Faraday Discuss. Chem. SOC., 1985, 79, 55-72 Molecular Correlation in Thermotropic Copolyesters BY ALAN H. WINDLE," CHRISTOPHER VINEY, RUTH GOLOMBOK, ATHENE M. DONALD? AND GEOFFREY R. MITCHELL$ Department of Metallurgy and Materials Science, University of Cambridge, Pembroke Street, Cambridge CB2 342 Received 14th December, 1984 Uniaxially oriented samples of thermotropic random copolyesters of hydroxybenzoic and hydroxynaphthoic acids, and of hydroxybenzoic acid and ethylene terephthalate, have been characterised in detail using wide-angle X-ray diffraction. The technique was used to measure the global chain orientation, and in the case of the first polymer the meridional scattering has been analysed in terms of diffraction from an isolated straight random chain. Optical microstructures were observed between crossed polars, with circularly polarized light and in plane-polarised light with no analyser present.Interpretation of the contrast seen shows that the material is optically biaxial and leads to the conclusion that, in the liquid-crystalline phase, there is long-range correlation of the rotations of the molecules about their chain axes. The polymers are examples of 'biaxial nematics'. Thermal analysis indicates that the solid phase has a higher level of conformational order than the melt and that the melting range is very broad. Annealing below the melting point leads to the development of localised regions of enhanced order, especially in specimens with a high degree of overall orientation. The combination of electron diffraction and electron microscopy provides evidence that the lateral growth of ordered entities does not necessarily require regular sequences within the otherwise random copolymer molecules.Small crystals based on identical but non-periodic sequences within the molecules are (NPL crystals) proposed as being consistent with the experimental evidence and the implications of a brief statistical analysis. Building polymer chains by connecting small mesogenic molecules leads to considerable increases in both the crystalline melting point (T,) and the liquid- crystalline to isotropic transition temperature. In fact, for any rigid homopolymer molecule, T, tends to be in the temperature range where chemical decomposition is beginning to be a problem, while the upper transition is often not seen at all.The development of random copolymers of such rigid units has enabled substantial reductions in T, to be achieved, with the stabilization of the liquid-crystalline phase in a temperature range where conventional processing is pra~ticable.'-~ The lack of periodicity along the rigid but random chains also greatly reduces the ability of the material to crystallise in any conventional sense, although there is evidence for the presence of some type of ordered entities which melt out over a wide temperature range up to T,. Investigation of a number of rigid-chain random copolyesters has raised the basic structural issues of the local organization in the liquid-crystalline phase itself and the nature of the additional order which appears on solidification. In general, the optical microstructures seen in thermotropic polymers are smaller in scale than those characteristic of small-molecule materials and are sometimes at the limit of resolution of light microscopy.They do, however, show many of the same and in conjunction with a hot stage may give useful indications of t Present address: Cavendish Laboratory, Madingley Road, Cambridge. $ Present address: J. J. Thomson Laboratory, Reading University, Whiteknights, Reading RG6 2AF. 5556 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS the appropriate Friedelian classification. The ready orientation of polymeric mesophases as a consequence of flow fields,6 while opening up a range of potential practical applications, also enables X-ray diffraction measurements to be carried out on well aligned samples.The information from diffraction patterns is not especially easy to interpret, although some progress has been made by analysis of the scattering from isolated random copolymer chains7** and through the calculation of cylindrical distribution functions.' Electron diffraction and microscopy of necessarily thin samples has proved very valuable, not only in understanding the origin of banded textures seen in the light microscope,'o*l' but also in observing the changes in lacal molecular order and orientation as a consequence of heat treatments. This paper gathers together the results of a number of different techniques used to assess the nature of the local order in three copolyesters based on rigid aromatic units.The experimental variety means that some features of the methods are not described fully, although in most cases reference is made to additional detail elsewhere. MATERIALS Three main-chain thermotropic copolyesters feature in this work. The first is a random copolymer of hydroxybenzoic and hydroxynaphthoic acids', in number fractions of 0.7 and 0.3, respectively; it is referrred to as B-N [structure (I)]. The molecule is comparatively rigid, although some conformational changes are possible, especially those involving 'crankshaft'-type rotations about bonds nearly parallel to the chain axis. The melting temperature of the 0.7/0.3 composition is 280 "C. There is no indication of any upper transition to an isotropic melt before the polymer decomposes.The scarcity of suitable solvents makes molecular weight determination difficult; however, current estimates of the degree of polymerization are between 150 and 250. The polymer was kindly supplied by Celanese Corporation and ICT (P and P). The second system examined is a random copolyester built from hydroxybenzoic acid and ethylene tere~hthalate'~ in number fractions of 0.6 and 0.4, respectively; it is referred to as B-ET [structure (II)]. The polymer was manufactured by Tennessee Eastman and was one of the first to be made widely available. Its main melting endotherm is at 190 "C, although as can be seen from fig. 1 there are two additional peaks at 250 and 340 "C before the significant peak associated with the mesophase to isotropic transition at 400°C. The implications of this endotherm have been discussed before in relation to the observed optical microstructures; however, it is significant to note here that the polymer does not flow freely until above the small 250 "C transition.The presence of the relatively flexible (CH,), units can be seen as responsible for the lower melting temperature (compared with B-N) and the fact that the isotropic phase is observed. Again the degree of polymerization is considered to be between 150 and 250. (11)WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 57 190 120 Fig. 1. Thermal analysis plot of an unoriented sample of B-ET. Heating rate 20 "C min-'. Peak temperatures in "C. A third random copolyester which features briefly in this work is designated- ClQT-QG [structure (III)].It melts at 300 "C and has a lower molecular weight than either B-N or B-ET, corresponding to a degree of polymerization of cu. 100. CI X-RAY CHARACTERIZATION OF THE COPOLYMERS The polymers B-N and B-ET were obtained in the form of extruded pellets. Preliminary X-ray diffraction patterns showed that there was marked alignment of the molecular-chain axes with the extrusion axis, that the orientation distribution was symmetrical about this axis and that the degree of molecular orientation was uniform across the section normal to the axis, there being no suggestion of a skin-core-type texture. Fig. 2 ( u ) shows the two-dimensional scattering patterns for the two poly- mers. The extrusion axis is vertical. The patterns were recorded in transmission using symmetrical geometry and are plotted as the s- weighted interference function si(s, a) [where s = 47r sin 8/A, a is the angle to the unique axis of the sample and i( s, a ) = I,,,,( s, a) - C f2( s), where I,,,, is the fully corrected intensity function and f2( s) is the independent coherent scattering]. Meridional and equatorial sections are shown in fig.2(6). By using a method based on spherical-harmonic analysis it has proved possible to utilize the azimuthal spread of the most intense meridional peak to measure the orientation distribution function for the two specimens. In effect, the arcing of the diffraction peak is recorded, expressed as harmonic coefficients and corrected for the spread of the peak due to the comparatively short-range correlations typical of these structures.The method is already documented, l4 so here the orientation of58 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS 0 1 2 3 4 5 6 s/A-' 0 1 2 3 4 5 6 S / k ' 0 1 2 3 4 5 6 s/A-' 0 1 2 3 4 5 6 s/A-' Fig. 2. Wide-angle X-ray scattering data from samples of B-N (top) and B-ET (bottom). The samples are oriented and have uniaxial symmetry about the vertical axis. The diffracted intensity is plotted as interference functions and represented by contours in ( a ) and equatorial (dashed line) and meridional (full line) sections in (b). Table 1. Amplitude coefficients for B-Nand B-ET ( P n ) B-N B-ET Po 1 1 P6 0.006 0.12 PS 0 0 PI0 0 0 p2 0.53 0.58 p4 0.17 0.37 the two specimens will be simply recorded as amplitude coefficients, (P,,), of the spherical-harmonic series.t These are shown in table 1.It must be emphasised that the measured orientations are global averages for the local chain axes with respect to the external reference (extrusion) axis. The local orientation of the chain axes t Th? even-order terms of the spherical-harmonic series are, for x = cos a: Po = 1, P2 = $(3x2 - l), p4=$(35x4-30x2 + 3), P6 = &j(231x6-315x4+ 1 0 5 ~ ~ - 5 ) , Pg = etc.WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 1 0 1 2 3 4 5 6 s/A-’ 59 Fig. 3. Comparison of the meridional section of the two-dimensional weighted interference function measured from a 70/30 unannealed fibre of B-N ( b ) with the calculated meridional scattering intensity for linear lattices having nearest-neighbour spacings of 6.3 and 8.3 A, sequenced at random for ( a ) and in blocks of 10 similar units for (c).60 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS with respect to their neighbours is likely to be very much more regular.Comparison of the orientation measured from the azimuthal distribution of the equatorial peak with that obtained from the intense meridional maximum at s = 3 8,-‘ indicates that the orientation within the correlation distance associated with interchain diffraction, the local orientation, is described by a (PJ of very close to unity for B-N,” although there is some suggestion that the local orientation is not quite as high in B-ET. Accurate knowledge of the global molecular orientation is important for the consider- ation of optical properties which follows. As received, the copolymers were nominally random.N.m.r. measurements on B-ET as polymerized underline the randomness of the chain.16 In the case of B-N the essential randomness of the molecule has been confirmed by analysis of the meridional X-ray scattering from the axially oriented sample [fig. ? ( a ) ] . Following B ~ n a r t , ’ ~ it is possible to apply the equation derived by Hosemann and Bagchi18 to calculate the scattering from a random copolymer chain with two components. The equation is where F( s) is the transform of the nearest-neighbour distribution function. Fig. 3 ( a ) shows the scattering intensity along the meridian calculated for a chain of points of nearest-neighbour distances 6.3 and 8.3 8, sequenced at random and in the relative proportions 0.7/0.3.The distances are those encountered in the polymer B-N (hydroxybenzoic 6.3 A, hydroxynaphthoic 8.3 A). The simplicity of the linear point model means that the relative magnitudes of the calculated peaks will be approximate. However, this first-order approach predicts the number and positions of the peaks, as can be seen by comparison with the experimental scan of fig. 3 ( b ) obtained from a fibre of 0.7/0.3 B-N. Further development of the model* to account for finite persistence lengths and the scattering represented by the transform of the chemical unit improves the agreement with experiment. Fig. 3 ( c ) is the scattering calculated for the same model except that the different units are segregated into unit blocks of 10. The scattering is profoundly different with many more peaks present.The observed meridional scattering can thus be considered as the fingerprint of a random copolymer. There is no evidence for blockiness in the B-N sample. In addition to confirming the polymer as being essentially random, the develop- ment of an understanding of the origins of the meridional scattering also provides a basis for the treatment of annealing effects considered below. OPTICAL MICROSTRUCTURE Initially sections were microtomed from the extruded samples of B-N and B-ET parallel to the extrusion axis, as in fig. 4. Great care was taken in order to avoid introducing cutting artefacts,” and any specimens showing knife or judder marks were discarded. Plate 1 (top) shows the microstructures observed between crossed polars for B-N and B-ET.As noted previously,20 the striking feature is that the optical textures do not reflect any of the preferred molecular orientation so evident in the diffraction pattern (fig. 2). The diffraction patterns in plate 1 (bottom) are obtained from the actual optical specimens, using a microbeam X-ray camera. They demonstrate that the preferred molecular orientation has not been changed or destroyed by the sectioning. As the crossed polars are rotated in relation to the sample, the contrast within individual domains? changes through the expected t The even-order terms of the spherical-harmonic series are, for x = cos a: Po = 1, P2 = 1/2(3x2 - l), P4=i(35x4-30x2+3), P6=&(231x6-315x4+ 104x2-5), P, = etc.WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 61 draw axis , Fig.4. Illustration of the relationship of the section plane to the extrusion (symmetry) axis of the sample. light-dark-light sequence every 90" and yet there is no change in the transmitted intensity integrated over the field of view. Plate 2 shows the microstructure for different polar rotations for the B-N sample and also the absence of contrast with no polars present. The B-ET sections appeared the same. The samples of each polymer were 3-5 pm thick, which is of the same order as the domain size. In order to check the influence of sample thickness, a series was prepared ranging from 2 to 15 pm. As the thickness increased, the general appearance of the domain structure did not change, although above I 0 pm the contrast became very weak. The micro- structure appears to be a reliable indication of the variation in local optical properties for the experimental conditions used, and thus can give a fairly direct measure of the orientation of the principal axes of various optical tensors as a function of position within the specimen plane.The fact that there is no preferred orientation of the axes describing the local optical anisotropy within the plane of the sample, despite the obvious preferred orientation of the molecular-chain axes, suggests that the polymer may be optically biaxial. If this is the case, the projection of the mean chain axis within a domain onto the specimen plane need no longer be parallel to either of the principal axes of the section of the optical indicatrix, which are the observed extinction directions.21 In order to confirm the biaxiality of the indicatrix, a series of sections was cut at different angles 4 to the extrusion axis ( 4 being measured from the normal to the section).Each of these sections was examined between (crossed) circular polarizers. Dark contrast seen in this mode indicates that the microscope axis is parallel (or nearly parallel) to one of the optic axes of the polymer (an optic axis is defined as being an axis perpendicular to a circular section of the indicatrix, along which the birefringence is zero; there are two in the biaxial case). Micrographs for different values of the section angle 4 are shown in plate 3 ( a ) for the polymer B-N. The proportion of dark areas, as estimated by reducing each image to 10 grey levels and defining the blackest of these as 'dark', is plotted as a function of 4 in plate 3( b ) .Consider a domain such as is apparent as a dark region in the micrograph and assume that one of the three principal axes (different from optic axes) of the indicatrix is parallel to the chain director for that domain. The probability of a particular domain being 'dark' is related to both the' distribution function describing the preferred orientation of the molecular chains about the specimen symmetry axis and the possible rotations of the optic axes about the chain director within a domain, all of which are equally probable. Then, as the global chain orientation (as measured62 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS by X-rays) is defined by an even-order spherical-harmonic series with coefficients (PL), the distribution of optic axes about the external reference axis is given by a new series of harmonic coefficients given by the product (PL)(P:), where ( P : ) is the magnitude of the harmonic function at the angle p between the chosen principal axis of the indicatrix and the two optic axes (2p is known as the optic axial angle).The probability, P, that an optic axis will be parallel to the normal to a given section will be given by the magnitude of the distribution function at that particular angle, 4. Hence P'C (2n+l)(P',)(P;)(Pn cos 4). n This function is normalized such that it would equal unity for all values of the section angle, 4, for the case where any orientation of the indicatrix would be equally likely.It is plotted against 4 for a number of possible values of the semi-optic axial angle, p, in plate 3 ( c ) for B-N, using the appropriate global chain orientation function as measured by X-rays and expressed as harmonic coefficients (table 1). /3 = 0 corresponds to the case of a uniaxial indicatrix with its unique axis parallel to the chain director of the region under consideration. Similar results are obtained for B-ET. Comparison of the form of the plots determined from the known orienta- tion distribution of chain axes with that representing the proportion of 'dark' areas seen in circularly polarized light [ (6) with ( c ) in plate 3 1, leads to two conclusions: ( a ) the two polymers are emphatically biaxial and ( 6 ) in both cases the optic axial angle is greater than 60".Knowledge of the optic axial angle is not sufficient to determine the shape of the indicatrix and thus the relative magnitudes of the principal refractive indices, but the fact that it is much closer to 90" than to 0" indicates that one of the two principal refractive indices normal to the chain director will be either considerably larger or smaller than both of the other principal indices, one of which is in the chain direction. Another indication of optical biaxiality is provided by the examination of thin samples of polymer ClQT-QG prepared directly from the melt. The microstructure of such samples shows domains clearly delineated by walls. Between crossed polars (without wave plates) the normal extinction contrast is evident, as in plate 4 (top).However, if the analyser is removed some contrast remains which is due to dichroism [plate 4 (bottom)], the transmitted light following a dark-light-dark cycle for every 180" rotation of the polarizer.22 While the dichroism may be useful in circumventing the 0"-90" degeneracy associated with extinction contrast, there is, in this case, another important feature. Fig. 5 shows a plot of the transmitted intensity, estimated from grey levels, as a function of polar orientation for the two systems (one with the analyser and one without). It is clearly apparent that the polar orientations for maximum or minimum transmitted intensity are not the same, the discrepancy being ca. 25". If both the indicatrix and the absorption tensor were uniaxial, then the contrast variations would be 'in phase'.The observation that they are not, coupled with the fact that the greater absorption for light polarized parallel to the chain axis is associated with conjugation along the chain which is unlikely to be significant in any other direction, is circumstantial evidence for a biaxial indicatrix. OPTICAL PROPERTIES OF THE MESOPHASE MELT The arguments in favour of optical biaxiality have been organized on the basis of optical and X-ray observations made at room temperature. It is also important to determine whether the polymers examined retain this property in the mesophaseWINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL n Y .M c 0 30 60 90 rotation/' 63 -90 5 -60 -30 0 30 60 90 rotation/' Fig. 5. Measurements of transmitted intensity made at the point x on plate 4, for different rotation angles (4 is the clockwise angle between the vertical and the polarizer direction): ( a ) crossed polars and ( b ) polarizer only.melt. However, a difficulty in repeating the experiments already described above the melting point is that the global orientation of the molecular chains tends to be lost and an unoriented diffraction pattern is seen. There are, however, several observations at elevated temperatures which appear significant. The first is that the microstructure seen in sections of the oriented pellets does not change in scale or form when the specimen is taken through the melting point, save for the onset of mobility, the domains of light and dark contrast constantly changing position. It does appear that in the B-N sample the loss of diffraction orientation takes ca.1 min at 3 10 "C whereas the microstructural mobility occurs with a characteristic time of ca. 1 s, so if there was a loss of biaxiality associated with mobility, then transient evidence of the preferred orientation in the optical microstructure would be expected. There was no evidence of any such effect, the nature and scale of the microstructure not changing on melting. In the case of the polymer B-ET, the temperature range between the main melting endotherm at 190 "C64 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS and the small transition at 250 "C is especially interesting. For the microstructural mobility begins at 190 "C whereas the global molecular orientation does not begin to decay significantly with time until the temperature is in excess of 250°C.The microstructure within this temperature band remains characteristic of optical biaxiality in that it does not reflect the prefixred molecular orientation, and yet it is mobile. It is possible that the optical mobility is due to the variations of the orientation of the indicatrix by rotation about the local chain axes. The small 250 "C transition increases in strength with increasing hydroxybenzoic acid content of the copolymer and is possibly associated with very small crystallites of the homopolymer of that component only. There is also another aspect of the behaviour of B-ET which has been previously documented.' The microstructure of a sample held between glass slides in the melt undergoes a pronounced change at 350 "C, ca.50 "C below the transition to the isotropic phase. It is possible that the new texture, which is characteristic of nematic small-molecule liquid crystals, represents the loss of biaxiality, although the extent to which ordering is dictated by the glass-slide surfaces is not clear. A further approach to the question of retained biaxiality in the melt can be made by monitoring the microstructural changes in a series of specimens cut at different angles to the pellet axis, as a function of temperature, when observed in circularly polarized light. When specimens of B-N are heated above 280 "C, the microstructure has mobility on a timescale of ca. 1 s, as described above. There is also a more gradual decrease in the proportion of dark regions in specimens cut at large angles, 4, to the pellet axis, and an increase in the proportion of such areas in specimens cut at small angles to the pellet axis, to a common value on a timescale of a few minutes; this can again be related to the loss of preferred molecular orientation in the molten phase.In B-ET changes in the proportions of light and dark regions only become apparent above 250 "C. STRUCTURAL IMPLICATIONS OF BIAXIAL OPTICAL PROPERTIES A single copolyester molecule does not have axial symmetry; in fact if it were possible for the aromatic groups to be coplanar with the esters then it would be clearly 'lath' like. Conformational-energy calculation^^^ suggest that steric hindrance between the doubly bonded oxygen of the ester group and a hydrogen atom of the opposing aromatic ring will twist the aromatic ring 30" away from the plane of the ester.However, it is possible that sequences of ester groups along one molecule remain within the same plane. The fact that the polymers are optically biaxial, a bulk rather than a molecular property, implies that the molecules must be rotationally correlated about their chain axes over distances that are substantial compared with their diameters. Hence the non-axial symmetry of the individual molecules must be transmitted to the material over distances of a micrometre or more. A possible structural arrangement is represented in fig. 6 . The structural classification of a liquid crystal with this additional level of long-range orientational order is commonly referred to as biaxial nematic in deference to its optical characteristic.Biaxial nematics have been pro- posed on theoretical grounds a number of time^,^^-^^ although they are not normally seen in small molecule liquid crystals, as the uniaxial-biaxial transition temperature (on cooling) is likely to be below the crystallization temperature. In polymers,Plate 1. Micrographs of 3-5 pm sections of the two polymers [ ( a ) B-N and (6) B-ET) viewed between crossed polars. The X-ray microbeam diffraction patterns were obtained from the same thin sections and show the same preferred orientation apparent in the dihction patterns of the unseaioned sample (fig. 2).Plate 2. Microstructure of the section of the B-N sample for different rotations of the crossed polars.There is no indication of the preferred orientation shown by the diffraction patterns and for the experimental conditions used there is no contrast visible with the polars absent.Plate 3. ( a ) Micrographs of sections cut at different angles, 4, to the symmetry axis of the B-N sample prepared using circularly polarized light. For the section angle +=O, the microscope axis is parallel to the extrusion axis of the sample. (6) Relative proportions of dark areas estimated by comparison with grey levels. (c) Calculations of the relative propor- tions of dark areas as a function of section angle for different values of the semi optic axial angle, B : (1) 0, (2) 30, (3) 60 and (4) 90".Plate 4. Micrographs of the polymer ClQT-QG showing contrast associated with birefrin- gence seen with crossed polars (top), and dichroism apparent when the polariser alone is present (bottom).The angles are measured clockwise from the vertical, to the polariser direction. The point x defines the position at which the data plotted in fig. 5 are measured.Plate 5. Transmission electron ditfraction patterns of very thin samples of B-N: (a) oriented by shearing at 300 "C onto rocksalt and (6) after shearing and annealing at 200 "C for 20 min.Plate 6. Dark-field electron micrograph of a very thin sample after annealing for 20 min at 200 "C imaged in the equatorial reflection. The small entities of bright contrast are extended normal to the shear axis, which is vertical. They are not apparent in unannealed samples.WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 65 Fig.6. Schematic diagram illustrating the rotational correlation about the chain axes in a nematic which is indicated by the biaxial optical properties. Although the molecules are drawn as laths, it is not implied that the additional correlation is a result of their anisotropic cross-sections rather than asymmetry in the attractive bonds between the molecules. however, where the melting temperature has been drastically reduced by copoly- mefization, it appears that the biaxial nematic phase can be readily accessed. THE MELTING TRANSITION The melting endotherm of these random copolymers, as observed by differential scanning calorimetry, is difficult to reproduce accurately from run to run. Its size and shape are especially sensitive to the thermal history of the sample, and the determination of a reliable base line for the estimation of the heat of melting is a particular problem.Fig. 7 shows a series of thermal traces for the polymer B-N. Runs on as-received samples produce traces such as that of fig. 7 ( a ) . The main melting peak at 290°C appears to be superimposed on a much broader endotherm ranging from ca. 150 "C to above the sharp peak. Reruns on samples previously quenched from 340"C, a temperature below that at which any decomposition is evident but clearly in the melt, give traces which are essentially the same as those for the as-received material except that in the region above the main peak the exothermic trend is much less marked [fig. 7(b)]. It is possible that this difference is associated with the contribution during the first heating run from reactions which are completing the polymerization process.Faster cooling rates from the liquid- crystalline melt (up to lOOO"Cmin-') did not have any significant influence on subsequent thermal traces. It is important to be convinced that the perceived endotherm does indeed represent a melting process and is not instead a glass-transition temperature associ- ated with an inhomogeneous material, as has been suggested for B-ET.28 Several aspects of the data appear to confirm that the transition is associated with some form of crystalline melting. First, if the actual endothermic peak is to be interpreted as the 'overshoot' peak sometimes associated with the glass transition, then it should substantially increase in size for faster heating rates.Secondly, if a sample is given a solid-state anneal, quenched and then thermally analysed, the anneal temperature is marked by a small exotherm followed by an endotherm. This behaviour is apparent in fig. 7 ( c ) . It is characteristic of a modification of the distribution in crystallite66 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS T/ "C 100 2 00 3 00 L 00 I I I I 350 Fig. 7. Thermal-analysis traces for the polymer B-N with a heating rate of 20 "C min-': ( a ) As received, ( b ) after quenching from 340 "C, (c) after annealing at 220 "C and ( d ) after shearing onto a substrate at 3 10 "C, quenching and removing mechanically prior to analysis. Peak temperatures in "C.size and perfection associated with an improvement in order of those elements not quite molten at the anneal temperature. Annealing was seen to affect the thermal traces in this way down to 180 "C and demonstrates the large temperature range of the melting process. Fig. 7 ( d ) is a thermal trace of a B-N sample oriented by shear onto a glass substrate. The endotherm, obtained after removal of the sample from the substrate, is enhanced by the orientation, and the apparent melting temperature increased by 60°C. The enhanced peak does not recur when the sample is quenched from the melt and reanalysed, although the melt temperature (360 "C) is now approaching the range where degradation may be a factor. The explanation of such behaviour may parallel that accepted for similar effects seen in conventional crystalline poly- mers, namely that the higher melting temperature is due to the increased order in the oriented melt reducing the magnitude of the entropy increase on melting.The relaxation on final melting of particularly extended conformations, locked into the non-crystalline component of the polymer by the crystallites, will leave its imprint as a substantial endothermic contribution. Such an explanation, however, does not rule out the possibility that crystallites formed from an oriented melt may be larger or better ordered and thus have an intrinsically higher melting point. Annealing at 300 "C (10 "C above the melting point of the unoriented material) increased the melting peak by a further 30°C.WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 67 x Y .e m E - c .- 0 40 2 e / o 20 60 40 60 Fig.8. X-Ray diffractometer scans of an unoriented sample of B-N at: ( a ) 'O 2e/o 0 3 and ( - ) 300 "C. ORDER IN THE SOLID PHASE Whereas thermal analysis suggests some form of crystallinity in the solid phase, there is little evidence for sharp crystalline-type diff raqtion maxima in the wide-angle patterns, at least for the polymers examined. Given that the molecules are random copolymers this is not surprising: crystals of sufficient size to give sharp diffraction maxima would appear to be ruled Fig. 8 shows preliminary diffractometer traces of unoriented B-N both above and below the final melting temperature. On melting there is an increase in breadth of both the main interchain peak (at 20°, 28) and the most prominent meridional maximum at 42", 28.The half-width of the main peak can be used to give a lower limit to the lateral extent of the ordered68 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS regions in the solid phase. Such an estimate is 30 A, although as there is likely to be a contribution from type I1 (paracrystalline) disorder the actual dimension will almost certainly be larger. The evidence that optical biaxiality and thus rotational correlation about the chain axes persists into the melt raises the question as to the nature of the solid-state order which melts out at T,. If, in accord with normal polymeric behaviour, the melting endotherm is primarily associated with an increase in conformational di~order,~' then the improved molecular packing below the melting point may be seen as a corollary of the matching of conformations between neighbouring chains.Additional clues as to the nature of the ordered entities are provided by the structural changes introduced by annealing in the solid state. ANNEALING BELOW THE MELTING POINT In the current work the modification of diffraction patterns as a consequence of solid-state annealing has only been seen in the case of well oriented samples, although this may be because changes are more apparent in oriented diffraction patterns. There are two recognizable modifications to the diffraction patterns on annealing: the lateral spread of the meridional maxima is markedly reduced and the high-angle shoulder of the main equatorial component becomes more clearly divided into two components displaced above and below the equator by ca.0.5s. It is significant that for the polymers B-N and B-ET there is no change in the positions of the meridional components, indicating that the material remains a random copolymer. Some of the strongest annealing effects have been seen by electron diffraction in the transmission microscope. Plate 5 shows diffraction pat- terns of B-N before and after annealing at 200 "C. The first meridional maximum, that at s = 0.95 A-', has been changed from a diffuse lateral line into a compact peak on the meridian. On the other hand the meridional maximum at s = 3 A-' is comparatively unaffected. The implication of the lateral confinement of the first meridional peak on annealing is that there is considerable enhancement in the extent of lateral order in the solid state.The fact that the effect is confined to the first peak suggests that the development of longitudinal register between the neighbouring molecules is sufficiently precise to bring ester groups or aromatic rings into register, but not precise enough to maintain registry between corresponding atoms in the chains over any appreciable lateral distance. There is no evidence in B-N that the increase in order is associated with the packing of pre-existing homopolymeric sequences in the otherwise random chains or with regular sequences produced by transesterification during the anneal (i e. the development of blockiness). The increase in the intensity of the off -equatorial components of the high-angle shoulder of the main interchain peak at s = 1.55 A-' is not properly understood.However, it is significant that the vertical displacement (+ and -) of the components is not sufficient to place them on a 'layer line' corresponding to the first meridional maximum. Note also that a high-angle shoulder is a common feature of inter- molecular peaks in main-chain aromatic polymers3' and also occurs in benzene,32 where it is associated with face-to-face contacts of the ring groups, and that the components are at an azimuthal angle *75", similar to that between the normals to the planes of the aromatic groups and the axis of a polyester molecule in extended conformation. Equatorial dark-field images of B-N specimens annealed at 200°C have been obtained using the transmission electron microscope.These images show a fine distribution of regions with bright-diffraction contrast superimposed on the lower-WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 69 level contrast of the banded structure. Such regions can be seen in plate 6. They are thin in the direction of the molecular axes, d 200 A, and for this particular sample extend up to approximately ten times this distance in the lateral direction, although such pronounced anisotropy of shape is not always apparent. We interpret these entities as the ‘crystallites’ which have grown, as a consequence of the anneal, to dimensions sufficient to be seen in the transmission electron microscope, the resolution available being significantly limited by specimen beam damage, which precludes parallel observations on the more beam-sensitive B-ET.It was also observed that the development of ‘crystallites’ during annealing at 200°C was suppressed if the initial preferred molecular orientation in the sample was not very high. SOLID-STATE ORDER A MODEL The evidence of thermal analysis is that the transition from solid to liquid in these polymers is associated with some loss of order. The absence of sharp diffraction peaks and multiply sampled ‘layer lines’ in the oriented patterns means that the additional order characteristic of the solid state cannot be associated with three- dimensional crystals larger than ca. 50 A. Additionally, the random nature of the copolymers, as confirmed by analysis of the meridional scattering, precludes the formation of large three-dimensional crystals.Indeed one must presume that this is the mechanism by which random copolymerization decreases the melting point so effectively, as any small crystals which can form will have large surface energies in relation to their volume free energies of crystallization. However, solid-state annealing of the polymers appears to give rise to a distinct increase in lateral order, as indicated by the concentration of the first meridional maximum onto the peridian and the ability to image entities in dark-field electron microscopy, without any apparent development of blocky runs in the copolymer molecules. Such behaviour is also consistent with the appearance of the d.s.c. traces of annealed material [fig. These observations are reminiscent of those reported for atactic PVC gels,33 in which measurements of crystallite size were larger than expected for atactic molecules.However, in the case of B-N the absence of sampling on the first ‘layer line’ except on the meridian is an additional factor. In the light of this we suggest that the small crystallites which do develop are conformationally ordered and consist of laterally matched sequences of the random chain. They could be considered perfect and yet only one ‘unit cell’ thick in the direction of the chain axes or alternatively as a non-periodic sequence of layers of relatively large lateral extent compared with the intermolecular spacing. We refer to them as non-periodic layer (NPL) crystallites. Fig. 9 illustrates one. The conformation chosen [fig.9 ( b ) ] is the extended chain, partly because of the form of the interchain diffraction peak but also because this conformation is stabilized by extension and could thus account for the observation that orientation appears to enhance the rate of the annealing effects. Such a proposal immediately raises questions of a statistical nature. In particular, what is the probability that a particular sequence of length rn‘ might be found somewhere within a given search length rn along each of N adjacent molecules? If the probability is high then NPL crystals of substantial lateral extent can be expected to occur. The statistical exploration required is extensive and is still in progress; however, some results for the simple case of an A-B random copolymer with the components present in equal proportions are presented.7 ~ .70 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS I I I I I I I A B B A A B A A A A B A B 8 A A A A A A A A A A A A A A B S S B S P B A A A A A A A B B B B B B B g B B B 8 @ A B B B A B A B B A A B B A - B B B A B A B B B B B B B B - A A A A A A A B B A B A A A A B A A B A A B A B B A B B Fig. 9. Sketch indicating (a) the matching of random sequences in a non-periodic layer crystallite and (b) part of such a crystallite with the chains in the extended conformation. 1 P 0 1 5 m' 10 15 Fig. 10. Plots of the probability (P) of (a) a particular, but not necessarily regular, sequence of length rn' units being present in a chain 100 units long and (b) any sequence of length rn' being present in two 100 unit chains.The probability of one or more pre-defined sequences occurring in such a chain (neglecting end effects) is given by P = I -exp[-(1/2)"'(m-m'+1)]. As can be seen from fig. 10( a ) , drawn for a search length of 100 units, the probability rapidly decreases for lengths > 5 . Thus for an NPL crystallite of thickness 7 units,WINDLE, VINEY, GOLOMBOK, DONALD AND MITCHELL 71 which would be ca. 50 A for B-N, 50% of the chains would contain the required sequence and be able to contribute to lateral growth which would otherwise be restricted only by encounters with other crystallites. Such a proposition requires not only a measure of lateral sorting in addition to the relative longitudinal motion implied by the ‘search length’ but also opens up the possibility, through longer-range sorting and fractionation, of the formation of NPL crystals of greater thicknesses and volume fractions.This may be the mechanism occurring during solid-state annealing. The probabilities refer to any one particular sequence of length rn’ and thus must apply equally to regular blocks such as AAAAAAA or ABABABAB which occur by chance in the random chains. NPL crystals have been proposed for two reasons. First, the diffraction evidence from the annealed samples indicates the presence of random sequences with fairly extensive lateral correlation, for if the lateral correlation was the prerogative of regular sequences then the annealing would be expected to change the position and number of meridional sequences and also produce off-axial (hkl) peaks in the oriented pattern.Secondly, at the nucleation stage of a crystal, where a number of neighbouring chains are moving relative to each other in order to find a match over sufficient length, the statistical condition is more relaxed as any sequence in common will suffice. The probability of two chains (search length 100 units) having any sequence of length rn’ in common is given by the above equation but with the exponent multiplied by the factor (rn - m’+ 1). The probability in the case of a nucleus with two chains is plotted in fig. lO(6). There is a 50% probability of the chains having at least one sequence of 13 units in common or virtual certainty for any sequence of 7 units, as long as there is no restriction on the make up of the sequence.However, the possible presence of chemical blockiness in the molecules, as perhaps in B-ET, may well make the nucleation of crystallites based on regular sequences much more likely. This brief excursion into the statistical properties of random chains has shown that small crystallites, as suggested by the diffraction evidence, the transmission electron micrographs and the thermal-analysis data, can form without the necessity of blocks of regularly sequenced units either being introduced into the molecules at polymerization or created by subsequent processes such as transesterification. There is, however, no implication that regular blocks may not sometimes be present in polymers of this type. We thank Prof. Manfred Gordon for helpful advice in the formulation of the statistical approach.We also thank the S.E.R.C. for the provision of funding through a grant, a fellowship and a studentship, and Prof. R. W. K. Honeycombe and Prof. D. Hull for the provision of laboratory facilities. ’ J. Preston, in Liquid Crystalline Order in Polymers, ed. A. Blumstein (Academic Press, New York, * W. J. Jackson, Br. Polym. J., 1980, 12, 154. 1978), p. 141. J-I. Jin, S. Antoun, C. Ober and R. W. Lenz, Br. Polym. J., 1980, 12, 132. M. R. Mackley, F. Pinaud and G. Siekmann, Polymer, 1981, 22, 437. C. Viney and A. H. Windle, J. Muter. Sci., 1982, 17, 2661. ‘ J. R. Schaefgen, T. I. Bair, J. W. Ballou, S. L. Kwolek, P. W. Morgan, M. Planar and J. Zimmermann, in Ultra High Modulus Polymers, ed. A. Ciferri and I. M. Ward (Applied Science, London, 1979), p. 173. G. A. Gutierrez, R. A. Chivers, J. Blackwell, J. B. Stamatoff and H. Yoon, Polymer, 1983,24,937. G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1985, 263, 230. G. R. Mitchell and A. H. Windle, Polymer, 1982, 23, 1269. lo A. M. Donald, C. Viney and A. H. Windle, Polymer, 1983, 24, 155.72 MOLECULAR CORRELATION IN THERMOTROPIC COPOLYESTERS ‘ I A. M. Donald and A. H. Windle, J. Muter. Sci., 1983, 18, 1143. l2 G. W. Calundann, US. Patent 4161470, 1979. l 3 W. J. Jackson and H. F. Kuhfuss, J. Polym. Sci., Polym. Chem. Ed., 1976, 14, 2043. l4 G. R. Mitchell and A. H. Windle, Polymer, 1983, 24, 1513. l5 G. R. Mitchell, unpublished work. l6 F. E. McFarlane, V. A. Nicely and T. G. Davis, Contemp. Top. Polym. Sci., 1977, 2, 109. l7 R. Bonart, Bog. Colloid Polym. Sci., 1975, 58, 36. l8 R. Hosemann and S. N. Bagchi, Direct Analysis of Diflruction by Matter (North Holland, l9 C. Viney, Lab. Pracr., 1983,32, 87. 2o C. Viney, G. R. Mitchell and A. H. Windle, Polym. Commun., 1983,24, 145. 21 P. Gay, Introduction to Crystal Optics (Longman, London, 1984). 22 A. M. Donald, C. Viney and A. H. Windle, Philos. Mag., 1985, 852, 925. 23 J. P. Hummel and P. J. Flory, Macromolecules, 1980, 13, 479. 24 M. J. Freiser, Phys. Rev. Lett., 19?0, 24, 1041. 25 C. S. Shih and R. Alben, J. Chem. Phys., 1972, 57, 3055. 26 J. P. Straley, Phys. Riu. A , 1974, 10, 1881. 27 G. R. Luckhurst and S. Romano, Mol. Phys., 1980,40, 129. ** W. Meesiri, J. Menczel, U. Gaur and B. Wunderlich, J. Polym. Sci., Polym. Phys. Ed., 1982,20,719. 29 D. J. Blundell, Polymer, 1982, 23, 359. 30 B. Wunderlich and J. Grebowicz, in Advances in Polymer Science (Springer-Verlag, Berlin, 1984), 31 T. P. H. Jones, G. R, Mitchell and A. H. Windle, Colloid Polym. Sci., 1983, 261, 110. 32 A. H. Narten, J. Chem. Phys., 1977, 67, 2102. 33 S. J. Guerrero, A. Keller, P. L. Soni and P. H. Geil, J. PoZym. Sci., Polym. Phys. Ed., 1980,18,1533. Amsterdam, 1962). p. 1.