Ion separation distance

The first successful study of such an energy transfer was by Wang et al. (2001, 2002) in their studies of Pi3"1" and Er3"1" codoped CaAli2Oi9 crystals. They found an energy transfer efficiency of about 25% at room temperature, which was hampered by the large Pr-Er ion separation distance. 

The rates of ion separation from CIP to SSIP are apparently much less structure dependent. Again the solvent polarity plays the dominant role. The typical values of ksep vary from ca. 5 x 108 s 1 in acetonitrile to about 105 s 1 in dichloromethane [50b, 122,123]. The empirical Weller equation [123] (Eq. 8, where rj is the solvent viscosity in cPs-1, r is the ion separation distance within the pair and d = oo) accounts well for the ion dynamics. 

In equation (4-29) z+ and z are the ionic charges, e is electron charge, e is dielectric constant, k is Boltzmann s constant, and T is the absolute temperature. When the ion separation distance is less than D, ion pairing is regarded as taking place. The dielectric constant of a solvent plays a significant role. At the same critical distance (D) needed for ion-pair formation, a solvent with a high dielectric constant such as water ( 80) will be less favorable for ion-pair formation compared to a solvent that has a lower dielectric constant (<40, such as acetonitrile and methanol). 

The Bjerrum Model. Bjerrum (see Robinson and Stokes (19)) defined an "ion pair" as existing when two ions of opposite charge approached such that the mutual potential energy between them equalled 2kT (k is the Boltzman constant). At 25 C, this means that an "ion pair" exists if the ion separation distance is equal... 

With the continuing improvement in the time resolution of pulsed radiation equipment, it should soon be possible to measure the lifetimes of a significant portion of the ions that undergo geminate neutralization. This information will be valuable in determining the distribution of ion separation distances. 

It turns out that the water and acetone curves in Figure 1 are also not appreciably altered by the use of their respective complex dielectric constants, even if one uses rup for all ion separation distances. This is because the dielectric relaxation times of these liquids are so short that a negligible amount of ion neutralization occurs during an interval equal... 

Potential energy between two atoms/ions Attractive energy between two atoms/ions Repulsive energy between two atoms/ions Electronic charge Permittivity of a vacuum Force between two atoms/ions Separation distance between two atoms/ions... 

The reaction medium plays a very important role in all ionic polymerizations. Likewise, the nature of the ionic partner to the active center-called the counterion or gegenion-has a large effect also. This is true because the nature of the counterion, the polarity of the solvent, and the possibility of specific solvent-ion interactions determines the average distance of separation between the ions in solution. It is not difficult to visualize a whole spectrum of possibilities, from completely separated ions to an ion pair of partially solvated ions to an ion pair of unsolvated ions. The distance between the centers of the ions is different in... 

H20 molecule. Now (39) gives the magnitude of the mutual electrostatic energy of such a dipole and an ion separated by a distance r. When the OH group of a methanol or ethanol molecule is in contact with an atomic ion the value of r to be inserted in (39) presumably is roughly the same as when a water molecule is in contact with the same ion. This would lead us to expect that the force of attraction between an ion and an adjacent solvent molecule would be similar in the three liquids. 

Figure 5. Potentials felt by a cation located between two CF ions separated by distance d (top LF, bottom K ), (dj = 580 pm, d = d = 640 pm and dn = 680 pm).49 The relevant pair potentials taken from Ref 50 are also shown. The magnitude of the kinetic energy (3/2) kT at 1000 K is shown for comparison. (Reprinted from Ref 49 with permission from Z. Naturforschung.)...

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

Compartmental pyrazole ligands (14) can be used to form bimetallic complexes (15).157 This ligand enforces a separation distance between the metal ions. Stability constants were calculated showing a stability for both mononuclear and dinuclear compounds that was less than Cu11 but greater than Nin. 

It is also possible to form radical cations and radical anions on the same alumina or silica-alumina surface (88). One of the more interesting observations was that a marked enhancement of the radical anion spectrum for trinitrobenzene results when perylene is adsorbed on an alumina surface, and similarly the radical cation signal is reenforced by adsorption of trinitrobenzene. The linewidths of the spectra confirm that the radical ions are separated by a distance greater than 10 A. This means that the electron must be transfered through the lattice or that the ions separate after the transfer step, which seems unlikely. Oxygen was still required for the formation of the radical cation. 

Based on the main methods of ion separation, analyzers can be classified into two main groups those based on the separation of ions in space or the separation of ions in time. The former separate ions while they are travelling over a distance (some metres in the case of sector instruments, centimetres in the quadupole) (Table 2.4). In contrast, when separation occurs in time, ions are confined in a small region of space and their separation occurs by varying some parameters (Table 2.4). 

The ion-ion interaction is characterized by electrostatic forces between ions. These electrostatic forces are inversely proportional to the square of the separation distance and therefore have a much greater range than intermolecular forces which depend on higher powers of the reciprocal distance. 

Let us consider a dopant ion A (the central ion) placed at a lattice site, surrounded by an array of six regular lattice ions B ligand ions), separated by a distance a from the ion A. The ligand ions B are located at the corners of an octahedron, as shown in... 

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