The Physics of Photons and Neutrons with Applications of Deuterium Labeling Methods to Polymers
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THE PHYSICS OF PHOTONS AND NEUTRONS WITH APPLICATIONS OF DEUTERIUM LABELING METHODS TO POLYMERS
G. D. WIGNALL National Center for Small-Angle Scattering Research, Laboratory, Oak Ridge, Tennessee 37831
Oak Ridge National
INTRODUCTION Over the past decade small-angle neutron scattering (SANS), has found numerous applications in the fields of biology, polymer science, physical chemistry, materials science, metallurgy, colloids., and solid state physics. A number of excellent references are available [1-4] which contain basic neutron scattering theory though these text books reflect the origins of the technique and the examples are largely drawn from physics e.g., single crystals, simple liquids, monatomic gases, liquid metals, magnetic materials, etc. In view of the large numbers of nonspecialists who are increasingly using neutron scattering, the need has become apparent for presentations which can provide rapid access to the method without unnecessary detail and mathematical rigor. In the field of polymer science several reviews have been written to meet this need (5-81 including a recent comprehensive survey of neutron scattering studies of polymers [9] to Which reference will be made for detailed derivations of the expressions used below. This article, along with others in this volume, is meant to serve as a general introduction to the symposium "Scattering Deformation and Fracture in Polymers," and is intended to aid potential users who have a general scientific background, but no specialist knowledge of scattering, to apply the technique to provide new information in areas of their own particular interests. In view of space limitations, the general theory will be given in the case for neutron scattering and analogies and differences with photon scattering (x-rays) will be pointed out at the appropriate point. ENERGY AND MOMENTUM TRANSFER Scattering in the context of this article means the deflection of a beam of radiation (neutrons/x-rays, etc.) from its original direction by interaction with the nuclei or electrons of polymer or solvent molecules in a sample. In a scattering experiment a proportion of the incident neutrons is scattered and the remaining fraction is transmitted through the sample. The intensity of the scattered neutrons is measured as a function of the scattering angle and/or energy. The kinetic energy of a typical neutron, wavelength X = 5.3 A, is -4.7 x 10-15 ergs or 3 meV (9]. Such energies are very much lower than electromagnetic radiation, and are of the same order as the vibrational and diffusional energies of molecular systems. Exchanges of energy between the particle (neutron) and molecule give rise to inelastic scattering which depends on the dynamics of the system studied. While the angular dependence of the scattering of both x-rays and neutrons is easily measured, the energies of molecular vibrations (~-3 meV) are much lower than incident photons (-10 keV) and thus energy transfers are difficult to detect for x-ray scattering. In contrast, the energy transfers resulting from neut
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