Phase behavior of aligned dipolar hard spheres: integral equations and density functional results

Using reference hypernetted chain integral equations, we investigate the phase behavior of a system of dipolar hard spheres with perfect orientational order. At low densities, the correlation functions show a strong tendency to the formation of head-to-tail chains. The occurrence of a condensation of the chains, as suggested by a recent simulation, is critically discussed. At higher densities the structure of the liquid phase already reflects well defined positions of the chains relative to each other, similar to a body-centered-tetragonal structure. Minimizing a density functional of the grand canonical free energy which is based on the liquid correlation functions, we calculate the coexistence lines at freezing. Interestingly, the system freezes at much lower temperatures than the corresponding isotropic fluid.     

Structure and thermodynamics of a polar fluid at a discretely polarized wall

The structure and thermodynamics of a dipolar hard-sphere fluid at a discretely polarized hard wall are investigated using Monte Carlo computer simulation. In contrast to a continuously polarized wall, the discrete case exhibits significantly enhanced adsorption of the fluid at the surface relative to that observed for an unpolarized wall. Significant orientational ordering of the first liquid layer is observed plus correlation with the wall polarization that extends over several layers. The relative potential and free energy are calculated as a function of the polarization angle using thermodynamic integration.     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

The Nematic Phase of a System of Long Hard Rods

We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. We rigorously prove the existence of a nematic phase, i.e., we show that at intermediate densities the system exhibits orientational order, either horizontal or vertical, but no positional order. The proof is based on a two-scales cluster expansion: we first coarse grain the system on a scale comparable with the rods’ length; then we express the resulting effective theory as a contour’s model, which can be treated by Pirogov-Sinai methods.     

Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media

A binary quenched-annealed hard core mixture is considered in one dimension in order to model fluid adsorbates in narrow channels filled with a random matrix. Two different density functional approaches are employed to calculate adsorbate bulk properties and interface structure at matrix surfaces. The first approach uses Percus' functional for the annealed component and an explicit averaging over matrix configurations; this provides numerically exact results for the bulk partition coefficient and for inhomogeneous density profiles. The second approach is based on a quenched-annealed density functional whose results we find to approximate very well those of the former over the full range of possible densities. Furthermore we give a derivation of the underlying replica density functional theory.     

Study of the ferromagnetic transition in a positionally frozen Heisenberg spin system

Using extensive Monte Carlo simulations with both particle and cluster orientational moves, in conjunction with finite size scaling and histogram reweighting techniques, we have determined the Curie temperature for two models of positionally frozen Heisenberg spin systems: a system with spatial correlations corresponding to a hard sphere fluid and a spatially random system. We find that the results for the positionally frozen hard sphere Heisenberg system are fairly similar to those previously obtained for the Heisenberg spin fluid and quantitatively agree with the mean field theory estimates. The random system undergoes the ferromagnetic transition at a higher temperature since the lack of core repulsion increases the spin correlations. In this case however the mean field theory overestimates by far the critical temperature.     

A simple pseudomolecular fluid in contact with a wall: Exact and approximate local densities

A simple model mimicking a molecular fluid, introduced by Labik, Nezbeda and Smith (J. Chem. Phys.80 (1984) 5219] is applied to calculations of density profiles of a molecular fluid in contact with a hard wall. This model provides a useful means of investigating many of the quantitative features of more realistic fluid-wall models. In this work we have computed the spherical harmonic coefficients both of the local densities and of the one-particle background correlation functions and have examined the rate of convergence of these expansions. Moreover, we have used this model to test the accuracy of the zeroth-order RAM perturbational theory for the local densityThis work was supported by CPBP, under the Grant No. 01.08.E 2.     

Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Journal of Statistical Physics - Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any...     

An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation

An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities.     

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheim's theory as a perturbation to Tarazona's hard-sphere density functional theory. Each theory approaches Tarazona's theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazona's weighting of Wertheim's theory in the bulk is in good agreement with computer simulation results.     

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus be defined only for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find, in addition, that coexistence of several solids with a fluid phase is also possible.     

Chemical reactions at surfaces: Application of the reaction ensamble monte carlo method

The Monte Carlo simulation method introduced by Smith and Triska [J. Chem. Phys.100 (1994) 3019] is extended to the case of a reacting fluid in contact with a hard wall. The fluid structure for both spherical and nonspherical reaction products is discussed for simple models of reacting hard spheres near a hard wall and near a wall interacting via Lennard-Jones (9,3) potential. In the latter case the investigated model assumes that the probability of a chemical reaction changes with a distance from the surface. It is shown that the applied technique is suitable for the study of reacting nonuniform fluids. This work is supported by KBN under the Grant No. 3 T09A 062 10.     

Solvation force in hard ellipsoid fluids with HNW interaction

In present work, using density functional theory and extended restricted orientation model, the one particle density of hard Gaussian overlap fluid near the colloid walls is calculated. The hard needle–wall interaction between molecules and colloids are considered. Using non-linear equation, proposed by Grimson–Rickyazen, the solvation force of hard ellipsoidal molecular fluid with hard Gaussian overlap interaction is calculated. We could not find the exact or simulation results for comparison. The results in the case k = 2.0 are compared with the solvation force of one-dimensional hard rod fluids. The results are corresponded, qualitatively.     

Binary pusher–puller mixtures of active microswimmers and their collective behaviour

ABSTRACT

Microswimmers are active particles of microscopic size that self-propel by setting the surrounding fluid into motion. According to the kind of far-field fluid flow that they induce, they are classified into pushers and pullers. Many studies have explored similarities and differences between suspensions of either pushers or pullers, but the behaviour of mixtures of the two is still to be investigated. Here, we rely on a minimal discrete microswimmer model, particle-resolved, including hydrodynamic interactions, to examine the orientational ordering in such binary pusher–puller mixtures. In agreement with existing literature, we find that our monodisperse suspensions of pushers do not show alignment, whereas those of solely pullers spontaneously develop ordered collective motion. By continuously varying the composition of the binary mixtures, starting from pure puller systems, we find that ordered collective motion is largely maintained up to pusher–puller composition ratios of about 1:2. Surprisingly, pushers when surrounded by a majority of pullers are more tightly aligned than indicated by the average overall orientational order in the system. Our study outlines how orientational order can be tuned in active microswimmer suspensions to a requested degree by doping with other species.     

Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.     

Hydrophobic hydration at the level of primitive models. II: Large solutes and water restructuring

Details of structural changes that take place in water near an apolar solute have been studied by Monte Carlo simulations for hard sphere solutes of increasing size, including the limiting case of water at a hard structureless wall. Water has been modelled by two different types of extended primitive model, the four-site EPM4 model and five-site EPM5 model. Two different patterns of the orientational ordering of the water molecules around the solute as a function of its size have been found. For the EPM5 model, the structure of water and the orientation of its molecules near an apolar solute of finite diameter do not seem to be sensitive to the size of the solute, and only become more pronounced when the solute becomes a hard wall. On the other hand, the orientation ordering of the EPM4 molecules gradually changes with increasing size of the solute, and for solutes larger than approximately five times the size of the water molecule it is opposite to that near a small solute. A novel method to evaluate the excess chemical potential of large solutes has been implemented, and some thermodynamic quantities for water (distribution of hydrogen bonds and the excess chemical potential) have been computed as a function of the distance from the solute.     

Diffusion within a near-critical nanopore fluid

Results are presented for grand canonical Monte Carlo (GCMC) and both equilibrium and non-equilibrium molecular dynamics simulations (EMD and NEMD) conducted over a range of densities and temperatures that span the two-phase coexistence and supercritical regions for a pure fluid adsorbed within a model crystalline nanopore. The GCMC simulations provided the low temperature coexistence points for the open pore fluid and were used to locate the capillary critical temperature for the system. The equilibrium configurational states obtained from these simulations were then used as input data for the EMD simulations in which the self-diffusion coefficients were computed using the Einstein equation. NEMD colour diffusion simulations were also conducted to validate the use of a system averaged Einstein analysis for this inhomogeneous fluid. In all cases excellent agreement was observed between the equilibrium (linear response theory) predictions for the diffusivities and non-equilibrium colour diffusivities. The simulation results are also compared with a recently published quasi-hydrodynamic theory of Pozhar and Gubbins (Pozhar, L. A., and Gubbins, K. E., 1993, J. Chem. Phys., 99, 8970; 1997, Phys. Rev. E, 56, 5367.). The model fluid and the nature of the fluid wall interactions employed conform to the decomposition of the particle–particle interaction potential explicitly used by Pozhar and Gubbins. The local self-diffusivity was calculated from the local fluid–fluid and fluid wall hard core collision frequencies. While this theory provides reasonable results at moderate pore fluid densities, poor agreement is observed in the low density limit.     

Molecular dynamics simulations of a fluid near its critical point

We present computer simulations for the static and dynamic behavior of a fluid near its consolute critical point. We study the Widom-Rowlinson mixture, which is a two component fluid where like species do not interact and unlike species interact via a hard core repulsion. At high enough densities this fluid exhibits a second order demixing transition that is in the Ising universality class. We find that the mutual diffusion coefficient DAB vanishes as DAB approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from renormalization-group and mode coupling theory predictions for model H, which are DAB approximately xi(-1.065) and DAB approximately xi(-1), respectively.     

Decoupling phenomena in supercooled liquids: signatures in the energy landscape

A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the process as a distinct mode of orientational relaxation. Further, we find that the coupling between rotational and translational diffusion breaks down at a still lower temperature where a change occurs in the temperature dependence of the average inherent structure energy.