Viscoelastic properties of a bent and straight dimeric liquid crystal

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Viscoelastic properties of a bent and straight dimeric liquid crystal

Gregory Dilisi, E. Terentjev, Anselm Griﬀin, Charles Rosenblatt

To cite this version:

Gregory Dilisi, E. Terentjev, Anselm Griﬀin, Charles Rosenblatt. Viscoelastic properties of a bent and straight dimeric liquid crystal. Journal de Physique II, EDP Sciences, 1993, 3 (5), pp.597-602.

�10.1051/jp2:1993153�. �jpa-00247856�

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Classification Physics Abstracts

61.30E

Short Communication

Viscoelastic properties of

_a

bent and straight ^dimeric liquid crystal

Gregory

A.

DiLisi(~),

E-M-

Terentjev(~)~

Anselm C.

Griffin(~)

and Charles

ltosenblatt(~)

(~)Department

of Physics, Case Western Reserve University, Cleveland, Ohio 44106 U-S-A-

(~)Cavendish

Laboratory, University of Cambridge, Cambridge CB3 OHE, Great-Britain

(~)Melville

Lab for Polymer Synthesis, University of Carnbridge, Cambridge CB2 3RA, Great- Britain

(Received

27 November1992, revised 15 March 1993, accepted 19 March

1993)

Abstract. Absolute values for the elastic constants and viscosities _are reported in the nematic phase for two dimers based _upon the _monomer 4A'-dipentyloxyphenylbenzoate. One dinner has _an _even number ofmethylene units in the _spacer and,in consequence, is approximately straight in the all-trans conformation. The other dimer has _one less methylene unit, and is

therefore bent. We find that the ratio

K33/Kii

for the odd dimer is reduced relative to that for the _even member of the series. Moreover,

we find that the absolute elastic constants for the odd dimer _are of order one-half that of the _even dimer. The system ^is analyzed in terms of recent

theories by Terentjev, Rosenblatt, and Petschek, and by Terentjev and Petschek, with results in reasonable agreement with experiment.

Oligomeric liquid crystals

_are useful for the

insight they provide

about _crossover behavior

from the _monomer to the

liquid crystalline polymer regime.

In recent years we have _per-

formed _a number of

experiments

_on _a system ^of

oligomers

based _upon the _monomer

4,4'- dipentyloxyphenylbenzoate ("SOOS"

to elucidate its

viscoelastic, critical,

and interfacial _prop- erties

[1-6]. Recently

_we

reported

on a

fight scattering

measurement of the Frank elastic _con-

stants Kii> K22 and K33 for two dimers [S]. One dimer consists of two _monomers attached

end-to-end

(minus

_a

pair

of terminal

hydrogens),

thus

having

ten

methylene

units in the _spacer group; in consequence, the molecule is

approximately straight

in the all-trans conformation.

We refer to this dimer _as the "even" dimer. In the other molecule _a

CH2

unit is removed from the _spacer,

leaving

nine

methylene

units. This "odd" dimer exhibits _a kink between the

mesogenic

_groups in the all-trans conformation. We found that

although

the ratios of the twist to

splay

elastic modulus

K22/Kii

_are about the _same for the two

species,

the ratio of the bend to

splay

modulus

K33/1(ii

is

considerably

smaller for the odd dimer than it is for the

even member of the series. Such behavior _was

predicted by

Gruler [7] and Helfrich [8], ^who

suggested

^that a kinked molecule

might

exllibit _a reduced bend

elasticity by reorienting

_so _as

(3)

598 JOURNAL DE PHYSIQUE II N°5

to

partially

relieve the elastic strain. Since

publication

of the

elasticity

ratios _we have added _a

Faraday magnetic

susceptometer to our

laboratory.

This _now allows _us to extract the absolute values of the three elastic constants and associated

viscosities,

which is the central result of this communication. These

results,

_moreover, _are examined in

light

of the recent models of

Terentjev, Rosenblatt,

and Petschek [9] and

Terentjev

and Petschek

[10],

^which _were

developed specifically

for dimers with _a serniflexible _spacer.

Data from _our earlier measurements [S]

yielded

the ratios

K22/Kii

and

K33/Kii,

_as well

as the relaxation rates for

splay (ri

_"

Kiiq~/

nspiay)> ^bend

(r3

_"

K33q~/nbend),

and twist

(r2

_"

K22q~/71)

where qspjay, qt~end> and _ii _are the viscosities and q the

scattering

_wavevec-

tor. In

addition,

_we had

previously

obtained the ratio

I(ii/Axv using

_a

magnetically-induced

Freedericksz

technique

[2], ^where

Axv

is the volumetric

susceptibility anisotropy. Thus,

in order _to

absolutely

determine

I(ii,

_as well _as the other viscoelastic

constants,

_we have _sepa-

rately

measured the _mass

susceptibility anisotropy

Ax A 10 kG

electromagnet equipped

with

Faraday pole pieces

_was used in

conjunction

with _a Cahn model 2000

rnicrobalance,

sensitive to I pg. An empty quartz ^bucket ^with a

capacity

of

approximately

0,I cm~

was situated between the

pole pieces

at _a

point

where HT7H is

maximum,

where H is the

magnetic

field. The bucket

was first

weighed

in _zero

magnetic field,

then _at maximum

field;

the difTerence between the two

weights corresponds

to the

magnetic

force _on the empty bucket. The bucket _was then filled with KCI for calibration _purposes and

weighed

in _zero field to determine the _mass _mKci of the KCI. It _was then

weighed

at maximum

field, allowing

_us to extract the

magnetic

_component

of force

Fmag(KCI)

on the salt alone. Since

Fmag(KCI)

₌ XKcimKci

HT7H,

where XKCI is the

susceptibility

_per unit _mass of the salt

(which

can be obtained from standard

tables),

we were

able to

empricially

determine HT7H ₌ 1.35 _x

10? G~/

_cm at the location of the bucket. As _a

check,

this

procedure

_was

repeated

with

Nacl,

with

completely

consistent results. The bucket

was then filled with either odd _or _even dinner

(approximately

70

mg),

which _was

synthesized according

to

procedures

described elsewhere

[11-13].

^The

weight

of the bucket +

liquid crystals

was then determined in the absence and in the _presence of the

magnetic

field at several temper-

atures in the

isotropic phase.

From these measurements _we extracted _mdimer and

Fmag(dimer)

and,

since HT7H is

known,

_we _were able to obtain

fso,

the

magnetic susceptibility

in the

isotropic phase.

Measurements _were made at

approximately

five temperatures ^{in the}

isotropic phase

_near the nematic

transition,

and the value of Xiso _was taken to be the average of these

values. Scatter _was less than 2 ~. The

sample

_was then

brought

into the nematic

phase

and

weighed

with and without the

magnetic

field. Since the field is sufficient to

align

the bulk of the nematic in the bucket

(except

for _a

region

of thickness

f

_m _a few microns _near the

walls,

where

f

is the

magnetic

coherence

length),

_we extracted

Xjj ^as ^a function of temperature, where Xjj ^{is the} component of _mass

susceptibility parallel

to the nematic director.

Finally,

the

mass

susceptibility anisotropy (per gram) Ax

is

given by ((X

ii

-Xiso),

and is shown for both si ecies in

figure

I. Note that the scatter comes about because AX

corresponds

to _a small di ierence between similar values of

susceptibility.

A smooth _curve is drawn

through

the data

an I is used for

obtaining

Kii.

Then, assuming

the

density

of the dimer is

approximately

I g

Ii m~,

we obtain the volumetric

susceptibility

AXV _vs. temperature.

Along

with the threshold

fields Hth> _we are thus able to obtain Kii

absolutely

from the

Kii/AXV

data in reference [2].

Also,

since elastic constant ratios have been obtained [5], 1(22 ^and K33 _can be extracted _as well.

Finally,

since the viscosities

depend

_on absolute values of the elastic constants, _qspjay, _ii, and _qt~end _can also be obtained. Elastic moduli _are shown in

figures

2 and 3, and viscosities

are shown in

figures

4 and S. Liberal _error bars for Kii have _an upper limit of12

~,

for K22 20

~,

and for

K33

25

~,

about 10 ~

(half)

of which _come from

systematic

_error in AX. If AX _were

difTerent,

a~ values would

change systematically by

the _same relative amount. Error bars for the

respective

viscosities _are

slightly larger.

Note that _a

complete

_error

analysis

is

(4)

x lo "7 ^~~~~

~

[

Q

~

~ 0.4

~ 0,2

20 15

"TNT

Fig.

dimer (A). Solid

the

(5)

25_x10-7

~ EVEN DIMER ODD DIMER

a ~~ _,

£

_a

m m

£

is a £

< < ,

$ ' $

z a z

810

'

. , a

8

Q .

.

'a Q 4 a

~ a ~ a

m m a

. . .

~

20 15 _-10

S 0

T - Tp/j T - _TNj

Fig-

2

Fig.

3

Fig. 2. Elastic constants for _even dimer _vs. T-TNT.

(~)

represents Kii, _(m) _represents K2~, and

(A)

represents K33. Solid lines

are theoretical fits for

(from

_top to

bottom)

bend, splay, and twist.

Error bars _are discussed in reference [4].

Fig.

3. Same _as figure 2, except for odd dimer.

a

_

~

.

~

fl

~

a "

.

p

.

ml-S

'

. uj

~

.~ 8

, .

p

a

.

~

, " i

. ~,

.

81

, . . . . .

1..,,~

^~

, ^"

".'~

t

i

o-S

20 lS -lo S 0 20 15 -lo 5 0

T"~Nl ~'TNI

Fig.

4

Fig.

S

Fig.

4. Viscosities for the _even dinner

vs. T-TNT.

(~)

represents _qspjay, _(m) represents _m, and

(A)

represents _qbend. Error bars

are discussed in reference [4].

Fig.

5. Same _as figure 4, except for odd dimer.

fit for all three elastic constants _over the entire temperature range, we obtain the theoretical values shown in

figure

2.

Although

the theoretical values for

splay

and twist _are

reasonable, they

appear to exhibit

a

slightly

steeper

slope

with temperature than do the

experimental points.

Some of this

discrepancy

_may be due to

experimental

_error in the order parameter

dependence S(T)

deduced from

figure

I.

(Note

that the values for the

susceptibility

measured herein difTer from reference [14]

by

about 10

~,

which afTects the conversion from

K;;(S)

to

K;;(T)).

Additionally,

_we note that the conversion from order parameter to

temperature through

the

susceptibility

data is

likely

flawed since _we have assumed _a constant

AXsat, corresponding

to the

fully

extended _even dimer.

However,

the saturated

susceptibility anisotropy

is

likely increasing

(6)

with

decreasing

temperature,

owing

to

changes

in the distribution of spacer conformations with temperature.

Thus, S(T)

is in

actuality

less steep than that obtained from the

magnetic data,

and in consequence the

predicted

elasticities should

actually

be less steep than shown in

figure

2. The

large K33/1(ii

ratio

predicted

for the _even dimer is also

qualitatively

consistent with the

experimental data, although

it is somewhat

disturbing

that the theoretical second

derivative of K33 ^with respect to temperature ^is

negative.

It is obvious that factors

beyond

mean field which influence the bend

elasticity

would have to be considered to achieve better agreement ^with

experiment.

In order to construct _a

plot

of

Kjj(T)

for the odd

dimer,

the

experimental

data for the

corresponding

^order parameter

S(T)

should be

employed.

The nematic order parameter for the odd dimer is calculated

as

above,

where _we have chosen

AXsat

₌ 0.94 _x

10~~

erg

G~g~~,

based _on the molecular bend

angle.

For the _case of odd

dimers,

^both

S(T)

and

Kj;(T) strongly depend

_on the

given

combination of the

rigidity

and

equilibrium

bend

(Q, go)

^of ^the spacer.

Here _we have chosen Q

= 8 and go

= 37 ^° based _upon

aliphatic

_spacer

with nine

methylene

units [9]. ^Given ^these parameters and the _same

prefactor

W _as used for the _even

dimer, figure

4 shows the calculated elastic constants for the odd dimer. As for the

even

dimer,

there is

quantitative agreement

^with

experiment

for the

splay

and twist constants, which indicates that the chosen values of Q

= 8 and go Sd 37° for _a dimer with nine carbons in

the _spacer _are

quite appropriate. (We

note, _moreover, that these parameters also

predict

the

nematic-isotropic phase

transition temperature

TNI,

the

supercooling

temperature, and

S(T)

well below

TNI).

^The

quantitative

agreement ^is

particularly satisfying given

that the

magni-

tudes of the odd elasticities _are about _a factor of two smaller than those of the _even dimer. In

fact,

such difTerences in the elasticities _are not

predicted

_even

qualitatively

in references [7] and [8].

However,

_as with the _even

dimer,

the

predictions

of the

shape

of1(33 _are inconsistent with the

experimental

data. This arises from factors not described

by

the mean-field

calculation,

which afTect the bend

elasticity

of the uniaxial nematic

phase

of semiflexible

dimers,

and _are

beyond

the _scope of the current model.

Nevertheless,

it is clear that the trend to reduce the bend constant relative to

splay

is well described

by

the mean-field calculation

(consistent

with

experiment), especially given

the

qualitative

arguments ^and

experimental

_errors of at least 10 ~

throughout.

Viscoelastic

properties

of

rigid

rods

interacting

via

dispersive

forces _are

sufficiently

difficult to

predict;

when the molecule consists of two _or _more mesogens with _a semiflexible _spacer,

predictions

become _even _more

problematical.

In this communication _we have

reported

_on absolute viscoelastic measurements of _a dimer

consisting

of _an _even and odd number of

methylene

units in the spacer, and have

attempted

to compare these results with those of _a model de-

signed specifically

for this _purpose. The

important points

which _come about from this work

are that

experimentally,

_we find that

K33/Kii

is

substantially

reduced for _a bent dimer and that the elasticities of the odd dimer _are

considerably

smaller than for the _even

dimer,

and that

theoretically,

the model does _a reasonable

job

of

predicting

the elastic constants.

Acknowledgements.

We _are indebted to Rolfe Petschek for fruitful discussions. This work _was

supported by

the National Science Foundation Division of Materials Research under

grant

DMR-9122227.

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