Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D.

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Effect of particle polydispersity on the irreversible adsorption of fine particles on patterned substrates.

We performed extensive Monte Carlo simulations of the irreversible adsorption of polydispersed disks inside the cells of a patterned substrate. The model captures relevant features of the irreversible adsorption of spherical colloidal particles on patterned substrates. The pattern consists of (equal) square cells, where adsorption can take place, centered at the vertices of a square lattice. Two independent, dimensionless parameters are required to control the geometry of the pattern, namely, the cell size and cell-cell distance, measured in terms of the average particle diameter. However, to describe the phase diagram, two additional dimensionless parameters, i.e., the minimum and maximum particle radii, are also required. We find that the transition between any two adjacent regions of the phase diagram solely depends on the largest and smallest particle sizes, but not on the shape of the distribution function of the radii. We consider size dispersions up to 20% of the average radius using a physically motivated, truncated, Gaussian-size distribution, and focus on the regime where adsorbing particles do not interact with those previously adsorbed on neighboring cells to characterize the jammed state structure. The study generalizes previous exact relations on monodisperse particles to account for size dispersion. Due to the presence of the pattern, the coverage shows a nonmonotonic dependence on the cell size. The pattern also affects the radius of adsorbed particles, where one observes preferential adsorption of smaller radii, particularly at high polydispersity.

Analytical and numerical study of particles with binary adsorption.

Electro-oxidation of ethanol represents a key process in fuel-cell technology. We introduce a generalization of the random sequential adsorption model to study the long time scale and large length scale properties of the electro-oxidation process. We provide an analytical solution for one dimension and Monte Carlo results in two dimensions. We characterize the coverage and percolation properties of the jammed state and unveil the influence of quenched impurities in the selectivity of oxidation products.

Morphology of fine-particle monolayers deposited on nanopatterned substrates.

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius r(0) is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, a , and cell-cell separation, b . The model shows a surprisingly rich behavior in the space of the two dimensionless parameters alpha = a / 2r(0) and beta = b / 2r(0) . Extensive Monte Carlo simulations for system sizes of 500 x 500 square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.

Gap-size distribution functions of a random sequential adsorption model of segments on a line.

We performed extensive simulations accompanied by a detailed study of a two-segment size random sequential model on the line. We followed the kinetics towards the jamming state, but we paid particular attention to the characterization of the jamming state structure. In particular, we studied the effect of the size ratio on the mean-gap size, the gap-size dispersion, gap-size skewness, and gap-size kurtosis at the jamming state. We also analyzed the above quantities for the four possible segment-to-segment gap types. We ranged the values of the size ratio from one to twenty. In the limit of a size ratio of one, one recovers the classical car-parking problem. We observed that at low size ratios the jamming state is constituted by short streaks of small and large segments, while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment. This view of the jamming state structure as a function of the size ratio is supported by the various measured quantities. The present work can help provide insight, for example, on how to minimize the interparticle distance or minimize fluctuations around the mean particle-to-particle distance.