Analysis of the Beaucage model Hammouda, Boualem
Journal of applied crystallography,
December 2010, Volume:
43, Issue:
6
Journal Article
Peer reviewed
The Beaucage model is used to analyze small‐angle scattering (SAS) data from fractal and particulate systems. It models the Guinier and Porod regions with a smooth transition between them and yields ...a radius of gyration and a Porod exponent. This model is an approximate form of an earlier polymer fractal model that has been generalized to cover a wider scope. The practice of allowing both the Guinier and the Porod scale factors to vary independently during nonlinear least‐squares fits introduces undesired artefacts in the fitting of SAS data to this model. Such artefacts as well as an error in the original formulation of the model are discussed. This model is compared with other published models.
Cilj je ovoga preglednog rada ukazati na moguće rizike prijevremenoga poroda za daljnji razvoj djece te prikazati rezultate recentnih istraživanja psihofizičkoga zdravlja roditelja prijevremeno ...rođene djece. Istraživanja pokazuju da posljedice koje prijevremeno rođenje ima za djecu mogu biti ozbiljne, pri čemu rizik od neurorazvojnih poremećaja raste s nižom gestacijskom dobi djeteta i nižom porodnom težinom. Rizici prijevremenoga rođenja djeteta za roditelje mogu se očitovati neposredno i/ili dugoročno, od akutne stresne reakcije do poslijetraumatskoga stresnog sindroma, poteškoća u razvoju privrženosti, perzistirajuće intenzivne brige i straha za dijete, što je dodatno naglašeno prelaskom djeteta iz bolničkoga okruženja na kućnu njegu. Inicijalna emocionalna i informativna podrška medicinskoga osoblja, prakticiranje tzv. klokanske njege, dostupnost stručnjaka za mentalno zdravlje te neformalni izvori podrške izuzetno su važni čimbenici prilagodbe roditelja. Pregled suvremenih istraživanja upućuje na potrebu za daljnjim ispitivanjima čimbenika koji se dovode u vezu s (ne)uspješnom psihofizičkom prilagodbom roditelja na prijevremeno rođenje djeteta i skrb o nedonoščetu. Budući da je adekvatno suočavanje roditelja važan preduvjet razvojnih ishoda kod neurorizične djece, bitno je osigurati programe podrške roditeljima da bi se osnažila njihova znanja i kompetencije.
A new Guinier-Porod model Hammouda, Boualem
Journal of applied crystallography,
August 2010, Volume:
43, Issue:
4
Journal Article
Peer reviewed
Small‐angle scattering (SAS) curves are characterized by two main features: the Guinier region and the Porod region. Standard linear plots are available to fit SAS data and obtain a radius of ...gyration and a Porod exponent. A new Guinier–Porod empirical model is introduced to fit SAS data from spherical as well as nonspherical objects such as rods or platelets. It also applies to shapes intermediate between spheres and rods or between rods and platelets. The new model is used to fit SAS data from a Pluronic solution that sequentially forms unimers, then spherical micelles, then cylindrical micelles, then lamellar micelles upon heating. This single model can fit structures associated with all four phases as well as the intermediate structures.
Pronounced fibres are formed through simple shearing of a dense calcium caseinate dispersion. Both mechanical tests and scanning electron microscopy images demonstrate that the material is ...anisotropic. It is hypothesised that calcium caseinate aggregates, under shear, align into micro-fibres and bundle further into a hierarchical structure. Yet no direct evidence at the sub-micron length scale can support the assumption. Small angle neutron scattering (SANS) experiments were conducted on calcium caseinate samples prepared at different conditions. Analysis of the SANS data revealed that the micro-fibres have a diameter of ∼100nm and a length of ∼300nm. The addition of enzyme and air contributed to longer and thinner micro-fibres. Furthermore, the extent of fibre alignment at the micro-scale and the macroscopic anisotropy index followed the same trends with varying processing conditions. It is concluded that the material does indeed possess a hierarchical structure and the micro-fibres are responsible for the anisotropy on the macro-scale.
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•Micro-fibres in calcium caseinate were studied by small angle neutron scattering.•The micro-fibres have a diameter of ∼100nm and a length of ∼300nm.•The addition of enzyme and air contributed to longer and thinner fibres.•The micro-fibres are responsible for the mechanical properties at the macro-scale.
The formation of calcium carbonate (CaCO3) nanoparticles (NPs) in the presence of polystyrene sulfonate (PSS) as an additive was examined by time‐resolved small‐angle X‐ray scattering (SAXS) in a ...flow system that mimics experimental conditions used at home facilities where the precipitation can be achieved in a beaker. The experiments were carried out at low concentrations to remain in the dilute regime. A model‐independent analysis was performed using the Porod invariant which defines the scale factor, leaving only the distribution of radii as the adjustable parameter. The presence of the PSS additive strongly retards the precipitation of CaCO3 NPs. The formation of NPs reaches a state of equilibrium after a few minutes. Here, it is shown that the concentration of precursors at a fixed PSS concentration plays a key role in determining the size of the NPs obtained. A full analysis of the SAXS patterns was carried out using the Hurd–Flower model to account for the weaker intensity decay than the classical Porod behaviour. The temporal evolution of the particle radii was determined. Wide‐angle X‐ray scattering experiments carried out simultaneously show that the particles formed have the structure of vaterite with growth consistent with the evolution of the Porod invariant.
The kinetics of precipitation of CaCO3 particles in the presence of polystyrene sulfonate was studied by small‐ and wide‐angle X‐ray scattering. Employment of the Porod invariant and the Hurd–Flower model provides essential information on the kinetics.
Controlling particle dispersity is of huge importance for practical applications in nanoscience and technology. The analysis of small‐angle scattering of X‐rays and neutrons for strongly polydisperse ...particulate systems is considered from the point of view of describing the type of size distribution function without applying classical regularization approaches. This article presents the development of a method for determining the polydispersity parameters of nanoobjects, based on the analysis of the ratio of various moments of the size distribution function, which are proportional to different invariants of the scattering curve. The use of the unified exponential/power‐law approximation to describe small‐angle scattering data makes it possible to determine the type of distribution, the average size and the spread. The possibilities of the method were tested for several hydrosols of metallic nanoparticles.
This article introduces a generalized approach to determine polydispersity characteristics from small‐angle scattering analysis based on the Beaucage model without numerical integration of experimental data.
The concave behaviour of the Porod invariant observed during the calcination of CaCO3 powder samples suggests the following picture of the evolving internal structure of the samples. The outset ...sample is formed by a crystalline CaCO3 phase and a void phase. During the calcination, the first phase shrinks in volume at fixed density since the temperature increase breaks down the crystalline structure at the interface, leading to the formation of an amorphous phase comprising an equal number of CO2 and CaO atomic groups. The last groups gradually condense, forming a third phase of solid CaO of constant density and increasing volume fraction, while the companion CO2 groups flow out of the sample. The amorphous phase occupies, with a variable density, all the volume left free by the other two phases. At the end of the calcination, both the volume fraction of the first phase and the density of the amorphous phase vanish so that the sample will again be made up of two phases: the voids and the solid CaO. Best‐fitting the resulting theoretical expressions of the Porod invariant and of the Porod law coefficient to the observed values, one can determine the matter densities, volume fractions and specific surface areas of the phases.
The chemical structures of the phases of CaCO3 samples undergoing a calcination process, as well as the volume fractions and matter densities of those phases, are determined by the Porod invariant behaviour.
A new method to estimate the size distribution of non‐interacting colloidal particles from small‐angle scattering data is presented. The method demonstrates that the distribution can be efficiently ...retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log‐normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small‐angle X‐ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.
A new and efficient method for the estimation of particle‐size distribution from small‐angle scattering data is presented. This method is based on features of the Porod plot.
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