Achille Giacometti

On Hack's Law

Hacks law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hacks law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hacks exponent, elongation, and some relevant fractal characters are closely related. The self-affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to Hacks law. An explanation for Hacks law is derived from scaling arguments. From the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of Hacks law.

Phase diagram of Janus particles.

We thoroughly investigate a simple model representative of the recently synthesized Janus particles, i.e., colloidal spherical particles whose surface is divided into two areas of different chemical composition. When the two surfaces are solvophilic and solvophobic, these particles constitute the simplest example of surfactants. The phase diagram includes a colloidal-poor (gas), colloidal-rich (liquid) demixing region, which is progressively suppressed by the insurgence of micelles, providing the first model in which micellization and phase separation are simultaneously observed. The coexistence curve is found to be negatively sloped in the temperature-pressure plane, suggesting that Janus particles can provide a colloidal system with anomalous thermodynamic behavior.

Effects of patch size and number within a simple model of patchy colloids.

We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction chi of covered attractive surface. The simple model explored--the two-patch Kern-Frenkel model--interpolates between a square-well and a hard-sphere potential on changing the coverage chi. We show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square-well limit chi=1.0 down to chi approximately 0.6. For smaller chi, good numerical convergence of the equations is achieved only at temperatures larger than the gas-liquid critical point, where integral equation theory provides a complete description of the angular dependence. These results are contrasted with those for the one-patch case. We investigate the remaining region of coverage via numerical simulation and show how the gas-liquid critical point moves to smaller densities and temperatures on decreasing chi. Below chi approximately 0.3, crystallization prevents the possibility of observing the evolution of the line of critical points, providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials. Finally, we show that the stable ordered phase evolves on decreasing chi from a three-dimensional crystal of interconnected planes to a two-dimensional independent-planes structure to a one-dimensional fluid of chains when the one-bond-per-patch limit is eventually reached.

Flory theory for polymers

We review various simple analytical theories for homopolymers within a unified framework. The common guideline of our approach is the Flory theory, and its various avatars, with the attempt at being reasonably self-contained. We expect this review to be useful as an introduction to the topic at the graduate student level.

Phase diagram and structural properties of a simple model for one-patch particles

We study the thermodynamic and structural properties of a simple, one-patch fluid model using the reference hypernetted-chain (RHNC) integral equation and specialized Monte Carlo simulations. In this model, the interacting particles are hard spheres, each of which carries a single identical, arbitrarily oriented and attractive circular patch on its surface; two spheres attract via a simple square-well potential only if the two patches on the spheres face each other within a specific angular range dictated by the size of the patch. For a ratio of attractive to repulsive surface of 0.8, we construct the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs ensemble and grand canonical Monte Carlo simulations. We find that RHNC provides a quick and highly reliable estimate for the position of the fluid-fluid critical line. In addition, it gives a detailed (though approximate) description of all structural properties and their dependence on patch size.

Models of Fractal River Basins

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.

Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus: Yevick approximation

We discuss structural and thermodynamical properties of Baxters adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multicomponent fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first order, produce satisfactory results.

Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion

Closed analytical expressions for scattering intensity and other global structure factors are derived for a new solvable model of polydisperse sticky hard spheres. The starting point is the exact solution of the “mean spherical approximation” for hard core plus Yukawa potentials, in the limit of infinite amplitude and vanishing range of the attractive tail, with their product remaining constant. The choice of factorizable coupling (stickiness) parameters in the Yukawa term yields a simpler “dyadic structure” in the Fourier transform of the Baxter factor correlation function qij(r), with a remarkable simplification in all structure functions with respect to previous works. The effect of size and stickiness polydispersity is analyzed and numerical results are presented for two particular versions of the model: (i) when all polydisperse particles have a single, size-independent, stickiness parameter, and (ii) when the stickiness parameters are proportional to the diameters. The existence of two different reg...

Janus particle synthesis, self-assembly and applications

Soft, Nanoscale Janus Particles by Macromolecular Engineering and Molecular Assembly Design, Synthesis, and Applications of Dumbbell-like Nanoparticles Janus Particles with Distinct Compartments via Electrohydrodynamic Co-jetting Synthesis of Janus Particles by Emulsion Based Methods Particle Replication In Nonwetting Templates: A Platform for Engineering Shape- and Size-Specific Janus Particles Theoretical Calculations of Phase Diagrams and Self-assembly in Patchy Colloids Self-assembly of Amphiphilic and Dipolar Janus Particles Self-assembly of Janus particles under external fields DNA Self-Assembly: From Nanostructures to Macro Engineering Study on Colloidal Rotation and Diffusion Dynamics by Janus Particle Tracking Janus Balance and Emulsions Stabilized by Janus Particles Applications of Janus and Anisotropic Particles for Drug Delivery

Communication: From rods to helices: Evidence of a screw-like nematic phase

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C2 symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry, Z. Hensel, Z. Dogic, M. Shribak, and R. Oldenbourg, Phys. Rev. Lett. 96, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.