Polynuclear model

Between the extremes of the mononuclear model, in which the spreading velocity is infinite, and the polynuclear model, in which... 

In the mononuclear model, the limiting step is the formation of a nucleus. Once one is formed, the subsequent growth spreading across the crystal surface is infinitely rapid. For the polynuclear model, the spreading velocity is taken as zero and the crystal surface can only be covered by the accumulation of a sufficient number of nuclei. These two growth models represent two extreme cases. A third model, known as the birth-and-spread model, allows for formation of nuclei and their subsequent growth at a finite rate. In this case, new nuclei can form on top of uncompleted layers. 

The mononuclear model predicts that Vp depends on the area. A, of the dissolving crystal, while the polynuclear model predicts that the dependence of Vp on undersaturation, ct = (c - c) / Cp = Am / kT, should show a maximum. Such dependences have not been observed experimentally. 

Sjitberg and co-workers combined emf and nmr data to develop a model to describe polymerization and protonation of siUcate species in sodium sihcate solutions (43,44). Thirteen polynuclear species are described. This model yields useful insights into the changes in polymerization of sodium siUcate solutions as and [Si02] change. Higher order polynuclear species predominate as [Si02] increases or pH drops under alkaline conditions. The... 

Hydroxides. Thorium (TV) is generally less resistant to hydrolysis than similarly sized lanthanides, and more resistant to hydrolysis than tetravalent ions of other early actinides, eg, U, Np, and Pu. Many of the thorium(IV) hydrolysis studies indicate stepwise hydrolysis to yield monomeric products of formula Th(OH) , where n is integral between 1 and 4, in addition to a number of polymeric species (40—43). More recent potentiometric titration studies indicate that only two of the monomeric species, Th(OH) " and thorium hydroxide [13825-36-0], Th(OH)4, are important in dilute (<10 M Th) solutions (43). However, in a Th02 [1314-20-1] solubiUty study, the best fit to the experimental data required inclusion of the species. Th(OH) 2 (44). In more concentrated (>10 Af) solutions, polynuclear species have been shown to exist. Eor example, a more recent model includes the dimers Th2(OH) " 2 the tetramers Th4(OH) " g and Th4(OH) 2 two hexamers, Th2(OH) " 4 and Th2(OH) " 2 (43). 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

A number of complexes of copper with 1,1-dithiolenes are known they are interesting, inasmuch as they form (1) polynuclear species, e.g., [Cu4(i-mnt)3]2 . Recently, a copper(III) complex of 1,1-dicarboeth-oxy-2-ethylenedithiolate (DED ) was prepared (375) by oxidation of aqueous solutions of K2[Cu(DED)2] with a 10-15% excess of Cu(II) or H202, and of (BzPh3P)2[Cu(DED)2] with I2. The possibility of this system as a model for the Cu "/Cu. system in n-galactose oxidase has been pointed out. Lewis and Miller (113) also prepared M[Cu(S2C CHN02)2] (M = Cu, or Zn) and Cu[Cu S2C C(CN)2 2], and found that they are effective insecticides. 

This example shows that dipolar interactions can produce unexpected effects in systems containing polynuclear clusters, so that their complete quantitative description requires a model in which the dipolar interactions between all the paramagnetic sites of the system are explicitly taken into account. Local spin models of this kind can provide a description of the relative arrangement of the interacting centers at atomic resolution and have been worked out for systems containing [2Fe-2S] and [4Fe-4S] clusters (112, 192). In the latter case, an additional complication arises due to the delocalized character of the [Fe(III), Fe(II)] mixed-valence pair, so that the magnetic moments carried by the two sites A and B of Fig. 8B must be written... 

Pyridyl functionalized tris(pyrazolyl)borate ligands show some interesting properties including the formation of polynuclear zinc complexes.23,1 Some of these contain extensive H bonding and have potential as models for multinuclear zinc enzymes such as phospholipase C or PI nuclease.235 A bis-ligand complex of the hydrotris(5-methyl-3-(3-pyridyl)pyrazolyl)borate ligand (23) shows octahedral coordination of all six pyrazole nitrogen donors despite the steric bulk. 

Examples of the need for multimedia models are found in contemporary problem areas. Polynuclear aromatic hydrocarbons and metals are emitted into the atmosphere as trace impurities with the products of coal combustion. The organics have low vapor pressure and partially condense on emitted particulates in a stack plume. The particulates are transferred to the soil by dry deposition, rainout or washout. The metals manifest... 

To illustrate how this applies in the present circumstances we consider a passible group transfer reaction between A2 dihydro-naphthalene, (gQ) > a hydrogen donor, and phenanthrene,(g gr > a substrate (hydrogen acceptor) which models a polynuclear aromatic moiety commonly found in coal. In the overall group transfer reaction ... 

A metal cluster can be considered as a polynuclear compound which contains at least one metal-metal bond. A better definition of cluster catalysis is a reaction in which at least one site of the cluster molecule is mechanistically necessary. Theoretically, homogeneous clusters should be capable of multiple-site catalysis. Many heterogeneous catalytic reactions require multiple-site catalysis and for these reasons discrete molecular metal clusters are often proposed as models of metal surfaces in the processes of chemisorption and catalysis. The use of carbonyl clusters as catalysts for hydrogenation reactions has been the subject of a number of papers, an important question actually being whether the cluster itself is the species responsible for the hydrogenation. Often the cluster is recovered from the catalytic reaction, or is the only species spectroscopically observed under catalytic conditions. These data have been taken as evidence for cluster catalysis. 

In the preceding paper, Malcolm Chisholm (1) has presented a cogent case for the modeling by metal alkoxides of certain aspects of the structural chemistry and reactivities of metal oxides. The focus of this work has been the dinuclear and polynuclear alkoxides of molybdenum and tungsten, an area of research which has also attracted our interest 02-4) and upon which I would now like to take this opportunity to comment. 

In the case of polynuclear metal cluster SCO complexes in the solid state, there will be intra-cluster, as well as inter-cluster cooperativity. To eliminate inter-cluster effects totally, studies must be made in dilute solutions. Williams et al. have done just this for a dinuclear [Fe(II)2L3] helicate complex which does not contain a good superexchange pathway between the Fe(II) centre but, rather, three flexible bis-bidentate ligands. A very broad, two step, SCO was observed (LS-LS<->LS-HS<->HS-HS) and fitted to a model for negative cooperativity in which subtle structural changes around each Fe oc-... 

In an equilibrium study of the adsorption of molybdenum(VI) from aqueous solution onto activated carbon it has been found that the data are best explained in terms of an absorption model comprising the three species [HMo207] , Mo03(H20)3, and [HMo04] of which the dimer predominates by far (80). Computer treatment of potentiomet-ric (81) and spectrophotometric data (82) also indicated the possible existence of [HMo207] as a minor species in aqueous solution at low molybdenum concentration ( 2 X 104 Af). However, as its assumed stability region overlaps with several other polynuclear ions more direct evidence is needed before its existence can be accepted with certainty. 

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