Study of the chain conformation of thermotropic nematic main chain polyesters

(1)

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Study of the chain conformation of thermotropic nematic main chain polyesters

M. Li, A. Brûlet, J. Cotton, P. Davidson, C. Strazielle, P. Keller

To cite this version:

M. Li, A. Brûlet, J. Cotton, P. Davidson, C. Strazielle, et al.. Study of the chain conformation of

thermotropic nematic main chain polyesters. Journal de Physique II, EDP Sciences, 1994, 4 (10),

pp.1843-1863. �10.1051/jp2:1994236�. �jpa-00248082�

(2)

J Ph>'.v II Fiaii£ _~ 4 (1994) 1843-1863 OCTOBER 1994, PAGE 1843

Cla,,iiication P/i;ii< _I A/>i>ia£11

61.31)E 61.12E

Study of the chain conformation of thermotropic nematic main chain polyesters

M. H. Li

('),

A. Brfilet

('),

J. P. Cotton

('),

P. Davidson

(2),

C. Strazielle (~) and P. Keller

(')

1') Labor~itoire Ldon Brillouii ICEA-CNRSI, CE-Sacl;ty. ~l l~l Gii-,ur-Yvette Cedex. France

l~) Litboratoire de Phy,ique de, Solide,. Bit. sll). Univer,itd Pan, Xl. ~1405 Or,ay Cede~, France

l~) ICS-CRM, 6 _rue Bou,,ingault, 671)~3 Stra,bourg, Fr;tnce

lRe(eiie(/ ?0 A/>11/ /994, _ie( _nil c£/ _ii Iwo' /aim /7,/im£> /994. _at (£>/)>e£/ 2?./mie /994)

Rd~umd. La coniotmation de polye,ter, ^find;tire, md,omorphe, e,t dtudide par iiiitu,ion de

neulron, _Jux petit, angle, (DNPA) din, le, pha,e, i,otrope et ndmaiique _,ur de, mdlange, de

polyiibre, hydrogdnd,

et deutdrid,. Le, condition,

eJipdrimentale,

ant did choi,ie, alin de pouvoir ndgliger le, elfet, de la tran,e,tdriiicaiitJn obtenu, h hJu(e (empdr;tture _Jvec cette iaiiille de polymBre, en,tauJi

liquide,.

Dan, la pha,e

I,otrope,

_en ddpit de la

prd,ence

de

long,

_{e_t}

rigide,

grt)upement, md,ogBiie,, ^le, ^chaine, de polymBte, ont une conform;ttion gau,,ienne, comme le

montre la variation du rayon de

giration

_en fonction de la _masse moldculaire. Ce rd;ultat _est

coniirmd par le, _me,ure, iaite, <fan, le doiiaine interinddiaire du vecieur de dittu,ion. D;tn, la pha,e ndmatique, le, donnde, de DNPA ,ont bien aju,tde, _par _un modble de cylindre ditn, lequel lit chaine de polymbre e,t coniinde. Dan, la pha,e _non orienide, le, _lie,ure, iaite, din, le doiiJine

inieriiddimre donnent le, v;tleur, Lie, rayon, de, cylindre, (compri, entre II) I

et l~ I _,elon _le degrd de polymdri,ation de, chaine,). Dan, la pha,e ndi1Jatique orientde, le, figure, de iiiil'u,ion

,out trb, ani,otrope, et corre,pondent h de long, et dtroit, cylindre, bien orientd,. La longueur de la chaine totalei1Jent dlirde e,t calculde h pariir de la longueur du monomBre 11Je,urde _par diffraction

de rayon, X. Par comparai,on avec la hauteur du cylindre ^me,urde en DNPA, _nou, dddui,on,

l'e,i;tence de, dpingle, h cheveu~ et leur nombre par chaine. La conformation d'une chaine courte e,t coiiplklement dtirde don, la direction du champ ndmatique, >[or, que de, ddiaut, du type dpingle, b cheveuJi apparai,,ent dan, le, chaine, plu, tongue,. Le nombre de _cc, ddtaut, ddcroit

ldgbreiient _en diiiinuant la tempdrature. Le, fluctuation, d'orientation de, cylindre, autour de la directiin du champ ndi1Jatique ,ont iaible, _comme le montrent le, valeur, dlevde, de, parai1Jbtre, d'ordre de, cylindre, lpi _~ 0.~ ). Le, rd;ultat, ,ont iii,cuid,, pour deux longueur, d'e,paceur, _en ionction de la _ma,,e moldculaire et de la tempdrature.

Ab~tract, The conioniiation of i1Jain chain me,umorphic polye,ter, i, ,iudied by ,mall angle

neutron ,cattering (SANS) _in the i,otropic ^mid in the neurotic pha,e,, by u,ing ^mixture, ^oi

deuterated and undeuterated polymer,. Particular attention _i, given ^to neglect the turn,e,teritication effect, occurring mainly at high temperature l'or1he,e LC polyiier,. In the i,otropic pha,e, de,pite

the _pre,once of long rigid me,ogenic _group,, the LC polye,ten chain, have _a Gau,,ian

conformation ,hewn by ihe variation oi the radiu, oi gyration ah a junction of the molecular weight. Thi, re,ult1, coniiri1Jed from the

,cattering

variation in the intermediate range of the

(3)

;cattering

vector. In the nematic pha~e, the SANS data _are well fitted _to _a model of cylinder, in which the main chain polymer I, confined. In the unoriented pha;e, the mea;urement; in the intermediate range

give

the values of the radii of

cylinders

_: they lie in between lo

h

_and ₁₉

h depending

_on the degree ^oi

polymerization

of chain;. In the oriented nematic

pha;e,

the

~cattering

pattem~ are highly ani;otropic they correspond to very long, thin and well-oriented cylinders. We have calculated the

fully

extended chain length, u,ing for the _monomer length that mea,ured iii .~itu

by X-ray diffraction. Then the compari,on ^of ^thi, length ^with ^the ^measured height ^of ^the cylinder;

give; the exi~tence of hairpin~ and their number per chain. For the short chain, the conformation _i, almo;t completely elongated ⁱⁿ ^the ^nematic direction, whereas

hairpin

defects appear in longer chain;. Their number decrea,e, slightly with decrea~ing temperature. ^The orientational fluctuation, of

cylinder; relatively

to the nematic director _are weak _as ~hown from the high values of their order

parameter (Pi ~0.91. The~e re;ult~ _are di,cu,,ed for _two ,pacer length; _a; _a function of the molecular weight and of the temperature.

1. Introduction.

The molecule~ of low-molecular

weight liquid crystals

can be modelled

by

rods (or ^other

anisotropic

form~), The appearance of the

mesophase

i~ the consequence of the existence of

anisotropic

intermolecular interactions a~sociated with the form and with the chemical nature

of the molecules. A main-chain

liquid cry;talline polymer

(LCP) is _a linear chain of

repetitive

units that may, but sometimes do not, po~sess intrinsic

mesogenic

character. Therefore, the nematic character of the main chain LCP should also

proceed

from the rod like conformation of the chain backbone, Such _an extended conformation is the consequence of the

connectivity

of the repeat ^units. ^The ^main

interesting question

concerns the conformation of the LCP

molecule, We discuss here the

thermotropic

semi-flexible main-chain LCPS which _are

constituted

alternatively by rigid

rod-like segments

(mesogens)

and flexible segments

(spacers).

There _are two models first

proposed by

de Gennes about the way a LCP in _a nematic field

partially

recovers the entropy ^lo;t

by

the

preferred

orientation of the chain, One

theory

propo;es that the chain undulate; about the nematic director, wherea, the other

theory

propo,es ^that «

hairpin

_» defect; exi;t, at which the chain _execute,

abruptly

contour rever;al;.

In the

hairpin-theory,

de Genne; II ha;

predicted

that the di,tance between con,ecutive

hairpin,

^increa,e;

exponentially

with

decrea,ing

temperature ⁱⁿ ^the ^nematic

pha,e.

Warner and co-worker~ have

recently developed

;tatic; and

dynamics

of

hairpin;

in _worm like chain~

[2-4]

and

given

the theoretical temperature

dependence

of the chain dimension

along

the director for LCP; with different chain

length; [3

]. The exi;tence of

hairpin;

can

play

an

important

role in the

rheology,

in the _non linear dielectric and

optical propertie;

of main chain LCPS,

Although

the theoretical di;cu;;ion, of the

hairpin;

had been made since 198?, the fir,t attempt; to confirm their exi,tence _were _not

reported

until 1988

[5

and the fir;t

experimental

ob;ervation of the

hairpin,

ha; been achieved

only recently ]6].

The _mo;t efficient way to check the

hairpin

conformation con;I;t; in

mea,uring

the chain dimen;ion; in the direction,

parallel (fl)

_and

perpendicular

(£) to the nematic director. The exi;tence and the

den~ity

of the

hairpin,

can be, in turn, deduced from the compari,on of these dimension; to the total contour

length

of the chain. SANS is _a main tool to determine the conformation of _a

;ingle

chain in it,

bulk ;tate from _a mixture of 50 % deuterium labelled (D) and _non labelled (H)

polymer;

]7].

The LC

polye;ters

^have often been u;ed for such ;tudies but the _occurrence of the tran;e;terification reaction in the HID mixture interfere;

badly

with the determination of the chain conformation

]8-10].

The

major

difficultie; lie in

finding

;oluble nematic

polymers

(in order to obtain the H and D chain mixture from _a ;olution) with _a nem~itic

pha,e

ⁱⁿ a

relatively low-temperature

_range

(T~

200 °C ). Rather

good

candidates

belong

to the

family

of

mesomorphic polyester;.

(4)

N° lo CHAIN CONFORMATION OF NEMATIC CHAIN POLYESTERS 1845

The

following polyesters (I)

first

synthesized

and

widely

studied

by

^Blum;tein ^and co-

workers

II 2]

_appear to be excellent

;ample~

^for ^this conformational

~tudy

IO

° ' / ~"~

' /

°2C~(CX2)n~CO

₍₁₎

~~

CH DP

where DP I; the

degree

of

polymerization,

X I; either H _or D, and _n I; the spacer

length.

The

fir~t SANS re;ults of d'Allest _et al.

]5]

have ;hown that the

polyester

^chains (n ₌ 7 and

n = 10 in formula

(I))

are very extended in the nematic

phase, Nevertheless, quantitative interpretation

of their data i~ difficult since the author; did not mention

anything

about the tran~e~terification reaction. Due to the chemical nature of the chain, thi; reaction may occur

during

the

preparation

of

homogeneous ~amples

in bulk

by annealing

in the

isotropic ph»e

and al;o

during

measurement~ at

high

temperature;. ^The tran;esterification reaction, induced

by heating,

I; _a random ;cis;ion of the

carboxyl

_group; -(C=Oj-O- of the

polye;ter

and _a

recombination of the ~ubchains thu;

produced

]13,14]. But the recombination doe; not

neces,drily

take

place

between the _;ame ~ubchain; which

together

constituted the initial molecule. This leads to a mixture of H chain;, D chain; and

partially

deuterated chain; H-D block

copolye;ter;I.

From the neutron inten;ities scattered

by

such

samples,

it I; very difficult to extract the value

of the radius of

gyration

of the chain [15]. Thi,

point

was al~o di;cu;;ed

by Arrighi

et al., who

have undertaken _a conformational

;tudy

^of other

polyester; ]9, 16].

In _our work _we have

adopted

the

polye;ter;

II and have first to

begin

a

;y,tematic ;tudy

II

0]

of the kinetic; of the transe,terification reaction for

polye;ters

^with ^different spacer; (1> = 8, 10 and II- The SANS re;ults _are

analyzed u;ing

the theoretical

approach developed by

Benoit _et al.

[17].

Thi,

study

allowed _u, to ;elect the

appropriate polyester,

and _to determine the

experimental

condition,

under which (he effect~ of the tran;e;terification reaction _can be

neglected during

the

measurement; of the

polye;ter

^chain conformation. In other word;, the con;ervation of the

mean molecular

weight

of the

polymer

chain

(I,e,

of the ab,olute

inten;ity

;cattered at zero q value)

during

the

,ample preparation

and the SANS

experiment;

I; the

proof

of

negligible

tran;e;terification effects. Under these condition;, the exi;tence of

hairpin,

_wa;

recently

de;cribed in _a brief paper

]6].

We report ^here a more

systematic ;tudy

of the chain

conformation of two LC

polye;ters

(n ₌ 10 and _n

= II ). In the

following,

_we describe the

;ynthe,i;

and the characterization of the

LCP,amples

^(Sect. 2) and the _neutron

experiment

(Sect. 3). The determination of the nematic order of the LCP;

by

wide

angle X-ray ;cattering

(WAXS) I; di;cu,,ed in

paragraph

2.3. The chain conformation in the nematic

pha,e

as well _a;

in the

isotropic phase

I;

reported

in section 4. The effect; _on the number of

hairpins

a, a

function of the molecular

weight,

of the ;pacer

length

and of the temperature are discus;ed in

;ection 5.

2.

Synthesis

and characterization of the LC

polvesters

(Il.

2,I SYNTHESIS OF POLYMERS. The

polye;ter;

(I) _were

prepared

^from a

diphenol

and a

hydrogenated

_or deuterated

aliphatic

diacid dichloride ]. The

diphenol

4,

4'-dihydroxy-2, 2'-dimethyl-azoxybenzene

was

synthesized

from

3-methylphenol [18].

The diacid dichlorides

were

prepared

from the

corresponding

^acids and

oxalyle

chloride, The

hydrogenated

^diacids

were obtained from commercial _;ource,. The deuterated diacid, _were obtained

by catalytic

HID

exchanges

on

hydrogenated

diacids

using

Pt/C in

NaOH/D~O

at 180-200 °C under

high

J()UR~AL DE PHi~IQ[lL II -T 4 ~ lo t)( >t)BhR lot>4 7jj

(5)

pre;sure for about 10

day; II 9].

Thi;

procedure

^leads to 91-94 ~A deuteration ot the diacid,, The

degree

^of the deuteration _~~ _wa; mea;ured

by 'H-NMR

_and _taken into account in the

determination of the contrast factor in the SANS

experiments.

The

polye,ter;

were

;ynthe,ized

by

interfacial

polyconden;ation

from

diphenol

and diacid dichloride,. Each

polyester

^thu,

obtained _wa;

purified by di,,olving

in chloroform,

filtering

and

precipitating drop-by-drop

into

ethanol ten time, the volume of the chloroform. The

polye,ter,,

^after

being

dried under

vacuum, were fractionated

by

_u,ing

dichloroethane/methanol

_a, the

,olvent/precipitant.

For the sake

of,implicity,

the

polyester

I, named for in;tance PE10-H when the ,pacer i;

lCHj)ii

and PE10-D for

(CD~)j,j.

Each

polye;ter

fraction I; characterized

by

it, number

average

degree

of

polymerization

(DP)

following

^thi; name for

example

PE10-HDP?8.

2? CHARACTERIzATION OF THE POLYMERS BY SEC-LS _AND DSC. The molecular

weight;

of the fractionated

polye;ter ;ample;

were )mea;ured

by

;ize exclu,ion

chromatography

_on

line

light ,cattering

(SEC-LS) at ICS-CRM

(Stra;bourgj

from

polye,ter

^;olution; ⁱⁿ

tetrahydrofuran.

The refraction index of the ,olvent I, _i>,j =1.4n4

(wavelength

of

light

A~j =

63? nm) at room temperature. ^The increment; dn/d<. of refraction index of the ,olution

were determined

by

a differential refractometer (Brice-Phoenix) and the re;ult, _are

given

in table1.

Table I. lficien>ent dn/d<. (>J't/>e

ieJi.a<.lion

inde~v (>j

pal,ve.vtei,v (I),vo/union,v

in

tetiahi'ch.(>Ju-

i-an at loom tempeiatuie (A,~ ₌ ⁶³² nm ).

Pot ester PEB-D PE10-H PE10-D PE I I -H PET I -D

dn/dc (nfl/ 0.175 0.166 0.161 0.154 0.152

Table II. -Chaiacteii=anion ie.vu/t,i

(>f'the po/yeste>.,van>ple.i by

^SEC-LS ^ai>d ^DSC.

M~,

fiumbei ai>eiage mole<.iila>.

w'eight, M~. w'eight

ai>era,qe mole<.ulai

w'ei,qht. (a) T~~

iepie~iefit.i the tiafi,iition _range

fi.on>

the

<.iy.italline p/>a,ie

to the men>ati<.

phase,- T~~

it-i contiaiy.

T~j

rep>.e,rents ^the t>.ansitiofi _iafige f>.on> ^the nemati<.

p/>a,ie

to the

I,lot>.opi<.

phase

_; _T~~ its cant>-a>.y. (b)

Tj~

is t/>e tempe>.ature at the ma.vimum

oJ

the DSC _curl>e at the t>.ansition

isot>.epic

nematic

for

the HID

polyester

mi,inures. (c) Values

for

the mi.vtuie

of

H and D

po/yesteis.

Tale

Mn Mw/Mn DP

10P21 184

D 11500 9500 21 130~122

10P48 157

D 22600 48 l13~126 156~167

D 16100 136oo 19 ~~ '13~125 156~j65

156

~

~ ~,~ ~~~

148~157 148 104~ 93

D 5920 5080 jj

137 95~ 80

10P40 129~133 128 88~ 81

D

10P30 127

D 31 90~102

10P20 127~121 124 80~ 60

D 20

(6)

N° In CHAIN CONFORMATION OF NEMATIC CHAIN POLYESTERS 1847

The number and

weight

_average molecular

weights (M,,

and

M~

of the

polye;ters

obtained

by

the SEC-LS

technique

are listed in table II. The values of DP are deduced from these

measurements and the molecular

weights

_m of the _monomer units

(mp~g~

₌

425,

_mp~jt~~

= 453

and mp~j _j~ =

467).

Let _us notice the _narrow molecular

weight

distribution obtained for each

polye;ter

fraction.

The

phase

tran;ition temperatures ^of ^the ^LC

polyesters

were determined

by

DSC (differential

scanning calorimetry).

The re;ult, _are summarized in table II.

2.3 CHARACTERIzATION _OF _THE _NEMATIC _ORDER _BY WAXS. The

polymers

in the nematic

phase

_were ;tudied

by

WAXS at Laboratoire de

Physique

de; Solide;

(Or;ay)

in order to characterize the orientational and the

positional

order, of the repeat ^units. ^The

;ample

in _a

capillary glas;

tube _was

aligned

ii> ,iitii in the oven of the

X-ray

;et up

by

a

magnetic

field of 1.7 T and then measured (A

=

1.541

11at

_different temperature;. ^A

typical X-ray

diffraction pattern i;

given

in

figure

1.

~4"'

~

,

(7)

Table III. -WAXS Results. Monome>.

length d, positional

co>.relation

length i~ i~f

^the

monomer

belonging

to t/>e _same <.hair

OJ'LCP samples.

Pol ester d

Ii)

I

(I)

PE10 24. 5 t 0.5 120 t 20

PET1 23.5 t 0.5 90 t 20

In addition _to the u;ual wide

angle

diffuse

rings

(a), it ;hows four order, of diifu;e line;

16) perpendicular

to the nematic director and diffu;e ;pot; (c) located _at about 10° from the

director.

The diffuse line,

(b)

_are the inter;ection with the Ewald

~phere

of _a serie; of

equidi,tant

diffuse

planes perpendicular

to the director. These

planes classically

represent the Fourier

transform of modulated _rows

parallel

to the director, these _row,

being

uncorrelated

perpendicular

to the director. Such _rows

obviously originate

from the

polymeric

nature of the

compound

since the

mesogenic

_cores _are

chemically

^linked

together

in chains. These diffuse line; _can therefore be

interpreted

_as due to

longitudinal

interference; between repeat ^units

belonging

to the _;ame

polymer

chain

]20, 21].

The related di,tance cl

(independent

of

temperature, deuteration and DP within

experimental accuracyl corre;pond;

to the

length

of the repeat ^unit (see Tab. III). For in;tance, d

=

?4.5 _± 0.5

1

_for _PE10 _and _,hould _be

compared

with the e;timated

length (Dreiding

stereomodels) ?5?

I

_of _the

_totally

_extended

monomer.

This

compari;on

;how~ that the spacer

-(CH~)j,~

is very much

elongated.

It ;hould be noted that the

length

cl ?3.5

1

_obtained _for _PE

is smaller than that obtained for PE10 (24,5

hi,

This is due to _a cla;;ical odd-even effect of the spacer

length.

With the cl values and the number; of _monomer;, _we _can calculate the

length

of

totally

stretched

polymers

(I.e. without

hairpins).

We will _use these

lengths

in section 4 _to demon;trate the exi;tence of

hairpins.

The width of the diffuse lines

corre;ponds

to the

po~itional

correlation

length i~

of the monomers in

the ;ame chain

along

the director. Since all the diffu;e lines have the _;ame width,

i~

can

;imply

be evaluated

by applying

Scherrer _~ formula

]?2]

~~

~(2

o _cos o,~ J(2 o

where ? o is the

scattering angle

and

~(2

o the full width _at half maximum

(FWHM),

corrected of resolution effects, of the diffuse lines

along

the director and 2 _o~j the

angle

of the

maximum

inten;ity.

We have obtained

i~

₌ 120 ±

201

_for _PE10. _This

length

means that

about five consecutive repeat ^unit; ^of ^the same chain are

strongly positionally

correlated

along

the director, The value

i~

^obtained ^for ^PE ^is ^somewhat ^smaller

i~

=

90 _± ?0

I.

_This _I; _also

probably

due to the above mentioned odd-even effect. For both

compound;, i~

decrea~es

slightly

with

increasing

temperature (~10fl in the nematic

range)

but seems

quite

independent

of deuteration and of the

degree

of

polymerization

in the studied ranges.

The diffuse spots lc) arise from SmC fluctuation~

already reported

in the _case of PE10

[1?

but _are also present ⁱⁿ ^the case of PET I. The correlation

lengths

^of these fluctuations _are rather small _: about 40

I along

the director and 20

I perpendicular

to it.

The wide

angle

diffu;e

ring la)

at q 2 r/4.5

l~

'

(q

=

4 r sin o/A is the modulus of the

scattering

vector where 2 0 is the

scattering angle)

is

classically

due to lateral interferences between _monomers. The

intensity

distribution

along

^the

ring

^indicates that the _monomers _are oriented

parallel

to the

magnetic

field, and it allows _us to derive the nematic order parameter S

according

to

published

methods

[23,

?4].

Figure

2 shows the order parameter i<ei,ins reduced

(8)

09

S

,

^a

~

°~

~

. ~

i

07

o.6

~~

T

(9)

<z jj j~ji ~,i'=~

'if>~ ?~t>

Ii T d~f

hit ,";i_

I'#lr

W> 3

<,' l~

,12#

~

.>iy

~ ' lj~~

''

' ~

g

~," §

~'- 4~~'

,'~~~~.

q~~

~ ("ll'

~~l~ ~W%

~~

"~.

.#," ~£

~~~ ~~ ~~

'~

.~

0~4~

($ l"I'

j/~, ^'

~~

~l L',' /

Fig. 3. Typical

,cattering

pattern ^ob,erved on the XY multidetector for the PE10-DP28 at II 6 °C,

> II)

I.

_D ₃

m. H indicate; the direction of the magnetic field. Let _u, notice the ,trong ani,otropy oi the ;cattering pattern.

The SANS mea;urement, ;tart in the

i,otropic pha,e,

and _are carried out

during

le,, than

one hour in order _to have

negligible

efiect, oi the tran;e,terification reaction. Then for the

mea,urement, in the nematic

pha,e,

the

,ample

I, fir,t oriented ii> vitii with _a

magnetic

field of

1,4 T. Several hour, of

annealing

_near the

I,otropic-nematic

tran,ition _were nece,,ary to

align

the

,ample,

It _wa, not

po,,ible

to

,tudy

the

polye,ter

PEB in the oriented nematic

pha;e

becau;e of it,

higher

tran;ition temperature ^and ^of ^the

large

effect, of tran,e,terification

during

the

alignment step.

^Similar

problems

_were encountered with the

sample

PE10-DP48, the

viscosity

of which is _too

high

to be

aligned

within _a reasonable time.

For the scattering

experiment,

two

wavelength,

of the neutron beam lo A and 5

A)

_are u,ed. The di,tance between the

,ample

and the multidetector (128 _x 1?8 cell, of 5 _x 5 _mm _~) i, 3.~l _m. The in;trumental re,olution _can be e,timated from the ~A IA value of lo % and from the incident collimation defined

by

two hole, of diameters 16 and 7.6 _mm di;tant of ?.1~ _m. The

corre,ponding ;cattering

vector range, are 7.9 _x 10~

~ q ~ 6.7 _x lo

l~

_and

1.6 _x l~l~ ^~

~ cj ~ l.6 _x lo ^'

l~ '.

_The

,c~ittering

_pattern

by

the oriented

;ample

I;

extremely ani,otropic

(,ee

Fig.

3), Thu,, the inten,itie, recorded in the detector cell; of the _,ame q modulu; _are

regrouped by rectangular

,ector, of _x 1?8 cell, in the

parallel

direction _to the

magnetic

iield and 8 _x 1?8 cell; in the

perpendicular

_one. Thi,

give;

u, the

primary ,cattering

inten,itie, Iii (q) ^and

l~

_ICI

re;pectively.

The data treatment are carried _out

u,ing

the cla,,ical

procedure,

The incoherent

background

i~ determined irom the

weighted

_,um oi the incoherent inten,itie; delivered

by

a

sample

of H

polymer

and _one of D

polymer.

^Ab,olute calibration I; obtained from the direct determination of the number of neutron, in the incident beam

26(.

Thu,, the coherent

,cattering

cro;s ;ection

S(q

I,

expres,ed

in _cm ^'

in order to determine the molecular

weight

^from the ab;olute

inten,ity,

we need the _contra;t

(10)

constant

Ki

between the _monomers of the H and D

polye;ters.

It is calculated

following

the

relation

Kj

₌ i(I

i)N~[(a~ -a~) ~~]~

II)

where _i I, the volume fraction of the D

polymer

in the mixture (here _i ~~l.5) and

NT

the total number of _monomer; per unit volume deduced irom the

;ample den,ity

(p ₌ ^1.08 ± 0.05

g/cm

). a~ and a,, are the coherent

scattering length;

of the _monomer; and

~i~ I; the

degree

^of deuteration of the spacer in the D _monomer. We have

Kj

=

0.107 _cm for

PEB

;ample;, Kj

=

0.149 cm~ ^' t'or PE10 and

Kj

₌ ^0,187 cm~ ^' for PEI I.

The

inten;ity

;cattered

by

,uch

,ample;

I,

;imply expre;;ed

_a;

S(q

₌

M~/n>K~

P

(q

j?

where P

(q)

I; the form factor of _one chain.

In the Guinier range

[27a(,

the radius of

gyration

_R~ I; determined from the Zimm

repre;entation (27b(

~~

qi 1 +~

cj~Rj'

(31

S(C/) M~

3

^~

A; _a matter of iact,

-((cl

from _a mixture of _i D

polymer,

^and i H

polymers

with different

molecular

weight; (M,,jj, M~j~)

can be written

following

the random

pha,e approximation (?8 neglecting

the interaction between H and D _monomer,.

Kj

i. (I

i).ilql~ i.M~j~.Pj~(q)~

_(l

i).M~~j,P~j(ql'

^~~~

Since the fraction, of H and D

polye,ter,

ha~e quite ^,iniilJr iiioleculJr

weight,.

equation (4) reduces to

equation (3)

in the Guinier range.

4. Results.

4. CHAIN CONFORMATION IN THE ISOTROPIC PHASE. For flexible

~tmorphou, polymer,

(like the

polystyrene)

in bulk, the radiu, of

gyration

of the chain _wa, found _to be

proportional

to the ,quare ^root of _it; molecular

weight

M ^"~ Thi,

proved

the Gau;Sian character oi the chain

in the melt

(7].

We wonder whether the main chain LC

polye,ter,

al;o have a Gau,,ian

coniormation,

although

there I;

large

iraction oi

rigid

_me,ogen, in the backbone. Blum,tein _et al. ?9] have indicated the inherent

flexibility

and the random coil conforniation of the chain in the

I,otropic pha;e

on the ba~i, of

experiment,

with the induced

magnetic birefringence.

We will

give

here _a _more

quantitative proof

oi thi, from the determination of the chain

conformation

by

SANS.

The Gau,,ian character appear, for the

following

twu rea;on;. In the

large

_q _range

(1.6 _x 10~ ^~

~ cl ~ l.6 _x 10. ^'

l~

' j, the

repre,entation

_{of cj~}S iv _t.ei.iii.~ _q tend; to a

plateau

(see

Fig.

4), which reflect; the random conformation of _a chain until the monomer,ize

(cj~

101j.

_Be,ide;, _thi, _re;ult _I; _confirmed

_by

_the _variation _of _the _radiu; _of

_gyration

a, a

function of the molecular

weight.

The radii of

gyration

are mea;ured in the Guinier range

(7.9 _x 10~

~ cl ~ 6.7 _x 10. ^~

l~

_(;ee

_Fig.

₅₎

_u,ing _equation

_(~). _The _result; _for _different

;amples

are summarized in table IV. In

figure

6, the variation of Ln R~ a; a function of Ln

M~

is linear with _a

slope

^of 0.5

JJ ( $

' <Jl ~~ Jl Jl~' ~~" ~ i'/16

'l~ L''I t~-~-' ~.~-' J ~"

~

(11)

~ 0.004

~ S(~)

(l

^~

cm ~)

°'°°3

oo

p%~o~

a~Bh4%~'tRo°ql

^°O

0.002

~~

fl

g

0.001

0

0 0.035 0.07 0,105 0.14 0,175

q ('"

~)

Fig. 4, Repre,entation _{of q-} S(qj iwi vuv the ~cattering vector cl for the inten~ity S(q by PE10-DP28 after _one hour of

annealing

at T 160 °C.

2

6

1,2

~oo°

^°

o°o

~

-

oo°

cr

7 0.8

t/l

0.4

o

0 0.001 0.002 0.003 0.004 0.005

q~ (A'~)

Fig.

5. Zimm repre~entation (S~ ^'(q i<ei.;ii.v cl-) ^of the scattering _inten~ity by PET1-DP30 at 130 °C in the isotropic pha,e. The

experimental

data (cl _are adju~ted by _a linear function which give; the radius of

gyration R~ ^and ^the weight average molecular weight M~ ^of chains u~ing equation (3).

The exponent ^0.5 ^of

M~

confirm; the random coil conformation of the LC

polyester

chain;.

The;e re;ults indicate _a great

flexibility

of the chain, down to the scale of

101due

_to

a very

large flexibility

^of the ;pacer; in the

I,otropic pha;e.

(12)

Table IV. Radiu.i

of g_;ration

R~, and n>olecular

w>eight M~ of po/_»estei~i

in the

isofi.epic pha,ie

determined

by

SANS _at

the~tempeiatw.e

T.

T

PEB DP21 184 51 t 4 9650

160 88t3

3 16700

155 47± 8120

147 42 t 3

PET1 DP40 4 27600

PEll 130 74±4

DP20 130 64 ± 4 14500

5.o In

Rg

i-o

. PEB

o pE lo

n PE 11

~'~

8 9 lo II

In Mw

Fig. 6. Log Log repreqentation oi R~ iei.iii.I M~ for the different polye;ter; ;tudied. The ,lope 0.5 confirms the Gaussian confori1Jation of polyester chain; _in the >;otropic pha;e.

4.2 CHAIN CONFORMATION IN THE NEMATIC PHASE. In the nematic

pha,e

^the

polye;ter

conformation I; very

ani;otropic (5],

_a; confirmed from WAXS mea;urement; and ;hown in

figure

3. A

cylinder

is _a

simple

model for the chain. Its form factor which needs

only

two

parameter; ^the

height

?H and the radiu, R. The main

difficulty

lie; in

mea;uring

2 H. On the contrary R, much ;maller, _can be obtained

quite easily

in _a _cl range well ;uited to

the neutron

scattering.

The be,t way ^to determine R, without any influence of the ;ize

? H, is to _mea;ure the

;cattering

at

large

_q ICI. ^NW ⁱⁿ ^the ^unoriented ^nematic

pha;e.

? H _can be mea;ured under the,e condition;

only

if the chain conformation I; _not affected

by

tfie continuou; deviation of the nematic director due to

topological

defect~ (di~inclination line, characteri~tics oi thi~ unoriented

pha;e.

Thus _we

prefer

to determine it in the oriented

phase.

(13)

4.2.I Re.vii/t,v iii flit> ii>oiiente</ ncfiiati<.

pha,ie.

The

scattering intensity S(ql by

the LCP

sample

ⁱⁿ ^the ^unoriented

pha;e

i~

i;otropic.

For _a

randomly

oriented

cylinder

in the

intermediate _q range,

S(q)

can be

expressed

as follows

[2]

~ ~i

'q2R2) (2H)~~<C'<~

_~~~

sjq)= r-j- (@j'j

_~~~

4

A u~eful

repre~entation

for

S(</I

I; Ln

(c/Slc/I)

i>ei,v>i.v cj~. ^A

typical example

is shown in

figure

7. The fir;t part ^of ^the

experimental

data is fitted with _a

straight

line. The

comparison

with _a

cylinder

model _seems rather

good

and the deduced value; of the radiu; R and of Ml? H _are

R

=

12 _±

1,1

_M/2 _H

=

28 _± dalton

1

Thi,

procedure

I;

applied

to ;everal

polyester sample;

with different ;pacers, different molecular

weight;

and for different temperature;. The re;ult, _are li;ted in table V and ~hown in

figure;

8 and 9. The temperature

dependence

of R and of M/2 H indicate~ that the

anisotropy

of the

cylinder

dimen,ion, increa;es with

decrea,ing

temperature. ^{It I;} ^of ^interest to compare the

values obtained _to those of _a

totally

;tretched _monomer _R~,, and

(M/2

H )j,,. The latter is deduced

from the molecular

weight

of _a _monomer and from the _monomer

length

measured

by

WAXS.

The radiu; of the extended _monomer _R~,, I; e,timated from _a

Dreiding

,tereomodel. For all the

polye,ter;

;tudied, the value; of R _are between _two and four _times tho;e of _R~,, the value, of Ml? H are al,o

larger

than tho,e of (Ml?

H)~,,.

It I, the fir,t

proof

that the chain I, not

completely,

extended.

Let _u, _now di,cu,, the,e re,ult, in the frame of the _two model,

propo;ed by

de Genne, ].

In the fir,t _one, the chain undulate; around the nematic direction (,ee

Fig.

10a) in thi; _ca,e, the apparent radiu, and the linear

den,ity,

determined _at

large

_cl, ,hould have the value,

given

3

Ln(qs(qi)

3.5

4

c~ ^o coo _o

oo o

4.5 ^°

~ cc °

o

5

0 0.005 0.01 0.015 0.02 0.025

q~ ('

_~)

Fig.

7. Representation oi Ln (</S(</ )) _ici.vii.; _(/ of the scattering

inten,ity

by PEB-DP? I, after two hour, of annealing at 160 °C _in the nematic pha~e. The ;traight line corre,pond~ _to the fit _to

an

I,otropic

cylinder model.

(14)

Table V. The

fitted

^radii ^R ^arid ^lineal- den~vitie,v M/2 H

of'the

<.ylii>de>..v and t/>o.<e

of'the

<.omplete/>'

e.itended moron>e>.,i

(R~,

^arc/

(M/2H)~,,).

_T~~,j I-i the iedu<.ed ten>peiafiii.e

T/Tj~.

P°'Yester Tred(T/TIN) R

ii)

_M/2H (M/2H)m Rm

18.8

18.9 5.5

44.3 t 18.9

DP30 t 20.3

30

Nematic

phase

20

°~

~ 0

+ PE 8 Dp21 o pE11 Dp 30

. PE lo

Dp

28 n PE lo Dp 48

0

o 85 0 90 0 95 100

red

Fig. ^8. ^variation ^of ^the ^radius ^of ^the cylinder R with the reduced temperature T~~,j T/Tj~ (K/K) for

different polye~ter, (+) PEB-DP21, lo) PET1-DP~O, (+ PE10-DP28. (Cl PElu-DP48.

60

phase

fl (

₍₀

q

_~

~ ^o ^+o

~~4 ~

o

I

+ PE 8 Dp ²¹

. PE lo Dp 28

n PE lo

Dp

48

o pE11 Dp 30

o

o.85 o go o 95 oo

red

Fig. 9. variation of the linear den,ity M/2H of the cylinder with the reduced temperature

T,~~j iK/K) for different

polyeqter ,ample~

(~ee

caption

of

Fig.

~).

(15)

C

iii 11

la 16)

Fig. 10. Schematic representation of _two possible chain conformations _in the nematic phase (al _an undulating chain, (b) _a chain with hairpinq. The circle C represents ^the ^scale q~ ^' ^of observation.

for

elongated

chain. The second model

corre,pond,

to _a chain with

hairpin;

the

cylinder

_i,

compo;ed

of,everal wire; of the _,ame chain (,ee

Fig.

lob).

By increa,ing

the

degree

of

polymeri?ation

of PE10 from 28 _to 48 (~71) _{% ),} the radiu, R increa,es from I1.5

1

_to _18.7

1

(~ 63 % ). The value of R and it, variation with the molecular

weight

_i, not con,I,tent with the

fir;t model. On the

oppo;ite,

increase of both R and M/2 H with DP _can be

explained by

an

increa,e of the number of

hairpin;.

A definitive confirmation of the

hairpin

exi;tence will be obtained from the determination of the

longitudinal

and tran,verse dimen;ion, of the whole chain,

given

in the next ;ection.

4.2.2 Re.;ult.; _>n t/>e oiie»ted nemat><.

pha.~e.

The SANS

experiment;

are

performed

in the

range of ,mall _q values

(7.9

_x 10~

~ cl ~ 6.7 _x 10. ^~'

l~

').

According

to the Zimm

approximation (Eq.

(~jj, _we _can obtain the average di,tance of inertia _Rjj and

R~ ]22]

in the direction,

parallel

^and

perpendicular

to the _nematic direction

re,pectively.

The

R~

^value; are

ea,y to mea;ure

u;ing

the fit _to

equation

(6)

Sj'(</)

=

Sj'(0).

_II

+</~R) _</.R~

~ (61

The value, of

R~

and

M~

obtained for different

;ample;

are

given

ⁱⁿ table VI. We _are

confident in them for the

following

reason;

iii the molecular

weights

determined from

Sj

^' (0₎ _are almo,t the _wme _as in the

I;otropic pha;e

(see Tab. IV and _a, tho;e determined

by

^SEC ^LS (;ee Tab. II). Thi, re;ult confirms that the transesterification effects _are

quite negligible.

(ii

the

R~

value, _are well matched _to the Guinier range condition _q.

R~

_~ _so

they

_are

mea,ured

accurately.

On the contrary, from the data treatment of Sjj ICII with the Zimm

approximation

Sj'(</i

=

Sjj'(0).

_II

+c/~R/j

_j7)

(16)

Table VI. Parameters

of'the

chain

conformation

and results

of

the

fits

to a

c.ylinde>.

model

for po/yesteis

PE10 and PEI in the o>.iented nematic

phase.

T(°C) Tred Parameters ofthe model Number of Experimental data in the

wiresof Guinier range

DP28 686 135 0,951 _280i10 1212 0 970 2.45 14 iii 0 5 13100

8t2 0.983 2.14 II

PE10 DP15 368 130 0.957 23015 612 0.972 1.60 9 710.5 7300

11 0.912 25015 St1 0.982 47 7.610 5 7000

bj 172-270 124 0.968 ₁₇₅₁₅ ₅₁₂ _{0 968} bl 0 98-1 54 8 610 5 5900

114 18515 512 0 975 0.93-1 46 7 610 5 5900

DP40 987 119 0.978 270110 1612 0.848 366 27 Sit 22800

a) 114 0.965 285110 1512 0.896 3 46 24 St1 22000

95 0.918 305i10 1212 0.927 3 24 21 911 21000

DP30 705 l14 0.968 255i10 1012 0.908 2.76 19 611 14200

95 0.920 280i10 912 0.939 2.52 17.211 13700

DP20 493 114 0 975 ₂₀₅₁₁₀ ₁₀₁₂ 0.919 2 40 16 St1 1500

712

aj Two scattering experiments have been made at T =114 °C. The first _one after decreaqing the temperature ^from ^the i~otropic ~tate the ~econd _one _waq done after

a qet of experiments with increasing the temperature ^from ⁹⁵ ^°C. The result~ _are the _same for _instance R~ found _in the first experiment i~

?4.8 ₌ 1 whereas it is 24,2 ₌ h _in _the _second

one,

b) The value~ _are calculated with the two molecular weights of H and D polyesters.

arises the

following problem

the value of

Sj

(0), which should be

equal

to Sj ^'

(0),

is found

to bc much lower (even

negative).

It is _a _nonsen;e for the molecular

weight.

Thus, the

condition

(£/.Rjj

_~ I, not fulfilled and it is not

possible

to determine Rjj in this

cl range. This indicate; _a very

elongated

chain conformation.

Unfortunately,

^the

corresponding

low

scattering intensity

doe; _not allow _us _to work in _a ,maller _cl range. Moreover the

scattering intensity

in thi; direction ha; the c/~^~

dependence

at

higher

_cl value;, characteristic of _a

rigid

rod

parallel

to the _cl direction.

The be;t way to obtain the

parallel

dimension of the chain _i, to try to

adju~t

all the data with _a model of

cylinder

in the

parallel

and

perpendicular

direction;

simultaneously.

In the model, the axis of the

cylinder

ha; _an orientational di~tribution around the nematic direction. The form

factor is

[27]

~ ~

FIR, ? H, p, _cl

=

~~~

_~°" ~ ~~

~~'

^~ (8)

<IN co; p c/R sin p

where -Ii (v) I; the Be;;el function of the fir~t order and p the

angle

between the

scattering

vector and the axi~ of the

cylinder.

The di;tribution cho;en for

p

I; the

Maier-Saupe

di,tribution

(30(

(without real _reasons but for

;implicity)

~ ~~ ~ ~ ~ ^~" ~ ~ ~ _«

j,[~

^e ^~~ ^P ^;in ^p

^dp

^~~~

We define

P~

the order parameter ^of ^the

cylinder

P, 4 _w

~~~

~~

~°'~

_~

P la, p I. ,in p dp II 0)

<1

2

(17)

Finally

the

scattering

data are fitted with the

following

^functions

[3

Ii

w/i

Sjj

(q

₌ S (o P (a,

p

). F (R, 2 H, p, _q

dp

II

u

w/i

S~

(q ₌ ^S(0 P (a, p ). F (R, 2 H, w/2 p, _cl ),

dp

(12)

<1

where Sill

=

S~

(11) is not a fit parameter ^but ^the ^value ^determined ^above. ^The

adju;t~ible

parameter; are ? H, R and _a _;

they

intervene, _a p>.io>.I, ⁱⁿ ^both ^directions ^becau,e ^of ^the orientational fluctuation;. A; a matter of fact, the fit of the data Sjj ICI) are

e,,entially

determined

by

? H. Thi, _mean; that the chain, _are very

elongated

and that the fluctuation, of orientation are weak

enough

to

neglect

the influence of R in thi, direction. On the contrary, ^all the three parameter, ^R. ^{2 H} ^>nil a are

important

in the iit

oi,i~

_{(</ I.} In the

following,

the value oi ? H _i,

only

<ietermined from the iit oi

equation to,ijj

(</I. Then

u;ing

thi, value in the fit

of

St

_ICI), we determine the other two parameter, a and R.

Figure

,how; the fits in both directions for PE I11-DP?8 at 16 °C. The fit, _are

quite good

and

give

? H 32~l _±

101

_R

= 8 _±

?1

a = 87,

5

1

E

^~

~~

t3~ ~ tJl

o

'~

0 2

~

( 6 8

q A?] io'~

Fig, I. Ab;olute ;cattering inten,ity ^SI(/) measured in the direction parallel (.) and perpendicular (cl

to the magnetic field _a; _a junction of the qcattering vector </ for PE10-DP28 _at 116 °C in the oriented nematic pha,e. The full line, _are the calculated _curves for

a cylinder ³²⁰

1

_long with

a radiu, of 8

h

_(~ee

text in the paragraph 4?.2). The,e re,ult, _are interpreted _» the exi;tence of _two hairpin; in the chain confomiation.

-

H

Fig. 12. Schematic repre,entation of _a main chain with 2.5 hairpin~ _on _average. The cylinder _i~ the

model u,ed to fit the eJiperimental data. The ratio length over radiu, I; the real _one obtained for PE10- DP?8 at 135 °C.

(18)

If _we calculate the total

length

L of this ;tretched

polymer

from WAXS re;ults (;ee Tab. Ill L

=

28 _x c/

=

28 _x 24.5

=

6861,

we find _a value _more than twice 2 H. This prove~ the

existence of

hairpins

the chain conformation I,

compo~ed

_{of >i~}

=

L/2 H

=

2.14 wires in _a

cylinder

of radius R

=

81

_(see

_Fig.

_12). _The value _a

=

87

corresponds

to a very

high

order

Sjjlq)

5

lcm+)~

3

o

0 2 ( 6

~ ~

8

q 10 I

Fig. 13. Abwlute ,cattering intenqity _Sjj(</) in the nematic direction _iv> _vii; the ~cattering vector q for the PE10-DP28 _at 135 °C. The full lines _are the calculated _curves for

cylinder~

with different

2 H value~. (II 2 H 3001 ₁₂₎ _{2 H} 280 li ₍₃₎ ₂ _H

2501.

_The _other _parameter~

are

R

=121

_and

a 87 (P~ =0.983). Thi~

figure

~hows clearly the

sen,itivity

of the fit to the 2 H value.

5

1

~~

3

o

u1~

o

-1

0 2 ( 6 8

q i~

io~~)

Fig.

14. Ab,olute ,cattering inten~ity S(qj iw>.vii,I the ,cattering vector (/ parallel (.) and

perpendicular

(oj to the _nematic director for the PE10-DP28 _at 16 °C, The full line; _are the calculated _curves with the

,ame parameter, a; in figure I. But here _a Gau,,ian di,tribution of the

cylinder

length 2 H i~ taken _into

account, The be,t fit to the parallel direction i~ obtained with _a ;econd moment

(,=801

(? H 3?0