Aggregate Shape

There is no evidence to suggest that coarse aggregate shape or geological origin affect the amount of air entrainment obtained. The only exception is where crushed rock aggregates contain an appreciable quantity of dust which could influence the fine aggregate gradings considered below. 

Since their effective diffusivities are of the same magnitude as those of micellar solutions, the hquid crystalUne phases, though viscous, do not significantly hinder surfactant dissolution for these rather hydrophihc surfactants. Indeed, a drop of Ci2(EO)6 having Ro = 78 pm dissolved completely in only 16 s at 30 °C. Rapid dissolution is favored because free energy decreases as the surfactant is transferred from the Hquid surfactant phase L2 to liquid crystals) to aqueous micellar solution and the aggregate shape approaches that of a dilute Li phase, where its free energy is minimized at this temperature. 

Aggregate Shapes and Long-Range Order of the Aggregates... 

According to our observations and to literature data (4, 19, 22, 24, 47, 49, 50, 54, 56, 63, 64, 65), the following aggregate shapes occur in the end structures spheres, ellipsoids, long, substantially cylindrical rods in... 

Symbol Aggregate shape Aggregate - cement ratio water cement ratio Fines content % Fines ione... 

In conclusion, (radial) mixing and the accompanying thermal processing of the grains are evident from both remote sensing and laboratory studies of protoplanetary dust. These mechanisms will be discussed extensively in Chapter 8. Further development of the remote sensing techniques requires accurate models of the optical properties and predictions on the aggregate shapes expected to form in disks. These will be discussed in Chapter 7. 

The shapes of these self-assemblies are as varied as the capacity of the molecules to weave through space will allow. The accessible interfacial geometries span a rich range of structures from spheres and planes to highly intercormected bicontinuous honeycombs. So how are the structures of these complex liquid crystalline and disordered assemblies best described and understood Typically, the problem is tackled by recourse to thermodynamic principles. A complete statistical mechanical treatment is out of the question. (The difficulty is a fundamental one. We do not yet know how to write down a partition faction that describes the full ensemble of possible aggregate shapes and their associated free energies.)... 

Particle size distributions are important information for evaluating the synthesis, growth and kinetics of formation of nanoparticles and nanoparticle aggregates. The main contrasting techniques are imaging via TEM, and SAXS analysis. TEM analysis is independent of the type of aggregation, shape and size of nanoparticles, whereas SAXS interpretation requires assumptions about the nature of the sample. On the other hand, SAXS can be done on in situ systems, and often in real time during particle formation. 

A theoretical explanation of experimental results, obtained for modified (non rigid spacer) gemini surfactants, was presented by Andelman and Diamant.47 They noted that the aggregate morphology for dimeric surfactants is related mainly to the influence of the spacer on the specific area X. The geometrical parameter, that determines aggregate shape, is the packing parameter denoted by the formula 48,49... 

Finally, two Al-neutralized copolyimides from (4,4 -hexafluoroisopropylidene) diphthalic anhydride, (4,4 -hexafluoroisopropylidene) dianiline, and 3,5-diaminobenzoic acid exhibit a variety of aggregate shapes and sizes that have not been previously observed or even postulated. Scanning TEM shows Al-rich aggregates in both copolymers, but the aggregate size and shape distributions in the ionomer with a high ionic fraction are much more heterogenous than in the ionomer with a lower ionic fraction. This is despite... 

I RTICLE-SIZE DISTRIBUTION AND OTHER PARTICLE CHARACTERISTICS, including degree of aggregation, shape, and porosity, strongly influence the properties of numerous forms of colloidal and particulate silica (I). The rapid and accurate measurement of these distributions and characteristics... 

Fig. 11.3 depicts schematically a sampling system fitted to a flame reactor with which newly created particles can be captured on a transmission electron microscope (TEM) grid, enabling direct measurement of sizes and morphology. Comparison of average aggregate shapes obtained from simulation with actual TEM pictures confirms that modeling is successful [11.Ij. 

The variation of this standard ehemical potential with aggregate size is important in determining whether micelles or aggregates will form. This reference potential also determines polydispersity and aggregate shape. For the sake of discussion we consider the formation of (one-dimensional aggregates) linear ehains of surfactants. We approximate the pairwise binding energy (relative to separated speeies) as akT. The standard reference potential is then written ... 

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