Hard Spherical Cavity Research Articles

Aggregation of superparamagnetic colloids strongly confined in spherical cavities under magnetic fields

Aggregates of superparamagnetic colloids confined in liposomes in the presence of a controllable external magnetic field are studied here by computer simulation. A model of a hard sphere with a central dipole has been used to simulate secondary particles of colloids confined to move within a liposome, which is modelled as a hard spherical cavity. We focus our study on the structure of aggregates created by secondary particles, which in turn are formed by superparamagnetic particles. This study was performed by using the conventional Monte Carlo simulations and the cluster-moving Monte Carlo method. The results obtained with both methods show a dependence on the number of particles and on the ratio cavity-colloid diameters. However, the usual Monte Carlo method does not allow the collective movement of the aggregates. The simulation results show, that for the particular case of the liposome diameter obtained from the experiments , the formation of a single ribbons located at the centre of the cavity for N = 30 and N = 60. In addition, we analyse the structure formation for different values of , the equilibrium structures are chains for systems for lower , whereas ribbons formation are structures of equilibrium for .

Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere

A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius Rc , is developed by considering the ansatz wavefunction as the product of the free-atom 1s orbital times a cut-off function to satisfy the Dirichlet boundary condition imposed by the impenetrable confining sphere. Seven different expressions for the cut-off function are employed to evaluate the energy, the cusp condition, <r^-1>,<r>, <r^2>, and the Shannon entropy, and as a function of Rc in each case. We investigate which of the proposed cut-off functions provides best agreement with available corresponding exact calculations for the above quantities. We find that most of these cut-off functions work better in certain regions of Rc , while others are identified to give bad results in general. The cut-off functions that give, on average, better results are of the form (1- (r/Rc)^n), n=1,2,3

Fifth-order thermodynamic perturbation theory of uniform and nonuniform fluids

A recently proposed numerical third-order thermodynamic perturbation theory (TPT) is extended to its fifth-order counterpart. Extensive performance evaluation based on several model potentials indicates that the fifth-order version is generally superior to both the third-order version and a well-known second-order macroscopic compressibility approximation TPT, and is at least comparable to an accurate self-consistent Ornstein-Zernike integral equation approximation (SCOZA) with regard to predictions of varying bulk thermodynamic properties. A bulk second-order direct correlation function (DCF) free of numerical solution of a bulk OZ integral equation, is proposed, which, in combination with the framework of classical density functional theory (DFT) and a thermodynamic consistency condition, extends the uniform fifth-order TPT to nonuniform case. Grand canonical ensemble Monte Carlo simulation is carried out to produce density profile of a core-softened fluid confined in a hard spherical cavity, the resultant density profile is employed to evaluate the performance of the present nonuniform fifth-order TPT and a recently proposed third +second-order perturbation DFT. It is found that the present nonuniform fifth-order TPT is generally more accurate than the third+second-order perturbation DFT. Additional advantages of the present nonuniform fifth-order TPT over the third +second-order perturbation DFT is discussed.

Computer simulation study of a liquid crystal confined to a spherical cavity

The interplay of surface ordering and elasticity can be studied on the example of a liquid crystal confined to a cavity. We present a computer simulation study of a liquid of hard spherocylinders in a hard spherical cavity. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We studied how the surface order, the adsorption, and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations.

Theoretical Investigation of Uniform and Non-uniform Penetrable SphereFluid

A bridge function approximation is proposed for a single-componentfluid consisting of penetrable sphere interacting via a potential thatremains finite and constant for center-center distance smaller than theparticle diameter and is zero otherwise. The radial distribution function fromthe Ornstein–Zernike integral equation combined with the present bridgefunction approximation is in satisfactory agreement with the correspondingsimulation data for all of the investigated state points. The presentlycalculated excess Helmholtz free energy respectively based on virial routeand compressibility route is highly self-consistent, and is in very goodagreement with simulational results for the case of low temperatures.The present bridge function approximation, combined with the bridge densityfunctional approximation, can reproduce very accurately density profiles ofthe penetrable sphere fluid confined in a hard spherical cavity for all thecases where simulational results are available.

Further Test of Third Order + Second-Order Perturbation DFT Approach: Hard Core Repulsive Yukawa Fluid Subjected to Diverse External Fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.

Wetting and drying at a curved substrate: Long-ranged forces

We examine the interfacial properties of a hard spherical cavity, radius R , immersed in a solvent in which the fluid-fluid interaction potential contains both a hard-sphere repulsive part and an attractive - r(-6) component. Near to liquid-gas coexistence where the chemical potential deviation deltamu identical withmu- mu(co) (T) --> 0(+) complete wetting by the gas (drying) occurs and a coarse-grained effective Hamiltonian approach shows that the wall/liquid surface tension has a term in R(-2/3) , i.e., a leading-order power-law nonanalyticity in the curvature ( R-1 ) in the large cavity limit. For states sufficiently well removed from coexistence the surface tension can be expanded in integer powers of the curvature R-1 , provided R> R(c) with the length scale given by R(c) =2 gamma(gl) (infinity) / (Deltarhodeltamu) , where gamma(gl) (infinity) is the planar liquid/gas surface tension and Deltarho is the difference between the coexisting densities. However, even in these circumstances there are additional R-2 ln R contributions to the surface tension arising from the dispersion forces. An exact statistical mechanical sum rule is used to relate the density of the fluid at the point of contact with the cavity, rho ( R+ ,mu) , to the pressure of the reservoir and the surface tension. This predicts that rho ( R+ ,mu) acquires a term in R(-5/3) in the regime R< R(c) . Numerical results obtained by applying classical density functional theory to this model confirm all the predictions from the coarse-grained approach for both the surface tension and the contact density. We argue that our results for leading-order nonanalytic contributions are exact, i.e., they should remain valid in the presence of interface fluctuations, and we discuss briefly the repercussions for solvation phenomena and for other wetting situations.

Nonanalytic curvature contributions to solvation free energies: Influence of drying

We investigate the solvation of a hard spherical cavity, of radius R, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation deltamu is identical with mu-muco(T) is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale Rc=2gamma(gl)infinity/(Deltarhodeltamu), where gamma(gl)infinity is the planar gas-liquid surface tension and Deltarho is the difference in coexisting densities at temperature T. For R>Rc, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature R(-1), in keeping with the analysis of Stillinger and Cotter [J. Chem. Phys. 55, 3449 (1971)]. In the other regime, R<Rc, the interfacial free energy and its derivatives acquire terms depending on ln R. Since Rc(-1) can be made arbitrarily small this implies nonanalytic behavior, as R(-1)-->0, of the work of formation of a hard spherical cavity and of the Gibbs adsorption and the fluid density at contact with the wall. Our analysis, which is based on an effective interfacial Hamiltonian combined with exact statistical mechanical sum rules, is confirmed fully by the results of microscopic density functional calculations for a square-well fluid. We discuss the repercussions of our results for solvation phenomena, emphasizing that nonanalytic behavior equivalent to that we find for complete drying in solvophobic systems will also arise in the case of complete wetting, i.e. when liquid films are adsorbed on the surface of large (colloidal) particles or at curved substrates. We reassess various results in the important but neglected Stillinger-Cotter paper, where drying was not considered explicitly, in the light of our present analysis.

Depletion potential near curved surfaces.

We examine the depletion potential and force of a hard-sphere fluid on a single big hard sphere, located inside or outside of a hard spherical cavity, by Monte Carlo simulations to the hard-sphere fluid. The depletion potential is determined by the acceptance ratio method, while the force on the big sphere is obtained by two methods: numerical differentiation of the depletion potential and integration of the contact density of the fluid at the surface of the big sphere. The results are in excellent agreement with those obtained by density functional theory presented by Roth et al.

Depletion Forces near Curved Surfaces

Based on density functional theory the influence of curvature on the depletion potential of a single big hard sphere immersed in a fluid of small hard spheres with packing fraction ${\ensuremath{\eta}}_{s}$ either inside or outside of a hard spherical cavity of radius ${R}_{c}$ is calculated. The relevant features of this potential are analyzed as a function of ${\ensuremath{\eta}}_{s}$ and ${R}_{c}$. There is a very slow convergence towards the flat wall limit ${R}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our results allow us to discuss the strength of depletion forces acting near membranes both in normal and lateral directions and to make contact with recent experimental results.

Density Functional Theory for Small Systems: Hard Spheres in a Closed Spherical Cavity

We present a new approach to determining the equilibrium structure of a closed (canonical) inhomogeneous fluid which combines grand canonical density functional theory and a series expansion of the distribution functions in powers of $(1/\overline{N})$, where $\overline{N}$ is the average number of particles. For hard spheres in a hard spherical cavity, comparison with canonical Monte Carlo results shows that the method is rather accurate, even for small values of $\overline{N}$. In certain (high packing) situations the density profile develops a pronounced peak in the center of the cavity. Accounting properly for such peaks provides a severe test of any density functional approximation.

Quantum Monte Carlo studies of two-electron atoms constrained in spherical boxes

As part of their continuing study of the influence of the environment on the properties of atoms and molecules, the authors calculate the ground-state energies of three two-electron atoms and ions-H-, He and Li+-constrained at the centre of a hard spherical cavity. The calculations are performed using the techniques of quantum Monte Carlo (QMC); the particular QMC algorithm employed is unique in that the associated timestep error is quadratic, rather than linear, and thus yields highly accurate energies, a typical error bound being +or-0.0003 Hartree. This accuracy exceeds that previously obtained in studies employing self-consistent field Hartree-Fock and configuration interaction methods.