Aggregation rate constant

Schudel, M., Behrens, S. H., Holthoff, H., Kretzschmar, R., and Borkovec, M. (1997). Absolute aggregation rate constants of hematite particles in aqueous suspensions a comparison of two different surface moiphologies. J. Colloid Interface Sci. 196, 241-253. 

By using [P(H)LJ = )3 [P(H)][L] (ligand on and off fluxes are high enough to maintain the equilibrium of the population with the undeuterated amide site) and that [L] does not change as the site is deuterated, one obtains Equation 11.16 for the concentration of unreacted sites on the free protein beginning with the initial concentration of [P(H)],j and with the aggregate rate constant... 

In the presence of repulsive interactions, the sticking probability becomes smaller than 1 and the so-called slow aggregation regime may be realized. The slow aggregation rate constant, F may be estimated as ... 

While there is no point in reviewing many of the interesting developments in this rapidly advancing field, it is probably helpful to discuss one example illustrating the substantial potential of these techniques. Let us focus on the recent measurements of absolute aggregation rate constants of particle aggregation (13). This example does not only illustrate the possibilities of such time-resolved techniques for the study of kinetic processes, but also demonstrates that simultaneous SLS and DLS can provide access to novel information. 

Figure 18.9. Scatter plot of the static signal as a function of the dynamic signal V for latex particles of 580 nm diameter in M KCL electrolyte. The intercept of the straight line yields an absolute aggregation rate constant of 7.3 x s ...

Thus, plotting the static signal 5 as a function of the dynamic signal V yields a straight line, and its intercept gives the absolute aggregation rate constant. This analysis is now free of any assumptions about the optical or hydrodynamic properties of the dimer. However, the prerequisite is simultaneous availability of time-resolved SLS and DLS data. 

Solutes bound to micellar and microemulsion aggregates are in rapid equilibrium with free solute and aggregates. Rate constants for the exit of neutral solutes from ionic micelles are estimated at 10 -10 s ". Rates for recapture are near or at diffusion control. Rates of these processes are similar to equilibration rates between micelles and surfactant momomers. Solutes in micelles and microemulsions are most probably solubilized near the Stern layer or in the interfacial region. Hydrophilic or hydrophobic environments will be preferred depending on the properties of the particular solutie. There is little evidence for deep solute penetration into the core of the aggregate. Vesicles have much slower dynamics of solute equilibria. 

FIGURE 13.11 Aggregation rate constant versus degree of surface coverage for BSAm- and BSAp-covered samples at pH 4.8 and 0.700 M KCl. The lines show the best fit according to Equation 13.9. The corresponding fitting parameters are also included in the plot. 

The time evolution of the cluster size distribution, arising in an aggregating system may be obtained in the framework of Smoluchowski s equation once the aggregation kernel, that is, the set of aggregation rate constants is known. However, no valid kernel for the description of aggregation processes of functionalized particle suspensions is known [54]. In order to overcome this difficulty, we use the kernel... 

In case the active molecules split-off from aggregate rate constant ->0 (decay process of aggregates is neutralized), the concentration of active molecules outside the aggregate tends... 

In particular, it follows that the aggregation rate constant k depends on the average aggregate size, which is proportional to their overall mass F zst ... 

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