Average hole size

Dlubek et al [49] studied a series of metallocene-catalyzed poly a-olefins) with progressively longer chains as the pendant side groups from polypropylene to poly-l-eicosene (20 carbons). Their results show an interesting relationship between the o-Ps lifetime and intensity in the amorphous phase for this series of polymers. They found that the average hole size and o-Ps intensity from the amorphous phase, decreased from polyethylene to polypropylene, followed by a slight increase to poly-1-butene. There was a rapid rise in hole size and intensity to poly-l-dodecene. 

On the molecular level, the ratio vo/vf) is a measure of the average volume of the polymer relative to that of the holes. Thus, when vq > Vf, i.e., the polymer chain is larger than the average hole size, the viscosity will be correspondingly high, and when vq < Vf, the viscosity will be low. 

PC was exposed to high pressure CO2. The free-volume hole size was observed to monotonically increase with CO2. Upon depressurization, a large hysteresis was seen. After CO2 exposure, the fractional free volume and average hole size were larger. This behavior results from the strong conditioning effect of CO2 that was described in a previous section. 

Most of the literature has presented data for trays with holes of 1 -in. through M-in. diameter. The work of Hunt et al. [33] includes l in. holes. Some commercial units have used % and 1-in. holes, although these sizes should be used with caution when adequate data are not available. The recommended hole size for the average clean service is f(i-in. based on present published data. Holes of l in. 

Trenches excavated across the veins are typically flooded by surface water however, three partially flooded trenches have exposed bedrock. From small (< 5m ) outcrops exposed in three of the trenches, it is apparent that the average grain size of the clastic sedimentary rocks and the abundance of coarse-grained detritus, increases from NE to SW away from the buried Caradocian shale, with arkosic sandstone most abundant in the SW near the Christopher vein. An extensive array of 98 drill holes provides excellent downhole, 3-D control on our understanding of the geology. 

Obviously, a hole of 3 to 5 mm cannot take a very large tube. In general, it is safe to insert a tube which is about 1 to 2 mm in diameter larger than the original hole size. As can be seen in Table 1.8, you can only insert 6- to 8-mm-diameter tubes or rods into the holes of size 2 or greater stoppers (about the diameter of the average glass thermometer). 

For comparison the theoretical values of the electron-hole recombination rate from several recent papers are included as well. One can see that below a crystallite size of about 4 nm the agreement between the measured data and the theory is reasonably good. The relatively high PL intensity from samples with an average crystallite size of > 5 nm is probably due to the presence of a small fraction of small crystallites in such films [19,25]. 

In deviations from the Nernst-Einstein equation in a molten salt, one hypothesis involved paired-vacancy diffusion. Such a model implies that holes of about twice the average size are available at about one-fifth the frequency of averagesized holes. Use the equation in the text for the distribution of hole size to test this model. 

In the Fiirth hole model for molten salts, the primary attraction is that it allows a rationalization of the empirical expression = 3.741 r p. In this model, fluctuations of the structure allow openings (holes) to occur and to exist for a short time. The mean hole size turns out to be about the size of ions in the molten salt. For the distribution function of the theory (the probability of having a hole of any size), calculate the probability of finding a hole two times the average (thereby allowing paired-vacancy diffusion), compared with that of finding the most probable hole size. 

The theoretical basis of the transport of solute ions during iontophoresis can be compared to electrophoresis through a gel network. When the ionized solute has a mean Stokes radius smaller than the average mesh size (hole in the network), the solute is considered as a rigid sphere undergoing Brownian movement, with a mobility dependent on the frequency of solute interaction with the porous network. The sphere mobility is assumed to be proportional to the fractional volume of the pore that is accessible to the sphere [92]. The electrophoretic mobility, u, of such a solute sphere has been shown to be directly related to the molecular weight of the solute [93] ... 

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