We have observed visible light emission from nanosize gold clusters. Liquid chromatographic analysis of the metal clusters shows that relatively intense photoluminescence occurs only when the size of the metal nanocluster is sufficiently small (<5 nm). The emission is strongly Stokes shifted and is assigned to radiative recombination of Fermi level electrons and sp- or d-band holes. The electron and/or hole states are perturbed by surface states, as indicated by the dependence of the emission spectrum on the nature of the cluster surface. Finally, we found that large, nonemitting gold clusters can also be made luminescent by partial dissolution using KCN.

The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

Measurement of the fractal dimension, D, of colloidal aggregates of small silica particles is reported. We observe power-law decay of the structure factor [S(k) -k o] by both light and x-ray scattering showing that the aggregates are fractal. D is found to be 2.12+0.05, which is intermediate between recent numerical results for the kinetic models of diffusionlimited aggregation (D = 2.5) and cluster aggregation (D = 1.75), but is rather close to the value for lattice animals (D = 2.0), which are equilibrium structures. PACS numbers: 64.60.Cn, 05.40.+j, 61.10.Fr Understanding aggregation has been a primary goal in the field of colloidal physics for many years. 'In addition to its importance in commercial processes, aggregation is a prototypical example of a complicated random process which may display such features as self-similarity, scaling, and universality. 2 These features have been revealed by computer simulations.It has been shown recently, for example, that the two most popular models, diffusion-limited aggregation3 4 (DLA) and cluster-cluster aggregation 6 (CA), produce ramified structures that are self-similar in that the two-point density-density correlation function p2(r) is of a power-law form, p, (r) -r ", for values of r intermediate between the lattice constant or monomer size a and the cluster size R. Structures described by Eq. (1) are self-similar and are known as fractals; their essential geometric properties are independent of length scale. In ddimensional space, they are characterized by a fractal or Hausdorff-Besicovitch dimension D related to A by D = d -A. An immediate consequence of Eq.(1) is that the radius of gyration of a cluster RG is related to the number of particles it contains N, by N, -RD (2) A uniform object has D = d, while more open structures in which the density decreases with distance from the center have D & d. Numerical simulations have shown D to be -Sd/6 for DLA in d dimensions for both lattice (2~d~6) and nonlattice (d=2, 3) diffusion, independent of sticking coefficient s (0. 1» s~1). Cluster aggregation in which many particles diffuse and stick together to form clusters which also diffuse and stick yields self-similar aggregates having D =1.45 and 1.75 in two and three dimensions, respectively.

Near the sol-gel transition, gelling systems exhibit an extremely slow relaxation of thermally driven density Auctuations. %'e have made a detailed quasielastic light scattering study of the decay of density fluctuations in reacting silica sol-gels in the pre-and post-gel regimes, and at the gel point. In the pre-gel regime the dynamic structure factor S(q, t) for the branched polymer melt has a stretched exponential tail whose characteristic time diverges at the gel point. This critical slowing down is due to the divergence of the average cluster size and is distinct from the usual critical slowing down observed in second-order thermodynamic phase transitions, since the initial decay rate of S(q, t) is nondivergent at the gel point. In fact, at the gel point, S(q, t) becomes a power law, indicating a fractal time set in the scattered field. These observations are accounted for by considering the dynamics of percolation clusters, and in this connection the analogy to viscoelasticity is described. Beyond the gel point S (q, t) remains a power law, but the amplitude of the relaxing part of the intensity autocorrelation function diminishes. Finally, the dynamics of clusters diluted from the reaction bath is studied, and a crossover from power law to stretched exponential decay of S (q, t) is observed. It is shown that at infinite dilution the long-time tail of the correlation function describes the internal modes of a single percolation cluster.

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Using a dynamic scaling theory for the viscoelasticity of cross-linking polymers near the gel point, we predict the superposition of viscoelastic functions at differing extents of reactions. For example, to superpose the stress relaxation modulus, a vertical shift is needed to account for the increase in the equilibrium modulus with cure, G" ~e8/3, and a horizontal shift for the divergence of the characteristic relaxation time, ~e~4, where < is the critical extent of reaction. Experiments on model epoxies show excellent superposition both below and above the gel point and give G" ~e2-8±0•2 and rz ~c~3'9±0•2. The critical regime where this superposition is valid is surprisingly wide, encompassing over half of the reaction.

The dynamics of the sol-gel transition is probed by use of quasielastic light scattering. A type of critical dynamics is observed that is associated with a divergent friction, rather than a singularity in a thermodynamic quantity. Several novel effects are reported, including power-law time decay of the intensity autocorrelation function, critical slowing down of the average relaxation time, and observation of a fractal time set in the scattered field.PACS numbers: 82.70. Gg, 61.41.+e A gelling solution at the sol-gel transition is a unique state of matter that is neither liquid nor solid, but rather is in transition between these states. For example, the viscosity of the incipient gel is infinite, but the modulus is zero. Recently we have come to appreciate the unusual dynamics of this transition state by using the technique of quasielastic light scattering x to probe the relaxation of density fluctuations of wave vector q by the autocorrelation function of the scattered intensity, l(q,t) =(1(0)/(/)). In many systems the decay of density fluctuations can be described by a single relaxation time (exponential time decay). More complex materials, such as polymeric melts near the glassy transition temperature, exhibit a spectrum of relaxation times that gives a "stretched" exponential decay, exp[ -(t/r) b ] where 0 < b < 1. Regardless of the form, all known I(q,t) can be described by some characteristic time T. In this paper we demonstrate that in a gelling solution the characteristic time diverges at the sol-gel transition. This observation is unexpected and must not be confused with the usual critical slowing down in second-order thermodynamic phase transitions, since scattered-intensity measurements show that the compressibility does not diverge at the gel point. The fact that a critical slowing down should not be observed in quasielastic light scattering at the gel point has been elaborated by de Gennes, 2 who points out that the longitudinal modes observed in a quasielastic light-scattering experiment should be insensitive to the formation of a weak gel phase.The observation of an infinite characteristic time implies two possible modes of decay. First, the decay can be described by a function that is scaled by a divergent characteristic time, e.g., an exponential decay with r-• <». This is precisely the description of critical slowing down in second-order phase transitions. Second, the form of the decay can be independent of the time scale, at least on times short compared with the characteristic time. This is possible if the decay is described by a function that does not contain a time scale-a power law. In fact, we will show that at the gel point a decay of the form I(q,t)~-\/t 021 is observed over the experimentally accessible 5 decades in time. Before the gel point, this power-law decay is truncated by a stretched-exponential tail, at a certain divergent characteristic time. A simple description of these phenomena is proposed, and we show that the detected photons divide the time axis in a selfsimilar wa...

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