Transport phenomena and microscopic structure in partially miscible binary fluids: A simulation study of the symmetrical Lennard-Jones mixture

Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model

For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing fact, referred to as the Mpemba effect (ME), during ordering in ferromagnets. By performing Monte Carlo simulations of a generic model, we have obtained results on relaxation of systems that are quenched to sub-critical state points from various temperatures above the critical point. For a fixed final temperature, a system with higher starting temperature equilibrates faster than the one prepared at a lower temperature, implying the presence of ME. The observation is extremely counter-intuitive, particularly because of the fact that the model has no in-built frustration or metastability that typically is thought to provide ME. Via the calculations of nonequilibrium properties concerning structure and energy, we quantify the role of critical fluctuations behind this fundamental as well as technologically relevant observation.

Phase behavior of a binary fluid mixture of quadrupolar molecules

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Direct calculation of the critical Casimir force in a binary fluid

We show that critical Casimir effects can be accessed through direct simulation of a model binary fluid passing through the demixing transition. We work in the semi-grand-canonical ensemble, in slab geometry, in which the Casimir force appears as the excess of the generalized pressure, P_{⊥}-nμ. The excesses of the perpendicular pressure, P_{⊥}, and of nμ, are individually of much larger amplitude. A critical pressure anisotropy is observed between forces parallel and perpendicular to the confinement direction, which collapses onto a universal scaling function closely related to that of the critical Casimir force.

Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling

The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

Lattice Boltzmann method for diffusion-limited partial dissolution of fluids

A lattice Boltzmann model for two partially miscible fluids is developed. By partially miscible we mean that, although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region, each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit. We allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters. The approach is to define two regions within the fluid: one interfacial region having finite width, across which most of the concentration change occurs, and in which a surface tension force and color separation step are allowed for and one miscible fluid region where the concentration of the binary fluids follows an advection-diffusion equation and the mixture as a whole obeys the Navier-Stokes incompressible flow equations. Numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness. The model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to simulate a range of practical invasion problems such as injecting supercritical CO(2) into a porous material saturated with water for sequestration purposes.

Surface tension and density of Si-Ge melts

In this work, the surface tension and density of Si-Ge liquid alloys were determined by the pendant drop method. Over the range of measurements, both properties show a linear temperature dependence and a nonlinear concentration dependence. Indeed, the density decreases with increasing silicon content exhibiting positive deviation from ideality, while the surface tension increases and deviates negatively with respect to the ideal solution model. Taking into account the Si-Ge phase diagram, a simple lens type, the surface tension behavior of the Si-Ge liquid alloys was analyzed in the framework of the Quasi-Chemical Approximation for the Regular Solutions model. The new experimental results were compared with a few data available in the literature, obtained by the containerless method.

An analysis of fluctuations in supercooled TIP4P/2005 water

Large-scale, long-time molecular dynamics simulations are used to investigate fluctuations in the TIP4P/2005 water model in the supercooled region (240-190 K). Particular attention is focused in the vicinity of a previously reported liquid-liquid critical point [J. L. F. Abascal and C. Vega, J. Chem. Phys. 133, 234502 (2010)]. Water is viewed as an equimolar binary mixture with "species" defined based on a local tetrahedral order parameter. A Bhatia-Thornton fluctuation analysis is used to show that species concentration fluctuations couple to density fluctuations and completely account for the anomalous increase in the structure factor at small wave number observed under supercooled conditions. Although we find that both concentration and density fluctuations increase with decreasing temperature along the proposed critical isochore, we cannot confirm the existence of a liquid-liquid critical point. Our simulations suggest that the parameters previously reported are not a true liquid-liquid critical point and we find no evidence of two-phase coexistence in its vicinity. It is shown that very long simulations (on the order of 8 μs for 500 molecules) are necessary to obtain well converged density distributions for deeply supercooled water and this is especially important if one is seeking direct evidence of a two-phase region.

Phase separation in antisymmetric films: a molecular dynamics study

We have used molecular dynamics (MD) simulations to study phase-separation kinetics in a binary fluid mixture (AB) confined in an antisymmetric thin film. One surface of the film (located at z = 0) attracts the A-atoms, and the other surface (located at z = D) attracts the B-atoms. We study the kinetic processes which lead to the formation of equilibrium morphologies subsequent to a deep quench below the miscibility gap. In the initial stages, one observes the formation of a layered structure, consisting of an A-rich layer followed by a B-rich layer at z = 0; and an analogous structure at z = D. This multi-layered morphology is time-dependent and propagates into the bulk, though it may break up into a laterally inhomogeneous structure at a later stage. We characterize the evolution morphologies via laterally averaged order parameter profiles; the growth laws for wetting-layer kinetics and layer-wise length scales; and the scaling properties of layer-wise correlation functions.

Surface-directed spinodal decomposition: a molecular dynamics study

We use molecular dynamics simulations to study surface-directed spinodal decomposition in unstable binary AB fluid mixtures at wetting surfaces. The thickness of the wetting layer R1 grows with time t as a power law (R1∼tθ). We find that hydrodynamic effects result in a crossover of the growth exponent from θ≃1/3 to 1. We also present results for the layerwise correlation functions and domain length scales.

Analysis of the static properties of cluster formations in symmetric linear multiblock copolymers

We use molecular dynamics simulations to study the static properties of a single linear multiblock copolymer chain under poor solvent conditions varying the block length N, the number of blocks n, and the solvent quality by variation of the temperature T. We study the most symmetrical case, where the number of blocks of monomers of type A, n(A), equals that of monomers B, n(B) (n(A) = n(B) = n/2), the length of all blocks is the same irrespective of their type, and the potential parameters are also chosen symmetrically, as for a standard Lennard-Jones fluid. Under poor solvent conditions the chains collapse and blocks with monomers of the same type form clusters, which are phase separated from the clusters with monomers of the other type. We study the dependence of the size of the clusters formed on n, N and T. Furthermore, we discuss our results with respect to recent simulation data on the phase behaviour of such macromolecules, providing a complete picture for the cluster formations in single multiblock copolymer chains under poor solvent conditions.

Analysis of the cluster formation in two-component cylindrical bottle-brush polymers under poor solvent conditions: a simulation study

Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations, varying the grafting density [Formula: see text] and the solvent quality. Whereas for poor solvents and large enough [Formula: see text] the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of the cylinder, for intermediate values of [Formula: see text] an axially inhomogeneous structure of "pearl-necklace" type is formed, where microphase separation between monomers of different type within a cluster takes place. These "pearls" have a strongly non-spherical ellipsoidal shape, due to the fact that several side chains cluster together in one "pearl". We discuss the resulting structures in detail and we present a comparison with the single-component bottle-brush case.

A combined molecular dynamics and Monte Carlo study of the approach towards phase separation in colloid-polymer mixtures

A coarse-grained model for colloid-polymer mixtures is investigated where both colloids and polymer coils are represented as point-like particles interacting with spherically symmetric effective potentials. Colloid-colloid and colloid-polymer interactions are described by Weeks-Chandler-Andersen potentials, while the polymer-polymer interaction is very soft, of strength k(B)T/2 for maximum polymer-polymer overlap. This model can be efficiently simulated both by Monte Carlo and molecular dynamics methods, and its phase diagram closely resembles that of the well-known Asakura-Oosawa model. The static and dynamic properties of the model are presented for systems at critical colloid density, varying the polymer density in the one-phase region. Applying Lees-Edwards boundary conditions, colloid-polymer mixtures exposed to shear deformation are considered, and the resulting anisotropy of correlations is studied. Whereas for the considered shear rate, [Formula: see text], radial distribution functions and static structure factors indicate only small structural changes under shear, an appropriate projection of these correlation functions onto spherical harmonics is presented that allows us to directly quantify the structural anisotropies. However, the considered shear rate is probably not high enough to see anisotropies in static structure factors at small wavenumbers that have been predicted by Onuki and Kawasaki (1979 Ann. Phys. 121 456) for the critical behavior of systems under shear. The anomalous dependence of the polymer's self-diffusion constant on polymer density is referred to the clustering of the colloid particles when approaching the critical point.

Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

Critical dynamics in a binary fluid: simulations and finite-size scaling

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories provided finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.

Bridge functions near the liquid-vapor coexistence curve in binary Lennard-Jones mixtures

We have carried out extensive molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194-197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

Spinodal decomposition in thin films: molecular-dynamics simulations of a binary Lennard-Jones fluid mixture

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width D. The pore walls are assumed to be flat and structureless and attract one component of the mixture (A) with the same strength. The pairwise interactions between the particles are modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S. K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E 72, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly two-dimensional geometry is also discussed.

Molecular dynamics study of phase separation kinetics in thin films

We use molecular dynamics to simulate experiments where a symmetric binary fluid mixture (AB), confined between walls that preferentially attract one component (A), is quenched from the one-phase region into the miscibility gap. Surface enrichment occurs during the early stages, yielding a B-rich mixture in the film center with well-defined A-rich droplets. The droplet size grows with time as l(t) proportional t(2/3) after a transient regime. The present atomistic model is also compared to mesoscopic coarse-grained models for this problem.

Kinetics of phase separation in thin films: simulations for the diffusive case

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (i) both walls preferentially attract the same component (A), and (ii) one wall attracts and the other wall attracts (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as surface-directed spinodal decomposition (SDSD). The formation of SDSD waves at the two surfaces, with wave vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as "stratified morphology"). This state is reminiscent of the situation where the thin film is still in the one-phase region but the surfaces are completely wet, and hence coated with thick wetting layers. This metastable state decays by spinodal fluctuations and crosses over to an asymptotic growth regime characterized by the lateral coarsening of pancakelike domains. These pancakes may or may not be coated by precursors of wetting layers. We use Langevin simulations to study this crossover and the growth kinetics in the asymptotic coarsening regime.

Direct measurement of relative and collective diffusion in a dilute binary colloidal suspension

Experimental characterization of the dynamics of multicomponent fluids is a problem of general importance to the field of complex fluids. We demonstrate a new experimental approach, termed two-color Fourier imaging correlation spectroscopy, which allows direct measurement of the partial dynamic structure factors, S(11)(k,tau), S(22)(k,tau), and S(12)(k,tau), where 1, 2 label the component species of a binary colloidal suspension. Linear combinations of the partial dynamic structure factors yield the characteristic time-correlation functions of the binary fluid. These are the correlation functions of concentration fluctuations S(CC)(k,tau), number density fluctuations S(NN)(k,tau), and cross-correlations between number density and concentration fluctuations S(NC)(k,tau). Test measurements are performed on a dilute symmetric mixture of fluorescently labeled 0.5 and 1.0 microm polystyrene spheres. From these data, we determine generalized collective and relative diffusion coefficients, and compare them to the predictions for an ideal mixture of noninteracting particles.

Critical phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility, and coexistence diameter

The critical behavior of a model colloid-polymer mixture, the so-called Asakura-Oosawa (AO) model, is studied using computer simulations and finite size scaling techniques. Investigated are the interfacial tension, the order parameter, the susceptibility, and the coexistence diameter. Our results clearly show that the interfacial tension vanishes at the critical point with exponent 2nu approximately 1.26 . This is in good agreement with the 3D Ising exponent. Also calculated are critical amplitude ratios, which are shown to be compatible with the corresponding 3D Ising values. We additionally identify a number of subtleties that are encountered when finite size scaling is applied to the AO model. In particular, we find that close to the critical point, the finite size extrapolation of the interfacial tension is most consistent when logarithmic size dependences are ignored.

Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces

The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation C(k)<=>mu(k) between the concentrations C(k) and the chemical potentials mu(k) of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation C(k)<=>mu(k) implies in fact two problems: a direct problem C(k)=>mu(k) and an inverse problem mu(k)=>C(k). Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 A thick gypsum interface. The major unexpected observation is the repulsion of SO(4) (2-) ions towards the reference solution and the attraction of Ca(2+) ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.

Structure and diffusion in amorphous aluminum silicate: A molecular dynamics computer simulation

The amorphous aluminum silicate (Al2O3)2(SiO2) [AS2] is investigated by means of large scale molecular dynamics computer simulations. We consider fully equilibrated melts in the temperature range 6100 K> or =T> or =2300 K as well as glass configurations that were obtained from cooling runs from T=2300 to 300 K with a cooling rate of about 10(12) K/s. Already at temperatures as high as 4000 K, most of the Al and Si atoms are fourfold coordinated by oxygen atoms. Thus, the structure of AS2 is that of a disordered tetrahedral network. The packing of AlO4 tetrahedra is very different from that of SiO4 tetrahedra in that Al is involved with a relatively high probability in small-membered rings and in triclusters in which an O atom is surrounded by four cations. We find as typical configurations two-membered rings with two Al atoms in which the shared O atoms form a tricluster. On larger length scales, the system shows a microphase separation in which the Al-rich network structure percolates through the SiO2 network. The latter structure gives rise to a prepeak in the static structure factor at a wave number q=0.5 A(-1). A comparison of experimental x-ray data with the results from the simulation shows good agreement for the structure function. The diffusion dynamics in AS2 is found to be much faster than in SiO2. We show that the self-diffusion constants for O and Al are very similar and that they are by a factor of 2-3 larger than the one for Si.