Splay-induced order in systems of hard tapers.

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Splay and polar order in a system of hard pear-like molecules: confrontation of Monte Carlo numerical simulations with density functional theory calculations.

Recent experimental discoveries of novel nematic types with polar order, including ferroelectric nematic and splay nematic, have brought the resurgence of the interest in polar and modulated phases. One of the most important factors that is widely believed to be crucial for the formation of new phases is the pear-like shape of mesogenic molecules. Such molecules were treated using second-virial density functional theory in [De Gregorio, P et al., Soft Matter, 2016, 12(23), 5188-5198], where the authors showed that the K11 splay elastic constant can become negative due to solely entropic reasons leading to long-range splay and polar correlations. To verify whether the predictions are correct, we performed Monte Carlo simulations of the same hard-core molecules used in the DFT study. As our results suggest, no polar or modulated liquid crystalline phases emerge; polar and splay correlations are either at most short-range or completely absent. On the other hand, a polar ferroelectric splay crystal was observed.

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.

Lévy Flights Diffusion with Drift in Heterogeneous Membranes.

The modelling of diffusion in membranes is essential to understanding transport processes through membranes, especially when it comes to improving process efficiency. The purpose of this study is to understand the relationship between membrane structures, external forces, and the characteristic features of diffusive transport. We investigate Cauchy flight diffusion with drift in heterogeneous membrane-like structures. The study focuses on numerical simulation of particle movement across different membrane structures with differently spaced obstacles. Four studied structures are similar to real polymeric membranes filled with inorganic powder, while the next three structures are designed to show which distribution of obstacles can cause changes in transport. The movement of particles driven by Cauchy flights is compared to a Gaussian random walk both with and without additional drift action. We show that effective diffusion in membranes with an external drift depends on the type of the internal mechanism that causes the movement of particles as well as on the properties of the environment. In general, when movement steps are provided by the long-tailed Cauchy distribution and the drift is sufficiently strong, superdiffusion is observed. On the other hand, strong drift can effectively stop Gaussian diffusion.

Conformational degrees of freedom and stability of splay-bend ordering in the limit of a very strong planar anchoring.

We study the self-organization in a monolayer (a two-dimensional system) of flexible planar trimer particles. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend (S_{SB}) and chiral smectic-A (S_{A}^{*}) phases. The S_{SB} phase is also stable in the limit, where only cis- conformers are allowed. The second phase that occupies a considerable portion of the phase diagram is S_{A}^{*} with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis- conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the S_{A}^{*} phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay-bend (N_{SB}) phase for trimers, the free energy of the N_{SB} and S_{SB} phases is calculated within DFT for the cis- conformers, for densities where simulations show stable S_{SB}. It turns out that the N_{SB} phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of S_{SB}, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.

Numerical Study of Drift Influence on Diffusion Transport through the Hybrid Membrane.

Sodium alginate membranes filled with iron oxide nanoparticles consist of a mixture of organic and inorganic phases. This design offers the possibility to combine the polymer's easy processability and superior separation performance. For a better understanding of the mechanisms of mixture separation, we analyze the diffusion motion of a particle in the hybrid membrane environment. We model structures of two-dimensional heterogenic membranes, which resemble real membrane structures, and then we simulate a random walk on them. We investigate how the additional action of drift changes the motion properties of the diffusing particles through the polymeric membrane filled with inorganic powder. We test the effect of two parameters: the distribution of obstacles (filling) in the membrane and the value of drift on the nature of diffusion. It appears that the synergy between drift, the diffusion, and the membrane structure affect the occurrence of the superdiffusive and subdiffusive character of particle motion as measured by the time-averaged mean square displacement. An important point is the observation that the strong drift supports subdiffusive motion as it increases the chances of particle trapping. Moreover, there exists the optimal value of drift, for which the transport through a membrane speeds up and does not cause trapping.

Random sequential adsorption: An efficient tool for investigating the deposition of macromolecules and colloidal particles.

Random Sequential Adsorption (RSA) is one of the most efficient theoretical models used to investigate adsorption of macromolecules and particles, with a long-standing tradition in the field of colloid and interface science. In the first part of this paper, we demonstrate how the RSA model can be applied to interpret the experimental data and extract information about the density of the adsorption monolayer, the kinetics of its growth, and microstructural properties such as pair-correlation function and monolayer roughness. We briefly summarized the most important generalizations of the RSA model for monolayers and reviewed its extensions considering, e.g., various particle shapes, the introduction of electrostatic interaction, or adsorption on non-uniform substrates. We thoroughly scrutinized the extended RSA model developed for bilayer and multilayer formation. We collected the mean saturated packing fractions of various two- and three-dimensional objects and provided the most accurate result for two-dimensional disk packing. In the second part of this paper, we summarize various numerical algorithms and techniques that allow one to effectively implement RSA algorithms. We describe efficient methods for detecting intersections of various shapes and techniques enabling generation of strictly saturated RSA packings built of a wide range of different shapes. We hinted at how an inherently sequential RSA scheme can be parallelized. Finally, we critically discuss the limitations of the model and possible directions for future studies.

Diffusion in crowded environments: Trapped by the drift.

The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square displacement in Markovian systems because the presence of nontrivially placed obstacles puts constraints on possible displacements. We investigate how the additional action of drift changes properties of the diffusion in the crowded environment. It is shown that the action of a constant drift increases chances of trapping, which suppresses the persistent ballistic motion. Such a diffusion becomes anisotropic because the drift introduces a preferred direction of motion which is further altered by interactions with obstacles. Moreover, individual trajectories display a high level of variability, which is responsible for the macroscopic properties of the diffusing front. Overall, the interplay among drift, diffusion, and a crowded environment, as measured by the time-averaged mean square displacement, is responsible for the emergence of superdiffusive and subdiffusive patterns in the very same system. Importantly, in contrast to free motion, the constant drift can enhance signatures of subdiffusive motion as it increases trapping chances.

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.

Deposition of Polymer Particles with Fibrinogen Corona at Abiotic Surfaces under Flow Conditions.

The deposition kinetics of polymer particles with fibrinogen molecule coronas at bare and poly-L-lysine (PLL) modified mica was studied using the microfluid impinging-jet cell. Basic physicochemical characteristics of fibrinogen and the particles were acquired using dynamic light scattering and the electrophoretic mobility methods, whereas the zeta potential of the substrates was determined using streaming potential measurements. Subsequently, an efficient method for the preparation of the particles with coronas, characterized by a controlled fibrinogen coverage, was developed. This enabled us to carry out measurements, which confirmed that the deposition kinetics of the particles at mica vanished at pH above 5. In contrast, the particle deposition of PLL modified mica was at maximum for pH above 5. It was shown that the deposition kinetics could be adequately analyzed in terms of the mean-field approach, analogously to the ordinary colloid particle behavior. This contrasts the fibrinogen molecule behavior, which efficiently adsorbs at negatively charged substrates for the entire range pHs up to 9.7. These results have practical significance for conducting label-free immunoassays governed by the specific antigen/antibody interactions.

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.

A Simple Mechanism Causing Wealth Concentration.

We study mechanisms leading to wealth condensation. As a natural starting point, our model adopts a neoclassical point of view, i.e., we completely ignore work, production, and productive relations, and focus only on bilateral link between two randomly selected agents. We propose a simple matching process with deterministic trading rules and random selection of trading agents. Furthermore, we also neglect the internal characteristic of traded goods and analyse only the relative wealth changes of each agent. This is often the case in financial markets, where a traded good is money itself in various forms and various maturities. We assume that agents trade according to the rules of utility and decision theories. Agents possess incomplete knowledge about market conditions, but the market is in equilibrium. We show that these relatively frugal assumptions naturally lead to a wealth condensation. Moreover, we discuss the role of wealth redistribution in such a model.

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.

Random sequential adsorption of particles with tetrahedral symmetry.

We study random sequential adsorption (RSA) of a class of solids that can be obtained from a cube by specific cutting of its vertices, in order to find out how the transition from tetrahedral to octahedral symmetry affects the densities of the resulting jammed packings. We find that in general solids of octahedral symmetry form less dense packing; however, the lowest density was obtained for the packing built of tetrahedra. The densest packing is formed by a solid close to a tetrahedron but with vertices and edges slightly cut. Its density is θ_{max}=0.41278±0.00059 and is higher than the mean packing fraction of spheres or cuboids but is lower than that for the densest RSA packings built of ellipsoids or spherocylinders. The density autocorrelation function of the studied packings is typical for random media and vanishes very quickly with distance.

Mechanisms of Fibrinogen Adsorption on Silica Sensors at Various pHs: Experiments and Theoretical Modeling.

The adsorption kinetics of human serum fibrinogen at silica substrates was studied using optical waveguide lightmode spectroscopy (OWLS) and quartz crystal microbalance (QCM) techniques. Measurements were performed at pH 3.5, 4, and 7.4 for various ionic strengths. The experimental data were interpreted in terms of a hybrid random sequential adsorption model. This allowed the mass transfer rate coefficient for the OWLS cell and maximum coverages to be determined at various pHs. The appearance of different, pH-dependent mechanisms of fibrinogen adsorption on silica substrates was confirmed. At pH 3.5 the molecules mostly adsorb in the side-on orientation that produces a low maximum coverage of ca. 1 mg m-2. At this pH, the kinetics derived from the OWLS measurements agree with those theoretically predicted using the convective-diffusion theory. In consequence, a comparison of the OWLS and QCM results allows the water factor and the dynamic hydration of fibrinogen molecules to be determined. At pH 7.4, the OWLS method gives inaccurate kinetic data for the low coverage range. However, the maximum coverage that was equal to ca. 4 mg m-2 agrees with the QCM results and with previous literature results. It is postulated that the limited accuracy of the OWLS method for lower coverage stems from a heterogeneous structure of fibrinogen monolayers, which consist of side-on and end-on adsorbed molecules. One can expect that the results acquired in this work allow development of a robust procedure for preparing fibrinogen monolayers of well-controlled coverage and molecule orientation, which can be exploited for efficient immunosensing purposes.

Multimodal stationary states under Cauchy noise.

A Lévy noise is an efficient description of out-of-equilibrium systems. The presence of Lévy flights results in a plenitude of noise-induced phenomena. Among others, Lévy flights can produce stationary states with more than one modal value in single-well potentials. Here we explore stationary states in special double-well potentials demonstrating that a sufficiently high potential barrier separating potential wells can produce bimodal stationary states in each potential well. Furthermore, we explore how the decrease in the barrier height affects the multimodality of stationary states. Finally, we explore the role of multimodality of stationary states on noise-induced escape over the static potential barrier.

Investigation of quaternary structure of aggregating 3-ketosteroid dehydrogenase from Sterolibacterium denitrificans: In the pursuit of consensus of various biophysical techniques.

In this work we analyzed the quaternary structure of FAD-dependent 3-ketosteroid dehydrogenase (AcmB) from Sterolibacterium denitrificans, the protein that in solution forms massive aggregates (>600 kDa). Using size-excursion chromatography (SEC), dynamic light scattering (DLS), native-PAGE and atomic force microscopy (AFM) we studied the nature of enzyme aggregation. Partial protein de-aggregation was facilitated by the presence of non-ionic detergent such as Tween 20 or by a high degree of protein dilution but not by addition of a reducing agent or an increase of ionic strength. De-aggregating influence of Tween 20 had no impact on either enzyme's specific activity or FAD reconstitution to recombinant AcmB. The joint experimental (DLS, isoelectric focusing) and theoretical investigations demonstrated gradual shift of enzyme's isoelectric point upon aggregation from 8.6 for a monomeric form to even 5.0. The AFM imaging on mica or highly oriented pyrolytic graphite (HOPG) surface enabled observation of individual protein monomers deposited from a highly diluted solution (0.2 µg/ml). Such approach revealed that native AcmB can indeed be monomeric. AFM imaging supported by theoretical random sequential adsorption (RSA) kinetics allowed estimation of distribution enzyme forms in the bulk solution: 5%, monomer, 11.4% dimer and 12% trimer. Finally, based on results of AFM as well as analysis of the surface of AcmB homology models we have observed that aggregation is most probably initiated by hydrophobic forces and then assisted by electrostatic attraction between negatively charged aggregates and positively charged monomers.

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.

Random sequential adsorption of cuboids.

The subject of this study was random sequential adsorption of cuboids of axes length ratio of a : 1 : b for a ∈ [0.3, 1.0] and b ∈ [1.0, 2.0], and the aim of this study was to find a shape that provides the highest packing fraction. The obtained results show that the densest packing fraction is 0.401 87 ± 0.000 97 and is reached for axes ratios near cuboids of 0.75:1:1.30. Kinetics of packing growth was also studied, and it was observed that its power-law character seems not to be governed by the number of cuboid degrees of freedom. The microstructural properties of obtained packings were studied in terms of density correlation function and propagation of orientational ordering.

Random sequential adsorption of cubes.

Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.