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strength data. This analysis applied to our experimental data provided the two Weibull parameters: namely the characteristic strength, σc, and Weibull modulus m, which are given in Table 3.1 for different temperatures. As the characteristic strength increased from 2.2 GPa to 3.6 GPa for nanofibers produced at 1400°C the Weibull modulus also increased to about 6, which is an average value for brittle materials. The Weibull modulus is a measure of the distribution of flaw sizes. Large values (>10 - 15) indicate small dependence of the material strength on the specimen size and, therefore, for large values of m a well defined flaw size and distribution exist. Small values of m (<5 - 6) indicate a diverse population of flaws in size and/or in orientation. The mechanical strength scales with the specimen size as σ1/σ2=(l2/l1)1/m, where σ1 and σ2 are the failure strengths of specimens with sizes l1 and l2, respectively [68]. The latter denote specimen length, surface area or volume depending whether the flaws that cause failure are evenly distributed along the specimen length, surface area or volume. It is, therefore, evident that for m ≈ 6 (1400°C) the nanofiber strength scales rather weakly with its length. This favorable trend changes for carbonization at 1700°C when m ≈ 3. As described earlier, this was due to the large and randomly distributed turbostratic carbon crystallites which acted as stress concentrations and sites for failure initiation. This random distribution and size of the crystallites are captured by the low Weibull modulus and characteristic strength listed in Table 3.1. Table 3.1. Weibull modulus, characteristic strength and fiber modulus as a function of carbonization temperature. Carbonization Temperature (oC) 800 1100 1400 1700 Carbon Characteristic Content Strength (%) σc (GPa) 81.2 2.20 92.7 2.90 N/A 3.60 N/A 1.95 Young’s Modulus (GPa) 80 ± 19 105 ± 27 172 ± 40 191 ± 58 Weibull Average Crystallite Modulus Thickness (# of m graphene layers) 3.1 3.3 ± 0.9 6.4 3.9 ± 0.9 5.9 6.6 ± 1.4 3.0 7.9 ± 1.9 37PDF Image | HIGH STRENGTH CARBON NANOFIBERS DERIVED FROM ELECTROSPUN POLYACRYLONITRILE
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