Volume Transition of ematic els K. Urayama, Y. Okuno* and. Kohjiya* Department of Material Chemistry, Kyoto University, ishikyo-ku, Kyoto 15-8510 *nstitute for Chemical Research, Kyoto University, Uji, Kyoto-fu 11-0011 E-mail: urayama@scl.kyoto-u.ac.jp n the present study, we have investigated the equilibrium swelling and phase behavior of liquid crystalline (LC) polymer networks swollen in isotropic solvents[1] or low molecular mass LCs[2-4]. We have found that the nematic ordering inside the gel induces the discontinuous reduction in gel volume. The side chain LC networks were prepared by radical copolymerization of the mesogenic acrylate monomers and 1,-hexanediol diacrylate (cross-linker). The cylindrical gels with diameter of several hundreds micron were immersed in each solvent, and the swelling was equilibrated at each temperature. The measurement of degree of equilibrium swelling and the phase observation were made by polarlizing microscopy. Figure 1 and 2 display the equilibrium swelling-temperature curves of the LC gels in di-nalkyl phthalates (isotropic solvents) and a low molecular mass LC, respectively. n di-n-amyl phthalate or di-n-butyl phthalate, the swollen isotropic gel is discontinuously transformed into the shrunken nematic gel at a characteristic temperature ( ). n the nematic solvent, the system has two independent nematic-isotropic transition temperatures: One is that inside the gel ( ), and the other is that outside the gel (i.e., for pure nematic solvent) ( ). The LC network and the nematic solvent inside the gel form a single nematic phase below. As in the case of isotropic solvents, the nematic ordering inside the gel drives the discontinuous volume decrease at. n the range < T < 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 where the nematic ordering outside the gel takes place. n the totally isotropic and nematic phases at T > and T <, 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 the swelling of LC gel. Essentially the same behavior is observed in the LC networks composed of dissimilar mesogens and different nematic solvents, which indicates that the swelling and phase characteristics observed are universal for nematic gel in nematic solvent with >. 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,. Kohjiya, Macromolecules, 3,229 (2003). [2] K. Urayama, Y. Okuno, T. Kawamura,. Kohjiya, Macromolecules, 35, 457 (2002). [3] K. Urayama, Y. Okuno, T. akao,. Kohjiya, J. Chem. Phys., 118, 2903 (2003). [4] Y. Okuno, K. Urayama,. Kohjiya, J. Chem. Phys., 118, 9854 (2003). [5] M. Warner, X. J. Wang, M, Macromolecules, 25, 445 (1992). [] X. J. Wang, M. Warner, Macromol. Theory imul., 37 (1997). [7] A. Matsuyama, T. Kato, J. Chem. Phys., 114, 3817 (2001).[8] Matsuyama, A., Kato, T., J. Chem. Phys., 11, 8175 (2002). Equilibrium swelling degree Q isotropic, swollen 25 30 35 40 45 50 55 0 5 70 T / o C nematic, shrunken Fig. 1. Equilibrium swelling-temperature curves of a liquid crystalline gel swollen in di-n-amyl phthalate (DAP) and di-n-butyl phthalate (DBP). Equilibrium swelling degree Q 18 1 14 12 10 8 4 2 el olvent Crossed Polarized Un-crossed Polarized 0 48 50 52 54 5 58 0 2 4 8 70 Temperature / C Fig. 2. Equilibrium swelling-temperature curve of a liquid crystalline gel swollen in a low molecular mass liquid crystal. The insets show the optical micrographs of the gels in the corresponding temperature regions. The arrows indicate the boundary of the gel surface.
Volume Transition of ematic els K. Urayama, Y. Okuno Arai,*. Kohjiya* Department of Material Chemistry *nstitute for Chemical Research Kyoto University JAPA
wollen and hrunken tates of el hrunken wollen temperature, solvent compositions, ph,...etc swelling equilibriumbalance between attractive and repulsive forces on network rubber elastic forceattractive isotropic mixing interaction (repulsive (good solvent) ionic force hydrophobic interaction hydrogen bonding
welling of ematic etworks presence of nematic interaction nematic network + isotropic solvent nematic network + nematic solvent nematic network isotropic solvent nematic network nematic solvent isotropic ( = 0 ) isotropic ( = 0 ) D D nematic ( > 0 ) nematic ( 0 < < 1 ) Correlation between swelling and phase behavior
Experimental ample preparation * LC monomer () O * tyrene monomer (t) * cross-linker1 mol% O * initiator (AB ) 1 mol% diameter 0.4 mm O CH 2 O COO OCH 3 O CH 2 O O ample... LC-100/0totally composed of LC-90/10comprising (90 mol%) and t (10 mol%) Polymerization ( 80 C, 48 h ) wash dry immersed in solvents welling solvent... di-n-alkyl phthalate DEP ( a = 1 ) DBP ( a = 3 ) COO CH 2 a CH n 3 DAP ( a = 4 ) DOP ( a = 7 ) COO CH 2 an CH 3 Polarlizing Microscopy as a function of temperature (by ikon E00POL & Linkam LK-00PM) Equilibrium swelling degree (Q) : Q = V / V 0 = (d / d 0 ) 3 d : diameter of fully swollen gel d 0 : diameter of dry gel
welling of nematic network in isotropic solvents 15 LC-90/10 DEP (cooling) DBP(a = 3), DAP(a = 4) Discontinuous shrinking into the nematic state at Equilibrium swelling degree Q 13 11 9 7 5 3 isotropic, swollen DBP (cooling) DAP (cooling) DOP (cooling) Crossed Polarizers LC-90/10 in DAP Uncrossed Polarizers 47.9 o C 48.1 o C ematic ordering-induced volume transition nematic, shrunken 1 20 30 40 50 0 70 80 90 100 Temperature / o C T (DBP: 31.3 o C, DAP: 47.9 o C, DOP: 79.8 o C) As Q in the isotropic phase increases, decreases. dilution effect of nematicity
chematics for nematic ordering-induced volume transition T olvent el mesogen on gel = 0 : orientational order prameter discontinuous volume reduction driven by nematic ordering 1 > 0 0 Temperature
Mean field theory for nematic network in isotropic solvents ( Warner et al. 1992,Matsuyama et al. 2001) F = F el + F mix + F nem F el : elastic free energy of nematic network F el F mix F nem ( k B T t ) = 3 2n È Ê Í f Í Á Î Ë ( 1+ 2 m ) 1- m ( ) 2 ˆ 1 3 ( k B T t ) = ( 1-f)ln( 1-f) + cf ( 1-f) ( k B T t ) = f m n m Ú ( ) f q m ( )( 1- m ) 2 + 1 3 ln 1+ 2 m F mix : free energy of mixing of network with solvent F nem : free energy of nematic ordering ln4p f ( q m )dw m - 1 2 n mmf 2 2 m m kb : Boltzmann constant T : absolute temperature t : total number of the unit cells inside the gel f ( = 1/Q ) : volume fraction of the network m ( = P 2 (cosq ) f(q ) dw ) : nematic (orientational) order parameter for mesogen n ( = (n m + n s )t ) : number of the segments on a network chain n m : number of sites (segments) occupied by a mesogen n s : number of sites (segments) occupied by a non-mesomorphic unit (spacer) t : number of a repeating unit c ( ~ A / ( k B T ) ) : Flory-Huggins parameter characterizing the mixing interactions between network and solvent f m : volume fraction of mesogen n mm ( U / ( k B T )) : Maier-aupe interaction parameter between the mesogens
m 0 (f, m ) = m 0 o Equilibrium-swelling condition equality of chemical potentials of the solvents inside and outside the gel self-consistent equation for m m = 1 Ê 3 Z m 2 cos2 q m - 1 ˆ Ï Ê 3 Ú Á exp h Ë 2 m 2 cos2 q m - 1 ˆ Ì Á Ó Ë 2 d cosq m with h m = n m n mm f m m - Ï Ô È 3n m f Ì Í nf m ( 1+ 2 m )( 1- m ) 2 Ô Í ( 1+ 2 m )( 1- m ) 2 Ó Î 1/ 3 Ô -1 Ô m ( 1- m )
Comparison of the experimental data with the theoretical prediction Equilibrium swelling degree Q 13 11 9 7 5 3 1 0.9 0.95 1 1.05 1.1 1 T/ (DAP) LC-90/10 in DAP LC-90/10 in DBP Theoretical c 1 /n = 0.19, c 2 /n = -0.475 c 1 /n = 0.15, c 2 /n = -0.375 c = c 1 / T + c 2 / T 2 Fitting parameters n =30 0, n m = 2.75, n 0 = 1.0, p = 0.154 c. Order parameter m 0.8 0. 0.4 0.2 0 0.9 0.95 1 1.05 1.1 T/T (DAP)
nematic network + nematic solvent nematic network nematic solvent isotropic phase ( = 0 ) D nematic phase ( 0 < < 1 )
Experimental ample preparation * LC monomer or ample composition ( mol % ) crosslinker AB toluene ( ml / mmol ) O O CH 2 O COO OMe LC- 98-1 1 218 LC- - 98 1 1 251 O CH 2 O O * crosslinker O O * initiator AB CH 2 C O O polymerization ( 80 C, 48 h ) H 3 C washing swelling in LC or CH 2 COO C drying diameter 0.4 mm H 3 C CH 2 O 5 C Polarlizing microscopy as a function of temperature degree of equilibrium swelling Q = V / V 0 = ( d / d 0 ) 3 d : diameter of equilibrium swollen gel d 0 : diameter of dry gel
welling of nematic network in nematic solvent LC- Phase of LC mesogen on gel solvent inside gel solvent outside gel single nematic phase Equilibrium swelling degree Q C B 18 1 14 12 10 8 4 el olvent 2 0 Crossed Polarized Un-crossed Polarized 48 50 52 54 5 58 0 2 4 8 70 Temperature / C A volume transition induced by nematic ordering inside gel (T = ) reswelling upon cooling ( < T < ) continuous volume change at nematic ordering outside gel (T = )
LC- Phase of LC mesogen on gel solvent inside gel solvent outside gel single nematic phase 7 C B A volume transition ( T = ) Equilibrium swelling degree Q 5 4 3 cooling heating reentrant swelling continuous volume change at no significant thermal hysteresis in swelling and phase behavior 2 45 50 55 0 5 70 75 80 Temperature ( C )
LC - V nematic network in similar nematogen Phase of LC mesogen on gel solvent inside gel solvent outside gel single nematic phase Equilibrium swelling degree Q C B 8 7.5 7.5 70 72 74 7 78 80 82 84 8 88 Temperature ( C ) A essentially similar swelling and phase behavior as that of the LC networks in dissimilar nematogens Figure 4. Equilibrium swelling degree ( Q ) of LC- in nematic liquid crystalline solvent as a function of temperature. ( = 79. C, = 74.9 C )
chematics for correlation between swelling and phase behavior T olvent el mesogen on gel LC sovlent A m = 0 = b = 0 : orientational order prameter discontinuous volume change (volume transition) driven by nematic ordering inside gel m = mc > 0 0 = 0c > 0 b = 0 1 C B A B reswelling induced by an increase in nematic order m b m > mc 0 > 0c b = 0 0 C continuous volume change at nematic ordering outside gel m > 0 0 > 0 b = bc > 0 0 Temperature
Mean Field Theory of ematic etwork in ematic olvent (Warner et al. 1997, Matsuyama et al. 2001 ) F = F el + F mix + F nem F el : elastic free energy of nematic network F el ( k B T t ) = 3 2n È Ê Í f Á Î Í Ë ( 1 + 2 m ) 1 - m ( ) 2 F mix : free energy for isotropic mixing ˆ 1 3 ( )( 1 - m ) 2 + 1 3 ln 1+ 2 m t : number of total unit cells f ( = 1/Q ) : volume fraction of network A ( 1 + 2 m )( 1 - m ) 2 m ( = P 2 (cosq ) f i (q ) dw ) : order parameter of mesogen on network f m : orientational distribution function for mesogen n ( = (n m + n s )t ) : total segments between cross-links n m : axial ratio of mesogen on gel n s : number of segements of non-mesomorphic units t : number of repeating units between cross-links F mix ( ) = 1- f k B T t ( ) n 0 ln( 1- f) + c ( 1- f s )f s c ( ~ A / ( k B T ) ) : Flory-Huggins parameter for spacer/nematogen n 0 : axial ratio of nematic solvent f : volume fraction of spacer F nem : free energy for nematic ordering F nem / t kt = Â i = m,0 f i n i f(q i ) ln4pf (q i )dw i - 1 2 n mmf 2 m 2 m - 1 2 n 00( 1 - f) 2 2 0 - n m0 f m ( 1 - f) m 0 0 : order parameter of solvent inside gel; f m : volume fraction of mesogen n ij ( U ij / ( k B T ), i, j = m, 0 ) : Maier-aupe interaction parameters
m 0 (f, m, 0 ) = m 0 o ( b ) Equilibrium-swelling condition equality of chemical potentials of the solvents inside and outside the gel self-consistent equations for m, 0, b i = 1 Ê 3 Z i 2 cos2 q i - 1 ˆ Ï Ê 3 Ú Á exp h Ë 2 i 2 cos2 q i - 1 ˆ Ì Á Ó Ë 2 dcosq i (i = m,0,b) h m = n m [ n mm f m m + n m0 ( 1- f) 0 ] - Ï Ô È 3n m f Ì Í nf m ( 1+ 2 m )( 1- m ) 2 Ô Í ( 1+ 2 m )( 1- m ) 2 Ó Î 1/ 3 Ô -1 Ô m ( 1- m ) h 0 = n 0 [ n mm f m m + n 00 ( 1- f) 0 ] h b = n 0 n 00 b
Comparison of experimental data with theoretical prediction Q 0.7 0. 0.5 0.4 0.3 0.2 0.1 0 45 50 55 0 5 70 18 1 14 12 10 8 4 2 0 C LC- n = 120, n 0 = 2.5, n s = 0.98, n m = 3.3, B T A m 0 b 45 50 55 0 5 70 T n 00 /c = 0.5, n mm / n 00 = 1.05, n m0 / n 00 = 0.99 mmesogen on gel 0 solvent inside gel b solvent outside gel Mesogen on gel and solvent inside gel simultaneously transform into nematic phase. (single nematic phase formation) order parameter ( ) as a function of temperature swelling degree (Q ) as a function of temperature Discontinuous volume reduction (T = ) is caused by nematic ordering inside gel Reswelling ( < T < ) is induced by an increase in nematic order inside gel ( m, 0 ). m = 0 mc 0 = 0 0c at
LC- n = 25, n 0 = 2.5, n s = 0.9, n m = 5.1, n 00 /c = 0.2, n mm / n 00 = 1.0, n m0 / n 00 = 0.94 LC- n = 120, n 0 = 2.55, n s = 0.98, n m = 3.3, n 00 /c = 1.0, n mm / n 00 = 1.0, n m0 / n 00 = 0.985 1 0.8 0. m 0 b 0.8 0.7 0. 0.5 0.4 m 0 b 0.4 0.3 0.2 0.2 0.1 Q 7.0.0 5.0 4.0 3.0 2.0 0 40 50 0 70 80 C T B A Q 0 5 70 75 80 85 90 24 22 20 18 1 14 12 10 8 C B T A 1.0 40 50 0 70 80 T 5 70 75 80 85 90 T
ummary welling characteristics of nematic networks Volume transition resulting from isotropic-nematic transition inside gel (ematic ordering drives a discontinuous reduction in gel volume) n nematic solvents, reswelling upon cooling in the range T < T < continuous volume change at isotropic-nematic transition outside gel welling of nematic network is mainly governed by nematic order. A mean field theory successfully describes the experimental results.
Thermal hysteresis - LC-90/10 in DBP, DAP - Equilibrium swelling degree Q 13 11 9 7 5 3 DBP (cooling) DAP (cooling) DBP (heating) DAP (heating) Heating Process is shifted to higher temperature region. (DBP: +10 o C, DAP: +4 o C) The - transition and accompanied volume change are broadened. broad size distribution of nematic domains? 1 20 30 40 50 0 70 80 Temperature / o C
Effects of cross-linking density LC--C x / Equilibrium swelling degree Q 18 1 14 C x = C 1= 1 C x = C 1.5 = 1.5 C C = 3 x = 3 C C = 10 x = 10 T 12 10 8 4 2 0 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 An increase in cross-linking density yields reduction in swellability shift of T to higher temperatures decrease in magnitude of discontinuous volume change C x = 10 (high cross-linking density) Q is almost independent of temperature. o significant volume change takes place at T. T/
Comparison of the theory with the data (cross-linking density effect) Equilibrium swelling degree Q 20 15 10 5 LC--C x / C x = 1 Theoretical C x = 1.5 n = 900, n m = 2.75 C x = 3 n = 400, n m = 2.74 C x = 10 n = 10, n m = 2.73 Fitting parameters n = 900, n m = 2.75, n 0 = 2.5, p = 0.14, n 00 /c = 0.3, n mm / n 00 = 1.24, n m0 / n 00 = 1.003 variable parameters: n : segment numbers between cross-links cross-linking density n m : axial ratio of mesogen original nematicity of nematic network (for dry gel) 0 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 T/ The theory successfully describes the effects of cross-linking density.