The mean cluster diameter is 2.9 nm.
A typical mass distribution spectrum of the obtained TiN+ clusters is presented in Figure 2. The mean cluster diameter was estimated from the cluster masses by using the specific density and the molar volume of the TiN. Figure 2 Mass spectrum of (TiN) + n clusters.
The uncoated Pt/alumina catalysts before and after the WGSR are shown in Figures 5 and 6, respectively, and the KOH-coated Pt/alumina catalysts before and after the WGSR are shown in Figures 7 and 8. Before the WGSR, the Pt nanoparticles were homogeneously distributed on the surface with a mean cluster diameter of 2.66 (arithmetic mean) to 2.81 nm (center of Gaussian distribution).
The mean Pt cluster diameter increased from 3.2 nm (for the uncoated catalyst) to 4.4 nm (center of Gaussian distribution) or 5.0 nm (arithmetic mean).
The size distribution is assumed to be of lognormal form and is expressed in the diameter of mean cluster volume, d vc, i.e., the mean volume equivalent cluster diameter, the mean of volume weighted size distribution, d wvc, and the geometric dispersion parameter σ c (Table 1), derived from the CMSM fit.
The following characteristic size parameters were obtained in geometry-optimized calculations for undoped CNT 3,3) cluster: distance along the nanotube axis between the outermost C6 rings was ~24.7 Å, distance between outermost H6 rings (cluster length) was ~26.5 Å, mean distance between "contralateral" C nuclei of the central C6 ring (cluster diameter) was ~4.21 Å.
In this situation more commonly used clustering methods (such as k-means) could not have been applied because they require the user to provide either the number of desired clusters or a threshold on cluster diameter or on intercluster distance.
Interestingly, the plastidic compartment revealed the largest cluster diameter based on the maximum clusterwise normalized Manhattan distance (0.16±0.02; 0.24) compared to the cytosolic (0.13±0.03; 0.17) and vacuolar (0.14±0.01; 0.19) compartment (within-gradient diameter as mean ± SD followed by between-gradient diameter).
In addition, clustering was strongly enhanced since we observed much larger fractions of clustered sensors (Fig. 2c), as well as a dramatic increase of the mean cluster size, from 0.04±0.01 µm2 (n = 22) to 0.15±0.04 µm2 (n = 13) and 0.14±0.06 µm2 (n = 13), respectively, corresponding to an increase of the equivalent diameter from 230 nm to 440 and 420 nm.
The mean cluster coefficient.
Mean cluster size (na)= 354.
