Diameter distribution

The diameter distribution of single-wall carbon nanotubes is of great interest for both theoretical and experimental reasons, since theoretical studies indicate that the physical properties of carbon nanotubes are strongly dependent on the nanotube diameter. Early results for the diameter distribution of Fe-catalyzed single-wall nanotubes (Fig. 15) show a diameter range between 0.7 nm and 1.6 nm, with the largest peak in the distribution at 1.05 nm, and with a smaller peak at 0.85 nm [154]. The smallest reported diameter for a single-wall carbon nanotube is 0.7 nm [154], the same as the diameter of the Ceo molecule (0.71 nm) [162]. 

Fig. 15. Histogram of the single-wall nanotube diameter distribution for Fe-catalyzed nanotubes [154], A relatively small range of diameters are found, the smallest diameter corresponding to that for the fullerene Ceo.

Whereas multi-wall carbon nanotubes require no catalyst for their growth, either by the laser vaporization or carbon arc methods, catalyst species are necessary for the growth of the single-wall nanotubes [156], while two different catalyst species seem to be needed to efficiently synthesize arrays of single wall carbon nanotubes by either the laser vaporization or arc methods. The detailed mechanisms responsible for the growth of carbon nanotubes are not yet well understood. Variations in the most probable diameter and the width of the diameter distribution is sensitively controlled by the composition of the catalyst, the growth temperature and other growth conditions. 

Fig. 5. Diameter distributions of nanotubes produced via different methods (a) Fe catalyst in an Ar/CH4 atmosphere, adapted from Ref. 2 (b) Co catalyst in He atmosphere, adapted from Ref. 5 (c) Co catalyst with sulfur, about 4 at. % each, adapted from Ref. 5.

By using different catalysts and growth temperatures for the synthesis of ropes of SWCNTs, it is possible to obtain a different diameter distribution for SWCNT samples. At present, it is possible to vary the peak in the diameter distribution between 0.9 and 2.0 nm [7,27,29]. By carrying out Raman experiments on CNT samples with different diameter distributions, changes in the characteristics of the Raman spectra can be investigated. 

The preparation by dispersion polymerization of the microsphere sample employed in this study was previously described [8]. The microsphere sample utilized in this study has a monomodal diameter distribution with mean diameter value d= 3.09 pm and standard deviation dsdev= 0-74 pm. The microsphere surface is covered by a poly(methacrylic acid-co-ethylacrylate) whose percent by weight is 1.1... 

Figure 9. TEM micrographs of Pd /K1221 in low (a) and high (b) resolution Pd nanoclusters diameter distribution (c).

Model Fit or Direct Evaluation Similar to the ID case we can now fit a model to the projected intensity or to the CLD. What we get in this case is the needle-diameter distribution of the microfibrils. Nevertheless, there are two other possibilities to directly evaluate the data. 

If we assume that the shape of each disc is circular, the CLD of an uncorrelated hard-disc fluid is the Mellin convolution of the intrinsic chord distribution, gc r 2), of an ideal disc of diameter 1 and the diameter distribution, ho (D) which characterizes the structure. The definition of the Mellin convolution (Titchmarsh [202], S. 53 Marichev [203] ... 

Figure 8.38. Structural parameters of an ensemble of needle-shaped soft domains in a poly(ether ester) as a function of elongation . D (open circles) is the average needle diameter, a/D (filled circles) is the relative standard deviation of the needle-diameter distribution. Square symbols demonstrate the lateral compressibility of the soft needles during elongation... 

Bearing in mind the aim to determine structural parameters, we resort to the measured CLD, gobs (r). By means of numerical integration we compute some of its moments, n[ gobs) For the sought-after moments of the sphere-diameter distribution,... 

The common measure for the breadth of the sphere-diameter distribution is the standard deviation (cf. p. 5, Eq. (1.8). 

Bandow S, Asaka S, Saito Y, Rao AM, Grigorian L, Richter E, Eklund PC (1998) Effect of the growth temperature on the diameter distribution and chirality of single-wall carbon nanotubes. Physical Review Letters 80 3779-3782. 

The commercial mercury porosimeters can usually provide pore diameter distribution data in the range of 3.5 nm to 7.5 microns. It is a useful and commonly used method for characterizing porous particles or bodies. Figure... 

Fig. 4 Profiles of particle diameter distribution for Mg/Al-COs LDHs with different ratios prepared using (a) the new method using rapid mixing and nucleation in a colloid mill followed by a separate aging step and (b) conventional coprecipitation at constant pH. The new method affords materials with a much narrower range of diameter. Reprinted with permission from [20], Copyright ACS Journal Archives...

DIAMETER AND DIAMETER DISTRIBUTIONS OF POLY(l-LACTIDE) MICROSPHERES BY RING-OPENING POLYMERIZATION OF l-LACTIDE AND FROM EARLIER SYNTHESIZED POLYMERS... 

Diameter and Diameter Distributions of Poly(L-lactide) Microspheres by Ring-Opening Polymerization of L-Lactide and from Earlier Synthesized Polymers... 

Microspheres made of various polymers biodegradable to nonharm-ful compounds that could be metabolized and/or removed from organisms found many applications in medicine as carriers of drugs or other bioactive compounds [1 ]. Besides chemical composition there are also other properties of microspheres that are of primary importance to their medical applications. In particular, average diameters and diameter distributions illustrated in Table 1 based on data published in [5] are the relationship between the diameters of microspheres and their localization in various cells and tissues of the human body. 

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