Radii apparent

An indirect indication of the presence of interactions between micellar phase and drugs is given by molecular and dynamic parameters of the drug and the micelles (ionic mobility, diffusion coefficient, hydrodynamic radius, apparent molecular mass), which are altered by the solubilization of lipophilic substances in a significant manner. 

Xi+ and X2+ are diffusion-disguised rate constants 4>i = Thiele modulus R = effective crystallite radius (apparent agglomerate size) (Figure 3)... 

It is apparent that, in order to satisfy Eq. 30, the JKR model requires that detachment occurs, not when the contact radius vanishes, as might at first be thought, but rather at a finite value 0.63a(0). 

Upon comparison of Eqs. 29 and 36, it is readily apparent that both theories predict the same power law dependence of the contact radius on particle radius and elastic moduli. However, the actual value of the contact radius predicted by the JKR theory is that predicted by the DMT model. This implies that, for a given contact radius, the work of adhesion would have to be six times as great in the DMT theory than in the JKR model. It should be apparent that it is both necessary and important to establish which theory correctly describes a system. 

However, if one attempted to determine iua from the DMT theory, one would get an unrealistically large value. In the same paper, the authors also presented micrographs of particles in contact with the substrate under a negative applied load that was not quite sufficient to effect detachment. It was reported that the observed contact radius under those circumstances was approximately 70% of the expected contact in the absence of the applied load. This observation is in apparent agreement with the JKR prediction that detachment occurs under negative loads that reduce the contact to about 63% of the equilibrium contact radius. 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Compressive forces on enamel applied to a convex surface are less than when a concave surface is coated, and it is therefore apparent that the sharper the radius of the metal the weaker the enamel applied to it will be. This fact is also relevant to mechanical damage. 

In pressing, the threshold concentration of the filler amounts to about 0.5% of volume. The resulting distribution of the filler corresponds, apparently, to the model of mixing of spherical particles of the polymer (with radius Rp) and filler (with radius Rm) for Rp > Rm as the size of carbon black particles is usually about 1000 A [19]. During this mixing, the filler, because of electrostatical interaction, is distributed mainly on the surface of polymer particles which facilitates the forming of conducting chains and entails low values of the percolation threshold. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

Calculate the apparent volume (in pnt1) and radius (in pm) of a helium atom as determined from the van der Waals parameters,... 

Since every atom extends to an unlimited distance, it is evident that no single characteristic size can be assigned to it. Instead, the apparent atomic radius will depend upon the physical property concerned, and will differ for different properties. In this paper we shall derive a set of ionic radii for use in crystals composed of ions which exert only a small deforming force on each other. The application of these radii in the interpretation of the observed crystal structures will be shown, and an at- Fig. 1.—The eigenfunction J mo, the electron den-tempt made to account for sity p = 100, and the electron distribution function the formation and stability D = for the lowest state of the hydr°sen of the various structures. 

Within the first-order estimations made here, it is apparent that no change in d-d repulsion energy accompanies the hydration process. Second-order adjustments would, of course, take account of the change in mean i/-orbital radius on complex formation. Let us agree to stop at the simple level of correction here. Overall, therefore, the significant Coulombic change on hydration concerns the loss of exchange stabilization. 

This result suggests that the sintering resistance of samples are enhanced as the ionic radius of A becomes large. It is, therefore, apparent that La is superior as the large cation in the mirror plane of the hexaaluminate in achieving both high thermal resistance and high activity to other tri-valent A cations with small ionic radii. 

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

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