Related papers: Gelation Paradox
We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical…
The addition of enough non-adsorbing polymer to an otherwise stable colloidal suspension gives rise to a variety of phase behavior and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a…
We report a numerical study, covering a wide range of packing fraction $\phi$ and temperature $T$, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number $n_{\rm…
Melting is well understood in terms of the Lindemann criterion, essentially stating that crystalline materials melt when the thermal vibrations of their atoms become such vigorous that they shake themselves free of the binding forces.…
The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule: While a significant increase of the distance $r$…
The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi…
Since more than 100 years, melting is thought to be governed by the Lindemann criterion. It assumes that a crystal melts when, upon heating, the growing atomic vibration amplitudes become sufficiently large to destabilize its crystalline…
The relationship between glasses and gels has been intensely debated for decades; however, the transition between these two phases remains elusive. To investigate a gel formation process in the zero-temperature limit and its relation to the…
It has been verified that the theory of gelation with cyclization effects is in good accord with experimental observations of gel points and gel fractions. Encouraged by this success we scrutinize the prediction limit of the theory through…
Within the framework of the random distribution assumption of cyclic bonds, the theory of gelation is extended to mixing systems of the R-Ag + R-Bf-g model, which is expected to have wider application such as micell formations in biological…
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based on a novel Markovian gluing principle. In contrast, we then…
Recently, a universal relation between the thermal expansion coefficient of glasses $\alpha_g$, their glass-transition temperature Tg, and the so-called fragility index m of the corresponding supercooled liquid state was found to be valid…
In this paper, a partial integro-differential equation modeling of coagulation and multiple fragmentation events is studied. Our purpose is to investigate the global existence of gelling weak solutions to the continuous coagulation and…
The theory of gelation is tested by the recent experiments in poly(urethane) network. The result supports strongly the physical soundness of the theory.
The sol-gel transition (SGT), upon which the infinite cluster (IC) of thermoreversibly bonded particles (gel fraction) appears against a background of a set of finite clusters (sol fraction), is first quantitatively considered with due…
A two-site spatial coagulation model is considered. Particles of masses $m$ and $n$ at the same site form a new particle of mass $m+n$ at rate $mn$. Independently, particles jump to the other site at a constant rate. The limit (for…
The gelation kinetics of silica nanoparticles is a central process in physical chemistry, yet it is not fully understood. Gelation times are measured to increase by over 4 orders of magnitude, simply changing the monovalent salt species…
Glassy matter like crystals resists change in shape. Therefore a theory for their continuous melting should show how the shear elastic constant $\mu$ goes to zero. Since viscosity is the long wave-length low frequency limit of shear…
We find a limit cycle in a quasi-equilibrium model of evaporative cooling of a two-component fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that…
The Marcus-Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get…