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Notes: Small-angle x-ray scattering is used to study size distributions of noble metal nanoparticles embedded in polyelectrolyte hydrogels with oppositely charged surfactants. A procedure is proposed to subtract matrix scattering and to extract pure scattering due to the nanoparticles allowing to evaluate their size distribution functions by means of a regularization technique. Two kinds of collapsed gel-surfactant complexes were studied: a complex of a cationic gel of poly(diallyldimethylammonium chloride) with an anionic surfactant sodium dodecyl sulfate (PDADMACl/SDS), and that of an anionic gel of poly(methacrylic acid) with a cationic surfactant cetylpyridinium chloride (PMA/CPC). Addition of a gold compound (HAuCl4⋅3H2O) to the PDADMACl/SDS system forms the metal compound clusters and leads to a partial distortion of the gel structure. After subsequent reduction of the gold compound with sodium borohydride (NaBH4) ordering in the gel disappears and gold nanoparticles are formed. Their size distribution includes a fraction of small particles with approximately the same size as the compound clusters before reduction and a fraction of larger particles with the radii up to 40 nm. For the collapsed PDADMACl/SDS gels, aging does not change the size distribution profile; for the noncollapsed PDADMACl gels without surfactant, metal particles are found to grow with time. This suggests that the aggregation of metal colloids is prevented by the ordering in the collapsed gel-surfactant complex. The addition of HAuCl4⋅3H2O and the subsequent reduction of the metal ions in the PMA/CPC system does not distort the gel structure as the degree of incorporation of AuCl4− ions is very low. Particle sizes in the PMA/CPC system are found to be somewhat larger than those in the PDADMACl/SDS system. The PDADMACl/SDS gels loaded with the PtCl4 compound were also studied to analyze the influence of the reducing agent type on the particle size distribution distributions. Fast reduction with NaBH4 yielded mostly small particles with the radii around 2 nm grown from the compound clusters similar to those observed for the gold-loaded gels. In contrast, slow reduction with N2H4⋅H2O was found to produce larger nanoparticles and the size distribution function shows a major fraction of the particles with the radii up to 30 nm. © 1998 American Institute of Physics.

Notes: A method for nonlinear fitting of x-ray scattering data from polydisperse mixtures was developed. It was applied to the analysis of the structural changes in the droplet phase of oil-rich water-in-oil (w/o) sodium bis(2-ethylhexyl) sulfosuccinate (AOT) microemulsions with increasing temperature or upon addition of salt. Data were collected at different temperatures (15 to 60 °C) and salt concentrations (up to 0.6% NaCl) within the one-phase region of the L2 phase (w/o microemulsion) for different droplet sizes (water/AOT molar ratio wo=25 to 56) and concentrations (droplet weight fraction cw=2% to 20%). This allowed us to distinguish between contributions from individual scattering particles, e.g., droplets and cylinders to the total scattering intensity. The complete data set containing over 500 scattering curves could be interpreted by fitting the scattering of weighted sums of AOT covered water droplets, long cylinders, and inverse AOT micelles containing bound water only, to the experimental scattering curves. The polydispersity of the droplets and cylinders is described by Schulz distributions and the interactions between the droplets are calculated using a sticky hard-sphere potential in the Percus–Yevick approximation. The volume fractions of the components, their average sizes and polydispersity, and the stickiness of the water/AOT droplets are determined by a nonlinear fit to the experimental data. © 2000 American Institute of Physics.

Notes: A method is presented for automated best-matching alignment of three-dimensional models represented by ensembles of points. A normalized spatial discrepancy (NSD) is introduced as a proximity measure between three-dimensional objects. Starting from an inertia-axes alignment, the algorithm minimizes the NSD; the final value of the NSD provides a quantitative estimate of similarity between the objects. The method is implemented in a computer program. Simulations have been performed to test its performance on model structures with specified numbers of points ranging from a few to a few thousand. The method can be used for comparative analysis of structural models obtained by different methods, e.g. of high-resolution crystallographic atomic structures and low-resolution models from solution scattering or electron microscopy.

Notes: Three different small-angle neutron scattering facilities, the "YUMO" camera at JINR (Dubna, Russia), the V4 camera at HMI (Berlin, Germany) and D11 camera at ILL (Grenoble, France), were used in the investigation of 30S ribosomal subunit from Thermus thermophilus. Parallel X-ray measurements on X33 camera at DESY (Hamburg, Germany) were used to control the identity of deuterated particles. The neutron and x-ray contrast variation data were interpreted by direct method using spherical harmonics. Structural models of the 30S ribosomal subunit from Thermus thermophilus and its RNA -rich core with the resolution 3.5 nm were constructed. A comparison between the 30S Thermus thermophilus and 30S E.coli models shows that primary difference between them consists in the special distributions of the protein component whereas the special distributions of the RNA component coincide well in both models.

Notes: A method for ab initio low-resolution shape and internal structure retrieval from contrast variation solution scattering data is described. The method uses a multiphase model of a particle build from densely packed dummy atoms and employs simulated annealing to find a compact interconnected configuration of phases that fits the available experimental data. In the particular case of a single phase particle (shape determination) the method is compared to another ab initio method using low resolution envelope functions. Examples of the shape determination of several proteins from experimental X-ray scattering data are presented.

Notes: The problem of error propagation using indirect methods for small-angle scattering data treatment is considered. In these methods, the number of parameters to be determined is normally larger than the maximum number of independent parameters predicted by the Shannon sampling theorem and the solution has to be regularized. It is shown in model examples that evaluation of the error propagation via the covariance matrix can lead to significant overestimation of the propagated errors. The reason is that the procedure involves inversion of an ill-conditioned matrix. As an alternative, the Monte Carlo simulation procedure is recommended.

Notes: A program, MASSHA, for three-dimensional rendering and rigid-body refinement is presented. The program allows display and manipulation of high-resolution atomic structures and low-resolution models represented as smooth envelopes or ensembles of beads. MASSHA is coupled with a computational module to align structural models of different nature and resolution automatically. The main feature is the possibility for rigid-body refinement of the quaternary structure of macromolecular complexes. If high- or low-resolution models of individual subunits are available, the complex can be constructed on the computer display and refined to fit the experimental solution scattering data. MASSHA provides both interactive and automated refinement modes to position subunits in a heterodimeric complex (general case) and in a homodimeric complex with a twofold symmetry axis. Examples of application of the program (running on IBM PC compatible machines under Windows 9x/NT/2000) are given.

Notes: Applications of modern mathematical methods to the problems of small-angle scattering data treatment and interpretation are considered. Special possibilities in data treatment, namely simultaneous treatment of data sets obtained with different experimental conditions and joint data processing for the anomalous-dispersion experiments, are presented. The methods are further developments of the indirect method based on the regularization technique [Svergun, Semenyuk & Feigin (1988). Acta Cryst. A44, 244–250]. Recent improvements in the shape-determination technique based on the multipole expansion theory [Stuhrmann (1970). Z. Phys. Chem. (Frankfurt am Main), 72, 177–184, 185–198] are described. A new method is proposed for the determination of positioning and mutual orientation of subunits in complex particles using the spherical harmonics technique.