Thermal expansion and Grüneisen functions of polymer crystal models: 1. Central forces

Abstract

. Can. J. Chem. 66,718 (1988).With typical pair potentials, a bond is stretched by vibrations along the bond directions, while contraction is caused by the tension set up by vibrations normal to the bond direction. The r6le of these two effects is studied in calculations for parallel linear-chain and zigzag-chain models. For linear chains and rigid zigzag chains, expansion is positive in the plane normal to the chain direction, although it may be strongly anisotropic in this plane. Expansion along the chain direction is negative, and typically an order of magnitude less than that normal to the chain. For a flexible zigzag chain with bond angle 90°, expansion is positive in all directions; the Griineisen tensor is approximately isotropic, but elastic anisotropy leads to smaller expansion coefficients in the molecular planes. The Reuss-averaged Griineisen function derived from (6-12) pair potentials is about 3.5 for most of the models; this is higher than observed experimentally in polycrystalline polyethylene, indicating the need for more realistic models of organic polymers.RUTH MARGARET BARRON, THOMAS HUGH KENNETH BARRON, PAUL MALCOLM MUMMERY et MICHAEL SHARKEY. Can. J. Chem. 66,718 (1988).Avec des paires typiques de potentiel, une liaison est allongte par des vibrations le long des directions de la liaison, alors qu'une contraction rCsulte d'une tension causte par des vibrations normales a la direction de la liaison. On Ctudie le r61e de ces deux effets dans des calculs sur des modtles de chaines paralltles, 1inCaires ou en zigzag. Pour les chaines linkaires ou en zigzag rigides, l'expansion est positive dans 1e plan normal i la direction de la chaine, mime si cette expansion peut Ctre fortement anisotrope dans ce plan. L'expansion le long de la direction de la chaine est negative et, d'une f a~o n gCnCrale, elle est d'un ordre de grandeur plus faible que celle qui est normale ? i la chaine. Pour une chaine en zigzag flexible avec un angle de liaison de 90°, l'expansion est positive dans toutes les directions; le tenseur de Griineisen est approximativement isotrope, mais l'anisotropie Clastique conduit i des coefficients d'expansion qui sont plus faibles dans les plans molCculaires. La fonction de Griineisen moyenne selon Reuss, obtenue B partir de paires (6-12) de potentiels, est peu pres Cgale i 3,5 pour la plupart des modtles; cette valeur est plus ClevCe que celle observCe exptrimentalement dans le polyCthylene polycristallin et elle indique qu'il est nCcessaire d'avoir des modtles plus rCalistes pour les polymeres organiques.[Traduit par la revue]

Highly anisotropic thermal expansion in molecular films of dicarboxylic fatty acids

“…This situation resembles closely, albeit in 2D, the generic structure of 3D crystals of linear (or zigzag) polymers, where the (purely covalent) bonding along the polymer is orders of magnitude stronger than the chain-normal (purely vdW) interaction 2,4,31,32 . The thermal expansion along these directions are related by the Gruneisen theory 4,32 to the various vibrational modes excited in this structure. For a generic polymer, vibrations polarized along the stiffer chain are excited much less than the low frequency modes polarized in the softer, chainnormal direction.…”

“…The tension effect 4 , caused by the chain-normal vibrations, imparts in many polymers a negative thermal expansion (i.e. contraction) along the chain and a positive expansion normal to it 4,32 . This effect is found, e.g., in polyethylene, polypropylene and polyoxymethylene 4 .…”

“…This mode inhibition reduces α , as found for mode inhibition due to the presence of inter-chain hydrogen bonds 31 , and may also lead to a positive α . Moreover, if the zigzag polymer is flexible the tension-induced thermal stress can be relieved by a slight change in the C-C bond angle, which was shown to lead to a small but positive α in some polymers 32 . Here a similar stress relief may occur by relaxing slightly the length, or chain/bond angle, of the metal-ligand complex, which is much stronger than vdW, but, being not fully covalent, may perhaps be softer than the C-C covalent bonds.…”

Thermal expansion of polymers: Mechanisms in orthorhombic polyethylene

“…In this work the internal expansion ͑rearrangement of atoms within the unit cell͒ is treated simultaneously and on the same footing as the macroscopic expansion. 1,2 After summarizing the conclusions reached from the study of skeletal chain models, [3][4][5] we study several models and potentials for orthorhombic polyethylene ͑o-PE͒, with particular attention to the anisotropic thermal expansion at low and intermediate temperatures and the underlying mechanisms.…”

Analysis of Stress-Strain Curve of Polyethylene Films by Toda-Lattice Model

“…The larger slope (or bending) is considered due to underestimation of the strain in the necking region. Griineisen parameter I'G is defined as in the following equation 14 : YG= -dlnw/de (10) where w is the intrinsic frequency of an oscillator and e the intermolecular strain. Since the change in velocity with strain corresponds to the change in the intrinsic frequency with strain, Griineisen parameter can also be expressed as in the following equation 15 : YG=dlnv/de (11)…”