Single Ions

Figure Bl.25.9(a) shows the positive SIMS spectrum of a silica-supported zirconium oxide catalyst precursor, freshly prepared by a condensation reaction between zirconium ethoxide and the hydroxyl groups of the support [17]. Note the simultaneous occurrence of single ions (Ff, Si, Zr and molecular ions (SiO, SiOFf, ZrO, ZrOFf, ZrtK. Also, the isotope pattern of zirconium is clearly visible. Isotopes are important in the identification of peaks, because all peak intensity ratios must agree with the natural abundance. In addition to the peaks expected from zirconia on silica mounted on an indium foil, the spectrum in figure Bl. 25.9(a)...

Membrane Potentials Ion-selective electrodes, such as the glass pH electrode, function by using a membrane that reacts selectively with a single ion. figure 11.10 shows a generic diagram for a potentiometric electrochemical cell equipped with an ion-selective electrode. The shorthand notation for this cell is... 

Calibrating the electrode presents a third complication since a standard with an accurately known activity for H+ needs to be used. Unfortunately, it is not possible to calculate rigorously the activity of a single ion. For this reason pH electrodes are calibrated using a standard buffer whose composition is chosen such that the defined pH is as close as possible to that given by equation 11.18. Table 11.6 gives pH values for several primary standard buffer solutions accepted by the National Institute of Standards and Technology. 

A second use of arrays arises in the detection of trace components of material introduced into a mass spectrometer. For such very small quantities, it may well be that, by the time a scan has been carried out by a mass spectrometer with a point ion collector, the tiny amount of substance may have disappeared before the scan has been completed. An array collector overcomes this problem. Often, the problem of detecting trace amounts of a substance using a point ion collector is overcome by measuring not the whole mass spectrum but only one characteristic m/z value (single ion monitoring or single ion detection). However, unlike array detection, this single-ion detection method does not provide the whole spectrum, and an identification based on only one m/z value may well be open to misinterpretation and error. 

SIM. selected (or single) ion monitoring SIMS, secondary ion mass spectrometry SIR. selected (or single) ion recording... 

Fig. 1. The ballistic interactions of an energetic ion with a sohd. Depicted are sputtering events at the surface, single-ion /single-atom recoil events, the development of a collision cascade involving a large number of displaced atoms, and the final position of the incident ion. ° = normal atom ...

Applying a r-f voltage of frequency CO to the transmitterplates in the cell increases the orbital radius of the ions without changing CO, and after a few rotations the ions move together coherently and can be detected. The detection process is relatively inefficient, however, because between 10 and 100 ions are needed to produce a detectible signal. In contrast an electron multiplier can detect single ions. 

Confirmation of the identities of nitrosamines generally is accompHshed by gas chromatography—mass spectrometry (gc/ms) (46,87). High resolution gc/ms, as well as gc/ms in various single-ion modes, can be used as specific detectors, especially when screening for particular nitrosamines (87) (see Analytical LffiTHODS Trace and residue analysis). 

For measurement of local ion intensities in the direct imaging mode (see Fig. 3.19), amplification ensuring laterally uniform-single ion detection is necessary. Depending on the sensitivity of the detector a single or double channel plate is used. Two imaging devices are in use ... 

Resistive Anode Encoder (RAE). This detector has the advantage that the single-ion events are detected digitally. It therefore it delivers quantitative results, irrespective of local differences in the amplification of the channel plate. One disadvantage is that the count rate is limited to 200000. 

Because it is impossible to vary single ion concentrations independently, the activity coefficient of an electrolyte is a function of activity coefficients of the cation and anion of the electrolyte. For example, for 1 1 electrolytes the relationship is... 

Without some additional relationship it is impossible to resolve y into and "y. By introducing an extrathermodynamic assumption as this additional relationship, it becomes possible to estimate single ion transfer activity coefficients. A widely used assumption is that the transfer activity coefficients of the cation and anion of tetraphenylarsonium tetraphenylboride, Ph4As BPh4, are equal, i.e.,... 

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

Table 8-8 gives some nonelectrolyte transfer free energies, and Table 8-9 lists single ion transfer activity coefficients. Note especially the remarkable values for anions in dipolar aprotic solvents, indicating extensive desolvation in these solvents relative to methanol. This is consistent with the enhanced nucleophilic reactivity of anions in dipolar aprotic solvents. Parker and Blandamer have considered transfer activity coefficients for binary aqueous mixtures. 

A consequence of single-ion diffusion is that the mass movement must be compensated for by an opposing drift (relative to a fixed point deep in the metal) of the existing oxide layer if oxidation is not to be stifled by lack of one of the reactants. The effect may be illustrated by reference to a metal surface of infinite extent (Fig. 1.81). 

Isolation "b memhnnt Ifncmbranc T solution k = single ion distribution coefficient ... 

It is worth mentioning that single-ion conductivities of lithium ions and anions at infinite dilution, and transference numbers of ligand-solvated lithium ions estimated therefrom, increase due to the replacement of more than one (generally four) solvent molecules. Table 6 demonstrates this beneficial feature. 

Table 6. Single-ion conductivities of solvated lithium ions and anions at 25 °C in PC at infinite dilution [13]...

The patch-clamp technique is based on the formation of a high resistance seal (109-10lon) between the tip of a glass micropipette and the cell membrane it touches (gigaohm-seal). This technique allows recordings of ionic currents through single ion channels in the intact cell membrane and in isolated membrane patches at a... 

Spin Warns.—In Application to Point Groups, above, we considered the irreducible representations of magnetic point groups. These would be useful in obtaining the symmetry properties of localized states in magnetic crystals, as impurity or single ion states in the tight... 

From the difference between the reference solution (taken as the ideal one governed by Raoult s law) and the one with ions, the expression for the activity coefficient for a single ion is... 

In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite noticeable.72 These deviations can be used290 to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126 279"284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface. 

Moreover, for the constants j2m and Mm-, the critical potential coefficient with respect to the single-ion activity a of the cation, the minority ion, is written using Eq. (51)... 

R. Gomer, and G. Tryson, An experimental determination of absolute half-cell emfs and single ion free energies of solvation, J. Chem. Phys. 66, 4413-4424 (1977). 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

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