Domain Structure Created by Irreversible Adsorption of Dimers

The Journal of Chemical Physics

Dybiec

Sokolov

et al. 2015

We study two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is formed from a monolayer of elongated molecules [Cieśla J. Chem. Phys. 140, 044706 (2014)] of known concentration. Within this mesh structure, a tracer molecule is allowed to perform a Cauchy random walk with uncorrelated steps. Our analysis shows that the presence of obstacles significantly influences the motion, which in an obstacle-free space would be of a superdiffusive type. At the same time, the selfdiffusive process reveals different anomalous properties, both at the level of a single trajectory realization and after the ensemble averaging. In particular, due to obstacles, the sample mean squared displacement asymptotically grows sublinearly in time, suggesting a non-Markov character of motion. Closer inspection of survival probabilities indicates, however, that the underlying diffusion is memoryless over long time scales despite a strong inhomogeneity of the motion induced by the orientational ordering.

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Taming Lévy flights in confined crowded geometries

The Journal of Chemical Physics

Dybiec

Sokolov

et al. 2015

“…However, in order to compare results with other works and experiments it is worthy to introduce yet another order measure, independent of the mechanism that forces molecules to align in parallel. For that purpose we define a global order parameter dependent only on geometrical properties of the coverage [22,23]:…”

Section: A Adsorption Of Fibrinogen Moleculesmentioning

confidence: 99%

Tracer diffusion inside fibrinogen layers

The Journal of Chemical Physics

Gudowska–Nowak

Sagués

et al. 2014

We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen molecules are significantly anisotropic and therefore they can form structures where orientational ordering, similar to the one observed in nematic liquid crystals, appears. The work focuses on the dependence between level of the orientational order (degree of environmental crowding) of fibrinogen molecules inside a layer and non-Fickian character of the diffusion process of spherical tracer particles moving within the domain. It is shown that in general particles motion is subdiffusive and strongly anisotropic, and its characteristic features significantly change with the orientational order parameter, concentration of fibrinogens and radius of a diffusing probe.

“…The situation changes when rectangles' orientations are arbitrary. For unoriented squares, the packing fraction equals 0.527640 (18) [9,10], and for unoriented rectangles, it reaches the maximum at 0.549632 (17) for a side length ratio of 1.492 (22) and then decreases monotonically with the growth of side length ratio [11,9]. It is worth noting, that the highest RSA packing fraction for this kind of system was recently reported for horizontally or vertically aligned rectangles with random side length ratio but constant surface area [12,13].…”

Section: Introductionmentioning

confidence: 57%

“…The third aspect of random arrangements of anisotropic shapes like rectangles is their tendency to form orientationally oriented clusters. Typically in RSA packings, the range of orientational ordering is very short [9,19,20,21], however, for very elongated molecules it can be significant [17], and orientationally oriented domains can appear [22]. It appears that especially in lattice packings, where orientations are discrete, one can observe long-range connectivity, which could lead to percolation transition, typically observed and studied for RSA on lattices [23,24,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 97%

Random sequential adsorption of oriented rectangles with random aspect ratio

Luca¹,

2021

Phys. Rev. E

We study saturated packings produced according to random sequential adsorption (RSA) protocol built of identical rectangles deposited on a flat, continuous plane. An aspect ratio of rectangles is defined as the length-to-width ratio, f = l/w. The rectangles have a fixed unit area (i.e., l × w = 1), and therefore, their shape is defined by the value of f (l = √ f and w = 1/ √ f ). The rectangles are allowed to align either vertically or horizontally with equal probability. The particles are deposited on a flat square substrate of side length L (measured in units of particle length, L ∈ [20, 1000]) and periodic boundary conditions are applied along both directions. The finite-size scaling effects are characterized by a scaled anisotropy defined as α = l/L = √ f /L. We showed that the properties of such packings strongly depend on the value of aspect ratio f and the most significant scaling effects are observed for relatively long rectangles when l ≥ L/2 (i.e. α ≥ 0.5). It is especially visible for the mean packing fraction as a function of the scaled anisotropy α. The kinetics of packing growth for low to moderate rectangle anisotropy is to be governed by ln t/t law, where t is proportional to the number of RSA iterations, which is the same as in the case of RSA of parallel squares. We also analyzed global orientational ordering in such packings and properties of domains consisting of a set of neighboring rectangles of the same orientation, and the probability that such domain forms a percolation.