Introduction

Upon the cessation of shear of main-chain nematic andcholesteric liquid crystalline polymers (LCP) dark linesperpendicular to the ¯ow direction can appear whenviewed under crossed-polarizers. This pattern has be-come known as a band texture. Its formation duringrelaxation following simple and elongational shear, inboth lyotropic and thermotropic LCP, is now a well

investigated phenomenon but is still not fully under-stood. Interest in the structure and formation of bandtexture is generated not only because of its e�ects on themacroscopic properties of LCP ®bres (Morgan et al.1980, 1983; Takeuchi et al. 1988; Allen and Roche 1989;Krause and Vezie 1989) and ®lms (Wang and Labes1992), but also because an explanation of the develop-ment of this texture is fundamental to any comprehensiveunderstanding of the ¯ow processes occurring in LCP.

Rheol Acta 38: 569±593 (1999)Ó Springer-Verlag 1999 ORIGINAL CONTRIBUTION

Philip HarrisonPatrick Navard

Investigation of the band texture occurringin hydroxypropylcellulose solutionsusing rheo-optical, rheological and smallangle light scattering techniques

Received: 2 March 1999Accepted: 26 July 1999

P. Harrison á P. Navard (&)Ecole des Mines de ParisCentre de Mise en Forme des Mate riauxUMR CNRS 7635, BP 207, F-06904Sophia Antipolis Cedex, Francee-mail: patrick.navard@cemef.cma.fr

Presented at EuroRheo 99-1May 3±7, 1999, Sophia-Antipolis, France

Abstract The band texture occurs inlyotropic and thermotropic main-chain polymers after cessation of¯ow. This paper begins with a reviewof work concerned with band textureformation following shear and isfollowed by the presentation oforiginal results obtained during arecent investigation. The evolutionof band texture formation in aKlucel EF, 50% hydroxypropyl-cellulose (HPC) water solution, hasbeen observed using polarized opti-cal microscopy. The relationshipdetermined between the primaryshear rate and the rate of evolutionof the band texture is complex andthree di�erent behaviours have beenobserved corresponding to threeshear rate regions. Both steady ¯owand dynamic rheological investiga-tions have been conducted on theHPC solution, the results of whichhave been related to the opticalbehaviour of the band texture. Datafrom steady ¯ow investigations sug-gest that the viscosity of the solutionwhen the band texture is present,

decreases following increasing pri-mary shear rates, is shear thinningand increases linearly with the timefollowing its formation. Dynamicinvestigations suggest a de®nite linkbetween the band texture evolutionand the evolution of both G¢ and G¢¢.In addition, the perfection of theband texture versus the primaryshear rate has been quanti®ed bystudying the evolution of tan(d)following the cessation of the pri-mary shear. Dynamic experimentsshow that the structure of the bandtexture remains longer than sug-gested by the optical aspect of thetexture. Small angle light scatteringpatterns have been correlated withthe development of the band textureand con®rm the continuing presenceof the band texture structure fol-lowing its optical disappearance.

Key words Liquid crystallinepolymer á Hydroxypropylcellulose áBand texture á Rheo-optics áRheology

Over the last 20 years, the structure and evolution ofthe band texture have been investigated in detail using avariety of techniques. However, throughout the litera-ture there exist a host of con¯icting results and diversetheoretical explanations regarding the band textureformation. The absence of a recent comprehensivereview paper means that selected reading of the litera-ture can give a confusing and even misleading under-standing of the band texture phenomenon. Thus, inorder to clarify the current state of research, a review ispresented here which provides a guide to the largenumber of investigations that have already been con-ducted on the subject of band texture formation, andwhich also clari®es which aspects of the phenomenon areand are not understood. The review begins with workconcerned with the molecular structure of the textureand continues with work concerning the causes, mech-anisms and in¯uences on its formation. In doing so theorganisation of the review re¯ects the development ofunderstanding which has progressed considerably overthe past two decades.

In the current investigation the results of polarisedmicroscopy observations, steady ¯ow and dynamicrheological testing, and small angle light scatteringmeasurements (SALS) are combined in observing theband texture evolution occurring in a 50% hydroxy-propylcellulose (HPC) water solution. The aim is toidentify the e�ects of the band texture evolution on therheology and structure of the LCP. The paper ispresented in three sections. The ®rst section describesthe experimental apparatus and procedure, the secondsection is a presentation and discussion of the results andthe third section consists of the conclusions of thisinvestigation. Within the ®rst two sections the work issubdivided into four parts, each part deals with aparticular experimental technique corresponding to:rheo-optical polarised light microscopy measurements,rheological measurements of the simple shear viscosityof the band texture, rheological measurements of thedynamic functions during relaxation and SALS patternsduring relaxation.

Band texture formation: a review

The term band texture is commonly used to describeoptical or structural features where objects or ¯uctua-tions are aligned in a periodic parallel manner. In thecase of LCP, such arrangements occur in nematic andcholesteric LCP after the cessation of ¯ow and fornematic polymers under magnetic ®elds. In both casesthe bands are due to a periodic orientation ¯uctuation ofthe director. We will review here the formation of a bandtexture due to ¯ow. Such a band texture is seen as aseries of periodic long thin dark lines running perpen-dicular to the ¯ow direction when observed between

crossed polarisers. This e�ect is very common for mostlyotropic and thermotropic, nematic or cholesteric mainchain LCP and can also be seen in nematic surfactants.

The band texture seems to be a relaxation phenom-enon occurring after a shear or elongational ¯ow,although the presence of a similar band texture existingduring ¯ow in poly(benzyl-L-glutamate) (PBLG) andpoly(benzyl glutamate) (PBG) solutions has been re-ported. On these occasions the band texture occurs as atransient phenomenon which occurs during the ®rst fewunits of strain. However, this band texture occurs onlyafter the director ®eld has been previously well-orien-tated uniaxially in the shear plane (Kiss and Porter1980b; Larson and Mead 1992; MuÈ ller et al. 1994, 1996).Relaxation of the Frank elasticity, arising from an out-of-plane splay in the director ®eld, was suggested as themotivating force behind the production of the bandtexture (MuÈ ller et al. 1994, 1996). The connectionbetween this type of band texture and that occurringfollowing the cessation of shear is unclear, thus a ®nalrestriction to the work encompassed in the followingreview is that it is focused solely on the band texturewhich forms following the cessation of shear.

Structure of the band texture

During the years following its ®rst observation, thestudy of band texture structure and formation wasmainly centred on the band texture occurring in poly p-phenylene terephthalate (PPT) ®bres and, consequently,a sharply kinked pleated structure possessing a radialorganisation was proposed (Ballou 1976; Dobb et al.1977a, b; Hagege et al. 1979; Simmens and Hearle 1980;Morgan et al. 1980; Roche et al. 1986). Attempts toexplain the exceptionally high modulus of these ®breswere made by suggesting either further structuralfeatures onto which the band texture is superposed(Panar et al. 1983), or else by the suggestion that certain®bres run through more than one layer of the bandstructure (Li et al. 1983).

Later studies turned their attention towards LCP®lms and sheared samples, in these investigations theobvious geometrical di�erences between these samplesand cylindrical ®bres meant that the pleated structurewas unsuccessful in describing the director path; so anin-plane sharply kinked zigzagging director orientationwas consequently proposed for both PBLG and HPCsolutions, which are cholesteric at rest, and also forthermotropic LCP (Kiss and Porter 1980b; Horio et al.1985; Hu et al. 1985; Thomas and Wood 1985). Aslightly more complicated structure was also suggestedfollowing the observation of an out-of-plane componentto the zigzag structure found in both thermotropic andlyotropic HPC (Nishio and Takahashi 1984; Nishioet al. 1985). Further electron microscopy observations

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clearly revealed that the texture was composed of ®brilsrunning in a zigzag manner through sheared thermotro-pic and lyotropic LCP (Chen et al. 1987a, b).

Concurrent with this zigzag model, following a seriesof investigations on various thermotropic LCP in whichthe structure was frozen upon cooling, a more smoothlyvarying sinusoidal trajectory was proposed in place ofthe sharply kinked trajectory (Donald et al. 1983;Donald and Windle 1983a; Viney et al. 1983; Nishioand Takahashi 1984) and the small in-phase out-of-plane component was repeatedly observed (Donald1984; Donald and Windle 1984). However, later obser-vations by the same workers using alternative techniquesmeant that a more ¯at-topped pro®le for the director®eld had to be considered instead of a purely sinusoidaltrajectory (Donald 1983, 1984; Donald and Windle1983b, 1984).

Since these initial reports various trajectories havebeen observed, including a serpentine director ®eld inlyotropic HPC and poly(p-phenylenebenzbisthiazole)(PBZT) ®lms (Navard 1986; Donald et al. 1986; Fischeret al. 1994; Patnaik et al. 1995) and a hybrid director®eld sharing characteristics of both the zigzag andserpentine models in a thermotropic cellulose derivativeand in HPC-acid solutions (Navard and Zachariades1987; Fried and Sixou 1988). In addition, recentinvestigations using relatively new techniques havecon®rmed and quanti®ed the out-of-plane componentof the band texture occurring in ®lms cast from lyotropicsolutions along with the presence of ®brils which followthe director path (Fischer et al. 1994; Patnaik et al.1995).

The angle the director ®eld makes with the ¯owdirection depends on the material and the processingconditions. Various values lying between 6° and 45°have been reported in the literature and some of thesevalues have been summarised by Qian and Chen (1992).Finally, it is worth noting that additional ®ner periodicstructural arrangements within the larger band texturehave also been observed (Chen et al. 1987b; Fried andSixou 1988; Patnaik et al. 1995) and in one report thise�ect was attributed to the restoring of a cholestericstructure.

Some of the variations and contradictions in thetrajectories observed could be linked to the techniquesused to observe the structure. The possibility exists thatthe principal optical vibration direction and the longaxis of the molecules in some LCP do not coincide.Consequently a periodic rotation of the molecules, andpossibly an out-of-plane component of the moleculartrajectory, were suggested in an attempt to explain theanomalies between optical microscopy and electrondi�raction observations (Viney et al. 1985). To sum-marise, despite numerous and sometimes con¯ictingideas, a common feature of almost all reports on thestructure of the band texture is a periodic variation in

the director ®eld. The detailed form of the molecularstructure usually lies somewhere on the spectrum offorms ranging from the zigzag to the serpentine modeland often contains an in-phase, out-of-plane componentto the periodicity. Grouping of molecules into ®brils,which follow the periodic structure, has also beenobserved but it is as yet unclear if this is a universalfeature of all band textures. Numerous factors play anin¯uence in determining the exact form of the molecularstructure, including: type of material, processing condi-tions, molecular rigidity, temperature etc., but as yet noprecise rules have been formulated that can directlyrelate these factors to the exact form of the bandstructure. It is interesting to note that the onlyprocessing conditions under which band texture appearsto be successfully prevented from forming in LCP is inthe glands of spiders and insects (Kirkam et al. 1991).

Relaxation of energy stored during shearthrough band texture formation

Band texture formation occurs during the relaxation ofLCP and is generally regarded to be the preferredmechanism for releasing energy, which has been storedin the material during shear. This energy is usuallythought to be stored as some kind of elastic potentialenergy (Nishio et al. 1984; Horio et al. 1985; Marrucci1985; Fincher 1988; Ernst and Navard 1989; Marsanoet al. 1989; Ma�ettone et al. 1989; Picken et al. 1991,1992; Gleeson et al. 1992; Vermant et al. 1994; Vineyand Putnam 1995; Fischer et al. 1996; Riti et al. 1997).However, the exact nature of the stored elasticity is stillunclear. The problem lies in the fact that duringsu�ciently high shear the director appears to be forthe most part in a well-aligned state, at least whenconsidering the in-plane two-dimensional (2-D) director®eld (Fincher 1988; Picken et al. 1990). A well-aligneddirector ®eld points to small amounts of stored elasticenergy. Thus, if the release of elastic potential energy iscited as being the cause of the band texture the questionof where this elastic energy is stored has to be addressed.

The buckling of the director ®eld due to therelaxation of viscoelastic stresses has been proposed asone possible cause of the in- and out-of-plane periodicityof the band structure (Nishio et al. 1984; Horio 1985;Fincher 1988; Fischer et al. 1996). However, the originof this viscoelasticity is still unclear. Recently, it hasbeen suggested that the origin of the viscoelasticiy iscaused by an underlying elastic network existing inconjunction with the nematic phase (Fischer et al. 1996).In this respect, it is interesting to note that band texturehas been observed in cross-linked HPC solutions (Yanget al. 1993). However, evidence has been found whichsuggests that the behaviour of the dynamic moduli, andhence the viscoelastic behaviour of the material, is

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controlled by the average molecular orientation ratherthan by the domain size. Consequently, it seems that theviscoelasticity of the material is not determined by theFrank elasticity contained in the texture (Moldenaersand Mewis 1993).

Another idea to evolve was that the band texturecould be a modi®ed form of the polydomain texture(Zachariades et al. 1984; Nishio et al. 1985). This ideawas elaborated on with the suggestion that the bandtexture could be a form of coherent tumbling occurringbetween coalescing domains. The angle of the director inthe zigzag path would be determined by a competitionbetween Frank elastic forces, tending to align thedirector at 90° to the ¯ow direction, and the shearingand polymeric forces, tending to align the moleculesalong the ¯ow direction (Marrucci 1985). However, thisidea appears to con¯ict with various experimentalevidence. For example, using this theory it is di�cultto explain observations of smoothly varying director®elds, ®brils orientated along the direction of ¯ow andband texture occurring following elongational shearwhere tumbling behaviour should not occur.

The prevailing view in the literature is now thatelastic energy stored in the texture of the LCP duringshear is the main driving force for the band textureformation. However, the exact details of where and howthis texture elasticity is stored are still under debate.Fincher (1988) deduced that the elastic energy of theLCP during ¯ow was possibly contained in large valuesof the out-of-plane splay elasticity of the director ®eld, adistortion which is undetectable when analysing thesheared samples under crossed-polarisers in the shear-vorticity plane. Later, by using a continuum mechanicalapproach, the relaxation of a random perturbation in a2-D director ®eld was modelled in simulating therelaxation of the director of poly(benzyl-D-glutamate)(PBDG) solutions. Band formation was found to bepossible when using a large ratio between the splay andbend elastic constants in driving the relaxation (Pickenet al. 1992). However, problems with this approach areevident. First, an unrealistically large ratio between thesplay and bend Frank elasticities was required in orderto form the band texture. Second, since these Frankelastic constants depend individually on concentrationone would expect the growth kinetics of the bands inturn to depend on concentration. This criteria is notobserved in experiments on PBG solutions (Vermantet al. 1994).

An alternative form of texture elasticity is providedby the Frank elastic energy contained in defects ordisclination loops. These defects o�er a speci®c locationfor the energy stored in the texture. It has been suggestedthat during ¯ow these defects possibly congregate inlocalised areas (Takebe et al. 1990; Ernst et al. 1990)and are squeezed, increasing their distortion and thusincreasing their elastic energy. This energy is thought to

be released upon cessation of ¯ow, resulting in theformation of the band texture (Ernst and Navard 1989;Ma�ettone et al. 1989; Takebe et al. 1990; Picken et al.1991). Although it is now known that band textureforms only after the cessation of shear (Fincher 1988;Ernst and Navard 1989; Picken et al. 1991) [the transientband texture seen during ¯ow by Kiss and Porter(1980b) is now thought to be the result of the initialconditions of the experiment (Larson and Mead 1992;MuÈ ller et al. 1994, 1996)], the origins of the texture haverecently been convincingly linked to the rearrangementof defects which exist during shear in a thermotropicLCP (Riti et al. 1997). This observation provides directevidence that the band texture is indeed the result of therelaxation or re-organisation of defects, which arepresent during ¯ow.

The reason for a periodic structure forming duringthe relaxation of defects has been suggested to bebecause the ¯ow pattern leading to this structuralarrangement most e�ciently disperses the texture'selastic energy, whilst retaining a relatively high degreeof molecular orientation (Ernst and Navard 1989; Vineyand Putnam 1995). Alternatively, it has been suggestedthat the contraction of disclination loops stretchedduring ¯ow (Picken et al. 1991; Marrucci and Ma�et-tone 1994) causes recoil leading to the compression andsubsequent buckling of the director ®eld and hence tothe periodic structure (Vermant et al. 1994). Finally, aless obvious manner in which the defects may havecaused the band texture is by providing a driving forceorthogonal to the director axis, analogous to the forceprovided by orthogonal magnetic ®elds which producesa similar e�ect to band texture when applied to well-orientated monodomains (Ma�ettone et al. 1989).

Despite the increasing dominance of the idea thatdefects provide the main driving mechanism of bandtexture formation, there are still certain experimentalobservations which are di�cult to incorporate with thisnotion. For example, a threshold value of the Deborahnumber has been observed in lyotropic solutions belowwhich the band texture fails to form. The Deborahnumber gives a measure of the molecular elasticity of theLCP, thus it has also been suggested that molecularelasticity plays a crucial, albeit indirect or perhapstriggering, role in the formation of the band texture(Gleeson et al. 1992). However, before this thresholdvalue is considered to be a general rule for the formationof the texture, further investigations on a variety ofmaterials should be conducted to con®rm the connection.

Finally, it is worth noting that despite the generalconsensus that band texture is the result of therelaxation of texture elasticity stored during ¯ow,recently, following observations on the relaxation ofmagnetically aligned LCP this mechanism has beenquestioned. It was suggested that a possible alternativeenergy source was the spontaneous extension of the

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liquid crystalline structure, which causes compressiveforces in the sample and hence buckling of the director®eld (Fischer et al. 1996).

In¯uences on the formation and relaxationof the band texture

Over the last ten years or so, many experimentalinvestigations have been conducted in an attempt tounderstand the in¯uences a�ecting the formation andrelaxation of the band texture. In order to review thiswork the e�ects of changing parameters such as; sample¯ow history, molecular weight, solution concentration,solvent, temperature and sample thickness, on factorssuch as; texture appearance, minimum and maximumshear rate required to produce the texture, rate andkinetics of texture evolution, band spacing and rheolog-ical behaviour are each considered in turn. However,when reading the literature it soon becomes clear that,even when trying to write a structured review, there areso many di�erent factors involved in the variousexperiments and so many con¯icting reports that it isimpossible to give de®nitive statements regarding thee�ects of many of the experimental parameters. How-ever, the most important parameter is undoubtedly thetype of material under investigation, for this reasonthe various e�ects will be considered with respect to thematerial itself. At best we hope this section of the reviewwill provide clari®cation of the e�ects of certainparameters and at worst it will serve as a guide to thelarge body of literature available on the subject.

Type of evolution

The optical evolution of the band texture occurring inboth lyotropic and thermotropic LCP is generallydescribed as developing relatively quickly following thecessation of shear, before fading away over a longerperiod of time (Kiss and Porter 1980b; Horio et al. 1985;Chen and Qian 1990). However, this behaviour is notalways the case for all LCP. For example, the bandtexture of a thermotropic LCP was observed to appear,fade, reappear and then to fade once again to a wormor polydomain texture (Graziano and Mackley 1984).In addition, the details of the band's kinetics duringrelaxation are related to the type of LCP underconsideration. For example, the bands appearing duringthe relaxation of HPC solutions disappear by a gradualdecrease in regularity and visibility and possibly passthrough a so-called parabolic focal conic texture(Donald et al. 1986), which is probably linked to thereformation of their cholesteric order, before eventuallyending in a polydomain state (Ma�ettone et al. 1989).In contrast, bands in PBG solutions tend to increase in

length and then width (Picken et al. 1992; Gleeson et al.1992; Larson and Mead 1992; Vermant et al. 1994)before fading to a ®nal well-oriented ®nal state (Ver-mant et al. 1994). Similar band evolution to thatobserved in PBG solutions has been seen in a thermo-tropic LCP, but importantly in this case the ®nal statewas a polydomain texture (Riti et al. 1997). Followingvery high shear rates the band spacing in HPC solutionshas been observed to pass through a minimum spacing(Putnam and Viney 1991; Viney and Putnam 1995)before increasing with time (Wang and Labes 1992;Viney and Putnam 1995). It appears therefore that thevisual evolution of the band texture relaxation appearsto be particular to the LCP under investigation andlinked to the ¯ow conditions. As yet the reasons behindthe di�erences in these behaviours is still far from beingunderstood.

Shear history

Increasing the primary shear rate usually has the e�ect ofincreasing the regularity or perfection of the resultingband texture in HPC and PBG solutions (Kiss and Porter1980b; Gleeson et al. 1992; Picken et al. 1992; Larsonand Mead 1992; Vermant et al. 1994). Furthermore, thedevelopment of the band texture has been found todepend crucially on the primary shear rate applied to theLCP. A minimum primary shear rate is often observedbelow which the band texture will not form. This shearrate has been observed in HPC solutions (Horio et al.1985; Marucci et al. 1987; Marsano et al. 1988a; Ernstand Navard 1989; Ma�ettone et al. 1989; Peuvrel andNavard 1990, 1991; Tsakalos et al. 1997), PBG solutions(Kiss and Porter 1980b; Picken et al. 1992; Vermantet al. 1994) and various other lyotropic (Marsano et al.1988b, 1989; Chen and Qian 1990) and thermotropic(Grazano and Mackley 1984) LCP, and consequentlyappears to be a general feature of band texture formationin all types of LCP.

Interestingly, experiments that involved a smallsecond primary shear in a direction orthogonal to the®rst primary shear revealed that the second primaryshear is conducive to the formation of the band texture.This second shear was also shown to signi®cantlydecrease the minimum shear rate required to producethe band texture (Ma�ettone et al. 1989). Anothermethod of reducing this minimum value has been foundto be by the use of elongational shear. For example, theminimum shear rate required to form the band texturewas reduced by a factor of about 20 when comparing theminimum elongational shear rate with the usual mini-mum shear rate (Peuvrel and Navard 1990, 1991).

In addition to the minimum primary shear rate, amaximum primary shear rate has been reported abovewhich the band texture failed to form in PBG solutions

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(Vermant et al. 1994). However, it is unclear if thismaximum rate applies to other LCP and has yet to beobserved even following very high shear rates in certainother lyotropic LCP (Marsano et al. 1989; Putnam andViney 1991; Viney and Putnam 1995).

A ®nal factor for the formation of band texture isthat the sample has also to be sheared through aminimum amount of strain in order to produce thetexture, the size of this minimum strain depends on thesize of the primary shear rate producing the strain(Marrucci et al. 1987; Marsano et al. 1988a, b, 1989).

Apart from the threshold values of the shear rate,which are linked to the formation of the band texture,the primary shear rate is also of great importance indetermining the rate of evolution of the band texture.For example, numerous reports suggest the rate ofevolution of the band texture increases with increasingprimary shear rate. This has been observed for HPCsolutions (Donald et al. 1986; Navard 1986; Fried andSixou 1988; Ernst and Navard 1989), PBG solutions(Kiss and Porter 1980b) and thermotropic LCP(Zachariades et al. 1984). In fact, more detailed studieson PBG solutions found that while the time before theappearance of the bands in PGB solutions decreasedwith increasing shear rate, the growth kinetics of thebands themselves were una�ected by the primary shearrate (Picken et al. 1992).

However, while observations of this kind have oftenbeen reported, a series of investigations on variouslyotropic LCP revealed that this behaviour may not bethe whole picture. In these tests the rate of evolutionwas found to increase with increasing primary shearrate following relatively low rates, as previously ob-served, but following higher rates the rate of evolutionwas seen to decrease with increasing shear rate (Mar-sano et al. 1988a, b, 1989; Chen and Qian 1990).Results from the current investigation con®rm thislatter result.

The primary shear rate has also sometimes beenobserved to in¯uence the band spacing of the texture.For example, many workers report a decrease in bandspacing when increasing the primary shear rate in certainthermotropic (Zachariades and Logan 1983; Navardand Zachariades 1987; Chen et al. 1987a) and lyotropic(Fischer et al. 1994) LCP. However, the relationshipseems to depend on both the material and solvent underconsideration since no in¯uence of the primary shearrate on band spacing was observed in either HPC watersolutions, HPC acid solutions or PTTA acid solutions(Fincher 1988; Ernst and Navard 1989; Fried and Sixou1988; Chen and Qian 1990; Ding et al. 1995) or in athermotropic LCP (Riti et al. 1997).

Finally, the structure of the band texture in HPC-water solutions has been shown to be very stable evenwhen being subject to a secondary shear of up to 10(Ernst and Navard 1989) or 14 (Tsakalos et al. 1997)

shear units away from and back to its original position.This stability has led some workers to suggest that a lackof tumbling occurs during this secondary shear (Ernstand Navard 1989). These results also con®rm the closeconnection that exists between the polydomain and bandtextures, in that the visual appearance of an out-of-register band texture is the same as that of a polydomaintexture (Bedford and Windle 1990; Tsakalos et al. 1997).A more in-depth study of the stability of the bandtexture will be presented in this work.

Polymer molecular weight, solution concentrationand solvent

Changing the molecular weight and solution concentra-tion of LCP can have various e�ects on di�erent aspectsof band formation. For example, the molecular weightof the LCP has been related to the size of both theminimum (Ernst and Navard 1989) and maximum(Vermant et al. 1994) primary shear rates linked to theformation of the band texture. Various behaviours havebeen found when changing solution concentration. Thebehaviour seems to depend on the material underconsideration. For the case of HPC solutions theconcentration had little in¯uence on the minimum shearrate required to form the band texture (Ernst andNavard 1989) and the only requirement appears to bethat the concentration should be su�ciently high suchthat the solution becomes birefringent (Horio et al.1985). However, for the case of PTTA solutions, theminimum shear rate showed a signi®cant decrease whenthe concentration was increased by just a few percent(Chen and Qian 1990).

The connection between solution concentration andthe rate of band texture evolution is more di�cult toascertain from the literature because of con¯ictingresults. For example, increases in the concentration ofHPC-water solutions have been reported to increase therate of evolution (Putnam and Viney 1991; Viney andPutnam 1995) or alternatively have little e�ect (Mar-sano et al. 1988a, b). In addition, increases in the rate ofevolution have been reported for increasing concentra-tions of PTTA solutions (Chen and Qian 1990) and alack of in¯uence was observed on the band growthkinetics in PBG solutions (Vermant et al. 1994). Mattersare further complicated by the result that the solventused in forming the solution plays a major role in therate of evolution. For example, the rate of evolution inHPC methanol solutions, in contrast to HPC watersolutions, was found to decrease with increasing solu-tion concentration and the e�ect of the solvent wasthought to be caused by the di�erent degrees ofentanglement that occurred in the LCP when usingdi�erent solvents (Putnam and Viney 1991; Viney andPutnam 1995).

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As mentioned previously, the sense of the rate ofevolution for certain lyotropic polymers has been foundto change upon reaching a certain primary shear rate.The value at which the rate of evolution changed froman increasing to a decreasing relationship with primaryshear rate was found to decrease as the viscosity ofthe solution decreased (Marsano et al. 1989a, b). How-ever, since the viscosity depends on numerous factorsincluding the molecular weight, solution concentrationand polymer ¯exibility, at this point it is impossible tospecify the role of each of these parameters in changingthe value of this shear rate.

While increasing the molecular weight appears toincrease the band spacing (Donald et al. 1986), at leastin HPC water solutions, the e�ects of solution concen-tration on band spacing are far from clear. For example,the band spacing in HPC water solutions has beenobserved both to increase (Donald et al. 1986) and todecrease (Fincher 1988) with increasing solution con-centration. In the latter case the decrease was such thatthe wavenumber extrapolated to zero at the concentra-tion where the mesophase formed. Alternatively, noobvious correlation was reported between the bandspacing and solution concentration in HPC acid solu-tions (Fried and Sixou 1988) or PBG solutions (Vermantet al. 1994). Again, it appears that the type of LCP andsolvent under investigation is critical to the resultingbehaviour of the system and the discrepancy betweenresults on HPC water solutions has yet to be resolved.

Temperature

Changes in temperature have also been observed toin¯uence numerous aspects of the band texture forma-tion occurring in a variety of di�erent LCP. For a start,in a recent investigation the minimum shear raterequired to form the band texture in a thermotropicLCP was found to increase quickly with increasingtemperature (Harrison et al. 1999), while as one mightexpect given the sensitive temperature-viscosity depen-dence of thermotropic LCP, decreasing the temperaturecaused the rate of evolution of the band texture todecrease (Graziano and Mackley 1984).

The temperature also in¯uences the band spacing.For example, in thermotropic LCP the band spacingis seen to decrease with a reduction in temperature(Donald and Windle 1983). Although this kind ofrelationship is not shared by either HPC acid solutionsor PBG solutions (Fried and Sixou 1988; Vermant et al.1994), changes in temperature have been observed toa�ect the time before which the band kinetics changefrom 1-D to 2-D growth in PBG solutions (Vermantet al. 1994).

Other miscellaneous e�ects which have been observedinclude increases in both the angular spread of the

molecular orientation and the out-of-plane componentof the periodicity with increases in temperature ofthermotropic LCP (Donald and Windle 1983, 1984;Donald 1984). Further studies revealed that annealingthe band texture in a thermotropic LCP for a shortperiod of time caused the optical aspect of the bandtexture to disappear, even though the microstructure ofthe texture remained intact. In contrast to the bandtexture arrangement, the annealing also caused thebands to turn into domains elongated in the sheardirection (Donald and Windle 1984a, b). Band textureformation has also been observed without the usual pre-shearing. This spontaneous band texture occurs inPBLG solution-cast ®lms following heating and subse-quent cooling. It was suggested that a possible cause ofthe band texture was local internal stresses created in themelt during quenching (Qian and Chen 1992).

Thickness of sample

The minimum shear rate required for the production ofthe band texture in HPC solutions was found to decreasewith increasing layer thickness, suggesting that the bandtexture was some kind of ¯ow instability (Marucci et al.1987). In addition, decreasing the thickness of thesample was observed to decrease the rate of evolutionof bands in PTTA-H2SO4 solutions and HPC solutions(Chen and Qian 1990; Viney and Putnam 1995), and tohinder the growth of bands in PBG solutions (Vermantet al. 1994). However, once again con¯icting results havebeen reported as gap thickness was found to be of littleimportance on either the optical appearance, rate ofevolution or band spacing in HPC water solutions(Marsano et al. 1988a; Fincher 1988; Ernst and Navard1989), or on the rate of growth of bands in PBGsolutions (Picken et al. 1992; Gleeson et al. 1992). Theprocess of observing possible e�ects of gap thickness onband texture kinetics may be further complicated bynon-linear velocity pro®les occurring throughout thegap (Guido et al. 1990).

While band texture evolution has been reported to berelatively insensitive to the type of material of thecontaining walls (Atkins et al. 1980; Donald et al. 1983),it has been suggested that appreciable contact with thesubstrate may prevent the out-of-plane component ofband texture developing (Nishio and Takahashi 1984).Finally, a notable e�ect of the sample thickness of HPCwater solutions was that the sample acted more e�-ciently as a di�raction grating as the thickness increased(Fincher 1988).

Normal stress

Many LCP are known to produce negative normalstresses during ¯ow within certain ranges of shear rates.

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A correlation between the occurrence of a negative ®rstnormal stress di�erence,N1, and the presence of the bandtexture has been reported in PBLG solutions (Kiss andPorter 1978; 1980a, b). Their experimental evidencesuggested that if a solution did not show a negative N1 atany shear rate then the band texture failed to appear.However, this hypothesis is in contradiction to bandtexture formation in thermotropic LCP which generallyfail to show a negative normal stress (Cidade et al. 1995).Furthermore, the closer the shear rate moved towards theshear rate range that contained the negativeN1, the fasterthe band texture appeared following the cessation ofshear. The appearance of the band texture was immedi-ate within the shear rate range of negative N1. Duringlater investigations, both similar (Navard 1986) andcontrary (Marsano et al. 1988) results were found forHPC water solutions. Thus, the correlation foundbetween the negative normal stress and band textureformation in lyotropic LCP is still open to question.

Stress relaxation

By using a variety of complementary experimentaltechniques the stress relaxation following ¯ow of aPBZT polyphospheric acid was related to the orientationof molecules of ®rst the solvent and then the polymermolecules of the material (Odell et al. 1993). In partic-ular, the initial fast relaxation of the stress wasattributed to disorientation of the solvent molecules.Immediately afterwards, the appearance of the bandtexture marked the transition to a second slower stage ofstress relaxation during which the mesogen orientationstarted to decrease. The ®nal stage was related to thetransformation of the banded texture to a polydomaintexture and corresponded to the very slow decay ofmesogen orientation. At present it is unclear howgeneral this behaviour is to other lyotropic LCP.

Experimental methods

Sample material

HPC `Klucel EF' polymer (batch 9453) of molecular weight 80,000g mol)1 was dried for at least 3 h in an evacuated oven at atemperature of 70 °C. The dried polymer powder was then mixedwith distilled water at a concentration of 50 wt%. This main batchof solution was stored in a fridge at 4 °C for 2 weeks during whichtime the solution was repeatedly remixed. This procedure ensuredthat the polymer was completely dissolved and that the solution wasfully homogeneous. Before testing, a small quantity of the solutionwas taken from the main batch and the air bubbles were removedusing a `Heraeus Sepatech Labofuge A' centrifuge. In this way, allthe tests were conducted on exactly the same concentration solution.

Rheo-optics

Optical observation of the band texture was conducted using both amodi®ed `Instron 3250' rheometer, described by Riti and Navard

(1994) and a `Linkam CSS 450 Cambridge Shearing System'. Allobservations were conducted under cross-polarized light. TheInstron 3250 was used with a cone and plate geometry. The conehad a 40 mm diameter with an angle of 0.1 rad (i.e. 5.73°) and atruncation gap of 45 lm. Observations were performed witha Wild-Leitz microscope through a 5´ objective lens equippedwith a `Cohu High Performance Color CCD' camera. The systemgave a combined magni®cation of 236 times in the horizontaldirection and 232 times in the vertical direction. The line of sightpassed approximately 5 mm from the extremity of the cone wherethe gap was around 600 lm. The experiments performed with thissystem were conducted at room temperature, which was main-tained between 19 and 21 °C.

The Linkam system used had a parallel plate geometry. Theimage produced when using the Linkam system was of lowercontrast than that produced using the Instron 3250, this loss inimage quality was attributed to light scattered by the opaque wallssurrounding the viewing windows on the Linkam system. Bycollimating the light beam as well as possible and using a slightlylarger gap of 700 lm, the clarity of the band texture was found toimprove. Preliminary experiments using SALS with the Instron3250 failed to detect any obvious change in the evolution time ofthe band texture when the gap was changed from 440 to 720 lm,similar results have been previously reported (Marsano et al.1988a, b; Fincher 1988; Ernst and Navard 1989), hence thedi�erence in the gap used for the Instron 3250 (600 lm) andLinkam systems (700 lm) was considered to be of little importancewhen comparing results. The same microscope and camera wereused with the Linkam system as with the Instron 3250 rheometer.Experiments were again conducted at room temperature which wasmaintained between 19 and 21 °C. The Instron 3250 enabled theband texture to be observed following high shear rates (>60 s)1)which proved unobtainable using the Linkam system because of thehigh torques involved in applying the shear. At shear rates below60 s)1 both instruments were used, a procedure which ensured thereliability of the data.

Two di�erent investigations were conducted, the ®rst utilisedboth systems and was intended to determine the relationshipbetween the applied shear rate and the subsequent rate of evolutionof the band texture. The second investigation was conducted usingonly the Linkam system and was aimed at determining the stabilityof the band texture once it had formed following the cessation ofthe primary shear.

Optical evolution of band texture

Investigations into the evolution of the band texture wereperformed by applying a `primary shear' to the sample at apredetermined shear rate for at least 200 strain units. This allowedthe sample to reach a steady ¯ow state before the applied shear wasstopped. The position of both the cone and plate, and parallel platesystems in this investigation and in all subsequent investigationswere ®xed upon cessation of shear, thus preventing recoil of theplates during the relaxation of the sample. The development of theband texture was then monitored following the cessation of shearand the times at which its visibility reached certain stages in itsevolution were noted. Each measurement was repeated at least fourtimes, ensuring repeatability within about 10%, and the averagevalue was calculated. The various stages recorded during thedevelopment of the texture were the time before which the bandtexture; ®rst started to appear, reached maximum visibility andalmost completely disappeared.

Optical stability of band texture

The aim of the experiments, following investigations by Ernst andNavard (1989) and Tsakalos et al. (1997), was to determine the

576

maximum strain through which the band texture could bedeformed such that it reappeared upon returning the cone andplate to its original position. However, in this study the relationshipbetween this maximum strain and the rate of primary andsecondary shear was also investigated.

The procedure used was as follows: a `primary shear' wasapplied for at least 200 strain units such that the band textureformed following a certain period of time after the cessation of thisprimary shear. A `rest period' allowed for the band texture to formand then a `secondary shear' was applied, ®rst of all for a set periodof time in one direction, and then returning in the oppositedirection to the original position existing before the onset of thesecondary shear. The only constraint in choosing the secondaryshear rate in these particular experiments was to ensure that thedisappearance time of the texture was longer than the rest periodplus the period of secondary shear. During the secondary shear theoptical aspect of the band texture disappeared. On returning thecone and plate to the original position the sample was viewed todetermine whether the band texture had reappeared or had beendisrupted by the action of the secondary shear.

Steady ¯ow rheology

The work presented in this section is essentially a continuation andextension of work conducted by Tsakalos et al. (1997). Steady ¯owtime-sweep tests were conducted using the RMS 800 rheometer®tted with a cone and plate geometry measuring 50 mm indiameter, with a cone angle of 0.04 rad (i.e. 2.29°) and a truncationgap of 47 lm. As with the rheo-optical experiments, the sample wassheared through at least 200 strain units before stopping the ¯ow.Following a predetermined rest period a secondary shear wasapplied to the sample in the previous shear direction and the torquewas measured and recorded. Analysis of the viscosity versus the`time following cessation of shear' curves provided informationregarding the viscosity of the band texture.

Dynamic testing

Both Stresstech and RMS 800 rheometers were used for theseinvestigations. The Stresstech was ®tted with a cone and plategeometry. The cone measured 40 mm in diameter, with a coneangle of 2 and a truncation gap of 70 lm. The temperature controlof the Stresstech system enabled the temperature to be maintainedat 20 � 0.1 °C. Most of the tests were conducted using this systembecause of its accurate temperature control. With our solutions, therheometer proved unreliable when imposing shear rates above30 s)1.

Measurements recorded following shear rates of 50 s)1 andabove were made using the RMS 800 rheometer, which was ®ttedwith the same cone and plate geometry as employed in the steady¯ow tests. The RMS 800 operated by imposing a ®xed shear rateand measuring the resulting shear stress. Thus, this system wasreliable at high shear rates. However, at low temperatures thesystem lacked the ®ne temperature control of the Stresstechrheometer. The temperature was maintained at 20 � 0.8 °C usinga refrigeration system designed to regulate the temperature of thesurrounding environment. Hence, results obtained using the RMS800 at these higher shear rates are likely to contain larger errors,caused by ¯uctuations in the temperature, than those produced bythe Stresstech rheometer.

The experiments involved shearing the sample at a predeter-mined shear rate until it had reached a steady state. Oscillatorytesting was then started in order to monitor the evolution of theviscoelastic functions following the cessation of shear. Preliminaryexperiments were performed to ensure that the measurements wereconducted in the linear region. Following these experiments afrequency of 10 rad s)1 and a strain amplitude of up to 5% werechosen for the whole of the dynamic investigation.

After performing numerous tests it became apparent thatbecause of the long duration of each experiment evaporation atthe edge of the sample was a problem. In order to reduce thisunwanted e�ect an anti-evaporation unit to saturate the watervapour was placed around the sample. However, even when thismeasure was employed the sample had to be changed followingeach test. The gap between the cone and plate was reset in eachexperiment before loading the next sample.

Small angle light scattering

Experiments were conducted using both the Inston 3250 and theLinkam systems using the same geometries as used in the rheo-optical investigations. A `Melles Griot' helium-neon laser was usedto provide a coherent light source of 632.8 nm wavelength. Thesheared sample was positioned in the laser beam and the di�ractionpattern was displayed on a white screen. Images were recordedusing a `U-matic SP' VO-9600P videocassette recorder andsubsequently analysed using the time resolved measurement andanalysis scattering system (TRAMS; Rosati 1998).

As with the optical experiments two di�erent investigations wereconducted: the ®rst was intended to determine the relationshipbetween the applied shear rate and the subsequent rate of evolutionof the scattering patterns; the second investigation was aimed atdetermining the stability of the band texture once it had formedfollowing the cessation of the primary shear.

Rate of evolution of the scattering patternsversus primary shear rate

A primary shear rate was applied to the sample for at least 200 strainunits until it had reached its steady state. The ¯ow was then stoppedand the plates remained stationary during the subsequent relaxationof the sample. The evolution of the pattern formed by the scatteredlaser beam on a white screen was then recorded. Previous studieshave already correlated the occurrence of two intensity maxima withthe formation of the band texture (Donald et al. 1983; Viney et al.1983; Horio et al. 1985; Hu et al. 1985; Roche et al. 1986; Navardand Zachariades 1987; Fincher 1988; Ernst and Navard 1989;Takebe et al. 1990; Chen and Qian 1990; Riti et al. 1997). However,in this study, the time evolution of the intensity of these maximaduring the relaxation of the sample was determined using theTRAMS software. This evolution could then be compared withboth the optical evolution of the band texture and also therheological behaviour of the solution. In addition, using Bragg'slaw the spacing of the bands was determined, along with the changein this spacing throughout the evolution of the band texture andfollowing di�erent primary shear rates.

Stability of the ®rst order scattering patterns

A similar procedure was employed in this investigation to that usedfor the investigation of the stability of the optical aspect of theband texture under cross-polarised light. The only di�erence beingthat, instead of observing the optical aspect of the band texture, theintensity of the ®rst order scattering patterns was monitored. Onceagain, using the TRAMS software package the intensity of thescattering was quanti®ed for analysis.

Results and discussion

Optical evolution of the band texture

In this section we examine how the band texture evolvesduring relaxation following the cessation of shear, i.e.

577

the time before which it appears, reaches its maximumvisibility and subsequently disappears, as a function ofthe primary shear rate. We also con®rm that it ispossible to shear the HPC water solution while the bandtexture is present without destroying its underlyingmolecular structure. This important fact was exploitedin determining the viscosity of the material while theband texture was present, the results of these experi-ments are presented in a subsequent section.

Well-documented published data and preliminaryexperiments conducted during this investigation haverevealed that the evolution of the band texture followscertain typical patterns. After any given primary shearrate the band texture appeared relatively quickly com-pared with the time before which it faded away. Also,the visibility or `perfection' of the band texture wasbetter following higher primary shear rates. This behav-iour is similar in these respects to the band textureobserved in HPC solutions and PBLG solutions (Kissand Porter 1980b; Vermant et al. 1994). No obviouschange in the spacing of the band texture was observedwith changes in the primary shear rate. The averageband spacing over 30 bands was found to be11.1 � 1 lm, a value in keeping with similar measure-ments of the band spacing made on HPC solutions(Shimamura 1983; Horio et al. 1985; Navard 1986;Fincher 1988).

E�ects of changing the primary shear rate

The rate of evolution of the band texture was found todepend crucially on the rate of the primary shear.Figure 1 shows the evolution time of the band texture atvarious stages in its development.

As reported in previous work a critical primary shearrate exists, below which the band texture fails to appearfollowing the cessation of shear for HPC-water solu-tions. This critical shear rate is thought to dependinversely on molecular weight (Ernst and Navard 1989)and was found to be approximately 1.4 s)1 for thesolution under investigation. Previously reported (Ernstand Navard 1989) values of the critical shear rate of1.1 and 2.6 s)1, corresponding to molecular weights of100,000 and 60,000 g mol)1 in HPC water solutions,fall on either side of the value found in this investi-gation which is expected given the molecular weightof 80,000 g mol)1 for the HPC polymer used in thisinvestigation.

Three di�erent stages in the behaviour of thedisappearance time of the band texture can be distin-guished according to the primary shear rate. The ®rststage, indicated by region I in Fig. 1, occurs at relativelylow shear rates between about 1 and 10 s)1, here the rateof evolution of the texture increases with increasingprimary shear rate as reported previously for HPC-watersolutions (Donald et al. 1986; Navard 1986; Ernst andNavard 1989), HPC acid solutions (Fried and Sixou1988), PBLG solutions (Kiss and Porter 1980b) and athermotropic LCP (Zachariades et al. 1984). The secondstage, region II in Fig. 1, occurs at moderate shear ratesbetween 10 and 40 s)1 the disappearance time of thetexture is almost constant as observed by Viney andPutnam (1995). Finally the third stage, region III inFig. 1, occurs at relatively high shear rates, above 40 s)1;the disappearance time of the texture increases withincreasing primary shear rate, as reported earlier fora variety of lyotropic LCP including an HPC watersolution albeit of a higher molecular weight than the oneinvestigated here (Marsano et al. 1988a, b, 1989).

Fig. 1 Various stages in theoptical evolution of the bandtexture exhibited by HPC solu-tions, as seen under cross-polarised light. Tests were con-ducted using both the Instronand Linkam systems and in-corporated samples taken fromthe main batch of HPC watersolution. Regions I, II and IIIshown on the graph correspondto three di�erent stages in thebehaviour of the disappearancetime of the band texture

578

Equations ®tted to the data of Fig. 1 suggest that thedisappearance time in region I, and the appearance andmaximum visibility times in regions I and II obey powerlaw relationships with the primary shear rate; see, forexample, Eqs. (1) to (3):

tq � 47:9 _cÿ1:47 ; �1�

tm � 77:9 _cÿ1:23 ; �2�

td � 201 _cÿ0:99 ; �3�here _c is the primary shear rate and ta, tm, and td are thetimes before; the appearance, the maximum visibilityand the disappearance of the band texture, following thecessation of the primary shear. The time before thedisappearance of the band texture is particularly inter-esting in that rearrangement of Eq. (3) gives (td * _c) to bealmost constant. This suggests that in the lower shearrate region, region I, the optical disappearance of theband texture scales with (time following the cessationof shear * primary shear rate) or `pseudostrain'. Thisscaling behaviour has already been found for the longscale relaxation of stress in LCP's following thecessation of ¯ow (Molden and Mewis 1990) and alsoin recoil experiments in which the stress was removedfollowing shear (Larson and Mead 1989; Riti et al.1997).

In Fig. 1 region II the behaviour changes and thetime before the disappearance of the band texturebecomes constant with increasing primary shear rate.At these shear rates the band texture appears almostimmediately after the cessation of ¯ow (within a fractionof a second). This short time and the subjectivity indetermining the exact time of appearance of the bandtexture meant that accurate results were impossible toobtain for the appearance of the band texture at shearrates higher than 20 s)1 and for the maximum visibilityof the texture at shear rates higher than 40 s)1.

Finally, in Fig. 1 region III, at shear rates above40 s)1, the disappearance time again obeys a power lawrule but now the time increases with increasing shearrate; the form of the ®tted power law model is given byEq. (4).

td � 0:53 _c0:86 ; �4�here td is the disappearance time and _c is the primaryshear rate. Also of interest is the observation that, afterextremely high shear rates (about 260 s)1), the appear-ance time of the texture is once again delayed, and at thisrate occurs after about 13 s.

This is the ®rst time that this behaviour has beenobserved in HPC water solutions of such low molecularweight. However, given the result found by Marsanoet al. (1989) that the shear rate at which the rate ofevolution changed from an increasing to a decreasing

relationship depended on the viscosity of the solution,then for solutions of di�erent molecular weight onewould expect this value to be shifted. The shear ratefound in Marsano's investigation was less than 18 s)1

for HPC solutions of Mw of 100,000 g mol)1. In thisinvestigation the shear rate was approximately 260 s)1

using a Mw of 80,000 g mol)1. It would be interesting todetermine if it is really the viscosity which determinesthis value, as suggested by Marsano et al. (1989), orwhether the change in viscosity is just another conse-quence caused by the change of molecular weight.

The three di�erent shear rate regions of the opticalevolution of band texture can be related to curvesshowing the viscosity and normal stress as a function ofshear rate. As already observed (Sigillo and Grizzuti1994), and previously explained in terms of the bi-phasicnature of HPC solutions (Guido and Grizzuti 1995), theviscosity versus shear rate curve fails to show theclassical three region form described by Onogi andAsada (1980). In place of the Newtonian region,identi®ed as region II, the HPC curve displays insteada region of less-shear thinning behaviour, the change inbehaviour occurred at a shear rate of about 1.5 s)1.Thus, the minimum shear rate required for the forma-tion of band texture (about 1.4 s)1) is fairly close to theonset of the second shear thinning region, an observa-tion which has been discussed previously (Ernst andNavard 1989).

The primary shear rate at which the negative normalstress begins has previously been reported to coincidewith the primary shear rate at which the band texture®rst appears instantaneously following the cessation ofshear in both PBLG solutions (Kiss and Porter 1980a)and HPC water solutions (Navard 1986); an observationwhich has been included in a semi-theoretical attempt toexplain the formation of band texture (Marrucci 1985).However, a later investigation of HPC solutions threwthis connection into doubt (Marsano et al. 1988a).Measurements in our investigation suggest that theappearance time follows the power law relationship upto primary shear rates as high as 20 s)1 before becominginstantaneous. The shear rate at which the appearancebecomes instantaneous is therefore slightly higher thanthe shear rate of about 15 s)1, which corresponds to thechange to negative normal stress, determined in thesteady ¯ow experiments (Fig. 2).

Optical stability of the band texture

The results of this investigation suggested that the bandtexture can be sheared up to a maximum of 14 strainunits away from its original position, before beingirreparably disrupted by the shearing action. This ®gurecompares with a value of about 10 strain units reportedby Ernst and Navard (1989) and from 11 to 14 strain

579

units reported by Tsakalos et al. (1997), both observingHPC water solutions. A new result found in thisinvestigation is that this value is independent of theboth the primary and secondary shear rates. Theseobservations con®rm the important conclusion that theband texture can exist even whilst remaining undetect-able when viewed under polarized light. A similar resultwas found when band texture seen in thermotropic LCPwas annealed (Donald and Windle 1984). The pheno-menon was recently explained, at least for the case ofdisappearance due to secondary shear, by the conjecturethat the structure remains intact along the ¯ow directionwhilst being disrupted along the gradient direction(Tsakalos et al. 1989), a view which is supported byexperimental observation (Bedford and Windle 1990).

Discussion of optical results

The optical evolution of the band texture as a functionof the primary shear rate follows previously seen trends.An important result is the con®rmation of the behaviourseen following high shear rates (Marsano et al. 1989)where the rate of evolution of the band texture decreaseswith increasing shear rate (region III in Fig. 1). Thisbehaviour must be connected to the way in which energyis stored and released. For low shear rates (region I inFig. 1) the disappearance time is scaled with (timefollowing cessation of shear) * (primary shear rate),as are all processes in LCP which are connected withtexture driven mechanisms. This suggests, or con®rms,that in the shear rate range identi®ed as region I theband texture occurs as a means of releasing Frank elasticenergy stored in defects. If this is the case, this explainswhy there is a minimum shear rate and shear strain

which are required before the band texture forms. Belowthese minimum values either the stored energy is toosmall (minimum shear strain) or it has been released bydirector reorganisation during ¯ow (minimum shearrate). The appearance time is probably linked to theamount of stored energy. When this energy is too smallit may take time to organise its release by means of theco-operative director relaxation into the band texture.

The total amount of energy stored in the defects is theaverage amount of energy stored in each defect multi-plied by the number of defects. At intermediate shearrates (region II in Fig. 1) the total energy is such that theband texture appears almost immediately. At lowershear rates (region I in Fig. 1) the stored energy is small(we postulate that some energy can be released bydirector reorganisation during ¯ow) and consequentlyan induction time is needed to distort the director ®eldinto the band texture morphology. At higher shear rates(region III in Fig. 1) the director tends to align in the¯ow direction, reducing the number of defects. How-ever, following these high shear rates optical observa-tions suggest an increase in the perfection of the bandtexture and consequently an increase in the storedenergy. Since the number of defects, and hence the totalamount of energy stored in defects, decreases at thesehigh shear rates the question of where the increasingamounts of energy is stored arises. This puzzle might beanswered by advocating another alternative drivingmechanism as the cause of the band texture occurringin region III. This proposal is supported by the opposite`rate of evolution versus primary shear rate' behaviourobserved in region III as compared with that of region I.Given the monodomain nature of the texture at thesehigh shear rates, the most likely alternative choice todefects as the driving mechanism is the elasticity

Fig. 2 Normal force of 50%HPC water solution versusshear rate, T = 19 � 1 °C

580

resulting from an out-of-plane splay of the director ®eld(Fincher 1988; Larson and Mead 1992; Picken et al.1992; MuÈ ller et al. 1994, 1996).

The connection between the negative normal forcesand the region where the band texture appears imme-diately following the cessation of shear is con®rmed.However, we believe that they are not directly connectedsince many LCP that do not have a negative normalstress region do display a band texture during relax-ation. The fact that the negative normal force and thezero induction time are at the same shear rate could bedue to the total amount of stored energy. The negativenormal force region occurs when the LCP moves from atumbling to a ¯ow-aligning regime. It is in this regionthat the number of defects is largest (the texture isre®ning) and it is there that the total stored energyshould be at its maximum.

In¯uence of the band texture on the steady ¯owrheology of the HPC water solution

The aim of these particular experiments was to distin-guish the in¯uence of the band texture on the form of theviscosity versus `time following the start of shear' curvesfrom the e�ects of the usual changes in structure whichmanifest themselves as the transient features during theinitial stages of the curves. As shown previously(Tsakalos et al. 1997), it is possible to measure theviscosity of the HPC water solution while the molecularstructure of the band texture is present. After isolatingthe e�ect of the band texture, experiments were con-ducted in order to determine the behaviour of the bandtexture viscosity, both with changes in the appliedprimary and secondary shear rates, and also during theperiod of time following its formation.

In order to isolate the e�ect of the band texture, asecondary shear was applied to HPC solutions in whichthe band texture had been formed, and also to solutionsin which the band texture had been formed but had thenbeen left undisturbed for a period of time su�cientlylong for its relaxation to take place. The form of theviscosity versus time curves during the secondary shearwas monitored in both instances. Comparison betweenthe resulting curves enabled the e�ect of the band textureon the ¯ow curve to be determined.

Figure 3 shows two such viscosity versus time curves.Each was obtained following a primary shear of 8 s)1

while applying a secondary shear rate of 2 s)1, thedi�erence between the two experiments being the resttime between primary and secondary shears. In oneinstance the rest time was 30 s (still displayed a bandtexture at the start of secondary shear) and in the other200 s (the band texture had completely disappearedbefore the start of secondary shear). The shapes of thecurves are dominated by the start up transients, the

behaviour of which have already been studied (Mortier1995). However, in the curve following the 30-s restperiod, a kink is evident following the initial overshoot(denoted by point A in Fig. 3). This kink is missing fromthe 200-s rest period experiment. Various tests con®rmedthis feature and so, following Tsakalos et al. (1997), thekink was associated with the presence of the bandtexture. This view was re-enforced by the observationthat the kink became more apparent following higherprimary shear rates, re¯ecting the increasing perfectionof the texture.

Relationship between viscosity of band textureand primary shear rate

A series of experiments was conducted in which theprimary shear rate was varied and a secondary shear rateof 1 s)1 was applied. The viscosity of the band texturewas measured at the point of the kink on each viscosityversus time curve. In this way, the viscosity of the bandtexture was determined as a function of the primary shearrate. The rest time chosen between the primary andsecondary shear rates in each test was the time before theband texture reached its maximum visibility. This wascalculated using Eq. (2) for shear rates less than 10 s)1

while for tests following higher shear rates this time wasapproximated and a rest period of about 2 s was usedbefore beginning the secondary shear. The results ofthese experiments are plotted in Fig. 4. The dashed linerepresents the steady ¯ow viscosity at a shear rate of1 s)1. As expected, the viscosity of the band texturedecreases following higher primary shear rates re¯ectingthe increased orientation occurring at higher shear rates.

Experiments were conducted in order to compare thebehaviour of the band texture occurring after a given

Fig. 3 Viscosity versus time curves produced during the secondaryshear of a sample which in one instance contained the band texture,and in the other did not contain the texture. Point A in the graphlocates the position of the kink and is connected to the presence of theband texture

581

primary shear rate to that of the steady ¯ow textureoccurring at the same shear rate. Figure 5 shows theviscosity during the presence of the band texture as afunction of the secondary shear rate. The primary shearrate used to create the band texture was 8 s)1. When theband texture viscosity was measured using a secondaryshear rate equal to the previously applied primary shearrate, the viscosity of the steady ¯ow texture was found tobe higher than the viscosity of the band texture by afactor of about 1.5 to 1.8. Preliminary experiments byTsakalos et al. (1997) revealed a factor of about 2.0 foranother HPC water solution of higher molecular weight.This result suggests that the degree of structure in the¯uid actually increases during relaxation, as the LCPtransforms from the steady ¯ow structure to thestructure of the band texture.

Behaviour of the viscosity of the band textureduring the time following its formation

In order to determine how the viscosity of the bandtexture changes during the time following its appear-ance, experiments were performed in which both theprimary and secondary shear rates were held constantbut the rest time between the two shears was varied. Twosimilar sets of tests were performed, both used primaryshear rates of 8 s)1, but one used a secondary shearrate of 1 s)1 and the other, 2 s)1. The results of theexperiments are shown in Fig. 6.

The viscosity of the band texture is seen to increaselinearly with time following its appearance, towards thatof the steady ¯ow viscosity. Extrapolating linear equa-tions ®tted to the two sets of data, until their intersec-

Fig. 4 Band texture viscosity asa function of the primary shearrate. Dashed line corresponds tothe steady ¯ow viscosity at ashear rate of 1 s)1

Fig. 5 Band texture viscosity asa function of the secondaryshear rate. The dashed lineshows the steady ¯ow viscosityfor a shear rate of 8 s)1. Notethat at a secondary shear rate of8 s)1 the band texture viscosityis lower than the steady ¯owviscosity of the same shear rate

582

tions with the steady ¯ow viscosities, gives estimates ofthe time before which the band texture is completelydisrupted. Values of about 130 and 160 s were obtainedfrom the two sets of data using this technique. However,these times do not correspond with the disappearancetime indicated by the rheo-optical experiments, calcu-lated to be about 44 s using Eq. (3). This apparentinconsistency can be resolved by the hypothesis that theoptical and actual disappearance of the band texture donot occur at the same time. This idea is supported byresults from rheo-optical investigations into the stabilityof the band texture, which proved that the texture couldexist whilst remaining undetectable when viewed underpolarised light.

Discussion of steady ¯ow viscosity results

Several important features can be deduced from thisseries of experiments. One is that it is possible tomeasure the viscosity of the HPC water solution withtwo types of texture present, either the normal texturewhich is present during steady-state shear or else thetexture which occurs during the presence of the bandtexture. Previous experiments by Tsakalos et al. (1997)have suggested that the band texture has a textualorganisation which was more ordered than that foundduring ¯ow because its viscosity was much smaller, thisidea has been con®rmed here and is especially clear whenthe band texture is sheared at the same secondary shearrate as the primary one. The band texture viscosity isinitially lower than the steady ¯ow viscosity andincreases with increasing rest time.

The only di�erence between the visual and viscositymeasurements concerns the disappearance time, which ismuch larger than that determined by visual measure-ments. This factor is examined again in the followingsections by using alternative probes of the existence of

the band texture. The overriding question which remainsfollowing these tests is why the band texture viscositysuggests a better textual organisation for the bandtexture in comparison with the usual steady ¯ow texture.We hypothesise that in going back to a polydomain reststate the HPC water solution must go through arelatively ordered transient state, which is observed asthe band texture under crossed-polarisers. This stateseems to be better organised when the primary shear rateis increased, since the band texture is seen more clearlywhen using optical microscopy, and its viscosity de-creases following higher primary shear rates.

Probing of the band textureby oscillatory measurements

Since the band texture re¯ects a transient texturalmorphology, its probing by oscillatory measurementsshould be instructive. Both G¢ and G¢¢ were measured asfunctions of time at a frequency of 10 rad s)1 followingthe cessation of shear at various primary shear rates.The evolution of the two viscoelastic functions followingshear displayed three di�erent forms, depending on therate of the preshear (see, for example, Fig. 7). After verylow shear rates (<0.4 s)1) there was a slight decrease inboth the functions. Following moderate shear rates(>0.4 s)1 and <3 s)1) the values of both G¢ and G¢¢increased (Mortier et al. 1992; Hongladarom et al. 1994)for a certain period of time before steadily increasing ata second slower rate. At higher shear rates (>3 s)1) thecurves rapidly increased, developed an overshoot andthen slowly increased again at the second slower rate.The overshoot seen in these experiments was previouslyreported to occur only in HPC solutions of lowmolecular weight (Hongladarom et al. 1994). However,

Fig. 6 Change in the band texture's viscosity during the timefollowing the cessation of primary shear. The steady shear viscositiesat 1 and 2 s)1 are shown by the dashed lines

Fig. 7 Three di�erent forms of G¢ following the cessation of shear.The form of G¢ was found to depend upon the primary shear rate.Similar behaviour was found for G¢¢

583

in this study small changes in temperature were found tobe crucial to the form and rate of evolution of thecurves, hence the need for accurate temperature controlduring the experiments. The general relaxation behav-iour is di�erent to that displayed by PBG solutions, thedynamic functions of which decrease following thecessation of shear (Moldenaers and Mewis 1986; Larsonand Mead 1989).

The rate of development of the viscoelastic functionswas plotted as a function of the primary shear rate. Inorder to do this, characteristic points were needed tomark the same stages in the development of each curve.Thus, both the time before the maximum of the initialovershoot and the minimum following the overshootwere plotted against the primary shear rate. These twocharacteristic points are marked as A and B in Fig. 7.Figure 8 shows the rate of relaxation of the G¢ and G¢¢functions versus primary shear rate along with datarepresenting the time before the disappearance of theband texture, as shown previously in Fig. 1.

The underlying form of the plotted data is clearlysimilar to that of the `time of disappearance of the bandtexture versus primary shear rate' curve found duringthe rheo-optical experiments. The three ranges ofprimary shear rates, regions I to III in Fig. 1 corre-sponding to the di�erent stages in the optical evolutionbehaviour of the band texture, can be directly related tothe evolution behaviour of the viscoelastic functions.The close similarities between the behaviour of theoptical and viscoelastic properties strongly suggest a linkbetween the two. However, there exist certain di�erencesbetween the two sets of data. Firstly, the evolution timesof the viscoelastic functions are slower than that of thevisible band texture. Secondly, the value of the powerlaw exponents governing the relationship between time

of evolution and primary shear rate, in the ranges ofprimary shear corresponding to regions I and IIIof Fig. 1, are clearly di�erent for the optical evolutionof the band texture and the evolution of the viscoelasticfunctions. These di�erences could again be resolved ifthe optical disappearance of the texture, rather thansignifying its complete disruption, corresponds to just anintermediate stage in its evolution; a possibility whichhas already been suggested by the behaviour of thesteady ¯ow viscosity of the band texture following thecessation of shear.

Initial and ®nal values of G¢ and G¢¢following the cessation of shear

A notable connection between the optical evolution ofthe band texture and the `long time' values of theviscoelastic functions has also been observed. In eachcase the long time values of the functions were noted2000 s following the cessation of shear and are referredto as the `®nal' value. (It should be noted that this valueis not the actual ®nal value of the viscoelastic functionssince they continue to increase at a slow rate for at least3000 s. It proved impossible to determine the timebefore the functions eventually reach their ®nal valuesbecause evaporation began to a�ect the results of theselong time measurements). Figure 9 shows both the`initial' and `®nal values' of G¢ and G¢¢ versus primaryshear rate.

Following a shear rate of about 0.4±0.6 s)1 thedi�erence between the initial and ®nal values of thefunctions increases following increasing shear rates.These results are typical of those found by Grizzutiet al. (1990) and Hongladarom et al. (1994). From

Fig. 8 Shows the time beforethe disappearance of the bandtexture and the time before themaximum of the overshoot ofG¢ and G¢¢ plotted against theprimary shear rate

584

about 0.4 to 1.5 s)1 the change in the dynamic functionsincreases dramatically with increasing primary shearrate. However, following higher primary shear ratesthe change increases at a much slower rate. Thus,the behaviour of the viscoelastic functions and thus thelong-term structure of the solution undergoes a transi-tion following a primary shear rate which correspondsvery closely to the minimum shear rate required for thegeneration of the band texture seen under cross-polar-ised light. Experiments by Grizzuti et al. (1990) revealeda similar transition between the initial and ®nal values ofthe complex viscosity. However, this transition occurredat much lower shear rates (see their Fig. 9). Though theydo not report the minimum shear rate required to formthe band texture for the HPC water solution in theirinvestigation, given that they are using a polymer ofhigher molecular weight one would expect the minimumshear rate to be shifted to lower values (Ernst andNavard 1989); if the transition does indeed correspondto the minimum shear rate required to form the bandtexture, their results are at least in keeping with thistrend.

The connection between the behaviour of the dy-namic functions and the band texture presents ananomaly. The relaxation of elastic energy stored indefects is widely believed to be the driving force of theband texture (see review) and the connection foundbetween the two phenomena implies that the behaviourof the dynamic functions is also determined by therelaxation of defects. However, the behaviour of thedynamic functions has been shown to be the result ofchanges in the average molecular orientation in PBGsolutions, rather than the result of texture relaxation(Moldenaers and Mewis 1993). Thus, there is anapparent contradiction in these results.

Connection between tan(d) and optical evolutionof band texture

Tan(d) gives the ratio between the two parameters G¢¢and G¢, which represent the viscous and elastic compo-nents of ¯ow respectively. The structural organisation ofthe band texture could be expected to in¯uence thesetwo components of ¯ow by di�ering degrees during itsevolution. Hence, the study of tan(d) can reveal therelative behaviour of the two functions.

The evolution curves of tan(d) in Fig. 10 showvarious interesting features; certain behaviours can beobserved depending on whether the solution is shearedat primary shear rates either below or above a certaincritical shear rate. As will be seen, this critical shear ratelies between 1 and 2 s)1 and therefore corresponds to thecritical shear rate required for the visible appearance ofthe band texture.

The ®rst noticeable feature of Fig. 10 is the verticalshifting of the curves produced following low primaryshear rates (i.e. between 0.2 and 2 s)1). In Fig. 11 thevalue of tan(d) in each experiment, measured 2000 safter the cessation of shear, is plotted against theprimary shear rate and the relationship between thevertical shift and the primary shear rate is illustrated.

A prominent feature of Fig. 11 is the downwardvertical shift in the tan(d) curves which occurs follow-ing shear rates ranging from 0.2 to 2 s)1. This featuresuggests that even though both the elastic and viscouscomponents of ¯ow increase following shear, at theserates there occurs a relative increase in importance ofthe elastic component of ¯ow with respect to theviscous component, inherent in the rest or `polydo-main' state of the material. This range of primary shearrates contains the critical shear rate at which the band

Fig. 9 Initial and ®nal valuesof G¢ and G¢¢ following thecessation of shear

585

texture ®rst becomes visible under cross-polarised light,i.e. 1.4 s)1.

A second signi®cant feature can be seen in Fig. 10. Asalready mentioned, in certain experiments the tan(d)curve develops a drop soon after the cessation ofprimary shear. This drop in tan(d) occurs only followingshear rates of at least 1.4 s±1 and therefore coincides withthe range of primary shear rates which produce a bandtexture under polarised light. It is also very close to theprimary shear rate at which the transition in thebehaviour of the dynamic functions comes to an end(see section on G¢ and G¢¢).

Evidence from both rheo-optical observations andsteady ¯ow viscosity experiments has already indicatedthat the perfection of the band texture increases with

increased primary shear rates. Thus, if the drop in tan(d)is indeed related to the formation and disruption of theband texture then it is not unreasonable to expect anincreasingly large drop in tan(d) following increasinglarge primary shear rates. Figure 11 shows the magni-tude of the drop in tan(d) versus primary shear rate. Thesize of the drop does indeed increase with increasingprimary shear rate, thus suggesting a connection withthe presence of the band texture. Furthermore, the rateof increase of the drop in tan(d) increases when movingfrom region II to region III. This result supports theargument of a change in the driving mechanism of theband formation when moving from region II to regionIII. This drop in the value of tan(d) presents a method ofactually quantifying the `perfection' of the band texture.It would be particularly interesting to see if a similardrop in tan(d) occurs in PBG solutions, since thebehaviour of the dynamic functions during relaxationis opposite to that occurring in HPC solutions (Mortieret al. 1992).

Figure 12 shows the time before the tan(d) versustime curves reach their maxima, minima and plateauvalues (which signify the beginning, bottom and end ofthe drop respectively) versus primary shear rate. Alsopresented are the results shown previously in Fig. 1, i.e.the rate of optical evolution versus primary shear rate.

This comparison between the optical evolution of theband texture and the evolution of tan(d) versus primaryshear rate clearly shows that the maximum visibility ofthe band texture corresponds to the maxima of thetan(d) curves. This is strong evidence to suggest that thedrop in tan(d) is directly attributable to the developmentof the band texture. Also, the time before the minimumin the tan(d) curve corresponds closely to the time beforethe maxima of the G¢ and G¢¢ curves (see Fig. 8) and like

Fig. 10 Tan(d) versus time following cessation of primary shear atvarious primary shear rates. Two noticeable features of the graph are;the vertical shifting of the curves which occurs following low shearrates (<2 s)1) and the drop in tan(d) which occurs following highshear rates (>2 s)1)

Fig. 11 Value of tan(d) follow-ing 2000 s versus primary shearrate. An obvious change inbehaviour occurs following acritical shear rate which corre-sponds to that required for theoptical formation of band tex-ture. In addition the drop intan(d) versus primary shear rateis also plotted. The size of thedrop increases following in-creasing primary shear rates

586

these dynamic functions, shows the same three regionform as the `optical disappearance time' versus primaryshear rate curve. Like the evolution curves of thedynamic functions the evolution curve of the minimaof tan(d) is once again shifted to times later than thedisappearance times of the band texture.

In summary tan(d), and consequently the ratiobetween the viscous and elastic components of ¯ow,increases until the time corresponding to the maximumoptical visibility of the band texture, after this point theratio decreases for a period of time which extends wellbeyond the optical disappearance of the band texture.Finally, the ratio increases once again and eventuallyattains a value, which is common to all polydomainstates created following the appearance of a bandtexture, irrespective of the previously applied primaryshear rate. Thus, the band texture is a process whichenables a speci®c ratio between the viscous and elasticcomponents of ¯ow to be attained. If the band texturedoes not form then the ratio between the viscous andelastic components is of a higher value.

Discussion of oscillatory results

The band texture is a transient restructuring phenom-enon. This is clearly seen when measuring G¢ and G¢¢during relaxation following the cessation of ¯ow. Bothfunctions show behaviours whose rate of change as afunction of primary shear rate very closely follows therate of optical evolution of the band texture as afunction of shear rate. Steady ¯ow viscosity measure-ments showed that the transient state initially has a lowviscosity which steadily increases to that of its steady-state counterpart. This suggests that shortly after thecessation of ¯ow the molecular organisation is better

orientated than that which exists during the steady ¯owtexture (better overall orientation and a lower density ofdefects), however this orientation is gradually disruptedduring relaxation. This behaviour is re¯ected in thesteady increase of both G¢ and G¢¢ following thecessation of shear. Measurements of tan(d) suggest acomplicated change in the ratio between the viscous andelastic components of ¯ow during the relaxation of theband texture. Again the rate of evolution of tan(d) asa function of primary shear rate very closely followsthe rate of optical evolution of the band texture as afunction of primary shear rate.

The measurement of tan(d) seems to be a verye�cient and objective way of probing the occurrenceand perfection of band texture formation. Once again,the rheological signature of the band texture lasts longerthan its optical visibility. This apparent anomaly will besolved in the next section by showing that the bandtexture, as seen by optical microscopy, disappears muchfaster than its underlying molecular arrangement. Rheo-logical measurements are more reliable indicators ofchanges in the band textures molecular arrangement.

Probing the band texture by light scattering

The behaviour of the SALS patterns was investigated asa function of the primary shear rate by analysing thescattering patterns using the TRAMS program. In orderto produce signi®cant ®rst order light scattering parallelto the direction of ¯ow (i.e. perpendicular to the bandtexture) primary shear rates of at least 1.4 s)1 had to beapplied to the sample. This shear rate is the same as thecritical shear rate necessary for the optical appearance ofthe band texture when viewed under polarised light and

Fig. 12 The maxima and mini-ma which mark the beginningand the end of the drop intan(d) respectively, plotted withthe data of Fig. 1. The maximaof tan(d) and the maximumvisibility of the band texturesuperpose. The minima oftan(d) shows a similar form tothe optical disappearance of theband texture

587

so provides the ®rst connection of this investigationbetween the ®rst order light scattering maxima and theband texture. An asymmetry in the intensity of the twoscattering peaks was noted as reported by previousworkers (Picken 1990; Vermant 1996; Riti 1996; Ritiet al. 1997).

Variations in the intensity of scattering were observedfollowing the cessation of shear. Figure 13 shows anexample of the scattering intensity versus scatteringangle 68 s after cessation of shear at 3 s)1. Onemaximum is visible which corresponds to the ®rst orderscattering. As mentioned earlier, the ®rst order maximahave been correlated with the formation of the bandtexture and have frequently been used to investigate itsstructure and evolution. The zero order scattering is thecombined result of the una�ected transmission of thelaser beam and scattering from large-scale irregularitiesin the material.

The intensity of the ®rst order maximum increased,reached a maximum value and then decreased during therelaxation of the sample (see, for example, Fig. 14).Following higher shear rates, for a period of time therelative magnitude of scattering from long range irreg-ularities increased and e�ectively hid the scattering dueto band formation. Also the ®rst order scattering fromthe band formation was spread over a range of angles,re¯ecting a distribution of the band wavelength, makingthe peak di�cult to discern. The combination of thesetwo factors meant that following high shear ratesmeasurements of the ®rst order scattering peak couldbe made only after the level of scattering from large scaleirregularities had su�ciently decreased and the ®rstorder peak had become apparent.

In Fig. 15 a direct comparison between the evolutiontimes of the ®rst order scattering data and the opticalevolution of the band texture, as seen under crossed-polarised light, is made. Three stages in the evolution of

the ®rst order intensity peak are plotted versus theprimary shear rate, corresponding to the times at whichthe peak; ®rst became apparent, reached its maximumintensity and ®nally disappeared.

Referring to Fig. 15, the form of the optical andscattering data versus primary shear rate both show thesame characteristic shape, hence con®rming a commoncause. However, one might have expected the opticalappearance of the band texture to coincide with theinitial appearance of the ®rst order scattering peaks.Instead, the appearance of the ®rst order peaks super-pose onto the curve representing the maximum opticalaspect of the band texture. Once again, as with theviscoelastic functions, the disappearance of the scatter-ing peaks occurs much later than the optical disappear-ance of the band texture.

In Fig. 16 the scattering angle corresponding to themaximum of the ®rst order scattering peak is plottedversus time, following a shear rate of 3 s)1. Thebehaviour and size of this scattering angle followed asimilar trend after shear rates of up to 7.5 s)1, althoughthe rate of evolution of the curve depended on theprimary shear rate. Following higher shear rates theangle stayed relatively constant with time.

Using Bragg's law (Eq. 5) the scattering angle can beused to give the band spacing, which is found to be17.4 lm at the beginning of the evolution and 12 lmduring the maximum of the scattering angle.

nk � d sin�h=2� �5�Here, n is the scattering order, k is the wavelength of thelight, d is the band texture wavelength and h is thescattering angle measured from the straight-throughdirection. In these experiments k = 632.8 nm andn = 1 for ®rst-order scattering. Thus, the spacingcorresponds reasonably well, at least during the maxi-

Fig. 13 Scattering intensity versus scattering angle 68 s after thecessation of shear at a primary shear rate of 3 s)1. The scattering peakcorresponds to the ®rst order Bragg di�raction

Fig. 14 Intensity of the ®rst-order scattering peak versus timefollowing the cessation of shear. The primary shear rate was 5 s)1.The arbitrary value of 30 on the intensity scale represents themaximum intensity discernable using the TRAMS analysis software

588

mum of the scattering angle, to that observed underpolarised light, i.e. 11.1 � 1 lm.

Light scattering experiments also revealed that thesample can be sheared up to a maximum of about 13strain units away from its original position and stilldisplay the ®rst order scattering associated with theformation of the band texture, upon returning the platesto their original positions. This value was found to beindependent of both the primary and secondary shearrates and corresponds closely to the value of 14 strainunits found for the stability of the band texture asdetermined using optical microscopy under crossed-polarised light. This result once again provides con®r-mation that the band texture can exist even whileremaining undetectable using polarised microscopy andlight-scattering techniques.

Discussion of light-scattering results

The main result of this part of the investigation is theoccurrence of the band texture at times where the opticalvisibility has disappeared. There is general agreementbetween the results obtained by steady ¯ow viscosity,oscillatory and light scattering experiments. For exam-ple, after a shear rate of 8 s)1 the time before the opticaldisappearance is approximately 26 s, whereas: steady¯ow viscosity data suggest a period of at least 120 to140 s (the period required for the viscosity to increaseto the steady ¯ow value), the change in the dynamicfunctions suggests a time of at least 150 s (the periodrequired to reach the minimum which follows themaximum in the values), the change in tan(d) suggestsa time of at least 100 s (the time before the functionreaches the minimum value) and ®nally the timesuggested by the SALS experiments is approximately100 s (the time before the disappearance of the Braggscattering peaks). The scattering angle has been found topass through a maximum following relatively low shearrates which corresponds to a minimum in the wave-length of the band spacing. This result is in agreementwith previous reports on HPC solutions (Putnam andViney 1991; Viney and Putnam 1995), the band spacingof which was also observed to pass through a minimumband spacing before gradually increasing with time.

Conclusions

The rate of evolution of the band texture as seen undercross-polarised light has been found to depend upon theprimary shear rate applied to the sample. The behaviourcan be divided into three regions with respect to the

Fig. 15 Comparison betweenvarious stages in the evolutionof the optical aspect of the bandtexture and the ®rst order lightscattering intensity versus pri-mary shear rate. As for theviscoelastic functions, the evo-lution of the scattering patternis delayed in relation to theoptical evolution of the bandtexture as seen under cross-polarized light

Fig. 16 Evolution of the scattering angle and hence the wavelength ofthe band texture during the time following the cessation of shear,following a primary shear rate of 3 s)1

589

primary shear rate. The rate of evolution of the bandtexture increased, remained constant or decreasedaccording to whether the sample was observed followinglow, intermediate or high shear rates. The optical aspectof the band texture was also found to be stable evenafter being sheared up to 14 strain units away from andback to its original position.

Rheological experiments determined that the viscos-ity of the band texture decreases following increasingprimary shear rate and also with increasing secondaryshear rate. Furthermore, the value of the viscosity of theband texture following a given primary shear rate, islower than the steady ¯ow viscosity of the texture whichoccurs during ¯ow at the same shear rate. The simplestexplanation of this point is to consider the band textureto be a more ordered state than the steady ¯ow texture.Why the material should go from a textured state during¯ow to a polydomain state at rest through the moreordered state of the band texture is di�cult to under-stand. Another possibility is that the main contributionof the steady-state viscosity is the energy distributedthroughout the highly distorted defects. The bandtexture having relaxed most of the stored energy of the¯uid can once again ¯ow more easily. This highlightsone of the main missing points in the understanding ofthe ¯ow of main-chain LCP, namely, the behaviour ofthe defects during ¯ow. They are the key to understand-ing most of the phenomena that are still unexplained,from the occurrence or not of tumbling to the origin ofthe band texture. Finally, the viscosity of the bandtexture was found to increase linearly with timefollowing the cessation of shear, towards the steady¯ow viscosity. Using this technique to monitor therelaxation of the band texture suggests that the structurerelated to the band texture continues to exist long afterits optical disappearance as seen under crossed polars.

Oscillatory rheological experiments revealed a con-nection between the behaviour of the dynamic functionsduring relaxation and the optical evolution of the bandtexture. In particular, the rate of evolution of thedynamic functions showed a similar dependence withprimary shear rate as the evolution of the optical aspectof the band texture. However, the evolution of thedynamic functions was slower than the optical evolutionof the band texture. A critical primary shear rate wasfound following which an increase in the long-termvalues of the dynamic functions occurred, this criticalshear rate was close to the minimum shear rate requiredfor the production of the band texture.

Investigations of the phase angle, d, between theinput and output waveforms of the stress and strain alsorevealed interesting behaviour which was correlated tothe evolution of the band texture. A downward shiftingof the tan(d) versus `time following the cessation ofshear' curves was found with increasing primary shearrate. This shifting ended following shear rates higher

than the minimum shear rate required for the produc-tion of the band texture. Also, a drop in the tan(d) versus`time following the cessation of shear' curves was foundto be a signature of the band texture's formation. Thesize of the drop re¯ected the perfection of the bandtexture.

SALS experiments con®rmed the previously observedconnection between the band texture and the two ®rstorder scattering spots. The intensity of these spots wasagain found to show the familiar dependence on primaryshear rate as displayed by the rate of evolution of theoptical aspect of the band texture, the dynamic functionsand the drop in tan(d). Once again, as with therheological behaviour of the HPC solution, the two ®rstorder intensity maxima disappeared only after a signi-®cant length of time after the optical disappearance ofthe band texture. In addition, the plates could be rotatedup to 13 strain units away from and back to theiroriginal con®guration and still reform the ®rst ordermaxima corresponding to the existence of the bandtexture.

The evidence presented by these results suggests thatthe relaxation process which causes the band textureseen under crossed-polarisers, continues long after theoptical disappearance of the texture. Also, the bandtexture has been found to be extremely insensitive toshearing. Despite the correlation which has been notedbetween the onset of a negative normal stress and theband texture, the fact that the band texture can alsooccur following elongational shear rules out any causalconnection between director tumbling and band textureformation. Furthermore, as has been seen in other LCP,a negative normal force region is not a necessarycondition for the formation of the band texture follow-ing the cessation of shear. Thus, we conclude thatdirector tumbling is unlikely to be the generationmechanism behind band texture formation.

Defects are proposed as the driving mechanism of theband texture formation in region I. Increasing the shearrate increases the number of defects and consequentlythe amount of elastic energy stored in the material. Thisexplains the increasing rate of evolution of the bandtexture with increasing shear rate in region I. The scalingof the disappearance time of the band texture multipliedby the primary shear rate gives further reason toadvocate defects as the driving mechanism in region I.

It is known that the number of defects fails toincrease inde®nitely with increasing primary shear rate.If the number of defects becomes approximately con-stant with increasing primary shear rate in region II thenthis would explain the approximately constant rate ofevolution of the band texture with increasing shear rateseen in this region. In addition, if the size of the drop oftan(d) is used as an indirect measure of the energyreleased by the band texture, then the approximatelyconstant size of the drop in region II is also explained by

590

the proposal of defects as the driving mechanism of theband texture in regions I and II. The main questionwhich remains is why the evolution behaviour changeswith further increases in the primary shear rate intoregion III.

It was observed that in region III the high shear ratesresult in the texture gradually adopting a monodomainstructure as the primary shear rate increases. A mono-domain implies a low defect density and consequently alower amount of total energy stored by defects in the¯uid. Initially, one might use this argument to explainthe decreasing rate of evolution of the band texturewith increasing shear rate in region III. However, thisexplanation fails to encompass the facts that both theoptical perfection of the band texture and the size of thedrop in tan(d) dramatically increase in region III. Thesetwo factors are both highly suggestive of an increase inthe amount of energy released by the band texture inregion III. If this really is the case, then the release ofenergy stored by defects cannot provide the drivingmechanism for the band texture seen in region III.

In answer to this anomaly we suggest that inmoving from region II to region III the drivingmechanism behind the band texture formation chan-ges. More speci®cally we feel that, following the workof Larson and Mead (1992), and MuÈ ller et al. (1994,1996), the most probable driving mechanism of theband texture of region III is the relaxation of energycontained in an out-of-plane splay of the director ®eld.We assume that increasing the shear rate increases theamount of Frank elastic energy stored in the splay ofthe director ®eld. The avocation of two di�erentdriving mechanisms for the band texture occurring inthe same LCP could help resolve the apparent con¯ictbetween the di�ering ideas found in the literature. Theidea places great importance on the previous texturefrom which the LCP is relaxing in determining whichmechanism plays the dominant role in creating theband texture. Furthermore, it implies that bandtexture formation is a general relaxation phenomenonin LCP whose genesis may be the result of a variety ofdi�erent mechanisms.

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