30,384 research outputs found

    Small Angle Neutron Scattering of Aerogels: Simulations and Experiments

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    A numerical simulation of silica aerogels is performed using diffusion-limited cluster-cluster aggregation of spheres inside a cubic box (with periodic boundary conditions). The volume fraction cc is taken to be sufficiently large to get a gel structure at the end of the process. In the case of monodisperse spheres, the wavevector dependent scattered intensity I(q)I(q) is calculated from the product of the form factor P(q)P(q) of a sphere by the structure factor S(q)S(q), which is related to the Fourier transform of g(r)−1g(r)-1, where g(r)g(r) is the pair correlation function between sphere centers. The structure factor S(q)S(q) exhibits large-qq damped oscillations characteristics of the short range (intra-aggregate) correlations between spheres. These oscillations influence the I(q)I(q) curve in the qq-region between the fractal regime and the Porod regime and quantitative comparisons are made with experiments on colloidal aerogels. Moreover, at small-qq values, S(q)S(q) goes through a maximum characteristic of large range (inter-aggregate) correlations. Quantitative fits of the maximum in the experimental I(q)I(q) curves of base-catalyzed aerogel are presented. In the case of polydisperse spheres, I(q)I(q) is calculated directly from a single aggregate simulation. It is shown that increasing polydispersity shifts the location of the cross-over between the fractal and Porod regimes towards low qq-value.Comment: RevTex, 9 pages + 11 postscript figures, compressed using "uufiles". Proceeding of the 4th International Simposium on Aerogels (To appear in J. of Non-Cryst. Solids

    Irradiation-induced Ag nanocluster nucleation in silicate glasses: analogy with photography

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    The synthesis of Ag nanoclusters in sodalime silicate glasses and silica was studied by optical absorption (OA) and electron spin resonance (ESR) experiments under both low (gamma-ray) and high (MeV ion) deposited energy density irradiation conditions. Both types of irradiation create electrons and holes whose density and thermal evolution - notably via their interaction with defects - are shown to determine the clustering and growth rates of Ag nanocrystals. We thus establish the influence of redox interactions of defects and silver (poly)ions. The mechanisms are similar to the latent image formation in photography: irradiation-induced photoelectrons are trapped within the glass matrix, notably on dissolved noble metal ions and defects, which are thus neutralized (reverse oxidation reactions are also shown to exist). Annealing promotes metal atom diffusion, which in turn leads to cluster nuclei formation. The cluster density depends not only on the irradiation fluence, but also - and primarily - on the density of deposited energy and the redox properties of the glass. Ion irradiation (i.e., large deposited energy density) is far more effective in cluster formation, despite its lower neutralization efficiency (from Ag+ to Ag0) as compared to gamma photon irradiation.Comment: 48 pages, 18 figures, revised version publ. in Phys. Rev. B, pdf fil

    The Sol-Gel Process Simulated by Cluster-Cluster Aggregation

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    The pair-correlation function g(r,t)g(r,t) and its Fourier transform, the structure factor S(q,t)S(q,t), are computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in a box. This numerical analysis shows that the time evolution of the characteristic cluster size ξ\xi exhibits a crossover close to the gel time tgt_g which depends on the volumic fraction cc. In this model tgt_g tends to infinity when the box size LL tends to infinity. For systems of finite size, it is shown numerically that, when t<tgt<t_g, the wave vector qmq_m, at which S(q,t)S(q,t) has a maximum, decreases as S(qm,t)−1/DS(q_m,t)^{-1/D}, where DD is an apparent fractal dimension of clusters, as measured from the slo pe of S(q,t)S(q,t) . The time evolution of the mean number of particles per cluster nˉ\bar {n} is also investigated. Our numerical results are in qualitative agreement with small angle scattering experiments in several systems.Comment: RevTex, 13 pages + 9 postscript figures appended using "uufiles". To appear in J. of Non-Cryst. Solid

    Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime

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    Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussian-like distribution characterised by a mean a0a_0 and a standard deviation σ\sigma. The wave vector dependent scattered intensity I(q)I(q) is computed in order to study the influence of the particle polydispersity on the crossover between the fractal regime and the Porod regime. It is shown that, given a0a_0, the location qcq_c of the crossover decreases as σ\sigma increases. The dependence of qcq_c on σ\sigma can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.Comment: RevTex, 4 pages + 6 postscript figures, compressed using "uufiles", published in Phys. Rev. B 50, 1305 (1994

    Exploiting limited valence patchy particles to understand autocatalytic kinetics

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    Autocatalysis, i.e., the speeding up of a reaction through the very same molecule which is produced, is common in chemistry, biophysics, and material science. Rate-equation-based approaches are often used to model the time dependence of products, but the key physical mechanisms behind the reaction cannot be properly recognized. Here, we develop a patchy particle model inspired by a bicomponent reactive mixture and endowed with adjustable autocatalytic ability. Such a coarse-grained model captures all general features of an autocatalytic aggregation process that takes place under controlled and realistic conditions, including crowded environments. Simulation reveals that a full understanding of the kinetics involves an unexpected effect that eludes the chemistry of the reaction, and which is crucially related to the presence of an activation barrier. The resulting analytical description can be exported to real systems, as confirmed by experimental data on epoxy-amine polymerizations, solving a long-standing issue in their mechanistic description

    Evolution of Nanoporosity in Dealloying

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    Dealloying is a common corrosion process during which an alloy is "parted" by the selective dissolution of the electrochemically more active elements. This process results in the formation of a nanoporous sponge composed almost entirely of the more noble alloy constituents . Even though this morphology evolution problem has attracted considerable attention, the physics responsible for porosity evolution have remained a mystery . Here we show by experiment, lattice computer simulation, and a continuum model, that nanoporosity is due to an intrinsic dynamical pattern formation process - pores form because the more noble atoms are chemically driven to aggregate into two-dimensional clusters via a spinodal decomposition process at the solid-electrolyte interface. At the same time, the surface area continuously increases due to etching. Together, these processes evolve a characteristic length scale predicted by our continuum model. The applications potential of nanoporous metals is enormous. For instance, the high surface area of nanoporous gold made by dealloying Ag-Au can be chemically tailored, making it suitable for sensor applications, particularly in biomaterials contexts.Comment: 13 pages, PDF, incl. 4 figures. avi movies of simulations available at http://www.deas.harvard.edu/matsci/downdata/downdata.htm

    Emergence of fractal behavior in condensation-driven aggregation

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    We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size xx, grows by an amount αx\alpha x over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling c(x,t)∼t−βϕ(x/tz)c(x,t)\sim t^{-\beta}\phi(x/t^z) accompanied by the emergence of fractal of dimension df=11+2αd_f={{1}\over{1+2\alpha}}. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the dfthd_f^{th} moment of c(x,t)c(x,t) is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents β\beta and zz are locked with the fractal dimension dfd_f via a generalized scaling relation β=(1+df)z\beta=(1+d_f)z.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

    Experimental evidence on the development of scale invariance in the internal structure of self-affine aggregates

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    It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes among neighbor growing structures. Scaling relationships applied to these structures provide a method to evaluate relevant exponents and to characterize growing systems into universality classes. The analysis is applied to quasi-two-dimensional electrochemically formed silver branched patterns showing that the size distribution of frozen structures exhibits scale invariance. The measured exponents, within the error bars, remind us those predicted by the Kardar-Parisi-Zhang equation.Comment: 11 pages, 4 figure
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