Contraction radii

As the laminate industry grew, this anisotropic behavior was accepted and fabrication techniques adapted to it. For example, expansion and contraction space was left between wall panels, very strong adhesives were developed for bonding the product to substrates, special substrates were qualified, and where it was necessary to cut holes into the laminates the corners were radiused to prevent cracking from stress concentration. 

Chemical Properties. Although the chemical properties of the trivalent lanthanides are quite similar, some differences occur as a consequence of the lanthanide contraction (see Table 3). The chemical properties of yttrium are very similar too, on account of its external electronic stmcture and ionic radius. Yttrium and the lanthanides are typical hard acids, and bind preferably with hard bases such as oxygen-based ligands. Nevertheless they also bind with soft bases, typicaUy sulfur and nitrogen-based ligands in the absence of hard base ligands. 

By contrast, the ionic radius in a given oxidation state falls steadily and, though the available data are less extensive, it is clear that an actinide contraction exists, especially for the -f3 state, which is closely similar to the lanthanide contraction (see p. 1232). 

A diffusion-limited reaction proceeding in spherical particles (radius r) obeys a rate expression obtained by combining eqn. (10) with the contracting volume relation [eqn. (7), n = 3], viz. 

Hulbert [77] discusses the consequences of the relatively large concentrations of lattice imperfections, including, perhaps, metastable phases and structural deformations, which may be present at the commencement of reaction but later diminish in concentration and importance. If it is assumed [475] that the rate of defect removal is inversely proportional to time (the Tammann treatment) and this effect is incorporated in the Valensi [470]—Carter [474] approach it is found that eqn. (12) is modified by replacement of t by In t. This equation is obeyed [77] by many spinel formation reactions. Zuravlev et al. [476] introduced the postulate that the rate of interface advance under diffusion control was also proportional to the amount of unreacted substance present and, assuming a contracting sphere (radius r) model... 

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

The atomic radii of the second row of d-metals (Period 5) are typically greater than those in the first row (Period 4). The atomic radii in the third row (Period 6), however, are about the same as those in the second row and smaller than expected. This effect is due to the lanthanide contraction, the decrease in radius along the first row of the / block (Fig. 16.4). This decrease is due to the increasing nuclear charge along the period coupled with the poor shielding ability of /-electrons. When the d block resumes (at lutetium), the atomic radius has fallen from 217 pm for barium to 173 pm for lutetium. 

Hg is much more dense than Cd, because the decrease in atomic radius that occurs between Z = 58 and Z = 71 (the lanthanide contraction) causes the atoms following the rare earths to he smaller than might have been expected for their atomic masses and atomic numbers. Zn and Cd have densities that are not too dissimilar because the radius of Cd is subject only to a smaller d-block contraction. 

Random coil conformations can range from the spherical contracted state to the fully extended cylindrical or rod-like form. The conformation adopted depends on the charge on the polyion and the effect of the counterions. When the charge is low the conformation is that of a contracted random coil. As the charge increases the chains extend under the influence of mutually repulsive forces to a rod-like form (Jacobsen, 1962). Thus, as a weak polyelectrolyte acid is neutralized, its conformation changes from that of a compact random coil to an extended chain. For example poly(acrylic acid), degree of polymerization 1000, adopts a spherical form with a radius of 20 nm at low pH. As neutralization proceeds the polyion first extends spherically and then becomes rod-like with a maximum extension of 250 nm (Oosawa, 1971). These pH-dependent conformational changes are important to the chemistry of polyelectrolyte cements. 

Bronchial smooth muscle tone. Changes in bronchial smooth muscle tone are particularly important in the bronchioles compared to the bronchi. Recall that the walls of the bronchioles consist almost entirely of smooth muscle. Contraction and relaxation of this muscle has a marked effect on the internal radius of the airway. An increase in bronchial smooth muscle tone, or bron-choconstriction, narrows the lumen of the airway and increases resistance to... 

One of the consequences of the lanthanide contraction is that some of the +3 lanthanide ions are very similar in size to some of the similarly charged ions of the second-row transition metals. For example, the radius of Y3+ is about 88 pm, which is approximately the same as the radius of Ho3+ or Er3 +. As shown in Figure 11.8, the heats of hydration of the +3 ions show clear indication of the effect of the lanthanide contraction. 

A further effect during evolution up the AGB is mass loss through stellar winds, at an increasing rate as the star increases in luminosity and radius and becomes unstable to pulsations which drive a super-wind in the case of intermediate-mass stars. For stars with an initial mass below some limit, which may be of order 6 M , the wind evaporates the hydrogen-rich envelope before the CO core has reached the Chandrasekhar limiting mass (see Section 5.4.3), the increase in luminosity ceases and the star contracts at constant luminosity, eventually becoming a white dwarf (Figs. 5.15, 5.19). A computed relation between initial stellar mass and the final white-dwarf mass is shown in Fig. 5.21. 

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