We performed variational Monte Carlo simulations of an alkali ion impurity (Li ϩ , Na ϩ , K ϩ , and Cs ϩ ) in liquid 4 He at the equilibrium density and Tϭ0 K using the shadow wave function technique. We calculated the chemical potential, the local order, the single-particle excitation spectrum, and the effective mass of the ions. In all cases the first shell of He atoms is ordered, forming what is usually called a snowball. The radial density profiles and angular correlations show that the microscopic structure of the snowball is remarkably different for each ion. Only in the case of Na ϩ and K ϩ are the atoms of the first shell essentially localized so that the snowball can be considered as a solid. In the case of Li ϩ and Cs ϩ these He atoms readily exchange with the others and this difference shows up dramatically in the values of the effective masses. The local order is simple cubic in the case of Li ϩ and face-centered cubic in the case of K ϩ .
We describe two distinct approaches to obtaining the cloud-point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand-canonical ensemble. The first method determines the chemical potential distribution mu(sigma) (with the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution rho(sigma) match a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p(n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns mu(sigma) such that an equal-peak-weight criterion is satisfied for p(n) for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining mu(sigma). We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are exponentially small in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a polydisperse lattice-gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.
We present the results of variational Monte Carlo calculations of clusters of He4 systems: We study the pure He4 case and the case of a cluster doped with a single alkali–ion impurity. The results are compared with similar calculations in bulk He4. Our trial wave function is a glue-shadow wave function that can describe successfully self-binding and localization in space. The local Bose–Einstein condensate in the pure clusters is calculated. We give the results on the microscopic structure of the doped cluster in terms of the radial density profile around the ion and of angular correlations. We have studied the case of Na+ and K+. In both cases the local order of the atoms in the first shell around the ion is quite distinct compared to that present in the bulk liquid.
The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focussed on the local density distribution ρ(σ, z), measuring the number density of particles of diameter σ at a distance z from the wall. The form of ρ(σ, z) is obtained for bulk volume fractions η b = 0.2 and η b = 0.4 for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity δ = 11.5% and δ = 40.4%, and a truncated Schulz form having δ = 40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at η b = 0.2. A detailed analysis of ρ(σ, z) confirms the presence of oscillatory size segregation effects observed in a previous DFT study (Pagonabarraga et al., Phys. Rev. Lett. 84, 911 (2000)). For large δ, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive σ-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity δ(z) is suppressed in this region, while further from the wall it exhibits oscillations.
We report a joint simulation and theoretical study of the liquid-vapor phase behaviour of a fluid in which polydispersity in the particle size couples to the strength of the interparticle interactions. Attention is focussed on the case in which the particles diameters are distributed according to a fixed Schulz form with degree of polydispersity δ = 14%. The coexistence properties of this model are studied using grand canonical ensemble Monte Carlo simulations and moment free energy calculations. We obtain the cloud and shadow curves as well as the daughter phase density distributions and fractional volumes along selected isothermal dilution lines. In contrast to the case of sizeindependent interaction strengths (N.B. Wilding, M. Fasolo and P. Sollich, J. Chem. Phys. 121, 6887 (2004)), the cloud and shadow curves are found to be well separated, with the critical point lying significantly below the cloud curve maximum. For densities below the critical value, we observe that the phase behaviour is highly sensitive to the choice of upper cutoff on the particle size distribution. We elucidate the origins of this effect in terms of extremely pronounced fractionation effects and discuss the likely appearance of new phases in the limit of very large values of the cutoff.
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