Heterocoagulation of latexes of types A and B implies that collisions involving identical particles do not lead to aggregation, successful collisions being those involving A and B particles. If each collision between suitable particles systematically leads to interparticle sticking, the process is diffusion limited. On the contrary, when chemical reactions are required before sticking succeeds, the

FIG. 1 Representation of the variation of the exponents w (O), z (□) and T (•) as a function of the degree of surface coverage 8 determined using Eqs. (1) and (2) for aggregation of polystyrene latex particles of diameter 900 nm induced by adsorption of a spherical rigid ligand of diameter close to 80 nm. Full surface coverage is expected to occur when 500 ligand molecules are deposited on the latex surface.

FIG. 1 Representation of the variation of the exponents w (O), z (□) and T (•) as a function of the degree of surface coverage 8 determined using Eqs. (1) and (2) for aggregation of polystyrene latex particles of diameter 900 nm induced by adsorption of a spherical rigid ligand of diameter close to 80 nm. Full surface coverage is expected to occur when 500 ligand molecules are deposited on the latex surface.

process is reaction limited. Studies of the influence of unsuccessful A-A and B-B collisions on the aggregation rate in simulations of heterocoagulation provided the exponents of the dynamic scaling laws as a function of the composition x of the system. The dynamic exponents z(x) and w(x) of the heterocoagulation kinetics expressed by the temporal variations of the weight S(t) and number N(t) average masses were found to be strongly correlated to and independent of the aggregation ability (mobility and reactivity) [11,12]:

For reaction-limited heterocoagulation, which seems to control aggregation processes based on site-ligand interactions, the slowing of the kinetics resulting from the existence of inefficient collisions is expressed as follows:

where z and w are the exponents of the temporal variations of S(t) and W(t) derived from simulation studies of homocoagulation. The value of the exponent z(x) of the temporal variation of S(t) is given by:

where k, always smaller than 1, depends only on the nature of the process. Therefore, assuming the efficiency of collisions P(9) to be correlated with the kinetics of aggregate growth, P(9) is expressed by a power law of the surface coverage. Three extreme situations can be envisaged [24,25]:

1. The antigen is initially immunoadsorbed on latex A with a degree of coverage equal to 9' while latex B remains free of antigen. The probability P(0') of doublet formation is given by:

2. The antigen is rapidly immunoadsorbed on the two latexes A and B with a degree of coverage equal to 9 = 9'/2 on each latex, with the probability of doublet formation being given analogically by:

In the case of asymmetrical coverage 9j and 92, with 9j + 92 = 9', Eq. (8) is modified to:

Asymmetrical situations were studied by Meakin and Djordjevic, who determined the reaction rate as a function of the composition of the system and the functionality of the latices [10]. These authors concluded that S(t) and N(t) always followed a power law behavior after an initial non-scaling growth regime.

3. The kinetics of the immunoadsorption limits the aggregation rate. In this situation, the probability of doublet formation increases with antigen concentration and the aggregation is delayed.

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