Poly-12-hydroxystearic acid (PHSA) is widely used as a coating on colloidal spheres to provide a "hard-sphere-type" interaction. These hard spheres have been widely used in fundamental studies of nucleation, crystallization, and glass formation. Most authors describe the interaction as "nearly" hard sphere. In this paper we directly measure this interaction, using layers of PHSA adsorbed onto m...

We show that the equilibrium state of an infinite system of interacting hard spheres can be obtained in the grand canonical formalism by means of a variational principle. We give also a simple application deriving the Salsburg-Zwanzig-Kirkwood expressions for correlation. functions of the equilibrium state of one dimensional systems of hard spheres. §

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic so...

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the app...

The scattering intensity of polydisperse systems of core-shell and layered hard spheres is considered. The Percus-Yevick solution for the partial structure factors is cast in a form suitable for numerical and analytical treatment. Closed-form, analytical expressions are given for an effective hard-sphere model of the scattering intensity of particles with an internal layered structure and a siz...

The settling and packing properties of colloidal suspensions of large hard spheres in an effective gravitational field are investigated by a Monte Carlo constant-NPV simulation. The ratio of an effective gravitational potential to the repulsion/attraction potential in the hard sphere (G/ε) is a critical parameter that determines the surface coverage and packing properties of the system. The sur...

The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fraction of binary mixtures of amorphously packed spheres is recapitulated. Next, the packing of a bina...

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s>0.07. For 0.02<s<0.07, we fi...

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs' free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-...

We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement o...