Mixture Of Soft Spheres Research Articles

Segregation of penetrable soft spheres under gravity: Mean-field approach

We study the segregation of the additive and non-additive soft-sphere mixtures, which have the purely repulsive interactions, on the relative range of temperature, the cross-interaction between unlike species, the buoyant mass, and the layer numbers. The results show that the most segregation is found at m2/m1=1 and a low temperature, where mi is the mass of species i. The crossover point corresponding to the mixing phase is shifted toward a large mass ratio with increasing the temperature. For the non-additive soft sphere mixture, the crossover point is shifted toward a small mass ratio with increasing the cross-interaction between unlike species. The increase of gravitational strength drives the larger particles sinking to the bottom. The pressure at height z has been calculated from the force balance on a slab of fluids adjacent to the wall. The pressure at the bottom decreases with decreasing the temperature, whereas the pressure at a high altitude increases because of the large particles at the top. For the mixing phase, the large pressure discontinuity is found at z=σ1 because of the density difference between two particles. Through this work, we show that the center of mass of the species, <zi>, is a proper factor for studying the particle segregation.

Non-equilibrium dynamics of glass-forming liquid mixtures

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in glass-forming liquids [P. Ramírez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010)] is extended here to multi-component systems. The resulting theory describes the statistical properties of the instantaneous local particle concentration profiles nα(r, t) of species α in terms of the coupled time-evolution equations for the mean value n̄α(r, t) and for the covariance σ(αβ)(r, r'; t) ≡ δn(α)(r, t)δn(β)(r', t) of the fluctuations δn(α)(r, t) = n(α)(r, t) - n̄α(r, t). As in the monocomponent case, these two coarse-grained equations involve a local mobility function bα(r, t) for each species, written in terms of the memory function of the two-time correlation function C(αβ)(r, r'; t, t') ≡ δn(α)(r, t)δn(β)(r', t'). If the system is constrained to remain spatially uniform and subjected to a non-equilibrium preparation protocol described by a given temperature and composition change program T(t) and n̄α(r, t), these equations predict the irreversible structural relaxation of the partial static structure factors Sαβ(k; t) and of the (collective and self) intermediate scattering functions Fαβ(k, τ; t) and F(αβ)(S)(k, τ; t). We illustrate the applicability of the resulting theory with two examples involving simple model mixtures subjected to an instantaneous temperature quench: an electroneutral binary mixture of equally sized and oppositely charged hard-spheres, and a binary mixture of soft-spheres of moderate size-asymmetry.

Nonlinear active micro-rheology in a glass-forming soft-sphere mixture

We present extensive molecular dynamics computer simulations of a glass-forming Yukawa mixture, investigating the nonlinear response of a single particle that is pulled through the system by a constant force. Structural changes around the pulled particle are analyzed by pair correlation functions, measured in the deeply supercooled state of the system. A regime of intermediate force strengths is found where the structural changes around the pulled particle are small, although its steady-state velocity shows a strong nonlinear response. This nonlinear response regime is characterized by a force-temperature superposition principle of a Peclet number and anisotropic diffusive behavior. In the direction parallel to the force, mean-square displacements show anomalous superdiffusion in the long time limit. We analyze this superdiffusive behavior by means of the van Hove correlation function of the pulled particle. Perpendicular to the force, the driven particle shows diffusive behavior for all considered force strengths and temperatures. We discuss the dynamics perpendicular and parallel to the force in terms of effective temperatures.

Replica theory of the rigidity of structural glasses

We present a first principle scheme to compute the rigidity, i.e., the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the replica method which enables disentanglement of thermal fluctuations in liquids into intra-state and inter-state fluctuations, we extract the rigidity of metastable amorphous solid states in the supercooled liquid and glass phases. The result can be understood intuitively without replicas. As a test case, we apply the scheme to the supercooled and glassy state of a binary mixture of soft-spheres. The result compares well with the shear-modulus obtained by a previous molecular dynamic simulation. The rigidity of metastable states is significantly reduced with respect to the instantaneous rigidity, namely, the Born term, due to non-affine responses caused by displacements of particles inside cages at all temperatures down to T = 0. It becomes nearly independent of temperature below the Kauzmann temperature T(K). At higher temperatures in the supercooled liquid state, the non-affine correction to the rigidity becomes stronger suggesting melting of the metastable solid state. Inter-state part of the static response implies jerky, intermittent stress-strain curves with static analogue of yielding at mesoscopic scales.

Localization phenomena in models of ion-conducting glass formers

The mass transport in soft-sphere mixtures of small and big particles as well as in the disordered Lorentz gas (LG) model is studied using molecular dynamics (MD) computer simulations. The soft-sphere mixture shows anomalous small-particle diffusion signifying a localization transition separate from the big-particle glass transition. Switching off small-particle excluded volume constraints slows down the small-particle dynamics, as indicated by incoherent intermediate scattering functions. A comparison of logarithmic time derivatives of the mean-squared displacements reveals qualitative similarities between the localization transition in the soft-sphere mixture and its counterpart in the LG. Nevertheless, qualitative differences emphasize the need for further research elucidating the connection between both models.

Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order response function analyzed in multidimensional nonlinear spectroscopy. Here, we provide comprehensive numerical results of the four-point, three-time density correlation function from longtime trajectories generated by molecular dynamics simulations of glass-forming binary soft-sphere mixtures. We confirm that the two-dimensional representations in both time and frequency domains are sensitive to the dynamical heterogeneity and that these reveal the couplings of correlated motions, which exist over a wide range of time scales. The correlated motions detected by the three-time correlation function are divided into mobile and immobile contributions that are determined from the particle displacement during the first time interval. We show that the peak positions of the correlations are in accord with the information on the non-Gaussian parameters of the van Hove self-correlation function. Furthermore, it is demonstrated that the progressive changes in the second time interval in the three-time correlation function enable us to analyze how correlations in dynamics evolve in time. From this analysis, we evaluated the lifetime of the dynamical heterogeneity and its temperature dependence systematically. Our results show that the lifetime of the dynamical heterogeneity becomes much slower than the alpha-relaxation time that is determined from the two-point density correlation function when the system is highly supercooled.

From equilibrium to steady-state dynamics after switch-on of shear

A relation between equilibrium, steady state, and waiting-time-dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semiquantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios [M. Krüger and M. Fuchs, Phys. Rev. Lett. 102, 135701 (2009)]. For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.

Double Transition Scenario for Anomalous Diffusion in Glass-Forming Mixtures

We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced difference in the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport.

Anomalous dynamic arrest in a mixture of large and small particles

We present molecular dynamics simulations of the slow dynamics of a mixture of large and small soft spheres with a large size disparity. The dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of the large size disparity, large and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: (i) sublinear behavior for mean-squared displacements, (ii) concave-to-convex crossover for density-density correlators, by varying the temperature or wave vector, and (iii) logarithmic decay for specific wave vectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades and strongly resemble predictions of the mode coupling theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the large particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulklike dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of large particles.

Geometrical properties of the potential energy of the soft-sphere binary mixture

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K versus temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K versus energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.

Generalized compressibility in a glass-forming liquid

Abstract We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass-forming liquid consisting of a two-component mixture of soft spheres in three dimensions. As the temperature is lowered, the generalized compressibility drops sharply at the glass transition. Our results are consistent with the kinetic view of the glass transition, but not with an underlying second-order phase transition.

Computer simulation study of the velocity cross correlations between neighboring atoms in simple liquid binary mixtures

The dynamic behavior of atoms in simple liquid binary mixtures is analyzed by molecular dynamic simulation. Time correlation functions between the initial velocity of a tagged particle and latter velocities of neighboring particles are calculated for soft-sphere liquid mixtures of species with different mass and/or size. The transfer of momentum from a tagged particle to its neighbors as well as the differences between the velocity cross correlation between particles of the same or different species is discussed.

SIMULATIONS OF GLASS FORMING LIQUIDS: WHAT HAS BEEN LEARNED

Molecular dynamics simulations of supercooled fluid mixtures of soft-spheres and of Lennard-Jones particles have revealed the existence of a kinetic transition that occurs above the glass transition temperature. This transition appears to be thermodynamic in origin. It is associated with a change in the local mobility of the particles. The basis for these conclusions is discussed.

Study of the α and β relaxations in a supercooled fluid via molecular-dynamics simulations

Incoherent scattering function (self-part of the density autocorrelation function) F s( k, t) is computed by molecular-dynamics (MD) simulation in supercooled fluids of binary soft-sphere mixtures. The full density autocorrelation function F( k, t) was also computed. It is found that F s( k, t)'s at various temperatures and wavenumbers can be fitted over a wide range of time steps (at least over three orders of the decay) by a Williams-Watts stretched exponential function F s( k, t) = A exp[ -( t/ t 0) β ], where A, β and t 0 are adjustable parameters. Significant dynamical behaviours are also presented for mean square displacements and non-Gaussian parameters. With results obtained from different system size, N = 500 and N = 4000 a significant size dependence is suggested. Generalized susceptibility χ( k, ω) and dynamical structure factor S( k, ω) are also computed over a wide range of ω (over five orders) using a new algorithm for the numerical integrations. Computational results are presented for the imaginary part of the generalized susceptivility, χ′( k, ω), which indicates both α and β peaks in such spectra for the first time by the present MD computation. The present MD results are in good agreement with the predictions of the trapping diffusion model, which we have previously proposed for the glass transition.

Glass Transition Singularities and Slow Relaxation

AbstractGeneralized susceptibility for the binary soft-sphere mixtures is computed for the frequency range including both the a and β peaks in a supercooled fluid phase with a superlong-time molecular dynamics simulation. It is shown that the a peak has a non-Debye type frequency dependence and the β peak is essentially of a Debye-type. The slow dynamics is analyzed on the basis of the trapping diffusion model which takes account of two types of diffusive dynamics. With the use of the coherent medium approximation, the frequency dependence of dynamical quantities are shown to agree with the observation. The primary relaxation time is shown to exponentially diverge at a certain temperature below the glass transition point, in line with the Vogel-Fulcher equation. A unified view for the Vogel-Fulcher temperature, the glass transition temperature and the kinetic transition temperature is give on the basis of the trapping diffusion model.

α-relaxation in a supercooled binary mixture

The α-master functions of the mode coupling theory for a binary soft-sphere mixture are presented. They are directly determined by the static structure factors S q . The asymmetric stretching of the susceptibility spectra, which is mainly caused by the common von Schweidler high frequency asymptote, is well described by Kohlrausch fits. The stretching parameters and α-relaxation times for various correlation functions are discussed as functions of the wave vector. For small wave vectors two peaks appear in the density-density spectrum due to an interference of the inter-diffusion pole and the Mountain peak.

Freezing of simple fluids in terms of the Ornstein-Zernike equation: Soft-sphere fluids and binary hard-sphere mixtures.

The solution of the Martynov-Sarkisov closure (MS) of the Ornstein-Zernike equation has to satisfy the condition for the mean force potential w≥-1. It is shown both for one-component soft-sphere fluids and for two-component hard-sphere mixtures that densities at which this condition becomes broken are close to the freezing densities provided by computer simulation (CS). For pressure data, the agreement between MS and CS is rather poor. In particular, for hard-sphere mixtures, MS exhibits only the spindle-type diagram while CS presents also azeotropic and eutectic forms

Theory of supercooled liquids and glasses for binary soft-sphere mixtures via a modified hypernetted-chain integral equation.

We discuss the equilibrium properties of highly supercooled binary soft-sphere fluids by a modified hypernetted-chain (MHNCS) equation proposed recently by us. The MHNCS approximation is made by a proper interpolation of the bridge functions of the Percus-Yevick hard-sphere model and the leading term of the elementary diagrams that were first successfully applied to classical one-component plasmas. The MHNCS approximation has been found to work well for one-component soft-sphere fluids above and below the freezing point. For a more crucial test, the MHNCS equation is extensively studied for the binary soft-sphere fluids. We have obtained numerical solutions of the MHNCS equation for a binary mixture of the 12th-inverse power potential with different core diameters. These results are compared with those of computer simulations and the Rogers-Young approximation. Below the freezing temperature, the solution of the MHNCS equation reproduces a splitting of the second peak of the pair distribution function (PDF) for various core size ratios, compatible with the computer simulations. Using the PDF thus obtained, thermodynamic and structural properties of the highly supercooled binary soft-sphere fluids are investigated.

Short-wavelength collective modes in a binary hard-sphere mixture.

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.

Phase separation in binary nonadditive soft-sphere mixtures.

Recent careful studies showed that the phase separation of a system of hard disks with strongly positive nonadditivity predicted by Tenne and Bergmann [J. Chem. Phys. 70, 1952 (1979)] using scaled particle theory is dubious. As exact computer calculation results are still lacking for these systems, we demonstrate here the phase separation by molecular-dynamics calculations with hard soft-sphere mixture (HSS) potentials (the softness of the potential is so small that it can be regarded as a hard potential). The HSS potential represents the hard-sphere (HS) potential with regard to computation of fluid properties to a very good approximation. HSS systems with extremely positive and negative nonadditivity are considered. While the former separate already at a density of only 3.5% of the closed-packed value, the latter remain homogeneous up to very high densities, as expected. Apparently the numerical method used by Tenne and Bergmann fails to account correctly for the phase separation in strongly (positive) nonadditive HS systems, while it gives good results for the Widom-Rowlinson model recently investigated by computer calculations.