Dependence of viscoelastic properties on spacer length and molecular weight for a side-chain liquid crystal polymer in a nematic solvent

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Dependence of viscoelastic properties on spacer length and molecular weight for a side-chain liquid crystal

polymer in a nematic solvent

D. Gu, S. Smith, A. Jamieson, M. Lee, V. Percec

To cite this version:

D. Gu, S. Smith, A. Jamieson, M. Lee, V. Percec. Dependence of viscoelastic properties on spacer

length and molecular weight for a side-chain liquid crystal polymer in a nematic solvent. Journal de

Physique II, EDP Sciences, 1993, 3 (6), pp.937-949. �10.1051/jp2:1993232�. �jpa-00247879�

Classification

Physics

Abstracts

61.30G 61.40K 62.10

Dependence ^of viscoelastic properties

_on

_spacer length and molecular weight for

_a

side-chain liquid crystal polymer in

_a

nematic solvent

D.

Gu,

S. R.

Smith,

A. M.

Jamieson,

M. Lee and V. Percec

Macromolecular Science Department, Case Westem Reserve

University,

Cleveland, Ohio 44106, U-S-A-

(Received l0November1992,

accepted

in final

form

8February 1993)

Abstract. The

light

scattering

technique

_was used to

investigate

the viscoelastic parameters

characterizing

director distortions in miscible nematic mixtures of

pentacyanobiphenyl

(SCB) with

a side-chain

liquid

crystal

polymer

(LCP)

having

different spacer

lengths

(n ₌ 2, 3, 5, 7, II ). To separate ^{the elastic} constants from the

corresponding

viscosities, two

approaches

_were

attempted

_: (a) _an AC electric field _was

applied

to

homeotropically-aligned

nematic monodomains of the mixtures, and the

field-dependent scattering

intensities and director distortion relaxation rates were

measured to obtain the twist

viscosity

_yj and elastic constant K~~ (b) _an electric field _was

applied

to a

homogeneously aligned

monodomain and the

voltage-dependent capacitance

and the threshold voltage _were measured to obtain the dielectric _constants and the splay elastic constant. The

remaining splay

viscosity, bend

viscosity

and bend elastic constant were

subsequently

determined

by fitting

the

angular-dependent

relaxation _rates in three

scattering geometries

which correspond

principally

to

splay,

twist, and bend modes of the director distortions for nematic mixtures. The

addition of

liquid crystal polymers

_causes

significant

decreases of the relaxation rates for all three distortion modes of SCB which _are due _to small decreases in the elastic constants and large increases in the

viscosity

coefficients. The molecular weight

dependence

of the viscosities for

n = 3 is weak. The largest increase in viscosities is found for the LCP with shortest spacer

length

n = 2. The

dependence

of

viscosity

_{on spacer}

length disappears

when _{n m} 5. The

anisotropy

in the three

viscosity

increments of the nematic mixtures also becomes smaller when _{n m} 5. Our results

indicate that, for side-chain LCPS in _a nematic solvent, the backbone

configurational anisotropy

is enhanced by a strong

coupling

between the

mesogenic

group in the side-chain and the chain backbone.

1. Introduction.

In _a nematic

liquid crystal,

_an intense

depolarized light scattering

is

produced

due _to

thermally

driven

long-wavelength

fluctuations in the director orientation. The

intensity

and the

frequency

spectrum ^{of the}

scattering light

_can be measured to characterize the viscoelastic

properties

of

the nematic matrix

[I].

The differential

scattering

cross sections for _two diffuse deformation

modes, corresponding

to

splay-bend

and twist-bend director

distortions,

_are

inversely proportional

to the Frank elastic _constants Ki~

[I]

where I

=

1, 2, 3, correspond

to the

splay, twist,

and bend distortions

[I].

The relaxation rates of each mode _can be determined

by dynamic light scattering (DLS)

which involves

photon

correlation

analysis

of the

scattering light [1-6].

^The ratios between the various elastic constants _as well _as ratios of the elastic

constants to

viscosity

coefficients _can be determined

by measuring

the

scattering

intensities

and relaxation rates of the pure

splay, twist,

and bend modes at

appropriate scattering angles, polarizations

of the

incoming

and scattered

light,

and director orientations

[7].

In order _to

quantitatively

characterize the viscoelastic behavior of _a nematic system, one needs to obtain individual values of the elastic constants and

viscosity

coefficients. This

decoupling

of the

viscosity

and

elasticity

in

light scattering experiments

_can be achieved

by application

of _an extemal field

[I].

For

example,

if _an electric field is

applied along

the director of _a

homeotropic

monodomain which has _a

positive

dielectric

anisotropy,

the twist

viscosity

and the twist elastic _{constant can} be determined from the

field-dependent scattering intensity

dtr/dD and relaxation _rate

r~

of the pure twist distortion

[1, 8, 9].

$

K~~

q( ~eo

_he

E~

and

r2

=

K22 q( _/Y

i + So he

E~/Yi (2)

where so is the electric

permittivity

in _vacuum, E is the field

strength,

he is the dielectric

anisotropy

of the

nematics,

_qi is the

perpendicular

_component of

scattering

vector with respect

to the

director,

_y

j and K~~ are the twist

viscosity

and elastic constant of the

nematics,

and A is _a constant. A second

approach

to obtain individual elastic _constants is the Freedericksz transition

technique [I].

When _an electric field is

applied

to a nonconductive nematic

liquid crystal

monodomain which has _a

positive

dielectric

anisotropy,

the director will tend _to be

aligned parallel

to the field. This director

realignment happens only

above _a threshold

voltage

V~~ for _a certain

geometric arrangement

^{of the director and the field. The}

realignment

of the director can be monitored

by measuring

the dielectric

permittivity

_e, which is

proportional

to the

sample

cell

capacitance.

If the monodomain is

homogeneously aligned,

the threshold

voltage

value is related _to the

splay

elastic constant

by [10]

:

V~

=

Kji ar~/(e~

he

). (3)

The

advantages

of

using

_an electric field instead of _a

magnetic

field _to

produce

and _to

probe

the director distortion _are that _{one can} also obtain _e values in the measurement and _one does not need _to determine the

sample

cell thickness.

Knowing

the

splay

elastic constant, twist elastic

constant and

viscosity,

one can obtain all the other elastic _constants and viscosities

by fitting

the

angle-dependent

relaxation _rates in the

scattering geometries

which

correspond principally

to the

splay,

twist and bend director distortions

[7].

In the

applications

of the LCP

materials,

it is of interest _to know what is the behavior of the flexible chain backbone and how does it influence the

specific liquid crystal properties

such as

macroscopic viscoelasticity,

_type of

mesophase,

transition

temperature,

^{electrical and}

optical anisotropy.

One

approach

is to

study

the

hydrodynamic properties

of dilute solutions of the

polymers

in low molar _mass

liquid crystal (LMMLC)

solvents in _a fashion

analogous

to that

applied

to flexible

polymer

chains in

isotropic

^{solvents. In} common with the

latter,

since the LCP chain

occupies

is _a

large

volume in the

anisotropic solution,

dissolution of _a small

quantity

of LCP induces

large changes

in

hydrodynamic properties.

A

major distinction, however,

is

that,

when _an LCP is dissolved in _a nematic LMMLC

solvent,

the director rotation

can

couple

with

cooperative

motions of the

backbone,

and therefore the backbone has to

adjust

to the director

orientation, making

the backbone

configuration nonspherical.

The

resulting configurational anisotropy

has been observed

directly

via

small-angle scattering experiments

for side-chain and main-chain LCPS in LMMLC solvents

[11-12],

and also for pure side-

chains LCPS

[13-15].

This effect of

polymer

backbone

configuration anisotropy

has been further

reported

in

rheological

studies of LCP solutions

[16],

in measurements of transport

properties

such _as diffusion coefficients of LCP in nematic medium

[17],

in

dynamics

of nematic-nematic

phase separation [18],

and in deuteron NMR studies _on molecular order of spacer and backbone for _two side-chains LCPS

[19].

A theoretical

analysis

of the

viscosity

increments due to dissolution of

polymer

chains in _a nematic fluid _was described

by

Brochard

[20],

who

developed expressions

in terms of _a few

microscopic

parameters ^such as

R~,

_Rjj

(the

radii of

gyration

of

polymer perpendicular

and

parallel

to the

director),

and the rotational relaxation time of the

chain,

_r~. Brochard's

analysis

suggests ^that information _on the

polymer

chain

configuration

in nematic solvent _can be deduced

by measuring

the

viscosity

increments of the various

viscosity

coefficients.

The viscoelastic behavior of nematic monodomains

containing

side-chain LCPS has been

investigated by

several groups

using light scattering techniques,

Freedericksz transition measurements and NMR

analysis.

Here _{we are} interested

particularly

in miscible mixtures of side-chain LCP dissolved in low molar _mass nematogens

[9, 21-26].

It has been established that the addition of LCP _{causes a} substantial decrease in the relaxation rates of the director

distortion

modes,

which is due

principally

to increases in the associated viscosities. The

magnitude

of the viscosities increases

substantially

with

polymer

concentration and

depends

on

temperature,

^molecular

weight,

_spacer

length

and

flexibility

of backbone. The

correspond- ing

elastic constants _are less influenced

by

the addition of LCP and remain close in

magnitude

to those of the LMMLC solvents.

In _{our recent} studies

[25],

the relaxation rates of the

splay,

twist, and bend distortion modes

were examined for side-chain LCP and main-chain LCP mixtures with SCB _at various

concentrations,

molecular

weights,

and spacer

lengths.

We found that the relative decreases in the relaxation _{rates are}

substantially larger

for

2-PVE,

which has the shortest spacer

length,

n =

2,

than those of 7-PVE which has

longer

_spacer

length

n ₌ 7. Since the relaxation rates _are

proportional

to the ratio of the elastic constant to the

corresponding viscosity,

it is of interest to know

(a)

what _are the relative contribution of the elastic constants and the

viscosity

coefficients _to the variations in the relaxation _rates,

(b)

what is their

dependence

on spacer

length, (c)

what is their molecular

weight dependence.

Here we

report

^{results of such} an

analysis by combining light scattering

measurements with Freedericksz transition

experiments

on nematic mixtures

containing

a side-chain LCP with different spacer

lengths.

We _are able _to obtain _a

complete

set of elastic constants and

viscosity

coefficients

characterizing

the nematic

matrix and demonstrate that the addition of the LCP to the nematic solvent results in

exceedingly

small decreases of the elastic constants, and

large

increases of the viscosities _as found earlier for another side-chain LCP mixture system

[7, 25].

Our results show that the

anisotropy

in the

dynamical

behavior of the director distortions is

dependent

_on ^the

degree

of

coupling

between the

mesogenic

_group in the side-chain and the

backbone,

_as well _{as on} the

flexibility

of the backbone.

2.

Experimental.

The chemical structures of the side-chain LCP

species

used in _our

study, poly[n~[4-cyano-4'- biphenyl]oxy] n-alkyl vinylether] (n-PVE),

_n

= 2,

3,

5,

7,

11 _are shown in

figure

I. The

n-PVE: ~~'~2~~f~

«CHanO O O

c~

scB: cH~(ca~~ Q Q

cN

Fig,

I. Molecular structures of the side-chain

liquid crystal polymers

n-PVE, and the nematic solvent SCB.

polymers

have been

extensively

characterized

[27].

In _a concentration range of 0-15

9bw/w,

these

polymers

were found _to be

completely

miscible with SCB in both nematic and

isotropic

states. The low molar _mass nematic

liquid crystal

solvent SCB used in this

study

_was

purchased

from BDH Ltd and used _as received. A Carl Zeiss

optical polarizing microscope equipped

with _a Mettler FP82 hot stage ^and a Mettler FP 800 central processor was used to evaluate the

miscibility

and determine the nematic _to

isotropic

transition temperature T~ _; ^{of the}

sample.

The T~

_,

of SCB _was measured _as 35.0 °C. The T~ ^{for the LCP mixtures}

were found to be

slightly higher

than that of SCB and to exhibit _{a narrow}

biphasic region

at the

T~_,, depending

_on the

polymer

concentration. The nematic mixtures _were sandwiched between _two clean

conductively

coated slides

glass separated by

25 _~Lm

Mylar

_spacers. Planar and

homeotropic

monodomains _were

prepared using

surface-treatment

techniques

described

elsewhere

[7].

The

sample

cells _were filled

by capillary

action and sealed with epoxy.

Freedericksz transition studies _were

performed by measuring

^the

capacitance

of the

sample

cell while _an

increasing

bias

voltage

is

applied.

The

capacitance

_was monitored

by

a three-

terminal

arrangement

^with a

guard

electrode. One of the conductive inner surfaces

(50 Qlinch2)

of the

sample

cell _was divided into two parts ^either

by

_an

etching technique

_or

by scoring

with _a fine diamond

tip.

The central effective _{area was} used for

capacitance

measurement and the

surrounding region

for the

guard

electrode. The effective _areas of the

planar

monodomains _were

typically

about 1~ l.5

cm~

and the

separating

_gaps between the

guard

electrode and the effective _{area were} about 30 _~Lm.

However,

_no differences _were found between the

grounded

electrode

guarded

cell and the

unguarded

cell in the

capacitance

measurements within

experimental

error.

Figure

^{2 shows} the circuit

diagram

used for

capacitance

determination. The

impedance

of the

sample

cell _can be considered to be

composed

of _a resistance and _a

capacitance

in

parallel.

The value of the

probe

resistance R~ ^{is much smaller than the}

impedance

of the

sample

cell

Z~(

_[Z~

_[/R~

~ 400

)

so that the

probe signal voltage

V~ across R~ ^is

inversely proportional

to the value of the cell

impedance.

The

lock-in

amplifier (EG&G model124A)

_measures both the

amplitude

and the

phase

of

V~, ^{and hence}

generates

^the values of the resistance and

capacitance

of the cell. An AC bias

voltage V~

was

applied

to the cell _to

produce

the Freedericksz transition. The

frequencies

of the bias

voltage

^{and the}

probe signal

were

f~

=

50 Hz and

f~

₌ 000 Hz

respectively.

The field-

dependent

dielectric _constant

e was determined

by comparison

of the measured

capacitance

^for the filled cell _to the

empty

^{cell. The}

sample

cell _was

placed

in _{an oven} whose

temperature

was

regulated

5 °C below the

T~_,

of the nematic mixture

by

_a temperature ^controller

(YSI

model

72)

accurate to 0,2 °C.

Figure

3 shows _e

V~

curves at three

temperatures

^{for SCB.}

The value of ei ^was measured _{at zero} field _{or at}

voltages

below the threshold and the value of ejj ^was determined

by extrapolating

the _e

I/V~

_curve to infinite

voltage [28].

The threshold

Lccell

f~ lock-in

R~

f,

Fig.

2. Block

diagram

for the Freedericksz transition measurement set-up. ^Across

Rs,

the

phase

and

amplitude

of the

probe signal

with

frequency f~

_are each monitored to obtain the dielectric

permittivity

of the nematic

sample

cell.

voltage

at which the transition _{occurs was} determined

graphically.

The overall accuracy in

measuring

he is about 3

9b,

and in

V~

is about 19b.

A

photon

correlation spectrometer

equipped

with _a 15 mW He/tQe laser and _a Brookhaven Instruments BI 2030AT 256-channel

digital

correlator _was used in the

light scattering

measurements. The refractive indices for SCB and the mixtures _were determined

using

_a

Bausch & Lombs Abbe refractometer model

60/HR equipped

with _a Fisher

refrigerated

circulator,

model 9100. The

sample

temperature was controlled 5 °C below the

T~_;

^of the nematic mixture

by

_a

refrigerated circulating

bath _{accurate to} better than 0, I °C. We used three

scattering configurations

in

dynamic light scattering experiments

in the absence of _an electric field. In these three

configurations

which _were described in detail

previously [7],

_we

probe separately

the

scattering

contribution from the three director deformation modes. In _con-

figuration A,

with the director

perpendicular

to the

scattering plane,

^the

V~ scattering

is

principally

due to the

splay

mode _{over a} certain range of

scattering angles (18°

33° in the

laboratory frame).

In

configuration B,

with the director in the

scattering plane

and

orthogonal

to the incident _wave vector, the

V~ scattering

is

principally

due to the bend mode with _a minor contribution from the twist mode. In

configuration C,

with the director

parallel

_to the incident

wave vector, ^the

V~ scattering

is

principally

due to the twist mode with _a minor contribution from the bend mode. The

angular dependences

^of the

scattering

vector in these

configurations

are different which enhances _our

ability

to extract numerical values of the various elastic constants and

viscosity

coefficients. The

methodological

details _are described elsewhere

[7].

The autocorrelation functions of the scattered

intensity,

obtained

by photon

correlation

analysis

in each of these

configurations

exhibit

single-exponential decay

within measurement error,

confirming

that the pure

scattering

modes have been isolated. For measurements of

light scattering

in the presence an electric

field, configuration

C is utilized and the relaxation rates and

scattering

intensities _are measured at low

scattering angles (15

~

21°)

where the pure twist mode is detected

[7].

The AC electric field

applied

to the

homeotropic sample

_was

provided by

a Hewlett-Packard

audio-frequency signal

_generator model 200CDR _at 3 000 Hz.

18

g

o o

~ ~

o. ^{° . .}

.

l~

^{O. ~ +}

+ + + +

~

+

p +

I ~*

f12

^o

o

~l

lo

£

g~

° dielecAT-io°c dielec,AT-5o~

+ dj~j~~~ ~

(a)

0 2 4 6 8

Voltage (volt)

+ _.

° dielec.AT-10°C

. °

#

dielec.AT-5°C *

I

+ dielec.AT-3°C ₊

zz . O

l$ ^~ _O

~

_* o

~ l$

o +

w

+ o

+

. .

O O O °

°°

6

o.4 0.5 o.6 0.7

o.8

Fig. 3. - _Results of

dielecuic easurements

Figure 3b

Table I. Results

for

elastic _constants in

n-PVE/SCB

Mixtures.

he _± 3 9b Vj~ ± I fb

K11

± 5 9b

K~~

± 5 9b

K~~

± 5 9b

(volts) (10-8 dynes) (10-8 dynes) (10-8 dynes)

pure SCB I 1. 0 0.705 49 32 56

8 9b 2-PVE 8,19 0.610 27 24 45

N

= 22

8 fb 3-PVE 8.44 0.680 35 26 46

N

= 30

8 fb 5-PVE 9.03 0.700 40 26 46

N

= 30

8 fb 7-PVE 8.87 0.690 38 27 45

N

= 30

8 9b 11-PVE 8,16 0.700 36 26 42

N

=

30

backbone in the nematic matrix. The

largest

he and

Kii

values _were found for the 5-PVE

mixture,

whose spacer

length

is

equal

to the

length

of the

alkyl

tail of SCB. This may

produce

more effective interaction since the

mesogenic

_group of n-PVE is the _{same as} that of SCB. We also found that it takes _a

longer

time to obtain

e-V~

data in the transition

region

for side-chain LCP mixtures because the response of _{e to} the

change

in

V~

^{is slower due} to the

higher

twist

viscosity

of the system

compared

with pure SCB.

Theoretically,

the value of the bend elastic constant also _can be obtained

by measuring

the

slope

of the

post-transition

_part of the

e-V~

curve

[29]. However,

because of the very

large

he values and the very small differences

between

Kii

^and K~~ ^{for SCB and its LCP}

mixtures,

it is

impossible

to obtain reliable K~~ ^values

using

this

approach

for the

systems

^{studied here.}

Analysis

of

light scattering

in the presence of _an electric field confirmed that the decrease in relaxation _rates is

principally

due _{to an} increase of the viscosities. In

figure

4 the inverse relative

scattering

intensities of pure SCB and the side-chain LCP mixtures at a concentration of 8 9bw/w are

plotted against

the field

parameter

so

hev~/d~.

_The

slopes

of these lines _are the

inverse twist elastic constants

I/K~~. According

_to the results of the

intensity

measurement shown in

figure 4,

the difference between the values of K~~ ^{for SCB and LCP mixtures is}

comparable

to the

experimental

_error which is about lo

9b, indicating

that the

changes

in K~~ ^due to addition of LCP _are very small. This is consistant with _our

previous findings

_on

mixtures of _a different side-chain LCP with _a

methacrylate

backbone

[7].

A _{more accurate} determination of K~~ can be achieved from the

field-dependent

relaxation _rate because of the intrinsic accuracy of the autocorrelation measurement. In

figure

5 the

field-dependent

relaxation rates of the twist mode for the

polymer

mixtures and pure SCB _are shown _as functions of the field parameter.

According

to

equation (2),

the

slopes

of the lines in

figure

5

are the inverse twist viscosities

I/yi,

and the twist elastic _constant K~~ can be extracted from the zero-field relaxation _rate. It is clear that the addition of the side-chain LCP results in the decreases of both the zero-field relaxation rate and the field

dependence

^of the relaxation _rate.

The values obtained for the twist

viscosity

and elastic constant _can

subsequently

^{be used} in the

curve

fitting analysis

of the

angular dependences

of the zero-field relaxation rates in the three

scattering geometries

mentioned earlier to

generate

the bend elastic constant, the bend

viscosity,

and the

splay viscosity.

^An

example

of this _curve

fitting

^is illustrated in

figure

6 _: the bend elastic _constant and the

corresponding viscosity

coefficients of the 3-PVE mixture

o .

6i

+

~

, a

w _. ,

f

I

_1.8

(

+

~i~

o ma

#

1.6

§

_{* 2-PVE}

. ~PVE

. ~PVE

> ^'

fi ~ ^{+ 7-PVE}

a 11-PVE

0 20 40 60 80

go Agv2 /d2 ( cvm"3

Fig.

4. Electric field

dependence

of the inverse scattering intensities for pure SCB and its mixtures with the side-chain LCP n-PVE (n

= 2, 3, 5, 7, 11 ) at 8 9bw/w concentration.

28O0

<

11

~ fl

₂₀₀₀

~

§

#

" 1200

~~0

20 40 60

eoAev2/d2 (CVm"~l

Fig.

5. Electric field

dependence

of the relaxation rates for the twist distortion mode for pure SCB and its mixtures with side-chain LCP n-PVE (n

= 2, 3, 5, 7, 11 ) at 8 fbw/w concentration.

Symbols

used here _are as in

figure

4.

~_

100000

TO

l~U

j g

d

z

f #

~~o

20 30 40 50 60

Sca«erring Angles (°

in lab

frame)

Fig.

6. The relaxation rates

r~

in

scattering

_geometry B

plotted

_{as a} function of the

scattering

angles for pure SCB and its mixtures with side-chain LCP n-PVE (n

= 2, 3, 5, 7, II )at 8 9bw/w concentration.

Symbols

used here _{are as} in

figure

4.

(89bw/w)

_were

adjusted

_so that the calculated relaxation _rates for

geometry

^{B fit the}

experimental

values in the whole range of

scattering angles. Likewise,

the

splay viscosity

_can

be obtained

by

_curve

fitting

in geometry ^A.

To demonstrate the spacer

length

effect _on the

viscosities,

in

figure 7,

the increments of the

I

-

0.6

I

f~ .

splay

ij

° Mist

fi

oS

" b6nd

j

0.4

'

oS

j

0.2

%

0.0

0 2 4 6 8 lo 12

Spacer Length (number

of

methylene units)

Fig.

7. Influence of the spacer

length

_{n on} the

viscosity

increments for the

splay,

twist and bend distortion modes of 8 9bw/w nematic solutions of n-PVE in SCB.

splay, twist,

and bend viscosities for 8

9bw/w polymer

^mixtures are

plotted

_as functions of the spacer

length,

The

polymer, 2-PVE,

which has the shortest spacer

length,

shows the

largest

increase in the

viscosities,

_even

though

it has _a lower molecular

weight

than the other

polymers.

This effect

disappears

when the spacer

length

n m 5. Another aspect ^which was

investigated

in _our

study

is the influence of molecular

weight

_on the intrinsic

viscosity

increments. For the intrinsic

viscosity [yi],

lYil

=

(Yi Yl)/Ylc ₍₄₎

where _c is the

polymer concentration, y)

_and

yi is the twist viscosities for pure SCB and

mixture. We carried _out

light scattering

studies on 3-PVE with different

degrees

of

polymerization (N

=

6, 18, 23,

30

).

^The results for the intrinsic twist and bend viscosities _are shown in

figure

8. In _{contrast to our}

previous

observation

[25]

_{on a} different side-chain LCP

poly[6-[(4methoxy-a-methylstilben-4-yl)oxy]hexyl methyacrylate] (MSHMA),

_we find that 3-

PVE has _a rather weak molecular

weight dependence

^{of the intrinsic}

viscosity.

We note

however,

that the range of molecular

weights

available for 3-PVE is

significantly

smaller than that accessible in _our earlier

study

of MSHMA.

20

~y i£

^~~

) g

)

_lo

o

j

g

?

C

~

O [burst]

" J~end~

~0

_{lo 20} 30 40

Degree

of

Polymerization

Fig. 8. The intrinsic twist and bend viscosities for the mixtures of side-chain LCP 3-PVE and SCB at different degrees of

polymerization,

N

= 6, N

= 18, N

=

23, N

=

30.

In Brochard's theoretical

analysis [20]

of the viscosities of such nematic

mixtures,

the increment of the twist

viscosity

due to addition of

polymer

_can be

expressed

_as a function of _a few molecular

parameters

yi =

ckT(R( Ri)~ r~/NR( Ri (5)

where _c is _mass concentration, N is

degree

of

polymerization,

k is Boltzmann constant,

T is

temperature, Ri

and

Rj

_are the radii of

gyration perpendicular

and

parallel

to the director

respectively,

and r~ is the rotational relaxation time of the

chain,

r~ =

hi hi R( Ril(Ai R(

₊ A

ii

Ri)

kT

(6)

where

A~

^{and A}

ii

is the translational frictional coefficient

perpendicular

and

parallel

to the director.

According

to

equation (5),

if _an

anisotropy

in the

polymer

backbone

configuration

exists in _an nematic solvent, ^{then the} twist

viscosity

of the nematic mixture will be increased

by

the addition of the

polymer.

In other

words,

if yi #

0,

then

R~

#

Rjj.

Note that the side- chain LCPS used in this

study

have the _same

degree

of

polymerization (D.P.

=

30)

_except for that with spacer

length

_{n =} ²

(2-PVE),

which is lower

(D.P.

=

22).

Thus the differences between the

viscosity

increments for the various LCP are due

predominantly

_to differences in backbone

configuration

and hence the

coupling

between the

mesogenic

_groups and the backbone.

Specifically,

2-PVE has

strongest coupling

^{of the} mesogen

mobility

with the

polymer backbone,

since it does not form _a stable nematic

mesophase by

itself.

Therefore,

what _{one sees} in

figure

7 is

principally

_a result of

increasing degrees

of

decoupling

of the

mesogen motion from the

polymer backbone,

with increase of the spacer

length.

The results

are consistant with NMR studies

[19, 30-32]

of _some side-chain LCPS in which decrease in molecular order _or increase in

mobility

_was found for the

methylene

units in the spacer which

are not

adjacent

to the

mesogenic

_group. In

principle,

^from Brochard's

derivation,

_{one can} estimate the

anisotropic

ratio

R~

/Rjj

by comparing

the increments of different viscosities. For instance,

according

to Brochard's

theory,

the increment of _a Miesowicz

viscosity

_{t~~ is}

given by,

t~~ =

(ckT/N )

_r~

RilR( ₍₇₎

Taking

the ratio of

equation (5)

and

equation (7),

we

have,

yi/&

_t~~

=

(R( Ri _)~/R( (8)

For oblate

configurations,

with

R~/Rj ~/, _{equation (8)}

_is

single-valued;

for

0 _~

R~ /Rj

_~

/, _{equation (8)}

_is

double-valued,

and _{recourse must} be made _{to a} second

ratio, preferably

_one

containing

the incremental Miesowicz

viscosity

_&t~~. We found that

t~~ could be extracted with

good

_accuracy from the fits _to the

angle-dependence

of the

relaxation _rates for

light scattering

in

geometries

B and C. In table

II,

the

viscosity

increments yi, t~~, and the ratios _y

i/&

_t~~,

together

with calculated values of

Ri

_{/Rjj are} listed for all _n- PVE

species.

For

comparison,

data for _a main-chain LCP mixture _at 3

fbw/w

concentration

[25]

_are also listed in table II. The results

indicate,

via

equation (8), that,

in _{contrast to} the

main-chain

LCP,

the side-chain LCP n-PVE

adopts

_an oblate rather than a

prolate configuration

in the nematic solvent. This agrees with the values of

Ri /Rj reported recently by Pashkovsky

et al.

[26]

for _a similar side-chain LCP in SCB. We _note that direct measurements of

Ri

and

Rj

^for side-chain LCP in the bulk state indicate that _a

prolate configuration

^is present for certain side-chain LCPS with

methylsiloxane

_or

acrylate

backbones

[15, 19],

whereas _an

oblate

configuration

is

present

^{for others which} have _a

methacrylate

backbone

[13-15, 19].

We also

remark, however,

that, in the dilute nematic solutions examined in _our

studies,

the relative orientation of backbone and

mesogenic

_{group may} be different from _that in the bulk state. Table II indicates that t~~ increases with spacer

length which, according

to

equation (7), implies

an increase in the ratio Rjj

/Ri. However,

_t~~ remains

small,

in _{contrast to} the situation in mixtures of main-chain

LCP,

in which t~~ becomes very

large, numerically comparable

to

yi. It is thus clear that the

configurational anisotropy

in side-chain LCP is much smaller than

Table II.

Viscosity

increments and

anisotropic

ratios.

Yi ± 5 fb ~lc ± 20 9b _y

j/&

_{t~~ ±} 25 9b R

i /Rjj ± 7 9b

(poise) (poise)

8 9b 2-PVE 0.64 0.08 8.0 2.0

N

=

22

8 9b 3-PVE 0.42 0.08 5.3 1.8

N

= 30

8 fb 5-PVE 0.29 0,12 2,4 1.6

N

= 30

8 fb 7-PVE 0.28 0.12 2.3 1.6

N

= 30

8 9b 11-PVE 0.31 0,17 1.8 1.5

N

= 30

3 9b 11-TPB 4.78 4.80 1.0

~ 0.3

N ₌ 44

in main-chain

LCP,

and decreases with increase of the spacer

length.

This is in accord with the model considerations

[33, 34]

on side-chain LCPS that _an increase in the

length

of the

decoupling

_spacer enhances the

configurational mobility

of the

polymer, making

the backbone

configuration

more

spherical.

In

conclusion,

the

dependence

_{on spacer}

length

and molecular

weight

of the viscoelastic parameters ^{have been studied} for _a side-chain LCP in _a nematic mixture with _a low molar _mass LC. The results agree with earlier observations that the addition of LCP _causes

relatively large

increases in viscosities and small decreases in the elastic constants. We find

that,

for

longer

spacers, the

viscosity

increments of the twist and the

splay

modes become

smaller,

and _are

numerically comparable

to that of the bend mode. As shown in table

II,

the

origin

of this effect is that the Miesowicz

viscosity

_t~~ increases and the twist

viscosity

decreases for

longer

spacers.

Application

of the Brochard

theory

indicates that the LCP has _an oblate

configuration

whose

anisotropy

decreases _as spacer

length

increases. In future

work,

_we

hope

to

provide

_a

quantitative

test of

equation (7)

and

equation (8) by

direct measurement of

small-angle

neutron

scattering

from deuterated LCP.

Acknowledgments.

This

study

_was

supported by

the National Science Foundation

through

the Science and

Technology

Center ALCOM and the Materials Research

Group

DMR 01845.

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