Dynamical studies of crystalline polymers by inelastic neutron scattering

 

A thesis submitted for the degree of Doctor of Philosophy in the University of Oxford

by J.F.Twisleton M.A. of St. John’s College, Oxford July 1973.

 

Abstract

 

Experimental parameters of the interchain force field of polyethylene and polytetrafluoroethylene (P.T.F.E.) are measured by inelastic neutron scattering spectroscopy and provide some of the first anisotropic information about the forces between carbon chains in simple polymeric systems.  Spectroscopic studies of polymers have long been restricted by the unavailability of samples with full single crystal texture and so the preparation of such a specimen of deuteropolyethylene reported here can be seen as a very significant development, one that is much exploited in this thesis.

 

Comparative studies of the low frequency incoherent neutron spectra of normal and deuteropolyethylene obtained by the time-of-flight method are described and facilitate assignment of the density of states function for external chain vibrations in the crystalline regions of this polymer.

Some deficiencies in the existing Urey-Bradley interchain force models for polyethylene become apparent from these data.

 

Coherent acoustic features in the neutron time-of-flight spectra of isotropic and uniaxially oriented deuteropolyethylene are investigated. Dynamical structure factor calculations illustrate the predominant contribution of longitudinal acoustic phonons polarized along [ξ ξ 0] in the isotropically averaged phonon spectrum. On this basis the observed singularities are assembled onto a dispersion curve which defines an elastic constant of the interchain force field, the first of such measurements. Persistence of anisotropic contributions within the isotropically averaged phonon spectrum is seen as a remarkable consequence of the anisotropy of the polyethylene unit cell and the high symmetry of the molecular basis therein, both of which act to simplify the dynamical structure factors. A technique for extracting anisotropic information about lattice vibrations from polycrystalline or partially oriented material is recognised and some criteria are established for the choice of suitable systems for further investigations of this kind.

 

Preparation of a bulk specimen of deuteropolyethylene with full single crystal texture is reported. Biaxially oriented specimens are annealed at high pressure with a constraint on their shape following a recently devised procedure. Sudden cooling of the annealed material preserves the induced single crystal texture. Conditions of temperature, pressure and annealing time are adjusted to optimize the mosaic in the basal plane of the polymer as characterized by X-ray and neutron diffraction. The resulting specimens are assembled to give a target suitable for triple axis spectro­metry which represents the closest approach to a single crystal of polyethy­lene yet achieved.

 

Triple axis neutron spectrometry is applied to this material and phonon measurements in the basal plane are described. Three acoustic slopes qualifying interchain phonons are reported together with two zone centre frequencies for external chain rotatory and translatory modes, assigned on the basis of dynamical structure factor calculations. These five parameters are combined with far infrared data and Raman data obtained in conjunction with the author to give a total of seven experimental parameters of the interchain force field of polyethylene, which are then used to test the available force models. Overall fits of 10 and 20% are provided to these data by two Urey-Bradley force fields, both of which include interactions between nearest neighbour nonbonded hydrogens only.

 

Calculations of the interchain phonon dispersion curves of deuteropoly­ethylene based on an atom-atom potential parameter model are reported. Inter­molecular force constants are derived from an analytical 'six-exp' form for the potential between nonbonded atoms which reproduces a wide range of structural and thermodynamic data for the hydrocarbon system. This model fits the observed dynamical parameters within an average error of 5% which is significantly better than the fits obtained using the Urey-Bradley force fields. Moreover the close reproduction of the experimental elastic constants gives support to the related elastic moduli perpendicular to the chain axis crystallographic axes perpendicular to the chain axis in the orthorhombic cell are very similar in contrast with earlier predictions. The values of 8 and 9x10 to the 10th dyne cm-2 are moreover in very close agreement with an average interchain crystal modulus derived from bulk measurements. The basis of this derivation is a two phase 'sandwich' model of composite polyethylene in which the bulk stress is assumed to be homogeneous across alternate crystalline and amorphous layers. Such a model is consistent with present understanding of polyethylene morphology and is lent additional support by the agreement obtained here between interchain crystal moduli derived from macroscopic and microscopic sources.

 

Neutron time-of-flight spectra of P.T.F.E. exhibit coherent acoustic features strongly analogous to those observed in deuteropolyethylene. An acoustic slope for longitudinal acoustic phonons propagating along the [ξ 0 ξ 0] direction in the basal plane of hexagonal P.T.F.E. is derived from

these data. The elastic constant c11 is evaluated from this slope and provides the first anisotropic information about the interchain force field of this polymer. Comparison of c11 with the elastic constant c33 derived from earlier measurements of acoustic phonons propagating within the chain

itself is effected. A ratio c33:c11 of 8 compares with a figure of 22 for deuteropolyethylene also obtained in this work and highlights the greater anisotropy of the hydrocarbon force field. Other features in the time-of- flight spectra of P.T.F.E. suggest strong coupling between the lowest

frequency intrachain torsional mode and the external chain vibrations, questioning the applicability of an isolated chain description of the internal vibrations of this molecule. Changes in the low frequency time­-of-flight spectra at the 19 degrees C phase transition in P.T.F.E. are attributed to a decrease in external librational frequencies occurring parallel to the onset of dynamical disorder about the chain axis.

 

Acknowledgements

 

I should like to thank my supervisor, Dr. J.W. White, for his guidance and inspiration throughout this project and Drs. P.A. Reynolds, R.J. Young and C.P. Buckley for helpful discussions and advice about the experimental techniques of neutron inelastic scattering and the preparation of oriented polymers. I also thank Dr. N.G. McCrum for extending to me the facilities of his research group, Dr. R.W. Gray for assistance in the measurement of X-ray pole figures and Drs. G.S. Pawley and D.I. Marsh for the loan of their computer programs. Mr. H.A. Willis and Drs. J.S. King and H.W. Starkweather provided polymer specimens vital to this work.

 

Practical assistance from the staff at A.E.R.E. Harwell, A.E.K. Risφ, Denmark and the Oxford University Computing Laboratory is gratefully acknowledged, especially that provided by Mr. G.E. Haines and Dr. J.K. Kjems. I am also grateful to the technical staff of the Physical Chemistry and Engineering Laboratories, Oxford University who constructed the die set and sample moulds employed in this work. Finally I think Mr. D. Kozlow for helping to draw some of the diagrams and Miss A.B. Onions, Oxford Typing Service Ltd., for typing this thesis.

 

Financial support from the Science Research Council and St. John's College, Oxford is gratefully acknowledged.