Multiple scattering in small-angle neutron scattering measurements on polymers

Multiple scattering corrections in small-angle neutron scattering experiments on polymers have been examined. Numerical calculations show that, for typical experimental conditions, the second-order scattering is less than 2% of the first-order scattering for QR_g up to 10.0. An approximate expression is also given for obtaining a rough estimate of the second-order scattering without numerical calculation.     

Structural characterization of semicrystalline polymer blends by small-angle neutron scattering

A series of phase-separated polyethylene-polypropylene blends, which have undergone different thermal treatments, have been analysed by small-angle neutron scattering (SANS). The coherent scattering from normal hydrogenated blends is virtually zero, but strong contrast may be induced by partial or complete deuteration (labelling) of either phase. Here, the scattering from blends with complete labelling of the polyethylene phase was analysed to provide the domain dimensions by means of a theory due to Debye using an exponential correlation function. By this means the mean chord intercept lengths of both phases were shown to be in the range 1000–10000Å. The scattering from blends with partial labelling of the polyethylene was analysed to give the radius of gyration of the molecules in the polyethylene domains, which was found to be close to that measured in the homopolymer. For melt-quenched blends the deuterated polyethylene was shown to be statistically distributed in the polyethylene phase, whereas for slow-cooled blends, partial segregation of the labelled molecules occurred.     

Crosslink distribution of epoxy networks studied by small-angle neutron scattering

Crosslink distribution of epoxy networks of diglycidyl ether of bisphenol A (DGEBA) cured with stoichiometric amounts of meta-phenylene diamine (mPDA) was examined by small-angle neutron scattering (SANS). A monodisperse DGEBA resin with the smallest molecular weight was used to enhance the crosslink density and to simplify the network structure for deuterium-labelling. Meta-phenylene-d₄ diamine (mPDAd₄) was applied to label definitively the crosslinks. SANS measurements covered a reciprocal space range from 0.016 to 0.220 Å^?1 or, equivalently, real-space distances from 400 to 30 Å. Application of SANS on the deuterium-labelled epoxy networks consistently produces a constant excess intensity over the unlabelled epoxy networks. Since the scattering intensity from total correlation of the network was negligible, as evident from measurements of SANS on the unlabelled epoxy networks and small-angle X-ray scattering on the epoxy networks, the constant excess SANS intensity can only be attributed to a uniform spatial distribution of the amine curing agent. In other words, the crosslinks are distributed uniformly throughout the epoxy network.     

Preparation of cellulose triacetate and cellulose tricarbanilate by nondegradative methods

A method for obtaining triacetate having a D.S. of 3.0 has been obtained by acetylating the cellulose with acetic anhydride–pyridine reagent containing a catalytic amount of acetyl chloride. The process is rapid and nondegradative. Cellulose tricarbanilate can be prepared without recourse to pyridine solutions by using dimethylformamide (DMF) as solvent and triethylenediamine (1,4-diazobicyclo[2.2.2]octane) as catalyst. The DMF solution of the cellulose tricarbanilate can be cast directly into films or the polymer easily recovered owing to the solubility of the reaction solvent and impurities in water.     

Pore structures in shungites as revealed by small-angle neutron scattering

The analysis of the small-angle neutron scattering data from shungites, one of the natural forms of carbon, is reported. Samples from different deposits are investigated. It is shown that shungites have a complex pore structure at a nanoscale of 1-100 nm depending on their origin. Along with it, common features, in particular, two-level organization at the given scale can be observed. The absorption of deuterated water by shungites is used to match the scattering from open pores and to separate the information about the open and closed porosity in the samples. The revealed structural units are compared with the previous experimental results obtained by the complementary techniques.     

Analysis of C-S-H gel and cement paste by small-angle neutron scattering

The role of small-angle X-ray and neutron scattering (SAXS and SANS) in the characterization of cement is briefly reviewed. The unique information obtainable from SANS analysis of C-S-H gel in hydrating cement is compared with that obtainable by other neutron methods. Implications for the nature of C-S-H gel, as detected by SANS, are considered in relation to current models. Finally, the application of the SANS method to cement paste is demonstrated by analyzing the effects of calcium chloride acceleration and sucrose retardation on the resulting hydrated microstructure.     

Conformation of polymer molecules at solid-liquid interfaces by small-angle neutron scattering

A wide variety of physical-chemical phenomena depend on the behavior of the polymer at solid-liquid interfaces. The feature that distinguishes such phenomena from their small-molecule counterparts is the long-chain structure of the polymer molecules. Just as in solution and the bulk, the conformational statistics of the polymer molecules in the interface is an important determinant of interfacial properties. Conformational statistics of interfacial polymer is expressed in terms a function called the polymer density profile ϕ(Z), which is just the volume fraction of polymer as a function of Z, the distance from the solid surface out into the continuum liquid. There is only one experimental technique that is purported to be able to determine polymer density profiles of polymers confined to the interface between finely divided substrate and dispersant, and that technique is small-angle neutron scattering (SANS). In this paper we present a protocol for the analysis of SANS data on spherical particles with adsorbed polymer for the determination of ϕ(Z). We give an example for nearly-monodisperse chains of poly(n-butyl methacrylate) with a molecular weight of 45,000 tethered to silica spheres with a diameter of 2150 Å. The polymer density profile demonstrates a deep depletion layer next to the surface with a maximum in ϕ(Z) of about 0.7 at about Z = 40 Å. Our experimental ϕ(Z) is compared with various theoretical predictions.     

A small-angle neutron scattering study of activated carbon fibers

Phenolic resin based activated carbon fibers are widely used as filter materials in industry. We studied the fiber type ACFY-0204-3-18 which is applied to recover 2-propanol from air. The fibers were characterised by measuring the chemical composition, the apparent density, the wide angle X-ray diffraction data, and the sorption isotherms for nitrogen at 77.4 K and 2-propanol at 308.2 K. The porous structure was studied by small-angle neutron scattering. The two-dimensional contour patterns show an anisotropic intensity distribution I(q) at scattering vectors |q|<0.4 nm⁻¹. In this q-range I(q) is perpendicular to the fiber axis due to a refraction of the neutrons by the fibers, and I(q) increases abruptly with decreasing q. At |q|>0.4 nm⁻¹ scattering is isotropic and I(q) shows a weak interference peak due to the presence of micropores. The mean pore size of ∼2 nm was determined by fitting a monodisperse and a polydisperse Percus-Yevick hard sphere model to the experimental I(q) data. The microstructure of ACFY differs basically from the microstructure of polyacrylonitrile and pitch based carbon fibers.     

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein-Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ⁻²I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.     

Interaction of nanogel with cyclodextrin or protein: Study by dynamic light scattering and small-angle neutron scattering

The structure of hydrogel nanoparticles (CHP nanogels), formed by self-aggregation of cholesterol-bearing pullulan (CHP) was studied by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The interactions between the CHP nanogel and methyl-β-cyclodextrin (CD) or protein (hen egg white) were also investigated. It was revealed by SANS that the nanogels were spherical in shape with a radius of 6.7 nm. The following two functions were disclosed. (1) CHP nanogels were dissociated by the addition of CD and formed inclusion complexes with cholesteryl groups, leading to suppression of hydrophobic interaction between the cholesteryl groups. (2) The nanogel behaved as a molecular chaperone (heat shock protein-like activity) when CHP nanogel was mixed with hen egg white and heated up to 75 °C. The egg white aqueous solutions with CHP nanogel remained transparent while the egg white without CHP nanogel became opaque.     

Pressure induced changes in fractal structure of detonation nanodiamond powder by small-angle neutron scattering

The results of the experiments on small-angle neutron scattering from the industrial detonation nanodiamond powder under a pressure in the range of up to 1000 MPa are reported. It is shown that at a scale of 10–100 nm the scattering is determined by the fractal pore structure within aggregates of nanodiamonds. Its fractal dimension monotonously decreases with pressure from 1.8 to 1.2, which indicates the recombination of pores as a result of mobility of nanodiamonds in the powder under pressure. The mean pore size under the highest pressure (6 nm) is close to the characteristic size of nanodiamonds in the sample (5 nm) found from the width of X-ray diffraction peaks. The difference can be explained by the existence of a non-diamond carbon shell around diamond crystallites.     

Evidence of polyion hydration from X-ray and neutron small-angle scattering experiments

Summary The recently published small-angle scattering curves of semidilute solutions of poly (methacrylic acid) indicate some differences in neutron and X-ray data. At high degree of neutralization (>0.6), with increasing the neutron intensity decreases and X-ray intensity increases. A new series of experiments confirms this apparent discrepancy. We suggest an explanation of the observed phenomenon, based on a simple model which considers hydration of macroions. Using the proposed model, about one water molecule is estimated to be in excess in the hydration shell.     

Gradient dependence of viscosity of cellulose tricarbanilate in tetrahydrofuran

Summary The dependence of viscosity of cellulose tricarbanilate in tetrahydrofuran on the velocity gradient D <2500 s^–1 for molecular weights up to 1.2×10⁶ was determined, and an empirical equation for the determination of the limiting viscosity number for zero velocity gradient was derived. Errors involved in the viscosity determination from a single concentration using an approximate formula were also ascertained.     

A study of the porosity of nuclear graphite using small-angle neutron scattering

Small-angle neutron scattering (SANS) measures porosity in nuclear graphites, including both open pores, caused by escaping decomposition gases, and internal cracks (in coke particles) generated by anisotropic thermal contraction along the c-direction (Mrozowski Cracks). Porosity changes on the length scale observable by SANS must control the development of internal stresses and hence of cracking in AGR graphite due to irradiation (both fast neutron displacements of carbon atoms and radiolytic corrosion by CO₂). Such cracking may cause premature reactor shutdown. SANS measurements show that porosity is fractal on a length scale between ∼0.2 and 300 nm, presumably due to Mrozowski cracks – because the fractal index of the SANS signal depends only on the porosity of the graphitic filler. We report here two novel uses of the SANS technique as applied to reactor graphite – contrast matching with D-toluene (to measure the fraction of the porosity open to the surface) and the temperature dependence of the scattering (to measure pore width changes up to 2000 °C). These results provide important new information on AGR graphite porosity and its evolution during irradiation.     

Non-Newtonian viscosity and non-linear flow birefringence of cellulose tricarbanilate

The shear rate dependence of the intrinsic viscosity and of the intrinsic property, which can be derived from the extinction angle, was investigated for a sample of cellulose tricarbanilate. Its number-average molecular weight was 4.4 × 10⁵; the solvents used were dioxane at 25°C and phenyl benzoate at 75°C, the latter being known to break most intramolecular hydrogen bonds. The onset of non-Newtonian viscosity was found at a reduced shear rate of about 0.1, whereas non-linear behaviour in the extinction angle was noticed already at 0.02. The obtained data were compared with the theory by Noda and Hearst¹⁰, which deals with the influence of chain stiffness on the viscoelastic properties of polymer solutions. The qualitative outcome of this theory agrees fairly well with the experimental results. However, the onset of non-linear behaviour, especially in the extinction angle, occurs at lower values of the reduced shear rate than predicted. The stress—optical law remains surprisingly valid for this stiff polymer throughout almost the whole accessible range of reduced shear rates. However, some experiments with the highly viscous solvent tri-o-cresyl phosphate at 30°C show appreciable deviations at reduced shear rates larger than 1.0.     

A small-angle neutron scattering study on poly(ethylene oxide) crystals

Small-angle neutron scattering measurements were made on poly(ethylene oxide) (PEO) crystallized from the melt. Samples with the deuterated species (DPEO) as a matrix present distinct Bragg peaks from which the lamella spacings can be determined. As a result of strong void-scattering, quantitative analysis of the low-angle regime of these scattering curves is not possible. Samples with the protonous species as a matrix, for which void-scattering is expected to be negligibly small, present unusual scattering curves indicating that they consist of two components, i.e. the intramolecular and intermolecular interference terms. A quantitative analysis of these curves indicates: (1) the solute DPEO molecules are embedded in the crystalline structure of the matrix, assuming rod-like conformations but (2) forming essentially homogeneous aggregates of a few to tens of the DPEO molecules, depending on the crystallization temperature and the DPEO concentration; (3) the DPEO molecules or aggregates are distributed in space in a non-random manner that corresponds to the presence of inhomogeneous ‘domains’ having root-mean-square radii of about 250 Å, and each containing about 100 DPEO molecules.     

Thermodynamics of polyolefin blends: small-angle neutron scattering studies with partially deuterated chains

Small-angle neutron scattering is used to evaluate the binary interaction parameter χ in molten blends of polyethylenes having different levels of ethyl branching along the backbone. The labelled chains were partially deuterated to minimize the isotope effect on χ. The present results for equal-volume-fraction binary blends at 150°C can be summarized as χ=0.4×10⁻⁴+0.014ΔX²_br. The first term is from the hydrogen-deuterium isotope effect for chains labelled with about 33% deuterium. The second term is due to chemical composition differences, expressed here as the difference in X_br, the fraction of four-carbon repeat units having an ethyl branch. The observed contributions to χ are in reasonable accord with calculated estimates.     

Conformational change studies by intrinsic viscosity of cellulose tricarbanilate as a function of temperature

Summary The experimental variation of the intrinsic viscosity [] as a function of temperature for various molecular weights of cellulose tricarbanilate in solution in dioxane displays a S-shaped character with two plateau regions, respectively at low and high temperatures. The use of the Yamakawa model leads to two distinct values for the chain stiffness q, one which may be_o associated to a rather rigid conformation of the macromolecule (q=139 Å), the other which may correspond to a rather flexible conformation (q = 84Å).