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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 Gaussianlike distribution characterised by a mean a0 and a standard deviation σ. The wave vector dependent scattered intensity 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 a0, the location qc of the crossover decreases as σ increases. The dependence of qc on σ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.PACS numbers: 61.43.Bn, 61.43.Hv Small-angle X-ray scattering as well as small-angle neutron scattering have been widely used to study the structure of disordered systems 1-8 . In particular they have allowed to demonstrate that silica aerogels are made of connected fractal "blobs" 3,4 . In such materials, the wave vector dependent scattered intensity I(q) exhibits two crossovers related to the two characteristic lengths, mean particle diameter a 0 and mean blob size ξ. The first one separates the low-q (q << ξ −1 ) saturation, called the Guinier regime 9 , from the intermediate power-law behaviour 3,4 , called the fractal regime. The second one, on which we will focus in this letter, separates the fractal regime from the high-q (q >> a −1 0 ) q −4 behaviour, called the Porod regime 9 .In some previous studies, it was assumed that the crossover between the fractal regime and the Porod regime was always exactly located at q c = 2π/a 0 . This assumption was even used by some authors to quantitatively determine the average diameter 5,6 or the gyration radius 4,7 of the particles. In several other papers, an average particle radius was extracted from a fit of the scattered intensity I(q) to analytical expressions which do not include polydispersity 2,8 . Such kind of analysis has been done in the case of base catalysed and neutrally reacted silica aerogels where the particle size polydispersity impedes the determination of a 0 by conventional methods such as electron micrography. In this letter we show that such an assumption is only valid when the standard deviation σ of the particle size is small compared to the average a 0 .In previous papers 10,11 it has been shown that cluster-cluster aggregation models 12 can satisfactorily reproduce the structure of aerogels. Furthermore, if we are only interested in short range correlations, it is sufficient to consider a single aggregate obtained with a simplified aggregation process: the hierarchical cluster-cluster model 13 .Here for simplicity we have considered the case of chemically limited cluster-cluster aggregation (CLCA) 14 using a three dimensional off-lattice hierarchical procedure. The hierarchical scheme is an iterative method which starts with a collection of N p = 2 p particles at iteration i = 0 and ends with a unique aggregate of N p particles at iteration p. At an interme...

Simulated minimum cross-section histograms of breaking Al nanocontacts are produced using molecular dynamics. The results allow a new interpretation of the controverted conductance histogram peaks based on preferential geometrical arrangements of nanocontact necks. As temperature increases, lower conductance peaks decrease in favor of broader and higher conductance structures. This reveals the existence of shell and supershell structures favored by the increased mobility of Al atoms.

The pair-correlation function g(r, t) and its Fourier transform, the structure factor S(q, t), are computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in abox. This numerical analysis shows that the time evolution of the characteristic cluster size ξ exhibits a crossover close to the gel time t g which depends on the volumic fraction c. In this model t g tends to infinity when the box size L tends to infinity. For systems of finite size, it is shown numerically that, when t < t g , the wave vector q m , at which S(q, t) has a maximum, decreases as S(q m , t) −1/D , where D is an apparent fractal dimension of clusters, as measured from the slope of S(q, t) . The time evolution of the mean number of particles per clustern is also investigated. Our numerical results are in qualitative agreement with small angle scattering experiments in several systems.

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We perform a representative series of semiclassical molecular dynamics simulations of aluminum nanocontact breakages, coupled to full quantum conductance calculations. This approach allows to obtain realistic conductance histograms of polyvalent species and understand the origin of their peaked structures. The results show that the conductance depends linearly on the contact minimum cross section for the geometrically favored nanocontact configurations. Valid in a broad range of conductance values, such relation suggests the definition of a transport parameter for the nanoscale, that represents the novel concept of ballistic resistivity. One of the major industrial challenges is to profit from some fascinating physical features present at the nanoscale. The production of dissipationless nanoswitches ͑or nanocontacts͒ is one of such attractive applications. 1 The inelastic electron mean free path is usually larger than nanocontact typical cross sections ͑of the order of few atoms in controlled experimets͒ even at room temperature, and, therefore, the electronic transport through these nanoconstrictions is expected to be ballistic. Nevertheless, the lack of knowledge of the real efficiency of this electronic ballistic/nondissipative transport limits future innovations.For contact sizes of the order of a few Fermi wavelengths F , well defined modes ͑channels͒ appear associated with the transversal confinement of electrons. For this situation, the conductance G is given by the Landauer formula G = G 0 ͚ n=1 N T n , where G 0 =2e 2 / h is the conductance quantum ͑e being the electron charge and h Planck's constant͒, T n is the transmission probability of the nth channel, and N is the number of propagating modes with energies below the Fermi energy. 2 It has been shown that the number of conducting channels is determined by the number of valence electrons of the respective chemical element. 3 For monovalent noble metals such as Cu, Ag and Au, the transmission probability T has been estimated to be approximately equal to 1 ͑i.e., each noble-metal atom contact contributes with G 0 to the conductance value 4,5 ͒. But for monovalent alkali metals or polyvalent chemical species, single-atom contact studies revealed that this channel transmittivity can have a result smaller than one. 3,6,7 Nowadays, there exist several experimental techniques to characterize the electronic transport through nanocontacts. Among them, the measurement of the conductance histogram during nanocontact breakages 8-10 is one of the most used. By putting in contact two opposite electrodes and then separating them, one observes a stepwise decrease in the electrical conductance ͑i.e., a conductance scan͒, until the breakpoint is reached. [11][12][13][14] It has been shown that each scan of the conductance dependence on the electrode retraction differs from one another, since the nanocontact structural evolutions during breakages are not identical. 15 Notwithstanding for fixed experimental parameter conditions ͑such as temperature and applied voltage...

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