Second harmonic generation in a liquid-crystalline elastomer

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Second harmonic generation in a liquid-crystalline elastomer

Harald Hirschmann, Dolors Velasco, Helmut Reinecke, Heino Finkelmann

To cite this version:

Harald Hirschmann, Dolors Velasco, Helmut Reinecke, Heino Finkelmann. Second harmonic genera- tion in a liquid-crystalline elastomer. Journal de Physique II, EDP Sciences, 1991, 1 (5), pp.559-570.

�10.1051/jp2:1991189�. �jpa-00247539�

J

Phys

III

(1991)

559-570 _MAI 1991, PAGE 559

Classification

Physics

Abstracts

42 65K 61.30 6141

Second harmonic generation in

_a

liquid-crystalline elastomer

Harald

Hirscl~mann,

Dolors

Velasco,

Helmut Remecke and Heino Finkelmann

Institut fi~r Makromolekulare Chemie der Un~versitit

Freiburg, Gerrnany

(Received

29 October 1990,

accepted

_m

final form

I

February 1991)

Smmnary. A

liquid-crystalline

elastomer with NLO active nJtrogroups ^bonded covalently to a

siloxane network has been

investigated

By means of polarizing

microscopy, X-ray

diffraction and UV-VIS spectroscopy it was found that the elastomer exhibits _a S~

phase

and _is

macroscopically

ordered The elastomer _is transparent for

wavelengths

above 450nm and the amsotropy of refractive index at room temperature is about 01

Applying

_an extemal electric

poling

field breaks centrosymmetry and second harmonic generation similar to

crystals

_can be observed. The

poling

process is

single

exponential with _an activation energy of 190 kJ/mol and _is identified _{as a} &- process In contrast to low molar _mass

liquid crystals

no director reorientation is observed

by

the laser field

strength.

From Maker

fnnge

expenments m the

liquid crystalline phase

at _room

temperature ^the second-order

susceptibilities

are X=:: = 0 92

pmiv

and X=xx = 0 06

pmiv

for _a

poling

field of 19V/~Lm

1. Inwoduction.

Apart

from organic and inorganic

crystals, polymers

have been

intensively investigated

with respect to their non-linear

optical

_properties

_[1, 2].

Two

approaches

_are

generally

used to obtain

polymenc

materials containing NLO active

chromophores

the first

approach

_is to swell _a

polymer

matrix w~th the

chromophores.

This

procedure

_is often limited

by

the poor

solubihty

of

chromophores

_m the matnx To _overcome this

problem

the second

approach

is to

covalently

link the

chromophores

to the

polymer

matnx. With this

procedure

matenals with

h~gh

non-linear

susceptibilities

are available.

However,

not

only

^{the chemical} structure of the

chromophores

but also the

degree

of order of the matr~x

strongly

influences the non-linear

susceptibilities.

Theoretical considerations show that the value of the

susceptibilities

_is smaller for _an isotropic medium than for the

limiting

_case of _an

Ismg

medium

[3]. Considenng liquid crystals

their state of order is between the

perfect

order of the

crystalline

state and the disorder of an isotropic ^{medium This fact makes}

l~quid crystals

_very interesting ^{matenals for} non-linear

optics

because _m the I _c state the molecules _can be

easily macroscopically aligned

with

respect

to the

long

molecular _axis

(director) by applying

extemal electnc _or

magnetic

fields. For

polymeric liquid crystals, however,

_a

perfect alignment

of the director often fails _in the electnc _or magnetic ^{field and} defect structures _{remain in} the

samples.

These defects _cause

h~gh optical damping

which

prevents

^their

applicability

To _overcome these

problems

_we

560 JOURNAL DE

PHYSIQUE

II M 5

choose _{a new} way Detailed investigations on crosslinked lc. side chain

polymers (lc.

elastomers) proved,

that uniform onentation of the director _can be obtained

by applying

_a

mechanical field. The effect of the mechanical field

strongly

exceeds magnetic ^{and electric} field

[4]

In this way I-c- elastomer films _can be

prepared

whose

optical

_{properties are} similar to the

optical

properties of

anisotropic single crystals.

Furthermore the

opt~cal damping

of

these elastomer films is very low _in the range of1-2

dB/cm [5].

In th~s paper we investigate a

liquid crystalline

elastomer where the NLO active

chromophores (e.g n~trogroups)

_are

covalently

bonded to the

polymer

network. The

phase

structure, the

poling

behaviour and the second-order

optical susceptibilit~es

w~ll be

reported.

2.

Experimental.

2, I SYNTHESIS _{oF THE ELASTOMER.} It _is well known that matenals

containing h~ghly polar end-groups (e.g. -NO~ groups)

_are ideal matenals to observe second harmonic generation

[6].

Therefore _we choose _an elastomer with _a chemical structure shown _in

figure

I. The

liquid

crystalline

siloxane network with the mesogenic side chains M _is

synthesized by

_a

Pt-catalyzed

addition _reaction of the

liquid crystalline

molecules and the crosshnker CLA to _a linear

polyhydrogensiloxane, according

to _a well known

synthesis

route

[7]

Elastomer films of 100- 200 _~m th~ckness _are

prepared by

_spin casting

technique

For

punfication

the elastomer is

extracted

by swell~ng

in toluene and

deswelling

in

petrolether.

The elastomer _is charactenzed

by

_a

glass

transition at T~ = 258 K w~th _a

change

of

specific

heat

AC~

= 0.21

J/gK

and _a first order transformation _at T

= 373 K

(Onset)

with _an

enthalpy change

of AH

= 4

Jig.

Above

CH~ CH3

-o-f

o

-f

-o-

[M]~~

^(cH~)~

c~$[~~

~M]~~ (cH~j2

-o-S o -s -o-

Ci§ Ci§

cLA

-S(c~)~~o-S(CH~)~)~-o-s(CH~)~-

M~~(@)n~o"[~f~o~fjRi

^~

o R~

n F~ R~

a 4

N~

^F

b 3 CN H

c 3 OC~H~~ ^H

a-b c = 03.005 065

Fig

I Chemical _structure of the elastomer

(M Mesogen,

CLA

Crosshnkmg agent)

M 5 SHG IN A

LIQUID-CRYSTALLINE

ELASTOMER 561

this

temperature

^{the elastomer}

displays

_an isotropic

phase

The values for

AC~

^and

AH indicate the existence Of _a smectic A _{or a} smectic C

phase.

The elastomers _are

completely transparent

^{and do} not absorb above 450 _nm

2 2 CHARACTERIZATION oF THE ELASTOMER

Thermodynamic properties

were determ~-

ned

by

differential _scanning

calonmetry (DSC-7,

Perkm

Elmer)

and

polanzing

_m~croscopy

(Leitz-Ortholux

2 Pol

BK).

Structural

investigations

were

performed by X-ray

diffraction

(CuKa

=

0 154

nm)

and

recording

of the scattered intensity on flat film

plates

^{The refractive}

indices at A =1064nm

(fundamental

_m SHG

expenments)

and A

= 532nm

(second

harmonic)

_were calculated from measurements of the

angle

of total reflection.

2.3 SHG-EXPERIMENT For the SHG

experiment

the elastomer film has _to be

poled

to

obtain the

noncentrosymmetric

structure. The film _was sandwiched between two conductive

glass plates (Balzers)

which _are connected to _a DC _source

The SHG

expenmental

set-up is shown

schematically

m

figure

2 A

pulsed

Nd-YAG Laser

(DCR 3G, Spectra Physics,

A

=1064nm, pulse

width 8 _ns,

10pulses/s)

^with a Gaussian beam

profile TEMOO

is used The

sample

_is mounted _{on a} temperature ^{controlled rotation} stage ^The

angle position

^of the

sample

_is directed

by

_a

personal

computer. ^The incident

polarized light

_is focussed

(lenses L)

m the

v~c~nity (4-5 cm)

^of the

sample.

After passing the

sample

the fundamental _{wave is} blocked

by

_a filter-element

(Schott BG39)

and _a monochromator

(filters).

The

intensity

of the second harmonic beam _is detected

by

_a

photomultiplier

tube

(PMT)

and the

signal

_is then

passed

after

amplification (AMP)

via _a

gated integrator

and boxcar _averager

(BOXCAR)

to _a

personal computer (PC).

To avoid absolute measurements of the

intensity

of the fundamental _{wave a} reference method _was chosen

using

_a

_quartz crystal (010

onentation, _xXxX

= 0.5

pm/V)

The measured maker

fringe

data _are fitted with theoretical calculated _curves to determ~ne the second-order

susceptibilities

x~~; and x~~~

SAMPLE /

Nd YAG

PMT

L FILTERS

pMT L

BOXCAR AMP

PC

Fig

2.

Expenmental

set-up for SHG expenments

~Pol

Polan2er, L Lens, HV

High voltage,

PMT

Photomultiplier

tube, AMP _:

Amplifier,

BOXCAR Gated integrator and boxcar averager, PC Personal

computer).

3. Results and discussion.

3 STRUCTURE. For _a quantitative

description

of the NLO

properties

of the

synthes~zed

elastomer,

_an

analysis

of the

phase

_{structure is}

required,

because the

polanzation

_m a medium

562 JOURNAL DE

PHYSIQUE

II M 5

caused

by

_an incident

l~ght

beam _is

directly connected

to the symmetry ^{class of this medium.}

In _{our case} the type of smectic

phase

and the onentation of the dJrector with

respect

to the

macroscopic

dimension of the

sample

has to be known for the second harmon~c

experiments [8]. Polannng

m~croscopic observation indicate _a uniaxial

phase

structure, where the

optical

axis _is

parallel

to the fihn normal To decide whether the elastomer exhibits _a smectic A

phase

or a two

dimensionally

ordered smectic

phase, X-ray investigations

_were

performed.

X-ray scattering diagrams

_were recorded _{at room} temperature ^{with the} incident beam

perpendicular

and

parallel

to the film normal

(Figs. 3a-c). Perpend~cular

to the film normal

(Figs.

3a and

3b)

the

diagram

is characterized

by

_a diffuse vnde

angle

reflection B

(d=0.42nn1)

and several small

angle

reflections A

corresponding

to

di

=

3.3nm, d~

=

2.2 nm,

d~

= 1.2 _nm,

d~

= 0.84 _nm, d5 = 0.65 nm, where

only

-the reflection

correspond- ing

to

di

is

sharp.

Parallel to the film normal

(Fig 3c)

the reflect~on B

(d

= 0.42 _nm

)

and _a

reflection C

(d

= 0.71 _nm

)

_are observed _as diffuse _nngs

conf~rm~ng

the

opt~cal

observation, With respect to the

phase

structure of the elastomer _a

positional long

_range order is

only

indicated in the

sharp

^reflection

correspond~ng

to _a

layered

structure with the

periodicity di.

This _is consistent with _a smect~c A

phase.

The

layer

thickness

di

^does not coincide with the

I'

-'

~/ S

.~

i'

cj

Fig

3 X-Ray

diagrams a) perpendicular

to film normal

(sample-film

d~stance 7

cm),

b)

perpendicular

to fflln norrnal

(sample-fihn

distance 17 cni), c)

parallel

to fihn normal

(sample-fihn

distance 7

cn1).

lK° 5 SHG IN A LIQUID-CRYSTALLINE ELASTOMER 563

length

of the _monomer units

(2.0

_nm for the -CN and

-NO~

substituted and 2.4 _nm for the

hexyloxy-substituted

_monomer

_unit)

_and

a

partially bilayer

has to be assumed. The diffuse reflections

corresponding

to

d~ d~

charactenze short _range order Reflection B _is attributed

to the _mean distance between the side groups. Reflection C

m~ght

be due to Si-Si

correlations

3.2 THEORY _{oF sEcoND HARMONIC GENERATION} It _is known that _a

light

_wave

travelling

through

_a medium _{can excite}

lugher

harmonic _{waves m} th~s medium

depending

_{on its} intensity ^{The i-th} component ^of the

polanzation P,

_in the medium _is then given

by

~< _{" X~j~~}

l~j

+ X~j~~

l~jk

+

X$~i l~jki

+

Ii )

where

E,

denotes the i-th component ^{of the laser field}

strength

and the

x~~~

are the components of the

susceptibility

tensor

[9].

^{The second} term in equation

(I)

_is

responsible

for the second

harmonic,

the third term for the third harmonic etc

The

poled

and therefore

non-centrosymmetric

structure of the elastomer under investi- gation is

represented by

_a

C~

symmetry. For the chosen beam geometry

(Fig 4)

with the electric

poling

field

Eo parallel

to the Z _axis the elements of the second-order

polanzation

pN~ =

(Pm P~, P=)

are

given by [10]

P~

=

2 _x

zxx

E~ E= (2a)

P,

= 2 xzxx

E,. E~ (2b)

P=

=

x=xx(Ej

₊

Ej)

_{+ x===}

Ej _(2c)

where x;<x and x=;= are the second-order

susceptibilities

The second-order

susceptibilities

_are

related _to the molecular

hyperpolanzabihty

element

p;== by

xz;= =

Np

;~~

F

(cos~

if

) (3a)

x:xx =

Np=== F( (cos

if

) (cos~

if

) )/2 (3b)

where N _is the number

density,

F includes local field factors and if _is the

angle

between the molecular _axes of the

single

non-linear

optical

moieties and the external

applied

electnc field

Eo

For the

limiting

_cases of _a

poled isotropic

medium and _a

poled Ising

medium the

following

expressions have been denved from

calculating

_equations

(3a)

and

(3b) [3, 8]

Component

Poled isotropic ^Poled

Ising

medium medium

x=;=

fl

;== H

Eo/5

kT

p

=~~

»Eo/kT

^~~~

xzxx

fl

==z H

Eo/15

^{kT 0}

x:xJx;z= 1/3

^o

» is the

dipole

moment of the molecule

Expressions (4)

show _a l~near

relationship

between the non,linear

susceptibility

and the

applied poling

^field

Eo.

As the distnbution function for _a

liquid crystalline

matenal _is intermediate between these _two

limits,

the _ratio of the second,

order

susceptibil~ties xzxjx===

should also he _in between

The

dependence

of the second harmonic _{power on} the second-order

polarization

_{as a}

function of incident

angle (Maker fnnge expenment)

has been calculated

[11, 12]

For _s

polanzation

E

=

E(0,1,

0

(see Fig 4)

and from equation

(2a-2c)

follows

10

PN~

=

p~(&)

0

(5a)

xxE~~

564 JOURNAL DE PHYSIQUE II lK° 5

Z

ELASTOMER ~~

HV

'~°'

x~y

8

Q ^{S POL LASER BEAM}

1064 nm

/ P POL

Fig

4 Beam geometry for

poling

m SHG expenment (HV

High Voltage)

The intensity of the second harmonic is then g~ven

by

~(2

_W

)

"

~(W

)~

~~L l~~(8)

_X

1/(~$ _~~w)~

_X

SIn~( ll') (5b)

ll'

=

arL/2) (4/A )(n~

_cos

8~

_n~

~

cos

8~ ~) (6)

For p

polarization

E

=

E(cos _{&~, 0,}

sin

&~) (see Fig 4)

and from

equation (2a-2c)

follows 2 _x

~~~

E^~ _cos

&~

_sin

&~

P~q~ = p P(^& 0

(7a)

x=xx

E~ _{C°S~ 8w}

₊

xzzz

E~

Slll~ &w The intensity of the second harmonic _is then given

by

~(2

_W

= I

(W

)~

Pj~L ~( 8)

_X

I/(n$ _n~w)~

X

SIn~( ll') (7b)

&, &~

and &2

w

denote the extemal and the internal

angles

of

incidence, I~

_is the intensity ^of the

light

_wave at

frequency

_w,

T(&)

and

p(&)

_are transmission factors

resulting

from

boundary

condJt~ons, _n~ and n~

~

are the refract~ve indices at the fundamental

respectively

the second

harmonic,

and L _is the thickness of the

sample.

The sinusoidal behav~our _m

equations (5b)

and

(7b)

descnbes the interference of the second harmonics

produced

at different points ^{in the medium.}

3 3 DYNAMICS

Poling

of _an elastomer _{m an} extemal electnc field

y~elds

_a relaxation of the molecules from _a

centrosymmetric

to _a non-centrosymmetnc ^structure

[13]

To determine

absolute values of the non-linear

susceptibilities

it _is important ^{to be} m an

equilibrium

state Therefore it _is necessary to know the relaxation of the molecules _{as a} function of temperature.

The relaxation of the molecules from the

poled

non-centrosymmetnc to the centrosymmetnc structure is

directly

indicated

by

the

disappearance

^of the second harmonic

intensity

The intensity of the second harnlonic _{as a} function of time when

applying

_{or removing an} electnc DC field _was measured Due to the low

glass

transition temperature of the elastomer the

relaxation times _are below the resolution of the

expenmental set-up

ⁱⁿ a

temperature

interval

near room temperature. ^{To obtain} information about the relaxation

mechanism,

_we

analysed

a

corresponding

elastomer which contains

only

^the

N02-substituted

_mesogen~c side chains For this elastomer T~ ^{is elevated}

by approximately

^{15 K} causing a

slowing

down of the

relaxation in the

investigated

temperature regime. The

diagram

of these measurements

(Figs.

5a and

5b)

show that the relaxation behaviour _is

single exponential reaching

_an

equihbnum

state w~th the _same relaxation times for rise and

decay

of the intensity From _an

M 5 SHG IN A LIQUID-CRYSTALLINE ELASTOMER 565

' ~ . ~;

~~.

:'

_.

_{.°_°}

,

.

in

- '

"O-,' _,

. o.

m ,

.-' ' '

% ,

-

~j

;,

.

.'

,

f8

~°~' Mm' ~

"*

N

<' ~

~

Hfl

*<

.C

-

f.

o

o Baa ieoa 27aa asaa <50a

TIME/s.

*, m *'<.«

, ._+

~

',f,

' ~',,

fn ^~ ./

,-',

' ~~

- m $~_-

B ~

C~Q '/

*m'

'~-

h~

~'/.

o

o Boa ieoa 27no asno <son

TIME/s.

Fig

5 Second harmonic intensity versus time at 293 K for

a) poling

field _on

b) poling

field off

566 JOURNAL DE PHYSIQUE II lK° 5

Arrhenius

plot

^{of the}

logarithm

of the relaxation

frequency

_versus the

reciprocal

temperature

m the

liquid crystalline phase

close to T~

(Fig. 6)

_we achieve an activation energy of 190

kJ/mol

This value _is

only slightly higher

than the _activation energy of the

&process

found for

liquid crystalline

side chain

polymers [14].

From these results _{we can} conclude that due to the

single exponential

relaxation behaviour and the

magnitude

of the activation energy, the

poling

_{process is} determined

by

the

&process

of the mesogenic moieties. The

&process

is due to a rotation of the side group around the _main chain _m the direction of the

applied

electric

poling

field All

following

experiments were

performed

_m the

equilibrium

state which _is reached when

switching

_on the

poling

field.

34 STATIC SHG PROPERTIES In

equations (4), (5b)

and

(7b)

_a linear

relationship

between non-linear

susceptibilities

and

applied poling

field and _a

quadratic relationship

between second harmonic intensity and

applied poling

field _is

predicted.

From low molar

mass systems it _is known that the

intensity

of the laser field _can influence the onentation of the director.

Depending

on the laser field

strength

a director reorientation can occur which

can be

easily recognized

if the

predictions

made _m

equations (4), (5b)

and

(7b)

are not fulfilled

[15].

To

verify

whether director reorientation _{occurs m} the elastomer the behaviour of the second harmonic _{as a} function of the incident laser power

respectively

_{as a} function of the

applied poling

field _was

investigated. Figures

7 and 8 indicate _a

quadratic dependence

of the second harmonic _on the incident laser power as well _{as on} the electric

poling

field

strength

This _{is m} agreement ^{with the}

prediction

_{m equations}

(5b)

and

(7b)

and proves that

no director reorientation processes occur. The elastomer behaves similar to a conventional organic material _in the

crystalline

state.

-- 1

-~

~

~ ₆

6 w

a. 25 a. a a. as a. 4 a. 45

j~-

^I

*iQ3 /~-

^l

Fig

6 Activation

diagram

from second harmonic intensity versus time

lK° 5 SHG IN A

LIQUID-CRYSTALLINE

ELASTOMER 567

m

tO ₆

'

'~ N

e

C~Q

FR

o

o

' 12 lu) la,u,

Fig.

7 - Second

linear fit

m

t~ /

' ,

j

m

/

i~

~ /~

o

o i z a

El _la.u.

Fig

8 Second harmonic intensity versw square of electnc

poling

field, (li) measured points,

(-)

linear fit

JOURNAL DE PHYSIQUF -T N' MAT 199> N

568 JOURNAL DE

PHYSIQUE

II lK° 5

35 MAKER _FRINGE EXPERIMENT. To prove whether the second harmonic _can be

descnbed

completely by

_equations

(5b)

and

(7b)

and to determ~ne the second-order

susceptibilities

_xzxx and _x==z the intensity ^{of the second harmonic} wave was measured _{as a} function of the incident

angle (Maker fnnge expenment).

The

expenment

was

performed

for

s- and

p-polanzed

incident

light

at room

temperature

for _a definite

appl~ed pol~ng

field.

Figure

9 shows a

diagram

for

p-polanzed

incident

light.

A

symmetric

increase of second harmonic intensity is observed starting ^{from the 0}

deg. position.

^At

higher angles fnnges

occur

resulting

from the

phase mismatch,

because refractive indices n~

~~, n~~ and

optical path length change continuously by

rotating ^the

sample. Interestingly, sharp fnnges

_are

observed,

wh~ch indicates the uniform director orientation. For

samples having

lower

order, only

the

envelope

of tins _{curve is} observed. To check whether the measured values _can be fitted

by applying

_equations

(5b)

and

(7b)

the refractive indices of the fundamental and second

harmonic _{wave m} the elastomer have to be known. Table I shows the measured refractive indices The

birefnngence

_is 0 at _room temperature. ^With these values and equations

(5b)

and

(7b)

the

expenmental

results of

figure

9 _can be

reproduced

The calculated _{curve is} indicated

by

the solid line _m

figure

9 On the basis of tins fitted _curve and measurements of the absolute intensity ^{of the second harmonic with the} quartz

reference,

the second-order

susceptibilities

are determ~ned For _a

poling

field of 19

V/~m

_we found x=z= = 0 92

pm/V

and x=xx = 0.06

pm/V

The ratio of

x~~jx===

is about

1/15.3 indicating

that the state of order of the elastomer _is w~tlun the

limiting

_cases of _an isotropic

poled

and _an

Ismg poled

field system

(Eqs (4)).

The value _is in

good agreement

^{with the values found for}

doped polymer

films in _a smectic A

phase [12].

5

6

~~i

H

6

6

6 o

52.

ANGLE/deq.

Fig

9 Maker

fnnge diagram

for

p-polanzed

^incident

light

_;

(li)

measured points,

(-)

calculated

curve

M 5 SHG IN A LIQUID-CRYSTALLINE ELASTOMER 569

Table I.

Refractive

indices _as calculated

from

measurements

ofthe angle oftotal reflection for dfferent wavelengths of light

A/nm

_{n~ no}

532 1.608 1.494

632.8 1.598 1.485

064 1.580 1.478

4. Conclusion.

We have shown that

liquid crystalline

elastomers _are suitable materials for non-linear

optics.

A uniform director onentation can be

easily

achieved

by

_a

simple

mechanical deformation of the elastomer

avoiding

defect structures which

normally

_{appear m} low molar _mass

hquJd crystals

and

liquid crystalline

side chain

polymers Although

the elastomers _are not _{m a} solid

state but _{m a}

hquJd-crystall~ne

_state, the behav~our _is

comparable

to solid bodies The

network prevents any director reonentation

by

the laser field

strength.

On the _one hand the non-linear

susceptibilities

_can be enhanced

by

vanation of the chemical structure. On the other hand ferroelectnc I-c- elastomers should allow to observe second harmonic generat~on

without any extemal

poling

field

Acknowledgements.

Financial support

by

the Deutsche

Forschungs

Gememschaft and Verband der Chem~schen Industrie _is

gratefully acknowledged

References

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