Volume Transition of Nematic Gels

K. Urayama, Y. Okuno* and S. Kohjiya*Department of Material Chemistry, Kyoto University, Nishikyo-ku, Kyoto 615-8510

*Institute for Chemical Research, Kyoto University, Uji, Kyoto-fu 611-0011E-mail: urayama@scl.kyoto-u.ac.jp

In the present study, we have investigated the equilibrium swelling and phase behavior ofliquid crystalline (LC) polymer networks swollen in isotropic solvents[1] or low molecular massLCs[2-4]. We have found that the nematic ordering inside the gel induces the discontinuous reductionin gel volume.

The side chain LC networks were prepared by radical copolymerization of the mesogenicacrylate monomers and 1,6-hexanediol diacrylate (cross-linker). The cylindrical gels with diameter ofseveral hundreds micron were immersed in each solvent, and the swelling was equilibrated at eachtemperature. The measurement of degree of equilibrium swelling and the phase observation were madeby polarlizing microscopy.

Figure 1 and 2 display the equilibrium swelling-temperature curves of the LC gels in di-n-alkyl phthalates (isotropic solvents) and a low molecular mass LC, respectively. In di-n-amyl phthalateor di-n-butyl phthalate, the swollen isotropic gel is discontinuously transformed into the shrunkennematic gel at a characteristic temperature (TNI

G). In the nematic solvent, the system has twoindependent nematic-isotropic transition temperatures: One is that inside the gel (TNI

G), and the other isthat outside the gel (i.e., for pure nematic solvent) (TNI

S). The LC network and the nematic solventinside the gel form a single nematic phase below TNI

G. As in the case of isotropic solvents, the nematicordering inside the gel drives the discontinuous volume decrease at TNI

G. In the range TNIS < T < TNI

G

where the LC phases inside and outside the gel are different, i.e., nematic and isotropic, respectively,the degree of swelling increases again upon cooling. The swelling curve exhibits the inflection at TNI

S

where the nematic ordering outside the gel takes place. In the totally isotropic and nematic phases at T> TNI

G and T < TNIS, respectively, the temperature dependence of the degree of swelling is weak. The

degree of swelling is dominated by nematic order of each LC molecule, which is characteristic of theswelling of LC gel. Essentially the same behavior is observed in the LC networks composed ofdissimilar mesogens and different nematic solvents, which indicates that the swelling and phasecharacteristics observed are universal for nematic gel in nematic solvent with TNI

G > TNIS. The swelling

and phase behavior observed is well described by a mean field theory for nematic gel [5-8].

References: [1] K. Urayama, Y. Okuno, S. Kohjiya, Macromolecules, 36,6229 (2003). [2] K. Urayama, Y. Okuno,T. Kawamura, S. Kohjiya, Macromolecules, 35, 4567 (2002). [3] K. Urayama, Y. Okuno, T. Nakao, S. Kohjiya, J.Chem. Phys., 118, 2903 (2003). [4] Y. Okuno, K. Urayama, S. Kohjiya, J. Chem. Phys., 118, 9854 (2003). [5] M.Warner, X. J. Wang, M, Macromolecules, 25, 445 (1992). [6] X. J. Wang, M. Warner, Macromol. Theory Simul. 6,37 (1997). [7] A. Matsuyama, T. Kato, J. Chem. Phys., 114, 3817 (2001).[8] Matsuyama, A., Kato, T., J. Chem.Phys., 116, 8175 (2002).

0

2

4

6

8

10

12

25 30 35 40 45 50 55 60 65 70

(90/10)/DAP

(90/10)/DBP

Equi

libriu

m s

wellin

g de

gree

Q

T / oC

TNIG

TNIG

isotropic, swollen

nematic, shrunken 0

2

4

6

8

10

12

14

16

18

48 50 52 54 56 58 60 62 64 66 68 70

Equi

libriu

m s

wellin

g de

gree

Q

Temperature / ˚C

TNIG

TNIS

Crossed Polarized Un-crossed Polarized

Gel Solvent

Fig. 1. Equilibrium swelling-temperature curves of aliquid crystalline gel swollen in di-n-amyl phthalate(DAP) and di-n-butyl phthalate (DBP).

Fig. 2. Equilibrium swelling-temperature curve of a liquidcrystalline gel swollen in a low molecular mass liquidcrystal. The insets show the optical micrographs of the gelsin the corresponding temperature regions. The arrowsindicate the boundary of the gel surface.

Volume Transition of Nematic Gels

K. Urayama, Y. Okuno Arai,* S. Kohjiya*

Department of Material Chemistry*Institute for Chemical ResearchKyoto UniversityJAPAN

temperature, solvent compositions, pH, ...etc

Shrunken Swollen

Swollen and Shrunken States of Gel

swelling equilibrium　＝　balance between attractive and repulsive forces on network

＊rubber elastic force　（attractive）＊isotropic mixing interaction (repulsive (good solvent)）

＊ionic force＊hydrophobic interaction＊hydrogen bonding

?

Swelling of Nematic Networks

＊ presence of nematic interaction

nematicnetwork

TNIG

nematicsolvent

TNIS

isotropic( S = 0 )

nematic( 0 < S < 1 )

D

nematic network + nematic solvent

nematicnetwork

TNIG

isotropicsolvent

isotropic( S = 0 )

nematic( S > 0 )

D

nematic network + isotropic solvent

Correlation between swelling and phase behavior

diameter ≈ 0.4 mm

* LC monomer (I)

* initiator (AIBN ) ：1 mol%

Sample preparation

wash dry

Polarlizing Microscopy as a function of temperature (by Nikon E600POL & Linkam LK-600PM)

Equilibrium swelling degree (Q) : Q = V / V0 = (dS / d0)3

Polymerization ( 80 ˚C, 48 h )

dS : diameter of fully swollen geld0 : diameter of dry gel

* cross-linker：1 mol%

Experimental

… Swelling solvent ... di-n-alkyl phthalate 　・DEP ( a = 1 ) 　・DBP ( a = 3 )　 ・DAP ( a = 4 )　　 ・DOP ( a = 7 )

* Styrene monomer (St)

… Sample ... ・LCN-100/0：totally composed of I ・LCN-90/10：comprising I (90 mol%) and St (10 mol%)

OO CH2 O COO OCH36

OO CH2 O

O6

immersed in solvents

COO

COO

CH2

CH2

CH3

CH3

n

n

a

a

＊ DBP(a = 3) , DAP(a = 4) Discontinuous shrinking into the nematic state at TNI

G

＊ As Q in the isotropic phase increases,TNI

G decreases.

dilution effect of nematicity

Swelling of nematic network in isotropic solventsEq

uilib

rium

swe

lling

degr

ee

Q

Temperature / oC

LCN-90/10

1

3

5

7

9

11

13

15

20 30 40 50 60 70 80 90 100

DEP (cooling)

DBP (cooling)

DAP (cooling)

DOP (cooling)

TNIG

TNIG

TNIG

TNIG (DBP: 31.3 oC, DAP: 47.9 oC, DOP: 79.8 oC)

LCN-90/10 in DAP

47.9 oC 48.1 oC

Crossed Polarizers Uncrossed Polarizers

isotropic, swollen

nematic, shrunken

Nematic ordering-inducedvolume transition

Schematics for nematic ordering-induced volume transition

T

S = 0

mesogen on gel

I S > 0N

TNIG・・discontinuous volume reduction driven by nematic ordering

Solvent

I I

Gel

S : orientational order prameter

S

TNIG

Temperature

1

0

†

Fel kBTN t( ) =3

2nf

1+ 2Sm( ) 1- Sm( )2

Ê

Ë Á Á

ˆ

¯ ˜ ˜

1 3

+13

ln 1+ 2Sm( ) 1- Sm( )2È

Î

Í Í

˘

˚

˙ ˙

†

Fmix kBT N t( ) = 1-f( ) ln 1-f( ) + cf 1-f( )

†

Fnem kBTN t( ) =fm

nm

f qm( )Ú ln4p f qm( )dWm -12

n mmfm2 Sm

2

＊ Fel : elastic free energy of nematic network

＊ Fmix : free energy of mixing of network with solvent

＊ Fnem : free energy of nematic ordering

F = Fel + Fmix + FnemkB : Boltzmann constantT : absolute temperatureNt : total number of the unit cells inside the gelf ( = 1/Q ) : volume fraction of the networkSm ( = ∫ P2 (cosq ) f(q ) dW ) : nematic

(orientational) order parameter formesogen

n ( = (nm + ns )t ) : number of the segments on anetwork chain

nm : number of sites (segments) occupied by amesogen

ns : number of sites (segments) occupied by anon-mesomorphic unit (spacer)

t : number of a repeating unitc ( ~ A / ( kBT ) ) : Flory-Huggins parameter

characterizing the mixing interactionsbetween network and solvent

fm : volume fraction of mesogennmm ( ≡ U / ( kBT )) : Maier-Saupe interaction

parameter between the mesogens

( Warner et al. 1992,　Matsuyama et al. 2001)Mean field theory for nematic network in isotropic solvents

Equilibrium-swelling condition

†

m0(f,Sm ) = m0o

• equality of chemical potentials of the solvents inside and outside the gel

• self-consistent equation for Sm

†

Sm =1

Zm

32

cos2 qm -12

Ê

Ë Á

ˆ

¯ ˜ Ú exp hm

32

cos2 qm -12

Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

dcosqm

†

hm = nmn mmfmSm -3nm

nfm 1+ 2Sm( ) 1- Sm( )2f

1+ 2Sm( ) 1- Sm( )2

È

Î Í Í

˘

˚ ˙ ˙

1/ 3

-1Ï Ì Ô

Ó Ô

¸ ˝ Ô

˛ Ô Sm 1- Sm( )with

＊ The nematic ordering of the gel (a jump of S)induces a discontinuous decrease in gel volume.

＊ The difference of TNIG in DAP and DBP is primarily

due to the difference in c.

＊ In the shrunken nematic state, Theory (mono-domain) Experimental (poly-domain)

Q ≈ 1 Q ≈ 2 (almost full shrinking) (including 50 vol% solvent)

LCN-90/10 in DAP LCN-90/10 in DBPTheoretical c1/n = 0.19, c2 /n = -0.475 c1/n = 0.15, c2/n = -0.375

1

3

5

7

9

11

13

0.9 0.95 1 1.05 1.1

Equi

libriu

m s

wellin

g de

gree

Q

T/TNIG(DAP)

n =30 0, nm = 2.75, n0 = 1.0, p = 0.154Fitting parameters

0

0.2

0.4

0.6

0.8

1

0.9 0.95 1 1.05 1.1

Ord

er p

aram

eter

Sm

T/TNIG(DAP)

Comparison of the experimental data with the theoretical prediction

c = c1/ T + c2/ T2

nematic network

TNIG

nematicsolvent

TNIS

isotropicphase( S = 0 )

nematicphase

( 0 < S < 1 )

D

nematic network + nematic solvent

diameter ≈ 0.4 mm

* LC monomer Ⅰ or Ⅱ

* initiator AIBN

＊ Sample preparation

washing drying

swelling in LC Ⅲ or Ⅳ

composition ( mol % )Sample

Ⅰ Ⅱ crosslinker AIBNtoluene

( ml / mmol )

LCN-Ⅰ 98 - 1 1 218LCN-Ⅱ - 98 1 1 251

polymerization( 80 ˚C, 48 h )

＊ Polarlizing microscopy as a function of temperature

Q = V / V0 = ( dS / d0 )3dS : diameter of equilibrium swollen gel

d0 : diameter of dry gel

Ⅰ

Ⅱ

* crosslinker

Ⅲ

Ⅳ

O CNOO

CH2 6

OOO

CH2O

6

CNH3C CH2 O5

OMeCOOO6CH2OO

COO6CH2H3C CN

degree of equilibrium swelling

Experimental

0

2

4

6

8

10

12

14

16

18

48 50 52 54 56 58 60 62 64 66 68 70

Equi

libriu

m s

wellin

g de

gree

Q

Temperature / ˚C

LCN-I／IIIPhase of LC

TNIGTNI

S

N

N

I

IN I

mesogen on gelsolvent inside gelsolvent outside gel

＊ volume transition induced by nematic ordering inside gel (T = TNI

G )　

＊ reswelling upon cooling (TNI

S < T < TNIG )

ABC

＊ single nematic phase

Crossed Polarized Un-crossed Polarized

Gel Solvent＊ continuous volume change at nematic ordering outside gel (T =TNI

S )

Swelling of nematic network in nematic solvent

2

3

4

5

6

7

45 50 55 60 65 70 75 80

coolingheating

LCN-II／III

Phase of LC

Equi

libriu

m s

wellin

g de

gree

Q

Temperature ( ˚C )

N

N

I

IN I

＊ volume transition ( T = TNIG )　

＊ reentrant swelling

TNIGTNI

S

ABC

no significant thermal hysteresis inswelling and phase behavior

mesogen on gelsolvent inside gelsolvent outside gel

＊ single nematic phase

＊ continuous volume change at TNIS

6

6.5

7

7.5

8

70 72 74 76 78 80 82 84 86 88

Figure 4. Equilibrium swelling degree ( Q ) of LCN-II innematic liquid crystalline solvent Ⅳ as a function of temperature.(TNI

G = 79.6 ˚C , TNIS = 74.9 ˚C )

Equi

libriu

m s

wellin

g de

gree

Q

Temperature ( ˚C )

LCN - II／ IV

Phase of LC

TNIGTNI

S

N

N

I

IN I

＊essentially similar swelling and phasebehavior as that of the LC networks indissimilar nematogens

ABC

mesogen on gelsolvent inside gelsolvent outside gel

＊ single nematic phase

・・・・nematic network in similar nematogen

Schematics for correlation between swelling andphase behavior

TSolvent

I Sm = S0 = Sb = 0

mesogen on gelLC sovlent

I

Gel

・・・ reswelling induced by an increase in nematic order

ISm > SmcS0 > S0cSb = 0

N

TNIS・・continuous volume change at nematic ordering outside gel

NSm > 0S0 > 0Sb = Sbc > 0

N

ISm = Smc > 0S0 = S0c > 0Sb = 0

N

TNIG・・discontinuous volume change (volume transition) driven by nematic ordering inside gel

A

B

C

S : orientational order prameter

S

Sm

S0

Sb

TNIGTNI

S

Temperature

1

0

ABC

Mean Field Theory of Nematic Network in Nematic Solvent(Warner et al. 1997, Matsuyama et al. 2001 )

Fmix k BTN t( ) =1- f( )n0

ln 1- f( ) + c 1- f s( )fs

＊ Fel : elastic free energy of nematic network

＊ Fmix : free energy for isotropic mixing

＊ Fnem : free energy for nematic ordering

c ( ~ A / ( kBT ) ) : Flory-Huggins parameter for spacer/nematogen

n0 : axial ratio of nematic solventfS : volume fraction of spacer

S0: order parameter of solvent inside gel; fm: volume fraction of mesogennij ( ≡ Uij / ( kBT ), i, j = m, 0 ) : Maier-Saupe interaction parameters

F = Fel + Fmix + FnemNt : number of total unit cellsf ( = 1/Q ) : volume fraction of networkA ≡ ( 1 + 2Sm )( 1 - Sm )2

Sm ( = ∫ P2 (cosq ) fi(q ) dW ) : order parameter ofmesogen on networkfm: orientational distribution function for mesogenn ( = (nm + ns )t ) : total segments between cross-linksnm : axial ratio of mesogen on gelns : number of segements of non-mesomorphic unitst : number of repeating units between cross-links

Fnem / NtkT =fi

nif (qi )

i = m,0Â ln4pf (qi )dWi -

12

nmmfm2 Sm

2 -12

n00 1 - f( )2 S02 - nm0fm 1 - f( )SmS0

Fel kB T Nt( ) =3

2nf

1 + 2Sm( ) 1 - Sm( ) 2

Ê

Ë Á

ˆ

¯ ˜

1 3

+13

ln 1+ 2Sm( ) 1 - Sm( )2È

Î Í Í

˘

˚ ˙ ˙

Equilibrium-swelling condition

†

m0(f,Sm ,S0) = m0o(Sb )

• equality of chemical potentials of the solvents inside and outside the gel

• self-consistent equations for Sm, S0, Sb

†

Si =1Zi

32

cos2 qi -12

Ê

Ë Á

ˆ

¯ ˜ Ú exp hi

32

cos2 qi -12

Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

d cosqi

†

hm = nm n mmfmSm + n m0 1- f( )S0[ ] -3nm

nfm 1+ 2Sm( ) 1- Sm( )2f

1+ 2Sm( ) 1- Sm( )2

È

Î Í Í

˘

˚ ˙ ˙

1/ 3

-1Ï Ì Ô

Ó Ô

¸ ˝ Ô

˛ Ô Sm 1- Sm( )

†

h0 = n0 n mmfmSm + n 00 1- f( )S0[ ]

†

hb = n0n 00Sb

(i = m,0,b)

Sm：mesogen on gelS0 ：solvent inside gelSb ：solvent outside gel

・・・order parameter (S ) as a function of temperature

・・・swelling degree (Q ) as a function of temperature

Comparison of experimental data with theoretical prediction

Mesogen on gel and solvent inside gelsimultaneously transform into nematicphase. (single nematic phase formation)

Discontinuous volume reduction (T = TNIG )

is caused by nematic ordering inside gel

Reswelling (TNIS < T < TNI

G) is induced byan increase in nematic order inside gel(Sm,S0).

Sm = 0　→　 Smc

S0 = 0 　→　 S0c at TNI

G

＊

＊

＊

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

45 50 55 60 65 70

SmS0Sb

0

2

4

6

8

10

12

14

16

18

45 50 55 60 65 70

T

Q

TNIGTNI

S

TAC B

S

LCN-Ⅱ／Ⅲ n = 120 , n0 = 2.5 , ns = 0.986 , nm = 3.3 ,n00 /c = 0.5 , nmm / n00 = 1.05, nm0 / n00 = 0.99

n = 120 , n0 = 2.55 , ns = 0.986 , nm = 3.3 ,n00 /c = 1.0 , nmm / n00 = 1.0, nm0 / n00 = 0.985

LCN-Ⅱ／Ⅳ

6

8

10

12

14

16

18

20

22

24

65 70 75 80 85 90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

65 70 75 80 85 90

SmS0Sb

T

SQ

T

TNIGTNI

S

AC B

1.0

2.0

3.0

4.0

5.0

6.0

7.0

40 50 60 70 80

0

0.2

0.4

0.6

0.8

1

40 50 60 70 80

Sm

S0

Sb

T

T

TNIS TNI

GS

Q

AC B

LCN-Ⅰ／Ⅲ

n = 25 , n0 = 2.5 , ns = 0.9 , nm = 5.1 ,n00 /c = 0.2 , nmm / n00 = 1.0, nm0 / n00 = 0.94

＊ Swelling characteristics of nematic networks

　　 ・ Volume transition resulting from isotropic-nematic transition inside gel

(Nematic ordering drives a discontinuous reduction in gel volume)

　　 ・ In nematic solvents,

・ reswelling upon cooling in the range TNIS < T < TNI

G

　　 ・ continuous volume change at isotropic-nematic transition outside gel

＊ Swelling of nematic network is mainly governed by nematic order.

＊ A mean field theory successfully describes the experimental results.

Summary

Thermal hysteresis - LCN-90/10 in DBP, DAP -

Heating Process

＊ TNIG is shifted to higher temperature region.

(DBP: ≈ +10 oC, DAP: ≈ +4 oC)

＊ The N-I transition and accompanied volumechange are broadened.

Equi

libriu

m s

wellin

g de

gree

Q

1

3

5

7

9

11

13

20 30 40 50 60 70 80

DBP (cooling) DBP (heating)DAP (cooling) DAP (heating)

Temperature / oC

broad size distribution ofnematic domains ?

Effects of cross-linking density　 LCN-I-Cx / IIIEq

uilib

rium

swe

lling

degr

ee Q

Cx = 10 (high cross-linking density)＊ Q is almost independent of temperature.　 ＊ No significant volume change takes place at TNI

G.0

2

4

6

8

10

12

14

16

18

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

C = 1

C = 1.5

C = 3

C = 10

T/TNIS

An increase in cross-linking density yields・reduction in swellability・shift of TNI

G to higher temperatures・decrease in magnitude of discontinuous volume change

Cx = 1

Cx = 1.5

Cx = 3

Cx = 10

TNIG

(cross-linking density effect)

n = 900, nm = 2.75, n0 = 2.5, p = 0.14,n00 /c = 0.3, nmm / n00 = 1.24, nm0 / n00 = 1.003

Fitting parameters

0

5

10

15

20

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

Equi

libriu

m s

wellin

g de

gree

Q

T/TNIS

LCN-I-Cx / III

Cx = 1 TheoreticalCx = 1.5 n = 900, nm = 2.75Cx = 3 n = 400, nm = 2.74Cx = 10 n = 160, nm = 2.73

TNIN (for dry gel)

Comparison of the theory with the data

variable parameters:

n : segment numbers between cross-links

nm : axial ratio of mesogen

cross-linking density

original nematicity ofnematic network

The theory successfully describes theeffects of cross-linking density.