Banded spherulitic growth in a liquid crystal · macromolecular systems, which typically freeze at inconveniently slow rates [32]. Spherulitic growth in 10OCB occurs at approximately

*Corresponding author. Present address: Department ofPhysics and Astronomy, University of Western Ontario, Lon-don, Ont., Canada N6A 3K7. Tel.: #1-519-661-2111, ext.86719; fax: #519-661-2033.

E-mail address: [email protected] (J.L. Hutter).

Journal of Crystal Growth 217 (2000) 332}343

Banded spherulitic growth in a liquid crystal

Je!rey L. Hutter*, John Bechhoefer

Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Received 29 September 1999; accepted 18 April 2000Communicated by M.E. Glicksman

Abstract

Spherulitic growth produces radial arrays of polycrystalline aggregates in a wide variety of materials, ranging frompure elements to macromolecules. Despite more than a century of study, a generally accepted theory of spherulitic growthis lacking; indeed, the existence of a common mechanism is debated. One commonly seen subset of this growthmorphology* banded spherulites* exhibits bands concentric about the spherulite centers. These bands have been wellcharacterized in polymer spherulites, but remain poorly understood. Comparisons of such bands in a diverse variety ofmaterials will help establish a general mechanism for their formation. Here we present a detailed optical and atomic-forcemicroscopy study of banding in a liquid crystalline material. ( 2000 Elsevier Science B.V. All rights reserved.

PACS: 61.50.Jr; 64.70.Md; 81.30.Fb

Keywords: Solidi"cation; Crystal morphology; Spherulite; Banded spherulite

1. Introduction

Spherulites consist of radially oriented micro-crystals arranged at noncrystallographic angleswithin a spherical envelope. This growth form ismost familiar in polymers, where spherulites arethe typical crystallization mode [1}6] (althoughnot all polymer solids are crystalline). However,spherulites have also been investigated in materialsas dissimilar as elemental selenium [7}9], low mo-lecular weight systems with polymeric impurities[10], organic materials [11,12], biological molecu-

les [2], mineral aggregates (references in mineralsdate to Refs. [13}15]), and liquid crystals [16}18].The presence of spherulites in#uences the me-chanical properties of commercial materials. Forexample, the carbon in cast iron often formsspherulites [19], resulting in a metal which is muchless brittle than cast iron in which the carbon formsgraphite sheets. Here, the formation of spherulitesis desirable. In biological sciences, where largesingle crystals of proteins are required for X-raystructural studies, spherulites are a common `fail-ure modea [2,20]. Clearly, an understanding ofwhen spherulites form would bene"t many areas ofscience and technology.

Despite this importance * and a century ofstudy [13]* there is no generally accepted theoryof spherulitic growth. Even more mysterious is theorigin of the concentric bands which often accom-pany spherulitic growth. Although the nature of

0022-0248/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 4 7 9 - 6

1Despite the striking simularities between spherulites in di-verse systems, proposed models of spherulite banding are oftenspeci"c to polymers, implying that the phenomenon may bematerial speci"c. See Refs. [23,24].

Table 1Properties of 10OCB

Quantity Symbol Value Units Ref.

Chemical name * 4}cyano}4@}decyloxybiphenyl * *

Formula * C23

H29

ON * *

Molecular weight * 335.49 g/mol *

Chemical abstracts no. * 70247-25-5 * *

Density (solid) o 1.098 g/cm3 [28]Viscosity (SmA)! g &0.2}1 Pa sThermal di!usivity (SmA)" D

h&10~3 cm2/s

Speci"c heat (SmA) cp

&2 J/g 3C [31]Latent heat of solidi"cation ¸ 115 J/g [31]Solid}smectic A transition# ¹

K}S.A59.5 3C

Smectic A}isotropic transition# ¹S.A~I

84 3C

!Viscosity data for a similar compound, 8OCB, have been measured as a function of temperature by K. Negita [29]."Thermal di!usivities of similar compounds are given by U. Zammit et al. [30].#BDH Limited, Broom Road, Poole, BH12 4NN, England.

2The 10OCB is nominally pure, but does contain 0.15%water at the saturation limit. Samples prepared by heating undervacuum to remove volatile impurities, as well as samples dopedwith &2 mol% C

2Cl

6, showed the same solidi"cation behav-

ior, suggesting that the morphologies are not impurity driven.

these bands is known in some systems (for instance,in polymers the bands are associated with a peri-odic rotation of the optical axis along the spheruliteradius [1}3,21,22]), the mechanism responsible fortheir formation remains elusive.

The striking similarity of spherulites in diversesystems suggests a corresponding similarity ingrowth mechanisms.1 If a common mechanismexists, comparison of spherulitic growth in dissim-ilar materials can identify those features that arefundamental to such a mechanism. Here, we com-pare and contrast both banded and unbandedspherulites solidi"ed from a liquid crystalline ma-terial with those grown from other systems. In thefollowing section, we motivate the choice of mater-ial studied and describe the experimental tech-niques used. In Section 3, we discuss the generalfeatures of the spherulites formed and comparewith other spherulitic systems. Section 4 presentsstudies of the growth dynamics. We conclude witha discussion of implications for the general mecha-nism of spherulitic growth.

2. Experimental procedure

We chose to study spherulitic solidi"cation of theliquid crystalline material 4}cyano}4@}decyloxy-biphenyl (10OCB). In previous publications[18,25}27], we described the wide variety of growthmorphologies exhibited by 10OCB, and showedthat transitions between these morphologies occurat well-de"ned growth temperatures and are ac-companied by sharp changes in growth propertiessuch as the growth velocity and front shape. Thissystem is experimentally convenient: it is availablein quite pure form,2 it is chemically stable, and itsproperties are well known (see Table 1).

The ìntermediatea properties of liquid crystalsresult in natural growth velocities between those ofsimple molecular systems, which often grow tooquickly to allow detailed observations, and those ofmacromolecular systems, which typically freeze atinconveniently slow rates [32]. Spherulitic growthin 10OCB occurs at approximately room temper-ature and with velocities of the order of 100lm/s.

333J.L. Hutter, J. Bechhoefer / Journal of Crystal Growth 217 (2000) 332}343

3HS1-i Microscope Hot Stage and Temperature Controller,Instec, Inc., Boulder, CO 80306.

4Olympus BH-2 Olympus Optical Company, Lmt., Tokyo,Japan.

5Pulnix TM-7CN, Pulnix America, Inc., Sunnyvale, CA94086.

6Scion LG-3, Scion Corporation, Frederick, MD 21701.7 Image processing was performed using the software package

NIH Image, v. 1.61. National Institute of Health, Division ofComputer Research and Technology, USA The procedure isdescribed in more detail in Ref. [27].

8Universal AFM/STM. Park Scienti"c Instruments, Sun-nyvale, CA 94089-1304. 9ZLI 2510, E. Merck, Darmstadt, Germany.

The samples consisted of thin (10lm) layers of10OCB sandwiched between two glass plates. Weused thin (&170 lm) plates to ensure rapid coolingto the desired temperature. A typical solidi"cationexperiment begins by melting the sample into theisotropic phase on a hot plate. The sample is thenquickly transferred to a computer-controlled hotstage3 set to the desired undercooling. The samplequickly enters a supercooled smectic phase, afterwhich the solid phase nucleates. Spherulitic growthwas observed for temperatures less than approxim-ately 403C, corresponding to undercoolings greaterthan approximately 203C.

We studied the solidi"cation front using opticalmicroscopy,4 recording the images with a videocamera5 and frame grabber.6 The front locationand shape were determined by applying a thresholdto the images and selecting the pixels dividing thedarker solidi"ed material from the melt.7 Wetracked the motion of this front to determine itsvelocity.

We also used optical microscopy to observespherulitic growth in directional solidi"cation [33].In a directional solidi"cation experiment, thesample is driven at a constant velocity througha temperature gradient produced by a narrow gapbetween two temperature stages. The temperaturedi!erence is set so that the solidi"cation front isvisible within the gap. After an initial transientwhen the sample motion begins, the front ap-proaches a steady state which is stationary withinthe lab frame, allowing the front to be studied fora period of time set by the sample dimensions.

Finally, the microstructures of the samples werestudied using an atomic-force microscope (AFM)8

after solidi"cation was complete. The sandwichcells described above could be pried apart, usuallyresulting in cleavage along one of the plates. Suchcleavage did not alter the visual appearance of thespherulites; in addition, AFM images of samplesprepared without a top plate exhibited similartopography.

3. Classical spherulitic growth in 10OCB

In this section, we examine the properties of10OCB spherulites and show that they exhibit fea-tures associated with spherulites in other systems.

3.1. Spherulites are round

Observations of spherulitic growth usually revealthat the growing solid phase de"nes a slowly ex-panding spherical envelope within a viscous #uid.One qualitative di!erence between the systemstudied here and more familiar spherulite formingsystems is that growth proceeds from a smecticliquid crystalline phase, rather than from an iso-tropic melt. Not surprisingly, solidi"cation from anordered phase can result in anisotropic growth. Formost of our experiments, we treated the glass plateswith an organosilane9 to impose homeotropic an-choring with the smectic layers parallel to the surfa-ces, thus creating a uniform, defect-free sample.This removes the anisotropy in the sample planeand results in round spherulites.

Experiments performed with cells treated forplanar anchoring (i.e., with smectic layers perpen-dicular to the surfaces) resulted in spherulites thatdi!ered only in the growth anisotropy: the growthwas slowest in the anchoring direction, resulting inoval `spherulitesa with an aspect ratio of &0.9, asshown in Fig. 1. We achieved this anchoring byslowly (&1 mm/min) drawing the plates froma beaker containing a polyimide solution to obtaina thin polymer layer with molecules aligned in thedrawing direction, baking at 1503C to removethe solvent, and gently rubbing with a "ne cloth in

J.L. Hutter, J. Bechhoefer / Journal of Crystal Growth 217 (2000) 332}343334

Fig. 1. Oval spherulite in a planar-anchored sample. The scalebar measures 100 lm.

Fig. 2. Collection of spherulitic domains viewed through cross-ed polarizers. Note the characteristic `Maltese crossa pattern,indicating a 3603 rotation in crystal orientation about the nuclei,and the concentric bands due to rotation of the optic axes aboutthis radial direction (by 1803 for each band). The scale barrepresents 25 lm.

the drawing direction. The resulting plates force theliquid crystal molecules to align along the drawingdirection, resulting in smectic planes perpendicularto this direction. Since this anchoring causes fastergrowth in the direction of the smectic planes, it ispossible that molecules aligned tangentially to thespherulite front are more easily incorporated intomicrocrystals. Other than the oval shape, there isno obvious di!erence between spherulites formedin planar and homeotropic anchoring. In the re-mainder of this paper, we consider homeotropicanchoring only.

3.2. Spherulites consist of radial arrays ofmicrocrystals

Aside from the spherical (or circular, in two di-mensions) shape of spherulites, the classicalcharacteristic of this growth morphology is a radialorientation of microcrystals. The cause of thisorientation is unknown and may be system-depen-dent. One way to achieve such a noncrystallo-graphic radial alignment is to impose a pressurebetween neighboring crystallites. In polymers,which form ribbon-like lamellae, Bassett, Keller,and Misuhashi [6,34,35] have proposed that thispressure is an entropic pressure due to danglingpolymer chains in the gap between lamellae. Sucha model cannot apply to materials formed fromsmaller molecules. In such cases, Tiller [36] has

suggested that the splay is due to viscous #ow of themelt induced by the density change during solidi"-cation. Flow through the narrow channels separat-ing adjacent needle crystals (towards the center ofthe spherulite, if the solid is more dense than theliquid) will generate a pressure according to theHagen}Poiseuille equation.

Although the microscopic mechanism of splay isquite di!erent for the two cases discussed above,both predict a radial arrangement of initially paral-lel crystals caused by crystal bending (or breaking,if the mechanical strain is great enough). Since thisrequires the orientation of the crystals to vary withangular position about the spherulite center,spherulites often exhibit a `Maltese crossa patternwhen viewed through crossed-polarizers [3]. Asshown in Fig. 2, this pattern is observed for 10OCBspherulites. Here, dark bands concentric with thenucleus are also seen. The AFM allows us to imagethe radial orientation directly (cf. Fig. 8 below).

There is good evidence for a density change andresultant #ow during the growth of 10OCBspherulites. We estimated the change in density bymeasuring the change in size of small droplets(200}800lm in diameter) sandwiched betweenglass plates held 25lm apart as they are solidi"ed.Since the solid phase is denser than the smectic A,


Fig. 3. Density change during solidi"cation of a small droplet of10OCB at an undercooling of 30 3C between glass plates 25 lmapart. The density change causes the droplet to shrink. Theoriginal shape is still visible because of a thin (estimated from thedepth of focus to be &1 lm) "lm of material which freezes tothe glass plates. The scale bar spans 200 lm.

Fig. 4. Evolution of the `sheaf-likea spherulite nucleus.

the drops shrink during solidi"cation, as shown inFig. 3. Note that the solid drop is not perfectlycircular because the solid phase does not usuallynucleate at the center. This results in increased #owfrom the regions further from the nucleus. Wefound that the density change is approximately10% for spherulitic growth, although the thin "lmof material left on the plates as the droplet shrinksmakes a precise estimate di$cult. We will see thatthe spherulitic morphology is not compact on themicroscopic scale. Thus, this density change mustbe regarded as an average value over the spherulitedomain, and is not representative of the intrinsicvolume change for the phase transition.

3.3. Spherulite nuclei

A model of microcrystals radiating from a cen-tral nucleus requires a defect at the origin. High-resolution studies of spherulite nuclei reveal a pat-tern known in the literature as a `sheaf of wheatamorphology, due to its resemblance to a tied sheaf

of wheat. The standard explanation [14,37] is thatthe spherulite initially nucleates as a single needle,from which new needles branch. As the spherulitegets larger, the needles are forced into a radialorientation. If there is a maximum branching angleand/or minimum radius of curvature, the result isan asymmetric nucleus with two cavities which areinaccessible to crystals branching from the originalnucleus, and a defect line where needles from oppo-site ends of the nucleus meet. This process is shownschematically in Fig. 4.

10OCB spherulites also exhibit this sheaf form,as shown by the AFM images in Fig. 5, which arealso complicated by concentric bands. Occa-sionally nuclei are seen with a spiral banded struc-ture, rather than the sheaf form (Fig. 6). These mayresult from nucleation at heterogeneous sites suchas dust particles.

3.4. Banded spherulites

Most of the spherulites discussed in this paperare banded. Banding in spherulites is generallyaccepted to be due to a birefringent e!ect[1}3,21,22]. Observations suggest that the optical


Fig. 5. AFM micrographs of spherulite nuclei with sheaf structures.

Fig. 6. Spherulite nucleus with a spiral structure.

axis of the crystallites follows a helical path aboutthe spherulite radius. When viewed through cross-ed polarizers, dark bands are seen at radii where theoptical axis lies along the line of sight. This hypoth-esis is supported by an apparent shift in bandposition when the sample is tilted, thus rotating theoptic axis about the tilt axis.

Twist in the unit cell orientation has been con-"rmed in some systems by electron microscopy

[1,2,6,38,39], microbeam X-ray di!raction [40],and micro-Raman spectroscopy [41]. The existenceof this twist can be due either to a continuous twistof individual crystallites or to a dependence onradius of the average orientation of (untwisted)crystals. The second possibility is generally believedmore likely [2,39]. However, some electron micro-graphs of polymer spherulites indicate that thelamellae are #at throughout most of the band, withthe twist occurring over a relatively short distance[2,6,39].

Fig. 7 shows an optical micrograph of a portionof a large spherulite. The center of the spherulite isfar outside the "eld of view, resulting in bands thatare nearly planar on the scale of the image. Notethat sharp phase shifts occur along the bands, re-sulting in lines perpendicular to the bands separat-ing regions of coherent banding. AFM images (Fig.8) show that these phase shifts are discontinuous atthe scale of the microcrystals which make up thespherulite.

If we view spherulites illuminated by unpolarizedlight through a single polarizer, we "nd that theband contrast is greatest when the polarizer is alig-ned parallel to the bands. When the polarizerpasses light polarized perpendicularly to the bands,the contrast is so weak that the bands cannot be


Fig. 7. Optical micrograph of a domain of banded spheruliticgrowth. Note that the structure is divided into sub-domainsseparated by phase shifts in the bands. This sample was solidi-"ed at an undercooling of about 403C, resulting in a bandspacing of 1.7 lm. The scale bar measures 50 lm.

Fig. 8. Atomic-force micrographs of spherulitic bands. The sam-ples were grown between glass plates, which were subsequentlypried apart. The bands are composed of radially orientedneedles with lengths on the order of the band spacing. (a)Spherulite grown at *¹"253C. (b) Spherulite grown at*¹"323C. Note the sharp change in band phase.

distinguished. This indicates that the contrast de-pends on an attenuation (by scattering, since ab-sorption is negligible in the visible for 10OCB) ofthe component of light polarized along the bands.This supports the picture of an optical axis thatrotates about the spherulite radius (i.e., about thelong axes of the microcrystals) * such a rotationdoes not alter the refractive index in the radialdirection, so that light polarized in the radial direc-tion encounters no variation in refractive index andproduces no contrast.

We used the AFM and scanning electron micro-scope (SEM) to study the structure of the bands onlength scales of the band spacing and smaller. Asseen in Fig. 8, the bands are composed of individualneedle crystals approximately 600As wide. Di!erentbanded domains are separated by discontinuities inthe band phase, as discussed earlier. The apparentseparation of bands within a single domain is not asreadily understood.

Fig. 8b shows many of the needle crystals endingat well-de"ned band edges. Fig. 8a, however, doesnot show such clear boundaries and contains exam-ples of needles which extend across more than oneband. In neither case is the AFM resolution sharpenough to reveal a twist in the needle crystals. It isimportant to realize that the image measured by

the AFM is a map of the sample height required tomaintain a constant de#ection force on the canti-lever. As such, the image contains both topographi-cal and mechanical information [42]. For instance,a soft region of the sample is di$cult to distinguishfrom a depression in the surface. The fact thatbands can be seen in these images indicates thatthey are associated with a modulation in eithersample height or sti!ness.


Fig. 9. Scanning electron microscope image of a bandedspherulite. The image shows a fractured spherulite with bandsvisible on both the surface and fractured edge. The growthdirection was to the lower left.

Fig. 10. Growth velocity as a function of undercooling in thespherulitic regime. The transition between unbanded andbanded spherulites occurs at &223C, with banded spherulitesat larger undercoolings.

A modulation in sample sti!ness could arisefrom a twist in the average orientation of micro-crystals: anisotropy in the mechanical properties ofthe needle crystals would result in a variation insample sti!ness across each band. It is perhapsmore likely that the bands seen with the AFMrepresent a real surface buckling that occurs aftercleavage to relieve stresses. Below, we present evid-ence for the existence of stress in 10OCBspherulites.

In order to examine the bands inside the do-mains, we used the SEM to image freshly fracturedspherulite edges. We prepared the spherulites forthe SEM study on a highly doped silicon wafer toprovide a conducting substrate. Both the siliconand glass cover plate were treated for homeotropicanchoring. After removal of the glass plate, thespherulite was fractured to provide fresh surfacesrevealing the interior banding structure. Anexample is shown in Fig. 9. To avoid sample dam-age and charging e!ects we accelerated the electronbeam through a relatively small potential (1 kV)and carefully adjusted the current so that theincident #ux was balanced by electrons emittedfrom the sample. The bands are clearly visiblethroughout the sample bulk. This image alsoshows some isolated needle crystals that havedetached from the spherulite. As with the AFMimages, these crystals have lengths of the orderof a band spacing.

4. Spherulite growth

Having established that the 10OCB spherulitesshow all of the features seen in spherulites of othermaterials, we turn our attention to the variation ofthese features with growth conditions.

4.1. Growth velocity and band spacing

In previous publications, we examinedtransitions between 10OCB growth morphologiesas a function of undercooling. Unlike the othertransitions studied, the unbanded to bandedtransition is not accompanied by a sharp change ingrowth velocity, although as shown in Fig. 10, thevelocity curve does undergo an unusual excursionin this vicinity (at &223C). We found that otherquantities such as the band spacing and measuresof #uctuations (for instance the band coherencelength) do appear to diverge at the transition.

We also measured the band spacing ofspherulites grown by directional solidi"cation. Theundercoolings for these domains were not mea-sured (accurate measurement of undercooling indirectional solidi"cation is di$cult), but the iso-thermal and directional solidi"cation results can becompared on a plot of band spacing vs. growthvelocity. Fig. 11 compares the band spacing forisothermal growth at a variety of sample thick-nesses and directional solidi"cation in an imposedtemperature gradient.


Fig. 11. Spherulite band spacing as a function of growth velo-city. Note that both sets of data * isothermal growth withsample thicknesses ranging from 10 to 50lm and directionalsolidi"cation with an applied gradient of 503C/mm* fall ontoa single curve.

Fig. 12. Spherulitic growth in small and irregular droplets. The bands are able to propagate through features with sizes of the order ofthe band spacing. In addition, banding is seen in droplets only two bands across. The scale bar of 25 lm applies to both images.

4.2. Dependence of bands on local features

The fact that the band spacing has the samedependence on growth velocity for di!ering condi-tions implies that the details of di!usion "elds and

other long-range properties are unimportant to thebanding mechanism. This conclusion is furtherstrengthened by observations of growth in verysmall domains. Examples are shown in Fig. 12. Thelarge droplet in Fig. 12a shows a spherulite witha nucleation point at the top edge. The bandeddomain was able to propagate to the lower sectionof the droplet through an isthmus only a few bandspacings wide. Fig. 12b shows several instances ofbanding in domains whose total extent is only a fewband spacing. These results indicate that the band-ing mechanism depends only on properties on thelength scale of the banding.

Occasionally, a growing spherulite would en-counter an air bubble within the sample. The result,as shown in Fig. 13, is a domain which is unpertur-bed save near the end of the bubble furthest fromthe spherulite origin, where the bands bend aroundthe far side of the bubble (this e!ect has also beendiscussed in polymeric spherulites [43]). This againdemonstrates the insensitivity to all but very localperturbations.


Fig. 13. Spherulitic growth around an air bubble. Note that thebands are unperturbed until forced to "ll in the region behindthe bubble. Growth was to the upper right and the scale barspans 25 lm.

Fig. 14. Fracture of banded spherulites. Within a period ofhours, 10OCB spherulites often crack along the bands. Radialcracks originating at the nucleus are also seen. A scale bar of 200lm is shown.

4.3. High-speed observations

High-resolution real-time observations ofbanded spherulite growth would aid in the develop-ment of a growth mechanism. The growth of10OCB is too rapid to allow AFM investigations.Instead, we studied the growth using high-speed(up to 5000 frames/s) video microscopy. One of theobjectives of this approach was to determinewhether or not the front velocity oscillates with thebanding. Such an oscillation would be incompat-ible with a continuous twist of microcrystals, forinstance. While some of our observations did revealsuch an oscillation, we saw no clear trend withundercooling (indeed, some runs showed no oscilla-tion at all). Thus, the apparent oscillation was mostlikely an e!ect of the band contrast* advance of thefront is more di$cult to see during phases when theband has low contrast with the surrounding melt.

4.4. Spherulite stability

Although banded spherulites are stable enoughto allow them to be studied, 10OCB spherulites arenot stable at room temperature. This is not surpris-

ing since they are grown far from equilibrium. Infact, spherulites of some materials can break upwith explosive force [4]. Our 10OCB spherulitesoften fracture concentrically along the bands (seeFig. 14) within a period of hours, indicating a built-in mechanical stress.

Over a period of several days, the bands disap-pear completely. This process can be accelerated byheating the spherulites. Annealing at a few degreesbelow the melting point causes the bands to disap-pear in a matter of moments. A well-de"ned frontassociated with this change can be seen in Fig. 15a.In this example the ùnbandinga front had a velo-city of &10 lm/s. Examination of the microstruc-ture after the destruction of the bands, Fig. 15b,shows that a change in morphology has occurred:the microcrystals have become much larger and allremnants of the band ordering have vanished (com-pare with Fig. 8). X-ray di!raction shows that thecrystal structure, or at least orientation, has alsochanged.

5. Conclusions

Spherulitic growth is a little-understood growthmorphology frequently seen in a diverse range of


Fig. 15. Annealing of banded spherulites. (a) Ùnbanding fronta sweeping toward the center of the spherulite. This image was taken aftera few minutes of annealing &53C below the melting point. (b) AFM micrograph of a spherulite after the front in (a) has passed. Notethat the bands are no longer present.

materials. The similarity of spherulites in these dif-fering materials suggests a common growth mecha-nism. We have studied spherulitic growth in aliquid crystalline material with the goals of identify-ing the features shared by other spherulites andstudying the growth kinetics in an experimentallyconvenient system.

Our spherulites, in common with those seen inother materials, are composed of radially orientedmicrocrystals originating from a sheaf-like nucleusand growing with a front that is smooth on a scalelarger than the individual crystals.

Our observations of banded spherulites grown intemperature gradients and in small and irregulardomains show that only properties very near thegrowth front are important * sample conditionsonly a few band wavelengths from the front are notimportant. This dependence on local propertiesgives hope that a simple model may be found.Other hints are provided by the evidence (such asthe diverging band spacing shown in Fig. 11) thatthe transition to the banded regime is analogous toa second-order phase transition and occurs in a re-gion where the front velocity is a decreasing func-tion of undercooling (Fig. 10) [26,27].

Many careful microscopic studies of spheruliticgrowth in a variety of materials exist in the litera-

ture. Further studies of their growth kinetics, parti-cularly near the transition to the banded regime,would be of great use in developing a universaltheory of spherulitic growth.

Acknowledgements

This work was funded by NSERC (Canada). Theauthors would like to thank Tom Pinnington andRobin Coope for the SEM micrograph shown inFig. 9, Tom Mason for the use of a high-speedvideo camera, and Mike Degen and Matthew Casefor help in analyzing the images.

References

[1] P.J. Phillips, Rep. Prog. Phys. 53 (1990) 549.[2] P.J. Phillips, Spherulitic crystallization in macromolecules,

in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, Vol.2, Elsevier, Amsterdam, 1993 (Chapter 18).

[3] A. Keller, J. Polym. Sci. 17 (1955) 291.[4] H.D. Keith, F.J. Padden Jr., J. Appl. Phys. 34 (1963) 2409.[5] G. Schuur, J. Polym. Sci. 11 (1953) 385.[6] D.C. Bassett, CRC Crit. Rev. Solid State Mater. Sci. 12

(1986) 97.[7] G. Ryschenkow, G. Faivre, J. Crystal Growth 87 (1988)

221.


[8] J. Bisault, G. Ryschenkow, G. Faivre, J. Crystal Growth110 (1991) 889.

[9] M. Mohan, A.K. Singh, Philos. Mag. B 67 (1993) 705.[10] R.R. Lagasse, J. Crystal Growth 140 (1994) 370.[11] J.H. Magill, D.J. Plazek, J. Chem. Phys. 46 (1967) 3757.[12] F.P. Price, A. Keith Fritzsche, J. Phys. Chem. 77 (1973)

396.[13] P. Iddings, Am. J. Sci. 33 (1887) 36.[14] H.W. Morse, J.D.H. Donnay, Am. Mineral. 21 (1936) 391.[15] P.J. Heaney, A.M. Davis, Science 269 (1995) 1562.[16] F. Rinne, Trans. Faraday Soc. 29 (1933) 1016.[17] S.C. Jain, S.A. Agnihotry, V.G. Bhide, Mol. Cryst. Liq.

Cryst. 88 (1982) 281.[18] J.L. Hutter, J. Bechhoefer, Physica A 239 (1997) 103.[19] B. Miao, D.O. Northwood, W. Bian, K. Fang, M.H. Fan,

J. Mater. Sci. 29 (1994) 255.[20] A. Ducruix, R. GiegeH (Eds.), Crystallization of Nucleic

Acids and Proteins: A Practical Approach, Oxford Univer-sity Press, Oxford, 1992.

[21] H.D. Keith, F.J. Padden Jr., J. Polym. Sci. 31 (1958) 415.[22] A. Keller, J. Polym. Sci. 39 (1959) 151.[23] H.D. Keith, F.J. Padden Jr., Polymer 25 (1984) 28.[24] A.J. Owen, Polymer 38 (1997) 3705.[25] J. Bechhoefer, J.L. Hutter, Physica A 249 (1998) 82.[26] J.L. Hutter, J. Bechhoefer, Phys. Rev. Lett. 79 (1997)

4022.[27] J.L. Hutter, J. Bechhoefer, Phys. Rev. E 59 (1999) 4342.[28] S. Gupta, S. Paul, Indian J. Phys. 68A (1994) 465.[29] K. Negita, Int. J. Mod. Phys. B 13 (1999) 2005.

[30] U. Zammit, M. Marinelli, R. Pizzoferrato, F. Scudieri,S. Martellucci, Phys. Rev. A 41 (1990) 1153.

[31] J.L. Hutter, Solidi"cation of a liquid crystal: morphologiesand transitions, Ph.D. Thesis, Simon Fraser University,Burnaby, BC, Canada, 1997.

[32] J. Bechhoefer, Nonequilibrium phenomena in liquid crys-tals, in: P.E. Cladis, P. Pal!y-Muhoray (Eds.), Spatio-Tem-poral Patterns in Nonequilibrium Complex Systems,Santa Fe Institute: Studies in the Sciences of Complexity,21, Addison-Wesley, Reading, MA, 1994, pp. 107}122.

[33] J.D. Hunt, K.A. Jackson, H. Brown, Rev. Sci. Instr. 37(1996) 805.

[34] D.C. Bassett, A. Keller, S. Mitsuhashi, J. Polym. Sci.A 1 (1963) 763.

[35] D.C. Bassett, Philos. Trans. Roy. Soc. London A 348(1994) 29.

[36] W.A. Tiller, The Science of Crystallization: MicroscopicInterfacial Phenomena, Cambridge University Press,Cambridge, 1991, pp. 342}347.

[37] A. Keller, J. Polym. Sci. 17 (1955) 447.[38] D.C. Bassett, A.M. Hodge, Polymer 19 (1978) 469.[39] D.C. Bassett, A.M. Hodge, Proc. Roy. Soc. London A 377

(1981) 61.[40] Y. Fujiwara, J. Appl. Polym. Sci. 4 (1990) 10.[41] H. Tanaka, T. Ikeda, T. Nishi, Appl. Phys. Lett. 48 (1986)

393.[42] N.A. Burnham, Appl. Phys. Lett. 63 (1993) 114.[43] G.E.W. Schulze, M. Biermann, J. Mater. Sci. Lett. 12

(1993) 11.


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Banded spherulitic growth in a liquid crystal · macromolecular systems, which typically freeze at inconveniently slow rates [32]. Spherulitic growth in 10OCB occurs at approximately