Two-dimensional Mixture Research Articles

Phase separation in three-component lipid membranes: From Monte Carlo simulations to Ginzburg-Landau equations

Preferential affinity of cholesterol for saturated rather than unsaturated lipids underlies the thermodynamic process of the formation of lipid nanostructures in cell membranes, that is, of rafts. In this context, phase segregation of two-dimensional ternary lipid mixtures is formally studied from two different perspectives. The simplest approach is based on Monte Carlo simulations of an Ising model corresponding to two interconnected lattices, from which the basic features of the phenomenon are investigated. Then, the coarse-graining mean field procedure of the discrete Hamiltonian is adapted and a Ginzburg-Landau-like free energy expression is obtained. From this latter description, we construct kinetic equations that enable us to perform numerical simulations and to establish analytical phase separation criteria. Application of our formalism in the biological context is also discussed.

Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory

We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus–Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.

Exotic superconducting phases of ultracold atom mixtures on triangular lattices

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in the work of Mathey et al. [Phys. Rev. Lett. 97, 030601 (2006)]. Using functional renormalization-group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of s-, p-, extended d-, and f-wave symmetries, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between p- and f-wave symmetries. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.

Heterogeneous dynamics in polycrystal and glass in a binary mixture with changing size dispersity and composition

Using molecular dynamics simulation we investigate the dynamics in a two-dimensional binary mixture at a low temperature and at high densities. We increase the size ratio of the diameters of the two components or the fraction of the larger particles. Then changeovers occur from polycrystal to glass with proliferation of defects. The relationship between the degree of disorder and the slow dynamics is studied by simultaneous visualization of a disorder variable D{j} introduced in our previous paper T. Hamanaka and A. Onuki[Phys. Rev. E 74, 011506 (2006)] and the particle displacement Deltar{j} in a long time interval. In polycrystal, the particles in the grain boundary regions have large D{j} and a relatively large mobility, producing significant dynamic heterogeneity on long time scales. In the crossover from polycrystal to glass, the crystalline regions become narrow, but the particles with relatively large D{j} still trigger the formation of chainlike particle motions, leading to the dynamic heterogeneity.

Computational fluid dynamics (CFD) simulation of flow in the rotary drum for pyrite bio-preoxidization

A two-dimensional algebric slip mixture (ASM) CFD model was developed to simulate the flow and mixing of liquid–gas-particle system in a rotary drum. The simulations show that there are several flow regimes in slurry phase, including anti-clockwise circulation flow of liquid, rising stream of bubbles, circumferential flow and eddy. The gas disperses mainly in a limited area in the vertical region of bubble stream. Pyrite particle mixing is mainly arised from the movement of baffles, and the distribution of particles is well. The increase of aeration rates would give rise to an increase of the volumetric averaged gas holdup. The increase of rotation speed has little influence in the averaged gas holdup. When three gas spargers were molded in the drum, there is not obvious improvement of gas holdup and particle mixing.

Scale effect and geometric shapes of grains

The rule-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline (NC) materials are treated as three-phase composites consisting of grain core phase, grain boundary (GB) phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect of mechanical properties of NC materials due to the geometrical polyhedron characteristics of crystal grain. For different multi-sided geometrical shapes of grains, the corresponding regular polygon model is adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.

Phase behavior of lipid mixtures

Biological membranes are two-dimensional mixtures of an enormous number of different components. Modeling cell membranes as simple bilayer mixtures reveals rich phase behavior, but how can we use the observed phase behavior to understand the real membranes?

Microphase structuring in two-dimensional magnetic colloid mixtures

Suspensions of super-paramagnetic colloids trapped in the water–air interface arean excellent model system for the study of two-dimensional systems. Here, weinvestigate the structural behaviour of two-component mixtures of such particles. Theinterparticle interactions are tunable through the application of a magnetic fieldperpendicular to the air–water surface. Further, they can be influenced by thechoice of the relative magnetic susceptibilities of the two colloidal species. We haveperformed integral equation theory and computer simulations to study the staticproperties of such a binary super-paramagnetic system. For all susceptibility ratiosstudied, no macroscopic phase separation takes place; the fluid phase remainsmacroscopically homogeneous but microphase structuring occurs: the interactionswith the large particles lead to a clustering of the smaller particles. We combinestructural information in reciprocal space together with morphological measures inreal space to characterize the ordering of the two species in the binary mixture.

A method to simultaneously image two-dimensional mixture fraction, scalar dissipation rate, temperature and fuel consumption rate fields in a turbulent non-premixed jet flame

A new imaging technique was developed that provides two-dimensional images of the mixture fraction (ξ), scalar dissipation rate (χ), temperature (T), and fuel consumption rate \((\dot{\omega}_{\rm F})\) in a turbulent non-premixed jet flame. The new method is based on “seeding” nitric oxide (NO) into a particular carbon monoxide–air flame in which it remains passive. It is first demonstrated that the mass fraction of NO is a conserved scalar in the present carbon monoxide–air flame configuration, using both laminar flame calibration experiments and computations with full chemistry. Simultaneous planar laser-induced fluorescence (PLIF) and planar Rayleigh scattering temperature imaging allow a quantitative determination of the local NO mass fraction and hence mixture fraction in the turbulent jet flame. The instantaneous mixture fraction fields in conjunction with the local temperature fields are then used to determine quantitative scalar dissipation rate fields. Advantages of the present technique include an improved signal-to-noise ratio over previous Raman scattering techniques, improved accuracy near the stoichiometric contour because simplifying chemistry assumptions are not required, and the ability to measure ξ and χ in flames experiencing localized extinction. However, the method of measuring ξ based on the passive NO is restricted to dry carbon monoxide–air flames due to the well-controlled flame chemistry. Sample imaging results for ξ, χ, T, and \(\dot{\omega}_{\rm F}\) are presented that show high levels of signal-to-noise while resolving the smallest mixing scales of the turbulent flowfield. The application, accuracy, and limitations of the present technique are discussed.

Competing Types of Order in Two-Dimensional Bose-Fermi Mixtures

Using a functional renormalization group approach we study the zero temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms in optical lattices, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. For spin-1/2 fermions we obtain a phase diagram, which shows a competition of pairing phases of various orbital symmetry (s, p, and d) and antiferromagnetic order. We determine the value of the gaps of various phases close to half filling, and identify subdominant orders as well as short-range fluctuations from the renormalization group flow. For spinless fermions we find that p-wave pairing dominates the phase diagram.

Coexistence diameter in two-dimensional colloid-polymer mixtures

We demonstrate that the law of the rectilinear coexistence diameter in two-dimensional mixtures of nonspherical colloids and nonadsorbing polymers is violated. Upon approach to the critical point, the diameter shows logarithmic singular behavior governed by a term t ln t, with t the relative distance from the critical point. No sign of a term t2beta could be detected, with beta the critical exponent of the order parameter, indicating a very weak or absent Yang-Yang anomaly. Our analysis thus reveals that nonspherical particle shape alone is not sufficient for the formation of a pronounced Yang-Yang anomaly in the critical behavior of fluids.

Correlations in charged fermion–boson mixture in dimensionalities [formula omitted] and [formula omitted

We numerically study the correlation effects in a two-component charged fermion–boson mixture at zero temperature investigating the role played by the statistical effects and Coulomb correlations in a model with different fermion and boson mass ratios in two and three dimensions. The local-field factors describing the correlation effects and collective excitation modes are determined through the self-consistent scheme. We find that the effects of correlations and statistics are more pronounced in two-dimensional mixtures.

Modulation of superconductivity by a magnetic template inNb∕BaFe12O19hybrids

Inhomogeneous magnetic fields generated by the ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$ ferromagnetic substrate create a magnetic template for superconducting condensate in the $\mathrm{Nb}∕{\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$ hybrids. Depending on the field and temperature, the magnetic template guides superconductivity to nucleate in different areas: above the magnetic domain walls of the ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$ forming the domain-wall superconductivity (DWS), above the reversed magnetic domains (RDS), and above the positive magnetic domains forming bulk superconductivity. The DWS, behaving as a superconducting wire network, survives in a broad field range. The RDS, existing in the form of isolated superconducting islands near the saturation field ${H}_{s}$ of ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$, can be described as a two-dimensional two-component random conductor mixture. Being related to the hysteretic domain evolution, superconducting condensate above the reversed domains shows pronounced switching behavior.

Tracer diffusion and cluster formation in mixtures of spheres and rotating rods

On the basis of Brownian dynamics computer simulation studies, we investigate thestructure and dynamics of two-dimensional mixtures of rods driven by an external torqueand spheres. First, we show that the tracer long-time diffusion of spheres in a system ofrotating rods can be efficiently tuned via the rod density. It behaves non-monotonically forincreasing rod density. In particular, the sphere diffusion becomes strongly enhanced acrossthe jamming transition of the rods. Second, we show that rotating rods in a densesuspension of spheres form aggregates of rod clusters which are rotating jointly. Thecluster size is in reasonable agreement with the predictions of a simple theory.

Experimental realization of a model glass former in 2D

We have studied binary two-dimensional (2D) mixtures of superparamagnetic colloidal particles interacting through magnetic dipole moments, which were induced by an external magnetic field B. By tuning B the effective system temperature could be widely adjusted. Time-dependent particle coordinates measured by video-microscopy provide radial pair-distribution functions, mean-square displacements as well as evidence for heterogeneous dynamics. Characteristic features of 3D glass formers are observed experimentally in 2D for the first time.

Demixing behavior in two-dimensional mixtures of anisotropic hard bodies

Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the isotropic phase, it is shown that isotropic-nematic demixing is possible in two-dimensional liquid-crystal mixtures composed of hard convex bodies. This bifurcation analysis is tested against exact calculations of the phase diagrams in the framework of the restricted-orientation two-dimensional model (Zwanzig model). Phase diagrams of a binary mixture of hard discorectangles are calculated through the parametrization of the orientational distribution functions. The results show not only isotropic-nematic, but also nematic-nematic demixing ending in a critical point, as well as an isotropic-nematic-nematic triple point for a mixture of hard disks and hard discorectangles.

Helium surface electron attachment to atomic hydrogen in applied magnetic field

We measured reaction rates of electron attachment to atomic hydrogen on liquid helium surface at 0.3 K in applied magnetic fields up to 11 T. The lifetime of electron-hydrogen gas in two-dimensional mixture becomes longer as the magnetic field is increased. It is found that the reaction rate coefficient behaves like ∼ B −2 and its value above 5 T is eight orders of magnitude smaller than the zero field value. We interpret our result that only electron spin singlet collisions produce negative hydrogen H −. It is consistent with the fact that the two bound electrons of H − are spin antiparallel.

Spin-polarization effect on electron attachment to atomic hydrogen on liquid helium surface

Reaction rates of electron attachment to atomic hydrogen are measured as a function of magnetic field. The reaction takes place in a two-dimensional mixture of hydrogen atoms and electrons on liquid helium surface. Surface electron density, measured by using vibrating capacitor electrometer technique, decreases when H atoms are introduced. Applied high magnetic field suppresses electron attachment, H + e− → H−, as well as hydrogen recombination, H + H → H2. Since the electronic state of negative hydrogen, H−, is spin singlet, electron attachment is suppressed by spin-polarization. Possible microscopic mechanisms to explain the measured magnetic field dependence of the reaction kinetics are discussed.

Quasicrystalline order in binary dipolar systems

Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar interaction potential does not exhibit an intrinsic length scale and cannot be tuned a priori to support the formation of quasicrystalline order, we find that configurations with long--range quasicrystallinity yield minima in the potential energy surface of the many particle system. These configurations emanate from an ideal or perturbed ideal decoration of a binary tiling by steepest descent relaxation. Ground state energy calculations of alternative ordered states and parallel tempering Monte-Carlo simulations reveal that the quasicrystalline configurations do not correspond to a thermodynamically stable state. On the other hand, steepest descent relaxations and conventional Monte-Carlo simulations suggest that they are rather robust against fluctuations. Local quasicrystalline order in the disordered equilibrium states can be strong.

Instability of a fluid–fluid interface in driven colloidal mixtures

A Rayleigh–Taylor-like interface instability is studied in a compressible Brownian Yukawafluid mixture on the ‘molecular’ scales of length and time of the individual particles. As amodel, a two-dimensional phase-separated symmetric binary mixture of colloidal particlesof type A and B with a fluid–fluid interface separating an A-rich phase from a B-rich phaseis investigated, by means of Brownian computer simulations, when brought intonon-equilibrium via a constant external driving field which acts differently on the differentparticles and perpendicular to the interface. Two different scenarios are observed whichoccur either for high or for low interfacial free energies as compared to the drivingforce. In the first scenario for high interfacial tension, the critical wavelengthλc of the unstable interface modes is in good agreement with the classical Rayleigh–Taylor formulaprovided that dynamically rescaled values for the interfacial tension are used. The wavelengthλc increases with time, representing an effect of self-healing of the interface due to a localdensity increase near the interface. The Rayleigh–Taylor formula is confirmed even ifλc is of the order of a molecular correlation length. In the second scenario for very largedriving forces as compared to the interfacial line tensions, on the other hand, the particlespenetrate the interface easily due to the driving field and form microscopic lanes with awidth different from the predictions of the classical Rayleigh–Taylor formula. The resultsare of relevance for phase-separating colloidal mixtures in a gravitational or electric field.