Reaction-limited aggregation

Let us illustrate first how different (idealized) aggregation processes may result in different structures. There is extensive literature on diffusion-limited aggregation (DLA) (for a comprehensive review, see Meakin, 1988). Three methods of simulation are common (standard) diffusion-limited aggregation (DLA), reaction-limited aggregation (RLA), and linear trajectory aggregation (LTA). DLA structures are generated by placing a seed particle in the middle of a lattice. Other particles are placed in the lattice... 

Fig. 37. Typical clusters obtained by diffusion-limited aggregation (DLA). Top Two-dimensional diffusion-limited aggregation. Bottom Reaction-limited hierarchical cluster-cluster aggregation (HCCA) (Meakin, 1988 with permission, from the Annual Review of Physical Chemistry, Vol. 39. by Annual Reviews www.Annual/Reviews.org).

In situ SAXS investigations of a variety of sol-gel-derived silicates are consistent with the above predictions. For example, silicate species formed by hydrolysis of TEOS at pH 11.5 and H20/Si = 12, conditions in which we expect monomers to be continually produced by dissolution, are dense, uniform particles with well defined interfaces as determined in SAXS experiments by the Porod slope of -4 (non-fractal) (Brinker, C. J., Hurd, A. J. and Ward, K. D., in press). By comparison, silicate polymers formed by hydrolysis at pH 2 and H20/Si = 5, conditions in which we expect reaction-limited cluster-cluster aggregation with an absence of monomer due to the hydrolytic stability of siloxane bonds, are fractal structures characterized by D - 1.9 (Porod slope — -1.9) (29-30). 

Cell or tissue lysates represent the crudest tissue fraction. Use of lysates is practical when the level of enzyme is relatively high. However, lysates have a tendency to form aggregates, which limits the maximum protein concentration which can be used and also limits the time for which the reaction to be studied is linear. Typically, protein concentrations of less than 3 mg/ml must be used and incubation time is limited to about 30 min. This can be an important limitation for substrates which are metabolized very slowly. In addition, cell fractionation is not limited to primary tissues. Fractions can be prepared from cDNA-expressing cell lines. This can provide a level of convenience to the researcher relative to the demands of maintaining multiple cell lines for extended periods of time. 

Figure 39. (a) XRD spectrum of 0.93% Ni2+ ZnO aggregates prepared by reaction-limited... 

P. Meakin, The effects of attractive and repulsive interaction on three-dimensional reaction-limited aggregation, J. Colloid Interface Sci. 134 235 (1990). 

The total volume fraction, 7 ( ), as a function of time for both reaction limited aggregation (RLA) and diffusion limited aggregation (DLA)... 

Computer simulations of a similar growth process, called reaction-limited cluster-cluster aggregation, have been performed (IS). This simulation... 

It tlocs can interpenetrate to some extent after contacting, the floe becomes denser and Df increases to Df 2.0-2.2, which corresponds to slow flocculation, or reaction-limited aggregation. ... 

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