Modified Fundamental Measure Theory Research Articles

Time-dependent density functional theory for the freezing/melting transition in interfacial systems

We propose a three-dimensional time-dependent density functional theory (TDDFT) to investigate the freezing/melting of Lennard-Jones fluids in interfacial systems including flat interfaces and nano-droplets. The theory is based on a modified fundamental measure theory (MFMT) for the hard-sphere reference system plus mean field theory (MFT) for the attractive contributions plus an additional weighted density approximation (WDA) contribution to enforce that bulk liquid equation of state is that of modified Benedict, Webb and Rubin (MBWR). By using different initial states, our theory generated a series of equilibrium structures including crystals and polyhedral particles. The non-linear effect and the irreversibility of the freezing/melting process were captured. The profiles for free energy and the order parameter indicate that the free energy barrier existing in the freezing/melting process is caused by the break in symmetry. Additionally, the time-dependent properties were also examined, and provided insight into the mechanism of the freezing process.

Effects of the confinement on wall pressure, interfacial tension, and excess adsorption at the nanocylindrical wall

In this article, a hard sphere fluid confined between two homocentric cylinders which formed a bicylindrical pore has been investigated. Our aim is investigation of the effect of an outer cylinder on the values of wall pressure, interfacial tension, and excess adsorption of fluid at a convex nanocylindrical wall, inner wall. To investigate this effect, the modified fundamental measure theory (MFMT) used. To do so at first we presented a general solution for weighted density integrals in cylindrical coordinate which is applicable for infinite and infinite lengths of cylindrical pore, bicylindrical pore, cylindrical wall, and even truncated cone. In the second step, the wall pressures, interfacial tensions, and excess adsorptions at a convex nanocylindrical wall are obtained for confined fluids in bicylindrical pores and compared with those values for bulk fluids. Our results showed that confinement leads to an oscillatory behavior for wall pressure, interfacial tension, and excess adsorption of the fluid at the wall. The reason for these oscillations lies in structural changes that occur for a fluid as a result of confinement. Variation of the type of interaction of inner wall with fluid from hard to attractive one can reverse the behavior of interfacial tension and adsorption versus size. Also in some cases, it changes their signs while the change in the type of interaction of the outer wall only leads to an increase in amplitudes of the oscillations.

Classical density functional theory for gas separation in nanoporous materials and its application to CH4/H2 separation

Three-dimensional classical density functional theory (CDFT) has been introduced and applied to predicting gas separation in metal-organic frameworks (MOFs). The formula of CDFT is based on modified fundamental measure theory (MFMT) and mean field approximation (MFA). The accuracy of the theory has been examined by simulations, and it has been implemented into a high-throughput screening of CH4/H2 separation materials. A total of 1200 MOFs have been examined, with selectivity ranging from 70 to 220 depending on the temperature, pressure and bulk CH4/H2 ratio, which is much higher than that of real MOFs. A set of promising CH4/H2 separation MOFs has been identified. According to the analysis of the isotherm and density profile, a MOF material with a pore size that can accommodate only one CH4 molecule seems to be the best for CH4/H2 separation.

The effects of inserting a tiny sphere in the center of a nanospherical pore on the structure, adsorption, and capillary condensation of a confined fluid (a DFT study).

The modified fundamental measure theory (MFMT) has been employed to investigate the effects of inserting a tiny sphere in the center of a nanospherical pore on the structure, adsorption, and capillary condensation of fluids confined in it. In the first part of this Article, we have solved the weighted density integrals for all pores with spherical symmetries, including spherical and bispherical pores. In the second part, we show that the structure, amount of adsorption, and position of the fluid's capillary condensation change drastically when even a very thin sphere, R(s) = 0.01σ, is inserted into the center of a spherical pore (SP). In fact, the existence of a forbidden region around the inner sphere for the case of bispherical pores, even when R(s) = 0.01σ, causes a remarkable shift in both the amount of adsorption and the bulk density at which the capillary condensation occurs. Moreover, the insertion causes a sudden increase in the value of the contact density of the liquid, or the liquid in equilibrium with its vapor, at the wall of the outer sphere compared to that for an SP. In other words, the insertion of a tiny sphere in an SP causes the liquid droplet, which is formed in the center of the SP, to sprinkle throughout the whole nanopore. Also, we have demonstrated that the critical temperature and densities decrease with decreasing radius of the inner sphere.

平行狭缝间缔合流体的平衡热力学性质

基于密度泛函理论(DFT)和改进的基本度量理论(MFMT)，研究了受限于平行狭缝间AB2型缔合流体的聚集态行为。根据平衡时的密度分布，对纳米狭缝中AB2型缔合流体的剩余吸附进行了计算。阐明了缔合程度和体积分数以及狭缝宽度对体系平衡时的剩余吸附和密度分布的影响。 The aggregation behaviors of AB2 associating fluid confined in slit pores were investigated by using the density functional theory (DFT) and modified fundamental measure theory (MFMT). According to the equilibrium density profiles, the excess adsorption of AB2 associating fluids was determined in slit pores. The influences of the volume fraction, the pore width, and the associating conversion on density profiles and excess adsorption were also demonstrated.

Prediction of Interfacial Structure and Tension of Binary Mixtures Containing Carbon Dioxide

In this work, a density functional approach was applied to describe the interfacial thermodynamic properties of CO2 binary mixtures including CO2 + heptane, CO2 + acetone, CO2 + ethanol, and CO2 + water. In the theoretical model, the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) was incorporated to describe the chemical potential of the bulk term, while, for inhomogeneous potential, the modified fundamental measure theory (MFMT) was employed to describe the hard sphere contribution, and a weighted density approximation was adopted for the attractive contribution. Without any adjustable parameter, the theoretical calculations have been well-testified by the available experimental data, showing a good predictive capability of the theory to the interfacial structure and tensions of CO2 binary mixtures with nonpolar, polar, and associating fluids.

Density Profile and Solvation Force for Hyperbranched Polymerization Fluids Confined in Parallel Plates

Within the framework of density functional theory(DFT),a free energy function was formulated in terms of modified fundamental measure theory(MFMT) for hard sphere repulsion and statistical mechanic theory with the weighted density approximation(WDA) for polymerization.A chemical potential for ABg hyperbranched polymerization fluids was determined and an expression of the density profiles of the polymerization fluids confined in parallel plates was derived.The influence of the reaction conversion,the volume fraction,and the number of B-kind functional groups on density profiles was discussed.Furthermore,the relationship between the reaction conversion or the plate width and solvation forces was also analyzed in terms of density profiles.

Orientation of rod molecules in selective slits: a density functional theory

A density functional theory (DFT) is used to investigate molecular orientation of rod fluids inselective slits. The DFT approach combines a modified fundamental measure theory (MFMT)for excluded-volume effect, the first-order thermodynamics perturbation theory for chainconnectivity and the mean-field approximation for van der Waals (vdW) attraction. To studythe molecular orientation, the intramolecular bonding orientation function is introducedinto the DFT. First, we investigate the orientation of the surfactant-like rod molecule ofAB6 (i.e. ABBBBBB)in a nanoslit of H = 20σ, where the walls selectively adsorb segment ‘A’. It is observed that, with the increase ofthe surface energy of the wall to head segment (i.e. ‘A’ segment) of the rod molecule, therod molecules adsorbed on the wall present the perpendicular orientation gradually, andassemble into a smectic-A-like monolayer finally. In addition, we also explore themolecular orientation of the rods with both end segments preferring to the wall,i.e. AB8A andAB7A, in ananoslit of H = 10σ.Interestingly, the AB8A rod monolayer is compatible with either a smectic-A-like or a smectic-C-like organization, butAB7A rod molecules exhibit the smectic-A-like organization. The orientation factor of theAB7A rod molecule reaches1, suggesting that AB7A rod molecules self-assemble into an ordered structure with perfectly perpendicularorientation to the wall.

Structure of two-dimensional hard-disk mixtures: Modified fundamental-measure theory

A modified fundamental-measure theory (MFMT), which is based on the semiempirical equation of state for the hard-disk mixtures, has been employed for studying the uniform and nonuniform structural properties of hard-disk mixtures. The test-particle method has been used to calculate the radial distribution functions of hard-disk mixtures. The particle density distributions near the large hard disk and within the hard circular cavity have been studied, and molecular dynamics simulations have been carried out to compare with the MFMT and other approximations. The depletion interactions acting between two large hard disks in a bath of the smaller hard disks and disk–disk second virial coefficients B 2 due to the disk-mediated interactions have been studied. Comparison with computer simulations shows that the MFMT yields an excellent agreement with computer simulation data even for higher packing fractions. The MFMT can provide an accurate reference for the further development of the statistical–thermodynamic theory of complex fluids at uniform and nonuniform conditions.

Density functional theory for molecular orientation of hard rod fluids in hard slits

A density functional theory (DFT) is used to investigate molecular orientation of hard rod fluids in a hard slit. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect with the first order thermodynamics perturbation theory for chain connectivity. In the DFT approach, the intra-molecular bonding orientation function is introduced. We consider the effects of molecular length (i.e. aspect ratio of rod) and packing fraction on the orientations of hard rod fluids and flexible chains. For the flexible chains, the chain length has no significant effect while the packing fraction shows slight effect on the molecular orientation distribution. In contrast, for the hard rod fluids, the chain length determines the molecular orientation distribution, while the packing fraction has no significant effect on the molecular orientation distribution. By making a comparison between molecular orientations of the flexible chain and the hard rod fluid, we find that the molecular stiffness distinctly affects the molecular orientation. In addition, partitioning coefficient indicates that the longer rodlike molecule is more difficult to enter the confined phase, especially at low bulk packing fractions.

Depletion interaction in colloid/polymer mixtures: application of density functional theory

Insert-route density functional approach (IRDFT), modified fundamental measure theory (MFMT) and thermodynamic perturbation theory (TPT1 and TPT2) are combined to study the depletion force between colloidal particles in hard sphere/hard sphere chain mixtures which represent a model of systems containing colloids dispersed in an athermal polymer solution. The predicted results are compared to simulations showing the reliability of the method used which captures the main characteristics of depletion interaction between colloids induced by polymers. Results of TPT2 are slightly more repulsive and better than that of TPT1 especially when the inter-particle distance is small than the diameter of polymer segment indicating the essential influence of the three-body correlations. Effects of the polymer density, polymer chain length and size ratio of colloid to polymer segment on the depletion force are studied in detail. Due to a little deterioration of the prediction in the high density region, further improvement is anticipated to better balance the competition between the excluded-volume effect and the chain connectivity.

Modified fundamental-measure theory for additive hard-disk fluids

A modified fundamental-measure theory (MFMT), which is based on the semiempirical equation of state for the hard-disk mixtures, has been proposed for studying the uniform and nonuniform structural properties of hard-disk fluids. The calculated results show that the MFMT theory yields in an excellent agreement with the computer simulations and is better than the original FMT proposed by [Rosenfeld and co-workers [Phys. Rev. A42, 5978 (1990); Phys. Rev. E55, 4245 (1997)]..

SEGREGATION OF FLUIDIZED BINARY HARD-SPHERE SYSTEMS UNDER GRAVITY

We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.

A self-consistent approach for modelling the interfacial properties and phase diagrams of Yukawa, Lennard-Jones and square-well fluids

A self-consistent density-functional approach is presented for describing the phase behaviour and interfacial tensions of van der Waals fluids represented by the hard-core Yukawa (HCY), Lennard-Jones (LJ) and square-well (SW) potentials. The excess Helmholtz energy functional is formulated in terms of a modified fundamental measure theory (MFMT) for the short-ranged repulsion and a density-gradient expansion for the van der Waals attractions. Analytical expressions for the direct correlation functions of uniform fluids are utilized to take into account the effect of van der Waals’ attraction on intermolecular correlations. For bulk phases, the density functional theory is reduced to an equation of state (EOS) that provides accurate saturation pressures and vapour–liquid phase diagrams. Near the critical region, the long-range fluctuations can be corrected by using the renormalization group (RG) theory. With the same set of molecular parameters, the theory also yields satisfactory surface tensions and interfacial density profiles at all relevant temperatures.