Disclination Structures in the Carbonaceous Mesophase

AD VANCES IN LIQUID

CR YSTALS,

VOLUME 5

DISCLINATION STRUCTURES IN THE CARBONACEOUS MESOPHASE J. E. Zimmer Acurex Corporation Mountain View, California J. L. White Materials Sciences Laboratory The Aerospace Corporation El Segundo, California

I. II.

III.

IV.

V. VI.

VII. VIII.

Introduction Carbonaceous Mesophase A. Description B. Transformation C. Physical Aspects D. Microstructures in the Carbonaceous Mesophase Disclination Structures A. Wedge Disclinations B. Twist Disclinations C. Layer Disclinations Wedge Disclinations A. Optical Micrography B. Scanning Electron Micrography C. Core Structures Twist Disclinations Disclination Arrays A. Additivity B. Disclination Loops C. Mixed Disclinations Formation and Interaction of Disclinations Summary References

I.

157 158 158 160 164 169 175 178 180 181 182 183 189 191 194 201 201 203 203 205 210 211

INTRODUCTION

T h e carbonaceous mesophase is a discotic nematic liquid crystal which forms during the liquid-phase pyrolysis of m a n y aromatic hydrocarbons, including such practical materials as coal tar a n d petroleum pitch. A m o n g 157 Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-025005-5

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the variety of reactions induced by thermal treatment, aromatic polymerization as well as the vaporization of volatile species acts to increase the size a n d concentration of large, flat, primarily aromatic molecules in the pyrolyzing organic milieu until these molecules precipitate in parallel arrays to form the anisotropic liquid k n o w n as the carbonaceous mesophase. This parallel stacking of aromatic layers constitutes the first step in the formation of graphitic materials because it is retained with only m i n o r modifications throughout graphitizing heat treatments as high as 3000°C. T h u s , graphite is unique a m o n g structural materials not only for its refractoriness, b u t also for its formation via a liquid crystal transformation. T h e morphology established in the carbonaceous mesophase, a n d locked into place as ongoing pyrolysis reactions cause hardening to semicoke, provides the basic framework for t h e microstructure of m o s t carbonaceous materials, including such varied materials as graphite electrodes for steel making a n d mesophase carbon fibers for the reinforcement of polymers. Since physical a n d mechanical properties often depend sensitively o n m i crostructure, the carbonaceous mesophase appears to play a vital role in determining the utility of graphitic materials. Although the rotational structural discontinuities k n o w n as disclinations have long been k n o w n in conventional liquid crystals [ i , 2], their existence in graphitic materials has only recently been recognized [60]. O u r present understanding of the m o r phology of the carbonaceous mesophase a n d its associated disclination structures stems directly from the pioneering work by Brooks a n d Taylor [3, 4], who first demonstrated that the mesophase transformation was fundamental to the formation of graphite from aromatic hydrocarbons. This article reviews the carbonaceous mesophase primarily as the m i crostructural determinator for graphitic materials a n d focuses o n the u n derstanding of disclination structures that is currently being developed. O n e should note that such studies enjoy a special advantage in that the carbonaceous mesophase can readily be quenched to a solid, which can t h e n be sectioned a n d studied by conventional metallographic m e t h o d s to define the morphology in three dimensions. In conventional liquid crystals, this advantage has been realized only by using systems that can be polymerized to solid bodies by thermal treatment [5].

II. C A R B O N A C E O U S M E S O P H A S E A.

Description

T h e carbonaceous mesophase consists of disklike molecules that display long-range orientational order in that the molecules lie approximately par-

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Fig. 1. Schematic model of the carbonaceous mesophase, a discotic nematic liquid crystal.

allel to each other. There is n o point-to-point registry between adjacent molecules. T h e orientation of each molecule is defined by its n o r m a l . T h e symmetry elements of the carbonaceous mesophase are (1) any translation, (2) any rotation about a n axis n o r m a l to the molecules, a n d (3) a rotation of π about any axis parallel to the plane of the molecules. Although the degree of symmetry is the same for a discotic n e m a t i c a n d a conventional nematic liquid crystal, the fact that for the discotic nematic the axis of symmetry is n o r m a l to the long dimensions of the molecules has i m p o r t a n t consequences for such characteristics as the optical properties, the response to mechanical stress, a n d the alignment in a magnetic field. A schematic model of the carbonaceous mesophase is shown in Fig. 1. This m o d e l suggests the stacking, size, a n d possible shapes of the disklike molecules, which m a y be quite irregular a n d contain vacant sites or holes [6], In the liquid-phase carbonization of m o s t polynuclear aromatic hydrocarbons, the reactions of cracking a n d aromatic polymerization b e c o m e rapid in the range 3 5 0 ° - 4 5 0 ° C , which is the t e m p e r a t u r e range in which carbonaceous mesophase usually appears. These pyrolytic reactions also sharply limit the plastic lifetime of the mesophase, b u t it is this brief critical stage that determines the microstructural characteristics of the coke or graphitic end product. T h e mesophase transformation has been observed in the pyrolysis of m a n y p u r e aromatic c o m p o u n d s , b u t the present understanding of the mesophase morphology is based primarily o n studies of the mesophase formed in the pyrolysis of petroleum a n d coal-tar pitch, natural bitumens, a n d even coking coals. I n d e p e n d e n t of the purity or complexity of the starting material, the m a n y reactions of pyrolysis produce a complex molecular milieu from which the mesophase precipitates, a n d the key features in the precipitating molecules are planarity a n d aromaticity [7].

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POLE

1

^POLE

Fig. 2. Structure of a spherule of carbonaceous mesophase, as determined by Brooks and Taylor [3].

B.

Transformation

T h e fact that the carbonaceous mesophase is usually observed as it forms from a dynamically reactive array of aromatic molecules leads to a transformation sequence that appears to differ from that of conventional nematic liquid crystals: ~400°C

Isotropic liquid

• Discotic nematic liquid crystal

~500°C

> Solidified coke.

Since the molecules constituting the mesophase grow in size a n d polymerize increasingly as pyrolysis continues, these transformations appear to be irreversible. However, two sets of recent observations clearly establish the liquid crystalline behavior of the carbonaceous mesophase. In one set of observations, Lewis [8, 9] observed the conventional thermotropic liquid crystal-to-isotropic transformation in a mesophase pitch produced by the high-pressure pyrolysis of naphthalene. With a hot-stage microscope, regions of the m e sophase were observed to convert to the isotropic phase o n heating from 350° to 475°C; o n cooling, the mesophase completely reappeared. T h u s , for portions of the naphthalene-derived pitch, the mesophase molecules were sufficiently stable to permit observation of the reversible thermotropic transformation before polymerization converted the mesophase to coke. In another set of observations, Riggs [10] a n d Riggs a n d Diefendorf [77] found that solvent-extraction m e t h o d s applied to various pitches could be used to concentrate those molecules contributing to the mesophase. For example, o n heating the toluene- or hexane-insoluble fractions of petroleum pitch, the solid fractions transformed almost instantaneously to a fine-structured, optically anisotropic mesophase that coarsened to the usual mesophase microstructures on further heating to temperatures in the neighborhood o f 4 0 0 ° C ; similar observations have been well d o c u m e n t e d in a recent film by Perrotta et al. [12].

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Fig. 3 . The coalescence of spherules to form bulk mesophase. The coalescence process introduces disclinations. The polar axes of the uncoalesced spherules are randomly oriented with respect to the plane of section. Crossed polarizers. Reprinted from White and Zimmer [60] by courtesy of Pergamon Press.

T h e characteristic mesophase m e c h a n i s m s that are involved in establishing the mesophase morphology are spherule precipitation, coalescence of spherules to bulk mesophase, a n d distortion of the mesophase by bubble percolation or mechanical deformation [18]. O n pyrolyzing a r o m a t i c hydrocarbons, either practical pitches derived from petroleum or coal tar, or pure precursors such as naphthacene or polyvinyl chloride, the mesophase spherules that precipitate were found by Brooks a n d Taylor [3] to have the structure sketched in Fig. 2. T h e disklike molecules lie perpendicular to the polar diameter a n d splay outward to lie perpendicular to the interface with the isotropic matrix from which they have precipitated. This characteristic " B r o o k s - T a y l o r m o r p h o l o g y " has been identified in spherules as small as a few microns; the spherules seldom grow b e y o n d 50 μτη without developing m o r e complex internal structures. It should be noted that alternative spherule structures have been observed in which the molecular layers lie parallel to the pitch interface; e.g., these onion-like structures have been reported

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PYROLYSIS TEMPERATURE (°C) Fig. 4. Mesophase transformation curves for four petroleum-based precursors pyrolyzed at 5°C/hr under room pressure: (1) gilsonite, (2) propane asphalt, (3) petroleum pitch, and (4) decant oil. The mass losses indicated by the dashed curves include the evaporation of nonmesophase molecules as well as the volatile products of polymerization reactions. From White 1371.

in the pyrolysis of synthetic pitches prepared from anthracene or naphthalene [13], from coal-tar pitch treated with carbon black [14], a n d from decacyclene [75]. However, in all cases, the interfacial energies are sufficiently high to establish spherical shapes even when the underlying m o r phology seems strained, as, for example, at the poles of the Brooks-Taylor spherule. Despite the significant influences operating at the mesophase interface, quantitative m e a s u r e m e n t s of interfacial surface energies have n o t been reported. As the pyrolysis reactions continue, the spherules grow a n d coalesce to produce large regions of bulk mesophase (Fig. 3). At this stage, it can be seen that the morphology of the liquid crystal is complex, as indicated by the patterns of polarized-light extinction contours. As in the case of conventional liquid crystals [2, 16], the nodes (where the contours pinch down)

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ο

>

0

100

200

300

Temperature

400

500

600

(°C)

Fig. 5. Viscosity as a function of temperature for a petroleum pitch heated at 40°C/hr. Mesophase formation begins at about 400°C. From Barr et al. [21].

a n d crosses (points of intersection) in the extinction contours identify the location of disclinations in the discotic nematic liquid crystal. In practical studies of mesophase formation in petroleum-derived or coalbased liquids, mesophase transformation curves have been determined to compare the pyrolysis characteristics of various types of feedstocks [77]. These are usually derived from m e a s u r e m e n t s of the solubility in pyridine or quinoline o n the assumption that these solvents dissolve the isotropic pitch but n o t the precipitated mesophase.* T h e transformation curves illustrated in Fig. 4 [37] provide measures of the t h e r m a l t r e a t m e n t required to induce mesophase transformation in a range of practical materials. In general, the mesophase appears before 3 8 0 ° C only for long-term thermal * Recent work with pitches specially prepared for the spinning of mesophase carbon fiber shows that this assumption cannot be relied upon, and quantitative micrographie methods [19, 20] should be used for more satisfactory measures of the extent of transformation.

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treatments a n d is complete before 5 0 0 ° C unless high pressures restrict the vaporization of nonmesophase molecular species. As pyrolysis proceeds, the viscosity of the mesophase rises sharply (Fig. 5) [21], a n d under usual experimental conditions the mesophase hardens to coke at 4 5 0 ° - 5 5 0 ° C . After hardening, the further effects of heat treatment include the formation of shrinkage cracks by anisotropic densification mechanisms, a n d fine-scale polygonizations associated with the approach to threedimensional graphitic registry in the final steps of graphitization [22, 23]. However these effects constitute only m i n o r modifications to the m o r phology introduced while the mesophase existed as a liquid crystal. C. Physical Aspects T h e carbonaceous mesophase has some physical properties that fit the nematic classification of liquid crystals. However, other physical properties differ from those for a typical nematic; these differences stem from the fact that the carbonaceous mesophase comprises disklike rather t h a n rodlike molecules. T h e observation of thermotropic m e s o m o r p h i s m in pure c o m p o u n d s of simple disklike molecules has aided the understanding of the molecular nature of the carbonaceous mesophase. T i n h et al. [24] a n d Destrade et al. [25] observed optical textures similar to those for nematic liquid crystals in hexaalkyl a n d hexaalkoxy benzoates of triphenylene. T h e structure was one in which the disklike molecules have translational freedom as well as rotational freedom about a n axis perpendicular t o the molecules, b u t with the plane of the molecule approximately parallel to a general plane. This liquid crystal structure is similar to the structure determined for the carbonaceous mesophase (Fig. 1). Disklike molecules have also been observed to orient in c o l u m n s with the molecules perpendicular t o the c o l u m n axis. Chandrasekhar et al. [26] first observed a c o l u m n a r nematic structure in benzene-hexa-«-alkanoates. Recently, evidence has been obtained that this c o l u m n a r nematic structure can exist in the carbonaceous mesophase. Auguie et al. [27] studied the microtexture of mesophase spherules by transmission electron microscopy. In high-magnification lattice-fringe images, the aromatic molecules were observed to be occasionally stacked in columns. T h e c o l u m n s were in close contact with each other a n d in c o m p a c t arrangement. There was n o relation between neighboring columns, a n d the c o l u m n s were curved a n d distorted. Thus, some carbonaceous mesophase can apparently form with local regions displaying molecular registry in the layer stacking corresponding to the degree of order described as c o l u m n a r nematic ( N ) . However, this order appears fragile a n d is readily reduced to discotic nematic order ( N ) by the molecular flow involved in coalescence a n d deformation. c

D

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2

Fig. 6. Some model structures for mesophase-forming molecules, based on Mochida et al [61 1.

MOLECULAR STRUCTURE

Precise determination of the constituent molecules a n d their distribution in the carbonaceous mesophase is complicated by the wide range of m o lecular sizes a n d shapes. Infrared spectroscopy, nuclear magnetic resonance spectroscopy, a n d vapor-pressure o s m o m e t r y can be used to estimate the structural configuration of the disklike aromatic molecules in the carbonaceous mesophase. M o c h i d a et al. [6] analyzed mesophase spherules prepared by pyrolysis of the quinoline-soluble fraction of a petroleum pitch; the weights of the constituent molecules ranged from 400 to 3000, with a number-average molecular weight near 1400. S o m e possible molecular models based o n these data are illustrated in Fig. 6. It should be noted that the molecular sizes a n d structures involved in the precipitation of mesophase m a y vary appreciably; for example, a recent patent [28] describes the preparation of a fully transformed mesophase with a number-average molecular weight near 900. 2.

MOLECULAR ALIGNMENT

T h e preferred orientation of molecules in the carbonaceous mesophase is parallel stacking. T h e degree of preferred orientation is well illustrated by the electron diffraction pattern (Fig. 7) presented in a n early article by Brooks a n d Taylor [3]. T h e sample was a m i c r o t o m e d section of a mesophase spherule oriented to place the average layer orientation approximately parallel to the electron b e a m . T h e diffraction arcs show a n average layer spacing of 3.47 À a n d appreciable deviation from parallel stacking; this

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Fig. 7. Electron diffraction pattern from part of a single mesophase sphere where the disklike molecules lie approximately parallel to the beam. The continuous rings are from the internal aluminum standard. Reprinted from Brooks and Taylor [3] by courtesy of Marcel Dekker, Inc.

pattern indicates that all diffracting layers lie within 25° of the m e a n layer orientation. In recent work, Auguie et al. [27] have applied similar techniques quantitatively to derive an approximate Gaussian distribution of layer orientations with a full width at half m a x i m u m of 2 5 ° ; this translates to an order parameter, as defined by de G e n n e s [33], of a b o u t 0.9. This electron diffraction result confirms x-ray diffraction observations of a full width at half m a x i m u m of 22° by Delhaes et al. [29a]; for the latter measurement, a magnetic field was employed to produce essentially a single liquid crystal of mesophase, well oriented a n d almost free of disclinations, a n d sufficiently large for x-ray diffraction. 3.

OPTICAL ANISOTROPY

T h e birefringence characteristic of crystalline graphite c o m m e n c e s in the liquid crystal from the parallel alignment of the large, flat aromatic molecules. T h e carbonaceous mesophase is uniaxial, b u t optically negative in

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(a)

BEAM LINE OF POLARIZATION

Fig. 8. Reflectance of polarized light from a graphite crystal: (a) (b) and (c), i? = 0.28, R = 0.16. air

0.08, i?

oil

= 0.008;

oil

that the optic axis, n o r m a l to the molecules, parallels the direction of vibration for the m i n i m u m refractive index [29b]. This contrast with the uniaxial positive behavior of conventional nematic liquid crystals results from the disklike structural unit with its long dimension perpendicular rather t h a n parallel to its symmetry axis. Most optical observations of mesophase, coke, a n d graphite are m a d e by reflection microscopy with polarized light. T h e reflection contrasts are illustrated for a graphite single crystal by Fig. 8; the n o r m a l reflectances were calculated by the Fresnel equation from the optical constants given by Ergun et al. [30]: n = 2.15, κ, = 1.81, ±

A= ±

1.42,

Ay = 0,

where η is the refractive index, A is the absorption coefficient, the subscripts refer to the orientation of the line of polarization relative to the optic axis, a n d the values refer to a wavelength of 546 n m . T h e reflection contrasts are favorable to the use of polarized light to establish molecular orientations, especially when an i m m e r s i o n oil (refractive index assumed here to be 1.515) is used as the coupling m e d i u m . Although Cornford a n d Marsh [31] found that the differences in the reflectances parallel a n d perpendicular t o t h e preferred orientation of mesophase molecules were smaller at earlier stages of heat treatment, crossed polarizers can be used to provide adequate contrast for the definition of the preferred molecular orientation o n most polished planes of section. 4.

M A G N E T I C PROPERTIES

T h e diamagnetic susceptibility of disklike, polynuclear aromatic molecules is larger perpendicular to the aromatic layer plane t h a n in the plane of the molecule. T h e disklike molecules of the carbonaceous mesophase align parallel to a magnetic field [32] as d o t h e rodlike molecules of a nematic liquid crystal. F o r the nematic liquid crystal, the long axis of the

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Fig. 9. Alignment of a nematic and a discotic nematic liquid crystal in a magnetic field. For the discotic nematic liquid crystal, the normals to the disklike molecules can lie anywhere in the plane perpendicular to the direction of the magnetic field.

rodlike molecules aligns parallel to the magnetic field, t h u s uniquely defining the molecular orientation of the sample. For the discotic nematic liquid crystal, the molecular orientation is n o t uniquely defined in that the normals to the molecules can lie anywhere in a plane perpendicular to the magnetic field (Fig. 9). Rotating a sample of the carbonaceous mesophase a b o u t an axis perpendicular to the magnetic field uniquely orients the liquid crystal such that the normals to the molecules lie parallel to the axis of rotation [32]. Delhaes et al. [29a] have measured the diamagnetic susceptibility of a magnetically oriented body of carbonaceous mesophase. At 2 2 ° C , χ,, = - 0 . 5 0 X 10^ e m u / g 6

χ

= - 1 . 1 9 X 10~ e m u / g 6

±

Xa = X± ~ Χ» = - 0 . 6 9 X 1 0 " e m u / g 6

where χ a n d %| are the diamagnetic susceptibilities measured with the magnetic field perpendicular a n d parallel to the aromatic molecules, respectively, a n d Xa is the diamagnetic anisotropy. T h e diamagnetic anisotropy for nematic liquid crystals is positive a n d smaller in magnitude: 0.121 X 10~ for PAA at 122°C a n d 0.123 Χ 1 0 " for MBBA at 19°C [33]. Delhaes et al. concluded that for disklike molecules with a molecular weight about 1000 and a carbon-to-hydrogen atomic ratio of 1.6, the molecules must be open structures, i.e., large molecules with smaller aromatic regions as proposed by Mochida et al. [6] (Fig. 6). ±

6

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ALIGNMENT AT SURFACES

Although freshly precipitated mesophase is easily distorted by flow, such as is occasioned by bubble percolation, the mesophase molecules are usually found oriented at large angles to a n interface with untransformed pitch, as in the Brooks-Taylor spherule of Fig. 2 (some specific exceptions to perpendicular orientation were noted in Section ΙΙ,Β). Recent work with a hotstage microscope with quenching capability [34, 35a] indicates that this perpendicular layer orientation also applies to free surfaces. Although the orienting influence m a y extend t o depths of only a few microns, it appears sufficient to explain the sharp reflectance contrasts of a free surface exa m i n e d by polarized light. Tendencies for mesophase molecules to align parallel to the surface of solid materials, such as graphite flakes, coke particles, pyrolytic carbon, a n d even glass a n d ceramics, were early recognized [3]. T w o cases observed by Dubois et al. [23] are illustrated by the structural sketches in Fig. 10. Unless disturbed by deformation, these alignment effects can extend to 20 μτη or more. Parallel alignment also occurs o n graphite fibers, a n d t h u s plays a d o m i n a n t role in the formation of the microstructure of the refractory materials k n o w n as c a r b o n - c a r b o n composites, which consist of graphitic matrices reinforced by graphite fibers [35b]. In fabricating such c o m p o s ites, the mesophase formed by pyrolysis within a fiber b u n d l e aligns to give the sheath effect shown by Fig. 11. This particular composite was chosen for illustration because m a n y of the carbon filaments (manufactured by spinning a mesophase pitch [41a]) display a radial open-wedge morphology that exposes graphitic planes in the wedge a n d the edges of graphitic planes on the radial periphery. C r a n m e r et al. [36] have shown that, in a partially transformed pitch, the mesophase preferentially wets the planar surfaces within the open wedge. However, w h e n transformation is complete, as in Fig. 11, the mesophase molecules are found aligned parallel to the substrate surface independent of the graphite layer orientation within the filament substrate. In the structural sketches of the morphology of the carbonaceous m e sophase, the lines or surfaces are m e a n t to denote the layers m a p p e d out by the average direction of the preferred orientation of the individual platelike molecules. W e refer to such a layer-like structure as a lamelliform morphology. D . Microstructures in the Carbonaceous Mesophase T h e range of microconstituents found in such varied mesophase products as petroleum coke, structural graphite, a n d carbon fiber spun from meso-

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Fig. 10. Alignment of layers of carbonaceous mesophase on solid substrates: (a) partially transformed mesophase wetting natural flakes of graphite; (b) fully transformed mesophase wetting particles of needle coke, after heat treatment to 600°C. Reprinted from Dubois et al. [23] by courtesy of American Elsevier Publishing Company, Inc.

phase pitch can be classified in t e r m s of a few characteristic microstructures developed in the mesophase as it hardens to coke. W h e n observed u n d e r crossed polarizers, these microconstituents display specific patterns of extinction contours that vary in n u m b e r a n d preferred orientation [17]. T h e petroleum coke illustrated at two levels of magnification in Fig. 12 displays three distinctive microconstituents—coarse, fibrous, a n d lamellar—as well as some intermediate or mixed microstructures, all located in close proximity. In t e r m s of the underlying lamelliform morphologies, these micro-

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Fig. 11. The sheath effect observed within a bundle of carbon fibers wetted by carbonaceous mesophase [35b]. The radial open-wedge filaments are characteristic of one type of carbon fiber spun from mesophase pitch. Section transverse to axis of fiber bundle, mapped by polarized-light micrography with immersion oil.

Fig. 12. The mesophase microstructures present in a typical petroleum coke. Three specific microconstituents are labeled: C, coarse; F, fibrous; L, lamellar. Crossed polarizers. Reprinted from White [73] by courtesy of the American Chemical Society.

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constituents differ in the type, density, a n d orientation of disclinations present as well as in the preferred orientation of the mesophase layers. T h e coarse microconstituents of Fig. 12 resemble the microstructures of nematic or discotic liquid crystals [24]. This microconstituent is essentially a randomized lamelliform array a n d lacks a preferred orientation o n a macroscale. Satisfactory definition of its disclination features requires information o n the dip as well as strike of the mesophase layers in the vicinity of each disclination. T h e nucleation a n d growth of gas bubbles within the mesophase can produce extensive plastic deformation, a n d this constitutes a m e c h a n i s m by which mesophase microstructures are oriented a n d reduced to finer textures. T h e bubbles form during pyrolysis because the processes of aromatic polymerization begin by dealkylation a n d dehydrogenation reactions producing gases, mainly m e t h a n e a n d hydrogen. T h e pyrolyzing liquid begins to bloat appreciably when the mesophase becomes the c o n t i n u o u s phase because mesophase bubble walls are relatively stable a n d can be subjected to extensive biaxial deformation without failure. T h e bloating also leads to buoyant forces that can subject other mesophase regions to extensive uniaxial deformation. T h u s deformation becomes the d o m i n a n t m e c h a n i s m for alteration of the coarse microstructures produced originally by mesophase coalescence, a n d the lamellar a n d fibrous microconstituents represent two ends of the spectrum of deformed microstructures that are found as mesophase fossils in various carbon a n d graphite products. Experiments o n the drawing of mesophase rods a n d fibers have shown that uniaxial deformation produces the fibrous microstructure that characterizes the acicular regions of those petroleum cokes k n o w n as needle cokes [38]. Fig. 13 offers views by polarized-light micrography of a coke needle sectioned perpendicular (transverse) a n d parallel (longitudinal) to the axis of the coke needle. T h e morphology is strongly oriented with the mesophase layers closely parallel to the axis; the layers t h u s stand n o r m a l to the transverse section. T h e fine lamellar microstructure of a bubble wall is illustrated in Fig. 14 on two perpendicular planes of section. T h e same type of striated microstructure appears o n b o t h sections, a n d in m o s t cases the polarized light extinction contours that constitute the striations can be traced over the edge at which the sections meet. T h u s , the biaxial extension resulting from bubble growth has forced a strong platelike preferred orientation with the mesophase layers lying parallel t o the bubble wall. T h e extinction contours are due to folds in the mesophase layers [39]. T h e fact that the mesophase can be drawn t o filaments less t h a n 10 μτη

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Fig. 13. The fibrous microstructure of an acicular region in a needle coke, sectioned transverse (a—crossed polarizers) and longitudinal (b—polarizer only) to the fiber axis. The longitudinal views, with polarizers perpendicular and parallel to the fiber axis, show that the mesophase layers lie parallel to the axis and thus normal to the transverse section. Reprinted from White and Zimmer [60] by courtesy of Pergamon Press.

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Fig. 14. Perpendicular cross sections of a mesophase bubble wall. Crossed polarizers. Rotation of the plane of polarization demonstrated that the mesophase layers were parallel to the bubble wall. Reprinted from White [37] by courtesy of the American Chemical Society.

in diameter is the basis for the invention of mesophase carbon fiber [40, 41]. T h e deformation in spinning such filaments can extend to strains (draw ratios) in excess of 1000 [41b]. As indicated by the scanning electron micrographs of Fig. 15, the mesophase layers are wrinkled a n d corrugated beyond resolution by optical microscopy. However, the scroll-like a n d pipelike features in the core of the filament constitute disclination structures.

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Fig. 15. Scanning electron micrograph of the structure of a mesophase carbon fiber revealed by oxidation of a fracture surface. The scroll-like features constitute S = +1 wedge disclinations.

These two distinct, deformed microstructures of the carbonaceous m e sophase provide background morphologies t h a t p e r m i t clear identification of the disclination structures in the mesophase. As will be shown, in the fibrous, uniaxially deformed microstructure, wedge disclinations with axial character are p r o m i n e n t . Twist as well as wedge disclinations are associated with the folds in the lamellar, biaxially deformed microstructure.

III. D I S C L I N A T I O N S T R U C T U R E S T w o distinct classes of disclinations appear t o b e conceptually possible in a lamelliform morphology: (1) layer-stacking disclinations consisting of discontinuities in the parallel stacking of layers owing t o the freedom of the preferred orientation to bend, splay, a n d twist as shown in Fig. 16; a n d (2) layer disclinations consisting of rotational distortions within a single layer [42]. Layer-stacking disclinations are a b u n d a n t in the carbonaceous m e sophase a n d readily observable by polarized-light micrography; they are

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(c)

Fig. 16. Curvatures of preferred orientation in a discotic nematic liquid crystal: (a) bend, (b) splay, (c) twist.

similar to disclinations in nematic liquid crystals b u t with disklike molecules substituted for the rodlike units of structure. Layer disclinations are found in surface crystals [43]; although reasonable structures can readily be predicted for similar disclinations in a graphite layer, their scale m u s t be closer to the scale of lattice dislocations t h a n that of layer-stacking disclinations, a n d we are unaware of published evidence of their existence in graphitic materials. F r o m a theoretical viewpoint, the concept of internal distortions in a continuous body was developed at the t u r n of this century by Weingarten [44] a n d Volterra [45]. T h e relationships between translational distortions

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SCREW

Fig. 17. Volterra distortions in a doubly connected, homogeneous body: (a) translational, (b) rotational. The vector t defines the line of dislocation or disclination. The orientation of the displacement vector b (the Burgers vector) defines the edge or screw character of a dislocation, whereas the orientation of the rotation vector ω defines the twist or wedge character of a disclination.

(dislocations) a n d rotational distortions (disclinations) are illustrated by Fig. 17. Despite this early basic development, only in the last 20 years has the study of disclinations flourished. T h e general theory has been reviewed a n d discussed by N a b a r r o [46] a n d by K r o n e r a n d A n t h o n y [47]. Harris [43] reviewed disclinations with emphasis o n defects in surface crystals. D e Wit [48] presented the general theory of disclinations in a linearly elastic, infinitely extended, h o m o g e n e o u s body along with the relations between dislocations a n d disclinations. A n t h o n y [49] also developed the theory of disclinations a n d discussed disclinations in crystals as well as in oriented bodies that m a y be noncrystalline b u t possess regular patterns. Interest in disclinations in conventional liquid crystals was rekindled by F r a n k [50], a n d reviews of various aspects have been m a d e by Saupe [57], de G e n n e s [33], Chandrasekhar [52], Stephen a n d Straley [53], a n d K l é m a n [54a,b]. Governed by the curvatures of bend, splay, a n d twist (cf. Fig. 16), the basic configurations of disclinations that m a y exist in the carbonaceous mesophase can be developed by certain conceptual operations k n o w n as the Volterra process. Referring to Fig. 18, where the lamellae represent the preferred orientations of mesophase molecules, consider a cut in a b o d y of

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ROTATION

(a)

lb)

(c)

Fig. 18. Formation of negative wedge disclination in a discotic nematic liquid crystal by the Volterra process, (a) A cut is made midway between two adjacent lamellae, (b) Face C is rotated about one edge of the cut relative to face C~. The axis of rotation is antiparallel to the disclination line, (c) Layers are added to heal the cut, retaining the parallel stacking away from the disclination core. +

lamelliform texture along a surface that is parallel to the molecular layers in an unperturbed region (Fig. 18a). T h e shape of the surface is arbitrary, and thus the disclination line, the line defining the edge of the surface, can be curved. T h e direction of the tangent to the disclination line is defined in a right-handed sense in that for a clockwise circuit when looking in the direction of the tangent, face C is encountered first. T h e two faces of the cut are t h e n rotated with respect t o each other a b o u t a n axis of rotation. T h e direction of rotation is right-handed about the rotation vector a n d thus the C face is rotated with respect to the C " face. T h e symmetry of the carbonaceous mesophase requires that the rotations be only multiples of π. If the two cut faces are rotated apart as shown in Fig. 18b, the rotation vector ω is antiparallel to the tangent to the disclination line; this is a negative wedge disclination. Additional material m u s t be added to heal the cut. For a positive wedge disclination, the rotation vector is parallel t o the tangent to the disclination line, a n d material m u s t be removed to heal the cut. For a rotation vector in the cut surface, b u t perpendicular to the tangent, a twist disclination would be imposed o n the lamelliform texture. +

+

A. W e d g e Disclinations A n equation developed by F r a n k [50] to describe wedge disclinations in a nematic liquid crystal is

where φ is the angle that the rodlike molecules m a k e with the χ axis a n d these molecules are assumed to lie in the x-y plane perpendicular to the

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(b)

(c)

(d)

(e)

(f)

Fig. 19. Wedge disclinations: (a) S = +V2; (b) S = -V2; (c) S = +1, φ = 0; (d) S = +1, φ = ττ/4; (e) S = +1, φ = ττ/2; (ΐ) S = - 1 . 0

0

0

disclination line. T h e rotation vector is parallel to the ζ axis. For the discotic nematic liquid crystal, this equation can be used without modification to represent the normals to the disklike molecules. For the carbonaceous m e sophase with twofold symmetry, disclinations of strength S = n/2, with η any integer, are allowed (S = ± h ± 1 , . . . ) . Wedge disclinations involving rotations of ±π (S = ±Vi) a n d ±2π (S = ± 1 ) are sketched in t e r m s of the molecular lamellae in Fig. 19. T h e strength of a disclination, a measure of the a m o u n t of rotation involved in the disclination, is determined by considering the change in the direction of the normals t o the disklike molecules a b o u t a circuit that encloses the disclination line. This m e t h o d was devised by N a b a r r o [46] a n d is analogous to constructing a Burgers circuit a b o u t a dislocation. Instead of counting lattice steps a b o u t a Burgers circuit, one observes the change in local orientation of the molecules along the closed curve. T h e disclination strength is t h e n defined as the n u m b e r of revolutions of the direction of the normals with respect to o n e revolution (2π) a b o u t the N a b a r r o circuit. A Nabarro circuit is illustrated in Fig. 20 for a negative wedge disclination of rotation π, i.e., a wedge disclination of strength S = —V2. This N a b a r r o circuit is traversed clockwise a b o u t the tangent to the disclination line. T h e rotation of the normals to the molecules is counter to the rotation about the circuit. l

9

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Fig. 20. Nabarro circuit. The rotation of the normal to the molecules for the wedge disclination is - π ; the circuit starts at the dashed line at the top of the sketch.

B. Twist Disclinations Twist disclinations involve rotations in which the rotation vector is perpendicular to the disclination line. A n equation used by Stephen a n d Straley [53] to describe twist disclinations is β ='δφ

+0n,

t a n ψ = γ/χ,

S = ±

±

1,

where θ is the angle that the layer normal, parallel to the x-z plane, makes with the χ axis. T h e rotation vector is parallel to the y axis. This equation assumes a uniform rotation a r o u n d the disclination core, as sketched in Fig. 21. For a N a b a r r o circuit a b o u t a twist disclination, the direction of the normals will vary out of the plane of the circuit. Twist disclinations of opposite signs are mirror images o n a plane n o r m a l to the disclination line.

~Λ D S C IT L N I A T O ITN J [ A N G E N

Fig. 21. Model of a twist disclination with uniform rotation about core. Each segment of the doubly connected body contributes π/4 to the total rotation involved in a Nabarro circuit about the disclination line.

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( Β Γ

(b)

Fig. 22. Twist disclinations of rotation π. t is the tangent to the disclination line and ω is the rotation vector. The shaded region is the ribbon-like core of these twist disclinations.

Depending o n the preferred orientations existing in the vicinity of the twist disclination, the rotation m a y be localized to various segments a r o u n d the disclination core. In a strongly lamellar region, the entire rotation of π is accomplished in the b e n d segment to give the folded structure illustrated by Fig. 22a; the disclination line t h u s appears as a narrow ribbon where the fold ends. T h e disclination structure of Fig. 22b m a y occur at a transition between two lamellar microconstituents; the rotation is localized to bending in two segments of the doubly connected body. T h e cores of the twist disclinations in the discotic nematic liquid crystal are represented by ribbons, since the discontinuity at the core has a finite width. C. Layer Disclinations U p to this point, the disclinations that have been described are layerstacking disclinations, t h a t is, singular discontinuities in parallel stacking that result from bend, twist, a n d splay in the preferred orientation of the disklike molecules. Layer disclinations might exist within a n extended graphite layer. Such disclinations c a n n o t exist in the liquid crystal itself since there is n o registry between individual molecules, b u t m a y conceivably exist in solidified mesophase or heat-treated cokes. Coplanar molecules in the carbonaceous mesophase can polymerize edgewise during pyrolysis a n d subsequent heat t r e a t m e n t to form extended layers. Crystallographically incorrect b o n d s m a y be expected to form between s o m e adjacent molecules, or even within a single, large molecule. Such misconnections would be

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Fig. 23. Layer disclinations of strength S = +% (a) and —% (b) in a graphitic layer with sixfold symmetry.

favored in regions of doubly curved mesophase surfaces. Layer disclinations are discussed briefly here because the liquid crystal, with its three-dimensional variations in preferred orientation, sets u p some skeletal arrays in which layer disclinations m a y form during the graphitization process. Regions of particular interest are those with strong double curvature, such as those found at the poles of Brooks-Taylor spherules (cf. Fig. 2). If an aromatic layer formed with such double curvature is to develop the crystal structure of the graphite basal plane, layer disclinations can be introduced to account for the overall nonplanarity. T w o such layer disclination structures are illustrated by Fig. 2 3 . These are wedge disclinations, relaxed to conelike or saddle-like structures t o permit the aromatic hexagons to extend indefinitely with only small distortions in b o n d angle. In principle, wedge disclinations of strength S = n/p are allowed, where η is a n integer a n d ρ = 6 for the rotational symmetry of the hexagonal layer. A n extensive description of b o t h wedge a n d twist disclinations in surface crystals has been given by Harris [43]. Twist layer disclinations have complex configurations that resemble M ô b i u s strips. IV. W E D G E D I S C L I N A T I O N S Both optical a n d scanning electron micrography have proved useful in delineating the configurations of disclinations in the carbonaceous mesophase. T h e m a p p i n g of disclinations by optical m e a n s usually involves the tracing out of the strike of mesophase layers o n a polished section by applying overlays to a series of polarized-light micrographs taken at various angles of rotation of the plane of polarization. This m e t h o d is tedious a n d limited by the precision of microscope imaging o n the focal plane; in practice, it is readily applicable only to coarse morphologies, such as those found in the early stages of mesophase formation. T h e finer level of resolution of scanning electron micrography is better suited to the scale of disclination arrays in deformed microconstituents; however, this m e t h o d has relied o n

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heat treatment to bring out the structural features a n d has t h u s been limited to hardened mesophase specimens. T h e structure of the disclinations underlying the rotation-invariant points in the polarized-light extinction contours was recognized soon after Brooks a n d Taylor [3] demonstrated that m o s t cokes a n d graphites form via a liquid crystal m e c h a n i s m [22, 55, 56]. However, the early work was limited to optical studies o n single planes of section, a n d the observations were inadequate to define such elementary points as the wedge or twist character of the disclination structures. These limitations have been overcome in recent work by multiple sectioning, by the study of microconstituents with well-defined preferred orientations, a n d by etching m e t h o d s which provide some information on the dip as well as strike of the mesophase layers.

A. Optical M i c r o g r a p h y T h e polarized-light response of the carbonaceous mesophase offers a m e a n s for determining the molecular orientations within a sample of the material. A n i m p o r t a n t property of the carbonaceous mesophase that facilitates optical micrography is its high viscosity, which permits mesophase specimens to be cooled to r o o m t e m p e r a t u r e with little or n o disturbance of the microstructure present at the pyrolysis t e m p e r a t u r e . Studies by hotstage microscopy [34, 35a, 57] show that the microstructures present in the bulk mesophase at the transformation temperatures are essentially the same as those in q u e n c h e d samples. T h e morphology of this liquid crystal can t h u s be studied o n solidified specimens, which m a y be sectioned as necessary to define fully the disclination structures. Although the mesophase is transparent in sufficiently thin section [29b], all detailed optical studies have been m a d e with reflected light. Conventional metallographic m e t h o d s are suitable for the preparation of polished sections of mesophase products that have been h a r d e n e d to coke or graphite by heat treatment; the sample should be v a c u u m - i m p r e g n a t e d with a suitable polym e r to fill the pores a n d shrinkage cracks [23]. However mesophase specimens solidified by cooling from the liquid crystalline state are b o t h soft a n d brittle, a n d special care is essential to prepare the intersecting sections required for three-dimensional definition of the underlying morphology (e.g., cf. Fig. 14). A m e t h o d used in o u r laboratories to prepare such sections begins by cutting a n d grinding (600-grit paper) the impregnated specimen to the desired planes of section. T h e polishing steps c o m m e n c e with 9-μπι d i a m o n d paste o n a silk cloth o n a slowly rotating wheel; the thinness of the silk cloth aids in keeping a flat surface. Polishing is continued with 3μπι d i a m o n d paste on silk cloth, a n d then with 0.25-μηι d i a m o n d paste o n

/. Ε. Zimmer

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20

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/im

Fig. 24. Configurations of S = — Vfe wedge disclinations (counterrotating nodes) by optical mapping technique. Crosses denote orientation of polarizers.

a microcloth whose n a p has been softened by boiling water. T h e polishing lubricant is water with a small addition of liquid soap. T h e final step in polishing uses 0.05-μπι cerium oxide. For identifying wedge disclinations, the specimen illustrated in Figs. 2 4 27 was produced by pyrolyzing a heavy petroleum oil (a decant oil from

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20m i/ Fig. 25. Configuration of S = +Vi wedge disclination (corotating node), along with S = -Vi and S = +1 wedge disclinations, by optical mapping technique.

a catalytic cracker) to 425 °C at 5 ° C / h r . At this stage of pyrolysis, the spherules had just begun to coalesce a n d the mesophase was relatively coarse (extinction contours spaced widely apart) a n d undeformed. T h e configurations of apparent wedge disclinations of strengths S = ± h a n d S = ± 1 were then determined by the optical m a p p i n g technique [58]. Micrographs with crossed polarizers were taken of selected nodes a n d crosses in the extinction contours at 15° intervals in the rotation of the polarizers. T w o l

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Fig. 26. Configuration of S = + 1 wedge disclination (corotating cross) by optical mapping technique.

nodes, where the extinction contours pinch do>yn to a thin line or point, are shown in Fig. 24. T h e extinction contours rotate a b o u t these nodes counter to the rotation a n d at twice the rate of the polarizers. These counterrotating nodes correspond to wedge disclinations of strength S = — h. Three disclinations appear in Fig. 2 5 . T h e corotating node, where the extinction a r m s rotate in the same direction a n d at twice the rate as the l

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Fig. 27. Configuration of S = - 1 wedge disclination (counterrotating cross) by optical mapping technique.

rotation of the polarizers, corresponds to a wedge disclination of strength S = + V 2 . A counterrotating n o d e a n d a corotating cross also appear in this sketch. A single corotating cross is shown in Fig. 26. T h e extinction a r m s rotate at the same rate as the polarizers. This cross is a wedge disclination of strength S = + 1 . A counterrotating cross, or wedge disclination of strength S = - 1 , is sketched in Fig. 27. Although these disclinations display two-

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(a)

(b) Fig. 28. Scanning electron micrographs of wedge disclinations in the fine fibrous structure of a heat-treated needle coke, (a) Wedge disclination of strength S = -V2; (b) wedge disclination of strength S = +V2. Reprinted from White and Zimmer [60] by courtesy of the Royal Society of Chemistry.

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dimensional structures similar to the sketches in Fig. 19, they can only be considered as disclinations with apparent wedge character since a single section through a coarse undeformed microstructure is inadequate to define the relative directions of the tangent a n d rotation vectors. T h e nodes a n d crosses c o m m o n l y observed in the carbonaceous mesophase are disclinations of strength S = ± h a n d S = ± 1. Disclinations of higher s t r e n g t h — f o r example, disclinations of strength S=— %, which would have six extinction c o n t o u r a r m s — h a v e n o t been reported. l

B. Scanning Electron Micrography Scanning electron micrography, with appropriate specimen heat treatm e n t a n d etching, can reveal directly the configurations of disclinations in the carbonaceous mesophase. W h e n the mesophase is heat-treated beyond the hardening point, the first microstructural effect is the appearance of shrinkage cracks d u e t o anisotropic densification. Lenticular cracks, r u n n i n g parallel to the mesophase layers, open as the result of greater shrinkage perpendicular to the layers t h a n parallel to t h e m . O n heat t r e a t m e n t to graphitizing temperatures ( ~ 2 5 0 0 ° C ) , this lamellar cracking extends d o w n to submicron dimensions a n d provides structural features that are visible by scanning electron microscopy (e.g., cf. Figs. 2 8 - 3 0 ) . If the polished surface is cleaned by ion etching [58], layers intersecting the plane of section at low angles display a fish-scale structure [59], t h u s providing r u d i m e n t a r y evidence of the dip as well as the strike of the mesophase layers. This evidence is sometimes sufficient to identify significant details of disclination structure. T h e interpretation of the scanning electron micrographs is simplified by the use of specimens with a morphology that has a specific geometry, including a strong preferred orientation. In the fibrous morphology (Fig. 13), the disclinations that exist m u s t be wedge disclinations with their disclination lines parallel to the fiber axis a n d perpendicular to a transverse plane. This plane is the plane of section for the electron micrographs of Figs. 2 8 30. T h e material used for this micrography was a premium-grade needle coke graphitized to 2700°C. Scanning electron micrographs of the wedge disclinations in the heat-treated carbonaceous mesophase are shown in Figs. 2 8 - 3 0 . In each figure, the intercrystalline cracks appear as dark lines separating the crystallites or packets of graphitic layers. T h e white areas are thin splinters of the graphite that protrude above the surface a n d that d o not absorb the electron b e a m as well a n d t h u s appear bright. Disclinations of strength S = ± h are shown in Fig. 28. T w o cases, φ = π/2 a n d 0, for l

0

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Fig. 29. Wedge disclinations of strength S = +1 with (a) φ = π/2 and (b) φ = 0. Reprinted from White and Zimmer [60] by courtesy of the Royal Society of Chemistry. 0

0

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Fig. 30. Wedge disclination of strength S = - 1 . Reprinted from White and Zimmer [60] by courtesy of the Royal Society of Chemistry.

the S = + 1 disclination are shown in Fig. 29, a n d a n S = —1 disclination is shown in Fig. 30. C. Core Structures For conventional nematic liquid crystals comprising rodlike molecules, Meyer [61] has shown that wedge disclinations of strength S = ± 1 have continuous cores in which the parallel alignment of rods is m a i n t a i n e d by tilting of the rods out of the transverse plane, a n d that disclinations with a continuous core have lower energy. This c o n t i n u o u s core structure m a y also apply to the carbonaceous mesophase, a n d in this case the platelike molecules would define doubly curved surfaces at the disclination cores. In polarized-light micrographs (cf. Figs. 2 4 - 2 7 ) , the extinction-contour crosses denoting S = ± 1 wedge disclinations usually have broad centers c o m p a r e d to the sharp, pinched-down centers of the nodes denoting S = ± h wedge l

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disclinations. This broad center is a n indication of a continuous core structure. T h e nature of the cores of the wedge disclinations in carbonaceous m e sophase and graphite has been delineated by scanning electron micrography [58]. For layers intersecting the plane of section at angles between a b o u t 30 a n d 45° from the n o r m a l , ion etching produces features having the appearance of fish scales. T h e fish-scaling is directional, indicating the direction of the tilt of the layers from the n o r m a l to the plane of section. A wedge disclination of strength S = + 1 a n d its core are shown in Fig. 31a. T h e orientation of the layers a r o u n d the core is n o r m a l to the surface. However, within the core itself, the layers are tilted outward as defined by the fish-scaling. This indicates that the configuration of the core is similar to a cup. A sketch of the core structure of an S = + 1 wedge disclination is shown in Fig. 32. T h e core configuration consists of doubly curved layers with the two radii of curvature o n the same side, a n d with parallel stacking of the layers throughout the core. A wedge disclination of strength S = - 1 is shown in Fig. 31b. T h e shrinkage cracks outline the layer orientations a n d indicate that the layers at a short distance from the core intersect the surface normally. Within the core, the fish-scale effect again indicates double curvature. T h e layers o n the t o p a n d b o t t o m sides tilt inward, whereas the layers o n the left (and somewhat o n the right) side tilt outward. This implies double curvature with the two radii of curvature o n opposite sides, that is, a hyperbolic paraboloid. This saddle-like configuration retains the parallel stacking throughout the core. Further evidence of the c o n t i n u o u s core of S = - 1 disclinations comes from optical studies of c a r b o n - c a r b o n composites in which the morphology of the mesophase matrix is d o m i n a t e d by the sheathlike alignment o n the fiber surfaces. In the transverse view of a fiber bundle, Fig. 33, the matrix exhibits m a n y counterrotating nodes a n d crosses, a n d the crosses have b r o a d centers. T h e longitudinal view displays occasional bright ribbons that resolve to well-defined extinction contours; these indicate a transverse preferred orientation midway between the fibers. A sketch of a n S = — 1 disclination that would give this polarized-light response is shown in Fig. 34. T h e sheath effect a r o u n d four fibers in square array establishes b o u n d a r y conditions consistent with the doubly curved saddle-like structure t h a t constitutes the continuous core of the S = — 1 disclination. W h e n the fibers approximate a triangular array, a counterrotating node, corresponding to an S = -V2 disclination with a discontinuous core, is usually found in the intervening matrix [35b].

Fig. 31. (a) Scanning electron micrograph of wedge disclination of strength S = +1 with core structure resembling a cup; (b) scanning electron micrograph of wedge disclination of strength S = — 1 with core structure resembling a saddle.

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PLANE OF FREE

Fig. 32. Lamelliform model of an S = +1 wedge disclination. The grid on one surface defined by the layer orientations shows the cup-shaped structure of the continuous core. The core becomes discontinuous at the intersection with the free surface.

V. T W I S T D I S C L I N A T I O N S Optical evidence of twist disclinations in the carbonaceous mesophase comes from studies of the lamellar microconstituent of the mesophase [39]. This type of disclination appears to be c o m m o n , b u t the twist character is readily distinguishable only o n favorable sections through the lamellar m o r phology. A bubble wall in a specimen of mesophase coke is shown o n two per-

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(a)

(b) Fig. 33. Negative wedge disclinations in the mesophase matrix of a carbon-fiber-reinforced composite: (a) transverse, (b) longitudinal. Crossed polarizers, oil immersion.

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Fig. 34. Lamelliform model of an S = - 1 wedge disclination formed in the matrix of a fiber bundle in a carbon-fiber-reinforced composite. The grid on one surface defined by the layer orientations shows the saddle-like structure of the continuous core.

pendicular sections in Fig. 35. T h e fine lamellar microstructures visible on both sections demonstrate a platelike preferred orientation within the bubble wall, with the mesophase layers tending to lie n o r m a l to the planes of section. T h e higher magnification micrographs of Fig. 36 show that, u n d e r crossed polarizers, the extinction b a n d s can be traced over the intersection a n d that some bands, e.g., the b a n d s m a r k e d D a n d F, change from a singlet extinction contour to a closely spaced doublet c o n t o u r when observed on the perpendicular section. This lamellar microstructure corresponds to the folded layer morphology of Fig. 37. F o r most planes of section n o r m a l to the layers, the fold appears as a narrow band, bright o n a dark background when the line of polarization is perpendicular to the preferred orientation of the layers a n d dark o n a light background when the line of polarization is parallel to the preferred orientation. U n d e r crossed polarizers, the fold

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Fig. 35. Perpendicular sections of a bubble wall formed in a mesophase coke. Reprinted from White and Zimmer [39] by courtesy of Pergamon Press.

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Fig. 36. Higher magnification view of perpendicular sections of Fig. 35. Crossed polarizers, oriented as shown for each section by arrows; oil immersion.

usually appears as a doublet, provided that the radius of curvature of the fold is sufficient for optical resolution. However, if the plane of section falls nearly parallel to the crease of the fold, the b a n d will disappear when the line of polarization is parallel to the preferred orientation a n d will n o t be resolvable to a doublet u n d e r crossed polarizers. Another region of Fig. 35, from the section A B C D , is illustrated at higher magnification for three polarization conditions in Fig. 38. T w o bands, marked D , disappear when the line of polarization is parallel to the preferred orientation of the mesophase layers a n d thus correspond to folds sectioned parallel to the creases of the folds. T h e points m a r k e d T, where the b a n d s end abruptly, correspond to disclinations with appreciable twist character (cf. Fig. 22a), because the disclination tangents t stand at a n angle relative to the rotation vectors ω, which lie in the plane of section. T h e polarized-light micrographs of Fig. 39 offer some further details of

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MODEL OF BUBBLE WALL WITH FOLD

CROSSED POLARIZERS

VERTICAL POLARIZER

HORIZONTAL POLARIZER

A

Fig. 37. Polarized-light reflection contrasts for a segment of lamellar microconstituent containing a single fold. Section Α-Α' lies parallel to the crease of the fold; section B-B' intersects the fold at an appreciable angle. Polarization conditions are indicated by arrows on each section. Reprinted from White and Zimmer [39] by courtesy of Pergamon Press.

the disclinated morphology of the lamellar microconstituent. T w o singlet extinction bands, m a r k e d a-a' a n d b - b ' , disappear w h e n viewed with the line of polarization parallel t o the background preferred orientation of the mesophase layers; thus, disclinations with some twist character underlie a, a', b , a n d b'. T h e extinction b a n d c o m m e n c i n g at c includes a segment that disappears w h e n observed with the line of polarization parallel t o the preferred orientation; segments o n either side of the disappearing segment can be resolved to doublets u n d e r crossed polarizers. This response is often observed a n d indicates that the rotation vector ω can vary in direction along a fold; i.e., the crease of the fold is curved in the plane of t h e fold. N o t e further that the fold a-a' is also gently curved o u t of the plane of the fold. These observations indicate that the double curvature characteristic of layers in the coarse undeformed mesophase is retained t o a degree in the lamellar microconstituent.

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Fig. 38. Polarized-light response, with oil immersion, of fine lamellar region indicated in Fig. 35. Disclinations with twist character underlie the points, marked T, where the disappearing bands D terminate. Polarizer conditions are indicated by arrows. Reprinted from White and Zimmer [39] by courtesy by Pergamon Press.

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Fig. 39. Polarized-light response of lamellar microconstituent. Disclinations with twist character lie at the ends of the disappearing bands a-a' and b-b'. Polarization conditions are indicated by arrows. Reprinted from White and Zimmer [39] by courtesy of Pergamon Press.

VI. D I S C L I N A T I O N ARRAYS A.

Additivity

Nehring a n d Saupe [16] have pointed out that, for a film of nematic liquid crystal with the rodlike molecules oriented parallel to the surface, the s u m of the strengths of the disclinations in a sample tends to be zero. T h e analogous situation for the carbonaceous mesophase is illustrated by Fig. 40. A fine fibrous microconstituent is sectioned transverse to the fibrous direction; thus, all disclinations are of wedge character. T e n disclinations are evident within the scanning electron micrograph; five disclinations are of strength S = +V2 a n d five are of strength S = —V2. N o t e that the zero sum for the total disclination strength is predicted from a rectangular Nabarro circuit a r o u n d the edges of the micrograph. Neighboring disclinations

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' f f >

Fig. 40. Scanning electron micrograph of an array of 10 wedge disclinations observed on a transverse section through a fine fibrous microconstituent. Five disclinations, marked by U in the structural sketch, are of strength S = +Vi, and five, marked by Y, are of strength 5 = -Vi. 1

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Fig. 41. Model of a disclination loop bounding a fold in the lamellar microconstituent of the carbonaceous mesophase. Adapted from White [57].

tend to be of opposite sign, a n d the total distortion energy of the disclination array should thus be relatively small. B. Disclination Loops T h e polarized-light extinction b a n d s indicative of folded regions in the lamellar microconstituent are usually terminated at b o t h ends (cf. Figs. 35 a n d 39), suggesting that the folded regions are finite in extent. Saupe [51] has pointed o u t t h a t disclination lines of strength S = ± li c a n n o t e n d within a liquid crystal a n d t h u s m u s t form closed loops or terminate at a free surface. T h e lamelliform model sketched in Fig. 41 (on the assumption that the rotation vector |ω| = π is fixed in direction over the full extent of the fold) Shows a folded region b o u n d e d by such a disclination loop. T h e character of the disclination line at any point depends o n the relative orientations of the rotation vector ω a n d the disclination tangent t. W h e n these vectors are parallel, or antiparallel, pure wedge disclinations b o u n d the fold; when the vectors are perpendicular, a pure twist disclination b o u n d s the fold. At other points o n the loop, the disclination structure m u s t be of mixed character, i.e., partially wedge a n d partially twist. x

C. M i x e d Disclinations T h e evidence for disclinations with twist character (Figs. 38 a n d 39) only implies that the relevant disclinations are n o t purely wedge in character,

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Fig. 42. Evidence of disclinations of mixed character in the lamellar morphology of carbonaceous mesophase. The right-hand micrographs are taken on a plane of section parallel to and 8 Mm below that for the left-hand micrographs. Polarized light, oriented as indicated by arrows.

because the single plane of section can only show that the disclination tangent is not parallel to the rotation vector. For a pure twist disclination, the disclination line would be perpendicular to the plane of section containing the crease of the fold a n d the rotation vector. Otherwise, the disclination at the end of a fold would be a mixed disclination [58]. M o r e precise definition of such disclinations can be obtained by making successive parallel sections, as illustrated in Fig. 42. Here the spacing between sections is 8 μηι. T h e extinction b a n d D D disappears when the line of polarization

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Mixed

Twist

.t Fig. 43. Model of a mixed disclination in the lamellar morphology of the carbonaceous mesophase.

is parallel to the b a n d ; thus the crease of the folded layers a n d the rotation vector lie in the plane of section. Since the fold lengthens by a b o u t 60 μηι in the second section, at least o n e of the disclinations at the points D m u s t have a tangent that is not n o r m a l to the plane of section; this disclination is a mixed disclination with b o t h wedge a n d twist character. A lamelliform model of such a mixed disclination is given in Fig. 4 3 . T h e mixed disclination can be envisaged as a tapered set of folds, with the degree of taper defining the extent of twist character.

VII. F O R M A T I O N A N D I N T E R A C T I O N O F D I S C L I N A T I O N S Most structural studies of the carbonaceous mesophase have actually been m a d e on specimens of mesophase glass, solidified from the liquid crystalline state by cooling to r o o m temperature. Although the conclusions have been confirmed, in large part, by a limited n u m b e r of hot-stage studies of m e sophase specimens between glass slides [57, 62, 63], direct observations of the d y n a m i c behavior of the mesophase seem to be inhibited by the reduced mobility of the mesophase in contact with the cover glass. A n i m p o r t a n t step in experimental technique was m a d e by H o o v e r et al. [64] by direct observations on the free surface of the pyrolyzing liquid; their films [12]

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TABLE I INTERACTIONS BETWEEN WEDGE DISCLINATIONS

s = +1

+ s = _i/

s = -1

+ s = +Vi

2

s = s = -Vi

s = + Vl +

s = -Vi

0

s = +1

+

s = -1

0

s = +Vi

+

s = +y

+

s = _i/

s = _i/

2

2

2

s = +Vi s = _i/

2

provide d y n a m i c evidence of such microstructural processes as mesophase coalescence a n d disclination annihilation. This technique has recently been extended by designing a quenching capability into the h o t stage [34, 65, 66] so that specimens representative of critical points in pyrolysis can be quenched to solidified specimens a n d studied o n polished sections t o relate the bulk microstructure t o the observations m a d e o n t h e free surface. Figure 44 illustrates a specimen of p e t r o l e u m pitch q u e n c h e d from a state of partial transformation to mesophase [35a], T h e fine cracking seen o n the free surface developed as the specimen cooled below the hardening t e m perature of a b o u t 2 5 0 ° C . O n the vertical section large bodies of coarsestructured mesophase underlie the similarly structured bodies observed o n the free surface. However, the mesophase o n the free surface differs in detail from that o n the vertical section: the extinction contours show greater contrast, all mesophase areas are responsive to polarized light, a n d the extinction crosses are sharply pinched in the same pattern as nodes. These points imply a n orienting influence to place the mesophase layers n o r m a l to the free surface. However, the structural sketch included in Fig. 44 indicates t h a t the orientating influence is weak a n d limited t o the i m m e d i a t e neighborhood of the surface. T h u s , analogous to the observations of Meyer [67] o n n e m a t i c liquid crystals, the S= ± 1 disclinations of the carbonaceous mesophase pinch d o w n to discontinuous cores as they intersect the free surface to meet the b o u n d a r y condition. T h e disclination interactions reported by Friedel [2] a n d illustrated by Saupe [57] for nematic liquid crystals are s u m m a r i z e d in Table I. Similar reactions have n o w been observed in the carbonaceous mesophase w h e n it is in a fluid state [34, 65, 66]. T h e micrographie sequence of Fig. 45 illustrates at least five disclination reactions observed within 2 m i n o n the free surface of a petroleum pitch pyrolyzed o n a h o t stage. In region A, two S = 1 disclinations of opposite sign appear t o be spontaneously generated; these then separate, the left disclination disappearing into a pool of u n -

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Fig. 45. Observations of disclination reactions by hot-stage microscopy (crossed polarizers): (A) generation of S = +1 and S = -1 disclinations; (B) annihilation of S = +1 and S = - 1 disclinations; (C) disclination reaction (S = +V2) + (S = - 1 ) —> (S = -V2). From Buechler et al. [66].

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Fig. 46. The formation of a multiply connected body by mesophase coalescence. Crossed polarizers.

transformed pitch, whereas the right disclination moves toward region B, where it undergoes an annihilation reaction with a n o t h e r S = 1 disclination of opposite sign. In region C the reaction is (S = + V i ) . + (S = - 1 ) —• (S = —Vi). T h e signs of the disclinations were identified by noting the direction of rotation of the extinction contours when the plane of polarization was rotated. T h e fact that the disclination reactions observed o n the free surface take place in b o t h possible directions seems to imply that the energies of disclination structures are small relative to the work of deformation by such mechanisms as bubble percolation. As pyrolysis is continued, the disclination reactions typified by Fig. 45 slow well before the deformation by bubble percolation is halted by the increasing viscosity. A simple probe has been used with the hot stage to impose deformation a n d to observe recovery m e c h a n i s m s [65]. W h e n the mesophase was quite fluid, recovery was rapid. As the viscosity increased by continued pyrolysis, the extent of recovery decreased, leaving increasingly fine deformed microstructures in the hardening mesophase. T h e fact t h a t deformation processes

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can be imposed o n the mesophase well beyond the point at which disclinations interact appreciably accounts for the high densities of disclinations observed in products fabricated from the carbonaceous mesophase. Coalescence to form multiply connected bodies, as evidenced by Fig. 46, offers a plausible m e c h a n i s m for the formation of disclinations. W h e n m u l tiple connections are formed between bodies with complex curved lamelliform morphology, there m a y exist some closed loops of material in which the direction of the preferred orientation of the molecules m a y be twisted in a pattern suggesting a M ô b i u s strip. For example, if the mesophase layer orientations about the coalesced loop resemble the pattern of Fig. 2 1 , then a twist disclination of strength Vi should appear within the loop w h e n the mesophase transformation is complete. It m a y be noted from Fig. 4 3 that twist disclinations can be distorted to mixed twist-wedge disclinations by appropriate shear strains; by large deformations such as those experienced in forming needle coke or in spinning mesophase fiber, the disclinations can be distorted to nearly pure wedge disclinations.

VIII.

SUMMARY

F r o m o u r outlook, the morphology of most carbons a n d graphites can be best understood by viewing these materials as mesophase fossils. In order of increasing structural subtlety, a n d therefore in order of increasing difficulty of observation, the basic microstructural features of these materials are as follows: 1. Deformed microconstituents, resulting from the concurrent processes of mesophase flow a n d aromatic polymerization. 2. Disclination structures, influenced in n a t u r e a n d n u m b e r by the deformation imposed as the mesophase hardens. 3. C a r b o n layers, with the a t o m s largely in the characteristic hexagonal array, that m a y display either single or double curvature. 4. Cross-linking of the layers, resulting from the fact t h a t the layer ordering in mesophase formation is still far from complete, so that layer disclinations, a n d edge a n d screw dislocations, m u s t be expected to form as the carbon layers are developed by continuing aromatic polymerization. This list emphasizes the residual structures from the liquid crystalline state a n d those chemical a n d physical properties of the mesophase that influence these structures. T h e evidence for wedge a n d twist disclinations as they exist in the deformed microconstituents of the carbonaceous meso-

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phase has been presented as an i m p o r t a n t step in understanding the m o r phology of graphitic materials. T h e motivation of most of the work o n the carbonaceous mesophase seems to vary from that of work conducted within the liquid crystal c o m m u n i t y . O u r work has been u n d e r t a k e n n o t only to u n d e r s t a n d the structures a n d behavior of an anisotropic liquid with a disklike unit of structure, b u t to understand how graphitic materials form in order to find paths to improved products, such as graphites with lower t h e r m a l expansion or fibers with higher elastic moduli. Disclinations are retained in these graphitic materials in contrast to the required absence of disclinations in liquid crystal displays. Accordingly, the fields of liquid crystal technology a n d graphitic materials have been developed with little cross-discussion. M a n y of the structural features of the carbonaceous mesophase were predictable, within reasonable approximation, from previous knowledge of conventional nematic liquid crystals. N o w that discotic liquid crystals have b e c o m e a topic of keen study, this situation m a y be expected t o improve. T w o research areas seem particularly pertinent for future work o n the carbonaceous mesophase. O n e topic concerns the dependency of the m e chanical properties of graphitic materials o n such characteristic mesophase structures as disclinations, splay, a n d layer cross-linking; work in this area should include the d e v e l o p m e n t of m e t h o d s to control these structures while the mesophase is in the plastic state. T h e second topic concerns the flow of the carbonaceous mesophase u n d e r various conditions of deformation a n d mesophase preparation, with the objective of understanding h o w to influence the morphologies produced in fiber spinning. In this area, basic studies of flow behavior in discotic liquid crystals could be of considerable practical value.

ACKNOWLEDGMENTS

The authors thank the Office of Naval Research, the Acurex Corporation, and The Aerospace Corporation for support. Special thanks are expressed to Dr. L. H. Peebles, Jr. for careful criticism of the manuscript.

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