Extraction of Structural Parameters of Polymer Melts and
Glasses from Wide Angle Neutron Scattering Patterns. An
Application to Polybutadiene.
Thomas Gkourmpis and Geoffrey R. Mitchell
Polymer Science Centre, J. J. Thompson Physical Laboratory, Department of Physics,
University of Reading, Reading, RG6 6AF, UK.
An efficient method of coupling neutron diffraction experimental data over an
extended Q range with single chain modelling is presented. We exploit this to map in
a quantitative way the organisation and chain conformation of glassy and liquid
polymers. The technique used is based on the assignment of a number of parameters
that are associated with the chemical structure of the polymer and define the structural
and spatial configuration and conformational characteristics. The variation of these
characteristics can be used in the minimisation of the differences between the
observed experimental data and the calculated scattering pattern from a computer
generated model. A simpler version of this method1 has been successfully used in the
identification of the local structure of polyethylene2 and PTFE3 in the past and this
time it has been applied for the first time to the more complicate and structurally
inhomogeneous system of 1,4 and 1,2 polybutadiene. A series of neutron scattering
data on the range 0.05-50Å-1 were collected at a number of temperatures in the range
20-400K allowing structural investigations to be carried out from deep in the liquid all
the way to the glassy regime. From the analysis of the experimental data the model
yields bond lengths and valence angles in agreement with previously reported
measurements and predictions, and a torsional angle distribution that is characterised
by cis and trans states around the double bond as well as gauche states in 60 and
120. The percentage of the trans state acquired from the model is 50% and the
molar fraction of both 1,2 and 1,4 component are in very good agreement with NMR
measurements, giving a clear indication of the technique’s sensitivity. Results show a
slow variation in the distributions of the torsional angles as a function of temperature
in the glassy region, in comparison with the more rapid expansion in the melt. On the
contrary valence angle distributions are almost frozen in the glass and they fluctuate
in the liquid state. 1,2 polybutadiene is characterised by long series of trans sequences
giving rise to a rather stiff chain, in comparison with 1,4 polybutadiene where the
double bond is flanked by gauche states resulting in a more flexible chain. A detailed
analysis of the technique with respect to the averaging over a substantial number of
configurations and the details of the generation of the initial model as well as the
method of scanning through the parameters is presented. A series of tests are used to
identify the level of coupling between the individual parameters, and their level of
orthogonality is discussed. Comparison of the configurations extracted from the
scattering data with the use of this technique and predictions coming from the
Rotational Isomeric Model, Molecular Dynamics and Reverse Monte Carlo, as well as
ab-initio and semiempirical quantum mechanical calculations have been performed
and the results are presented and discussed.
References
1. G. R. Mitchell, B. Rosi-Schwartz, Physica B, 1992, 180-181, 558.
2. B. Rosi-Schwartz, G. R. Mitchell, Nucl. Instr. and Meth. in Phys. Res., 1995, A 354, 17.
3. B. Rosi-Schwartz, G. R. Mitchell, Polymer, 1994, 35, 3139.