Quantitative analysis of small angle neutron scattering data from montmorillonite dispersions

A new model is presented which can describe quantitatively the small angle neutron scattering from montmorillonite-type clay dispersions and polymer-clay nanocomposites. The model is shown to be able to describe well the data from a series of dilute montmorillonite in water dispersions in which the deuterium content of the water phase is varied. The fits combined with information from other techniques suggest strongly that H-D exchange occurs in the montmorillonite-water dispersions. Deviations from Q⁻² behaviour often observed experimentally for clay dispersions are convincingly explained by the presence of a small proportion of tactoids.     

Structure of polymer within the coating: an atomic force microscopy and small angle neutrons scattering study

Synthetic latex is widely used as a binder in waterbased paints. Upon dehydration of the dispersion, latex particles are brought into contact with mineral pigments: this process results in coating structuration and consolidation. This composite layer is described as a porous mineral structure, whose pores are covered by latex particles. Therefore, it is of fundamental interest to study the ordering of binder particles in the coating, and the wetting of pigments by polymer particles, toward understanding properties of coating such as: optical properties, adhesion, cohesion, sensitivity to water, etc. In this regard, we have used small angle neutron scattering and atomic force microscopy to study the ordering, the spreading, and the adhesion of latex particles on calcium carbonate within the coating. We discuss the structure of the coating.     

Small angle neutron scattering of partially segregated polymer blends

Small angle neutron scattering (SANS) has been used extensively to investigate the conformation of macromolecules. However, the scattered intensity has been found to be extremely sensitive to the segregation of the isotopic labelled species. The segregation has resulted in enormous increases in both the radius of gyration and the molecular weight. A theoretical treatment based on the Zernicke-Prins equation with a modified pair correlation function has been developed in this work; the size and the degree of segregation can be calculated from the scattering data using the equations obtained herein.     

Small angle neutron scattering study of deuterated sodium dodecylsulfate micellization in dilute poly((2-dimethylamino)ethyl methacrylate) solutions

Poly((2-dimethylamino)ethyl methacrylate) with 60,000 g/mol and a narrow polydispersity (1.12) was synthesized using group transfer polymerization in order to investigate the structure of poly((2-dimethylamino)ethyl methacrylate)/sodium dodecylsufate complexes in water. The synthesized polymer chain conformation in water was studied as a function of deuterated sodium dodecylsulfate concentration using small angle neutron scattering. We found three transitions of the poly((2-dimethylamino)ethyl methacrylate) chain conformation induced by the added deuterated sodium dodecylsulfate. The transitions resulted from interactions between the polymer and the surfactant, so that micelles are formed along the polymer backbone above the critical aggregation concentration. The structure of micelles in a poly((2-dimethylamino)ethyl methacrylate)/deuterated sodium dodecylsulfate solution was analyzed through model fitting of the small angle neutron scattering data measured at the condition where the poly((2-dimethylamino)ethyl methacrylate) was contrast-matched with a mixture of 80% H₂O and 20% D₂O.     

Small angle neutron scattering study of the structure and formation of MCM-41 mesoporous molecular sieves

The nanoscale structure and synthesis mechanisms of the MCM-41 class of inorganic mesoporous materials have been investigated by small angle neutron scattering (SANS). SANS measurements with solvents imbibed in the pores to vary the scattering contrast demonstrate that the low angle diffraction peaks from these materials are entirely due to the pore structure and that the pores are fully accessible to both aqueous and organic solvents. Static and shear flow SANS measurements on the concentrated cationic surfactant and silicate precursor solutions typically used in the synthesis of the mesopore materials indicate that the existence of preassembled supramolecular arrays that mimic the final pore structure is not essential for the synthesis of these materials.     

Small angle neutron scattering from ionomer gels

Small angle neutron scattering intensities for sols and gels of the physically associating ionomer 1.39 mol% sodium sulphonated polystyrene with molecular weight 10⁵ g/mole in xylene have been obtained over a broad wavevector (q) and concentration range. In the low q and concentration range the scattering behaviour of this ionomer/solvent system can quite readily be interpreted using the open association aggregation model. In more concentrated solutions and at higher q, however, interpretation of the scattering behaviour for polymers associating via an open association mechanism (OAM) is more difficult, particularly if, as in this investigation, the single chains and aggregates have varying densities and fractal parameters. In this study various methods have been developed to interpret the low and high q scattering from systems whose extent of aggregation can be modelled using the OAM. Using these methods it has been possible to confirm that the open association model can be used to interpret the extent of aggregation of the above ionomer in xylene even after the solutions appear to be gelled. Single ionomer chains within both the dilute solutions and gels were found via modelling to have a radius of gyration of 60 Å, which compares with dimensions of 25 Å and 93 Å calculated for a solid sphere of polystyrene or an unperturbed polystyrene Gaussian coil, respectively. The aggregates, however, all had radii of gyration comparable with what would be expected for polystyrene of the aggregate molecular weight in an unperturbed state. These results suggest that gelation of ionomer solutions at particular concentration thresholds is not due to an abrupt change in the aggregate structures at some critical concentration but occurs as a result of interactions between the very large aggregates that the OAM predicts should gradually form as the ionomer concentration increases.     

Small angle neutron scattering study of the structure of a triblock copolymer of styrene and isoprene during extension

A triblock copolymer with a styrene weight fraction of 0.41, has been examined at various extension ratios using small angle neutron scattering. The original ‘polycrystalline’ material with a face centred cubic arrangement of styrene domains acquires orientation as the extension ratio increases. Affine deformation is not obeyed at the supramolecular level and there is some evidence for non-uniform stress at this level.     

Small-angle neutron scattering measurement of block copolymer interphase structure

The notion of an interfacial layer at the domain boundary in block copolymers is reviewed and the possibility of its measurement by small-angle X-ray and small angle neutron scattering discussed. Values of the interfacial layer thickness and its volume fraction have been obtained for a range of styrene-isoprene copolymers. Interfacial layer thickness is not strongly dependent on molecular weight whilst the volume fraction shows a dependence more in line with the theory of Helfand.     

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.     

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.     

Study of structure and scaling behavior of chemically unfolded β‐casein by means of small‐angle neutron scattering

Structures of β‐casein formed in water with various concentrations of guanidine hydrochloride (GdmCl) were studied by small‐angle neutron scattering (SANS). A transition in structure and properties of the protein seems to occur around a GdmCl concentration of 1.2 mol L^?1. The data are interpreted assuming that the protein molecules behave like multi‐block copolymers with alternating hydrophilic and hydrophobic sequences. Below the transition, the protein structure is still native and has a fractal dimension larger than that beyond the transition where the β‐casein has the feature of a three‐dimensional excluded‐volume coil. A possible interpretation of these results is that the presence of salt increases the value of the critical micelle concentration. This allows a comparison of the structure of β‐casein and synthetic macromolecules. We find that, although the protein is short, excluded‐volume interactions between monomers are present, and that the structure of β‐casein is very similar to what was found in dilute solutions of linear polymers in a good solvent. Thus, it is reasonable to assume that above the critical salt concentration, the protein is completely isolated, whereas below, some structure remains present. Copyright © 2006 Society of Chemical Industry     

On the structure of biocompatible,thermoresponsive poly(ethylene glycol) microgels

The aim of the present study is the preparation and characterization of microgel particles which are, contrary to other microgels, thermoresponsive as well as biocompatible. Hence, monodisperse p-MeO₂MA-co-OEGMA microgel particles were synthesized by precipitation polymerization. Swelling/deswelling behavior and the structure of poly(ethylene glycol) (PEG) based microgel particles were investigated. A combination of dynamic light scattering (DLS) and small angle neutron scattering (SANS) was used. Particle size and the volume phase transition temperature (VPTT) are adjustable by changing the amount of comonomer. SANS measurements indicate an inhomogeneous structure of the PEG microgels in the swollen state. At temperatures above the VPTT a compact structure was observed. An increase of the comonomer content leads to a densely packed core and a fuzzy shell in the swollen state. Additionally, nanodomains inside the polymer network were observed in the temperature range around the volume phase transition (VPT). Due to this heterogeneous structure in the swollen state two correlation lengths of the network fluctuations were observed.     

Small angle X-ray scattering from voids within fibers during the stabilization and carbonization stages

Five kinds of commercial carbon fibers heat-treated at various temperatures were adopted to investigate the scattering from voids within the fibers by small angle X-ray scattering (SAXS), since the voids produced during stabilization and carbonized processes provide unfavorable influence on mechanical properties of the carbon fibers. The theoretical calculation was carried out for SAXS by assuming ellipsoidal voids with different shapes. In this model system, the long axis of all ellipsoidal voids on the two-dimensional plane was assumed to be oriented predominantly with respect to the machine direction but the center of gravity of each void are assumed to be arranged in the transverse direction assuring one-dimensional lattice. To analyze inter-particle interference effect from ellipsoidal voids, the function H₁(y) proposed by Hoseman was introduced to represent the probability of finding the nearest-neighbor void at a displacement vector. In comparison with observed and calculated SAXS patterns, the inter-particle interference effect was observed for the fibers carbonized at 1200-1700 °C but the effect disappeared with further heat-treatment at 3000 °C. Namely, the scattering from the fiber heat-treated at 3000 °C, which is so-called graphite fiber, showed no inter-particle interference effect. Namely, void distribution of high modulus carbon fiber with graphite crystallites was different from that of high strength carbon fiber with turbostratic structures.     

A convenient neutron scattering method for studying monomer correlations in homopolymer melts

Small angle neutron scattering data are compared with given expressions of scattering cross section for isotropic and uniaxially stretched melts containing a large fraction ø_D of deuterated chains. An expression of the cross section as ø_D(1 ? ø_D)f(q), where f(q) is the correlation function of one chain, fits the data for equal molecular weights of hydrogenated and deuterated species. For different molecular weights in the case of isotropic melts an expression is given, which agrees well with the data. The data lie in a scattering vector range of 7.10^?2, 10^?1 Å; seven values of ø_D were used for each mixture; the following deuterated and hydrogenated weights¹⁹ were mixed: 138 000 and 155 000, 105 000 and 155 000, 620 000 and 675 000. Both the Guinier range and the intermediate range are explored. Possible technical artefacts of high deuteration are discussed, especially multiple scattering which is not observed under normal conditions, and void scattering which is more difficult to avoid.     

Conformation of the molecules in drawn polypropylene revealed by neutron scattering studies

It has not been possible previously to do a complete study of drawn polyolefins using SANS techniques because of void scattering. In the case of polypropylene this can be reduced sufficiently to permit measurements with the Q-vector perpendicular and parallel to the draw direction. A complete analysis has been carried out with a draw ratio 8:1 in which the PPD molecules of narrow molecular weight distribution and molecular weights in the range 390 000 to 50 000 are molecularly dispersed in a drawable PPH matrix. The dimensional changes on drawing are to extend the molecule by a factor of 2 with a corresponding reduction in diameter to a maximum of 40%. We have interpreted the data at high Q on the basis that the molecule is not uniformly distributed but the majority is folded into sub-units and the number of these is proportional to the molecular weight of the polymer. A further feature of the sub-units structure is that its length is approximately two lamellae thick, this dimension is similar to the SANS scattering length (I_n) identified in the study of isotropic material. The double stems belonging to the same molecule have been concentrated by the drawing process some 16 times and a consequence of this is to markedly change the Kratky curves from the isotropic case. Notwithstanding, this increase in the packing of the molecule, the stems are still, on average, some 40 Å apart and surrounded by many stems belonging to other macromolecules. Similarly, each sub-unit is surrounded by sub-units belonging to neighbouring molecules.     

The quantitative analysis of nano-clay dispersion in polymer nanocomposites by small angle X-ray scattering combined with electron microscopy

The main objective of this work is to propose a new approach for the quantitative analysis of the degree of dispersion of clay particles in the polymer matrix by small angle X-ray scattering (SAXS) combined with electron microscopy. Due to the low temperature processibility and good thermal stability, poly[(butylene succinate)-co-adipate] (PBSA) was chosen as a model polymer matrix for this study. The nanocomposites of PBSA with four different weight percentages of organically modified montmorillonite (OMMT) loadings were prepared via melt-blending method. The dispersed structure of the clay particles in the PBSA matrix was studied by SAXS. Results show that the clay particles are nicely dispersed in the case of all nanocomposites. However, with a systematic increase in clay loading, the dispersed clay structure of the nanocomposites changes from a highly delaminated to a flocculated and then to a stacked intercalated one. The probability of finding neighboring clay particles in the PBSA matrix as well as their thickness was calculated using the Generalized Indirect Fourier Transformation technique developed by Glatter and the modified Caillé theory proposed by Zhang. The morphology of the nanocomposites was also extensively studied by scanning transmission electron microscopy (STEM). In the case of all nanocomposites, SAXS results were in good agreement with STEM observations. Finally, a correlation between the predicted morphology of nanocomposites and their melt-state rheological properties is reported.     

Computer-aided experiment of using real-time small angle light scattering image processing technique for visual characterization flow field of polymer melts

The phenomenon of small angle light scattering (SALS) has been applied to the actual extrusion molding process. The current study utilizes a self-designed mold with built-in windows for observation of polymer melts within a slit die. A high-speed charge-coupled-device (CCD) camera is used to record the SALS images in real-time with different process conditions for subsequent analysis. Modification algorithm has been proposed to eliminate the effect of multiple scattering. Flow behavior of polymer melts is simulated and analyzed by real-time SALS image processing technique. Visualization is performed via a high-performance computer-aided analysis software which allows on-line data acquisition and characterization the flow field of polymer melts.     

Small-angle neutron scattering of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers

Small-angle neutron scattering was used to characterize the structure of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers dissolved in methanol-d4 (CD₃OD). A radial density profile based on a power law functional form provided a good fit to the scattering data. While a model with homogeneous density profiles in the core and shell, respectively, and with a size distribution (a polydisperse core-shell model) also fits the data comparably well, the extra parameters required for this fit are difficult to justify on the basis of the data. In addition, unconstrained fits using the core-shell model failed to converge to values of the overall molecular size and molecular weight which agreed with values determined from independent light scattering measurements which leads to the conclusion that the power law model is a more appropriate function for describing the radial density function of these molecules. The density profile from either model showed that the polystyrene core of the molecules is not collapsed. Values of the second virial coefficient, A₂, have been calculated from Zimm plots and it was found that A₂ decreased as a function of generation to close to zero for the highest generation (i.e. highest molecular weight) polymers. Finally, it was found that the radius of gyration of the polymers increases with the molecular weight according to the scaling relationship, R_g∼M_w^v with v=0.24±0.04.     

Quantification of organoclay dispersion and lamellar morphology in poly(propylene)-clay nanocomposites with small angle X-ray scattering

Intensity profiles of small angle X-ray scattering (SAXS) curves were analyzed to simultaneously gain quantitative information on nanoclay dispersion as well as lamellar ordering in polypropylene-clay nanocomposites. Different types of PP nanocomposites prepared with PP homopolymer (HPP), random propylene-ethylene copolymer (RCP) and a high impact polypropylene-ethylene propylene rubber (ICP) were analyzed. Various one-dimensional models for stacked structures were applied on Lorentz corrected SAXS spectra to derive long period, thicknesses of alternating high and low electron density layers and their distributions, and the number of stacks for both nanoclay and PP lamellae. We applied a mixed thickness distribution model comprising combined Gaussian and exponential for a simple stack of finite thickness, which was found to explain the experimental data better for both nanoclay tactoids and lamellar stacks, compared to simple Gaussian and exponential thickness distributions. Long period X and number of stacks N were derived as important parameters signifying changes in levels of nanoclay exfoliation in PP. Among the three types of polypropylenes studied, better nanoclay exfoliation was obtained for the high impact ICP grade compared to HPP and RCP. Complete exfoliation of nanoclay was achieved in ICP matrix, employing a masterbatch processing route. Moreover, role of nanoclay as a γ nucleating agent was evident from small and wide angle X-ray analyses, and was seen strongly in RCP. Changes in lamellar structure of PP as a result of nanoclay incorporation, double population consisting of both α and γ polytypes in the nanocomposites from that of a primarily α population in neat polymer matrices, were also analyzed in detail with the mixed thickness distribution model, thereby demonstrating its usefulness.     

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.