Counterion-only

The gold analog, [AujCOjj] is reported to be formed (with an [Sb2Fu] counterion) only under 100 bar CO [107]. The y(CO) bands of these species occur significantly above the stretching frequency of free CO (2143 cm ) for example the silver and gold tricarbonyl cations have IR absorptions at 2192 and 2212 cm respectively. This is taken to indicate that there is little or no metal —> CO Ti-backdonation in these species, which are termed non-classical metal carbonyls [109]. 

In the case of monomer 23 it appears that an equilibrium exists between ionic and covalent propagating species in polymerisations initiated by methyl iodide, though with OT counterion only ionic intermediates are observed. Presumably therefore the effective nucleophilicity of this monomer is very similar to that of I. N-(2-iodopropyl)-N-methyl formamide was prepared from an equimolar reaction of methyl iodide with 23, and H NMR spectroscopy in CD3CN showed that the following equilibrium was rapidly established ... 

Second, we bring the counterions to the surface. They are supposed to go directly to the surface at x = 0. The number of counterions is equal to the number of ions in the diffuse double layer. The first counterions are still attracted by the full surface potential. Their presence, however, reduces the surface potential and the following counterions only notice a reduced surface potential. To bring counterions to the surface the work d,G = tp 0da has to be performed, where ipo is the surface potential at a certain time of charging — or better discharging — process. The total energy we gain (and the double layer loses) is... 

The PRISM (Polymer-Reference-Interaction-Site model) theory is an extension of the Ornstein-Zernike equation to molecular systems [20-22]. It connects the total correlation function h(r)=g(r) 1, where g(r) is the pair correlation function, with the direct correlation function c(r) and intramolecular correlation functions (co r)). For a primitive model of a polyelectrolyte solution with polymer chains and counterions only, there are three different relevant correlation functions the monomer-monomer, the counterion-counterion, and the monomer-counterion correlation function [23, 24]. Neglecting chain end effects and considering all monomers as equivalent, we obtain the following three PRISM equations for a homogeneous and isotropic system in Fourier space ... 

Consider a dilute suspension of polyelectrolyte-coated spherical colloidal particles (soft particles) in a salt-free medium containing counterions only. We assume that the particle core of radius a (which is uncharged) is coated with an ion-penetrable layer of polyelectrolytes of thickness d. The polyelectrolyte-coated particle has thus an inner radius a and an outer radius b = a + d (Fig. 6.4). We also assume that ionized groups of valence Z are distributed at a uniform density N in the poly electrolyte... 

FIGURE 6.4 A polyelectrolyte-coated spherical particle (a spherical soft particle) in a free volume of radius R containing counterions only, a is the radius of the particle core. b — a + d. dis the thickness of the polyelectrolyte layer covering the particle core. (blR) equals the particle volume fraction (j>. From Ref. [9]. 

Electric behaviors of colloidal particles in a salt-free medium containing counterions only are quite different from those in electrolyte solutions, as shown in Chapter 6. In this chapter, we consider the electrostatic interaction between two ion-penetrable membranes (i.e., porous plates) in a salt-free medium [1]. 

Before considering the interaction between two ion-penetrable membranes, we here treat the interaction between two similar ion-impenetrable hard plates 1 and 2 carrying surface charge density cr at separation h in a salt-free medium containing counterions only (Fig. 18.1) [2]. We take an x-axis perpendicular to the plates with its origin on the surface of plate 1. As a result of the symmetry of the system, we need consider only the region 0 < x < h 2. Let the average number density and the valence of counterions be o and z, respectively. Then we have from electroneutrality condition that... 

We should note, however, that incorporation of a substrate into a micelle will accelerate its reaction with a micelle counterion only if the substrate is bound at the micellar surface, since ionic reagents cannot, apparently, penetrate into the micellar core. Thus, the hydroxyl ion-catalyzed hydrolysis of long-chain fatty acid esters of 3-nitro-4-hydroxybenzenesulfonic acid was inhibited by incorporation into micelles no matter whether these were uncharged, anionic, or cationic (68). 

A. G. Moreira and R. R. Netz (2001) Binding of similarly charged plates with counterions only. Phys. Rev. Lett. 87, p. 078301... 

The anionic polymerization of cyclosiloxanes was examined In benzene and toluene with lithium cryptates as counterions. Only one type of active species Is observed In the case of LI + [211] thus, the kinetics of the propagation and of the by-product cyclosiloxanes formation can be studied In detail for the first time. The reactivity of cryptated sllanolate Ion pairs toward the ring opening of D3 Is greatly enhanced compared to that of other systems. 

FIGURE 7 Structure of the calculated endo and exo transition states incorporating a K counterion. Only structures optimized with M06-2X are shown. Values below the middle stractures are relative energies (kcal/mol) calculated by M06-2X (B3LYP). Adapted with permission from reference 57. Copyright 2013 American Chemical Society. 

Briscoe WH, Attard P (2002) Counterion-only electric double layer a constrained entropy approach. J Chem Phys 117 5452-5464... 

Counterions only—no small anions other than HSiOj data slightly extrapolated. 

Odijk considered DH screening as being caused by uncondensed counterions only, which implicates that the screening parameter depends on Cm... 

Ni(II) complex, with two forms existing the asymmetric unit. One has the trans bromide ligands replaced by cis water ligands, the bromides being present as counterions only. In this form, the triazole N donors occupy the axial positions. In the second form, the apical positions are occupied by one of the triazole N donors and one of the water molecules. The apparent stereochemical nonrigidity of the complex (and by inference, the [Ni(L)Br2] complex) is proposed to be due to the lability of the Ni-N(triazole) bonds. 

W. H. Briscoe and P. Attard, J. Chem. Phys., 117, 5452 (2002). Counterion-Only Electrical Double Layer A Constrained Entropy Approach. 

P. Attard, D. J. Mitchell, and B. W. Ninham, /. Chem. Phys., 88, 4987 (1988). Beyond Poisson-Boltzmann Images and Correlations in the Electric Double Layer. I. Counterions Only. 

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