Numerical Modeling of Anisotropic Particle Diffusion through a Cylindrical Channel.

The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time.

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.

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.

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.

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.

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.

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.

Adsorption/Desorption Transition of Recombinant Human Neurotrophin 4: Physicochemical Characterization.

Bulk physicochemical properties of neurotrophin 4 (NT-4) in electrolyte solutions and its adsorption/desorption on/from mica surfaces have been studied using dynamic light scattering (DLS), microelectrophoresis, a solution depletion technique (enzyme-linked immunosorbent assay, ELISA), and AFM imaging. Our study presents a determination of the diffusion coefficient, hydrodynamic diameters, electrophoretic mobility, and isoelectric point of the NT-4 under various ionic strength and pH conditions. The size of the NT-4 homodimer for an ionic strength of 0.015 M was substantially independent of pH and equal to 5.1 nm. It has been found that the number of electrokinetic charges per NT-4 molecule was equal to zero for all studied ionic strengths at pH 8.1, which was identified as the isoelectric point (iep). The protein adsorption/desorption on/from mica surfaces was examined as a function of ionic strength and pH. The kinetics of neurotrophin adsorption/desorption were evaluated at pH 3.5, 7.4, and 11 by direct AFM imaging and the ELISA technique. A monotonic increase in the maximum coverage of adsorbed NT-4 molecules with ionic strength (up to 5.5 mg/m2) was observed at pH 3.5. These results were interpreted in terms of the theoretical model postulating an irreversible adsorption of the protein governed by the random sequential adsorption (RSA). Our measurements revealed a significant role of ionic strength, pH, and electrolyte composition in the lateral electrostatic interactions among differently charged NT-4 molecules. The transition between adsorption/desorption processes is found for the region of high pH and low surface concentration of adsorbed neurotrophin molecules at constant ionic strength. Additionally, results presented in this work show that the adsorption behavior of neurotrophin molecules may be governed by intrasolvent electrostatic interactions yielding an aggregation process. Understanding polyvalent neurotrophin interactions may have an impact on the reversibility/irreversibility of adsorption, and hence they might be useful for obtaining well-ordered protein layers, targeting the future development of drug delivery systems for treating neurodegenerative diseases.

Surface fine structure influence on saturated random packings.

Random packings of disks on a mesh are studied numerically using random sequential adsorption algorithm. The mesh is built of straight horizontal and vertical one-dimensional lines of a given distance between them. The packing fraction and structure as well as the kinetics of packing growth dependence on mesh size are analyzed to provide information, whether surface inhomogeneity will affect the properties of random packings. It has been shown that the number of disks in a packing slightly decreases with growing distance between mesh lines while the kinetics may change significantly even for very dense meshes. As packings obtained in random sequential adsorption resemble monolayers produced by irreversible adsorption processes, results of this study show that by measuring properties of a random packing it may be possible to determine fine structure of an underlying surface.

In a search for a shape maximizing packing fraction for two-dimensional random sequential adsorption.

Random sequential adsorption of various two dimensional objects is studied in order to find a shape which maximizes the saturated packing fraction. This investigation was begun in our previous paper [Ciesla et al., Phys. Chem. Chem. Phys. 17, 24376 (2015)], where the densest packing was studied for smoothed dimers. Here this shape is compared with the smoothed n-mers, spherocylinders, and ellipses. It is found that the highest packing fraction out of the studied shapes is 0.584 05 ± 0.0001 and is obtained for ellipses having long-to-short axis ratio of 1.85 ± 0.07.

Shapes for maximal coverage for two-dimensional random sequential adsorption.

The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to the maximum packing fraction of ellipsoids and spherocylinders and higher than other studied shapes. Discussion why this shape is beneficial for random sequential adsorption is given.

Taming Lévy flights in confined crowded geometries.

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 [Ciesla 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.

Human fibrinogen adsorption on positively charged latex particles.

Fibrinogen (Fb) adsorption on positively charged latex particles (average diameter of 800 nm) was studied using the microelectrophoretic and the concentration depletion methods based on AFM imaging. Monolayers on latex were adsorbed from diluted bulk solutions at pH 7.4 and an ionic strength in the range of 10(-3) to 0.15 M where fibrinogen molecules exhibited an average negative charge. The electrophoretic mobility of the latex after controlled fibrinogen adsorption was systematically measured. A monotonic decrease in the electrophoretic mobility of fibrinogen-covered latex was observed for all ionic strengths. The results of these experiments were interpreted according to the three-dimensional electrokinetic model. It was also determined using the concentration depletion method that fibrinogen adsorption was irreversible and the maximum coverage was equal to 0.6 mg m(-2) for ionic strength 10(-3) M and 1.3 mg m(-2) for ionic strength 0.15 M. The increase of the maximum coverage was confirmed by theoretical modeling based on the random sequential adsorption approach. Paradoxically, the maximum coverage of fibrinogen on positively charged latex particles was more than two times lower than the maximum coverage obtained for negative latex particles (3.2 mg m(-2)) at pH 7.4 and ionic strength of 0.15 M. This was interpreted as a result of the side-on adsorption of fibrinogen molecules with their negatively charged core attached to the positively charged latex surface. The stability and acid base properties of fibrinogen monolayers on latex were also determined in pH cycling experiments where it was observed that there were no irreversible conformational changes in the fibrinogen monolayers. Additionally, the zeta potential of monolayers was more positive than the zeta potential of fibrinogen in the bulk, which proves a heterogeneous charge distribution. These experimental data reveal a new, side-on adsorption mechanism of fibrinogen on positively charged surfaces and confirmed the decisive role of electrostatic interactions in this process.

Tracer diffusion inside fibrinogen layers.

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.

Human fibrinogen monolayers on latex particles: role of ionic strength.

The adsorption of human serum fibrinogen on polystyrene latex particles was studied using the microelectrophoretic and concentration depletion methods. Measurements were carried out for pH 3.5 and an ionic strength range of 10(-3) to 0.15 M NaCl. The electrophoretic mobility of latex was determined as a function of the amount of adsorbed fibrinogen (surface concentration). A monotonic increase in the electrophoretic mobility (zeta potential) of the latex was observed, indicating a significant adsorption of fibrinogen on latex for all ionic strengths. No changes in the latex mobility were observed for prolonged time periods, suggesting the irreversibility of fibrinogen adsorption. The maximum coverage of fibrinogen on latex particles was precisely determined using the depletion method. The residual protein concentration after making contact with latex particles was determined by electrokinetic measurements and AFM imaging where the surface coverage of fibrinogen on mica was quantitatively determined. The maximum fibrinogen coverage increased monotonically with ionic strength from 1.8 mg m(-2) for 10(-3) M NaCl to 3.6 mg m(-2) for 0.15 M NaCl. The increase in the maximum coverage was interpreted in terms of the reduced electrostatic repulsion among adsorbed fibrinogen molecules. The experimental data agree with theoretical simulations made by assuming a 3D unoriented adsorption of fibrinogen. The stability of fibrinogen monolayers on latex was also determined in ionic strength cycling experiments. It was revealed that cyclic variations in NaCl concentration between 10(-3) and 0.15 M induced no changes in the latex electrophoretic mobility, suggesting that there were no irreversible molecule orientation changes in the monolayers. On the basis of these experimental data, a robust procedure of preparing fibrinogen monolayers on latex particles of well-controlled coverage was proposed.

Mechanisms of fibrinogen adsorption at solid substrates at lower pH.

Adsorption of fibrinogen was theoretically studied using the three-dimensional random sequential adsorption (RSA) model. Fibrinogen molecule shape was approximated by the bead model considering the presence of flexible side arms. Various cases were considered inter alia, the side-on adsorption mechanisms and the simultaneous side-on/end-on adsorption mechanism. The latter mechanisms is pertinent to fibrinogen adsorption at lower pH (below isoelectric point of 5.8) where the entire molecule is positively charged. Extensive calculations enabled one to determine the jamming surface concentration (coverage) of molecules adsorbed under the side-on and end-on orientations as well as the total coverage. For the simultaneous side-on/end-on model the maximum surface concentration was 7.29 × 10(3) µm(-2) corresponding to the protein coverage of 4.12 mg m(-2) (without considering hydration). Additionally, the surface blocking functions for different adsorption regimes were determined and analytically approximated for the entire range of coverage by the interpolating polynomials. Using these blocking functions, fibrinogen adsorption kinetics for diffusion controlled transport conditions was evaluated. Comparison of these theoretical results with experimental data was made. It was demonstrated that the simultaneous side-on/end-on model properly reflects the maximum coverage of fibrinogen adsorbed on latex particles determined via the electrokinetic (electrophoretic mobility) and AFM measurements. Also, streaming potential measurements of fibrinogen adsorption kinetics on mica were successfully interpreted in terms of this model. The theoretical results derived in this work have implications for basic science providing information on mechanisms of anisotropic protein adsorption.

Random packing of spheres in Menger sponge.

Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.

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.

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.

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.