A globally accurate theory for a class of binary mixture models (original) (raw)
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The critical behaviour of an associating¯uid mixture, the so called Lin± Taylor model, has been studied, with focus on the critical exponents which characterize di erent points on the critical manifold. In general the critical behaviour of the mixture is found to be Ising-like, but there are some special situations: when two ordinary critical points merge into a double critical point or three critical points coalesce at a critical in¯ection point. A check has been made on the validity of the relations between critical exponents and predictions from the scaling laws.
Computing the phase diagram of binary mixtures: A patchy particle case study
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We investigate the phase behaviour of 2D mixtures of bi-functional and three-functional patchy particles and 3D mixtures of bi-functional and tetra-functional patchy particles by means of Monte Carlo simulations and Wertheim theory. We start by computing the critical points of the pure systems and then we investigate how the critical parameters change upon lowering the temperature. We extend the Successive Umbrella Sampling method to mixtures to make it possible to extract information about the phase behaviour of the system at a fixed temperature for the whole range of densities and compositions of interest.
The Journal of Chemical Physics, 2002
In this work we present structure factors and triplet direct correlation functions extracted from extensive Monte Carlo simulations for a binary mixture of hard spheres. The results are compared with the predictions of two integral equation theories, namely, a recently proposed extension to mixtures of Attard's inhomogeneous integral equation approach, and Barrat, Hansen, and Pastore's factorization ansatz. In general, both theories yield acceptable estimates for the triplet structure functions, though, by construction, the inhomogeneous integral equation theory is more suited to furnish triplet distribution function results, whereas the factorization ansatz provides a more handy approach to triplet direct correlation functions.
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The binary mixture of interacting disparate particles (heavy and light) in two dimensions has been modeled with the help of discrete-velocity Boltzmann-Broadwell models. These have been solved analytically for all integer and half-integer values of coupling constants. Depending on initial conditions the one-particle distribution functions and the entropy of light particles may exhibit a nonmonotonic behavior, as a function of time.
Physical Review E, 2021
A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O(n) loop model or ncomponent face cubic loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. In order to simulate the cluster weight Ising model and search for new universality class, we apply a cluster algorithm, by combining the color-assignation and the Swendsen-Wang methods. The dynamical exponent for the absolute magnetization is estimated to be z = 0.45(3) at n = 1.5, consistent with that by the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent yt and magnetic exponent ym, show that the universalities of the two models on the three dimensional lattice are different. We obtain the global phase diagram containing paramagnetic and ferromagnetic phases. The phase transition between the two phases are second order at 1 ≤ n < nc and first order at n ≥ nc, where nc ≈ 2. The scaling dimension yt equals to the system dimension d when the first order transition occurs. Our results are helpful in the understanding of some traditional statistical mechanics models.
Equilibrium cluster distributions of the three-dimensional Ising model in the one phase region
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Abstract We analyse equilibrium cluster distributions obtained numerically from a ferromagnetic Ising model (simple cubic lattice, 125000 sites and periodic boundary conditions) along the coexistence line and in the one-phase region below T c. We find evidences that the distribution of sizes and energies scales with temperature and external magnetic field giving Binder's droplet exponent y≈ 4/9.
The phase behavior of two-dimensional symmetrical mixtures
The Journal of Chemical Physics, 2010
Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles subjected to a weakly corrugated external field of a square symmetry. It is shown that the both vapor-liquid condensation and demixing transition in the liquid phase are not appreciably affected by a weakly corrugated external field. On the other hand, even a weakly corrugated external field considerably influences the structure of solid phases and the liquid-solid transition. In particular, the solid phases are found to exhibit uniaxially ordered distorted hexagonal structure. The triple point temperature increases with the corrugation of the external field, while the triple point density becomes lower when the surface corrugation increases. The changes in the location of the triple point are shown to lead to the changes of the phase diagram topology. It is also demonstrated that the solid phase undergoes a demixing transition, which is also very slightly affected by the weakly corrugated external potential. The demixing transition in the solid phase is shown to belong to the universality class of the Ising model.
Lattice Boltzmann model for binary mixtures
Physical Review E, 2002
An a priori derivation of the lattice Boltzmann equations for binary mixtures is provided by discretizing the Boltzmann equations that govern the evolution of binary mixtures. The present model leads to a set of two-fluid hydrodynamic equations for the mixture. In existing models, employing the single-relaxation-time approximation, the viscosity and diffusion coefficients are coupled through the relaxation parameter , thus limited to unity Prandtl number and Schmidt number. In the present model the viscosity and diffusion coefficient are independently controlled by two relaxation parameters, thus enabling the modeling of mixtures with an arbitrary Schmidt number. The theoretical framework developed here can be readily applied to multiplespecies mixing.
Zwanzig model of multi-component mixtures of biaxial particles:y3theory re-visited
Molecular Physics, 2006
The paper considers the thermodynamic and phase ordering properties of a multi-component Zwanzig mixture of hard rectangular biaxial parallelepipeds. An equation of state (EOS) is derived based on an estimate of the number of arrangements of the particles on a threedimensional cubic lattice. The methodology is a generalization of the Flory-DiMarzio counting scheme, but, unlike previous work, this treatment is thermodynamically consistent. The results are independent of the order in which particles are placed on the lattice. By taking the limit of zero lattice spacing, a translationally continuous variant of the model (the off-lattice variant) is obtained. The EOS is identical to that obtained previously by a wide variety of different approaches. In the off-lattice limit, it corresponds to a third-level y-expansion and, in the case of a binary mixture of square platelets, it also corresponds to the EOS obtained from fundamental measure theory. On the lattice it is identical to the EOS obtained by retaining only complete stars in the virial expansion. The off-lattice theory is used to study binary mixtures of rods (R 1 À R 2) and binary mixtures of platelets (P 1 À P 2). The particles were uniaxial, of length (thickness) L and width D. The aspect ratios À i ¼ L i /D i of the components were kept constant (À 1R ¼ 15, À 1P ¼ 1/15 and À 2R ¼ 150, À 2P ¼ 1/150), so the second virial coefficient of R 1 was identical to P 1 and similarly for R 2 and P 2. The volume ratio of particles 1 and 2, v 1 /v 2 , was then varied, with the constraints that v iR ¼ v iP and v 2R ¼ 150D 3 2R : Results on nematic-isotropic (N À I) phase coexistence at an infinite dilution of component 2, are qualitatively similar for rods and platelets. At small values of the ratio v 1 /v 2 , the addition of component 2 (i.e. a thin rod (e.g. a polymer) or a thin plate) results in the stabilization of the nematic phase. For larger values of v 1 /v 2 , however, this effect is reversed and the addition of component 2 destabilizes the nematic. For similar molecular volumes of the two components strong fractionation is observed: shorter rods and thicker platelets congregate in the isotropic phase. In general, the stabilization of the ordered phase and the fractionation between the phases are both weaker in the platelet mixtures. The calculated spinodal curves for isotropic-isotropic demixing are noticeably different between the R 1 À R 2 and the P 1 À P 2 systems. The platelet mixtures turn out to be stable with respect to de-mixing up to extremely high densities. The values of the consolute points for the R 1 À R 2 blends are remarkably similar to those obtained using the Parsons-Lee approximation for bi-disperse mixtures of freely rotating cylinders with similar aspect ratios [S. Varga. A. Galindo, G. Jackson, Mol. Phys., 101, 817 (2003)]. In a number of R 1 À R 2 mixtures, phase diagrams exhibiting both N À I equilibrium and I À I de-mixing were calculated. The latter is preempted by nematic ordering in all the cases studied. Calculations show the possible appearance of azeotropes in the N À I coexistence domain.