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A. Ciach

Publications and source records attributed to A. Ciach.

36 records · Page 2Linked to original sources
arXiv2013

Origin of similarity of phase diagrams in amphiphilic and colloidal systems with competing interactions

We show that amphiphilic and colloidal systems with competing interactions can be described by the same Landau-Brazovskii functional. The functional is obtained by a systematic coarse-graining procedure applied tosystems with isotropic interaction potentials. Microscopic expressions for the coefficients in the functional are derived. We propose simple criteria to distinguish the effective interparticle potentials that can lead to macro- or microsegregation. Our considerations concern also charged globular proteins in aqueous solutions and other system with effective short-range attraction long-range repulsion interactions.

cond-mat.soft↗
arXiv2013

Periodic ordering of clusters in a one-dimensional lattice model

A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first neighbors and repulsion J_2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J_2/J_1<1/3. In addition to the homogeneous phases, the third phase with periodically distributed clusters appears for J_2/J_1>1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J_2/J_1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J_2/J_1. Based on the exact results, for J_2/J_1>1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9<J_2/J_1<1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T=0, local spatial inhomogeneities appear for finite T. Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density ρthat we associate with formation of living clusters, and if the repulsion is strong, another maximum for ρ= 1/2.

cond-mat.soft↗
arXiv2012

Spatial inhomogeneities in ionic liquids, charged proteins and charge stabilized colloids from collective variables theory

Effects of size and charge asymmetry between oppositely charged ions or particles on spatial inhomogeneities are studied for a large range of charge and size ratios. We perform a stability analysis of the primitive model (PM) of ionic systems with respect to periodic ordering using the collective variables based theory. We extend previous studies [A. Ciach et al., Phys. Rev.E \textbf{75}, 051505 (2007)] in several ways. First, we employ a non-local approximation for the reference hard-sphere fluid which leads to the Percus-Yevick pair direct correlation functions for the uniform case. Second, we use the Weeks-Chandler-Anderson regularization scheme for the Coulomb potential inside the hard core. We determine the relevant order parameter connected with the periodic ordering and analyze the character of the dominant fluctuations along the $λ$-lines. We show that the above-mentioned modifications produce large quantitative and partly qualitative changes in the phase diagrams obtained previously. We discuss possible scenarios of the periodic ordering for the whole range of size- and charge ratios of the two ionic species, covering electrolytes, ionic liquids, charged globular proteins or nanoparticles in aqueous solutions and charge-stabilized colloids.

cond-mat.soft↗
arXiv2011

Origin of attraction between likely charged hydrophobic and hydrophilic walls confining near-critical binary aquaeous mixture with ions

Effect of ionic solute on a near-critical binary aqueous mixture confined between charged walls with different adsorption preferences is considered within a simple density functional theory. For the near-critical system containing small amount of ions a Landau-type functional is derived based on the assumption that the correlation, $ξ$, and the Debye screening length, $κ^{-1}$, are both much larger than the molecular size. The corresponding approximate Euler-Lagrange equations aresolved analytically for ions insoluble in the organic solvent. Nontrivial concentration profile of the solvent is found near the charged hydrophobic wall as a result of the competition between the short-range attraction of the organic solvent and the electrostatic attraction of the hydrated ions. Excess of water may be present near the hydrophobic surface for some range of the surface charge and $ξκ$. As a result, the effective potential between the hydrophilic and the hydrophobic surface can be repulsive far from the critical point, then attractive and again repulsive when the critical temperature is approached, in agreement with the recent experiment [Nellen at.al., Soft Matter {\bf 7}, 5360 (2011)].

cond-mat.soft↗
arXiv2011

Equilibrium Clusters in Concentrated Lysozyme Protein Solutions

We have studied the structure of salt-free lysozyme at 293 K and pH 7.8 using molecular simulations and experimental SAXS effective potentials between proteins at three volume fractions, 0.012, 0.033, and 0.12. We found that the structure of lysozyme near physiological conditions strongly depends on the volume fraction of proteins. The studied lysozyme solutions are dominated by monomers only for <0.012; for the strong dilution 70% of proteins are in a form of monomers. For 0.033 only 20% of proteins do not belong to a cluster. The clusters are mainly elongated. For 0.12 almost no individual particles exits, and branched, irregular clusters of large extent appear. Our simulation study provides new insight into the formation of equilibrium clusters in charged protein solutions near physiological conditions.

cond-mat.soft↗
arXiv2010

Mesoscopic theory for inhomogeneous mixtures

Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions for the correlation functions and for the grand potential are obtained for weak ordering on mesoscopic length scales. Stability analysis of the disordered phase is performed in mean-field approximation (MF) and beyond. MF shows existence of either a spinodal or a $λ$-surface on the volume-fractions - temperature phase diagram. Separation into homogeneous phases or formation of inhomogeneous distribution of particles occurs on the low-temperature side of the former or the latter surface respectively, depending on both the interaction potentials and the size ratios between particles of different species. Beyond MF the spinodal surface is shifted, and the instability at the $λ$-surface is suppressed by fluctuations. We interpret the $λ$-surface as a borderline between homogeneous and inhomogeneous (containing clusters or other aggregates) structure of the disordered phase. For two-component systems explicit expressions for the MF spinodal and $λ$-surfaces are derived. Examples of interaction potentials of simple form are analyzed in some detail, in order to identify conditions leading to inhomogeneous structures.

cond-mat.soft↗
arXiv2008

Density functional theory for soft matter with mesoscopic length scale fluctuations included within field-theoretic formalism

Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived from the microscopic theory by a systematic coarse-graining procedure. Within the framework of this theory we obtain the universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential we find the bicontinuous gyroid phase (Ia3d symmetry) that may be related to a network forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.

cond-mat.soft↗
arXiv2006

Field theory for size- and charge asymmetric primitive model of electrolytes. Mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of size-, λ, and charge, Z, ratios of the two ionic species. Two order parameters (OP) are identified, and their relations to physically relevant quantities are described for various values of λand Z. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation. A gas-liquid separation occurs for any Z and λdifferent from 1. In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found.

cond-mat.stat-mech↗
arXiv2006

Correlation functions in ionic liquid at coexistence with ionic crystal. Results of the Brazovskii-type field theory

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in the Gaussian approximation [Ciach at. al., J. Chem. Phys. {\bf 118}, 3702 (2003)]. The fluctuation contribution leads to a renormalization of both the amplitude and the decay length of the correlation functions. The renormalized quantities show qualitatively different behavior than their mean-field (MF) counterparts. While the amplitude and the decay length both diverge in MF when the $λ$-line is approached, the renormalized quantities remain of order of unity in the same dimensionless units down to the coexistence with the ionic crystal. Along the line of the phase transition the decay length and the period of oscillations are independent of density, and their values in units of the diameter of the ions are $α_0^{-1}\approx 1$ and $2π/α_1\approx 2.8$ respectively.

cond-mat.soft↗
arXiv2006

Field-theoretic description of ionic crystallization in the restricted primitive model

Effects of charge-density fluctuations on a phase behavior of the restricted primitive model (RPM) are studied within a field-theoretic formalism. We focus on a $λ$-line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field (MF) theories, but is absent in simulation results. In our study the RPM is reduced to a $ϕ^6$ theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the $λ$-line disappears. Instead, a fluctuation-induced first-order transition to a charge-ordered phase appears in the same region of a phase diagram, where the liquid -- ionic-crystal transition is obtained in simulations. Our results indicate that the charge-ordered phase should be identified with an ionic crystal.

cond-mat.stat-mech↗
arXiv2005

Mesoscopic theory for size- and charge- asymmetric ionic systems. I. Case of extreme asymmetry

A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $λ=σ_+/σ_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $λ\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $λ\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very dilute 'gas' phase and a crystalline phase in which the macroions form a bcc structure with the lattice constant $\approx 3.6σ_+$. Such coexistence was observed experimentally in deionized aqueous solutions of highly charged colloidal particles.

cond-mat.stat-mech↗
arXiv2004

Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall

The process of adsorption on a planar wall of long-flexible polymer chains in the medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power-low $ x^{-a}$ for large distances $x$, where ${\bf x}=({\bf r},z)$. Field theoretical approach in $d=4-ε$ and directly in $d=3$ dimensions up to one-loop order for the semi-infinite $|ϕ|^4$ m-vector model (in the limit $m\to 0$) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold $T=T_a$, which separates the nonadsorbed region from the adsorbed one is obtained. Moreover, we calculate the crossover critical exponent $Φ$ and the set of exponents associated with them. We perform calculations in a double $ε=4-d$ and $δ=4-a$ expansion and also for a fixed dimension $d=3$, up to one-loop order for different values of the correlation parameter $2<a\le 3$. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises. All the surface critical exponents depend on $a$. Hence, the presence of long-range correlated disorder influences the process of adsorption of long-flexible polymer chains on a wall in a significant way.

cond-mat.soft↗
arXiv2003

Critical adsorption of polymers in a medium with long-range correlated quenched disorder

We investigated the influence of short- and long-range correlated quenched disorder introduced into the medium on the process of adsorption of long-flexible polymer chains on a wall by using the field theoretical approach in $d=4-ε$ and the directly in d=3 dimensions up to one-loop order for the semi-infinite $|ϕ^4|$ m-vector model (in the limit $m \to 0$) with a boundary. This allows us to describe the critical behaviour of long-flexible polymer chains in the vicinity of the surface and to obtain the whole set of surface critical exponents at the special surface transition ($c=c_{ads}$), which separates the nonadsorbed region $c>c_{ads}$ from the adsorbed one $c<c_{ads}$. In the case of very strong correlation of the disorder we obtained that a polymer collapses and adsorbs on a wall. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises and show that polymer chains in solution with that type of disorder adsorb on a wall stronger than the polymer chains in pure medium.

cond-mat.dis-nn↗
arXiv2000

Effects of confinement on self-assembling systems

Systems in which particles can self-assemble into mono- or bilayers can form variety of stable and metastable structures on a nanometer length scale. For this reason confinement has a particularly strong effect on such systems. We discuss in some detail effects of confinement on lamellar and cubic phases with double-diamond structure. Structural deformations in slit geometry are described for large and small unit cells of the structure (in units of the thickness of the monolayer) and for various strengths of interactions with the confining surfaces. We show how the structural changes of the confined fluid are reflected in the measurable solvation force between the confining walls.

cond-mat.soft↗
arXiv2000

Switch of lamellae orientation in slits

Effect of hydrophilicity of the confining walls on lamellar phases in oil-water-surfactant mixtures is studied in a slit geometry. In contrast to strongly hydrophilic or hydrophobic walls, which induce parallel orientation of lamellae, the lamellae can be oriented perpendicularly to the neutral walls when the material properties and the termodynamical state of the sample are suitably chosen. When the elastic energy associated with compression or decompression of the lamellae parallel to very weakly hydrophilic walls is sufficiently large, then changes of the film thickness lead to a switch from the parallel to the perpendicular orientation of the lamellae. Our general arguments are confirmed by explicit mean-field calculations in a lattice vector model.

cond-mat.soft↗
arXiv2000

Field-Theoretic Approach to Ionic Systems: Criticality and Tricriticality

A Landau-Ginzburg functional of two order parameters (charge-density $ϕ$ and mass-density deviation $η$) is developed in order to yield a field theory relevant to ionic lattice gases as well as a family of off-lattice models of ionic fluids that go beyond the restricted primitive model (RPM). In a mean-field (MF) approximation an instability of a uniform phase with respect to charge fluctuations with a wave-number $k\ne 0$ is found. This second-order transition to a charge-ordered phase terminates at a tricritical point (tcp). Beyond MF, a singularity of a mass correlation function for $k\to 0$ occurs at ion concentration lower than that of the MF tcp. An effective functional depending only on $η$ is constructed. For low ion concentration the usual Landau form of the simple-fluid (Ising) functional is obtained; hence in this theory the critical point is in the Ising universality class.

cond-mat.stat-mech↗
arXiv1996

Critical Adsorption in Systems with Weak Surface Field: The Renormalization-Group Approach

We study the surface critical behavior of semi-infinite systems belonging to the bulk universality class of the Ising model. Special attention is paid to the local behavior of experimentally relevant quantities such as the order parameter and the correlation function in the crossover regimes between different surface universality classes, where the surface field h_1 and the temperature enhancement can induce additional macroscopic length scales. Starting from the field-theoretical phi^4 model and employing renormalization-group improved perturbation theory (epsilon expansion), explicit results for the local behavior of the correlation and structure function (0-loop) and the order parameter (1-loop) are derived. Supplementing earlier studies that focussed on the special transition, we here pay particular attention to the situation where a large c suppresses the tendency to order in the surface (ordinary transition) but a surface field $h_1$ generates a small surface magnetization m_1. Our results are in good agreement with recent phenomenological considerations and Monte Carlo studies devoted to similar questions and, combined with the latter, provide a much more detailed understanding of the local properties of systems with weak surface fields.

cond-mat↗