How to calculate average size of DLCA aggretaes at long times?

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Daniel José Pochapski

Through small-angle X-ray scattering (SAXS) measurements, you can determine the average size of the primary particles (the building blocks) of the fractal aggregate and their length and average size (calculated the gyration radius, correlation length, and fractal dimension). I suggest using the unified model of Guinier and Porod, and the mass fractal model. Furthermore, from the data provided by the SAXS curve fittings, you will be able to obtain 3D representations of the formed DLCA aggregates using the FracVAL algorithm. It is also possible to obtain other valuable information if dynamic light scattering (DLS) measurements are available.

I suggest reading this article for more information on determining such properties of nanoparticle aggregates (https://doi.org/10.1021/acs.langmuir.1c02056).

I also suggest reading this book: Suspensions of Colloidal Particles and Aggregates. In it, you will obtain information on how the primary particle influences the DLCA and RLCA aggregation mechanisms.

Sincerely, Daniel José Pochapski.

Mohamed Khedawy

You can read: Friction Coefficient and Mobility Radius of Fractal-Like Aggregates in the Transition Regime

Article Friction Coefficient and Mobility Radius of Fractal-Like Agg...

Chenxi Liang

Thank you for your advice and especially for the refence book! Besides, your paper about zeta potential is also very useful for me, since I'd like to use zeta potential to describe the stability of the primary particles.

I understand the average size of the primary particles can be determined through SAXS, but I'm looking for a theoretical formula to relate the size of the DLCA aggragates to the original concentration of the primary particles. Could you offer some advice?

You can do this in a few ways (directly and indirectly):

If SAXS or USAXS measurements are available, you will be able to determine the approximate number of first particles within the aggregate following the procedure described at https://doi.org/10.1063/1.1855391.

Another way to estimate the number of primary particles in an aggregate if SAXS or USAXS measurements are available can be found at https://doi.org/10.1016/j.cpc.2019.01.015. In this case, the number of particles within the aggregate (Np) can be determined by relating the gyration radius of the primary particle and the aggregate (Rg,p, and Rg,a, respectively) to the fractal dimension (df) and the proportionality constant kf, through the following equation: Np=kf(Rg,a/Rg,p)^df. For DLCA, df=~1.78 and kf=~ 1.40. Check this reference for the correct procedure:

Article Aggregate Morphology Evolution by Sintering: Number & Diamet...

Daniel José Pochapski.