Precise algorithm to generate random sequential adsorption of hard polygons at saturation

pH-response of protein-polysaccharide multilayers adsorbed on a flat gold surface: A surface plasmon resonance study

Polysaccharide-protein multilayers (PPMLs) consisting of bovine serum albumin (BSA) and chondroitin sulfate (CS) are assembled in acidic solution (pH 4.2) via layer-by-layer deposition method. The formation of PPMLs on gold surface and their responsiveness to pH change from 4.2 to 7 is investigated by Surface Plasmon Resonance Spectroscopy. The buildup of the multilayer at pH 4.2 exhibits non-linear growth while the formation of the first layers is strongly affected by the physicochemical properties of the gold surface. Neutral solution (pH 7) affects the interactions between the biopolymers and results in a partially disassemble (disintegration) of the multilayer film. On one hand, the single pair of layers, BSA-CS and the double pair of layers, (BSA-CS)2, assemblies are stable in neutral pH, a result that will be of interest for biomedical applications. On the other hand, multilayer films consisting of more than four layers that is (BSA-CS)2 Collapse

Key Words

• layer‐by‐layer
• multilayer
• pH‐responsiveness
• protein‐polysaccharide
• surface plasmon

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MESH Headings

• Gold/chemistry
• Surface Plasmon Resonance/methods
• Hydrogen-Ion Concentration
• Serum Albumin, Bovine/chemistry
• Adsorption
• Chondroitin Sulfates/chemistry
• Surface Properties
• Cattle
• Animals
• Polysaccharides/chemistry

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Affiliation(s)

Nikolitsa Katsenou Department of Physics, University of Patras, Patras, Greece
Nikolaos Spiliopoulos Department of Physics, University of Patras, Patras, Greece
Dimitrios L Anastassopoulos Department of Physics, University of Patras, Patras, Greece
Aristeidis Papagiannopoulos Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens, Greece
Chris Toprakcioglu Department of Physics, University of Patras, Patras, Greece

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Optimal three-dimensional particle shapes for maximally dense saturated packing

Saturated packing is a random packing state of particles widely applied in investigating the physicochemical properties of granular materials. Optimizing particle shape to maximize packing density is a crucial challenge in saturated packing research. The known optimal three-dimensional shape is an ellipsoid with a saturated packing density of 0.437 72(51). In this work, we generate saturated packings of three-dimensional asymmetric shapes, including spherocylinders, cones, and tetrahedra, via the random sequential adsorption algorithm and investigate their packing properties. Results show that the optimal shape of asymmetric spherocylinders gives the maximum density of 0.4338(9), while cones achieve a higher value of 0.4398(10). Interestingly, tetrahedra exhibit two distinct optimal shapes with significantly high densities of 0.4789(19) and 0.4769(18), which surpass all previous results in saturated packing. The study of adsorption kinetics reveals that the two optimal shapes of tetrahedra demonstrate notably higher degrees of freedom and faster growth rates of the particle number. The analysis of packing structures via the density pair-correlation function shows that the two optimal shapes of tetrahedra possess faster transitions from local to global packing densities.

Two-stage random sequential adsorption of discorectangles and disks on a two-dimensional surface

The different variants of two-stage random sequential adsorption (RSA) models for packing of disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD (sticks+disks) model, the discorectangles were first deposited and then the disks were added. In the DS (disks+sticks) model, the disks were first deposited and then discorectangles were added. At the first stage the particles were deposited up to the selected concentration and at the final (second) stage the particles were deposited up to the saturated (jamming) state. The main parameters of the models were the concentration of particles deposited at the first stage, aspect ratio of the discorectangles ɛ (length to diameter of ratio ɛ=l/d) and disk diameter D. All distances were measured using the value of d as a unit of measurement of linear dimensions, the disk diameter was varied in the interval D∈[1-10], and the aspect ratio value was varied in the interval ɛ∈[1-50]. The dependencies of the jamming coverage of particles deposited at the second stage versus the parameters of the models were analyzed. The presence of first deposited particles for both models regulated the maximum possible disk diameter D_{max} (SD model) or the maximum aspect ratio ɛ_{max} (DS model). This behavior was explained by the deposition of particles in the second stage into triangular (SD model) or elongated (DS model) pores formed by particles deposited at the first stage. The percolation connectivity of disks (SD model) and discorectangles (DS model) for the particles with a hard core and a soft shell structure was analyzed. The disconnectedness was ensured by overlapping of soft shells. The dependencies of connectivity versus the parameters of SD and DS models were also analyzed.

Random sequential adsorption of aligned regular polygons and rounded squares: Transition in the kinetics of packing growth

We study two-dimensional random sequential adsorption (RSA) of flat polygons and rounded squares aligned in parallel to find a transition in the asymptotic behavior of the kinetics of packing growth. Differences in the kinetics for RSA of disks and parallel squares were confirmed in previous analytical and numerical reports. Here, by analyzing the two classes of shapes in question we can precisely control the shape of the packed figures and thus localize the transition. Additionally, we study how the asymptotic properties of the kinetics depend on the packing size. We also provide accurate estimations of saturated packing fractions. The microstructural properties of generated packings are analyzed in terms of the density autocorrelation function.

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.

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.

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.

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

A computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane. The problem was analyzed for a wide range of discorectangle aspect ratios (ɛ∈[1;100]). We studied the anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing fraction found at different values of such the alignment are discussed. Partial ordering of the discorectangles significantly affected the packing fraction at the jamming state, φ_{j}, and shifted the cusps in the φ_{j}(ɛ) dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core-shell structure of particles.

Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line

Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A. Baule, Phys. Rev. Lett. 119, 028003 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.028003]. The results show that the kinetics is governed by the power law with the exponent d=1.5 and 2.0 for packings built of ellipses and rectangles, respectively, which is consistent with analytical predictions. However, for spherocylinders and dimers of moderate width-to-height ratio, a transition between these two values is observed. We argue that this transition is a finite-size effect that arises for spherocylinders due to the properties of the contact function. In general, it appears that the kinetics of packing growth can depend on packing size even for very large packings.

Saturated random packing built of arbitrary polygons under random sequential adsorption protocol

Random packings and their properties are a popular and active field of research. Numerical algorithms that can efficiently generate them are useful tools in their study. This paper focuses on random packings produced according to the random sequential adsorption (RSA) protocol. Developing the idea presented by G. Zhang [Phys. Rev. E 97, 043311 (2018)2470-004510.1103/PhysRevE.97.043311], where saturated random packings built of regular polygons were studied, we create an algorithm that generates strictly saturated packings built of any polygons. Then, the algorithm was used to determine the packing fractions for arbitrary triangles. The highest mean packing density, 0.552814±0.000063, was observed for triangles of side lengths 0.63:1:1. Additionally, microstructural properties of such packings, kinetics of their growth, as well as distributions of saturated packing fractions and the number of RSA iterations needed to reach saturation were analyzed.

Morphology and kinetics of random sequential adsorption of superballs: From hexapods to cubes

Superballs represent a class of particles whose shapes are defined by the domain |x|^{2p}+|y|^{2p}+|z|^{2p}≤R^{2p}, with p∈(0,∞) being the deformation parameter. 0<p<0.5 represents a family of hexapodlike (concave octahedral-like) particles, 0.5≤p<1 and p>1 represent, respectively, families of convex octahedral-like and cubelike particles, with p=1,0.5, and ∞ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as the low-entropy algorithm, which is about two orders of magnitude faster than the conventional algorithms that represent high-entropy methods. The two algorithms yield, respectively, precise estimates of the jamming fraction ϕ_{∞}(p) and ν(p), the exponent that characterizes the kinetics of adsorption at long times t, ϕ_{∞}(p)-ϕ(p,t)∼t^{-ν(p)}. Precise estimates of ϕ_{∞}(p) and ν(p) are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.

Random sequential adsorption of Platonic and Archimedean solids

The aim of this study is the analysis of packings generated according to random sequential adsorption protocol consisting of identical Platonic and Archimedean solids. The computer simulations performed showed that the highest saturated packing fraction θ=0.40210(68) is reached by packings build of truncated tetrahedra and the smallest one θ=0.35635(67) by packings composed of regular tetrahedra. The propagation of translational and orientational order exhibited microstructural properties typically seen in random sequential adsorption packings and the kinetics of three-dimensional packings growth were again observed not to be strictly connected with the dimension of the configuration space. Moreover, a fast overlap criterion for Platonic and Archimedean solids based on separating axis theorem has been described. The criterion, together with other optimizations, allowed us to generate significantly larger packings, which translated directly to a lower statistical error of the results obtained. Additionally, the polyhedral order parameters provided can be utilized in other studies regarding particles of polyhedral symmetry.