Random Sequential Adsorption Research Articles

Random sequential adsorption of oriented rectangles with random aspect ratio

We studied random sequential adsorption (RSA) of parallel rectangles with random aspect ratio but fixed area using a newly developed algorithm that allows to generate strictly saturated packing of this kind. We determined saturated packing fraction for several different distributions of a random variable used for selecting side length ratio of deposited rectangles. It was also shown that the anisotropy of deposited rectangles changes during packing generation. Additionally, we examined the kinetics of packing growth, which near saturation obeys the power law with the exponent 1/d≈1/3, typical for the RSA of unoriented anisotropic shapes on a two-dimensional surface. Kinetics in the low coverage limit is determined using the concept of the available surface function. The microstructural properties of obtained random packings are evaluated in terms of two-point density correlation function.

A hard-sphere model of protein corona formation on spherical and cylindrical nanoparticles

A nanoparticle (NP) immersed in biological media rapidly forms a corona of adsorbed proteins, which later controls the eventual fate of the particle and the route through which adverse outcomes may occur. The composition and timescale for the formation of this corona are both highly dependent on both the NP and its environment. The deposition of proteins on the surface of the NP can be imitated by a process of random sequential adsorption, and, based on this model, we develop a rate-equation treatment for the formation of a corona represented by hard spheres on spherical and cylindrical NPs. We find that the geometry of the NP significantly alters the composition of the corona through a process independent of the rate constants assumed for adsorption and desorption of proteins, with the radius and shape of the NP both influencing the corona. We further investigate the roles of protein mobility on the surface of the NP and changes in the concentration of proteins.

Surface growth during random and irreversible multilayer deposition of straight semirigid rods.

Surface growth properties during irreversible multilayer deposition of straight semirigid rods on linear and square lattices have been studied by Monte Carlo simulations and analytical considerations. The filling of the lattice is carried out following a generalized random sequential adsorption mechanism where the depositing objects can be adsorbed on the surface forming multilayers. The results of our simulations show that the roughness evolves in time following two different behaviors: an "homogeneous growth regime" at initial times, where the heights of the columns homogeneously increase, and a "segmented growth regime" at long times, where the adsorbed phase is segmented in actively growing columns and inactive nongrowing sites. Under these conditions, the surface growth generated by the deposition of particles of different sizes is studied. At long times, the roughness of the systems increases linearly with time, with growth exponent β=1, at variance with a random deposition of monomers which presents a sublinear behavior (β=1/2). The linear behavior is due to the segmented growth process, as we show using a simple analytical model.

Thermo-elastic properties in short fibre reinforced ultra-high temperature ceramic matrix composites: Characterisation and numerical assessment

The thermo-elastic properties of a novel class of ceramic composites based on an ultra-refractory matrix and containing short carbon fibre to provide failure tolerance and thermal shock resistance were experimentally characterised and numerically simulated. The composites samples were fabricated with fibre volume fractions ranging from 5 to 60 vol% and were featured by homogeneous dispersion of fibre along the basal plane due to the processing route. A random sequential adsorption algorithm was implemented to generate Representative Volume Elements (RVEs), following which finite element (FE) analyses were conducted to determine the elastic modulus and the coefficient of thermal expansion of the composites . Comparison of the experimental and modelling results showed good agreement for the modulus at low fibre volume fractions, and for CTE at higher volume fractions. Discrepancies are attributed to significant evolution of the composite microstructure upon processing at high temperatures, as revealed by microscopic analysis. The observations emphasise the need to account for the effects of microstructural changes on the constituent properties in the modelling of the thermo-mechanical properties in sintered ceramic composites.

Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1<d<2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t−1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model.

Jamming densities of random sequential adsorption on d-dimensional cubic lattices.

The rate of convergence of the jamming densities to their asymptotic high-dimensional tree approximation is studied, for two types of random sequential adsorption (RSA) processes on a d-dimensional cubic lattice. The first RSA process has an exclusion shell around a particle of nearest neighbors in all d dimensions (N1 model). In the second process the exclusion shell consists of a d-dimensional hypercube with length k=2 around a particle (N2 model). For the N1 model the deviation of the jamming density ρ_{r}(d) from its asymptotic high d value ρ_{asy}(d)=ln(1+2d)/2d vanishes as [ln(1+2d)/2d]^{3.41}. In addition, it has been shown that the coefficients a_{n}(d) of the short-time expansion of the occupation density of this model (at least up to n=6) are given for all d by a finite correction sum of order (n-2) in 1/d to their asymptotic high d limit. The convergence rate of the jamming densities of the N2 model to their high d limits ρ_{asy}(d)=dln3/3^{d} is slow. For 2≤d≤4 the generalized Palasti approximation provides by far a better approximation. For higher d values the jamming densities converge monotonically to the above asymptotic limits, and their decay with d is clearly faster than the decay as (0.432332...)^{d} predicted by the generalized Palasti approximation.

Computational Generation of Virtual Concrete Mesostructures.

Concrete is a heterogeneous material with a disordered material morphology that strongly governs the behaviour of the material. In this contribution, we present a computational tool called the Concrete Mesostructure Generator (CMG) for the generation of ultra-realistic virtual concrete morphologies for mesoscale and multiscale computational modelling and the simulation of concrete. Given an aggregate size distribution, realistic generic concrete aggregates are generated by a sequential reduction of a cuboid to generate a polyhedron with multiple faces. Thereafter, concave depressions are introduced in the polyhedron using Gaussian surfaces. The generated aggregates are assembled into the mesostructure using a hierarchic random sequential adsorption algorithm. The virtual mesostructures are first calibrated using laboratory measurements of aggregate distributions. The model is validated by comparing the elastic properties obtained from laboratory testing of concrete specimens with the elastic properties obtained using computational homogenisation of virtual concrete mesostructures. Finally, a 3D-convolutional neural network is trained to directly generate elastic properties from voxel data.

Quantifying the effect of two-point correlations on the effective elasticity of specific classes of random porous materials with and without connectivity

It is well-known by now that the Hashin–Shtrikman bounds imply that the two-point correlation functions are not in general sufficient to estimate accurately the response of composites, especially when their underlying phases exhibit infinite contrast, e.g., porous materials. Starting from this longstanding, albeit qualitative result, this work investigates quantitatively the relevance of using two-point correlations to model the effective elastic properties of specific isotropic porous materials with and without connectivity. To achieve this in an unambiguous manner, we propose three different microstructures that share almost identical two-point statistics by design but are rather different morphologically. The choice of these microstructures is driven by their wide use in several practical problems ranging from polymers to geomaterials. The first microstructure is obtained by a random sequential adsorption (RSA) of non-overlapping, polydisperse, spherical and ellipsoidal voids oriented randomly in a unit-cell. The second one, termed connected random sequential adsorption (CRSA), is obtained from the first one by adding controlled connectivity via cylindrical channels of circular cross-section. The porosity resulting from connectivity is compensated by reducing the size of the existing voids to have the same overall porosity. Interestingly, we find that connectivity does not affect the corresponding two-point statistics. Finally, using as an input the numerical one- and two-point correlations of the RSA, we reconstruct a thresholded Gaussian random field (TGRF) microstructure. Using FFT numerical simulations, we show that the resulting effective elastic properties are very different for the three generated microstructures, despite them sharing nearly the same two-point correlation functions. We show, further, that the introduction of connectivity, and in particular the partial volume fraction of the connected channels, even small, affects strongly the resulting effective elasticity of the composite.

Algorithms to generate saturated random sequential adsorption packings built of rounded polygons.

We present the algorithm for generating strictly saturated random sequential adsorption packings built of rounded polygons. It can be used in studying various properties of such packings built of a wide variety of different shapes, and in modeling monolayers obtained during irreversible adsorption processes of complex molecules. Here, we apply the algorithm to study the densities of packings built of rounded regular polygons. Contrary to packings built of regular polygons, where the packing fraction grows with an increasing number of polygon sides, here the packing fraction reaches its maximum for packings built of rounded regular triangles. With a growing number of polygon sides and increasing rounding radius, the packing fractions tend to the limit given by a packing built of disks. However, they are still slightly higher, even for the rounded 25-gon, which is the highest-sided regular polygon studied here.

Mechanism of Myoglobin Molecule Adsorption on Silica: QCM, OWLS and AFM Investigations.

Adsorption kinetics of myoglobin on silica was investigated using the quartz crystal microbalance (QCM) and the optical waveguide light-mode spectroscopy (OWLS). Measurements were carried out for the NaCl concentration of 0.01 M and 0.15 M. A quantitative analysis of the kinetic adsorption and desorption runs acquired from QCM allowed to determine the maximum coverage of irreversibly bound myoglobin molecules. At a pH of 3.5–4 this was equal to 0.60 mg m−2 and 1.3 mg m−2 for a NaCl concentration of 0.01 M and 0.15 M, respectively, which agrees with the OWLS measurements. The latter value corresponds to the closely packed monolayer of molecules predicted from the random sequential adsorption approach. The fraction of reversibly bound protein molecules and their biding energy were also determined. It is observed that at larger pHs, the myoglobin adsorption kinetics was much slower. This behavior was attributed to the vanishing net charge that decreased the binding energy of molecules with the substrate. These results can be exploited to develop procedures for preparing myoglobin layers at silica substrates of well-controlled coverage useful for biosensing purposes.

Adhesion Process of Biomimetic Myelin Membranes Triggered by Myelin Basic Protein.

The myelin sheath—a multi-double-bilayer membrane wrapped around axons—is an essential part of the nervous system which enables rapid signal conduction. Damage of this complex membrane system results in demyelinating diseases such as multiple sclerosis (MS). The process in which myelin is generated in vivo is called myelination. In our study, we investigated the adhesion process of large unilamellar vesicles with a supported membrane bilayer that was coated with myelin basic protein (MBP) using time-resolved neutron reflectometry. Our aim was to mimic and to study the myelination process of membrane systems having either a lipid-composition resembling that of native myelin or that of the standard animal model for experimental autoimmune encephalomyelitis (EAE) which represents MS-like conditions. We were able to measure the kinetics of the partial formation of a double bilayer in those systems and to characterize the scattering length density profiles of the initial and final states of the membrane. The kinetics could be modeled using a random sequential adsorption simulation. By using a free energy minimization method, we were able to calculate the shape of the adhered vesicles and to determine the adhesion energy per MBP. For the native membrane the resulting adhesion energy per MBP is larger than that of the EAE modified membrane type. Our observations might help in understanding myelination and especially remyelination—a process in which damaged myelin is repaired—which is a promising candidate for treatment of the still mostly incurable demyelinating diseases such as MS.

Particle Deposition to Silica Surfaces Functionalized with Cationic Polyelectrolytes

Positively charged water-solid interfaces are prepared by adsorption of a cationic polyelectrolyte poly(diallyldimethylammonium chloride) (PDADMAC) from aqueous solutions to planar silica substrates. These substrates are characterized by atomic force microscopy (AFM), optical reflectivity, and streaming current measurements. By tuning the amount of adsorbed polyelectrolyte, the surface charge of the substrate can be systematically varied. These substrates are further used to study deposition of sulfate latex nanoparticles, which is also accomplished by optical reflectivity. This deposition process is found to be consistent with an extension of the random sequential adsorption (RSA) model in a semi-quantitative fashion. Such deposition studies were further used to ascertain that the substrates obtained by in situ and ex situ functionalization behave in an identical fashion.

Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects.

Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of randomly distributed defective sites that are forbidden for particle deposition. However, using large-scale Monte Carlo simulations by depositing dimers on the square lattice and employing finite-size scaling, we provide evidence that the system does not exhibit such well-known universal features when the defects have spatial long-range (power-law) correlations. The critical exponents ν_{j} and ν associated with the jamming and percolation transitions, respectively, are found to be nonuniversal for strong spatial correlations and approach systematically their own universal values as the correlation strength is decreased. More crucially, we have found a difference in the values of the percolation correlation length exponent ν for a small but finite density of defects with strong spatial correlations. Furthermore, for a fixed defect density, it is found that the percolation threshold of the system, at which the largest cluster of absorbed dimers first establishes the global connectivity, gets reduced with increasing the strength of the spatial correlation.

Connectedness percolation in the random sequential adsorption packings of elongated particles.

Connectedness percolation phenomena in the two-dimensional packing of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption off-lattice models with preferential orientations of the particles along a given direction. The partial ordering was characterized by the order parameter S, with S=0 for completely disordered films (random orientation of particles) and S=1 for completely aligned particles along the horizontal direction x. The aspect ratio (length-to-width ratio) of the particles was varied within the range ɛ∈[1;100]. Analysis of connectivity was performed assuming a core-shell structure of the particles. The value of S affected the structure of the packings, the formation of long-range connectivity, and the behavior of the electrical conductivity. The effects can be explained by taking accounting of the competition between the particles' orientational degrees of freedom and excluded volume effects. For aligned deposition, anisotropy in the electrical conductivity was observed with the values along the alignment direction σ_{x} being larger than the values in the perpendicular direction σ_{y}. Anisotropy in the localization of the percolation threshold was also observed in finite-sized packings, but it disappeared in the limit of infinitely large systems.

Effect of single-fiber properties and fiber volume fraction on the mechanical properties of Ioncell fiber composites

The present study concentrates on a series of experiments and numerical analyses for understanding the effects of fiber volume fraction ( VF) and draw ratio ( DR) on the effective elastic properties of unidirectional composites made from an epoxy resin matrix with a continuous fiber reinforcement. Lyocell-type regenerated cellulose filaments (Ioncell) spun with DRs of 3, 6, and 9 were used. In accordance with the specimens in situ, the fibers were modeled as slender solid elements, for which the ratio between the diameter and length was taken to be much less than unity and deposited inside the matrix with the random sequential adsorption algorithm. The embedded element method was thereafter used in the numerical framework due to its computational advantages and reasonable predictions for continuous fiber reinforced composites. Experiments and numerical investigations were carried out, the results of which were compared, and positive trends for both fiber VFs and DRs on the effective properties were observed. The presented experimental and numerical results and models herein are believed to advance the state of the art in the mechanical characterization of composites with continuous fiber reinforcement.

Modeling Rydberg gases using random sequential adsorption on random graphs

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects, and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a Random Sequential Adsorption (RSA) process on a Random Geometric Graph (RGG), and a RSA process on a Decomposed Random Intersection Graph (DRIG). The latter model is new, and refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the former two models, it lends itself for a rigorous mathematical analysis; and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time-evolution of number of Rydberg atoms, and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdos-Renyi Random Graph (ERRG). Finally, we also come up with a new heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long time scales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short time scales the statistics are affected most by quantum mechanical effects.

Prediction of mechanical and thermal properties of particle reinforced hydrogel composites using the structural genome approach

In this paper, the structural genome approach is used for multiscale analyses to predict the mechanical and thermal properties of particle reinforced hydrogel composites. First, the structure genome model of particle reinforced hydrogel composites is created by the random sequential adsorption algorithm. Then the mechanical properties and equivalent thermal conductivity of hydrogel composites are numerically studied by the structural genome approach. The effects of particles with different volume fractions and material properties on their mechanical and thermal properties are investigated. From the simulation results, it can be found that within a certain range of volume fraction, the mechanical properties and equivalent thermal conductivity of hydrogel composites are positively correlated with the volume fractions of particles. We also find that with the increase of the mechanical properties and thermal conductivity of particles, the properties of hydrogel can be improved and eventually reach stabilization. The structural genome approach shows excellent efficiency in multiscale structure analysis. It is a convenient method for the simulation of complex soft material composites.

Adsorption kinetics and thermodynamic properties of a binary mixture of hard-core particles on a square lattice.

The adsorption kinetics and thermodynamic properties of a binary mixture on a square lattice are studied using the random sequential adsorption with surface diffusion (RSAD). We compare the adsorption of binary species with different equilibrium rate constants and effective rates of adsorption to a surface and find that the temporal evolution of surface coverages of both species can be obtained through the use of the blocking function of a system with irreversible adsorption of highly diffusive particles. Binary mixtures, when one of the components follows the random sequential adsorption (RSA) without surface diffusion and the other follows the RSAD model, display competitive adsorption in addition to cooperative phenomena. Specifically, (i) species replacement occurs over a long period of time, while the total coverage remains unchanged after a short time, (ii) the presence of the RSAD component shifts the jamming coverage to the higher values, and (iii) the maximum jamming coverage is obtained when the effective adsorption of the RSA type components is lower than the other adsorbing particles.

Nanoparticle deposition on heterogeneous surfaces: Random sequential adsorption modeling and experiments

The deposition of positively charged polymer nanoparticles on heterogeneous surfaces formed by a controlled self-assembly of larger particles on silica sensors was quantitatively described. Applying the Monte-Carlo type, random sequential modeling, the kinetics of particle deposition, their maximum coverage and the structure of the layers were determined. It is shown that the maximum coverage of the nanoparticles linearly decreases with the heterogeneity degree quantified in terms of the larger particle coverage. It is also confirmed that the nanoparticle layers exhibit a pronounced short-range ordering analogous to a two-dimensional liquid phase. The theoretical results derived from the modeling are used to interpret nanoparticle deposition kinetics acquired by the atomic force microscopy and the quartz microbalance (QCM). This allowed to determine the hydration function, which enables a proper interpretation of the QCM signal for the heterogeneous systems, extending the applicability range of this technique. Given that the kinetics of nanoparticle deposition on geometrically heterogeneous surfaces was not treated in the literature before, the results obtained in this work significantly advance the field of colloid science.

Glassy dynamics and equilibrium state on the honeycomb lattice: Role of surface diffusion and desorption on surface crowding.

The phase behavior and adsorption kinetics of hard-core particles on a honeycomb lattice are studied by means of random sequential adsorption with surface diffusion. We concentrate on reversible adsorption by introducing a desorption process into our previous model and varying the equilibrium rate constant as a control parameter. We find that an exact prediction of the temporal evolution of fractional surface coverage and the surface pressure dynamics of reversible adsorption can be achieved by use of the blocking function of a system with irreversible adsorption of highly mobile particles. For systems out of equilibrium we observe several features of glassy dynamics, such as slow relaxation dynamics, the memory effect, and aging. In particular, the analysis of our system in the limit of small desorption probability shows simple aging behavior with a power-law decay. A detailed discussion of Gibbs adsorption isotherm for nonequilibrium adsorption is given, which exhibits a hysteresis between this system and its equilibrium counterpart.