The scattered amplitude from a collection of objects, each small as compared with the wavelength of the radiation, is given by

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 [5–8] 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.

A general discussion of scattering from disordered materials is presented. The parameters which characterize structure are illustrated in real-space and are also identified in the reciprocal-space profile measured in a scattering experiment. Scattering from fractal objects is described in detail. To illustrate the interpretation of scattering data, the growth and structure of fumed silica is discussed. The flame growth of silica is explained in terms of monomer-cluster ballistic polymerization in the early stages and diffusion-limited aerosol aggregation in the latter stages.

This article discusses the application of small-angle neutron and X-ray scattering techniques to the study of bulk amorphous polymers, block copolymers and polymer blends. The subject matter discussed include density fluctuation in single component amorphous polymers, concentration fluctuation in compatible polymer blends and its interpretation in terms of the random phase approximation theory, analysis of the scattering from incompatible polymer blends as developed by Porod, determination of the phase boundary thickness, order-disorder transition in block copolymer, interpretation of the scattering from disordered block copolymer systems by means of the random phase approximation theory, characterization of ordered block copolymer structure, and the study of block copolymer micelles.

As it is well known the Flory-Huggins approach of the thermodynamic description of a mixture of two polymers A and B leads to an expression [1] for the Gibbs free energy of mixing ΔG

Molten and semi-crystalline mixtures of PEO and PMMA have been investigated by small angle neutron and X-ray scattering. It has been found that the Flory Huggins interaction parameter, evaluated from the intermolecular scattering function, is quite small and is apparently dominated by entropic contributions. Scattering profiles from the semi-crystalline mixtures clearly show that the PMMA is incorporated within the amorphous phase between the crystalline PEO lamellae.

Neutron scattering was used to investigate the molecular mechanism of large strain deformation in epoxies. Partially deuterated diglycidyl ether of bisphenol A (DGEBA) was cured with either tri- or di-amines of different molecular weights. The change of the average distance between crosslinks along the epoxy and the amine linkages could easily be determined from the shift in the positions of the scattering maxima. It was found that the average distance between crosslinks remained almost unchanged along both the amine and the epoxy linkages as the bulk material underwent a large deformation. The above results are discussed in terms of the functionality of the junctions as well as the molecular weight between crosslinks. Comparisons are also made between the solid state deformation results and those from swollen networks which did show a substantial increase inaverage distance between crosslinks.

This paper correlates the interlaminar shear strength of 7 different carbon fiber/epoxy composite with structural characteristics determined by Small Angle X-ray Scattering (SAXS) measurements. The carbon fibers were all of the same type but had different surface treatments. The SAXS patterns of the fibers and of the composites showed a highly nonlinear Guinier region which could not be approximated by traditional linear regression. A new approach to the Guinier approximation was developed to treat this nonlinear curve using a polynomial of second order. The radius of gyration (RG) of the fibers, as determined by this new method, correlated clearly with both the extent of the surface treatment and the interlaminar shear strength of the composite. Also the difference in scattering between a dry fiber and a glycerine soaked fiber provides a way to characterize the changes obtained by surface treatments. These methods provide new ways to estimate the efficiency of a surface treatment and its effect on the interlaminar shear strength by analyzing the SAXS patterns of the fibers.

This paper examines the effectiveness of scanning transmission electron microscopy (STEM) as an analytical tool for determining composition in multi-phase polymer blend microstructures. The polymer blend polystyrene (PS) - polyether sulphone (PES) thin film used in this study exhibited a two-phase microstructure consisting of PES-rich inclusions, ranging from 0.2μm to 1.2μm in diameter, in a PS-rich matrix. Emphasis in this presentation is placed on the use of annular dark-field (ADF) STEM image contrast to infer information concerning the local composition of adjacent microstructural features.

Critical behaviour of PSD-PVME polymer blends are presented. Spinodal and binodal transition temperatures have been determined by the use of a SANS-camera, and non-meanfield characteristics have been observed close to the critical point. A dynamic decomposition study has been performed by the use of a neutron double crystal diffraction.

The miscible blend of polystyrene (PSH) and tetramethyl-bisphenol A-polycarbonate (TMPC) has been previously studied by differential scanning calorimetry (DSC), viscoelasticity, and microscopy. In this study, small-angle neutron scattering (SANS) has been applied to obtain the quantitative interaction parameter (X) of this blend at room temperature. Deuterated polystyrene (PSD) was used for the scattering contrast in the study. The PSD/TMPC blends show a single Tg over the whole range of composition from the DSC measurements, whicg is the same as the Tg of PSH/TMPC blend.

The interaction parameter was calculated from the de Gennes scattering intensity function of miscible polymer blends, which is based on the random phase approximation. As expected for a miscible system, all X values are negative over the range of composition. It is also found that the X is composition-dependent. Furthermore, the correlation length of the concentration fluctuation is approximately twice the segment length 21–32 Å of the component polymer (PSD = 6.7 Å and TMPC = 18.3 Å), implying that the mixing of this blend is effectively at segmental level.

It is well known [1] that the majority of the classical polymers are incompatible. This means that it is impossible to mix them without having phase separation. This is sometimes advantageous for industrial applications but, from a fundamental point of view, it makes it difficult to measure the interaction parameter X between these polymers (for this purpose one has to have the two polymers in a single phase).

The order-disorder phase transition behavior exhibited by blends of a styrene-butadiene diblock copolymer (76% styrene) with a polystyrene of various molecular weight (from 2,200 to 50,000) is studied by means of small-angle X-ray scattering. With a polystyrene of a relatively short chain length the blend, on lowering the temperature, undergoes a microphase separation, and the scattering curve shows a peak at a finite scattering angle. With a polystyrene of relatively long chain length, the scattered intensity curve shows additional low angle component with intensity increasing rapidly as q→0, and this is interpreted in terms of the macrophase separation accompanying the transition from the disordered to ordered phase.

Binary mixtures of the perdeuterated and protonated isotopes of four amorphous polymerspolystyrenes, 1,4-polybutadienes, 1,2-polybutadienes, and 1,2-polybutenes – have been examined by small-angle neutron scattering (SANS). In each case, evaluation of the SANS results based on the RPA theory of de Gennes indicates non-ideal mixing characterized by a Flory-Huggins interaction parameter 10-4 < χ 10-3. All four χ parameters can be closely predicted based on the measured change in the carbon-hydrogen bond polarizability with deuterium substitution. These findings are discussed in the context of past SANS studies of amorphous polymers.

Extended x-ray absorption fine structure (EXAFS) spectroscopy has beensuccessfully applied to the analysis of the ionic domain microstructure inzinc and rubidium neutralized ionomers. In dehydrated zinc neutralizedionomers, the zinc cation was found to be tetrahedrally coordinated to oxygenatoms. For ionomers with hydrocarbon backbones, these oxygen atoms mayoriginate from the sulfonate or carboxylate groups. For ionomers withperfluorinated backbones, some of the oxygen atoms may be ascribed to watercoordination as well. In fully hydrated zinc neutralized ionomers, thezinc cation exists as Zn( H2O)62+. In contrast, the fully hydrated monovalentrubidium neutralized ionomers exhibited a highly disordered environmentabout the cation.

Small-angle neutron scattering studies of polystyrene-polybutadiene diblock copolymers of spherical morphology are discussed, with emphasis on the effect of this morphology on the spatial organization of the polymer chains. Three particular cases are examined: (i) the distribution within the matrix of added (matrix) homopolymer, (ii) the distribution within the spherical microdomains of added (microdomain) homopolymer, and (iii) isotopic effects occurring in the B domains when a B-deuterated diblock SBd is blended with a normal sample SB. Deviations from ideal mixing are found in all three cases.

The Fixman-Kovac formulation of chain dynamics with constraints is used to calculate the first cumulant Q(q) of the dynamic scattering function. This general formalism is applied to the case of freely jointed chains. It is shown that the large q limit (q being the scattering wavenumber) of Q(q) for a chain of N bonds in the absence of hydrodynamic interaction is proportional to the ratio (2N+3)/3(N+l) representing the fraction of unconstrained degrees of freedom of the chain. The inclusion of hydrodynamic interaction seems to enhance the apparent segmental diffusion. The use of constrained chain dynamics has no appreciable effects, however, on the behavior of Q(q) in the small and intermediate q regions for long enough chains. This formalism can be used to interpret neutron (spin echo) scattering experiments from semiflexible polymers in solution.

X-ray analysis methods have been used to investigate the structure of the high strength HM-50 copolyamide fiber produced by Teijin, Ltd. of Japan [1,2]. The fiber is prepared of a 50/25/25 mole ratio of the monomers shown below.

Fundamental optical properties of Langmuir-Blodgett polydiacetylene (LB PDA) ultra thin films are investigated. The LB films exhibit a strong absorption peak at about 16000 cm-1 and a weak and broad peak at about 17500 cm-1; the color of the film is blue. After annealing at 90°C, a blue shift of the absorption peaks is observed; that is, the color of the LB films changes from blue to red. The phase transition corresponding to the color change is studied using Raman spectroscopy as a function of annealing temperature. For annealing temperatures between 50 and 60°C, the results show significant change in the ratio of Raman line intensities due to C≡C and C=C stretch modes. Such a transition is also observed for laser annealed LB PDA films. Furthermore, the photoluminescence (PL) properties of pristine (blue), annealed (red) and ion implanted (red) LB PDA films are investigated. The photoluminescence of both pristine and annealed LB PDA films show sharp peaks at about 15500 cm-1. The annealed LB PDA films have an additional small peak or shoulder at about 18000 cm-1. The photoluminescence peaks of red films implanted with 200keV As+ ions are observed at about 16000 cm-1 and become broad with increasing ion implantation dose in the range 1012–1015 cm-2.

The possibility of using synchrotron radiation as a source of X-rays for scattering experiments has considerably improved the methods of the characterisation of the molecular orientation and molecular order in polymers. In another publication [1], it has been shown that the morphology of ultra highly drawn polyethylene is correlated to the kinetics of isothermal melting, as determined by X- ray scattering employing synchrotron radiation. In this paper we present some results on chain orientation and orientation of crystal lamellae surfaces in uniaxially and biaxially drawn films of polyethyleneterephthalate (PET). These results were obtained by inserting a pole figure goniometer into the synchrotron radiation beam and measuring the wide angle X-ray scattering (WAXS) and small angle X- ray scattering (SAXS) with different angles of incidence of the primary beam onto the sample.