Cooperative Sequential Adsorption Models Research Articles

Modeling directed self-assembly of nanoparticles under parallel electric fields

We design and model an experiment to study the effect of electric bias on particle-coverage densities produced during ionic nanoparticle self-assembly. The experiment involves the application of a uniform external electric field parallel to a glass substrate during the self-assembly of silica nanoparticles. We refer to this procedure as directed self-assembly of monolayers (DSAM). In our theoretical analysis, we modify existing cooperative sequential adsorption models to account for diffusion under an applied electric field. We use the mean field approximation to solve for particle-coverage densities. To ascertain the validity of this method, we compare our solutions to Monte Carlo simulations of the system.

Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

A cooperative sequential adsorption model for wireless gossiping

Wireless sensor networks require communication protocols for efficiently maintaining data in a distributed fashion. The Trickle algorithm is a popular protocol serving as the basis for many of the current standard communication protocols. In this paper we develop a mathematical model describing how Trickle maintains data, establish a relationship with a class of spatial stochastic models known as Cooperative Sequential Adsorption (CSA). We derive asymptotic results for the coverage ratio for a specific class of CSA models and investigate the scalability of the Trickle algorithm.

Cooperative sequential-adsorption model in two dimensions with experimental applications for ionic self-assembly of nanoparticles.

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 model to the concentration.

LISA: Locally Interacting Sequential Adsorption

We study a class of dynamically constructed point processes in which at every step a new point (particle) is added to the current configuration with a distribution depending on the local structure around a uniformly chosen particle. This class covers, in particular, generalized Polya urn scheme, Dubins–Freedman random measures, and cooperative sequential adsorption models studied previously. Specifically, we address models where the distribution of a newly added particle is determined by the distance to the closest particle from the chosen one. We address boundedness of the processes and convergence properties of the corresponding sample measure. We show that, in general, the limiting measure is random when it exists and that this is the case for a wide class of almost surely bounded processes.

Cooperative sequential adsorption models on a Cayley tree: analytical results and applications

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.

Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

We consider statistical inference for a parametric cooperative sequential adsorption model for spatial time series data, based on maximum likelihood. We establish asymptotic normality of the maximum likelihood estimator in the thermodynamic limit. We also perform and discuss some numerical simulations of the model, which illustrate the procedure for creating confidence intervals for large samples.

Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

We consider statistical inference for a parametric cooperative sequential adsorption model for spatial time series data, based on maximum likelihood. We establish asymptotic normality of the maximum likelihood estimator in the thermodynamic limit. We also perform and discuss some numerical simulations of the model, which illustrate the procedure for creating confidence intervals for large samples.

On a model of sequential point patterns

A finite point process motivated by the cooperative sequential adsorption model is proposed. Analytical properties of the point process are considered in details. It is shown that the introduced point process is useful for modeling both aggregated and regular point patterns. A possible scheme of maximum likelihood estimation of the process parameters is briefly discussed.

Theoretical analysis of the coverage dependence of enantioselective chemisorption on a chirally templated surface

The effect of the formation of ensembles of chiral templates on the enantioselectivity of model heterogeneous catalysts is studied theoretically in the framework of a cooperative sequential adsorption model. Analytical solutions are presented for random adsorption onto a chirally templated surface which indicate that the surface exhibits a maximum enantioselectivity of ∼2.5, in agreement with results of enantioselective chemisorption experiments carried out in ultrahigh vacuum. It is suggested that the high enantioselectivity (≳90%) encountered in commercial catalysts could be due to correlated adsorption of the template molecules, and that these effects can be modeled using Monte Carlo calculations.

Scaling of spatial correlations in cooperative sequential adsorption with clustering

We examine solvable cooperative sequential adsorption models on a linear lattice where adsorption rates produce strong clustering or island formation. We show that the spatial pair correlations in this regime assume a scaled form for separations comparable to a characteristic length (which diverges in the strong clustering limit). This scaled form is also determined directly from consideration of appropriate solvable continuum grain growth models.