Abstract
It is shown that textures with double-axis averaging similar to the a-texture, or Keller–
Machin Type I texture, are not specific to semicrystalline polymers exhibiting twisted lamellar growth. In this work, such texture is observed in extruded fibres of a typical discotic molecule, trans-diC60-Zn porphyrin. Experimentally, these textures can be detected from the characteristic
‘comma’-like azimuthal profiles of the non-equatorial diffraction peaks in twodimensional X-ray patterns. Analytical expressions for the azimuthal intensity distribution are developed, which are in good agreement with the experiment. In the proposed generalized coordinates, the diffraction peak shape becomes universal. This provides a simple means of checking the closeness of the sample morphology to the a-texture from just one twodimensional
pattern, without constructing the whole X-ray pole figure.
Keywords: X-ray refection broadening; Fibre texture; Liquid crystals; Double-axis averaging.
References
[1] Agarwal S.L. Changes in Orientation of Crystallites during Stretching and Relaxation of Polyethylene
Films / S.L. Agarwal, G.P. Tilley, O.J. Sweeting // Appl. Polym. – 1959. – Vol. IT – 1. – P. 91–100.
[2] Ashizawa H. An investigation of optical clarity and crystalline orientation in polyethylene tubular film /
H. Ashizawa, J.E. Spruiell // Polym. Eng. Sci. – 1984. – Vol. IT – 24. – P. 1035–1042.
[3] Chen H.Y. Orientation and property correlations for LLDPE blown films / H.Y. Chen, M.T. Bishop,
B.G. Landes // J. Appl. Polym. Sci. – 2006. – Vol. IT – 101. – P. 898–907.
[4] Dlugosz J. Morphological verification of «Row nucleation» in isotactic polystyrene; evidence for single
crystals within the bulk / J. Dlugosz, D.T. Grubb, A. Keller, M.B. Rhodes // J. Mater. Sci. –1972. – Vol IT –
7. – P. 142–147.
[5] Gearba R.I. The VNR Concise Encyclopaedia of Mathematics. Third edition / R.I. Gearba,
D.V. Anokhin, A.I. Bondar, M. Lehmann, Ivanov, W. Gellert, H. Kuestner, M. Hellwich. – New York: Van
Nostrand Reinhold Company. – 1975.
[6] Guichon O. Influence of the molecular architecture of low-density polyethylene on the texture and
mechanical properties of blown films / O. Guichon, R. Seguela, L. David, G. Vigier // J. Polym. Sci. Polym.
Phys. – 2003. –Vol. IT – 41. – P. 327–340.
[7] Holmes D.R. Crossed amorphous and crystalline chain orientation in polythene film / D.R. Holmes,
R.G. Miller, R.P. Palmer, C.W. Bunn // Nature (London). – 1953. – Vol. IT – 171. – P. 1104–1106.
[8] Keith H.D. Banding in Polyethylene and Other Spherulites / H.D. Keith, F.J. Padden // Macromolecules.
– 1996. – Vol. IT – 29. – P. 7776–7786.
[9] Keller A. The morphology of crystalline polymers // Nature (London). –1954. – Vol. IT – 174. –
P. 926–927.
[10] Keller A. Oriented crystallization in polymers / A. Keller, M.J. Machin // J. Macromol Sci. B. –
1967. – Vol. IT – 1. – P. 41–91.
[11] Lotz B. Enthalpic and entropic origins of nucleation barriers during polymer crystallization: the Hoffman–
Lauritzen theory and beyond / B. Lotz, S.Z.D. Cheng // Polymer. – 2005. – Vol. IT – 46. – P. 577–610.
[12] Luchnikov V.A. Microbeam X-ray diffraction from twisted lamellar crystals: theory and computer
simulation / V.A. Luchnikov, D.A. Ivanov // J. Appl. Cryst. – 2009. – Vol. IT – 42. – P. 673–680.
[13] Luchnikov V.A. Theory of geometrical broadening of diffraction peaks from twisted lamellar crystals
for interpretation of X-ray microbeam and selected-area electron diffraction experiments / V.A. Luchnikov,
D.A. Ivanov // J. Appl. Cryst. – 2010. – Vol. IT – 43. – P. 578–586.
[14] Polanyi M. Zur Frage der Plastizität. Verformung bei tiefen Temperaturen // Z. Phys. –1929. –
Vol. IT – 7. – P. 149–180.
[15] White J.L. Orientation Processes. In Encyclopedia of Polymer Science and Engineering, edited by H /
J.L. White, M. Cakmak. – New York: Wiley-Interscience, 1987. – Vol. 10.
[16] N.M. Mark Encyclopedia of. Polymer Science and Engineering, 2nd / N.M. Mark, C. Bikales,
Overberger & G. Menges. – New York: Wiley-Interscience, 1987. – Vol. 10. – P. 596–636.
[17] Zhang X.M. Effect of Crystalline Structure on Tear Resistance of LDPE and LLDPE-Blown Films /
X.M. Zhang, S. Elkoun, A. Ajji & M. A. Huneault // Polymer. –2004. – Vol. IT – 45. – P. 217–229.