Two-dimensional Mixture Research Articles

Supercooling in a two-dimensional Lennard-Jones mixture

A mixture of large and small Lennard-Jones particles is studied; in the study we focus on the relations among temperature, packing, structure, and transport in the supercooled state. As the temperature decreases, one sees increasing component separation, and local ordering. Clusters consisting of only small particles grow in size with time and cooling; the dominant local structure in those clusters is hexagonal. The rest of the system, including almost all large and some small particles, remains amorphous, with local order dictated by the geometry of dense packing of mixed large and small particles. To study these effects independently, we modified the conventional model by managing the relaxation of large particles. At low temperatures, the diffusion of small particles dramatically decreases when the large particles are frozen. An interpretation of these findings based on the local rearrangement kinetics is proposed.

Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow

We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier–Stokes and convection–diffusion equations. We propose a new scheme for imposing the shear flow which has the advantage of preserving mass and momentum conservation on the boundary walls without introducing slip velocities. We study how the steady velocity profile is reached. Our main results show the presence of two typical length scales in the phase separation process, corresponding to domains with two different thicknesses.

Two-Dimensional Mixtures of Stearic Acid and Partially Fluorinated Amphiphilic Molecule: A Grazing Incidence X-ray Diffraction Study

We report a grazing incidence X-ray diffraction (GIXD) study of mixed Langmuir monolayers of stearic acid (ST) and a fluorinated amphiphilic molecule (FEP). The mixing behavior of the two components was investigated at two different surface pressures, 5 and 30 mN/m. The ST molecules are found to be in the L2 mesophase at 5 mN/m and in the LS mesophase at 30 mN/m, whereas the FEP molecules appear disordered. In the mixture, the GIXD measurements, associated with previous thermodynamical and optical microscopy results, show that in the whole range of molar ratio, the two molecules are completely phase-separated. Also, we observed at 5 mN/m, relaxation in the pure ST monolayer and in the mixtures rich in ST; the tilt angle of the molecules and the rectangular distortion of the 2D-lattice decrease. By comparing mixed films and pure ST films, this relaxation could be correlated to the size of the domains.

Lipid Demixing and Protein-Protein Interactions in the Adsorption of Charged Proteins on Mixed Membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is “saturated” by adsorbed proteins), the membrane charges are “overcompensated” by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.

Chemical reaction between hydrogen atoms and electrons on the surface of superfluid 4He

Two-dimensional mixture of atomic hydrogen and electrons on the surface of superfluid 4He was realized below 0.5 K. Vibrating capacitor electrometer was employed to show that after the electron capture reaction, H+e −→H −, the product, H −, might penetrate into the bulk liquid.

Effective permittivity of mixtures: numerical validation by the FDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction.

Spinodal decomposition of two-dimensional fluid mixtures: A spectral analysis of droplet growth

The spinodal decomposition of two-dimensional fluid mixture is studied by numerical simulation. For the high viscous fluid mixture it has not been evident whether the interfacial tension is relevant to the droplet growth or not. A length scale R defined by the structure function extracting the effect of the long wavelength mode justifies a rapid growth close to R approximately t, but the length scale energetically defined reveals a much slower growth R approximately t(0.5), where t is time. This discrepancy represents the violation of the dynamical scaling with single length scale. The slow gowth of the length scale is attributed to the accumulation of the number of isolated droplets in phase separating state, whereas the rapid growth represents the relevance of the surface tension as the driving force in two dimensions. For a low viscous fluid mixture the dynamical scaling is a good assumption with the growth law R approximately t(2/3) up to a very large Reynolds number Re approximately 1500, which is the limit in the present simulation.

Chemical reaction of surface state electrons on liquid helium with atomic hydrogen

Chemical reaction in a two-dimensional mixture of electrons and atomic hydrogen (H) on the surface of superfluid 4He was observed. By monitoring the conductivity of surface state electrons with Corbino electrode, small amount of H atoms were introduced. Hydrogen destroyed the conductivity signal and we believe it is because of electron capture reaction, H+e −→H −. The reaction rates increased as the temperature decreased and it saturated below 200 mK. This temperature dependence agrees with our analysis which assumes that the chemical process takes place only in the surface state.

Relaxation dynamics and their spatial distribution in a two-dimensional glass-forming mixture

Molecular dynamics simulations are used to explore the spatial fluctuations associated with structural relaxation and particle transport in a supercooled binary mixture in two dimensions. The study includes (i) the characterization of heterogeneities in the local particle dynamics in terms of their length scale and lifetime, (ii) the relationship between local kinetics and local structure/composition, and (iii) preliminary identification of the principal collective motions involved in the long-time relaxation of the supercooled liquid.

Effect of ordering on spinodal decomposition of liquid-crystal/polymer mixtures.

Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering and phase-separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.

Stability and structure of a supercooled liquid mixture in two dimensions.

The structural and thermodynamic properties of a two-dimensional binary mixture of soft discs are reported over a range of temperatures down to large supercoolings using constant NPT molecular dynamics simulations. It is shown that the four orders of magnitude increase in the structural relaxation time is not accompanied by any significant increase in translational or orientational order. The phase diagram, calculated in the temperature/composition plane using thermodynamic integration, exhibits a deep eutectic point that is responsible for stabilizing the amorphous state. Voronoi analysis of the low-temperature ground state reveals a structure characterized by a network of linear arrays of fivefold and sevenfold sites. The heat capacity C(P) exhibits an asymmetric peak with a maximum at T(*)=0.55. It is argued that the initial rapid drop in C(P) for T*<0.55 is an equilibrium result and, hence, the peak in the heat capacity corresponds to the existence of an "enthalpy gap" with a characteristic temperature of T* approximately 0.35. This gap results from a minimum volume change associated with an anharmonic fluctuation.

Phase separation in two-dimensional additive mixtures

We study two-dimensional binary mixtures of parallel hard squares as well as of disks. A recent cluster algorithm allows us to establish an entropic demixing transition between a homogeneously packed fluid phase and a demixed phase of a practically close-packed aggregate of large squares surrounded by a fluid of small squares.

Molecular dynamics study of a phase-separating fluid mixture under shear flow

Molecular dynamics simulation is carried out to study domain structures and rheological properties of a two-dimensional phase-separating binary fluid mixture under shear flow. In the early stage of the phase separation, anisotropic composition fluctuations appear immediately after the quench. As the domain grows, the anisotropy in the composition fluctuations increases. The quenched system eventually reaches a dynamical steady state, in which anisotropic domain structures are preserved. In the steady state, the shortest characteristic length scale ${R}_{\ensuremath{\perp}}$ of domains decreases with increasing shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ as ${R}_{\ensuremath{\perp}}\ensuremath{\sim}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}^{\ensuremath{-}1/3}.$ Stringlike domain structures are observed in the strong shear regime, whereas randomly fluctuating patterns are observed in the weak shear regime. Moreover, the excess viscosity $\ensuremath{\Delta}\ensuremath{\eta}$ is found to decrease with increasing shear rate as $\ensuremath{\Delta}\ensuremath{\eta}\ensuremath{\sim}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}^{\ensuremath{-}1/2},$ indicating that the phase-separating fluid mixtures are highly non-Newtonian because of domain deformations.

Critical behaviour of two-dimensional Lennard-Jones fluid mixtures: a mean field study

The critical behaviour of two-dimensional Lennard-Jones fluid binary mixtures is investigated by using thermodynamic perturbation theory. Preliminary results show that the critical curves for the two-dimensional mixtures exhibit the same behaviour as that found in the corresponding three-dimensional fluid binary mixtures, with similar shortcomings as those found in mean field theories.

3D-2D asymptotic analysis of an optimal design problem for thin films

Abstract The Gamma-limit of a rescaled version of an optimal material distribution problem for a cylindrical two-phase elastic mixture in a thin three-dimensional domain is explicitly computed. Its limit is a two-dimensional optimal design problem on the cross-section of the thin domain; it involves optimal energy bounds on two-dimensional mixtures of a related two-phase bulk material. Thus, it is shown in essence that 3D-2D asymptotics and optimal design commute from a variational standpoint.

Spatially heterogeneous dynamics in a two-dimensional glass-forming binary mixture

A quantitative analysis is presented of the increasing degree of dynamical correlations with decreasing temperature in a fragile glass-former consisting of a two-dimensional binary mixture of soft discs with a diameter ratio of . The analysis involves a study of the spatial distribution of local relaxation times, defined as the time taken for each particle to first travel a distance r from its initial position. For the binary mixture, a temperature-independent optimum value of is found to maximize the spatial segregation of particles into different kinetic domains. The regions of `fast' and `slow' particles grow in size as the system is cooled, indicating an increasing degree of cooperativity in the particle dynamics. A measure of the linear dimensions of these clusters is provided. It is shown that only `slow' subsets of particles are caged on intermediate timescales and that the lifetime of these slow domains increases dramatically with decreasing temperature in the supercooled mixture. A substantial decay in the incoherent scattering functions can still be accomplished, however, on these timescales, despite the relative immobility of a significant fraction of the system. A further observation is a change in the manner in which relaxation progresses throughout the system with cooling. At high temperatures the initially fast relaxing sites are randomly distributed throughout the system, whereas at low temperatures they tend to be clumped together. This subsequently results in a less homogeneous progression of relaxation at the lower temperatures, since relaxation proceeds primarily by radiating outwards from existing fast centres.

Spontaneous Double Phase Separation Induced by Rapid Hydrodynamic Coarsening in Two-Dimensional Fluid Mixtures

We demonstrate by numerical simulations that spinodal decomposition of fluid mixtures is strongly dependent upon their ``fluidity,'' which characterizes the relative importance of the two relevant transport mechanisms, hydrodynamic flow and diffusion. Thus, it may not be ``universal,'' at least in two dimensions. For a high fluidity, we find ``spontaneous double phase separation.'' We confirm that this unusual phenomenon is caused by the following mechanism: High fluidity causes rapid geometrical coarsening of domains due to a hydrodynamic process, which is too fast for diffusion to follow. This brings the system out of equilibrium and induces secondary phase separation.

Surface Equation of State for Insoluble Surfactant Monolayers at the Air/Water Interface

A surface equation of state is derived and used to interpret the liquid-expanded (LE)−liquid-condensed (LC) phase transition. The monolayer is treated as a two-dimensional mixture consisting of LC domains, disordered molecules in the LE state, and free sites. The free sites are assumed to have two-dimensional size only and to be located at the internal surface between the headgroups and the tails of the surfactant. They are introduced to account for the translational freedom of the domains and of the disordered molecules on the surface. The model can explain the nonhorizontal LE/LC phase transition and its dependence on temperature. In addition, the equilibrium radius and equilibrium area fraction of the domains are calculated as a function of the average molecular surface area (A). In the absence of domains, the surface equation of state reduces to a modified two-dimensional van der Waals equation. The dependence of the surface cohesion pressure on the molecular surface area A is calculated by including three contributions: the dipole−dipole interactions, the chain van der Waals interactions, and the chain conformation. The theoretical model is compared with the experimental π−A isotherms for six phospholipid surfactants, and good agreement is obtained.

Ground-State Properties of Two-Dimensional 3He-4He Mixtures: Energetics and Structures

Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain (HNC) and Fermi hypernetted chain (FHNC) scheme with contribution from elementary diagrams, we analyze ground-state energies and structural properties of two-dimensional3He-4He mixtures. The mixtures are in equilibrium at lower density compared to a pure4He system because of the large zero-point energy and statistical correlations due to the fermionic nature of3He. We evaluate the lowering of ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the results with boson3He-4He mixtures, we evaluate the energy shifts coming from the statistics and analyze the enthalpy to study the miscibility and mobility of each component of the mixture.

Kinetic Heterogeneities in a Highly Supercooled Liquid

We study a highly supercooled two-dimensional fluid mixture via molecular dynamics simulation. We follow bond breakage events among particle pairs, which occur on the scale of the $\alpha$ relaxation time $\tau_{\alpha}$. Large scale heterogeneities analogous to the critical fluctuations in Ising systems are found in the spatial distribution of bonds which are broken in a time interval with a width of order $0.05\tau_{\alpha}$. The structure factor of the broken bond density is well approximated by the Ornstein-Zernike form. The correlation length is of order $100 \sigma_1$ at the lowest temperature studied, $\sigma_1$ being the particle size. The weakly bonded regions thus identified evolve in time with strong spatial correlations.