A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $θ(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates are supported by Monte Carlo simulation results.
We present a class of cooperative sequential adsorption models on a Cayley tree with constant and variable attachment rates and their possible applications for ionic self-assembly of thin films and drug encapsulation of nanoparticles. Using the empty interval method, and generalizing results known from reaction-diffusion processes on Cayley trees, we calculate a variety of quantities such as time-dependent surface coverage and time-dependent probabilities of certain particle configurations.
Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperati…
A model for the adsorption of a binary mixture on a one-dimensional infinite lattice with nearest neighbour cooperative effects is considered. The particles of the two species are both monomers but differ in the repulsive interaction experienced by them when trying to adsorb. An exact expression for the coverage of the lattice is derived. In the jamming limit, it is a monotonic function of the ratio between the attempt frequencies of the two species, varying between the values corresponding to each of the two single species. This is in contrast with the results obtained in other models for the…
I show that cooperative exclusion processes with selective kinetic constraints exhibit fluctuation-induced forces that can be attractive or repulsive, depending on the density of boundary reservoirs, when their density-dependent diffusion coefficient exhibits a minimum. A mean-field analysis based on a nonlinear diffusion equation provides an estimation of the magnitude and sign of such a tunable Casimir-like force and suggests its occurrence in interacting particle systems with a diffusivity anomaly.
Self-assembly of nanoparticles is an important tool in nanotechnology, with numerous applications including thin films, electronics, and drug delivery. We study the deposition of ionic nanoparticles on a glass substrate both experimentally and theoretically. Our theoretical model consists of a stochastic cooperative adsorption and evaporation process on a two-dimensional lattice. By exploring the relationship between the initial concentration of nanoparticles in the colloidal solution and the density of particles deposited on the substrate, we relate the deposition rate of our theoretical mode…
Diamine-appended metal{organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a firstorder phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transi…
We investigate cooperative exclusion, in which the particle velocity can be an increasing function of the density. Within a hydrodynamic theory, an initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena arise because of an inflection point in the current versus density relation. This anomaly leads to a group velocity that can either be an increasing or a decreasing function of the density on either side of these wave singularities.
We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can be concave, convex or both, depending on the density of boundary particle reservoirs. A mean-field analysis based on a diffusion equation with a density-dependent diffusion coefficient qualitatively reproduces this behaviour, and suggests its occurrence in liquids with a diffusivity anomaly.
The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by use of the random sequential adsorption with surface diffusion (RSAD) model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at an…
A theory is presented which quantitatively accounts for the cooperative adsorption of cationic surfactants to anionic polyelectrolytes. For high salt concentration we find that the critical adsorption concentration (CAC) is a bilinear function of the polyion monomer and salt concentrations, with the coefficients dependent only on the type of surfactant used. The results presented in the paper might be useful for designing more efficient gene delivery systems.
The random sequential adsorption (RSA) model is modified to describe damage and crack accumulation. The exclusion for object deposition (for damaged region formation) is not for the whole object, as in the standard RSA, but only for the initial point (or higher-dimensional defect) from which the damaged region or crack initiates. The one-dimensional variant of the model is solved exactly.
We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.
Institute of Research and Development, Duy Tan University（研发研究所，岘港大学）；Faculty of Natural Sciences, Duy Tan University（自然科学学院，岘港大学）；Faculty of Information Technology, Ho Chi Minh City University of Economics and Finance（信息技术学院，胡志明市经济与金融大学）
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical random sequential adsorption (RSA) model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model LK$_d$ is a generalized variant of the RSA model for both $k$-mers and a lattice with defects. Some of the occupying $k$ adjacent sites are considered as insulating and some of the lattice sites are occupied …
Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random sequential adsorption with diffusion, creates amorphous structures and terminates at a disordered state with random closest packing density that lies in the equilibrium solid regime. The approach towards random closest packing is characterized by two distinct power-law regimes, reflecting the formation of small densely packed grains in the long time regime o…
