3152 zyxwvutsrqponm Macromolecules 1988,21, zyxwvut 3152-3158 zyxwv (21) Chivers, R. A.; Blackwell, J. Polymer 1985, 26, 997. (22) Bonart, R. C.; BlackweIl, J.; Biswas, A. Makromol. Chem., Rapid Commun. 1985, 6, 353. (23) Geiss, R. H.; Street, G. B.; Volksen, W.; Economy, J. ZBM J. Res. Deu. 1983, 27(4), 321. (24) Tadokoro, H. Structure zyxwvutsrqp of Crystalline Polymers; Wiley: New York, 1979; Chapter 7. aday Discuss. Chem. SOC. 1985, No. 79, 73. 16, 1418. (25) Northolt, M. zyxwv S. Eur. Polym. J. 1974, 10, 799. (26) Blackwell, J.; Biswas, A.; Gutierrez,G. A.; Chivers, R. A. Far- (27) Blackwell, J.; Lieser, G.; Gutienez, G. A. Macromolecules 1983, Three-Dimensional Structure of Main-Chain Liquid-Crystalline Copolymers. 2. Interchain Interference Effects Amit Biswas and John Blackwell* Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106-2699. Received December 7, 1987 ABSTRACT: Previous analyses of the X-ray fiber diagrams of wholly aromatic copolyesters have shown that these systems consist of oriented arrays of chains with completely random comonomer sequence. Nevertheless, these copolymers exhibit sharp equatorial and off-equatorial Bragg maxima that are indicative of three- dimensional crystallinity. This paper shows that these diffraction characteristics are predicted when limited register occurs between adjacent chains. zyxwvu This is achieved when one monomer on each chain of the array comes into register in a plane perpendicular to the fiber (chain) axis. As such, this requires a small shift for each chain (-4 zyxwvutsrqp k, at the most) from the arrangement in a nematic structure. Analyses are developed to predict the interference effects for three-dimensionalarrays of copolymer chains, with or without chain register. The results show that in as-spun fibers even the limited register described above exceeds that necessary to generate the observed diffraction effects. Rather, there is a normal distribution of chain origins about the registry plane, with a standard deviation of -2 A, which corresponds to only a small preference for registration. Introduction The X-ray data for thermotropic wholly aromatic co- polyesters are very intriguing because these polymers ex- hibit substantial three-dimensional crystallinity despite the fact that they have a random comonomer sequence. The latter fact has been established by X-ray analyses in this and other laboratories over the last few years.14 The X-ray fiber diagrams contain a series of aperiodic merid- ional maxima, and it has been shown that these are re- produced in position and approximate intensity in theo- retical calculations for nematic arrays of extended chains of completely random ~equence.~.~ When nonrandom se- quence distributions are considered by variation of near- est-neighbor statistics, the agreement between the observed and calculated meridional data becomes unacceptable for all but minimal blo~kiness.~J The evidence for three-dimensional order comes from the presence of sharp equatorial and off-equatorial Bragg reflections in the fiber diagrams. Three-dimensional register is required by the presence of a sharp off-equa- torial at d zyxwvutsrqp z 3.3 A, which occurs at a layer line spacing of 12-15 A, depending on the chemical composition. Thermal annealing of these copolymers can result in a sharpening of these reflections corresponding to an increase in crys- tallite size? and there can be the generation of additional maxima, some of which may be due to development of an additional polymorphic structure.1° Application of the Scherrer equation to the equatorial maxima yields crys- tallite widths of 70-190 A,11 depending on the thermal history, which indicates large ordered regions consisting of -2200-1500 chains. In addition, degrees of crystallinity as high as 80% have been reported,12 based on division of the diffraction data into “crystalline” and “amorphous” components. Typical values for quenched specimens are in the range 30-50%, which increases on annealing.13 It should be noted that annealing does not lead to changes in the positions of the meridional maxima; i.e., there is no evidence for any departure from a random sequence dis- tribution.1° 0024-9297/88/2221-3152$01.50/0 Our previous analyses of the structure addressed a one-dimensional problem, since the diffraction along the meridian is derived from the projection of the “average” chain onto the fiber axis. In view of the approximate linearity of the chain, this projection is approximately independent of conformation. However, when we attempt to derive a three-dimensional structure from the entire diffraction pattern, it is necessary to consider the actual chain conformation. Our first step in analyzing the structure was to calculate the cylindrically averaged transform for individual chains of average sequence. The original approach described by Chivers and B1ackwelll4 for the copolyester of p-hydroxybenzoic acid (HBA) and 2- hydroxy-8naphthoic acid (HNA) has been generalized for other chemical structures and applied to different con- formation~.~~ The main conclusion is that the chains have a pseudo “dimer repeat”, with the successive ester groups pointed to opposite sides of the chain, analogous to the dimer repeats observed for homopoly(HBA)16 and poly- (p-~henyleneterephthalamide).~~ This pseudo dimer re- peat is necessary, since correlations between successive monomers in the dimer are responsible for the generation of the layer line on which the off-equatorial maximum lies. The present paper considers the interference effects that occur when these chains are packed with their origins on a two-dimensional network. If the origin atoms are co- planar but there is no radial correlation for the chain position, i.e., there is cylindrical averaging of the chains independent of the two-dimensional lattice, then the effect of interference is to sample the cylindrically averaged transform for the chain at the lattice points. The fact that layer line reflections are observed in the fiber diagrams means that we must have some sort of chain register. Such register is likely to involve stacking of aromatic groups or dipole-dipole interaction of the carboxyl groups, and hence there will be a spatial correlation between certain mono- mers on adjacent chains. The first possibility for chain register that comes to mind is the lateral alignment of homopolymer sequences, some 0 1988 American Chemical Society