arXiv subjects

Rémi Jullien

Publications and source records attributed to Rémi Jullien.

7 recordsLinked to original sources

arXiv1995

A Numerical Study of Phase Transitions Inside the Pores of Aerogels

Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering $q$-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for $q=4$ the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case $q=3$ (where the first order transition is weaker in three dimensions) and with the case $q=4$ but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.

cond-mat↗

arXiv1995

Small Angle Neutron Scattering of Aerogels: Simulations and Experiments

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 $c$ 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 $I(q)$ is calculated from the product of the form factor $P(q)$ of a sphere by the structure factor $S(q)$, which is related to the Fourier transform of $g(r)-1$, where $g(r)$ is the pair correlation function between sphere centers. The structure factor $S(q)$ exhibits large-$q$ damped oscillations characteristics of the short range (intra-aggregate) correlations between spheres. These oscillations influence the $I(q)$ curve in the $q$-region between the fractal regime and the Porod regime and quantitative comparisons are made with experiments on colloidal aerogels. Moreover, at small-$q$ values, $S(q)$ goes through a maximum characteristic of large range (inter-aggregate) correlations. Quantitative fits of the maximum in the experimental $I(q)$ curves of base-catalyzed aerogel are presented. In the case of polydisperse spheres, $I(q)$ 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 $q$-value.

cond-mat↗

arXiv1995

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

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 $a_0$ 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 $a_0$, the location $q_c$ of the crossover decreases as $σ$ increases. The dependence of $q_c$ on $σ$ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.

cond-mat↗

arXiv1995

Percolation in Cluster-Cluster Aggregation Processes

Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel concentration, the morphology of the resulting spanning cluster at the gel time $t_g$ exhibits a crossover length $L_c$ between percolation ($l>L_c$) and aggregation ($l c_p$ the long-range correlations are similar to that of percolation, the vanishing links in the structure suggest that an homogeneous regime appears at small scales.

cond-mat↗

arXiv1995

Scaling Theory and Numerical Simulations of Aerogel Sintering

A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $ξ$, in order to conserve the total mass of the system. Scaling laws are derived which predict how $a$, $ξ$ and the specific pore surface area $Σ$ should depend on the density $ρ$. Following the general ideas of the theory, numerical simulations of sintering are proposed starting from computer simulations of aerogel structure based on a diffusion-limited cluster-cluster aggregation gelling process. The numerical results for $a$, $ξ$ and $Σ$ as a function of $ρ$ are discussed according to the initial aerogel density. The scaling theory is only fully recovered in the limit of very low density where the original values of $a$ and $ξ$ are well separated. These numerical results are compared with experiments on partially densified aerogels.

cond-mat↗

arXiv1995

The Sol-Gel Process Simulated by Cluster-Cluster Aggregation

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 a box. 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 slo pe of $S(q,t)$ . The time evolution of the mean number of particles per cluster $\bar {n}$ is also investigated. Our numerical results are in qualitative agreement with small angle scattering experiments in several systems.

cond-mat↗

arXiv1995

Gas Transport in Porous Media: Simulations and Experiments on Partially Densified Aerogels

The experimental density dependence of gas (argon and nitrogen) permeability of partially densified silica aerogels in the Knudsen regime is quantitatively accounted for by a computer model. The model simulates both the structure of the sintered material and the random ballistic motion of a point particle inside its voids. The same model is also able to account for the densit y dependence of the specific pore surface as measured from nitrogen adsorption experiments.

cond-mat↗