Cluster solution

In addition, hydrogen bonding was still observed at 3,583 cm (Fig.l A). IR peaks in VC.O region (Fig.l B) shifted to lower frequency after adsorption due to precursor-support interaction and differed from that of cluster solution implying that precursor was not intact after adsorption on support but still in the form of metal carbonyl species. 

In a more simple and cheap way, silver clusters can be prepared in aqueous solutions of commercially available polyelectrolytes, such as poly(methacrylic acid) (PM A A) by photo activation using visible light [20] or UV light [29]. Ras et al. found that photoactivation with visible light results in fluorescent silver cluster solutions without any noticeable silver nanoparticle impurities, as seen in electron microscopy and from the absence of plasmon absorption bands near 400 nm (F = 5-6%). It was seen that using PMAA in its acidic form, different ratios Ag+ MAA (0.15 1-3 1) lead to different emission bands, as discussed in the next section (Fig. 12) [20]. When solutions of PMAA in its sodium form and silver salt were reduced with UV light (365 nm, 8 W), silver nanoclusters were obtained with emission band centered at 620 nm and [Pg.322]

The concept of dynamic silver clusters capable to transfer between molecules was also pointed out recently by Ras et al. for silver clusters prepared by photoactivation using PM A A as scaffold [20], Every specific initial ratio of silver ions to methacrylate unit, Ag+ MAA, results in distinct spectral bands (Fig. 12a, b). Thus, an initial ratio 0.5 1 gives an absorption band at 503 nm, whereas a ratio 3 1 gives a band at 530 nm. The shuttle effect was proven when for a given silver cluster solution with ratio 3 1 and absorption at 530 nm, a blue shift was achieved by the addition of pure PMAA. For instance if the added amount of polymer decreases the ratio Ag+ MAA from 3 1 to 0.5 1, the new optical band will match exactly with the band corresponding to a solution with initial ratio 0.5 1, that is 503 nm (Fig. 12c). The explanation given for this blue shift was the redistribution of the existent silver clusters in PMAA chains over the newly available PMAA chains, in other words that the clusters shuttle from partly clusters-filled chains to empty ones. 

Fig. 12 (a) Image of PMAA-protected fluorescent silver clusters prepared with increasing initial ratio Ag+ MAA from 0.5 1 to 12 1 and equal irradiation time, (b) Absorption spectra of the same samples as in (a), (c) Variation of absorption maxima of some of the samples in (a) with molar ratio. Black arrows indicate how the absorption band shifts to the blue with the addition of extra polymer to a fluorescent cluster solution explaining the transfer effect of silver clusters among PMAA chains [20]... 

Since the correct number of clusters is unknown, a cluster validity measure needs to be consulted for the evaluation of the clustering solution (Section 6.7). 

The standard hierarchical clustering algorithms produce a whole set of cluster solutions, namely a partitioning of the objects into k 1, n clusters. The partitions are ordered hierarchically, and there are two possible procedures ... 

Rh6(CO)16 (107 mg, 0.1 mmol) is dissolved completely in a mixture of tri-chloromethane (150 mL) and acetonitrile (10 mL). A solution of trimethylamine /V-oxide (Me3N0-2H20) (12 mg, 0.11 mmol) in MeOH/CHCl3 (0.5/5.0 mL) is added dropwise under vigorous stirring to the cluster solution. The reaction mixture is allowed to stand for an additional 15 min. The product is isolated by the procedure described above. Yield of 70-75 mg of Rh6(CO)15NCMe 64-70%. 

As mentioned, hierarchical cluster analysis usually offers a series of possible cluster solutions which differ in the number of clusters. A measure of the total within-groups variance can then be utilized to decide the probable number of clusters. The procedure is very similar to that described in Section 5.4 under the name scree plot. If one plots the variance sum for each cluster solution against the number of clusters in the respective solution a decay pattern (curve) will result, hopefully tailing in a plateau level this indicates that further increasing the number of clusters in a solution will have no effect. 

RAND [1971] published an algorithm which enables comparison of cluster solutions by their similarity. So, the results of even conceptually different clustering procedures may be contrasted. 

The interpretation of the results is the last step of cluster analysis. Two possible cluster solutions may to be discussed. The first solution consists of two clusters obtained if the dendrogram is cut between linkage distances 3.04 and 5.34. Then we have to interpret the nature of the two sets of objects 2 = K2, K5 and 3 = Kl, K3, K4. The second possible solution is obtained by cutting the dendrogram betweeen linkage distances 1.41 and 2.83 which leaves none of the former clusters unaltered. In other words the previously found clusters now appear not to be homogeneous. Because of the greater distance between 3.04 and 5.34 than between 1.41 and 2.83, however, one should rather try to interpret the nature of solution number 1. 

We have five objects each with two features. The objects are classified according to the result of cluster solution 1 class 1 contains objects Kl, K3 and K4 (n1 = 3), class 2 has the two elements K2 and K5 (n2 = 2). With the objects written as... 

Apart from Eu3+ and Tb3+, few studies have been reported on optical properties of lanthanide ions doped in ZnS nanociystals. Bol et al. (2002) attempted to incorporate Er3"1" in ZnS nanociystal by ion implantation. They annealed the sample at a temperature up to 800 °C to restore the crystal structure around Er3"1", but no Er3"1" luminescence was observed. Schmidt et al. (1998) employed a new synthesis strategy to incorporate up to 20 at% Er3"1" into ZnS (1.5-2 nm) cluster solutions which were stabilized by (aminopropyl)triethoxysilane (AMEO). Ethanolic AMEO-stabilized Er ZnS clusters in solutions fluoresce 200 times stronger at 1540 nm than that of ethanolic AMEO-Er complexes. This is explained by the very low phonon energies in ZnS QDs, and indicates that Er3+ ions are trapped inside chalcogenide clusters. However the exact position of Er3+ in ZnS clusters remains unknown. Further spectroscopic and structural analyses are required in order to obtain more detailed information. 

Due to its relative simplicity, the DFT became extremely useful in the application to large heavy-element molecules, clusters, solutions and solids. Systems with the large number of atoms can be treated with sufficient accuracy. The computing time in the DFT for a system of many atoms grows as Nat2 or Nat3, while in traditional methods as exp(Nat). The present upper limit is of Na, 200. The modern DFT is in principle exact and the accuracy... 

There are four major steps in cluster analysis. (1) An appropriate set of features must be selected, and scaled in a meaningful way. (2) A similarity matrix must be constructed as a record of the distances between each pair of objects in the collection. (3) A decision must be made about the number and interpretation of the clusters. (4) The cluster solution must be validated by visual or statistical means. Figure 2 illustrates one possible clustering of a 10,000-member library using SPE. 

The advantage of a uniform size must be qualified for colloids, having a size distribution per se which, however, can be relatively narrow in some cases. In principle the solubility of ligand-protected clusters and colloids makes their use as homogeneous catalysts possible. But as it has turned out, cluster solutions tend to decompose during catalytic processes. The isolation of an unchanged cluster material after a homogeneously catalyzed reaction is indicated in only a very... 

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. 

Figure 10. Hypothetical ionic cluster solution as partitioned into a fraction containing all the dissociated (and hydrated) ions and free water, and a fraction containing all the bound ( ) ( — ) pairs with their requisite water of hydration (24).

Initial studies on the redox properties of the M6Yi2 " clusters were reported on poorly defined complexes simply noted as [TaeCli2] or [Nb(jCli2] (122). Aqueous cluster solutions were prepared from the sulfate salts TaeCli2S04 and Nb6Cli2S04 with various electrolytes. Some combination of water molecules and anions fills the coordination sphere of the MeY " cluster. Despite these ambiguities, the oxidized compounds M6Yi2 were obtained with various chemical oxidants by a two-electron transfer process (123) ... 

The cluster formation is also reversible [80]. After the solvatochromic changes take place at a given acetonitrile composition, decreasing the acetonitrile composition by adding toluene to the mixture can change the solution color and absorption spectrum back to those of the fullerene monomer. The absorption spectrum of the cluster solution also changes upon dilution. A gradual... 

Recently, a solution-based method for photochemical preparation of polyfullerences has been discovered [81,82]. In the photopolymerization, carefully deoxygenated fullerene cluster solutions are used. As discussed in the previous section, Cjo and C70 form microscopic aggregates or clusters in room-... 

Murray and co-workers have demonstrated that further funetionalization of these nanoparticles can be achieved by place exchange reactions, which occur when an excess of functionalized alkanethiol is added to an alkanethiolate-cluster solution." In this way, a new chemical functionality can be introduced without changes in the... 

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