A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

A hybrid hard sphere bridge function is proposed, which, in combination with the standard Ornstein-Zernike integral equation, can predict extremely accurately hard sphere compressibility, virial pressure, and correlation function. Second, a local formulation for determination of excess chemical potential is derived out, which, in combination with the present hybrid hard sphere bridge function and OZ integral equation, can predict the excess chemical potential also extremely accurately. The resultant excess entropy is in excellent agreement with that from the Carnahan-Starling equation of state. The present formalism performs excellently over the whole density range, i.e. from zero to freezing density, and is largely superior to a formalism available in the literature.

An investigation is carried out about the suitability of mapping attractive short-range potential of colloidal systems onto both hard core attractive Yukawa (HCAY) potential and adhesive hard sphere (AH) potential for prediction of the solid–liquid (S–L) transition. Asakura and Oosawa’s depletion potential of asymmetrical binary hard sphere mixture is taken as example of the attractive short-range potential. The S-L transition of the AH potential is based on a modified weighted density approximation, and that of the HCAY potential is based on first order thermodynamic perturbation theory for solid phase and a recently proposed analytical expression for the free energy of fluid phase. It is found that the second virial coefficient can be served as a tool for mapping between similar but different potentials for the case of S-L transition as well as for the case of fluid structure properties, and the HCAY potential is more suitable as a mapping potential than the AH potential.

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein–Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation, can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.

Several purely repulsive potentials (PRP) are investigated theoretically. In contrast to the traditional van der Waals picture, it is found that normal gas-liquid transition emerges only on condition that the PRP as a function of particle separation holds a discontinuous point, or an indifferentiable point, or is differentiable but with an additional length scale besides the hard sphere diameter.

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard-Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard-Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.

A recently developed third order+second order perturbation density functional approximation (DFA) is briefly described. The applicability of this theory is demonstrated in the study of the density profiles of Lennard-Jones (LJ) fluid next to a large hard sphere (mimicking a colloidal particle) of various sizes. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. The chosen density and potential parameters for the equilibrium bulk LJ fluid correspond to the conditions situated at ‘dangerous’ regions of the phase diagram, i.e. near the critical temperature or close to the gas-liquid coexistence curve. It is found that the DFA theory performs successfully for both supercritical and subcritical temperatures. It is also shown that the ‘universality’ of the adjustable parameter associated with this theory holds also in the present case of a large spherical particle as a source of external potential. Here the term universality means independence of this parameter on the particular external field responsible for the generation of a non-uniform density profile of the fluid. This DFA results can be used as a useful starting point for further investigation of solvent-induced excess potential of mean force in the similar systems.

Functional expansion of non-uniform first-order direct correlation function (DCF) around bulk density is rewritten with the concept of weighted density, it is found that the resulting first-order expansion term is actually the first-order expansion term of the Taylor series expansion of the uniform first-order DCF with weighted density as its density argument, the higher-order terms are incorporated into the first-order expansion approximation by Lagrangian theorem. Based on the functional integration view, the present Letter devises a numerical procedure to predict excess Helmholtz free energy from the approximation for the non-uniform first-order DCF. The physical foundation of the present discussion also applies to electronic density functional theory.

A universal formalism, which enables calculation of solvent-mediated potential (SMP) between two equal or non-equal solute particles with any shape immersed in solvent reservior consisting of atomic particle and/or polymer chain or their mixture, is proposed by importing a density functional theory externally into OZ equation systems. Only if size asymmetry of the solvent bath components is moderate, the present formalism can calculate the SMP in any complex fluids at the present development stage of statistical mechanics, and therefore avoids all of limitations of previous approaches for SMP. Preliminary calculation indicates the reliability of the present formalism.