Electrorheological creep response of tumbling nematics

Electrorheological creep response of tumbling nematicsNing Yao and Alex M. Jamieson

Citation: Journal of Rheology (1978-present) 42, 603 (1998); doi: 10.1122/1.550945 View online: http://dx.doi.org/10.1122/1.550945 View Table of Contents: http://scitation.aip.org/content/sor/journal/jor2/42/3?ver=pdfcov Published by the The Society of Rheology Articles you may be interested in Electrorheological response and orientational bistability of a homogeneously aligned nematic capillary J. Chem. Phys. 129, 084710 (2008); 10.1063/1.2971043 Response properties of immiscible polymer blend electrorheological fluids J. Rheol. 45, 773 (2001); 10.1122/1.1359760 Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal J. Appl. Phys. 86, 3042 (1999); 10.1063/1.371166 Model for the electrorheological effect in flowing polymeric nematics J. Chem. Phys. 110, 8197 (1999); 10.1063/1.478721 Azimuthal surface gliding of a nematic liquid crystal Appl. Phys. Lett. 70, 3359 (1997); 10.1063/1.119170

Redistribution subject to SOR license or copyright; see http://scitation.aip.org/content/sor/journal/jor2/info/about. Downloaded to IP: 2.233.42.114 On: Tue, 06 May 2014

14:24:30

http://scitation.aip.org/content/sor/journal/jor2?ver=pdfcov

http://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/test.int.aip.org/adtest/L23/1684144741/x01/AIP/HA_Pub2Web_ReregisterToCalert_JORO_PDFCovPg_1640x440_10_2013/pei_aipToCAlerts.png/7744715775302b784f4d774142526b39?x

http://scitation.aip.org/search?value1=Ning+Yao&option1=author

http://scitation.aip.org/search?value1=Alex+M.+Jamieson&option1=author

http://scitation.aip.org/content/sor/journal/jor2?ver=pdfcov

http://dx.doi.org/10.1122/1.550945

http://scitation.aip.org/content/sor/journal/jor2/42/3?ver=pdfcov

http://scitation.aip.org/content/sor?ver=pdfcov

http://scitation.aip.org/content/aip/journal/jcp/129/8/10.1063/1.2971043?ver=pdfcov

http://scitation.aip.org/content/sor/journal/jor2/45/3/10.1122/1.1359760?ver=pdfcov

http://scitation.aip.org/content/aip/journal/jap/86/6/10.1063/1.371166?ver=pdfcov

http://scitation.aip.org/content/aip/journal/jcp/110/16/10.1063/1.478721?ver=pdfcov

http://scitation.aip.org/content/aip/journal/apl/70/25/10.1063/1.119170?ver=pdfcov

Electrorheological creep response of tumbling nematics

Ning Yao and Alex M. Jamiesona)

Department of Macromolecular Science, Case Western Reserve University,Cleveland, Ohio 44106-7202

(Received 13 October 1997; final revision received 3 February 1998)

Synopsis

The shear creep response of homeotropic monodomains of 4,48-n-octylcyanobiphenyl~8CB! anddilute solutions of a side-chain liquid-crystalline polysiloxane~LCP! in N-~4-methoxybenzylidene!-4-butylaniline~MBBA ! is studied in the absence and presence of electric fields applied along thedirector. In the absence of the field, oscillations in strain rate are observed for 8CB and theLCP/MBBA solutions, indicative of director-tumbling flow. In the presence of electric fields, thetumbling flow is suppressed and, with increasing field strength, a systematic evolution is observedtoward flow-aligning, the apparent viscosity being determined by the balance in hydrodynamic andelectric torques. Due to a larger dielectric anisotropy, the tumbling flow of 8CB is suppressed at acritical field strength much lower than that of the LCP/MBBA solution. Moreover, a field-inducedasymmetry of the doublet peaks is observed in the creep deformation for 8CB at 34 °C. Based onEricksen’s transversely isotropic fluid theory, simulation of the influence of electric fields on theflow-tumbling behavior is performed and qualitative agreement with the experimental results isobtained. ©1998 The Society of Rheology.@S0148-6055~98!01003-7#

I. INTRODUCTION

When a liquid-crystalline material is subjected to an electric field transverse to theflow direction, a change in apparent viscosity may be observed. Such a field-inducedphenomenon is called an electrorheological~ER! effect @Jordan and Shaw~1989!#. Apositive ER effect, i.e., an enhanced viscosity, is commonly observed upon application ofan electric field transverse to the flow direction for liquid-crystalline materials with posi-tive dielectric anisotropy~De! @Yang and Shine~1992! and~1993!; Chianget al. ~1997!;Yao and Jamieson~1997!#. Either positive or negative ER effects may be observed fornematic fluids with negativeDe depending on the magnitude of the shear rate@Yao andJamieson~1997!#.

Analysis of the dynamics of nematic materials is generally carried out in the context ofEricksen’s transversely isotropic fluid~TIF! theory @Ericksen ~1960!# which, with thedirector initially aligned perpendicular to the flow direction and parallel to the velocitygradient, predicts a simple stress overshoot for a flow-aligning nematic, and a stressoscillation for a tumbling nematic, each subjected to a simple shear strain. Specifically,Ericksen’s TIF theory predicts that the apparent viscosityhapp varies as@Gu and Jamie-son ~1994a!#:

a!Author to whom all correspondence should be addressed.

© 1998 by The Society of Rheology, Inc.J. Rheol. 42~3!, May/June 1998 6030148-6055/98/42~3!/603/17/$10.00


14:24:30

txy 5 gFSa11~a21a3!2

a32a2Dsin2 u cos2 u1hb2

a32

a32a2G, ~1!

wheretxy is shear stress,g is shear rate,a1 , a2 anda3 are the first, second, and thirdLeslie viscosity coefficients,hb is one of the Miesowicz viscosities, andu, which is theangle of the director relative to the shear gradient direction, is given by

tanu 5 S2a2

a3D0.5

tanS~2a2a3!0.5

a32a2g D for a3 . 0 ~2!

and

tanu 5 Sa2

a3D0.5

tanhS~a2a3!0.5

a32a2g D for a3 , 0. ~3!

Moreover, for a tumbling nematic, the strain periodicitygp is a function ofd @Marrucci~1985!#:

gp 5p~11d2!

d, ~4!

whered 5 (2a3 /a2)0.5. Consideration of Eqs.~1!–~3! suggests that the apparent vis-cosity in a controlled-stress experiment will have a different time dependence to thatpreviously observed in controlled-strain experiments. However, the scaling ofhapp ver-sus shear strain should be the same in both experiments.

While flow-tumbling behavior is typical for lyotropic stiff-chain polymer solutions atlow shear rates@Grizzuti et al. ~1990!; Chow et al. ~1992!; Hongladarom and Burghardt~1993!; Yang and Shine~1992! and ~1993!#, only a few low molar mass nematics~LMMNs! are found to exhibit tumbling flow@Gahwiller ~1972!; Pieranski and Guyon~1974!; Jahnig and Brochard~1974!; Cladis and Torza~1975!; Skarpet al. ~1981!; Clarket al. ~1981!#. In previous work, we demonstrated for the first time the distinctive tran-sient stress response of homeotropic monodomains of a flow-aligning nematic(4,48-pentylcyanobiphenyl, 5CB! and a tumbling nematic~4,48-n-octylcyanobiphenyl,8CB! @Gu et al. ~1993!; Gu and Jamieson~1994b!#. At very small strains the stressoscillations could be accurately fit to Ericksen’s TIF theory. At large strains, the stressoscillations become damped, possibly due to nucleation of out-of-plane configurations ofthe director@Han and Rey~1995!; Matheret al. ~1997!#. Experimentally, in parallel-plategeometry, concentric twist walls are observed to propagate radially in 8CB monodomainsunder shear@Matheret al. ~1997!#. Thus it is clear that a three-dimensional~3D! hydro-dynamic analysis is required to fully understand the flow behavior of a tumbling nematicat high strains.

In this article, we report for the first time the shear creep response of homeotropicmonodomains subjected to a constant shear stress for tumbling nematics, 8CB (De. 0) and dilute solutions of a side-chain liquid-crystalline polysiloxane~LCP! in

N-~4-methoxybenzylidene!-4-butylaniline~MBBA ! (De , 0). The effect of an appliedelectric field on the deformation of the monodomains is observed and compared withsimulation results based on Ericksen’s TIF theory. Qualitative agreement is observedbetween the experimental results at small strain and the predictions of Ericksen’s TIFtheory.

604 YAO AND JAMIESON


14:24:30

II. EXPERIMENTAL METHODS

8CB and MBBA were purchased from Aldrich Chemical Company and used as re-ceived. The side-chain LCP~DP 5 198, n 5 3! was synthesized via hydrosilationreaction between polymethylhydrosiloxane and 4-@~undecylenyloxy!benzoyl#-48-methoxyphenyl@Yao and Jamieson~1997!#. The structures of 8CB, MBBA, and theside-chain LCP are shown in Fig. 1. L-a-lecithin was purchased from Sigma ChemicalCompany and used as a 0.5 wt % solution in ethanol.

Electrorheological creep experiments were performed on a Carri–Med CLS50controlled-stress rheometer with stainless-steel cone-and-plate geometry~coneangle5 1.5°, cone radius5 30 mm, gap5 41.2mm!. The inner surfaces of the coneand the plate were treated with a 0.5 wt % ethanol solution of L-a-lecithin to achievesurface anchoring for homeotropic alignment@Gu et al. ~1993!#. With the cone and theplate as electrodes, an electric field was applied across the sample by a Bertan Model 215high voltage power supply during the creep experiment. The sample temperature wascontrolled accurate to 0.1 °C. Each measurement was made 15 min after the sample wasloaded or subjected to a prior test.

III. RESULTS AND DISCUSSION

A. Creep experiments in the absence of electric field

It has been demonstrated that a homeotropic monodomain of 8CB shows strong stressoscillations in the nematic regime when subjected to a shear orthogonal to the director atconstant strain rate@Gu et al. ~1993! and ~1994b!; Jamiesonet al. ~1996!#. When ahomeotropic monodomain is subjected to such a shear deformation at constant stress,weak but persistent fluctuations are barely visible in the creep response of a homeotropicmonodomain of 8CB. Taking the time derivative of the strain, however, the presence ofoscillations in the strain rate is clearly revealed~Fig. 2!. As noted above, consideration ofEricksen’s TIF theory for a tumbling nematic indicates that, while the transient stressresponse in controlled-strain experiments and the creep response to a constant stress

FIG. 1. Structures of 8CB, MBBA and the side-chain LCP.

605ELECTRORHEOLOGICAL CREEP RESPONSE


14:24:30

should have different time dependences, the periodicities of the oscillations in stress andin strain rate should each show identical scaling with total shear strain defined asg5 100gt @Gu et al. ~1993! and~1994b!#. This behavior is indeed observed, as evident in

Fig. 2. Though the location of the strain rate curves shift slightly relative to each other,because the effect of inertia is different at each stress level, the strain periodicity of theoscillation in strain rate remains constant.

As shown in Fig. 3, oscillations in viscosity were observed over most of the nematicregime of 8CB and the oscillations became stronger when the temperature approaches thesmectic-to-nematic transition temperature of 8CB,TS-N 5 33.5 °C. While the stress os-cillations show the doublet peaks predicted by the TIF theory at most temperatures in thetumbling regime@Gu et al. ~1993! and ~1994b!#, this feature is evident in the derivativeof the creep curve only at 34 °C, i.e., very close to the smectic-to-nematic transition~Fig.3!. Two effects may contribute to this discrepancy. One is the inverse relationship be-tween viscosity and strain rate which makes it difficult to temporally resolve the doubletsin the creep curves particularly at high stress levels, as evident in Fig. 2. Also, it may bepossible that the constant stress deformation is more prone to out-of-plane motion, whichleads to a decrease in amplitude of the oscillations in strain rate and a disappearance ofthe doublet feature as shown in the simulations of Han and Rey~1995! and in therheo-optical study of Matheret al. ~1997!. It should be pointed out that multiple oscilla-tions were observed in the present study only in cone-and-plate geometry. Presumablybecause of destructive interference between the oscillations with different strain scalingfrequencies, only a single oscillation was observed when parallel-plate geometry wasused.

FIG. 2. Strain rate curves of 8CB at different stresses (T 5 37 °C).



14:24:30

Creep experiments were also performed on homeotropic monodomains of MBBA, andFig. 4 shows the apparent viscosity curves of MBBA as a function of strain at differenttemperatures. Since MBBA is a flow-aligning nematic@DeGennes and Prost~1993!#, nooscillations are observed in the strain dependence of the viscosity of MBBA in thetemperature range from 15 to 35 °C. After dissolution of a small amount of the side-chainLCP, however, oscillations in the apparent viscosity of the resulting LCP/MBBA solu-tions are observed at small strains, as shown in Figs. 5 and 6, indicative of flow-tumblingbehavior. It is well known that MBBA is a nematic with negativeDe @DeGennes andProst ~1993!#. In this work, the value ofDe remains negative for dilute LCP/MBBAsolutions as evident by the fact that the apparent viscosity of LCP/MBBA solutionsmeasured in the presence of an electric field is very close to that measured in the absenceof electric field@Yao and Jamieson~1997!#. It can be seen from Figs. 5 and 6 that thestrain periodicity increases slightly with the increase of temperature but decreases withthe increase of concentration. In Fig. 7, we show the stress transients for the LCP/MBBAsolution at different temperatures. The doublet peaks, predicted by Ericksen’s TIF theoryand clearly evident in the stress transients in Fig. 7, are not seen in the creep derivativesin Fig. 6, and the amplitude of the oscillations in apparent viscosity are reduced. Again,this may reflect an inherent insensitivity of the creep experiment to small changes instrain rate or that the creep experiment is more prone to out-of-plane motion of thedirector.

FIG. 3. Apparent viscosity curves of 8CB at different temperatures (stress5 0.4 Pa).



14:24:30

B. Creep experiments in the presence of an electric field

We turn now to investigate the change in creep response of the tumbling nematicswhen subjected to electric fields applied transverse to the flow direction. It is known thatthe flow behavior of a tumbling nematic changes when an electric field is applied trans-verse to the flow direction, and flow-aligning may be regained when the field strengthreaches a critical value@Skarp et al. ~1981!; Carlsson and Skarp~1981!; Carlsson~1984!#. Moreover, application of Ericksen’s TIF theory yields an expression for thiscritical field strength@Carlsson and Skarp~1981!#:

Ec4 5

4g2ua2ua3

e02De2 , ~5!

whereg is shear rate,e0 is the permittivity for vacuum, andDe is the dielectric anisot-ropy of the nematic. Figure 8 shows the field strength dependence of the apparent vis-cosity curves of 8CB at stress5 0.4 Pa andT 5 37 °C in cone-and-plate geometry. Itcan be seen from Fig. 8 that the amplitude of the oscillation in viscosity decreases as thefield strength increases, and that the mean viscosity increases. This reflects a suppressionof flow-tumbling and an increasing level of flow-aligning behavior, with a degree ofalignment determined by the balance in hydrodynamic and electric torques. Within ex-perimental error, the flow-tumbling is completely suppressed at a critical voltageUc5 50 V before the viscosity reaches an asymptotic maximum value at a saturated volt-

age Us 5 100 V. The viscosity measured at the critical field strength is the apparentcritical viscosity,h* , and the viscosity measured at the saturation field strength ishc ,one of the three Miesowicz viscosities. From Fig. 8 we determineh* 5 0.5 P and

FIG. 4. Strain rate curves of MBBA at different temperatures (stress5 0.4 Pa).



14:24:30

hc 5 0.8 P. The latter value is very close to the literature value 0.79 P@Kneppeet al.

~1981! and ~1982!#. As indicated by Eqs.~4! and ~5!, the ratioa3 /a2 and the producta2a3 can be calculated separately from measurements of strain periodicity and criticalfield strength. Thus, combination of these results generates the values ofa2 anda3 of8CB, which are listed in Table I. The effect of the electric field on the strain periodicityappears negligible except when the field strength is close to the critical value, where asmall shift of the peak positions to larger strain occurs.

For the LCP/MBBA solution, flow-tumbling is suppressed by electric fields and dis-appears at a much higher critical voltageUc 5 200 V, as shown in Fig. 9. The effect ofthe electric field on the strain periodicity is also negligible, although there appears to bea slight shift in the peak position to lower values of strain when the field strength is veryclose to the critical value. Following the same procedure as that for 8CB, the values ofa2anda3 of the LCP/MBBA solution were calculated fromgp andEc and the results arealso listed in Table I.

In order to study the influence of electric fields on the doublet peaks of 8CB, the creepcurves of 8CB atT 5 34 °C, near the smectic-to-nematic transition temperature, weremeasured in the presence of electric fields with increasing strength. The results are shownin Fig. 10. It is evident in Fig. 10 that the doublet peaks become asymmetric in thepresence of an electric field. Specifically, the amplitude ratio of the high-strain doubletpeak to the low-strain peak increases as field strength increases.

FIG. 5. Apparent viscosity curves of MBBA solutions of the side-chain LCP with different concentrations(T 5 20 °C, stress5 0.4 Pa!.



14:24:30

C. Analysis by Ericksen’s TIF theory

As the creep experiments show, the application of electric fields can suppress thetumbling behavior of a nematic and the critical field strength is strongly dependent on theabsolute value ofDe. According to Ericksen’s TIF theory, the critical field strength canbe calculated using Eq.~5!. When the field strength is greater thanEc , flow-aligning isregained and the orientation angleu, which is the angle of the director relative to theshear gradient direction, is determined by the balance between the hydrodynamic andelectric torques. Quantitatively, the orientation angle can be calculated using the follow-ing equation@Carlsson~1984!#:

tanu 5e0DeE2

2ga32AS e0DeE2

2ga3D 2

2ua2u

a3, ~6!

whereE is the field strength. The corresponding apparent viscosityhalign is given by

halign 5 a1 cos2 u sin2 u1hc1~a21a3!sin2 u, ~7!

wherea1 is the first Leslie viscosity coefficient andhc is one of the three Miesowiczviscosities. When the field strength is less thanEc , the director of a tumbling nematicrotates but the rotation is influenced by the field. The corresponding apparent viscosityh tum is @Yang and Shine~1993!#:

FIG. 6. Apparent viscosity curves of an MBBA solution of the side-chain LCP at different temperatures~c 5 0.02 g/mL, stress5 0.4 Pa. The curves are shifted by certain viscosity units to avoid overlapping!.



14:24:30

htum 5 a1 cos2 u sin2 u1hc1~a21a3!sin2 u2~a2 cos2 u2a3 sin2 u!2

a32a2

22k~a2 cos2 u2a3 sin2 u!2 sinu cosu. ~8!

The parameterk is defined as follows:

k 5e0DeE2

2~a32a2!g. ~9!

When k is small, the field-induced peak shift is negligible and the strain periodicityremains constant~Figs. 8, 9 and 10!. Therefore, Eq.~2! can be used to convert rotationangleu into shear straing @Gu and Jamieson~1994a!#.

The critical field strength, where the flow-tumbling is just suppressed, corresponds toa critical value,kc @Yang and Shine~1993!#:

kc 5~2a2a3!0.5

a32a2. ~10!

As Eq. ~10! shows,kc is independent of field strength and shear rate. From the data inFig. 8, the critical field strength at which flow-aligning behavior reaches the cone edge isdetermined to be 63.6 kV/m, very close to the theoretical value, 57.3 kV/m, calculatedfrom Eq. ~5!, using literature data of 8CB@Ratna and Shashidhar~1977!; Kneppeet al.~1981! and ~1982!#.

FIG. 7. Stress curves of an MBBA solution of the side-chain LCP at different temperatures~c5 0.02 g/mL, shear rate5 32 s21. The curves are shifted by certain stress units to avoid overlapping!.



14:24:30

Because the field strength varies radially in cone-and-plate geometry, a cylindricalsurface of critical field strengthEc exists, as schematically illustrated in Fig. 11. Withinthe Ec cylinder, tumbling nematics show flow-aligning behavior, and the orientationangleu changes gradually from 90° at the center to the critical angleuc at the surface.Outside theEc surface, tumbling nematics show flow-tumbling behavior, the rate ofwhich is dependent on radial distance. As the applied voltage increases, the radius of thecylindrical Ec surfacer cs increases which means the rheological response of tumblingnematics show progressively less flow-tumbling character and more flow-aligning char-acter. Whenr cs is equal to the cone radiusr co, all the molecules have changed fromflow-tumbling to flow-aligning. The voltage and the corresponding viscosity atr cs5 r co are the critical voltage,Uc , and the apparent critical viscosity,h* , respectively.

From Fig. 8, we determine, for 8CB at 37 °C,h* 5 0.5 P atUc 5 50 V.

FIG. 8. Apparent viscosity curves of 8CB in the presence of an electric field~T 5 37 °C, stress5 0.4 Pa!.

TABLE I. The second and third Leslie viscosity coefficients of 8CB and the LCP/MBBA solution.

Nematic 8CB LCP/MBBA solution

Temperature~°C! 34 15LCP concentration~g/mL! t 0.01a3 /a2 20.2316 0.005 20.02196 0.005a2a3(Pa2 s2) 20.0018960.0006 20.00036560.00008a2 ~Pa s! 20.09046 0.002 20.1296 0.002a3 ~Pa s! 0.02096 0.003 0.002836 0.004



14:24:30

Based on this model, and because the total applied stress and the rate of deformationare uniform for the entire sample, the apparent viscosityhapp can be considered as thesum of two component viscositieshdt andh fa :

happ 5 hdt1h fa . ~11!

Herehdt is the viscosity contribution from the tumbling 8CB outside theEc surface andh fa is the viscosity contribution from the flow-aligning 8CB within theEc surface. Arigorous description is difficult and we present a simplified analysis based on an approxi-mation to Eq.~11!:

happ 5 ~12xfa!h tum1xfahalign, ~12!

where h tum is the mean viscosity of tumbling 8CB in the presence of an electric fieldwith strength equal to the mean of the field at the perimeter andEc . halign is the meanviscosity of flow-aligning 8CB in the presence of an electric field with orientation angleu equal to the mean of the values ofu at Ec and the cone center.xfa is the areal fractionof flow-aligning 8CB:

xfa 5r cs

2

r co2 . ~13!

For cone-and-plate geometry, the shear rate is constant but the field strength variesradially. The field strength at radial distancer is

FIG. 9. Apparent viscosity curves of an MBBA solution of the side-chain LCP in the presence of an electricfield ~T 5 15 °C, c 5 0.01 g/mL, stress5 0.8 Pa. The curves are shifted by certain viscosity units to avoidoverlapping!.



14:24:30

E 5U

r tanb, ~14!

where U is the voltage applied to the cone and the plate andb is the cone angle.Substituting Eq.~14! into Eq. ~5! and writing g 5 s/happ, wheres is shear stress, wehave

FIG. 10. Apparent viscosity curves of 8CB in the presence of an electric field~T 5 34 °C, stress5 0.4 Pa!.

FIG. 11. The cylindricalEc surface in cone-and-plate geometry.



14:24:30

rcs2

5e0DeU2happ

2s tanbA2a2a3

, ~15!

and whenr cs 5 r co,

rco2

5e0DeU2h*

2s tanbA2a2a3

, ~16!

whereh* is the apparent critical viscosity. Substituting Eqs.~15! and~16! into Eq.~13!,we obtain

xfa 5U2happ

Uc2h*

. ~17!

Inserting Eq.~17! into Eq. ~12!, we have

happ 5 S 12U2happ

Uc2h* D h tum1

U2happ

Uc2h*

halign. ~18!

Noting that we can equatehalign to h* , rearrangement of Eq.~18! gives

happ 5Uc

2h tumh*

U2h tum1~Uc22U2!h*

. ~19!

FIG. 12. Calculated apparent viscosity curves of 8CB in cone-and-plate geometry (T 5 37 °C).



14:24:30

At 37 °C, the tumbling response is confined to smallk (k , kc 5 0.22) and the onlydetectable ER effects are the increase of apparent viscosity and decrease of the oscillationamplitude as field strength increases, which evidently results from the evolution of theEcsurface in cone-and-plate geometry. Thus, it is reasonable to utilize the viscosity curve atdc 5 0 V in Fig. 8 as an approximation forh tum, i.e., we can neglect terms coupling thedirector rotation to the electric field for 8CB at 37 °C.

Equatingh tum [ the viscosity function at voltageU 5 0 V ~Fig. 8! and h* [ theviscosity function at the critical voltage,Uc 5 50 V ~Fig. 8! in Eq. ~19!, simulation ofthe ER effects in Fig. 8 was performed and the results are shown in Fig. 12. Comparisonof Figs. 8 and 12 indicates that this simple model accurately reproduces two principalcharacteristics of the creep response of 8CB in electric fields, viz. when the field strengthincreases, the mean value of the apparent viscosity increases, and the oscillation ampli-tude decreases and disappears at the critical voltageUc 5 50 V.

To gain a better understanding of the influence of an electric field on the oscillationsin the apparent viscosity of 8CB and the LCP/MBBA solutions, calculation was alsoperformed using Eqs.~2! and~8!. The results are shown in Figs. 13 and 14. It can be seenfrom Figs. 13 and 14 that the predicted amplitude ratio of the doublet peaks becomesasymmetric when an electric field is applied and the degree of asymmetry increases asfield strength increases. These simulation results are qualitatively consistent with theexperimental behavior of 8CB and the LCP/MBBA solution. Physically, the asymmetryarises because, at constant stress, whenDe . 0, the electric torque slows down thedirector when it moves away from homeotropic alignment, and speeds it up when itmoves toward homeotropic alignment. The opposite is true forDe , 0.

FIG. 13. Calculated apparent viscosity curves of 8CB with differentk values (T 5 34 °C).



14:24:30

For 8CB ~Fig. 13!, the ratio of the high-strain doublet peak to the low-strain peak inthe simulated Ericksen’s TIF response increases ask increases. This is consistent with theobserved result~Fig. 10!. The asymmetry of the doublets is clearly visible in the ERcreep experiments for 8CB when the temperature is close to the smectic-to-nematictransition. For the LCP/MBBA solution, on the other hand, the ratio of the high-strainpeak of the doublets to the low-strain peak is predicted to decrease ask increases, but theeffect is comparatively small~Fig. 14!. The fact that the applied field has little effect onthe shape or position of the experimental strain rate oscillations of the LCP/MBBAsolution is consistent with the weak effect of the field in the simulations. In fact, the smallshift observed in the peak locations to lower strain near the critical field~Fig. 9! isconsistent with the predicted increase in amplitude of the low-strain doublet peak~Fig.14!. A more definitive test of Ericksen’s TIF description of the ER behavior of tumblingnematics can be gained by performing controlled-strain experiments.

IV. CONCLUSIONS

Oscillations in strain rate are observed in creep experiments on homeotropic mon-odomains of 8CB and LCP/MBBA solutions in the absence of electric field. Upon ap-plication of an electric field, the tumbling response is suppressed and disappears at acritical voltage. The absolute value ofDe of a tumbling nematic, not the sign ofDe,determines the critical field strength at which tumbling behavior is suppressed by anelectric field and flow-aligning is regained. Thus a much weaker field is required tosuppress the flow-tumbling of 8CB compared to the LCP/MBBA solutions. The applied

FIG. 14. Calculated apparent viscosity curves of the LCP/MBBA solution with differentk values ~T5 15 °C, c 5 0.01 g/mL!.



14:24:30

field produces an asymmetry of the doublet peaks in 8CB but has relatively little effect onthe shape of the oscillations of the LCP/MBBA solution. Simulation based on Ericksen’sTIF theory successfully reproduces the suppression of flow-tumbling and the field-induced asymmetry of the doublet peaks in qualitative agreement with the experimentalobservations.

ACKNOWLEDGMENTS

The authors gratefully acknowledge financial support from the National Science Foun-dation Science and Technology Center ALCOM. They also thank Professor Shi-QingWang and Jingrong Xu for useful discussions.

References

Carlsson, T., ‘‘Theoretical investigation of the shear flow of nematic liquid crystals with the Leslie viscositya3 . 0: Hydrodynamic analogue of first order phase transitions,’’ Mol. Cryst. Liq. Cryst.104, 307–334~1984!.

Carlsson, T. and K. Skarp, ‘‘The stabilizing effect of an electric field on the shear flow of nematic liquid crystalswhena3 . 0: Flow alignment regained,’’ Mol. Cryst. Liq. Cryst.78, 157–171~1981!.

Chiang, Y.-C., A. M. Jamieson, M. Kawasumi, and V. Percec, ‘‘Electrorheological behavior of main-chainliquid crystal polymers dissolved in nematic solvents,’’ Macromolecules30, 1992–1996~1997!.

Chow, A. W., R. D. Hamlin, and C. R. Ylitalo, ‘‘Transient shear response and flow-induced microstructure ofisotropic and nematic rigid-rod poly~p-phenylenebenzobisthiazole! solution,’’ Macromolecules25, 7135–7144 ~1992!.

Cladis, P. E. and S. Torza, ‘‘Stability of nematic liquid crystal in couette flow,’’ Phys. Rev. Lett.35, 1283–1285~1975!.

Clark, M. G., F. C. Saunders, I. A. Schanks, and F. M. Leslie, ‘‘A study of flow alignment instability duringrectilinear oscillatory shear of nematics,’’ Mol. Cryst. Liq. Cryst.70, 195–222~1981!.

DeGennes, P. G. and J. Prost,The Physics of Liquid Crystals, 2nd ed.~Clarendon, Oxford, 1993!, Chap. 5.Ericksen, J. L., ‘‘Anisotropic fluids,’’ Arch. Rat. Mech. Anal.4, 231–237~1960!.Gahwiller, Ch., ‘‘Temperature dependence of flow alignment in nematic liquid crystals,’’ Phys. Rev. Lett.28,

1554–1556~1972!.Grizzuti, N. S., S. Lavella, and P. Cicarelli, ‘‘Transient and steady-state rheology of a liquid crystalline hy-

droxypropylcellulose solution,’’ J. Rheol.34, 1293–1310~1990!.Gu, D. and A. M. Jamieson, ‘‘Rheological characterization of director dynamics in a nematic monodomain

containing mesogenic polymers of differing architectures,’’ Macromolecules27, 337–347~1994a!.Gu, D. and A. M. Jamieson, ‘‘Shear deformation of homeotropic monodomains: Temperature dependence of

stress response for flow-aligning and tumbling nematics,’’ J. Rheol.38, 555–571~1994b!.Gu, D., A. M. Jamieson, and S. Q. Wang, ‘‘Rheological characterization of director tumbling induced in a

flow-aligning nematic solvent by dissolution of a side-chain liquid crystal polymer,’’ J. Rheol.37, 985–1001 ~1993!.

Han, H. W. and A. D. Rey, ‘‘Simulation and validation of temperature effects on the nematorheology ofaligning and nonaligning liquid crystals,’’ J. Rheol.39, 301–322~1995!.

Hongladarom, K. and W. R. Burghardt, ‘‘Molecular alignment of polymer liquid crystals in shear flow. 2.Transient flow behavior in poly~benzyl glutamate! solution,’’ Macromolecules26, 785–794~1993!.

Jahnig, F. and F. Brochard, ‘‘Critical elastic constants and viscosities above nematic-smectic A transition ofsecond order,’’ J. Phys.~Paris! 35, 301–306~1974!.

Jamieson, A. M., D.-F. Gu, F.-L. Chen, and S. Smith, ‘‘Viscoelastic behavior of nematic monodomains con-taining liquid crystal polymers,’’ Prog. Polym. Sci.21, 981–1033~1996!.

Jordan, T. C. and M. T. Shaw, ‘‘Electrorheology,’’ IEEE Trans. Electr. Insul.24, 849–878~1989!.Kneppe, H., F. Schneider, and N. K. Sharma, ‘‘A comparative study of the viscosity coefficients of some

nematic liquid crystals,’’ Ber. Bunsenges. Phys. Chem.85, 784–789~1981!.Kneppe, H., F. Schneider, and N. K. Sharma, ‘‘Rotational viscosityg1 of nematic liquid crystals,’’ J. Chem.

Phys.77, 3203–3208~1982!.Marrucci, G., ‘‘Rheology of liquid crystalline polymers,’’ Pure Appl. Chem.57, 1545–1552~1985!.Mather, P. T., D. S. Pearson, R. G. Larson, D. Gu, and A. M. Jamieson, ‘‘The origin of stress oscillation

damping during start-up and reversal of torsional shearing of nematics,’’ Rheol. Acta36, 485–497~1997!.



14:24:30

Pieranski, P., E. Guyon, and R. J. Plano, ‘‘Two shear-flow regimes in nematicp-n-hexyloxy-benzilidene-

p8-aminobenzonitrile,’’ Phys. Rev. Lett.32, 924–926~1974!.Ratna, B. R. and R. Shashidhar, ‘‘Dielectric studies on liquid crystals of strong positive dielectric anisotropy,’’

Mol. Cryst. Liq. Cryst.42, 113–125~1977!.Skarp, K., T. Carlsson, S. T. Lagerwall, and B. Stebler, ‘‘Flow properties of nematic 8CB. An example of

diverging and vanishinga3 ,’’ Mol. Cryst. Liq. Cryst. 66, 199–208~1981!.

Yang, I.-K. and A. D. Shine, ‘‘Electrorheology of a nematic poly~n-hexylisocyanate! solution,’’ J. Rheol.36,1079–1104~1992!.

Yang, I.-K. and A. D. Shine, ‘‘Transient shear flow of a unidomain liquid crystal polymer,’’ Macromolecules26, 1529–1536~1993!.

Yao, N. and A. M. Jamieson, ‘‘Electrorheological behavior of side-chain liquid crystalline polysiloxanes innematic solvents,’’ Macromolecules30, 5822–5832~1997!.



14:24:30

Date post:	25-Dec-2016
Category:	Documents
Upload:	alex-m
View:	213 times
Download:	0 times

Electrorheological creep response of tumbling nematics

Documents