Gaussian statistics carbonate

Extensive studies on different rubber compounds (see, for example, Table 1 in [105]) yield Ec 0.05 to 0.15 eV per filler-filler bond [105,106], i.e., typical values for physical (van der Waals like) bonds. Similar values were obtained within an approach which assumes a hypothetical analogy between the structure of a statistical carbon black network and that of a Gaussian elastomeric (unfilled) polymer network [107]. As in the Kraus approach, the carbon black network scission process is assumed to be thermally activated. 

The main quantitative developments of the random coil model of flexible polymers began in 1934 with the work of E. Guth and H. E Mark [12] and W. Kuhn [13]. Using the concept of free rotation of the carbon-carbon bond, Guth and Mark developed the idea of the random walk or random flight of the polymer chain, which led to the familiar Gaussian statistics of today, and eventually to the famous relationship between the end-to-end distance of the main chain and the square root of the molecular weight, described below. 

Fig. 5.3 Representative STEM micrographs forPi >36 (0.03 e/nm ) and 45 (0.04 and 0.06 e/nm ) clusters and their corresponding PSD, i.e. area statistics. The micrographs (100 x 100 nm ) for unselected Pt >3,6 (a) and two coverages of selected Pt4e clusters (c, e) on ultra thin carbon support are shown. Additionally the area statistics (b, d, f) are plotted as histograms. The obtained distributions are fitted (orange lines)—for the unselected by a log normal distribution and for the selected samples the primary peak by a gaussian function. The green curves show the integrated counts...

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