Aggregate model limitation

To explain these findings, we nse a compnter diffiision-hmited clnster-cluster aggregation model, as described in Section 3.1.1. The optical properties of the aggregates are compnted by the conpled dipole method and by a rigorous GMM and T-matrix methods. The bulk optical constants of metals are modified by the size-limiting effect of nanoparticles [20]. It was shown that a modified version of DDA [58] allows one to explain the shape of the experimental spectra for DLCA aggregates and the dependence of the spectra on the particle size. 

Fig. 11.8 A comparison between experimental moduli for low-density polyethylene filaments and values calculated using the aggregate model with values of (P2(cos 8)) and (P4(cos S)) derived from NMR measurements for the crystailine material. (Reproduced by permission of lOP Publishing Limited.)...

Another limiting case (chemically limited aggregation model) corresponds to Dj.= 2.11 [58]. According to the Eq. (76) this value corresponds to p 0.009, that is close to p = 0.01 according to the indicated model [125], Now a different factors effect on the value p (and, hence, kr) can be estimated, using the Eq. (76). 

The authors [10] used the considered above physical model for dimethyldial-lylammoniumchloride (DMDAACh) radical polymerization [1] description. As it was shown in work [8], the radical polymerization of DMDAACh was simulated by the diffusion-limited aggregation model according to mechanism cluster-cluster. This means, that the indicated process is realized by small macromolecular coils merging into larger ones. This treatment allows to simirlate DMDAACh polymerization as the Eq. (2) with the Eq. (4) or (6) depending on the space type, in which it is realized. In this case the value pA can be determined as follows [10] ... 

The fractal approach was also used to investigate adsorption and desorption mechanisms of water vapor on active carbons that were derived from coconut shell, coal, coke and pitch fiber featuring a wide range of BET specific surface areas [78]. A values were measured for the water clusters adsorbed on primary carbon centers. Values ranging from 1.64 to 1.67 implied a diffusion-limited aggregation model on a pore wall plane, whereas higher A values (up to 1.86), measured at a relative pressure X = 0.95, implied the formation of water clusters that were partly merged vertically to the walls. 

The main conclusion of the present paper is that, what reaction cessation in polycondensation process is limited by purely physical factor, namely, the achievement of macromolecular coil density of solution density in which reaction proceeds. The possibility of such treatment is due fully to macromolecular coil fractality. The indicated processes are simulated within the framework of an irreversible aggregation models over mechanism cluster-cluster. The critical values of molecular weight and reaction duration, above which a S5mthesis reaction ceases, exist. 

DLA Diffusion-limited-aggregation, an aggregation model in which monomers add to clusters upon contact... 

RLA Reaction-limited aggregation, an aggregation model similar to DLA, except with a finite probability of forming a bond upon contact between objects... 

Ferreira Jr, S.C. Effects of the screening breakdown in the diffusion-limited aggregation model. Eur. Phys. J. 42, 263 (2004)... 

Phys. Rev. Lett. 51(13), 1119-1122 (1983). doi 10.1103/PhysRevLett.51.1119 P. Meakin, The effects of rotational diffusion on the fractal dimensionality of stiuctures formed by cluster-cluster aggregation. J. Chem. Phys. 81(10), 4637-4639 (1984a). doi 10.1063/L447398 P. Meakin, Diffusion-limited aggregation in three dimensions results from a new eluster-eluster aggregation model. J. Colloid Interface Sci. 102(2), 491-504 (1984b). doi 10.1016/0021-9797 (84)90252-2... 

The concentration of monomers plays a very important role in aggregation models. We discussed this earlier in Section 9.4.2, where we noted that percolation through a network becomes realized only when a limit concentration of connections is exceeded. 

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