Pn+ cations

Uneven open shell Pn clusters are easier to ionize than even closed shell ones and the stability of the closed shell uneven P cluster cations is higher. For very large Pn+ cations with n = 25 + 8x (x — 0.1.2. 8) islands of stability were observed in the time of flight mass spectrum (TOF-MS) obtained by laser ablation of red phosphorus, suggesting that the more stable P clusters have connections with units of eight P atoms [71d]. A lot of effort has been put into the calculation of the most stable Pn+ cation structures. The respective global minimum structures of the more stable uneven P3+, Ps+, P71 and P<)h cluster cations are shown in Figure 2.6-10 [73, 74],... 

Potassium is the second most abundant cation in the body and is found primarily in the intracellular fluid. Potassium has many important physiologic functions, including regulation of cell membrane electrical action potential (especially in the myocardium), muscular function, cellular metabolism, and glycogen and protein synthesis. Potassium in PN can be provided as chloride, acetate, and phosphate salts. One millimole of potassium phosphate provides 1.47 mEq of elemental potassium. Generally, the concentration of potassium in peripheral PN (PPN) admixtures should not exceed 80 mEq/L (80 mmol/L). While it is safer to also stick to the 80 mEq/L (80 mmol/L) limit for administration through a central vein, the maximum recommended potassium concentration for infusion via a central vein is 150 mEq/L (150 mmol/L).14 Patients with abnormal potassium losses (e.g., loop or thiazide diuretic therapy) may have higher requirements, and patients with renal failure may require potassium restriction. 

To distinguish partition coefficients of neutral species from ionized species, the notation log PN and log/j/ may be used, respectively, or the symbol C or A may be used as a substitute for superscript /, denoting a cation or anion, respectively. [362],... 

Another, more indirect but perhaps more efficient method, would be to determine K for a number of typical systems, perhaps by use of model compounds, and then to select for kinetic experiments initiator systems for which K is so great that [Pn+] is effectively equal to c0, so that then the simple Equation (1) with [Pn+] = c0 is applicable. The trouble is that this method will probably only work for fairly polar solvents, because it is to be expected that Kp will be smaller, the less polar the solvent. This effect is probably one of the factors responsible for the improbably low kp value obtained by Higashimura for styrene in benzene solution [7]. In any case, for solvents of low polarity the participation of paired cations must be taken into account, which makes the relevant equations rather more complicated, but does not alter the relevance and importance of equilibrium (i). 

The present paper is an attempt to unravel a rather confused aspect of cationoid polymerisations. This concerns the phenomenon comprised in the term monomer complexation of the growing cation . The idea seems to have occurred for the first time in the work of Fontana and Kidder on the polymerisation of propene by AlBr3 and HBr in w-butane [3]. The kinetics indicated a reaction of zero order with respect to monomer, M to explain this, it was assumed that the growing end of the chain, written as a carbenium ion, Pn+, is complexed with M and that the rate-determining growth step is an isomerisation of this complex ... 

In the present context it will be useful to establish the conditions under which free cations or paired cations might be expected to determine the behaviour of a cationic polymerisation some aspects of this problem have been discussed previously [5]. Consider a system in which Pn+ are the growing polymer molecules and A is the anion derived from the catalyst or the syncatalytic system. Let [Pn+] + [Pn+ A"] = c, let [Pn+] = [A ] = i, [Pn+ A"] = q, and let K be the equilibrium constant for the dissociation of ion-pairs ... 

The most abundant propagating species must be the unpaired cation, i.e., the dissociation constant KD of the ion-pairs must be so great that the ratio y/p = [Pn+]/[Pn+A ] would be greater than 10, and preferably greater than 102. 

Several workers have attempted to use the common ion technique to depress [Pn+] and thus to achieve a monoeidic Pn+A system, as was done so successfully for anionic systems. However, because generally the solvents used for cationic polymerisations are much more polar, the KD of the chain-carriers and of the common-ion salts are considerably greater than in the anionic systems. Therefore the electro-chemical situation is likely to be complicated by triple ion formation and the effects of ionic strength on the KD and on the rate-constants, so that any results obtained by extrapolations to infinite ionic strength need to be scrutinised most carefully. 

The paired cation Pn+A The relative concentrations of the paired and unpaired cations are governed by an Ostwald-type equilibrium with dissociation constant KD. The magnitude of this is governed by the size and shape of the ions and the dielectric constant of the solvent. In contrast to anionic polymerisations, there is no definite evidence for distinguishing between tight and solvent-separated ion-pairs. 

The monomer-solvated cation Pn+M. Although this species first appeared in 1948, its importance was not realised until comparatively recently. Provided that its... 

The cation which is both solvated by M and paired Pn+M-A Whichever way one thinks of this species, the positive charge-density of the Pn+M is low compared to that of Pn+ so that for this reason and because of the mass-action effect the abundance of Pn+M A is likely to be much less than those of Pn+A" and Pn+M. 

The ionic conductivity at the end of a polymerisation is due to whatever cations Pn+ are formed or left when the monomer is exhausted and the anions A- of the initiating salt, plus a very minor contribution from the ions formed from impurities, which will be ignored. In order to analyse the relation between the observed iq, c0 and the ionic conductivity A of the electrolyte, it is necessary to clarify the electrochemistry of the solutions. We note first that the polymeric cations, whatever their structure, (i.e., as they were when propagating or subsequently isomerised), are much larger than the anions, SbF6, so that these carry virtually all the current so that A A, (SbF6), and therefore A, can be calculated-see below. Next, we note that all the iq- c0 plots, including that reported earlier [2], are rectilinear. This means ... 

Models (Hi) and (iv). Strictly, the only way of finding out definitely whether there is any complexation between the growing cation and the monomer or the polymer, or both, is to investigate whether (and if so, how) the apparent kp+ depends on monomer concentration [16, 17]. We have such evidence only for ACN and styrene and for these the value of kp does not depend on m. This is in accord with the prediction [15,17] that in a highly polar solvent the complexation of Pn+ by a Jt-donor monomer or its polymer is likely to be negligible. The likely behaviour of the w-donor vinyl ethers and their polymers is less clear, but a consideration of the dipole moments and concentrations involved makes it extremely unlikely that these monomers or their polymers could compete successfully for a place in the solvation shell of the growing cations. 

The reason is that these alleged kp values are mostly composite, comprising the rate constants of propagation of uncomplexed Pn+, paired Pn+ (Pn+A ), and Pn+ complexed with monomer or polymer or both, without or with an associated A" [17]. Even when we will eventually have genuine kp values for solvents other than PhN02, it will not be possible to draw many (or any ) very firm conclusions because the only theoretical treatments of the variation of rate constants with solvent polarity for (ion + molecule) reactions are concerned with spherically symmetrical ions, and the charge distribution in the cations of concern to us is anything but spherically symmetrical. 

We now suppose that the initiator 1 in EtN02 has formed the cationated aci-acid 4-ClC6H4C(0)-0N+( CHMe)0H (HI) and that this initiates a normal cationic polymerisation by protonating the monomer which then propagates to give Pn+ (Scheme 2) ... 

Polymerisations of undiluted, bulk monomer are rare except for those initiated by ionising radiations and they require a special treatment which will be given later. The most common situation is to have the propagating ions in a mixture of monomer and solvent, and as the solvation by the solvent is ubiquitous and may dominate over that by other components of the reaction mixture, mainly because of the mass-action effect, it will not be noted by any special symbol, except in a few instances. This means that we adopt the convention that the symbol Pn+ denotes a growing cation solvated mainly by the solvent correspondingly kp+ denotes the propagation constant of this species, subject to the proviso at the end of Section 2.3. Its relative abundance depends upon the abundance of the various other species in which the role of the solvent as the primary solvator has been taken over by any or all of the anion or the monomer or the polymer. The extent to which this happens depends on the ionic strength (essentially the concentration of the ions), and the polarity of the solvent, the monomer and the polymer, and their concentrations. 

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