Aggregate theory

From the discussion of various simulation methods, it is clear that they will continue to play an important role in further development of aggregation theories as they have advanced the state of knowledge over the last 20 years. The major limitation of the precise methods of Molecular and Brownian Dynamics continues to be difficulty associated with treatment of aggregates with complex geometry the same topic that limits the ability to model these systems using von Smoluchowski s approach. Research needs to be conducted on the hydrodynamics of interactions between fractal aggregates of increasing complexity in order to advance the current ability to describe these types of systems. 

T. L. Farias, M. G. Carvalho, U. 0. Koylii, and G. M. Faeth, Computational Evaluation of Approximate Rayleigh-Debye-Gans/Fractal Aggregate Theory for the Absorption and Scattering Properties of Soot, ASME Journal of Heat Transfer, 117, pp. 152-159,1995. 

Structure deduced from the distinct four point pattern observed in samples which were annealed after drawing. For cold drawn polymers the assumption of a single phase structure implicit in the aggregate theory may therefore be valid. Some of the materials to which the aggregate theory has been applied were hot stretched (i.e. drawn above the glass transition temperature), but the annealing in these cases would be far from complete, since the temperature was maintained for a relatively short time, and the filaments were always under tension. Thus again a distinct two phase structure may not have been well developed. 

The variation of compliances with draw ratio for cold drawn polypropylene filaments examined at 20°C appeared very similar to that of high density polyethylene, with an increase in all compliances but Sii, which was insensitive to draw ratio. Ward aggregate theory was not applicable except for low draw ratios, implying that other processes intervened in addition to an orientation of pre-existing units. It was probable that even above the glass transition temperature increasing orientation led to a reduction in molecular mobility, as was known to occur in polyethylene terephthalate. ... 

In a comprehensive study at room temperature, Hadley, Pinnock and Ward [20] determined the five independent elastic constants for oriented filaments of polyethylene terephthalate, nylon 6 6, low and high-density polyethylene and polypropylene. The orientation was determined in terms of draw ratio and optical birefringence. Subsequent studies indicated that it would have been appropriate to record not only the overall orientation, as derived from birefringence, but also the crystal orientation, obtainable from X-ray measurements. The results are summarized in Table 7.1 and Figures 7.9-7.13 (see Section 7.5 for discussion of the aggregate theory predictions). 

Figure 7.9 Low-density polyethylene filaments extensional ( 3), transverse ( 1) and torsional moduli (G) comparison between experimental results and simple aggregate theory for 3 and 1 ((a) and (b)) and for G (c)...

Monteagudo et al characterized the asphaltenes as a continuous ensemble for which the distribution function was taken from the fractal aggregation theory. The asphaltene family was discretized in pseudo-components by the Gauss-Laguerre quadrature. Only the asphaltene polydispersity was taken into account. All other components were represented by as solvent whose properties (molar volume and solubility parameter) were calculated form a cubic equations of state. Aggregation of asphaltenes was considered to be a reversible process. And it was assumed the phase equilibrium was between a liquid phase and a pseudo-liquid phase containing only asphaltenes. 

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