Application of fractals and kinetic equations to cluster formation

Slow and long-ranged dynamical heterogeneities in dissipative fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

Reversible Photoredox Processing of Transition Metal Oxides

We describe a novel laser chemical process having potential for optical data storage and processing applications. Reversible oxygen exchange involving WO3, using readily available laser sources offers improved durability and versatility over existing erasable optical data storage media. Being interconvertable using heat and blue-green laser sources, the well known yellow WO3 and blue W2O5 can function as erased and written states.

Measurement of nanoparticle mass distributions by laser desorption/ionization time-of-flight mass spectrometry

In this paper, access to the mass distribution analysis of nanoparticles is described based on laser desorption/ionization and time of flight mass spectrometry. Two examples are given, demonstrating the accurate mass distribution analysis of nanoparticles fabricated both ex situ and in situ during the laser-assisted desorption process. The potentials and the limitations of the method are discussed, with special emphasis on carbonaceous clusters and molecules.

Application of scaling and kinetic equations to helium cluster size distributions: Homogeneous nucleation of a nearly ideal gas

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected.

Scaling and the Smoluchowski equations

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K(jk). The K(jk) are said to scale if K(lambda j,gamma k) = lambda(mu)gamma(nu)K(jk) for j < or = k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak(a)e(-bk), where A is a normalization constant (a function of a, b, and time), a = -(mu+nu), and b(mu+nu-1) depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/square root of m(k) (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to m(k)(-0.577). This leads to mu+nu = 0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of mu+nu.

Observations of coarsening of air voids in a polymer-highly-soluble crystalline matrix during dissolution

A combination of magnetic resonance imaging and x-ray microcomputed tomography has been used to visualize the development of the internal micro-structure within compressed tablets made from a combination of insoluble particles (Eudragit, a polymer) and soluble particles (diltiazem hydrochloride, a drug), during dissolution in water. Air voids in the tablet are seen to coarsen. The size distribution of the air voids is well fitted by a log-normal distribution with a mean size that grows linearly with time. There is evidence for both diffusion of voids and sudden collapse of individual voids, presumably as they coalesce. The behavior of the voids is studied and compared with models of coarsening; the implications for tablet dissolution are considered.

Magic numbers, excitation levels, and other properties of small neutral He4 clusters (N⩽50)

The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expansion. These peaks appear at cluster sizes which can just accommodate one more additional stable excitation. The good agreement with experiment provides not only experimental confirmation of the energy level and the chemical potential calculations, but also evidence for a new mechanism which can lead to magic numbers in cluster size distributions. By accounting for the falloff of the radial density distributions at the surface and a size-dependent surface tension, the energy levels are demonstrated to be consistent with a modified Rayleigh model of surface excitations. The compressibility coefficient of these small clusters is found to be one order of magnitude smaller than the bulk compressibility.

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

Pure gold clusters (Aun+) were produced up to the cluster size of n = 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 HAuCl4/silver trifluoroacetate and the 2-(4-hydroxyphenylazo)benzoic acid (HABA) matrix. A linear correlation was found between the intensity ratio of AunAgm+ to Au(n+1)Ag(m-1)+ 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.

Raman spectroscopy of small para-H2 clusters formed in cryogenic free jets

Small para-H2 clusters (pH2)N with N=2,...,8 have been identified by Raman spectroscopy in cryogenic free jets of the pure gas, near the Q(0) Raman line of the H2 monomer. The high resolution in space, time, and number size makes it possible to follow their growth kinetics with distance from the orifice. At lower source temperatures liquid clusters appear early in the expansion and then undergo a gradual phase transition to the solid state. The technique is very promising for exploring superfluidity in pure (pH2)N clusters.

Diffraction of neutral helium clusters: evidence for "magic numbers"

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.

Late-stage coarsening of an unstable structured liquid film

Thin films of poly(styrene-b-methyl methacrylate) diblock copolymers above the bulk order-disorder transition temperature, within a certain thickness range, are structurally unstable on SiO(x)/Si substrates. They dewet autophobically, forming droplets on a self-assembled brush. We investigated the late-stage evolution, coarsening, of the droplets on the brush. The average droplet cross-sectional area <S> increased with time, <S> proportional, variant t(gamma). This was accompanied by a decrease in the number of droplets per unit area with time, N(t) proportional, variant t(-gamma). We analyzed the droplet size distribution, F(S/<S>) vs S/<S>, and found that the shape of the curve was virtually identical at different stages throughout the process. This suggests that a structural self-similarity is associated with the process. A comparison of F(S/<S>) vs S/<S> data with distributions based on Ostwald ripening and coalescence cluster coarsening (dynamic and static) mechanisms strongly indicates that the dominant coarsening mechanism involved motion of droplets across the brush and subsequent coalescence, i.e., dynamic coalescence coarsening, not Ostwald ripening.