Non-clasical Nucleation in Supercooled Nickel

The dynamics of homogeneous nucleation and growth of crystalline nickel from the super-cooled melt is examined during rapid quenching using molecular dynamics and a modified embedded atom method potential. The character of the critical nuclei of the crystallization transition is examined using common neighbor analysis and visualization. At nucleation the saddle point droplet consists of randomly stacked planar structures with an in plane triangular order. These results are consistent with previous theoretical results that predict that the nucleation process in some metals is non-classical due to the presence of long-range forces and a spinodal.Comment: 4 pages, 5 figure

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time declines with growing contour length $L$ as $\propto L^{-0.17}$, and with side chain length as $\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.Comment: 15 pages, 7 figure

ON THE STATISTICAL PROPERTIES OF THE ELECTRONIC LEVELS OF SMALL METALLIC PARTICLES

On examine dans ce travail les arguments de Kubo et Gor'kov-Eliashberg concernant les fluctuations des niveaux d'énergie des particules métalliques. Nous confirmons que la Théorie des Matrices Aléatoires n'est pas adéquate pour décrire le comportement de ces particules quand on leur associe le modèle des électrons libres avec conditions aux limites de Dirichlet. Dans le cadre d'un modèle à deux dimensions exactement soluble on détermine la répartition des écarts entre niveaux d'énergie et on ne constate pas de répulsion entre ces niveaux. Finalement on calcule numériquement la variation de la chaleur spécifique Cv en fonction de la température pour une collection de spectres dont la loi de répartition des écarts d'énergies est aléatoire.The arguments of Kubo and Gor'kov-Eliashberg concerning the level fluctuations of small metallic particles (s.m.p.) are reviewed. We make plausible that Random Matrix Theory is not applicable to be s.m.p. problem within the free electron picture and when Dirichlet boundary conditions are used. Next, in the frame of an exactly soluble two-dimensional model, we determine the level-spacing-distribution which shows no level repulsion. Finally we calculate numerically the specific heat Cv at finite temperature for an assembly of spectra following the random distribution law

E.: Concentration dependence of structural and dynamical quantities in colloidal aggregation: computer simulations

We have performed extensive numerical simulations of diffusion-limited ͑DLCA͒ and reaction-limited ͑RLCA͒ colloid aggregation to obtain the dependence on concentration of several structural and dynamical quantities, among them the fractal dimension of the clusters before gelation, the average cluster sizes, and the scaling of the cluster size distribution function. A range in volume fraction spanning two and a half decades was used for this study. For DLCA, a square root type of increase of the fractal dimension with concentration from its zero-concentration value was found: and, in the case of S w for low concentration, it crosses over to a power law increase. In the RLCA case the scaling is as in DLCA where now a power law decay of the function f defines the exponent , f (x)ϳx Ϫ g(x), with g(x) decaying exponentially fast for xϾ1. A slight dependence of the exponent on concentration was computed around to the value ϭ1.5

On the Concentration Dependence of the Cluster Fractal Dimension in Colloidal Aggregation

Abstract. We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d f ) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d f from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration 01, a = 0.91 ± 0.03 and β = 0.51 ± 0.02, and where φ is the volume fraction of the colloidal particles. In our second procedure, we get the d f via the particle-particle correlation function g cluster (r ) and the structure function S cluster (q) of individual clusters. We first show that the stretched exponential law g cluster (r ) = Ar d f −3 e −(r/ξ ) a gives an excellent fit to the cutoff of the g(r ). Here, A, a and ξ are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function S cluster (q), using its Fourier transform relation with g cluster (r ) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d f extracted from this plot coincides with the d f of the stretched exponential law. The concentration dependence of this new estimate of d f , using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r ), of the whole system. A recipe is given on how to obtain approximately this g(r ) from a knowledge of the S(q), up to a certain maximum q value