Ann Maconnachie

Neutron scattering and amorphous polymers

Abstract During the past ten years neutron scattering has become a much more widely used technique. The use of neutron scattering to study the conformation and dynamics of polymer chains in the bulk amorphous state and in solution is reviewed here. The basic theory of neutron scattering is introduced. The types of instruments which are currently used and the factors affecting neutron scattering experiments are discussed. The following sections are each concerned with a different type of scattering experiment and the information which has been obtained. At the beginning of each of these sections the theory relating to the particular topic under discussion is introduced. The three topics covered by this review are: conformation studies of polymers; dynamics of polymer chains and studies of side group motion in polymers.

Molecular dynamics of poly(ethylene oxide) in concentrated solution

Abstract Incoherent quasi-elastic neutron scattering measurements on aqueous poly(ethylene oxide) solutions show that as the concentration of water is increased to 1:1 mole ratio of water to ethylene oxide monomer units, the polymer chain mobility is not enhanced. Increased mobility is only observed when the water content is increased beyond this ratio. The activation energy for viscous flow shows a similar behaviour, it is unchanged as the system is diluted from the melt to the 1:1 solution and as more water is added it falls sharply. Similar studies on the system poly(ethylene oxide)/toluene show that chain mobility is enhanced and the activation energy for viscous flow falls continuously, at all concentrations. The difference is attributed to the formation of polymer-water hydrogen bonded complexes in aqueous solution. High resolution data for the aqueous systems suggest that the molecular dynamics obey the scattering law predicted for the Zimm model. In the melt the behaviour changes towards the limit given by the Rouse model.

Temperature dependence of chain dimensions

The dimensions of linear atactic polystyrene (Mw = 75 700) in cyclohexane have been determined at a series of temperatures using small-angle neutron scattering. Three solutions were examined: dilute (2% polymer), semi-dilute (19% polymer) and concentrated (47% polymer). End-to-end distances obtained from the data were compared with current theories of polymer solutions. For the semi-dilute solution results agreed with scaling law predictions, whereas results from the concentrated solution agreed with the formula obtained by Edwards. Furthermore, the latter results gave a characteristic ratio (C∞) of 9.5 ± 0.7 for polystyrene.

Compatibility and neutron scattering studies of mixtures of polystyrene with poly(2,6-dimethyl 1,4-phenylene oxide) and its brominated derivatives

Abstract Several narrowly disperse polystyrenes (PS) were mixed with three series of random copolymers of 2,6-dimethyl phenylene oxide (also known as xylenyl ether (XE)) and 3-bromo-2,6-dimethyl phenylene oxide (BrXE), each series having a fixed chain length. The critical BrXE comonomer concentration necessary to induce phase separation, xc′ was characterized for each blend series by a number of techniques. xc was extrapolated to a value of about 0.5 at infinite chain lengths of each polymer of the blend. This finding supports the negative heat of mixing of PS with PXE reported by other workers. Small-angle neutron scattering studies were carried out using small amounts of perdeuteropolystyrene in several matrices for which single phase behaviour had been shown to exist. The radius of gyration R2 and the second virial coefficient A2 were greatest in the pure PXE matrix reflecting the goodness of this material as a ‘solvent’ for PS. In matrices containing 50% PS 50% copolymer, A2 extrapolated to zero at xc ≥ 1 which was consistent with the phase behaviour of this series of blends.

On the assessment of incoherent neutron scattering intensities from polymer systems

Abstract The problem of assessing incoherent scattering intensities from polymer systems is outlined. The incoherent cross-sections of some hydrogenous polymers have been measured. The measurements show that the incoherent scattering is anisotropic and the cross-section is temperature- and wavelength-dependent. The change in cross-section is due to changes in the mobility of the polymers which affects the inelastic contribution to the scattering. Without an accurate knowledge of the polymer cross-sections as a function of temperature and wavelength, it is impossible to calculate the incoherent scattering.

Investigation of the methyl torsion in isotactic polypropylene — comparison between neutron inelastic scattering spectra and normal coordinate calculations

Abstract Incoherent neutron scattering spectra for polypropylene and its partially deuterated analogue allow identification of the methyl torsion at 230 cm −1 . Comparison of the experimental spectra with the calculated densities of states shows discrepancies with the expected intensity of the methyl torsional band. Results from a stretch-oriented sample arranged so that the wave vector Q is first parallel ( Q ∥ ) and then perpendicular ( Q ⊥ ) to the helical chain axis indicate that the torsion is more intense and probably has a small frequency dispersion around 240 cm −1 for Q ∥ and is weaker with a broad dispersion centred at 220 cm −1 for Q ⊥ .

Comparison of the local chain motion of a number of polymers in the melt observed by quasielastic incoherent neutron scattering experiments

Incoherent quasielastic neutron scattering results are reported for a number of polymer melts at temperatures well away from their glass transitions. The data are discussed in terms of the Rouse model, which is shown apparently to fit the scattering results over an unexpectedly wide range of frequency and momentum transfer. This effect is explained in terms of contributions to the observed scattering from interchain propagating modes.Differences between results are broadly explained by variation between polymers of their local backbone flexibility and by hindering effects of side groups. Values of monomeric friction coefficients are calculated from these results and give good agreement with those obtained from viscoelastic data.

Small-angle neutron scattering from a polymer coil undergoing stress relaxation

Abstract Small-angle neutron scattering measurements have been made on samples of polystyrene in which the stress has been allowed to relax at a constant strain. The radii of gyration parallel and perpendicular to the stretch direction have been measured as a function of time after the strain has been applied. After an initial rapid change, the radii of gyration tend towards asymptotic values which are close to those for the undeformed chain. The deformation appears to behave as if the affine deformation theory holds only for distances separating effective crosslinks. It is proposed that after the initial change in radii of gyration the stress is relieved by reorientation of the chain segments.

Small-angle neutron scattering from polymer solutions: 3. Semi-dilute solutions near the lower critical solution temperature

Abstract Measurements of the radius of gyration and the screening lengths have been made for semi-dilute solutions of polystyrene near the lower critical solution temperature. From these data two regions of behaviour are clearly discerned. By analogy with similar data near the upper critical solution temperature, a ‘phase diagram’ has been drawn from the results around the lower critical solution temperature.

Neutron Scattering from Macromolecules in Solution

Neutron scattering spectroscopy1–4 differs from scattering of electromagnetic radiation (light or x-rays) in two major ways. The relatively larger neutron mass, which associates a sizeable momentum transfer with a scattering event, totally changes the relationship between energy and wave vector. This property, which means, for example, that neutrons have very much smaller energies than x-rays of the corresponding wavelength, allows exploration of a unique region of the spatial and time domains. It is, however, doubtful whether this property would have led, alone, to the widespread use by polymer scientists of neutron spectrometers, confined as these are to a few reactor centers scattered worldwide, if it were not for the second property—the neutron-nuclear interaction. Since the neutron is uncharged it interacts with the nucleus via nuclear forces. It carries a magnetic moment which can also interact with the nucleus and with the unpaired electrons in a molecule. This magnetic scattering is relatively weak and does not concern us when dealing with polymer solutions. The nuclear interaction is strong, but very short range, and thermal neutrons have wavelengths very much larger than nuclear dimensions. For an isolated stationary nucleus, scattering is, therefore, spherically symmetrical and energy independent and can be characterized by a single parameter, the scattering length b. Values of b vary randomly from nucleus to nucleus, from isotope to isotope, and even with the spin state of the scattering nucleus. In particular, the values for 1H and 2D are of opposite signs.