Scattering particle assembly

The Rayleigh scattering cross section for a dilute assembly of N scattering particles per unit volume is N times the cross section per particle. Note that there seems little in common between the formulas for Thomson and Rayleigh scattering. 

In scattering theory, one seeks to relate two well-defined situations, involving a scattered particle and a particle (or assembly of particles) which... 

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

Finally, we have designed and synthesized a series of block copolymer surfactants for C02 applications. It was anticipated that these materials would self-assemble in a C02 continuous phase to form micelles with a C02-phobic core and a C02-philic corona. For example, fluorocarbon-hydrocarbon block copolymers of PFOA and PS were synthesized utilizing controlled free radical methods [104]. Small angle neutron scattering studies have demonstrated that block copolymers of this type do indeed self-assemble in solution to form multimolecular micelles [117]. Figure 5 depicts a schematic representation of the micelles formed by these amphiphilic diblock copolymers in C02. Another block copolymer which has proven useful in the stabilization of colloidal particles is the siloxane based stabilizer PS-fr-PDMS [118,119]. Chemical... 

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. 

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 ... 

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... 

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