Static Scattering Techniques

Scattering is the dispersal of radiation at an object (particle) that differs in the relevant material properties from its environment (continuous phase). Static scattering experiments record the scattering signal as a function of the angle of observation 0 or—more generally— as function of the scattering vector q  

Scattering experiments can be conducted with any kind of radiation (e.g. sound, electromagnetic waves, neutron radiation). This book will be confined to the scattering of light and X-rays, as these two types are most frequentiy used for the characterisation of colloidal suspensions. Both belong to electromagnetic radiation, yet the mechanisms of interaction with matter are completely dUferent. This difference becomes manifest in the refractive indices, which deviate qualitatively. For this reason, both types of radiation are separately discussed. 

Silica particles have a refractive index of approximately 1.45 in the domain of visible light. That is significantly different to the refractive index of walta (1.33), which often serves as suspension medium. In contrast, there is only a weak contrast between the two substances in the domain of X-radiation. At a wavelength of 1 A, one finds a complex refractive index of 0.999997-1.7 x 10 i for silica and 0.999999-2.1 x 10 -i for water (cf. Henke etal. 1993). 

The various static scattering techniques rely on different types of interaction between particles and radiation. Additionally, they are used for the determination of rather dissimilar measurands (e.g. average molecular weight, particle size distribution, shape parameters). This diversity of physical basis and experimental objective has led to very specific ways of data analysis, yet all of them are based on the following principal dependency of the scattering signal  

This is an inversion problem as defined in Eq. (2.2). Firstly, this means that its solution requires specifically adapted numerical algorithms and, secondly, that details of the size distribution can be resolved only to a certain extent. 

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In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

Bastide J, Candau SJ (1996) Structure of gels as investigated by means of static scattering techniques. In Cohen Addad JP (ed) Physical properties of polymeric gels. Wiley, New York... 

Characterisation of Pyrogenic Aggregates with Static Scattering Techniques... 

This quantity is measured in static scattering techniques using light, x-rays, and neutrons. 

Scattering techniques Static light scattering Mw( a) M>104 300a Moderate to high... 

The decay of the structural correlations measured by the static structure factor can be studied by dynamic scattering techniques. From the simulations, the decay of structural correlations is determined most directly by calculating the coherent intermediate scattering function, which differs from Eq. [1] by a time shift in one of the particle positions as defined in Eq. [2] ... 

Measurement of the static structure factor using scattering techniques also provides us with a nonintrusive method to probe the structure of dispersions and the nature of interaction forces in colloids. Structural changes in colloids are particularly of interest in colloid-based techniques for fabrication of structural and special-purpose ceramics. 

Hard X-ray scattering techniques have been applied to the chemical imaging of an enormous range of systems, primarily systems that are not perfectly ordered or static. Problems addressed include ... 

It is very well known that the nature of the monolayer partially depends on the strength of interfacial interactions with substrate molecules and that of polymer in-tersegmental interactions. And it is normal to expect that the viscoelastic properties of polymer monolayer are also dependent on these factors. The static and dynamic properties of several different polymer monolayers at the air - water interface have been examined with the surface quasi-elastic Light Scattering technique combined with the static Wilhelmy plate method [101]. 

The size distribution of solid samples can be determined by static and dynamic light-scattering techniques the size ranges from a few nanometers to a few microns. The concept uses the idea that small particles in a suspension move in a random pattern called Brownian motion. When the moving particles are irradiated by a... 

The structure, however, is not static but is subject to thermally driven fluctuations. The local structure changes continuously as a function of time due to orientational and translational molecular motions. The time scale of these motions may range from nanoseconds up to several hundred years. The structure of the amorphous state as well as its time-dependent fluctuations can be analysed by various scattering techniques, such as X-ray, neutron, electron and light scattering. 

Berth, G., Dautzenberg, H. and Rother, G. 1994. Static light scattering technique applied to pectin in dilute solution. Part II. The effects of clarification, Carbohydr. Polym., 25 187-195. 

Scattering techniques for measuring various static and thermodynamic properties of polymers, such as molar mass, size, conformations, interaction parameters, etc. were described in experimental sections of Chapters 1-5. In addition to static properties, scattering can provide important information about dynamic properties of polymeric systems. This section focuses on dynamic scattering from dilute solutions, but similar methods are used in semidilute and concentrated solutions."... 

Scattering methods provide detailed information about the structural parameters of colloidal particles. In the field of polyelectrolyte complexes, mainly light scattering techniques such as static, dynamic, and electrophoretic light scattering were employed. 

As already mentioned in the discussion of fractals, small-angle X-ray scattering (SAXS) and static light-scattering techniques may be used to measure the fractal dimension of objects with radii on the order of 102-104 A (12). 

Both static and dynamic light-scattering techniques will continue to find wide applications in the study of the structure of more concentrated systems. 

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