One-component Case Research Articles

Transport coefficients for binary Yukawa mixtures: theory and molecular dynamic simulations

We present the generalization to the binary Yukawa mixture of equilibrium molecular dynamic computations of the transport coefficients of the Yukawa one-component plasma (Salin and Caillol 2002 Phys. Rev. Lett. 88 065002, Salin and Caillol 2000 J. Chem. Phys. 113 10459–63). The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces and for all the currents which enter the Kubo formulae. Results include shear and bulk viscosities, ionic thermal conductivity, as in the one-component case, but also diffusion and interdiffusion coefficients. We will present the different coefficients and examples of simulations. We shall also compare our simulation results for large screening parameters with Chapman–Enskog theory (Chapman and Cowling 1970 The Mathematical Theory of Non-Uniform Gases 3rd edn (Cambridge: Cambridge University Press)).

Crystallization in charged two-component suspensions

We report on the crystallization of colloidal crystals comprising of charged particles with different size ratio dispersed in thoroughly deionized water. Single components were characterized carefully and their nucleation behavior was investigated before the preparation of mixtures. Mixtures investigated at constant particle number densities showed body centred cubic structure, conductivity, and shear moduli comply with the assumption of a randomly substituted crystal. Most importantly, for the first time we obtain the dependence of the nucleation rate densities in dependence on the composition and (for one fixed composition) the particle number density. The process of nucleation in random substitutional crystals is found to be similar to the one-component case.

Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension

The momentum distribution function for the two-component 1D gases of bosons and fermions is studied in the limit of strong interatomic repulsion. A pronounced reconstruction of the distribution is found at a temperature much smaller than the Fermi temperature. This new temperature scale, which equals the Fermi temperature divided by the dimensionless coupling strength, is a feature of the two-component model and does not exist in the one-component case. We estimate the parameters relevant for the experimental observation of the crossover effect.

Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates

Generalizing the one-component case, we demonstrate that the propagation of sound waves in two-component Bose-Einstein condensates can also be described in terms of effective sonic geometries under appropriate conditions. In comparison with the one-component case, the two-component setup offers more flexibility and several advantages. In view of these advantages, we propose an experiment in which the evolution of the inflaton field, and thereby the generation of density fluctuations in the very early stages of our universe during inflation, can be simulated, realizing a quantum simulation via analogue gravity models.

Density functional study of the phase behavior of asymmetric binary dipolar mixtures.

Using density functional theory in the modified mean-field (MMF) approximation we study the phase behavior of asymmetric binary mixtures of equisized dipolar hard spheres with different dipole moments in the fluid phase regime. We focus on "dipole-dominated" systems where isotropic attractive interactions are absent. Despite these restrictions our results reveal complex fluid-fluid phase behavior involving demixing and first- and second-order isotropic-to-ferroelectric phase transitions the relative importance of which depends on two "tuning" parameters, that is, the parameter Gamma measuring the ratio of the dipolar coupling strengths, and the chemical potential difference Deltamu controlling the composition. The interplay of these effects then yields three different types of phase behavior differing in the degree to which demixing dominates the system. A generic feature of the resulting diagrams is that the isotropic-to-ferroelectric transition is shifted towards significantly higher densities compared to the one-component case, and is therefore destabilized. Furthermore, demixing in the MMF approach turns out to be always accompanied by spontaneous ferroelectricity, which is in contrast to recent integral equation and simulation results for the limiting case of a mixture of dipolar and pure hard spheres (Gamma=0).

On the compressibility equation of state for multi-component adhesive hard sphere fluids

The compressibility equation of state (EOS) for a multi-component sticky hard sphere model alternative to Baxter's one is investigated within the mean spherical approximation (MSA). For this model and this closure, as well as for a more general class of models and closures leading to Baxter functions qij(r) with density-independent stickiness coefficients, no compressibility EOS can exist for mixtures, unlike the one-component case (in view of this, an EOS recently reported in the literature turns out to be incorrect). The reason is the failure of the Euler reciprocity relation for the mixed second-order partial derivatives of the pressure with respect to the partial densities. This is in turn related to the inadequacy of the approximate closure (in particular, the MSA). A way out to overcome this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.

Monte Carlo simulation of the homogeneous cooling state for a granular mixture

The Direct Simulation Monte Carlo (DSMC) method is used to numerically solve the Enskog equation for a granular binary mixture in the homogeneous cooling state (HCS). The fourth velocity moments, the temperature ratio, and also the velocity distribution functions are obtained and compared with approximate analytical results derived recently from a Sonine polynomial expansion [V. Garzo and J. W. Dufty, Phys. Rev. E 60, 5706 (1999)]. The comparison shows an excellent agreement between both approaches, even for strong dissipation or disparate values of the mechanical parameters of the mixture. In contrast to previous studies, the partial temperatures of each species are clearly different, so that the total energy is not equally distributed between both species. Finally, in the same way as in the one-component case, the simulation as well as the theory show a high energy tail of the distribution functions.

Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ11(r) = Φ22(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ11(r) ≠ Φ12(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram.

Conductivity of deionized two-component colloidal suspensions

The low frequency ac-conductivity of deionized aqueous suspensions comprising of charged latex spheres is investigated. For the one-component cases σ increases linearly with particle number density n, irrespective of the suspension structure. Two-component mixtures are found to form substitutional crystals and no phase separation is observed for small size differences. Then σ is proportional to the sum of the individual conductivity contributions. Further at fixed composition the linear increase with n is retained. The effects can be well described with an extension of Hessinger’s conductivity model to two-component systems.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case.

Analytic example of a free energy functional

We use the ideas of Percus for the construction of classical density functionals for two model interactions: simple hard spheres and adhesive hard spheres (AHSs). The required input, the properties of the uniform fluid, is taken from the analytic mean spherical solution for these two systems. For hard spheres we derive-via a bilinear decomposition of the direct correlation functions-a set of basis functions, which is the same as the one presented by Rosenfeld in his fundamental measure theory framework. For AHSs additional basis functions have to be considered to ensure the bilinear decomposition of the direct correlation functions; we present an expression for the free energy functional for the one-component case.

Variational extensions of the mean spherical approximation

In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein–Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E− TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy.

Homogeneous cooling state for a granular mixture.

The homogeneous cooling state for a binary mixture of inelastic hard spheres is studied using the Enskog kinetic theory. In the same way as for the one-component fluid, we propose a scaling solution in which the time dependence of the distribution functions occurs entirely through the temperature of the mixture. A surprising result is that the (partial) temperatures of each species are different, although their cooling rates are the same. Approximate forms for the distribution functions are constructed to leading order in a Sonine polynomial expansion showing a small deviation from Maxwellian, similar to that for the one-component case. The temperatures and overall cooling rate are calculated in terms of the restitution coefficients, the reduced density, and the ratios of mass, concentration, and sizes.

Thermodynamic perturbation theory for polydisperse colloidal suspensions using orthogonal polynomial expansions.

We present a method for calculating the thermodynamic and structural properties of a polydisperse liquid by means of a thermodynamic perturbation theory: the optimized random phase approximation (ORPA). The approach is an extension of a method proposed recently by one of us for an integral equation application [Phys. Rev. E 54, 4411 (1996)]. The method is based on expansions of all sigma-dependent functions in the orthogonal polynomials p(i)(sigma) associated with the weight function f(Sigma)(sigma), where sigma is a random variable (in our case the size of the particles) with distribution f(Sigma)(sigma). As in the one-component or general N-component case, one can show that the solution of the ORPA is equivalent to the minimization of a suitably chosen functional with respect to variations of the direct correlation functions. To illustrate the method, we study a polydisperse system of square-well particles; extension to other hard-core or soft-core systems is straightforward.

Analytical solution of the Yukawa closure of the Ornstein—Zernike equation III: the one-component case

A new general form of the multi-Yukawa closure of the Ornstein—Zernike equation is discussed for the case of one component and two exponentials. This closure is given in terms of a diagonal scaling matrix Γ. If we are dealing with a pure fluid then the general form of the closure is where β(m) is obtained by solving a linear matrix equation where the matrix M m , depends only on z n , and Γ(nn). Explicit expessions for the excess thermodynamic functions are also found.

Analytical solution of the Yukawa closure of the Ornstein-Zernike equation III: the one-component case

Analytical solution of the Yukawa closure of the Ornstein-Zernike equation III: the one-component case

Entropy of a convecting water-air system and the interpretation of cloud morphogenesis

Cloud-top entrainment in the stratocumulus-to-cumulus transition can be viewed as an entropy-decreasing, self-organizing process. an expression is derived for the entropy of a two-phase convecting water-air system which locates the entropy deficit in the region of the convection itself, generalizing a similar formulation of Dutton's for the one-component case. This expression is applied to a buoyancy-reversal model that simulates entrainment through convection driven by evaporative cooling. the overall entropy budget suggests that the evaporation/precipitation cycle is an essential ingredient of the stratocumulus-to-cumulus transition, underlying the difference between the behaviour of this system and that of the buoyancy-reversal system. the cumulus cloud system is thus rendered as a dissipative structure. the class of dynamical mechanisms that can explain the stratocumulus-to-cumulus transition, together with the associated high entrainment rates, is restricted to those which depend on the water cycle. the relocalized entropy expression, in conjunction with the second law of thermodynamics, implies an upper bound on the possible extent of change in cloud form for given flux of water substance through the evaporation/precipitation cycle over the history of cloud morphogenesis.

Mean spherical approximation for an arbitrary mixture of ions with surface adhesion in a neutralizing background

The mean spherical approximation for a multicomponent mixture of charged hard spheres with sticky interactions in a uniform neutralizing background is solved analytically. When the sticky parameters are of the form Λ ij ∼ w i w j ± v i v j , then the correlation functions and the excess thermodynamics properties are explicitly expressed through a single parameter Γ, which can be obtained by solving an algebraic equation. In the one-component case, an explicit expression for the parameter Γ is obtained.

One and two component adsorption layers of n-hexane and benzene on graphite studied by2H NMR spectroscopy

Deuteron (2H) nuclear magnetic resonance (NMR) spectra were measured at temperatures between 300 and 90 K for n-hexane (C6D14), benzene (C6D6), and a mixture of n-hexane and benzene (C6D14/C6H6 and C6H14/C6D6) adsorbed on the graphitized carbon black Carbopack B. The amounts adsorbed correspond to one monolayer coverage of each substance for both the single and the two-component adsorption. The single component layers each undergo a two-dimensional (2D) fluid/solid phase transition spread over a 30–40 K interval centred at about the transition temperatures reported from diffraction studies. The surface diffusion coefficients in the 2D fluid regime are reported. On cooling to temperatures of about 200 to 160 K, three-dimensional benzene crystallites are formed leaving the n-hexane component in the one monolayer 2D fluid state. On further cooling, the n-hexane layer undergoes a 2D fluid/solid phase transition analogous to the corresponding one-component case.

Influence of cubic and dipolar anisotropies on the static and dynamic coexistence anomalies of the time-dependent Ginzburg-Landau models.

In isotropic systems below the transition temperature, the massless Goldstone modes imply critical infrared singularities in the statics and dynamics along the entire coexistence curve. We examine the important question whether these coexistence anomalies are of relevance also in more realistic systems displaying anisotropies. By applying a generalized renormalization scheme to the time-dependent Ginzburg-Landau models, we treat two quite different but characteristic cases, namely the influence of (i) weak cubic anisotropies, and (ii) long-range dipolar interactions. In the presence of cubic terms, the transverse excitations acquire a mass and thus one expects the theory to approach an uncritical "Gaussian" regime in the limit ${\vec q} \rightarrow 0$ and $\omega \rightarrow 0$. Therefore, we first consider the one-component case in order to show that our formalism also provides a consistent description of the crossover into an asymptotically Gaussian theory. In the case of (weak) cubic anisotropies, the fact that for $n < 4$ the fluctuations tend to restore the $O(n)$-symmetry at the critical point proves to be most important, since under these circumstances coexistence-type singularities may be found in an intermediate wavenumber and frequency range. The dipolar interaction induces an anisotropy in momentum space, which does not completely destroy the massless character of the transverse fluctuations, but only effectively reduces the number of Goldstone modes by one. Remarkably, similar to the isotropic case the asymptotic theory can be treated exactly. For $n \geq 3$ we find coexistence anomalies governed by the isotropic power laws. However, the amplitudes of the respective scaling functions depend on the angle between order parameter and external wavevector.