Unpaired ion

It should be possible to obtain EV2 for unpaired ions either by Fleischmann s technique [13] (which was published too late for the Keele Research Group, now dispersed, to make use of it), or by extrapolating EV2 obtained conventionally with varying concentrations of supporting electrolyte, to zero ionic strength. 

The general effect is that the fraction of unpaired ions is underestimated. Two examples from many The calculations of the present author [17a, 18] for styrene and HC104 in CH2C12 and those of Sauvet [7] for 4-MeO-styrene the latter are likely to be more strongly affected because of the w-donor nature of this monomer, which implies greater values of Km and therefore a smaller population of Pn+A . 

The new rate-constants resulting from my analysis are listed. The lessons from these theoretical investigations will also be useful in the context of chemically initiated cationic polymerizations, especially for those in which propagation by unpaired ions is dominant. 

In this first attempt at a systematic definition of the problem it is recognized explicitly that there may be a multiplicity of chemically distinct chain-carriers growing simultaneously in the same reaction mixture (enieidic polymerisation). The fact that these may include paired and unpaired ions is considered from the point of view of conventional ionic equilibria, and a warning is given that there may be tight and solvent-separated ion-pairs to be considered. This idea, taken over from the theory of anionic polymerisations, was shown much later to be inappropriate for cationic polymerisations 154. ... 

Once again, in this paper, the electrochemical aspects of the ions and their equilibria are prominent. The Fuoss-Kraus equation is applied to the pairing of the carbenium ions with the anions. It is shown that since an increase in the solvent polarity reduces the propagation rate-constant, the increase in rate in changing from a less polar to a more polar solvent must be due to the increase in polarity augmenting the ratio of the concentrations of unpaired to paired cations, (here called Up and in later papers yip) on the assumption that as in anionic polymerisations, the unpaired ions propagate faster than the paired ions. 

One of the consequences of kp being greater (usually very much greater) than k is that in solvents of ec. 10, ion-pairs are largely irrelevant as far as the propagation is concerned. This can be illustrated by a simple example. Suppose that KD = 10"5, c = 10"3 mol l 1, then a 0.1. If kp = 106 and k = 104 1 mol 1 s 1, we have a situation where the c. 10 % of unpaired ions contribute ten times as much to the rate as the 90 % of paired cations. The value of Kd is typical for ions of the size and for the values of eT, which are relevant here, but c is rather large typically it is probably below 10"5 mol H-which makes a even greater and the contribution of paired cations to the rate even smaller. 

As for the effect of changing solvent polarity on the reactivity of paired cations, this is very much smaller than on the unpaired ion for simple electrostatic energetic reasons the charge density is so very much smaller and there is less space around both ions to accommodate... 

Complexation by reagents other than the monomer usually has several consequences the reduction of the charge density by the complexant and the increase in the effective size of the ion will both increase the KD of the propagating ion-pair so that y/p increases and also the unpaired ion is now encumbered by something different from the solvent molecules which solvate it in the absence of complexant, and one cannot predict generally whether the balance of these effects will augment or diminish the propagation, transfer, and termination rates. 

The monomer-complexing Equations (16) and (17) for unpaired ions [corresponding to... 

This effect, too, will cause the [P+J to be less than cQ. It is an as yet open question whether the complexed growing cations P+nM and P+nP can participate directly in BIE, The argument has been conducted in terms of unpaired ions, but paired ions may also be involved, so that there are concurrent Unary (Ostwald type) and BIE, However, this makes no difference in principle, as can be seen from the treatments of BIE, with ion-pairs by Grattan and Plesch (1979), Pask and Nuyken (1983) and Holdcroft and Plesch (1985). 

Since the propagating species was known to be an unpaired ion, P+n the rate-equation was written conventionally as... 

The effects of ion-pairing have been noted in countless experimental situations involving conductometry, potentiometry, spectroscopy, solvent extraction, separative techniques, activity measurement, and kinetic behavior among others. As far as chromatography is concerned, the electrical neutrality and the increased lipo-philicity of ion-pairs, compared to unpaired ions, are features of utmost importance involved in retention adjustment. 

According to this scheme, the solvolysis products are not only obtained from free unpaired ions, but also from the two different ion pairs, depending on the solvent-dependent degree of dissociation. 

Plesch showed by electrochemical methods that at the sufficiently low concentrations, the components exist in the 2-to-2 equilibrium with unpaired ions These salts were used to initiate polymerization of cyclic ethers and acetals but the structure of the tirst addition products has not yet been determined. Nevertheiess, several authors observed the corresponding end groups in oligomers (at the early stages of polymerization) or in high polymers . These observations indicate that the oxocarbenium salts initiate by simple addition, for instance ... 

A Theory of Membrane Internal Water Activity. From a thermodynamic standpoint, the (water-swollen) equilibrium membrane structure must depend, in part, upon the internal osmotic pres sure which is determined by the water activity, a, within the microscopic cluster regions, a, in turn, should IBe a function of the relative population of unpaired ions and free water molecules in the cluster solution. 

Fig. 1. Model of the HPA monolayer at a given pH and ionic composition of the substrate. The residues (a), (b) and (c) are ionized, (d) is in the acid form. In (a) and (b) the ions and/or form ion pairs with the carboxylates extending to an average depth a = t (c) is neutralized by counterions of the diffuse layer beyond x = d. The plane 2Xx = d separates the Paired Ion Region (P.I.R.) from the Unpaired Ion Region (U.I.R.). For the definition of o, d and x see the text.

M 2 bound to the negative sites and form ion-pairs extending to an average depth x=x. The plane located at separates these paired ions and the corresponding paired ion region P.I.R. , from the unpaired ions of the unpaired ion region U.I.R. diXx>d. The criterium of the choice of the distance d is not unique. For polyelectrolytes it is assumed that d is such that for where ze is the... 

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