Application of fractals and kinetic equations to cluster formation

Villarica, M.; Casey, M. J.; Goodisman, Jerry; Chaiken, J.

doi:10.1063/1.464989

Cited by 62 publications

(53 citation statements)

References 63 publications

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“…As it was shown by Villarica et al [27] that the asymptotic solution of the Smoluchowski equation yields a lognormal distribution giving physical meaning to many observed cluster-size distributions [28,29], therefore we used eq 1 for each intensity group of the bimetallic clusters.…”

Section: The Intensity Distributions Of the Clustersmentioning

confidence: 99%

Bimetallic silver-gold clusters by matrix-assisted laser desorption/ionization

Kéki

Nagy

Deák

et al. 2004

J. Am. Soc. Mass Spectrom.

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Pure gold clusters (Au n ϩ ) were produced up to the cluster size of n ϭ 100 by matrix-assisted laser desorption/ionization (MALDI). The mass spectrum of the resulting clusters showed alteration in the ion intensity at odd-even clusters size. On the other hand, intensity drops at cluster size predicted by the jellium model theory was also observed. Positively and negatively charged bimetallic silver-gold clusters were produced under MALDI conditions from the mixture of HAuCl 4 /silver trifluoroacetate and the 2-(4-hydroxyphenylazo)benzoic acid (HABA) matrix. A linear correlation was found between the intensity ratio of Au n Ag m ϩ to Au nϩ1 Ag mϪ1 ϩ cluster ions and the molar ratio of the gold to silver salt. It was observed that the composition and the distribution of the clusters can be varied with the molar ratio of the silver and gold salts. It was also found that the resulting cluster sizes obey the lognormal distribution. The variation of the atom types building up the cluster and/or the composition, as well as the size of the cluster offers various possibilities to engineer their properties for specific technological and scientific demands. However, to achieve these specific goals much information on the physical and chemical properties of the clusters as the function of their composition and size should be gained. Mass spectrometric methods provide a unique experimental tool for the investigation of the electronic and geometric properties of small-size metal clusters [6].In the past decades several methods were explored to induce gas-phase generation of metal clusters, and most of these techniques were based on the evaporation of metals by heating [7,8], or using laser ablation [9 -11] and ion-bombardment [12][13][14][15]. The production and investigation of binary silver-gold [2,16,17] and those of the pure silver [12][13][14]18] and gold clusters [12,13] has been reported by several research groups. However, in contrast to the information available on the pure silver and gold clusters, only very limited experimental [16,17] and theoretical studies [19] on the properties of small size silver-gold clusters have been reported. Recently, the generation of silver-cluster ions in matrix-assisted laser desorption/ionization (MALDI) [20,21] was reported using silver salts and various matrixes [22][23][24]. In a previous paper [24] we have shown that both positively and negatively charged silver clusters up to the size of 200 can be effectively produced from silver ions under MALDI conditions. It was noted that considerable reduction of Ag ϩ takes place in the plume and the matrices enhance the formation of silver clusters. As a continuation of our work, we utilized this method for the generation of pure gold clusters and for the production of mixed binary goldsilver clusters. To our best knowledge we are the first to apply the MALDI method to produce pure gold and bimetallic Au-Ag cluster ions. The present report shows that the resulting distribution of the binary gold-silver clusters can be effectively chan...

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Section: The Intensity Distributions Of the Clustersmentioning

confidence: 99%

Bimetallic silver-gold clusters by matrix-assisted laser desorption/ionization

Kéki

Nagy

Deák

et al. 2004

J. Am. Soc. Mass Spectrom.

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“…49,[62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79] Coarsening is a ubiquitous phenomenon. The most common example involves the morphology of a miscible A-B system quenched in a two-phase region of the phase diagram.…”

Section: Dynamics Of Pattern Evolution: Late-stage Coarsening Of Dropmentioning

confidence: 99%

Wetting and dynamics of structured liquid films

Green

2003

J Polym Sci B Polym Phys

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ABSTRACT:The stability of a sufficiently thin, supported, homopolymer film against the development of local thickness fluctuations which can become amplified, eventually leading to structural destabilization of the film, is typically determined by long and short-range intermolecular forces. In A-B diblock copolymers, the connectivity between the blocks, the preferential attraction of one block to an external interface, combined with an incompatibility between the A-B segments, the situation is very different. Two cases, largely dictated by N, wher is the Flory-Huggins interaction parameter and N is the degree of polymerization, can arise in thin copolyme films. When N is large, thin films exhibit comparatively stable topographical structures, where the dimensions of the topographies normal to the substrate reflect a natural length-scale associated with phase separation in the material. In the other situation, where N is sufficiently small, the copolymer bulk structure is homogeneous. An ordered structure can be induced into the otherwise compositionally homogeneous structure in the vicinity of a substrate. Here, depending on film thickness, a series of transient and stable topographies can develop. Wetting, early stage structural destabilization dynamics leading to the formation of droplets, and late stage coarsening of the droplets are discussed.

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“…Such a function was later applied by Chaiken to simulate the experimental distribution recorded in mass spectra and gave satisfying results [7,8]. Comparing with (15), it can be found that the parameter α, given by Jullien, is equal to a − 1 and the parameter β, is equal to 1/u.…”

Section: Different Expressions Of the Distribution Functionmentioning

confidence: 86%

“…Chaiken applied an asymptotic solution [7,8], n k = Ak α e −βk , to simulate the experimental distribution and got satisfying results. In the formula, k represents the size of particles and α, β are the parameters to be determined.…”

Section: Introductionmentioning

confidence: 86%

Application of the Smoluchowski equation to the formation kinetics of cluster ions

Huang

Zhang

Chen

et al. 1999

The European Physical Journal D

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Cluster ions with various sizes and compositions have been generated from direct laser vaporization. The Smoluchowski rate equation is extended to describe the formation kinetics of the cluster ions, which have been assumed to be produced from ion-molecule reactions with same-rate constants. By solving the kinetic equation analytically we obtained the distribution function of the cluster ions. Analysis of the distribution function showed that the function can characterize the statistical size distribution of the cluster ions and can be reduced to the asymptotic solution suggested by Jullien [1]

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Application of fractals and kinetic equations to cluster formation

Cited by 62 publications

References 63 publications

Bimetallic silver-gold clusters by matrix-assisted laser desorption/ionization

Bimetallic silver-gold clusters by matrix-assisted laser desorption/ionization

Wetting and dynamics of structured liquid films

Application of the Smoluchowski equation to the formation kinetics of cluster ions

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