰⁵ Orsay Cedex, ^France

(+)

Laboratoire de Chimie des Interactions Moléculaires,

Collège

^de France, 11,

place

^Marcelin Berthelot, ^{75005 Paris} Cedex, ^France

(Reçu

^le

10juillet

^1985, accepté

sous forme définitive

le 14 octobre 1985)

Résumé. 2014 Grâce à la diffraction des rayons X, ^{nous avons} montré que des molécules

coniques

peuvent ^{former des}

mésophases

^assez ordonnées. Parmi les quatre

mésophases

étudiées, ^{trois sont}

classiques puisque

^{les colonnes}

forment un réseau

régulier plan,

^tandis que la

quatrième

^est

quasi

cristalline : seules les chaînes

paraffiniques participent

^à l’ordre tridimensionnel bien

qu’elles

^{soient à} l’état fondu.

Abstract. ²⁰¹⁴ We have established

by X-ray

diffraction that

cone-shaped

^{molecules can form}

relatively

^{well ordered}

columnar

mesophases.

^Four

mesophases

^have been studied. Three of them have the classical two-dimensional

organization

ⁱⁿ

parallel

columns while the fourth one shows a

quasi-crystalline

structure :

3D-ordering

^takes

place

^at the level of the

long paraffinic

chains which surround the conical core

despite

^{the fact that} the chains are

in a « molten state ».

Classification

Physics

^Abstracts

61.30E

1. Introduction.

Since the 1977

discovery [1]

of the first

thermotropic mesophase

of disc-like

molecules,

^{it has been shown} that molecules with flat

rigid

^cores surrounded

by

^six

or

eight elongated

flexible chains ^can form

mesophases

in which the molecules ^are stacked in columns

[2].

The columns are

parallel

^{and form a}

periodic

^2D

lattice. The

paraffinic

medium which surrounds each column is in a molten state and therefore ensures

that there is no correlation across the

columns,

^{of the} molecular

positions along

the column axis. It has been shown

recently

^that

mesophases

^{can also be obtained}

when the flat core is

replaced by

^{a conical one}

[3, 4].

We

report

^{here a} structural

analysis

^{of some of these}

new

mesophases,

^{and we} compare their

symmetries

with those of the usual columnar

mesophases

^{of disc-}

like

compounds.

2.

Experiments.

We have studied the

mesophases

of the three hexa- esters of

cyclotricatechylene

^{la-c. The transition}

temperatures

^are

reported

in table I.

Under

optical microscope

^{the textures seem cha-}

racteristic of columnar

mesophases [3, 4],

^{but the}

viscosities are very

high

^{and the}

mesophases

^{have a}

Table I. ^- Transition temperatures

of

the three studied

cyclotricatechylene

hexaesters

(OC).

waxy appearance. It ^was

possible

^{to obtain}

regions

with a

homogeneous

^direction of extinction between crossed

polarizers

^{when the}

mesophase

^was

spread

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004702035100

352

out on a

glass plate

^{with a}

spatula.

^{We therefore used}

this

technique

^{for the obtention of}

samples

^for

X-ray

diffraction

experiments.

^{Two kinds of}

samples

^were

prepared :

very thin

samples spread

^{on a}

single crystal

of mica and thicker

samples

^{with a lower}

degree

^of

orientation which were

picked

^{out of a}

glass plate

with a rasor blade. The

X-ray

^set up is _very

simple, consisting

^{of a} monochromatic beam

(CuKa)

^issued

from a double bent

graphite pyrolitic crystal,

^{and a}

photographic plate collecting

the diffracted

X-rays.

With the

technique

^described

above,

^{we obtained}

fibre

samples

with the fibre axis

parallel

^{to the stretch-}

ing

direction. When this axis is

perpendicular

^{to the}

X-ray beam,

^{one obtains a} section of the

reciprocal

space

containing

^the fibre axis which

gives

^{all the}

information. We also used a Guinier camera with CuKa radiation in order to have a better accuracy

on the lattice

spacing

^values.

3.

Experimental

^results.

Typically,

^{in a columnar}

mesophase

of disc-like

molecules,

^a

single

^domain

gives

^a diffraction

pattern

that consists of one

equatorial plane containing

^all

the

Bragg spots

^{and two} kinds of diffuse features

lying

^{out this}

equatorial plane [5].

^One

part

^{of this} diffuse

scattering

^radiation

gives

^an

image

^{of the}

organization

^{of the}

paraffinic

^chains since this

part

can be

compared

^to the main diffuse

ring

^{seen for a}

molten

paraffin.

^{The other}

part

of the diffuse scat-

tering

is localized in a set of

reciprocal planes parallel

to the

plane containing

^the

Bragg peaks,

^and per-

pendicular

^{to the column axis. One can} relate the

Bragg peaks

^{to the} inter-column

order,

^{which is a two-} dimensional

crystalline order,

while the diffuse scat-

tering intensity

describes the way in which the cores are stacked in a column.

In

figure 1,

^we

present X-ray patterns

^of

aligned samples

^{for three of the} four studied

mesophases (the mesophase

^of

compound la

and the low-tem-

perature

^{one of}

compound 16

^are

isomorphous).

Among

^these

patterns,

^{two fit the}

general

^{scheme of a}

columnar

phase (Figs. 1,

^{iv and}

1, v);

^{the third one}

for

compound lc

^{at low}

temperature

^{is that of an}

imperfect

^3D

crystal (Figs.

^{1 i to}

1, iii).

^{In this last case,}

the information about its

organization

^{can be deduced}

from a

semi-quantitative analysis

^{of the}

pattern.

3.1 MESOPHASES OF

lc. - The

diffraction

patterns

of

figure 1,

^{i to}

1,

^{iii show}

Bragg spots lying

^on

layer

lines

perpendicular

^{to the} column axis

(Fig. 1 A).

The width of these

spots

^{increases with the}

length

of

scattering

^{vector. There are}

mainly

^two

independent

factors

responsible

^{for this}

broadening :

fluctuations of

orientation,

^which

spread

^{out the}

spots

^{on circular}

arcs of the same

angular width,

^{and an} increase of the width

parallel

^{to z}

(fibre axis)

^{with the} xy compo- nents of the

scattering

^{vector. The}

layer

^{lines corres-}

pond

^{to a}

periodicity along

the column axis of 20.96

A.

All the

rings

^{observed on the}

powder

pattern ^cor-

respond

^{to the}

spots

^{observed for the oriented}

samples,

and can be indexed on an orthorhombic lattice

a ⁼ 47.07

A,

^{b = 31.58}

A,

^{c = 20.96}

A.

^{In table II}

we have listed the measured and calculated lattice

spacing

values for the observed

spots.

It is clear that many

Bragg

reflections are

missing.

^{On each}

line,

we see one group of ^a few

peaks

^{which are all in the}

same range of

scattering angles.

^{As the index I}

increases,

the

perpendicular

component increases ^simultane-

ously.

Therefore all the 0 0 l reflexions vanish. This fact

implies

^{that the}

projection

of the electronic

density along

the column axis is uniform. Moreover the extinctions are consistent with the existence of three

perpendicular

helicoidal two-fold axes i.e. with the space group

P 212121.

Besides the

major layer lines,

^{we also observed a} second set of diffuse lines

(B) parallel

^{to the first set.}

The line of

highest intensity corresponds

^{to a scat-}

tering

^{vector of}

(4.82 Å) - 1

^while the others show a

modulation of this

period (4.82 A)

^{with a wave}

length

of 20.96

A.

A few weak

Bragg spots

^{are located on} this second set of

layer

lines. Therefore the structure must be modulated in the column axis direction.

The ratio between the two

periods

^{is close to the}

rational number

13/3.

^At

last,

^{a broad diffuse}

scattering ring (C)

indicates that

paxa,ffinic

^{chains are in a}

liquid

^state.

The

general description

of this diffraction pattern is consistent with a model ^{in which an}

assembly

^of

helicoidal columns ^{forms a 3D}

imperfect crystal.

The

pitch

^of the helices is 20.96

A,

^and the molecules

forming

the column are

equidistant

^{with a}

period

of 4.82

A.

This last value is

equal

^{to the} core-to-core distance in the column of the

cyclotriveratrylene crystals [3, 6].

^{For a more}

precise description,

^{we can}

use our

knowledge

^{of the core structure obtained from}

different

crystalline

structures

[6, 7]. Unfortunately

we have no information on the external ^crown formed

by

^the

aliphatic chains, except

^{for the} fact that an

important

statistical disorder takes

place

^{at this level}

as is evidenced

by

^the

corresponding

^diffuse

scattering

at about 4.5

A.

This lack of information

concerning

the

major part

^{of the}

compound, together

^{with the}

problem

^{of the} fluctuations of the lattice unit vectors,

precludes

^a

quantitative analysis

of the diffraction data.

Nevertheless,

^{one can derive some ideas on the}

organization

^{of the}

phase

^{from a}

comparison

^{of the}

reciprocal image

^{of a helix with our}

pattern.

Let us

give

the form factor -% of a helix of

pitch P,

radius R on which atoms with a

scattering

^{factor F}

are

regularly spaced

^{with a}

period p

^{in the helix axis}

direction. The relation

between p

^{and P is 13 p =}

3, p = C [8]

where

Sz

^and

Sl

^{are the two}

components

^{of the scat-}

tering

^{vector S}

respectively parallel

^and

perpendicular

Fig.

^{1. 2013} X-ray diffraction patterns ^of

aligned samples

^{of 1 band}

Ic :

9

(i)

^and

(ii) compound 1c

^{at room} temperature ^on mica,

(iii)

without substrate. A : Bragg spots, ^{B : diffuse} lines, ^{C :}

broad/

diffuse

scattering

from melted chains, ^{M : mica} Bragg spots;

*

(iv) compound 1c

^{at 115 OC, without substrate;}

9

(v) compound led

^{at 70 °C on mica.}

The column axis

(stretching direction)

^is

parallel

^{to the arrows.}

354

Table II. ^-

Assignment of

^Powder

rings

^{in the}

mesophases.

to the helix axis. 1 m n are

integers

^which

obey

^the

relation 1 = 13 m + 3 n and

J.

is the Bessel function of order n. If we

keep

^{in mind the}

general properties

of Bessel

functions,

^{we must assume that a} measurable contribution to the

intensity

^comes

only

from the low orders n and low values of the variable

(corresponding

to the first extrema of each

Jn).

^{The sum is reduced}

to one Bessel function for each value of I. The

position

of the visible

Bragg spots

^{on the first}

layer

^{line I = 3}

(m

⁼

0, n = 1) corresponds

^{to a helix of mean radius}

9

A.

Such an helix made of

equidistant rigid

^molecules

will

give

^a measurable

intensity

ⁱⁿ

Bragg spots

^for

/ = 6, (m = 0, n = 2),

^{/ = 7}

(m = 1, n = - 2),

^{1 = 10}

(m = 1, n = - 1),

^{1 = 13}

(m = 1,

^{n =}

0).

The intense diffuse lines for 1 = 13 and I = 10 mask the

Bragg spots

^{but for 1 =}

7,

^{we observe one}

Bragg peak lying

the diffuse line. Its

position

^is consistent with the ^same helix of radius 9

A,

^{and its}

intensity

^{is weak.}

According

to this

simple model,

^{the two}

layers

^{1 = 6 and 1 = 7}

(Fig. 2c)

^should be identical. In

fact,

^the

intensity

^of

the

Bragg spots

^is

higher

^{on level 1 = 6 than on level}

1 ⁼ 7 and the

position

of the intense visible

peaks corresponds

^{to a}

larger

^{value for}

S 1.

^{in this level}

(I

⁼

6).

^{The same}

problem

rises for the

comparison

between the

layers

^{1 = 9 and 1 = 4 since}

Bragg spots

are not

unambiguously

identified for / = 4.

Nevertheless,

^the

repartition

^{of the}

intensity

^{on the}

two

layer

^{lines 1 =} 6 and / = 9 is consistent with a

helicoidal structure. As no other lines

correspond

^to

the same

period,

^{we must admit that} this helix is continuous

(Fig. 2b),

^{and that the}

apparent pitch corresponds

^{to 20.96}

A/n.

The absence of

higher

^level

layer

^{line is}

probably

^a consequence of the

imper-

fections of the

crystal (the Bragg

reflexions are

only

visible in a limited domain of

scattering

^vector

[9]).

If the

apparent period

is divided

by

^{n, the helix}

is formed with molecules or

part

of molecules with a

n-fold

symmetry

^{and the structure} factor is propor- tional to

nJ_(2 nRS 1.)

where m is an

integer.

^From

the

positions

^{of the maxima of}

intensity,

^{we deduce}

that there are two

components

^{to the 3D helicoidal}

structure a first one with a two-fold

symmetry

^{and a}

Fig.

^{2. - Schematic}

representation

of the diffracted

intensity

^{versus the}

scattering

^vector

S(I S I = 2 sin 0

^{for one column}

of infinite

length

^{with three different} structures :

a)

Uniaxial stack of discs of radius of

gyration

^{R. The} distance between two discs

is p.

The diffracted

intensity

^is

proportional

to

6 S.. - ’ j 2(2 1tS 1. R). Sz and S 1.

^{are the two} components ^{of the}

scattering

^vector

respectively parallel

^and

perpendicular

p

to the column axis, ^{m is an}

integer

^and

Jo

^{the zero order Bessel function.}

b)

Continuous helix of radius R and

pitch

^{P. The} diffracted

intensity

^is

proportional

^to

b Sz - 1 J’(2 7rS.L

^{R); n is an}

integer and Jn

the nth order Bessel function.

c)

Discontinuous helix of radius R and

pitch

^{P with}

points lying

^on

equidistant planes perpendicular

^{to the column axis}

at a distance _{p. The} relation between the

period

C, ^the

pitch

^P

and p

^{is C =} 13, p ⁼ 3 P. The

intensity

^is

proportional

^to

b S - c Y- J (2 1tS1. R)J

^{where l, m, n are}

integers

^which

verify

the relation / = 13 ^m + 3 n.

(In

^fact

figures

^4a

and 4b are described

by

these last two relations in which n

(respectively

m) ^is

equal

^to

zero.)

Notice that we have the first maximum of each Bessel function and

neglected

^the contribution of

highest

^{order n} > 4. We have plotted ^{1, m} (therefore ⁱⁿ figure 2a, n ⁼ //13) and the relative value of

intensity

maxima for each layer line of the top of figures 2b and 2c. The diffraction patterns of different kinds of assemblies of

parallel

^{columns derive} from these three basic

examples :

^{for a column made} of i identical continuous helices obtained

by

successive rotations of 2 7c/i around their common

axis, ^{the scattered}

intensity

^{vanishes unless n = 0 modulo i. If} the columns form a 2D array,

only

^{the zero}

layer

^{line is dis-} continuous, ^{but if we have a 3D} lattice, ^{all the}

layer

^{lines become} discontinuous.

d) ^Schematic

representation

^{of the} pattern ^of

figure

^{2a : we have a}

superposition

^of figure ^{2a to which we add a super-}

structure of

period

P,

figure

2c, ^{with a}

large

^{radius R ~ 9}

A,

^and

figures

2b in which there are

only

^two

layers corresponding

to n ⁼ 2, n ^{= 3 with R}

equal

^to 4.3 and 4.9 A

respectively.

^{The diffuse}

scattering

indication of the molten state of the chain is not shown on this schematic

drawing.

356

mean radius of 4.3

A

and a second one with a three- fold

symmetry

^{and a} radius 4.9

A.

The existence of a

continuous helix inside a 3D

crystal

^of

regularly

stacked molecules ^can be described as follows : In each column the same

equation

^{of a helix}

gives

the relation between the

in-plane

coordinate and the

z coordinate of atoms, but in ^a

given

^{column the}

values of ^z are discrete : z ⁼ wp ⁺ 6 where w is an

integer

^{and 6 is fixed for one}

given column,

^{but can} take all the values between 0 and _p. The last feature that we have to take into account is the existence of the diffusive discs. All these discs have the ^same

aspect

and

correspond

^{to a mean}

period

^{of 4.82}

A (Fig. 2a)

with a modulation of 20.96

A.

The modulation

only

has a

longitudinal component

and therefore the helicoidal order has

disappeared

^at this level. The

intensity dependence along

^these

planes

agrees with the calculated one for a conical core made of the carbon atoms of the

ring (CH2CP)3 using

the structural data of references

[6]

^and

[7] (Fig. 3).

The presence of

a continuous line means

that,

^{if the cones are}

regularly

stacked in

columns,

^no correlation in their

positions along

the column axis is established between

neigh- bouring

^{columns. Let us}

put

all these observations

together

^{in order to have an} idea of the molecular

organization :

^the conical molecules ^are stacked in columns with a

period

^{of 4.82}

A.

^The

aliphatic

^chains

of each molecule ^are in a disordered state, but the

paraffinic

^{medium is not}

unformely spread

^around

the core and is wounded in a helix

(Fig. 4).

Parallel helices are correlated

along

^{the z direction}

with fluctuations of weak

amplitude.

^These fluctuations

are

responsible

^{for the width of the}

large angle Bragg

reflections. Between the helix of

paraffmic

^chains

and the non-helicoidal central

part

^{of the}

column,

the benzoate groups form ^a continuous helix : the orientation and the axial

positions

^are related in a

column,

the orientation at a

given

^{level is the same for}

two

equivalent

columns but the location of that

part

of the molecule is not identical for each column.

Fig.

^{3. -} Form factor of a conical core

rotating

^{around its}

axis calculated from the

crystal

^{structure data}

[6, 7]

^{at the}

level of the first diffuse

plane :

^{full line :}

taking

^{into account}

only

the carbon atoms of the

ring (CH2l/»3;

^{dashed line :}

adding

^{to this}

ring

^an external shell

including

^{the six}

-O-C

linkages.

Fig.

^{4. - Schematic}

representation

^of the helical structure of the

lc low-temperature mesophase (section

perpendicular

to the column

axis) :

^a, tribenzo conical core + the six benzoate _groups; b, ^the

paraffmic

^crown

consisting

^{of the}

six

n-dodecyl

^chains.

This correlation loss on

going

from the outside of a

column towards its ^core may be induced either

by

the

flexibility

^{of the ester}

linkages

^or

by

^{the existence}

of an orientational disorder of the cones

pointing

up ^or down.

The centre of the column is

isotropic

^{around the}

column axis. All this

description

^is derived from a

qualitative analysis

^of the fibre

pattern

^{and this}

analysis

^{does not}

provide

any information about the

phase relationship

between the different

parts

^{of the} helix. We can notice that weak

spots

^{seen on the} level I = 1

(m = 1, n

^{= -}

4)

^{can be due to inter-}

mediate ^zones between the benzoate _group

(R

^{= 4-5}

A)

and 9

A. Unfortunately

the number of

parameters

that one should introduce in a

quantitative

^evaluation

is too

high

ⁱⁿ

comparison

^{with the}

precision

^of

experi-

mental data

(the imperfection

^{of the}

crystal

^{is res-}

ponsible

for the low resolution in wave vector and for the small number of visible

reflexions).

^One

important point

about the molecular conformation

concerns the orientation of the conical cores. The

proposed

space group P

2t 2i 2i implies

^{that the two}

columns of the unit cell are

polarized

ⁱⁿ

opposite

directions but in fact a space group P

212 21

^{is not}

excluded. In such a case the two

possible

orientations

are still

equally probable.

^Then the orientation of the cones in one column is

probably

maintained over a

large

correlation

length,

^{but the} orientation inside

a column is

independent

^{of the}

position

^{of the column}

in the unit cell. This second space group

implies

^a

large longitudinal displacement

^{of the cores relative}

to the external

part

of the columns and

probably

is the best choice for the

description

^{of this}

organiza-

tion in which a

high degree

of disorder coexists with

a rather well defined

periodicity.

^On

heating

^this

mesophase,

^{the 3D} lattice and the modulation with

a 20.96

A period disappears (Fig. 1, iv) :

^{a diffuse}

scattered

intensity replaces

^{the 2nd and 3rd}

layer

^lines.

The helical structure therefore remains

although

^the

chains are in a less ordered state and the correlation between columns is lost. The 2D columnar lattice is

hexagonal

^and exhibits the same structure as that of the

Dbo

^columnar

phase

^of

triphenylene

^ethers

[10].

3.2 MESOPHASES ^OF

la

^AND

lb.

^- Derivative 1 b forms two columnar

phases

^which

only

^differ

by

^their

2D lattices

(Table II) :

^{at low}

temperatures,

^{we observe}

an

oblique

lattice with two columns _per unit cell. A similar

mesophase

^{is seen for}

compound la.

^At

high temperatures compound 1 b

^{forms an}

hexagonal

columnar

phase

with four columns per unit cell.

The diffraction

patterns

^{of oriented}

samples

^{of the two}

mesophases

^{are similar. The} cores are

regularly

stacked at a distance of 4.82

A.

The maximum of

intensity

^{on the diffuse}

plane

^{which is} characteristic of the core

ordering

^{in a column is}

split

^{out of the}

symmetry

axis. In fact if we refer to the

crystal

^struc-

ture of

cyclotriveratrylene [6, 7]

^the

intensity depen-

dence fits with a conical core

including

^the

carboxylic

groups

(Fig. 3).

^{In this case, since we have}

only

^{a 2D}

crystalline ordering,

^{we do not know}

anything

^about

the dielectric

properties

^{of the}

mesophases.

^The

hexagonal

^lattice

(confirmed by optical

observations

[4])

^{with four columns} per unit cell

corresponds

^to

a rather

peculiar phase,

in which three columns are

equivalent

^{and on low}

symmetry sites,

while the fourth one is on a

higher symmetry position [11, 12].

If each column is

polar (i.e.

^{with an}

unique

^orien-

tation,

up ^or

down,

^{of the conical}

cores)

^{we should}

have a ferroelectric structure of

symmetry

^{3 m or} 6 mm.

4. Conclusion.

Some of the

mesophases

made of molecules

having

a conical core are similar to those of disc-like mole-

cules. Besides these

mesophases

^an

original

^structure

exists for the

low-temperature mesophase

^of

1c :

the external shell of each

column,

^{i.e. the}

paraffinic medium,

^{has an} helical structure. The columns are

arranged

^{in an}

imperfect

tridimensional lattice in the

same way ^{as a set} of identical infinite screws threaded

one in another with a certain looseness.

Moreover,

the chains are not in an all-trans

conformation,

^but rather ⁱⁿ a « molten state » ; ^{the cores are}

regularly

stacked in a

column,

^but uncorrelated from one

column to another. This lack of correlation _may ori-

ginate

^{from an} orientational disorder due to an

inversion of the cone direction within each column

(the

^{half-life of a}

given

conical conformer is about one

minute at 100 OC in

solution).

^This

mesophase

^{is not}

ferroelectric.

The other

mesophases

of the three studied

cyclotri-

catechylene

derivatives ^can be ferroelectric if no

orientational disorder of the cores

(up

^and

down)

takes

place,

^but

X-ray

^{data do not}

give

any infor- mation on this

problem,

^{besides a} confirmation of the conical

shape

^{of the cores.}

Acknowledgments.

We are indebted to Dr. M. Cesario for

bringing

^some

of her

unpublished

^{data to our}

knowledge.

NB : Dr. Lin Lei has

brought

^{to our} attention his

publication (in

^{chinese Wuli 11}

(1982) 171)

^{in which}

the

symmetry properties

of eventual

mesophases

^made

of ^« bowl-like » molecules have been

already

^dis-

cussed.

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