Particle assembly, scattering from

Mandelkow et alP provided direct kinetic studies of nucleation by using 1 A synchrotron radiation to obtain time-resolved scattering data during cycles of assembly and disassembly after temperature shifts between 4 and 36°C. Small-angle scattering theory requires independent scattering from all particles in the solution, and the theory relates the intensity of scattering to other parameters as follows ... 

Other workers have adopted a different corpuscular model for quasielastic light scattering from a gel (122,123,124). The gel is treated as an assembly of identical, independent, harmonically bound particles, each in Brownian motion about a stationary mean position. The analysis of Garlson and co-workers (123,124) formally includes the presence of static interference scattering components resulting from spatial structuring of the polymer chains and from the consequent constraints in the diffusive motions of the chains. This formalism leads to the prediction of nonexponential scattered intensity autocorrelation functions. 

In the preceding theory only the scattering from individual particles has been considered. For an assembly of particles, the structure factor of eqn. (38) should be calculated by integrating over all particles in a unit volume as well as the surroundings of the particles. 

Melamed developed an elegant mathematical description of absorption and scatter from an assembly of close packed spheres [64], Unfortunately, it is remembered more for its failings than its elegance. The Melamed model embodied two assumptions There would be reflection from the front external surface of a particle (that would follow Lambert s cosine law for a sphere), and there would be isotopic scatter from inside the particle. Within the sphere, the model took into account an infinite number of internal reflections. The model predicts that reflectance would reach a maximum as the relative refractive index approached zero. Of course, if there is no refractive index difference between that of the particle and the medium, there is no reflection from the particle. 

As has been discussed previously(10-13), the X-ray scattering from assemblies of particles may be given by... 

E. Fucile, F. Borghese, P. Denti, R. Saija, Theoretical description of dynamic light scattering from an assembly of large axially S5unmetric particles, J. Opt. Soc. Am. A 10, 2611 (1993)... 

Order and polydispersity are key parameters that characterize many self-assembled systems. However, accurate measurement of particle sizes in concentrated solution-phase systems, and determination of crystallinity for thin-film systems, remain problematic. While inverse methods such as scattering and diffraction provide measures of these properties, often the physical information derived from such data is ambiguous and model dependent. Hence development of improved theory and data analysis methods for extracting real-space information from inverse methods is a priority. 

X-ray scattering (SAXS) plots of nanoparticle assembly indicating systematic control of inter-particle distance by dendrimer generations. Reprinted with permission from Frankamp, Boal, et al. (2002). Copyright 2002 American Chemical Society. 

These different casein monomers combine with calcium phosphate to form discrete particles on the nano-size scale. The phosphoserines of the caseins are seemingly clustered for the purpose of linking within the micelle to putative calcium phosphate microcrystallites, also known as nanoclusters (Holt, 1992 Home, 1998, 2002, 2003, 2006 Holt et al., 2003 Home et al., 2007). Structural evidence for the existence of such nanoclusters has come from neutron and X-ray scattering (de Kruif and Holt, 2003 Holt et al., 2003 Pignon et al., 2004 Marchin et al., 2007). The presence of nanoclusters allows native casein micelles to be effective natural suppliers of essential calcium salts in the human diet in a readily assimilated functional form. Protein-nanocluster interactions are the central concept of the cross-linking mechanism in Holt s model of casein micellar assembly (Holt et al., 2003 de Kruif and Holt, 2003). Any analogy with conventional soap-like micelles is considered to be... 

Fig. 5 a Nanoparticle assembly using PAMAM dendrimers. b Small-angle X-ray scattering plots, demonstrating increasing inter-particle distances with increasing dendrimer generation. Reprinted with permission from [76]... 

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