Recently, we have revealed that trimethylamine-N-oxide (TMAO) molecules in aqueous solutions are distributed generally like random spheres in space (A.V. Anikeenko et al. J. Mol. Liq. 245 (2017) 35–41). We have shown that the variance of the distribution of Voronoi region volumes for the TMAO molecules and the hard random spheres are identical at the corresponding concentrations up to the mole fraction x ~ 0.1 (or packing fraction η ~ 0.2). In the current work, we study clusters in TMAO solutions and calculate the weighted mean cluster size and some topological cluster characteristics. For all these parameters, a great matching of TMAO and random spheres is also observed. The same analysis for tert-butyl alcohol (TBA) and urea aqueous solutions is carried out. These molecules have a tendency to cluster even at very low concentrations. However, basic geometrical features of the clusters are the same both for solutions and for the system of random spheres, indicating that geometrical laws governing the allocation of non-overlapping spheres in space should be taken into account when describing the structure of solutions even at rather low concentrations.
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