arXiv subjects

A. Ciach

Publications and source records attributed to A. Ciach.

At least 19 recordsLinked to original sources

arXiv2026

Vortex formation in the Vicsek model with internal chirality of self-propelling objects

Effect of internal chirality on collective motion of a large number of active objects is studied by simulations of appropriately modified Vicsek model. We add a fixed angle to the noise and consider small ratios, $p$, between this angle and the maximal deviation from the average local direction of motion. When the above ratio is $p=1/120$, the traveling bands observed with the symmetrical noise are destroyed, and small bands moving in different directions appear. Circular rotating flocks of objects with the same orientation are formed for $p=1/7.5$. Stable vortexes in the stationary state were found from $p=1/60$ to $p=1/20$. Velocity autocorrelation function shows equilibrium between the inflow and the outflow to and from the vortex. Long-time evolution is considerably influenced by a temporary trapping of the objects in the vortex. The ballistic behavior for the symmetrical noise changes to the diffusive behavior for the chirality leading to the onset of vortexes.

cond-mat.soft↗

arXiv2025

Mutual effect of charge- and number-density correlations in ionic liquids and concentrated electrolytes

Correlation functions in concentrated ionic systems are studied within the mesoscopic theory at the level of the Gaussian approximation. The previously neglected fluctuation contribution to the inverse charge-charge correlation function is taken into account to verify the accuracy of the previous results. We calculate the correlation lengths and the amplitudes and show that the fluctuation contribution does not lead to significant changes of the results. We also derive necessary conditions for the presence of both, the oscillatory and the monotonic decays of the charge-charge correlations that must be satisfied by the noncoulombic contributions to the inverse charge-charge correlation function. At the level of the Gaussian approximation, these conditions are not satisfied. Extension of the theory beyond the Gaussian approximation is necessary to verify whether the asymptotic decay of the charge-charge correlations is monotonous or oscillatory, as suggested by the surface force apparatus or by the SAXS experiments, respectively.

cond-mat.soft↗

arXiv2024

Mesoscopic theory for a double layer capacitance in concentrated ionic systems

Effect of an oscillatory decay of the charge density in concentrated ionic solutions and ionic liquids on the double-layer capacitance is studied in a framework of a mesoscopic theory. Only Coulomb and steric forces between the ions that are present in all ionic systems are taken into account. We show that the charge oscillations lead to a rescaled distance between the electrode and the virtual monolayer of counterions in the Helmholtz capacitance, and the scaling factor depends on the period of the charge oscillations. Our very simple formula for large density of ions and small voltage can serve as a reference point for the double layer capacitance in concentrated ionic solutions and ionic liquids, and can help to disentangle the universal and specific contributions to the capacitance in particular systems.

cond-mat.stat-mech↗

arXiv2023

Spontaneous pattern formation in monolayers of binary mixtures with competing interactions

A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range repulsion between particles of the same species, and the cross-interaction of opposite sign. The model is inspired by oppositely charged hydrophilic and hydrophobic particles or macromolecules with preferential solubility in different components of a solvent that is close to a miscibility critical point. We determine the phase diagram in the chemical potentials and in the concentration - density planes for a few fixed temperatures in the mean-field one-shell approximation. We find that the presence of the second component significantly enlarges the temperature range of stability of the ordered phases. We obtain three stable phases with periodic concentration: the lamellar L phase with alternating stripes of the two components for similar chemical potentials, and a hexagonal arrangement of the clusters of the minority component in the liquid of the majority component. The latter two phases, however, are stable only at relatively high temperatures. At lower temperatures, the L phase coexists with a disordered one-component fluid or with very dilute gas with mixed components. At still lower temperatures, the one-component phase coexisting with the L phase can be disordered or ordered, depending on the chemical potentials. The theoretical results are confirmed by MC simulations for selected thermodynamic states.

cond-mat.soft↗

arXiv2022

Structure of ionic liquids and concentrated electrolytes from a mesoscopic theory

Recently, underscreening in concentrated electrolytes was discovered in experiments and confirmed in simulations and theory. It was found that the correlation length of the charge-charge correlations, $λ_s$, satisfies the scaling relation $λ_s/λ_D\sim (a/λ_D)^n$, where $λ_D$ is the Debye screening length and $a$ is the ionic diameter. However, different values of n were found in different studies. In this work we solve this puzzle within the mesocopic theory that yielded n=3 in agreement with experiments, but only very high densities of ions were considered [A. Ciach A. and O. Patsahan, {\it J.Phys.: Condens. Matter} {\textbf 33}, 37LT01 (2021)]. Here we apply the theory to a broader range of density of ions and find that different values of n in the above scaling can yield a fair approximation for $λ_s/λ_D$ for different ranges of $a/λ_D$. The experimentally found scaling holds for $2 <a/λ_D<4$, and we find n=3 for the same range of the reduced Debye length. For smaller $a/λ_D$, we find n=2 obtained earlier in several simulation and theoretical studies, and still closer to the Kirkwood line we obtain n=1.5 that was also predicted in different works. It follows from our theory that n=3 (i.e. $λ_s$ is proportional to the density of ions) when the variance of the local charge density is large, and $λ_s$ is proportional to this variance times the Bjerrum length. Detailed derivation of the theory is presented.

cond-mat.stat-mech↗

arXiv2021

Correct scaling of the correlation length from a theory for concentrated electrolytes

Self-consistent theory for concentrated electrolytes is developed. Oscillatory decay of the charge-charge correlation function with the decay length that shows perfect agreement with the experimentally discovered and so far unexplained scaling is obtained. For the density-density correlations, monotonic asymptotic decay with the decay length comparable with the decay length of the charge correlations is found. We show that the correlation lengths in concentrated electrolytes depend crucially on the local variance of the charge density.

cond-mat.soft↗

arXiv2020

Self-assembly in mixtures with competing interactions

A binary mixture of particles interacting with spherically-symmetric potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume fractions. Motivated by the mixture of oppositely charged particles with different adsorption preferences immersed in near-critical binary solvent, we assume short-range attraction long-range repulsion for the interaction between like particles, and short range repulsion long-range attraction for the interaction between different ones. In order to predict structural and thermodynamic properties of such complex mixtures, we develop a theory combining the density functional and field-theoretic methods. We show that concentration fluctuations in mesoscopic regions lead to a qualitative change of the phase diagram compared to mean-field predictions. Both theory and MD simulations show coexistence of a low-density disordered phase with a high-density phase with alternating layers rich in the first and the second component. The density and the degree of order of the ordered phase decrease with increasing temperature, up to a temperature where the theory predicts a narrow two-phase region with increasing density of both phases for increasing temperature. MD simulations show that monocrystals of the solid and liquid crystals have a prolate shape with the axis parallel to the direction of concentration oscillations, and the deviation from the spherical shape increases with increasing periodic order.

cond-mat.soft↗

arXiv2020

Correlation functions in mixtures with energetically favoured nearest-neighbours of different kind: a size-asymmetric case

Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the two components are taken into account. Semi-quantitative agreement between the simulation and theoretical results is obtained, except from very small distances. The correlation functions exhibit exponentially damped oscillations, with the period determined by the interaction potential, and both the amplitude and the correlation length increasing significantly with increasing diameter ratio. Increasing size asymmetry leads also to decreasing fluctuations of the number of the smaller particles in the attractive shell of the bigger ones. For small size asymmetry, the strongest correlations occur for comparable volume fraction of the two components. When the size ratio increases, the maximum of the structure factor moves to a larger volume fraction of the bigger particles, and for the size ratio as large as 4, the maximum goes beyond the accessible range of volume fractions. Our results show that when the neighbourhood of different particles is energetically favoured, the particles are much more uniformly distributed than in the random distribution even at relatively high temperature, especially for large size asymmetry.

cond-mat.soft↗

arXiv2020

Effects of fluctuations on correlation functions in inhomogeneous mixtures

Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a Brazovskii-type approximation. Explicit results are obtained for two model systems. In the two models, the diameters of the hard cores of particles are equal, and the interactions favour a periodic arrangement of alternating species A and B. However, the optimal distance between the species A and B is much different in the two models. Theoretical results for different temperature and volume fractions of the two components are compared with the results of Monte Carlo simulations, and the structure is illustrated by simulation snapshots. Despite different interaction potentials and different length scale of the local ordering, properties of the correlation functions in the two models are very similar.

cond-mat.soft↗

arXiv2020

Triangular lattice models for pattern formation by core-shell particles with different shell thicknesses

Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with hard-cores covered by shells of cross-linked polymeric chains. In model II, such inner shell is covered by a much softer outer shell. In both models, the hard cores can occupy sites of the triangular lattice, and nearest-neighbor repulsion following from overlapping shells is assumed. The capillary force is represented by the second- or the fifth neighbor attraction in model I or II, respectively. Ground states with fixed chemical potential $μ$ or with fixed fraction of occupied sites c are thoroughly studied. For T > 0, the $μ(c)$ isotherms, compressibility and specific heat are calculated by Monte Carlo simulations. In model II, 6 ordered periodic patterns occur in addition to 4 phases found in model I. These additional phases, however, are stable only at the phase coexistence lines, i.e. in regions of zero measure at the $(μ,T)$ diagram which otherwise looks like the diagram of model I. In the canonical ensemble, these 6 phases and interfaces between them appear in model II for large intervals of c, and the number of possible patterns is much larger than in model I. We calculated surface tensions for different interfaces and found that the favorable orientation of the interface corresponds to its smoothest shape in both models.

cond-mat.soft↗

arXiv2020

Mesoscopic theory for systems with competing interactions near a confining wall

Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT expression for the grand thermodynamic potential. Various levels of approximation can be considered for the obtained equations. The lowest-order nontrivial approximation (GM) resembles the Landau-Brazovskii type theory for a semiinfinite system. Unlike in the original phenomenological theory, however, all coefficients in our equations and BC are expressed in terms of the interaction potential and the thermodynamic state. Analytical solutions of the linearized equations in GM are presented and discussed on a general level and for a particular example of the double-Yukawa potential. We show exponentially damped oscillations of the volume fraction and the correlation function in the direction perpendicular to the confining surface. The correlations show oscillatory decay in directions parallel to this surface too, with the decay length increasing significantly when the system boundary is approached. The framework of our theory allows for a systematic improvement of the accuracy of the results.

cond-mat.stat-mech↗

arXiv2019

Adsorption anomalies in a 2D model of cluster-forming systems

Adsorption on a boundary line confining a monolayer of particles self-assembling into clusters is studied by MC simulations. We focus on a system of particles interacting via competing interaction potential in which effectively short-range attraction is followed by long-range repulsion, mimicking the so called SALR system. For the chemical potential values below the order-disorder phase transition the adsorption isotherms were shown to undergo non-standard behavior, i. e. the adsorption exhibits a maximum upon structural transition between structureless and disordered cluster fluid. In particular, we have found that the adsorption decreases for increasing chemical potential when (i) clusters dominate over monomers in the bulk, (ii) the density profile in the direction perpendicular to the confining line exhibits an oscillatory decay, (iii) the correlation function in the layer near the adsorption wall exhibits an oscillatory decay in the direction parallel to this wall. Our report indicates striking differences between simple and complex fluid adsorption processes.

cond-mat.soft↗

arXiv2018

Combined density functional and Brazovskii theories for systems with spontaneous inhomogeneities

The low-T part of the phase diagram in self-assembling systems is correctly predicted by the known versions of the density functional theory (DFT). The high-T part obtained in DFT, however, does not agree with simulations even on the qualitative level. In this work a new version of the DFT is developed. The contribution to the grand thermodynamic potential associated with mesoscopic fluctuations is explicitly taken into account. The expression for this contribution is obtained by the methods known from the Brazovskii field theory. Apart from developing the approximate expression for the grand thermodynamic potential that contains the fluctuation contribution and is ready for numerical minimization, we develop a simplified version of the theory valid for weakly ordered phases, i.e. for the high -T part of the phase diagram. The simplified theory is verified by a comparison with the results of simulations for a particular version of the short-range attraction long-range repulsion (SALR) interaction potential. Except from the fact that in our theory the ordered phases are stable at lower T than in simulations, a good agreement for the high-T part of the phase diagram is obtained for the range of density that was considered in simulations. In addition, the equation of state and compressibility isotherms are presented. Finally, the physical interpretation of the fluctuation-contribution to the grand potential is discussed in detail.

cond-mat.soft↗

arXiv2016

Critical point calculation for binary mixtures of symmetric non-additive hard disks

We have calculated the values of critical packing fractions for the mixtures of symmetric non-additive hard disks. An interesting feature of the model is the fact that the internal energy is zero and the phase transitions are entropically driven. A cluster algorithm for Monte Carlo simulations in a semigrand ensemble was used. The finite size scaling analysis was employed to compute the critical packing fractions for infinite systems with high accuracy for a range of non-additivity parameters wider than in the previous studies.

cond-mat.stat-mech↗

arXiv2015

Density functional theory for systems with mesoscopic inhomogeneities

We study effects of fluctuations on the mesoscopic length-scale on systems with mesoscopic inhomogeneities. Equations for the correlation function and for the average volume fraction are derived in the self-consistent Gaussian approximation. The equations are further simplified by postulating the expression for the structure factor consistent with scattering experiments for self-assembling systems. Predictions of the approximate theory are verified by a comparison with the exact results obtained earlier for the one-dimensional lattice model with first-neighbour attraction and third-neighbour repulsion. We find qualitative agreement for the correlation function, the equation of state and the dependence of the chemical potential $μ$ on the volume fraction $ζ$. Our results confirm also that strong inhomogeneities in the disordered phase are found only in the case of strong repulsion. The inhomogeneities are reflected in an oscillatory decay of the correlation function with a very large correlation length, three inflection points in the $μ(ζ)$ curve and a compressibility that for increasing $ζ$ takes very large, very small and again very large values.

cond-mat.soft↗

arXiv2015

Effects of rigid or adaptive confinement on colloidal self-assembly. Fixed vs. fluctuating number of confined particles

The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the Grand Canonical Ensemble (GCE) in [J. Pękalski et al. J. Chem. Phys. 142, 014903 (2015)]. The model considers a pair interaction defined by a short-range attraction plus a longer-range repulsion. We consider thermodynamic states corresponding to self-assembly into clusters. Both, fixed and adaptive boundaries are studied. For fixed boundaries, there are particular states in which, for equal average densities, the number of clusters in the GCE is larger than in the Canonical Ensemble. The dependence of pressure on density has a different form when the system size changes with fixed number of particles and when the number of particles changes with fixed size of the system. In the former case the pressure has a nonmonotonic dependence on the system size. The anomalous increase of pressure for expanding system is accompanied by formation of a larger number of smaller clusters. In the case of elastic confining surfaces we observe a bistability, i.e. two significantly different system sizes occur with almost the same probability. The mechanism of the bistability in the closed system is different to that of the case of permeable walls, where the two equilibrium system sizes correspond to a different number of particles.

cond-mat.soft↗

arXiv2014

Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation

The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced in [J. Pekalski, A. Ciach and N. G. Almarza, arXiv:1401.0801 [cond-mat.soft]] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases - the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our results concern spontaneous pattern formation on solid surfaces, fluid interfaces or membranes that is driven by competing interactions between adsorbing particles or molecules.

cond-mat.soft↗

arXiv2014

Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbour attraction and third-neighbour repulsion. At the ground state of the model ($T=0$) the lattice is empty for small values of the chemical potential $μ$, and fully occupied for large $μ$. For intermediate values of $μ$ periodically distributed clusters, bubbles or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For $T>0$ we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

cond-mat.soft↗