Research Article Polar Liquid Crystal Elastomers Cross Linked Far...

Hindawi Publishing CorporationAdvances in Condensed Matter PhysicsVolume 2013 Article ID 752060 11 pageshttpdxdoiorg1011552013752060

Research ArticlePolar Liquid Crystal Elastomers Cross Linked Far fromThermodynamic Phase Transitions Dislocation Loops inSmectic Clusters

Yusril Yusuf1 Shohei Yamaguchi2 Shinya Kawano2 Hirotaka Okabe2 Simon Krause3

Heino Finkelmann3 P E Cladis4 and Shoichi Kai25

1 Physics Department Faculty of Mathematics and Natural Sciences Gadjah Mada University Yogyakarta 55281 Indonesia2 Department of Applied Quantum Physics and Nuclear Engineering Graduate School of Engineering Kyushu UniversityFukuoka 819-0395 Japan

3Makromolekulare Chemie Universitat Freiburg 79104 Freiburg Germany4Advanced Liquid Crystal Technologies PO Box 1314 Summit NJ 07902 USA5Department of Life Engineering Graduate School of Systems Life Sciences Kyushu University Fukuoka 819-0395 Japan

Correspondence should be addressed to Yusril Yusuf yusrilugmacid

Received 5 February 2013 Accepted 16 June 2013

Academic Editor Michael C Tringides

Copyright copy 2013 Yusril Yusuf et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Nematic networks with three different concentrations of polar and nonpolarmesogens and the same concentration of a novel cross-linking agent give rise to unusual liquid single crystal elastomers (LSCEs) that are transparent monodomain nematic networks withsmectic clustersThe largest spontaneous length change is observed in the sample with 70mol of the polarmesogenwhich also hasthe highest glass transition temperature and smectic clusters with a slowly increasing but nearly constant layer spacing on coolingfrom 90∘C to 25∘C X-ray scattering intensity from smectic clusters with layer spacings that monotonically increase on cooling firstincreases to a maximum at 119879lowast sim 60∘C corresponding to clusters of about 30 layers Below 119879lowast the scattering intensity decreases asthe number of layers in a cluster decreases To account for this surprising nonlinear behavior that correlates with nonlinear featuresof the networksrsquo macroscopic spontaneous shape change and birefringence a model is proposed where dislocations form in thelayers at 119879lowast Below 119879lowast more dislocations form to break down the layer structure The possibility of dislocation formation at 119879lowastindependent of mesogenic concentrations is attributed to a conformational change in the crosslinker which is present at the sameconcentration in the three LSCEs

1 Introduction

Liquid crystal states of matter have long range orientationalorder characterized by a director n which can be orientedanywhere in three-dimensional space Liquid crystals arean example of a continuous medium where n is definedeverywhere in the sample except at line defects Neverthelessit is interesting to probe differences between low-molecular-weight nematic liquid crystals familiar as the light switchin flat panel displays and liquid crystal elastomers resultingwhen a low-molecular-weight liquid crystal is polymerizedand cross linked in one process to make a polydomain liquid

crystal elastomer (LCE) [1ndash5] Particulary as following poly-merization and cross linking monodomain LCEs where n islocked in the sample can be prepared and studied [2 4 6 7]The resulting liquid single crystal elastomers (LSCEs) changetheir lengths significantly in the vicinity of the cross-linkingtemperature119879

119888 which can be but need not be [8] within 5K

of the clearing temperature of the liquid crystal phase crosslinked in the elastomer

The notion that cross-linking temperature 119879119888 is a rel-

evant thermodynamic parameter is a novel concept in thefield of liquid crystal elastomers While being not obvious forLSCEs cross linked in the vicinity of the nematic-isotropic

2 Advances in Condensed Matter Physics

CH3

Si O

H

O COO

OCH3

OO

Polymer backbone

Mesogen

Mesogen

Crosslinker

Crosslinker

Polymer backbone

O

C

O

CN

O

n

n

Figure 1 Top sketch of one layer of polar mesogens and itscrosslinker in a side-chain liquid crystal elastomer (LCE) with layerspacing larger than one pendant cyano mesogen Below are thechemical structures of the compounds used to synthesize LSCEfilms300 120583m thick and several cm2 area with 7mol crosslinker and 5070 and 100mol of the polar cyano mesogens respectively CN50CN70 and CN100 Fully extended molecular lengths of the twomesogens are ℓ sim 205ndash21 A Including the siloxane as a chainextender adds another sim2 A to each monomer The layer spacingsare shown in Figure 2

phase transition temperature 119879NI of the LC moieties theirimportance became clearer while studying LCEs cross linkedfar from 119879NI [8 9] and thus is well supported by experi-ments and observations of the elastomers synthesized by theFinkelmann method and this leads to a natural explanationfor the unusual transparency of the monodomain elastomersdiscussed here It also opens the door onto new experimentsand questions concerning the physics of LC elastomers

Elastomers have no liquid phases and no critical fluc-tuations only relaxation dynamics Thus the symmetry ofnematic liquid crystalline elastomers is not the same as itis in low molecular-weight liquid crystals As a result LCEsof the type shown in Figure 1 are important to learn howpolymerization and cross-linking influence liquid crystalorder This is particularly the case for the polar cyanomesogen in Figure 1 where liquid crystal phases appear in theelastomer that did not exist before cross-linking [10]

To learn more about the correlation between liquidcrystalline order at themicroscopic level and themacroscopicproperties of spontaneous length change measured by 120582 nand degree of orientational order measured by birefringenceΔ119899 in the context of previous studies for bifunctional andtrifunctional cross-linked LSCEs [7 11ndash15] we synthesizedLSCEs with the two different mesogenic groups and thenovel cross-linker in Figure 1 with layer spacings in Figure 2and then studied their microscopic structure by synchrotronradiation (Figure 3)

An unusual feature of the elastomers in Figure 3 isthat they are more than 80 transparent at 20∘C near the

27

26

CN100CN70CN50

25

40 60 80

Tlowast

d(A

)

T (∘C)

Figure 2 Layer spacing 119889 (A) versus temperature 119879 (∘C) forsmectic clusters in ∙ CN50X CN70 and 998771 CN100 The data pointsare connected by lines

CN50CN70CN100

120

100

80

60

40

20

050 60 70 80 90 100

Mol CN

Tc

Ti

Tlowast

TgGlass

120585d lt 10 120585d10202530

30

2520

10

T(∘

C)

Figure 3 An overview of the nematic networks of ∙CN50XCN70and 998771 CN100 The solid curves are lines of constant number ofsmectic layers correlated in a cluster 120585119889 (shown to the right of thefigure) with 120585 the layer correlation length and 119889 the layer spacing(Figure 2) measured by synchrotron radiation 120585119889 is maximum(sim283 layers for CN70 and 315 layers for CN100) on the dashedline 119879lowast = 60∘C between CN70 and CN100 compared to about 10layers at119879

119894

where smectic clusters first appear119879119888

is the cross-linkingtemperature 119879

119892

is the glass transition temperature The maximumnumber of correlated layers in CN50 is 12 at sim 40∘C and is onlyabout 2 at 119879

119894

and 10 at 119879119892

The dashed curve for 119879119894

is deduced frommeasurements of spontaneous shape change 120582(119879) measured in theoptical microscope discussed in Section 23 119879

119892

is estimated fromthe 120582(119879)rsquos in Figure 4

Advances in Condensed Matter Physics 3

125

120Ti

Ti

CN70

115

CN50

Tlowast

CN100

110

105

Tlowast

1000 005 010 015 020

120576 = (Tc minus T)(273 + Tc)

120582

Figure 4 Length change data 120582 for998771CN100XCN70 and ∙CN50versus 120576 with 119879

119888

= 942∘C (CN50) 1106∘C (CN70) and 1126∘C

(CN100) plotted as symbols The 120576 ge 0 (119879 ≲ 119879119888

) solid curvessuperposing that the data are 6th-order polynomial fits To comparewith the phase plot in Figure 3 arrows show that 119879lowast = 60∘C for thethree CN compositions and 119879

119894

for CN70 (95∘C) and CN100 (90∘C)For CN50 119879

119894

sim 119879119888

Data for 119879 gt 119879lowast is linear for CN100 up to 120576 sim 02and nonlinear for CN70 (see text for details)

glass transition temperature 119879119892 taking 100 transparency at

130∘C well above 119879

119888 a kind of clearing temperature above

which there are no more changes in Δ119899 and 120582Up to now all the nematic elastomers we studied were

translucent rather than transparent Transparency meansthat the 2D network in a smectic layer is more ordered inthese LSCEs What would be a turbid reentrant nematic inlow-molecular-weight liquid crystals is interpreted for theseelastomers as resulting from dislocation formation leavingbehind a nematic network with enhanced orientational orderwith fewer andor smaller smectic clusters

The values for 119879119892in Figure 3 are estimates based on

an extrapolation of the fits to be discussed in the nextsection for Figure 4 to 119879 = 0

∘C They are about 10 Khigher than those obtained by Kundler and Finkelmann [5]for similar elastomers that did not exhibit reentrant behaviorMore research is needed to understand better the interplaybetween orientational order and a glassy state below 119879

119892 an

interesting but still open question [16] The data in theseexperiments suggests enhancement rather than saturationof orientational order as 119879 rarr 119879

119892 consistent with the

appearance of smectic clusters after polymerization andcross-linking of the cyano mesogen [10]

11 Low-Molecular-Weight Liquid Crystals In low-molecularweight liquid crystals the thermodynamic state callednematic is liquid in all three spatial dimensions so that lighttravels at the same speed in the two directions perpendicular

to n as it also does in the state called smectic A which islayered along the n axis and liquid in the layers similar tosoap bubblesTheoptic axis in low-molecular-weight nematicliquid crystals is unique It is an example of an uniaxial liquidcrystal designated119863

infinℎin group theory where119863 refers to the

n axis which can be oriented anywhere in space (hence thesubscriptinfin) with mirror planes designated by the subscriptℎ

The nematic X-ray diffraction pattern an interferenceprocess requiring information from at least two rays showsonly a diffuse wide angle ring corresponding to moleculardimensions and because of fluctuations in n little to noscattering along n In addition to the long-range orientationalorder of the nematic phase smectic A liquid crystals havelayers with spacing typically a molecular length 20ndash35 Acompared to aboutsim5 A corresponding to amolecularwidthAs a result in the small angle limit X-ray diffraction bysmectic layers in low-molecular-weight liquid crystals arenearly resolution-limited peaks along n [17] that is its lineshape or structure factor the Fourier transform of a freeenergy is a sharply peaked Lorentzian function [18] withdiffuse scattering on a wide ringperp n for a 2D isotropic liquid

The nematic-to-smectic A phase transition has beenstudied in great detail in low-molecular-weight liquid crys-tals see for example Chapter 6 in [19] It is a first-orderphase transition because fluctuations in the smectic A-orderparameter opens a gap in the spectrum of orientationalfluctuations of n [20]When the gap is small X-ray scatteringin the small angle limit grows from essentially nothing inthe nematic phase far below the transition temperature tothe smectic A phase 119879NA with a Lorentzian structure factorof characteristic width usually denoted by 1120585 that narrowscontinuously on approaching the transition temperature tothe smectic A phase that is 1120585 rarr 0 as 119879 rarr 119879NA For 1Dtranslational order (smectic A) while 120585 can be quite large itcan never be infinite because of the Landau-Peierls instability[19]

In low-molecular-weight liquid crystals there are manysmectic A phases differentiated by the difference between themolecular length of the compounds in the layers and the layerspacing exhibited by the smectic When the layer spacing isbetween one and two molecular lengths the smectic phaseis designated A

119889 where 119889 here stands for dimer In cyano

mesogens dimerization is believed to be important for theoccurrence of reentrant nematic phases because dimers donot pack efficiently into layers perpendicular to the long axisof the dimer Decreasing the free volume around a dimerby either increasing pressure or decreasing temperature caneasily destabilize dimers in favor of a more dense uniaxialnematic or a biaxial smectic C phase with layers tilted relativeto n [10 19 21]

12 Liquid Crystal Elastomers The layered structure per-pendicular to the orientation axis n is a 2D network inelastomers not the 2D isotropic liquid it is in low-molecular-weight liquid crystals Elastomers with a locked-in orienta-tion axis can never be isotropic [2 4 6 7] that is have noaccess to the full symmetry group of rotations and reflections


known as119874(3) As a result there is exponential decay to someconstant value above 119879

119888(the foot in [7]) but no jump at the

first-order phase transition at119879119888 We suggest that the nematic

phase in elastomers could be 119863119899ℎ

nematic with the directoran 119899-fold rotation axis with this 119899 an integer 119899 = 2 3 4 56

Adding layers perp n the director to a 119863119899ℎ

nematic leadsto a smectic phase with also 119899-fold rotational symmetry inthe layers rather than the continuous rotational symmetry ofthe smectic A phase in low-molecular-weight liquid crystalsthat is sometimes modeled as a 2D disordered network The119899-fold rotational symmetry in the plane of the layers accountsbetter for the unusual transparency of these elastomers thana disordered 2D network Its wide angle X-ray diffractionpattern would be a modulated diffuse ring with an integralnumber of more intense but still diffuse regions every 2120587119899While being difficult to observemodulated diffuse wide anglerings in the so-called homeotropic geometry [7 11ndash15] wherethe sample plane is perpendicular to n such an experimentwould provide valuable information currently missing onLSCE structure

Nematic phases with discrete rotational symmetryaround n would be more transparent and could conservevolume in the sense used to account for spontaneous lengthchange For example shrinkage parallel to n is exactlycompensated by expansion in the two directions perp n It iseasy to show that such a constant volume LSCE is biaxial[22]

A thermomechanical effect at a constant-volume first-order phase transition was early recognized as a candidate forthermally driven artificialmuscles [23 24] FollowingWarnerand Kutter we call this effect spontaneous shape change[25] and leave the important outstanding question of LCEsymmetry evident in LSCEs where 119879

119888is far from the clearing

temperature of themesogens cross linked in the elastomer forseparate discussions [22] More thoughts and data are neededto speak more about LSCE symmetry

2 Experiment and Analysis

21 Samples Involving Cyanophenyl-Alkoxybenzoates Themesogens are a nonpolar nematic with a methoxy (OCH

3)

end group and a polar nematic with a cyano (CN) end group[10] Aliphatic chains at the other end of eachmesogen attachto the siloxane polymer backbone cross linked with 7molof the flexible bifunctional crosslinker (Figure 1)The samplesare 50 70 and 100molofCNmesogens respectively CN50CN70 and CN100 in Figure 3 with layer spacings shown inFigure 2

Smectic phases with a CN-end group favor a combinationof partially overlappedmolecular pairs (fully extended dimersim27 A) and single molecules (fully extended sim21 A) Thedimer fraction extracted from layer spacing measurementsis sensitive to temperature With decreasing temperaturethe layer spacing increases signaling an increase in dimerformation (Figure 2)

Smectic phases with a nonpolar end group have a layerspacing typically a molecular length (sim205 A) On cooling

CN50 the slightly larger than monomolecular layer spacingfirst increases a little then at 119879lowast it decreases a little CN50behaves as a nematic network with smectic clusters down to119879119892(Figures 2 and 3)In CN70 there is a competition between these two types

of temperature dependence resulting in the layer spacingbeing nearly independent of temperature (Figure 2)

From what is known for the hexyl and larger members ofthe homologous series (4-cyanophenyl 41015840-n-alkoxybenzoate)for this polar mesogen [10] we estimate for 119899 = 4 thetransition to the isotropic liquid 119879NI ≃ 87

∘C and tocoexistence of smectic A with an unidentified state called1198702 for 119879NAdagger ≲ 65

∘C However on extended heating in theisotropic liquid state 1198702 melts leading to a nematic witha higher transition temperature to the isotropic phase anda smectic A phase on cooling [10] The shortest homologueshowing a smectic A phase is the octyl-alkoxybenzoate andthe reentrant nematic was only observed in its mixtures withshorter or less polar compounds

As the cross-linking temperature is so high it appearsthat enantiomeric properties of the lower temperature phasesof cyanophenyl compounds play an important role in thesynthesis of LC elastomers In the case of cyanophenyls theLCE has mesogenic properties that do not exist in neat 4-cyanophenyl 41015840-butyl-alkoxybenzoate including clusters of amore ordered dimerized smectic phase with layers that breakdown at lower temperatures In addition in the elastomer 119879

119888

is enhanced by sim25K and 119879119892is relatively high

This raises the question would a better understandingof how cross-linking temperature affects enantiomeric prop-erties of mesogens in the synthesis of LC elastomers berelevant to fields such as pharmacology and medicine whereenantiomorphism is known to be important

Kundler and Finkelmann did not observe reentrant-typebehavior in a similar but more complex LSCE with twocross-linking agents where the fraction of CN mesogens wasless than 50mol [5] and the glass transition temperatures119879119892asymp 0∘C With more than 50mol CN-mesogen and only

one cross linking agent the LSCEs studied here are nematicnetworks with smectic A clusters ranging from 10 to 30 layerswith reentrant behavior in CN70 and CN100 but not in CN50(Figure 3) Indeed CN70 and CN100 are the first LSCEs toshow reentranttype behavior

22 LSCE Samples with Polar and Nonpolar LCs The chem-ical structures of the LSCE are shown in Figure 1 Thepolymer backbone is a polymethylhydrosiloxane The pen-dentmesogens are 4-(3-butenoxy) benzoic acid-(4-methoxy)phenyl (nonpolar) and 4-(3-butenoxy) benzoic acid-(4-cyano) phenyl (polar) attached to the backbone via a hydrosi-lation reaction Three samples with different percentages ofthe two mesogens are synthesized that is 50mol (CN50)70mol (CN70) and 100mol of the CNmesogen (CN100)The fraction of nonpolar mesogen was the complementto complete 100mol for the mesogens The networks arechemically cross linked with the bifunctional (hydroquinonediundecyl ether) crosslinker at 7mol concentration for allthe samples Presumably in the vicinity of 60∘C the aliphatic


Δn

025

020

015

010

005

040 60 80 100 120

CN100CN70CN50

T (∘C)

(a)

120

115

110

105

10040 60 80 100 120

120582

CN100CN70CN50

T (∘C)

(b)

Figure 5 (a) The orientational order parameter measured by birefringence Δ119899 and (b) spontaneous shape change 120582 versus 119879 (∘C) For119879 gt 40

∘C Δ119899 shows the least order for the shortest mesogens ∙ CN50 and most for 998771 CN100 that with dimers are the longestX CN70 in themiddle has competing monomeric and dimeric tendencies For spontaneous shape change CN70 has the largest 120582 and highest 119879

119892

The solidcurves 6th order polynomial fits to the data extrapolated to 0∘C suggest glass transition temperatures 119879

119892

sim 7ndash10∘C for CN50 and CN100and about 10 K higher for CN70 The dotted line is at 119879lowast = 60∘C

chains of the cross-linker undergo a cis-trans isomerism orstiffening making dislocation formation more difficult

We prepared rectangular LSCEs samples for which thedirector n is in the plane of the sample The sample thicknessis sim300 120583m and area is sim1mm times 05mm

The samples were observed with a polarizing microscope(Nikon) equipped with a hot stage (Mettler Toledo FP90Central Processor) as a temperature controller that canbe used simultaneously as a photomonitor as well as fordifferential scanning calorimetry (DSC)The light source wasa He-Ne laser The temperature range scanned at 05 Kminwas 30∘C to 130∘C Birefringence Δ119899 is calculated as in [14]

23 Data Analysis Changes in 120582 and Δ119899 are correlated tothe microscopic smectic layer spacing by mapping 120582 and Δ119899to an exceedingly fine temperature scale The idea is that asthe materials are continuous such a temperature scale is notlimited by the precision of themeasurements In other wordsthere is in principle no limit to how fine the temperaturescale can be To optimize accuracy and to obtain a continuoustemperature mapping we fit their nonlinear temperaturedependence to a polynomial of order 6

A 6th-order polynomial is the least complicated con-tinuous function that fits the 119879 ≲ 119879

119888data well over the

whole temperature range while a 4th-order polynomial fitsdata in the 119879 sim 119879

119888region less well Both polynomials

show increasingly nonlinear behavior on approaching 119879119892 as

observed and fitted in CN70 (also in CN50 and CN100 atlower temperatures than in the figures) than a saturation-type behavior implied by a linear continuation from the last

data point This is a normal feature of continuous systemswith macroscopic nonlinear properties where information iscontained in the data taken together as a whole rather than anexceedingly precise determination of three data points for alinear systemThis is fortunate for LCEs which are nonlinearsystems for which it is difficult to obtain many data pointsbecause of time constraints

24 Spontaneous Length Change 120582 For spontaneous lengthchanges where strain is induced by temperature the usualcontrol parameter (temperature in Celsius) is 120576 = (119879

119888minus

119879)(119879119888+ 273) such that 120576 ge 0 for 119879

119888≳ 119879 In Figure 4 at 119879

119888 120582

andΔ119899 decreased slightly faster on heatingWe refer to119879119888as a

clearing temperature in the sense that far above119879119888 120582 = 1 and

Δ119899 = 0 are constants A more exact definition for 119879119888does not

exist as spontaneous shape change takes place over a broadrange of temperatures with exponential decay to the constantvalues at higher temperatures [6 7 13]

The 6th-order polynomial fits in Figures 4 and 5 excludethe constant valued data above119879

119888 For data below 119879

119888 fits with

a minimum in the vicinity of 119879 ≃ 119879119888were selected because

above 119879119888 120582 and Δ119899 are nearly constant In addition we chose

fits where Δ119899 and 120582 monotonically increase with decreasingtemperature The minimal polynomial best satisfying thesecriteria is of order 6

Figure 4 compares the three different samples For exam-ple CN100 approaches 119879100

119888

more slowly than CN70 andCN50 Indeed using 119879

119888in absolute units as a scaling factor

the temperature dependence of CN70 and CN50 nearlysuperpose in the vicinity of 120576 = 0 With 120582 = 1 at 120576 = 0


the slopes are 11989850119900

= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900

= 18 for CN100 In the intermediate regionshown by gray lines in Figure 4 the slopes are 11989850

119894

= 03511989870

119894

= 038 and 119898100119894

= 039 the slope of CN70 is moresimilar to CN100 in this temperature interval The curve 119879 =119879119894is the lower bound of the intermediate region Beyond

the intermediate regions (also shown by gray lines) CN100and CN70 show a steeper rise in 120582 119898100

119890

= 062 (offset= 103) and 11989870

119890

= 105 (offset = 098) that intersect 119898100119894

and 11989870119894

at the arrows in the figure flagged for CN70 andCN100 In CN100 this intersection corresponds to a changein slope between two linear regions while in CN70 there isdivergence from linearity rendering piecewise linear analysisimpractical motivating the search for the simplest functionalform to describe all the data

The solid curves through 120576 ≳ 0 data are the sixth-orderpolynomial fits with 120582

0≃ 1 at 120576 = 0 that reflect the

influence of a glassy state at 119879119892 We discussed 119879

119888in some

detail because the observation is that whether 120582 diverges ordisappears on approaching 119879

119892depends on how well the data

fit in the vicinity of 119879119888 When the data fit well 120582 and Δ119899

diverge that is the network becomes ldquostifferrdquo with increasingorientational order consistent with observations

The conclusion is that cross-linking temperature 119879119888(119870)

is a good thermodynamic scaling parameter leading toconsistent if not universal plots for spontaneous shapechange in these LSCEs In particular as mentioned abovethe cyanophenyl in CN100 requires very high temperaturesto activate the enantiomeric mesogenic phases of neat 4-cyanophenyl 41015840-n-alkoxybenzoate

25 Birefringence Δ119899 versus Spontaneous Length Change 120582Tomake theΔ119899 versus 120582 plot (Figure 6) the data are preparedby linear interpolation to create an evenly spaced temperatureaxis (200 points) As the data do not have massive curvaturebecause the elastomer is both continuous and incompressiblelinear interpolation is sufficient The data are plotted assymbols For example the RMS deviation of the Δ119899 and 120582data points from the fitted curves in Figure 5 is better than 2superposes theΔ119899 versus120582datawith a 10000 point expansionof the temperature axis (solid curves for the 120598 ge 0 data inFigure 4) and fits reasonably well in the vicinity of 119879

119888

To include all the data in this study we fit the interpolatedtemperature dependence to a polynomial of order 6 Thefitted Δ119899 temperature dependence is then replotted with thefitted 120582 as abscissa to obtain Figure 6 showing the correlationbetween the magnitude of the orientational order parameterwith spontaneous shape change

The degree of orientational order as measured by Δ119899 islinear in120582 as120582 rarr 1 andΔ119899 = 0when120582 = 1 Deviations fromlinearity are roughly in the vicinity of 119879lowast shown by arrows inFigure 6 A summary of these results is

Δ119899 =

075 (120582 minus 094) for 120582 lt 105 CN50077 (120582 minus 097) for 120582 lt 107 CN70128 (120582 minus 098) for 120582 lt 105 CN100

(1)

A perspective of the transition at119879119888for an incompressible

elastomer is given in [22]where it is argued that this transition

CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582

Figure 6 The optical birefringence Δ119899 versus 120582 shows a mono-tonic increase in orientational order for CN50 CN70 and CN100The symbols show the 120582 data points from Figure 5 As 120582 rarr 1Δ119899 is linear in 120582 (dashed lines) in all samples up to the value of 120582at 119879lowast (highlighted by arrows) in CN70 and CN100 The deviationfrom linearity in CN50 is below 119879lowast In CN70 Δ119899 departs fromsaturation type behavior at large 120582 in the proximity of an estimatedglass transition at 119879

119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573

Figure 7 Sketch of the experimental setup and the X-ray diffractionpattern of the CN100 LSCE film at 119879 = 60∘C In the figure the smallangle diffraction peaks (arrow 1) are due to smectic clusters and thewide angle diffraction peaks (arrow 2) are associated with orderperp n

is an unusual constant-volume first-order phase transitionwithmeasurable latent heats when119879

119888is far below the clearing

temperature of the LCmesogens cross linked in the elastomerTaking into account enantiomorphism a similar perspectivefor 119879119888far above the clearing temperature could also be

appliedIn Figure 6 the change in slope at 119879lowast is very small in

CN50 larger in CN100 and largest in CN70 In CN70 therelative increase in 120582 with decreasing temperature becomessmaller and smaller the closer one is to 119879

119892 In particular

with increasing the orientational order in CN70 the changein 120582 becomes smaller at a smaller 120582 than in CN50 and CN100because it has a higher 119879

119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C

Figure 8 Azimuthal (120573 in Figure 7) intensity profiles of the small angle peaks at several temperatures for CN50 CN70 and CN100 Theintensities are normalized by the background levels due to the polymer backbones In CN70 and CN100 the peak height (intensity) as wellas the peak area are maximum near 119879lowast = 60∘C

26 X-Ray Diffraction

261 Structure Factor To obtain details of the microscopicstructure of the elastomers we performed temperaturedependent X-ray diffraction measurements at beamline BL-15 of the Kyushu Synchrotron Light Research Center (Japan)where we used 800 keV X-rays (wavelength = 1550 A)filtered by a double crystal monochromator and an imageplate system with 4096 times 8040 pixels and 50 120583m resolutionThe distance between the sample and the image plate was180mmThe imaging geometry is shown in Figure 7

The temperature-dependent X-ray measurements of theCN50 and CN100 samples covered the temperature range

26∘Cndash80∘Cand 26∘Cndash90∘C forCN70 After careful extractionof the background intensity results for the small angle regimeshowing smectic information are plotted in Figure 8 Whilethe maximum in the small angle peak intensities at 119879 = 60∘Cis larger inCN100 than inCN70 there are the samenumber oflayers about 30 correlated in both samples As there are nevermore than 12 layers correlated in CN50 its peak intensity issmallest

The best-fit Lorentzian functions for the intensities inFigure 8 are shown with dotted lines On heating thedegree of smectic order in the CN70 and CN100 samples ismaximum in the vicinity of 119879lowast sim 60∘C that is decreases attemperatures both above and below 119879lowast


0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)

Figure 9 The small angle peak intensities (a) and 120585 the correlation length of the smectic layers calculated from the 2120579 profile line 3 inFigure 7 are plotted as a function of temperature for the CN50 CN70 and CN100 samples The solid and dotted lines are guides for the eyeThe maximum peak intensities (a) and the maximum correlation length (b) for CN70 and CN100 are observed at 119879lowast sim 60∘C

The inverse of the layer spacing 1199020 is defined by the

maximum intensity of 119902 along arrow 1 as indicated by arrow3 in Figure 7

262 Layer Spacing andCorrelation to120582 andΔ119899 Thetemper-ature dependence of the seven (CN50 and CN100) or eight(CN70) measured values of the layer spacings 119889 = 2120587119902

0

versus 120582 are shown in Figure 10 and versus Δ119899 in Figure 11For a reliable comparison the data points are connected bylines and the temperature axis expanded to 10000 points sothat the arrows for 60∘C point exactly to the correct datapoint easy to check in CN50 and CN70 but much harderin CN100 With 1000 data points the temperature scale asdefined by 120582 andΔ119899 is too coarse for these plots underscoringthe key role played by continuity on a macroscopic scale inthese materials

With increasing 120582 the layer spacing initially increases inall samples Above 119879lowast the layer spacing decreases in CN50hardly changes in CN70 and increases in CN100 As 119889-spacings are made with high precision the zig-zag appear-ance for CN70 is interpreted as arising from dislocationunbinding to keep a nearly constant layer spacing in thesample with the largest 120582 and closest to 119879

119892(Figures 3 and 10)

In contrast the layer spacing increase in CN100 is remarkablysmooth between 35∘C and 70∘C where the layers in the 119878

119860

clusters are well correlated (Figures 2 8 and 9)For 119879 gt 119879

lowast small angle peak intensities associatedwith smectic order decrease as 119879 rarr 119879

119888 This is normal

For example in CN50 there is no 119879lowast and the degree oforientational order saturates at about 60∘119862 However in thecases of CN70 and CN100 there is a maximum in the smallangle peak intensities at 119879lowast ≃ 60

∘C where 120582 deviates fromsaturation-type behavior to one that increases more stronglywith decreasing temperature (Figures 6 and 12)

3 Dislocation Loop Model

For CN70 and CN100 X-ray diffraction shows a maximumin scattering intensity (Figure 9(a)) and layer correlationlength where 120585 ≃ 700ndash800 A (Figure 9(b)) at 119879lowast sim 60∘C(Figure 8) As a result we associate119879lowast with two observationsthe onset of nonlinearity in 120582 with increasing Δ119899 (Figure 6)and the decrease in layer correlation length 120585 below 119879lowast(Figures 3 and 9) and attribute this behavior to dislocationloop formation

In Figure 12 we plot 120575120582 the deviation from linearity as afunction of temperature below 119879lowast for the CN70 and CN100samples The dotted lines in the 120575120582-119879 plot are best fits to120575120582 = 119886(119879

lowast

minus 119879) exp(1198640119896119887119879) Here 119886(119879lowast minus 119879) is related to

the number of dislocations in the smectic layers with 119886 =4 times 10

minus4 Kminus1 for both samples The activation energies are1198640= 432 times 10

minus21 J and 1198640= 379 times 10

minus21 J for the CN70and CN100 samples respectively 120575120582 continuously decreasesas the temperature increases and it does so quite rapidlyfor the CN70 sample The suggestion is that conservation oflayer spacing requires more dislocations in CN70 for which

Advances in Condensed Matter Physics 9d

(A)

27

26

25

24110 115 120

120582

CN50CN70CN100

Figure 10 Plot of 119889 versus 120582The data points are connected by linesCompared to CN70 andCN50 changes in layer spacings are smoothin CN100 The largest 120582 and the smallest variation in layer spacingare observed for CN70 which has the highest 119879

119892

Arrows point to 120582values at 119879lowast = 60∘C

d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100

Figure 11 Plot of 119889 versus Δ119899 Arrows point to Δ119899 values at 119879lowast =60∘C

119889 is nearly constant while in CN100 120575120582 is linear in 119879 aspair formation allows changes in layer spacing with fewerdislocations (Figure 10 see also Figures 3 and 6)

It also suggests that as 119879lowast sim 60∘C does not depend on thefraction of CN present it arises from a molecular transitionin the crosslinker present in the same concentration in bothCN70 and CN100 For example cis-trans transitions in thelong aliphatic chains of hydroquinone diundecyl ether wouldchange the crosslinker properties from ldquoflexible bifunctionalrdquo

0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast

Figure 12 120575120582 versus 119879 below 119879lowast The dotted lines are best fits to120575120582 = 119886(119879lowast minus 119879) exp(119864

0

119896119887

119879) where 119886(119879lowast minus 119879) corresponds to thenumber of defects andor smectic domains and 119864

0

is the dislocationactivation energy

T lt Ti rarr Tg

No defects 3 defect loops 5 defect loops

10d

Defect loop model

120585sim10 layers 120585sim2-3 layers

Figure 13 Sketch of the dislocation model that conserves layerspacing X marks where a loop enters the page and ⃝ where itemerges from the page Packets of layers associated with each loopare decorrelated ROM layer packets associated with other loops As119879 rarr 119879

119892

more dislocation loops form leading eventually to nocorrelated layers in the sample or in other words nematic order

to ldquorigid bifunctionalrdquo enforcing the appearance of moredislocations that become smaller and smaller as 119879 rarr 119879

lowast

leading to a breakdown in the layer structureThe idea of a loop is summarized in Figure 13 where

packets of correlated layers are held together by a loop how-ever with no correlation between layers in other packets Asmore loops form the number of layers in a packet decreasesand layer correlations decrease in the sample leading to thesituation shown in Figure 12

In low-molecular-weight nematic liquid crystals wherethere are large fluctuations in n that scatter light a reentrantnematic is easily observed in the optical microscope withthe onset of director fluctuations and sample turbidity Forsmectic clusters localized by cross linking in a nematicnetwork there is no flow and no change in sample turbidityat 119879lowast sim 60∘C Rather the effects of increasing dislocationcontent in LSCEs shows enhancement of orientational order


and a loss of coherence in the layer structure as more loopsform

4 Conclusions

We reported on the spontaneous length change (120582) thedegree of orientational order measured by birefringence Δ119899and the X-ray structure factor (Lorentzian) for the transpar-ent nematic network with smectic clusters in three differentconcentrations of polar and nonpolar mesogens attached toa crosslinked polymer backbone CN50 CN70 and CN100corresponding to 50 70 and 100mol of the polar mesogenIn the vicinity of 119879

119888 which depends on concentration of

polar moiety there is a linear relation between 120582 and Δ119899 thatprevails down to 119879lowast sim 60∘C As 119879lowast is independent of theconcentration of polar moiety it is attributed to stiffeningof the long aliphatic chains of the cross-linker which ispresent at the same molar concentration in all the samplesIn CN50 the maximum in intensity and correlation length ofthe smectic clusters at 119879lowast is maintained at about 10 layers tolower temperatures InCN70 andCN100 the decrease is fromabout 30 layers at 119879lowast to 10 layers at 119879

119892 On cooling the layer

spacing inCN50 clusters spacing decreases a little in CN70 itincreases a little and inCN100 it increasesmore A dislocationmodel accounts for themaximum in X-ray scattering at119879lowast asthe start of dislocation loop formation leading to a breakdownin layering below 119879lowast in CN70 and CN100 More thought anddata are needed to identify the structure (symmetry) of thesenovel smectic clusters

Acknowledgments

Thiswork is partially supported by the Japan-Germany Scien-tific Cooperative Program of Japan Society for the Promotionof Science (JSPS) and the Deutsche Forschungsgemeinschaftthe Grant for Scientific Research sponsored by JSPS and theGrant-in-Aid for Scientific Research from the Ministry ofEducation Culture Sports Science and Technology of Japan(nos 21340110 20111003 and 19031023) and Hibah Kompe-tensi DIKTI Yusril Yusuf thanks the Research Fellowships ofJSPS

References

[1] H Finkelmann H J Kock and G Rehage ldquoInvestiga-tions on liquid crystalline polysiloxanes 3 Liquid crystallineelastomersmdasha new type of liquid crystalline materialrdquo Macro-molecular RapidCommunications vol 2 no 4 pp 317ndash322 1981

[2] J Kupfer and H Finkelmann ldquoNematic liquid single crystalelastomersrdquoMacromolecular RapidCommunications vol 12 no12 pp 717ndash726 1991

[3] W Kaufhold H Finkelmann and H R Brand ldquoNematicelastomers 1 Effect of the spacer length on the mechanicalcoupling between network anisotropy and nematic orderrdquo DieMakromolekulare Chemie vol 192 no 11 pp 2555ndash2579 1991

[4] J Kupfer and H Finkelmann ldquoLiquid crystal elastomers influ-ence of the orientational distribution of the crosslinks on thephase behaviour and reorientation processesrdquo MacromolecularChemistry and Physics vol 195 no 4 pp 1353ndash1367 1994

[5] I Kundler and H Finkelmann ldquoDirector reorientation viastripe-domains in nematic elastomers influence of cross-linkdensity anisotropy of the network and smectic clustersrdquoMacro-molecular Chemistry and Physics vol 199 no 4 pp 677ndash6861998

[6] H R Brand and K Kawasaki ldquoOn the macroscopic conse-quences of frozen order in liquid single crystal elastomersrdquoMacromolecular Rapid Communications vol 15 no 3 pp 251ndash257 1994

[7] D U Cho Y Yusuf P E Cladis H R Brand H Finkelmannand S Kai ldquoTrifunctionally cross-linked liquid single crystalelastomers swelling dynamics and electromechanical effectsrdquoJapanese Journal of Applied Physics A vol 46 no 3 pp 1106ndash1113 2007

[8] S Krause Nematische Hauptkettenelastomere Synthese undUntersuchung der mechanischen Eigenschaften und der Ord-nungszustandes Albert-Ludwigs-Universitat Freiburg 2008

[9] Y Yusuf S Hashimoto P E Cladis et al ldquoMain chain liquid-crystalline elastomers swelling dynamics and electromechani-cal effectsrdquoMolecular Crystals and Liquid Crystals vol 508 pp367ndash379 2009

[10] P E Cladis P L Finn and J W Goodby in Liquid Crystals andOrdered Fluids A C Griffin and J F Johnson Eds vol 4 p203 Plenum Press New York NY USA 1984

[11] Y Yusuf P E Cladis H R Brand H Finkelmann and SKai ldquoHystereses of volume changes in liquid single crystalelastomers swollen with low molecular weight liquid crystalrdquoChemical Physics Letters vol 389 no 4ndash6 pp 443ndash448 2004

[12] Y Yusuf Y Ono Y Sumisaki et al ldquoSwelling dynamics of liquidcrystal elastomers swollen with low molecular weight liquidcrystalsrdquo Physical Review E vol 69 no 2 Article ID 021710 9pages 2004

[13] D U Cho Y Yusuf P E Cladis H R Brand H Finkelmannand S Kai ldquoThermo-mechanical properties of tri-functionallycrosslinked liquid single crystal elastomersrdquo Chemical PhysicsLetters vol 418 no 1ndash3 pp 217ndash222 2006

[14] Y Yusuf P E Cladis H R Brand H Finkelmann and S KaildquoBirefringence measurement of liquid single crystal elastomerswollen with low molecular weight liquid crystalrdquo ChemicalPhysics Letters vol 382 no 1-2 pp 198ndash202 2003

[15] Y Yusuf N Minami S Yamaguchi et al ldquoShape anisotropyand optical birefringence measurements of dry and swollenliquid single crystal elastomersrdquo Journal of the Physical Societyof Japan vol 76 no 7 Article ID 073602 4 pages 2007

[16] K Kawasaki ldquoPhase dynamics of irregular patterns and ultra-slow modes in glass-forming systemsrdquo Physica A vol 217 no1-2 pp 124ndash139 1995

[17] A Caille Comptes Rendus de lrsquoAcademie des Sciences B vol 274p 891 1972

[18] httpmathworldwolframcomLorentzianFunctionhtml[19] D Demus J Goodby GW Gray HW Spiess and V Vill Eds

Physical Properties of Liquid Crystals Wiley-VCH New YorkNY USA 1999

[20] M A Anisimov P E Cladis E E Gorodetskii et al ldquoExperi-mental test of a fluctuation-induced first-order phase transitionthe nematicsmectic-A transitionrdquo Physical Review A vol 41 no12 pp 6749ndash6762 1990

[21] P E Cladis in Physical Properties of Liquid Crystals D DemusJ Goodby G W Gray H W Spiess and V Vill Eds p 289Wiley-VCH New York NY USA 1999

[22] S Krause Y Yusuf S Hashimoto et al (in preparation)


[23] P G de Gennes M Hubert and R Kant ldquoArtificial musclesbased on nematic gelsrdquo Macromolecular Symposia vol 113 no1 pp 39ndash49 1997

[24] M Hubert R Kant and P G de Gennes ldquoDynamics andthermodynamics of artificial muscles based on nematic gelsrdquoJournal de Physique I vol 7 no 7 pp 909ndash919 1997

[25] M Warner and S Kutter ldquoUniaxial and biaxial soft deforma-tions of nematic elastomersrdquo Physical Review E vol 65 no 5Article ID 051707 9 pages 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


CH3

Si O

H

O COO

OCH3

OO

Polymer backbone

Mesogen

Mesogen

Crosslinker

Crosslinker

Polymer backbone

O

C

O

CN

O

n

n

Figure 1 Top sketch of one layer of polar mesogens and itscrosslinker in a side-chain liquid crystal elastomer (LCE) with layerspacing larger than one pendant cyano mesogen Below are thechemical structures of the compounds used to synthesize LSCEfilms300 120583m thick and several cm2 area with 7mol crosslinker and 5070 and 100mol of the polar cyano mesogens respectively CN50CN70 and CN100 Fully extended molecular lengths of the twomesogens are ℓ sim 205ndash21 A Including the siloxane as a chainextender adds another sim2 A to each monomer The layer spacingsare shown in Figure 2

phase transition temperature 119879NI of the LC moieties theirimportance became clearer while studying LCEs cross linkedfar from 119879NI [8 9] and thus is well supported by experi-ments and observations of the elastomers synthesized by theFinkelmann method and this leads to a natural explanationfor the unusual transparency of the monodomain elastomersdiscussed here It also opens the door onto new experimentsand questions concerning the physics of LC elastomers

Elastomers have no liquid phases and no critical fluc-tuations only relaxation dynamics Thus the symmetry ofnematic liquid crystalline elastomers is not the same as itis in low molecular-weight liquid crystals As a result LCEsof the type shown in Figure 1 are important to learn howpolymerization and cross-linking influence liquid crystalorder This is particularly the case for the polar cyanomesogen in Figure 1 where liquid crystal phases appear in theelastomer that did not exist before cross-linking [10]

To learn more about the correlation between liquidcrystalline order at themicroscopic level and themacroscopicproperties of spontaneous length change measured by 120582 nand degree of orientational order measured by birefringenceΔ119899 in the context of previous studies for bifunctional andtrifunctional cross-linked LSCEs [7 11ndash15] we synthesizedLSCEs with the two different mesogenic groups and thenovel cross-linker in Figure 1 with layer spacings in Figure 2and then studied their microscopic structure by synchrotronradiation (Figure 3)

An unusual feature of the elastomers in Figure 3 isthat they are more than 80 transparent at 20∘C near the

27

26

CN100CN70CN50

25

40 60 80

Tlowast

d(A

)

T (∘C)

Figure 2 Layer spacing 119889 (A) versus temperature 119879 (∘C) forsmectic clusters in ∙ CN50X CN70 and 998771 CN100 The data pointsare connected by lines

CN50CN70CN100

120

100

80

60

40

20

050 60 70 80 90 100

Mol CN

Tc

Ti

Tlowast

TgGlass

120585d lt 10 120585d10202530

30

2520

10

T(∘

C)

Figure 3 An overview of the nematic networks of ∙CN50XCN70and 998771 CN100 The solid curves are lines of constant number ofsmectic layers correlated in a cluster 120585119889 (shown to the right of thefigure) with 120585 the layer correlation length and 119889 the layer spacing(Figure 2) measured by synchrotron radiation 120585119889 is maximum(sim283 layers for CN70 and 315 layers for CN100) on the dashedline 119879lowast = 60∘C between CN70 and CN100 compared to about 10layers at119879

119894

where smectic clusters first appear119879119888

is the cross-linkingtemperature 119879

119892

is the glass transition temperature The maximumnumber of correlated layers in CN50 is 12 at sim 40∘C and is onlyabout 2 at 119879

119894

and 10 at 119879119892

The dashed curve for 119879119894

is deduced frommeasurements of spontaneous shape change 120582(119879) measured in theoptical microscope discussed in Section 23 119879

119892

is estimated fromthe 120582(119879)rsquos in Figure 4


125

120Ti

Ti

CN70

115

CN50

Tlowast

CN100

110

105

Tlowast

1000 005 010 015 020

120576 = (Tc minus T)(273 + Tc)

120582


119888

= 942∘C (CN50) 1106∘C (CN70) and 1126∘C



119894


119894

sim 119879119888










119892 an




























3)










119888







Δn

025

020

015

010

005

040 60 80 100 120

CN100CN70CN50

T (∘C)

(a)

120

115

110

105

10040 60 80 100 120

120582

CN100CN70CN50

T (∘C)

(b)



119892


119892














119888minus

119879)(119879119888+ 273) such that 120576 ge 0 for 119879

119888≳ 119879 In Figure 4 at 119879

119888 120582







119888 fits with





119888






= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900


119894

= 03511989870

119894

= 038 and 119898100119894



119890

= 062 (offset= 103) and 11989870

119890


and 11989870119894





119888in some








119888



Δ119899 =


(1)



CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582


119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573









119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




125

120Ti

Ti

CN70

115

CN50

Tlowast

CN100

110

105

Tlowast

1000 005 010 015 020

120576 = (Tc minus T)(273 + Tc)

120582


119888

= 942∘C (CN50) 1106∘C (CN70) and 1126∘C



119894


119894

sim 119879119888










119892 an




























3)










119888







Δn

025

020

015

010

005

040 60 80 100 120

CN100CN70CN50

T (∘C)

(a)

120

115

110

105

10040 60 80 100 120

120582

CN100CN70CN50

T (∘C)

(b)



119892


119892














119888minus

119879)(119879119888+ 273) such that 120576 ge 0 for 119879

119888≳ 119879 In Figure 4 at 119879

119888 120582







119888 fits with





119888






= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900


119894

= 03511989870

119894

= 038 and 119898100119894



119890

= 062 (offset= 103) and 11989870

119890


and 11989870119894





119888in some








119888



Δ119899 =


(1)



CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582


119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573









119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics

















3)










119888







Δn

025

020

015

010

005

040 60 80 100 120

CN100CN70CN50

T (∘C)

(a)

120

115

110

105

10040 60 80 100 120

120582

CN100CN70CN50

T (∘C)

(b)



119892


119892














119888minus

119879)(119879119888+ 273) such that 120576 ge 0 for 119879

119888≳ 119879 In Figure 4 at 119879

119888 120582







119888 fits with





119888






= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900


119894

= 03511989870

119894

= 038 and 119898100119894



119890

= 062 (offset= 103) and 11989870

119890


and 11989870119894





119888in some








119888



Δ119899 =


(1)



CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582


119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573









119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Δn

025

020

015

010

005

040 60 80 100 120

CN100CN70CN50

T (∘C)

(a)

120

115

110

105

10040 60 80 100 120

120582

CN100CN70CN50

T (∘C)

(b)



119892


119892














119888minus

119879)(119879119888+ 273) such that 120576 ge 0 for 119879

119888≳ 119879 In Figure 4 at 119879

119888 120582







119888 fits with





119888






= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900


119894

= 03511989870

119894

= 038 and 119898100119894



119890

= 062 (offset= 103) and 11989870

119890


and 11989870119894





119888in some








119888



Δ119899 =


(1)



CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582


119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573









119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





= 45 for CN50 11989870119900

= 48 for CN70and 119898100

119900


119894

= 03511989870

119894

= 038 and 119898100119894



119890

= 062 (offset= 103) and 11989870

119890


and 11989870119894





119888in some








119888



Δ119899 =


(1)



CN100

CN70

CN50

020

015

010

005

0100 105 110 115

Δn

120582


119892

≃ 17ndash20∘C

y

x

z

1

2

3

LCE film

120573









119892


Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Inte

nsity

Angle (deg)0 45 90 135 180

0

500

1000

1500

2000

2500CN100

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

0 45 90 135 180

CN70

Angle (deg)

Inte

nsity

0

500

1000

1500

2000

2500

CN50

0 45 90 135 180

26∘C35∘C40∘C50∘C

60∘C70∘C80∘C

28∘C35∘C40∘C50∘C

60∘C70∘C80∘C

27∘C35∘C40∘C50∘C

60∘C70∘C80∘C








0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

500

1000

1500

2000

2500

20 30 40 50 60 70 80 90

CN50CN70CN100

T (∘C)

Inte

nsity

Tlowast

(a)

CN100CN70CN50

Tlowast

0

200

400

600

800

1000

20 30 40 50 60 70 80 90

120585(A

)T (∘C)

(b)





0





119860









lowast







(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




(A)

27

26

25

24110 115 120

120582

CN50CN70CN100


119892


d(A

)

27

26

25

24010 012 014 016 018 020 022

Δn

CN50CN70CN100




0

001

002

003

004

005

30 35 40 45 50 55 60

CN70CN100

120575120582

T (∘C)

Tlowast


0

119896119887


0


T lt Ti rarr Tg


10d

Defect loop model



119892



lowast






4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





4 Conclusions






Acknowledgments


References
































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics












FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



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