Mean hole

The carbon dioxide comes from the air, and the water comes from the soil in which the plant grows. When a plant is watered or when it rains, water enters the root and is transported to the leaves by plant cells called xylem. To protect themselves against drying out, leaves have structures called stomata that allow gas to enter and leave. Stoma is from the Greek and means hole. Both carbon dioxide and the oxygen produced during photosynthesis pass in and out of the leaf through the opened stomata. 

Puka shells originated in Hawaii, where the flat broken tops of worn Conus shells were used as decorations or beads. Beach worn cone shells were often found as concave round fragments with a natural central hole where the spire had broken off. The Hawaiians took this a step further by creating their own pukas out of cone and other mollusk shells that were not quite so worn, but that were the right size and shape to be used as beads. A round shell, usually slightly concave, is drilled in the center and strung as beads. The word puka means hole in Hawaiian. 

What typical values of mean hole radius does Eq. (5.44) yield (Table 5.15) By using the macroscopic surface-tension value, Eq. (5.44) shows that the average radius of a hole in molten KCl at 1173 K is 190 pm. The mean ionic radius, however, is 160 pm. 

Mean Hole Radius for Various Molten Salts at 1173 K... 

Surface Tension, Mean Hole Volume Mean Hole Radius... 

At a fixed temperature, the only parameter determining the mean hole size is the surface tension. Though one is aiming at a microscopic (structural) explanation of the behavior of ionic liquids, one goes ahead and uses the macroscopic value of surface tension. The mean hole radius then turns out to have the same order of magnitude as the mean radius of ions comprising the liquid. 

Calculate the mean hole size in CsBr for which the surface tension is 60.7 dyn cm at 1170 K. 

Deduce an expression for the mean hole size from this function. Work out the mean radius ofholes for molten KCl near the melting point if the surface tension is 89.5 dyn cm and the melting point is 1040 K. 

Calculate the work of hole formation in molten sodium chloride, using the Furth approach. The surface tension of NaCl, molten salt at 1170 K, is 107.1 dyn cm" and the mean hole radius of NaCl is 1.7 x 10" cm. (Contractor)... 

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. 

Since Xpo follows a distribution and the relation between A.po and the hole radius r is nonlinear [Eq. (11.3)], we prefer to estimate the mean hole-volume as the mean of the number-weighted hole volume distribution. The radius distribution [the probability density function (pdf)], n(rfc), can be calculated from n (rh) = - 3 (A.) (dx/drh) [Gregory, 1991 Deng et al., 1992b] ... 

It is interesting to compare the hole sizes for polymers of different Tg values and different chemical structure. Such a comparison is made in Figure 11.5, showing plots of the temperature-dependent mean hole volume, ( ua ), and the standard deviation, <7ft, of the hole volume distribution for a large collection of polymers with Tg values between 200 and 500 K. We have grouped the polymers under discussion into... 

Several attempts to estimate the hole density from a comparison of the mean hole volume with the macroscopic volume are described in the literature. The drawback of such approaches is that assumptions must be made as to the value of or on the thermal expansion and compression of the volume that is not detected by o-Ps. Frequently, it is assumed that that this volume, denoted as occupied or bulk volume, expands Uke an amorphous polymer in the glassy state [Hristov et al., 1996 Dlubek et al., 1998c Band ch et al., 2000 Shantarovich et al., 2007]. Another assumption is that no variation with temperature or pressure is shown [Bohlen and Kirchheim, 2001]. Both assumptions are intuitive but physically not proved. The most successful attempt to estimate hole densities comes from a calculation of the hole free volume with... 

FIGURE 11.9 Specific total, V, free Vf = hV, and occupied, Vqcc = (1 — h)V, volume of PC as a function of T at ambient P. h is the hole fraction calculated from V using the S-S equation of state. Open symbols, experimental data dots, S-S equation of state fits to the volume in the temperature range T>Tg-, stars, free volume calculated from Vf=N v,), where (Vf,) is the mean hole volume from PALS and is the specific hole density, assumed to be constant at N f = 0.67 X 10 g (corresponding to 0.81 nm at 300 K). (Adapted from Dlubek et al., [2007d].)... 

Region I occurs below the glass transition Tincreases with increasing temperature (or decreasing pressure), while the mean hole size dispersion, a, seems to be constant. The latter observation may be interpreted as evidence of the fixed size of the spatial heterogeneity, which... 

Kilburn et al. [2002] carried out a PALS study of free volume in semicrystalline poly(ethylene-co-l-octene) (PO) copolymers as well as high-density polyethylene (HDPF). The degree of crystallinity was characterized by DSC and WAXD analyses. A method was proposed to estimate the fractions of the RAF and MAF phases based on the observation that the mean thermal expansivity of free-volume holes, ea = d vh)/dt, varies as a function of Xc, which implies that the individual mean expansivities of holes in RAF and MAF phases are different. Thus, the thermal expansivity of the mean hole volume (i.e., averaged over the entire amorphous phase) may be expressed above To by... 

This study shows that none of the various forms of relaxation function used to describe ageing are completely satisfactoiy and TRS is inappropriate. Correlation between results, (Figure 9) indicates the inherent connectivity between the processes. Curro et al (24,25) have studied the change in density fluctuation with temperature and annealing time for PMMA (25) and compared it with specific volume data. Positron annihilation data on PMMA (27,28) has been interpreted in terms of free volume. For a distribution of hole sizes there will exist many decaying exponentials each with a different characteristic lifetime. The composite of these many exponentials can itself be approximated to an exponential, and it is this decay constant that is used to represent the mean lifetime, and therefore mean hole size. 

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