The temporal variations of the average masses S(t) and N(t) represented in Fig.
7 show the aggregation process to develop extremely slowly up to doublet formation and to really start after 600 min. In domain I, the aggregation develops with features of the reaction-limited aggregation process: S(t) and N(t) increase
as exp(t) (not represented) . This behavior later develops in domain II according to power laws as usually observed in the reaction-limited aggregation process:
and the value t = -1.42 of slope of the reduced mass distribution agrees with that calculated using Eq. (3). In domain III, the mass distribution is represented by a bell-shaped distribution, which indicates that for such large aggregates the reaction-limited process tends to a situation where all collisions succeed insofar as a very large number of attempts are possible when one aggregate is exploring the total external envelope of the nearest neighbor. Once more, this behavior is usually observed in the long term in reaction-limited aggregation.
When the IgG-coated latex is only covered at 620 IU of IgM molecules per
latex, the aggregation process is reaction limited insofar as the process develops with features that were evidenced in numerical simulation of the reaction-limited process, and establishment of doublets resulting from the sticking of two single particles is a very time-consuming process . However, when the doublet concentration has reached a typical value, collisions between doublets and further between aggregates of greater masses lead to efficient sticking and the resulting aggregates appear to be extremely stable. Conversely to situations described in paragraphs 1 and 2, in the present case, the aggregation is not reversible, and the initially observed delay cannot be related to fragmentation but must be attributed to the fact that the low density of the IgM molecules on the IgG-coated latex does not favor efficient collisions.
When the system displays bell-shaped mass frequencies, which means that aggregates of a given mass are preponderant in the system, it should be noted that the aggregate mass present at the greatest concentration depends on the IgM
1 I I I 'l l I ll| 1 TTTTTTTj I I I I I I iij I TTTTTTTj
1 10 100 1000 10000 t (min)
FIG. 7 Concentration of IgM = 620 IU/g IgG-latex: representation of the number N(t) (□) and S(t) (O) average masses of the aggregates as a function of the aggregation time (min) (log-log scale).
concentration as represented in Fig. 8 using the reduced concentration and mass. When the concentration of IgM molecules passes form 620 to 1240 and 3770 IU/g latex, the mass of aggregates present at the greatest concentration goes from 0.18 to 0.28 and 0.44 x S(t), respectively. For an unknown system, the position of the concentration peak may serve to estimate the concentration of IgM molecules as shown in Fig. 9, without reference to additional tests.
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