Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

How critical fluctuations influence adsorption properties of a van der Waals fluid onto a spherical colloidal particle

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is extended to its 5th-order version and non-uniform counterpart by supplementing with density functional theory (DFT) and a number of ansatzs for a bulk 2nd-order direct correlation function (DCF). Employment of the ansatzs DCF enables the resultant non-uniform formalism devoid of any adjustable parameter and free from numerically solving an Ornstein–Zernike integral equation theory. Density profiles calculated by the present non-uniform formalism for a hard core attractive Yukawa (HCAY) fluid near a spherical geometry are favorably compared with corresponding simulation data available in literature, and are more accurate than those based on a previous 3rd + 2nd-order perturbation DFT. The non-uniform 5th-order TPT is employed to investigate adsorption of the HCAY fluid onto a colloidal particle; it is disclosed that a depletion adsorption can be induced when the coexistence bulk fluid is situated in neighborhood of a critical point or near a bulk vapor–liquid coexistence gaseous phase or liquid phase density. A physical interpretation is given for such depletion adsorption and for its connection with parameters of the potential under consideration, which is ascribed to critical density fluctuations existing within a wide region of the bulk diagram. For a large spherical external potential inducing wetting transition, it is found that only round wetting transition is found instead of 1st-order pre-wetting transition in the case of a planar wall external potential, and the wetting transition temperature increases relative to that for the planar wall external potential. The present theoretical results for wetting transitions are supported by previous investigation based on thermodynamic considerations and a phenomenological Landau mean field theory, and are also in conformity with the present qualitative physical interpretation.     

Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

On cell theory in relation to isostructural phase transitions due to core collapse

Qualitative features of phase diagrams for isostructural (fcc-fcc) solid-solid transitions are accounted for by a perturbative version of cell theory using a model “step” potential allowing for core collapse.     

Simulation and model development for the equation of state of self assembling non-additive hard chain–hard monomer mixture

Molecular dynamics simulations for a short hard chain composed of a head and three tail groups interacting with non-additive size interactions with a hard sphere solvent were performed. Different densities and non-additivities were used. The equation of state for this mixture was investigated and models based on the first-order thermodynamic perturbation theory (TPT1) and the polymeric analog of the Percus–Yevick approximation (PPY) were developed to predict the compressibility factor of the mixture. The models predicted the compressibilities of the mixtures accurately at zero and negative non-additivities. However, at positive non-additivities, the models overpredicted the compressibilities especially at high densities. The TPT1 model was generally more accurate in predicting the compressibility factor than the PPY model. Microphase separation was observed at high densities and positive non-additivities.     

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.     

Isostructural solid-solid transitions in binary asymmetrical hard sphere system: based on solvent-mediated potential

Size dependence is imparted onto a modified bridge functional, adopted for a recently proposed semi-analytical hard sphere reference system theory for calculation of solvent-mediated potential (SMP). The SMP for two large hard sphere particles immersed in a small hard sphere solvent bath predicted by the present improved version is in satisfactory agreement with the prediction from a theoretically based fitting formula. Isostructural solid-solid transitions in the binary asymmetrical hard sphere system are investigated based on a single-component macrofluid approximation combined with the improved version. It is found that the isostructural solid-solid transition appears when size asymmetry increases. The limiting asymmetry size ratio is near 1/8. As the size asymmetry increases, critical density for both large and small hard sphere components for the fcc isostructural solid-solid transition increases and decreases, respectively.     

A theoretical investigation on the honeycomb potential fluid

A local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive NVT-Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory's reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy, pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local self-consistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.     

Extended multicanonical method combined with thermodynamically optimized potential: application to the liquid-crystal transition of silicon

A novel method is proposed to study first-order phase transition in real materials. It is applied to the liquid-crystal transition of silicon successfully. It consists of two parts: a direct simulation of the transition by an extended multicanonical ensemble with an order parameter defined with structure factors that characterize the transition, and optimization of a model interatomic potential in terms of the ensemble from an accurate one. These provide a principle to project a first-principles approach on a model-based approach conserving thermodynamic properties of multiple phases.     

Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures

Free energies and correlation functions of liquid and solid hard-sphere (HS) mixtures are calculated using the fundamental measure density functional theory. Using the thermodynamic perturbation theory the free energies of solid and liquid Lennard-Jones (LJ) mixtures are obtained from correlation functions of HS systems within a single theoretical approach. The resulting azeotrope- and spindle-type solid-liquid phase diagrams of HS and LJ binary mixtures are in good agreement with the corresponding ones from computer simulations.     

Intermolecular forces and the glass transition

Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.     

用重整化群理论研究胶体模型体系的相行为

用yukawa势能函数表达胶体颗粒之间的吸引作用。用Duh-Mier-Y-Teran状态方 程表达液相Helmholtz自由能。用一阶微扰理论、固体硬球径向分布函数解析式和 改进的胞腔模型建立固相状态方程，结合建立的状态方程和重整化群理论。研究了 胶体模型体系的液-液相平衡和液-固相平衡。研究表明，颗粒之间色散作用量程参 数的变化对胶休到本世纪末茶杯 系的相行为有特殊需要影响。所得结果与分子模 拟数据吻合良好。     

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order?+?second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

Effect of temperature on the surface phase behavior of n-hexadecyl dihydrogen phosphate in adsorption layers at the air-water interface

We present the adsorption kinetics and the surface phase behavior of n-hexadecyl dihydrogen phosphate (n-HDP) at the air-water interface by film balance and Brewster angle microscopy (BAM). A phase diagram, which shows a triple point at about 25.8 degrees C, is constructed by measuring the surface pressure (pi)-time (t) adsorption isotherms. Below 25.8 degrees C, each of the pi-t curves shows a plateau at about zero surface pressure indicating the existence of a first-order phase transition. The BAM observation confirms the order of this phase transition by presenting two-surface phases during this plateau. However, the BAM observation also shows clearly another second-order phase transition from an isotropic phase to a mosaic-textured liquid condensed (LC) phase. The initial phase is a gas (G) phase. Considering the peculiarity of the middle phase, we suggest this phase as an intermediate (I) phase. Above the triple point, the pi-t curves predict the existence of two-step first-order phase transitions. Similar to the results at lower temperatures, the BAM images show two-surface phases during these first-order phase transitions together with a second-order phase transition from an isotropic phase to an LC phase. These transitions are classified as a first-order G-LE (liquid expanded) phase transition, which is followed by another first-order LE-I phase transition. The second-order phase transition is an I-LC phase transition. Contrary to these results, at 36 degrees C both the pi-t measurements and the BAM observation present only two first-order phase transitions, which are G-LE at zero surface pressure and LE-LC transition at higher surface pressure. The shape of the domains during the main transitions shows a peculiar change from a circular at 20 degrees C to an elongated at 24 degrees C and finally to a circular shape at 36 degrees C. Such a change in the domain shapes has been explained considering the dehydration effect at higher temperatures as well as the nature of phases.     

Simulation of multiple ordered phases in C23 n-alkane

Normal alkanes display multiple ordered phases, including an orthorhombic crystal (X) and two partially ordered rotator phases (RI and RII). The rotator phase transitions X-RI and RI-RII are of interest because they are weakly first-order, and because experiments suggest that crystalline polyethylene may nucleate via a metastable rotator phase. We have performed heating and cooling scans of all-atom NσT (isothermal, isostress) simulations of a pure C(23) solid. We find a sequence of phases, transition temperatures, structural and thermodynamic properties, all reasonably consistent with experiment, except that a monoclinic crystal is more stable in our simulations than the experimental orthorhombic structure. We find that the RI phase is well described as an orthorhombic crystal disordered by random ±90° rotations of molecules about their stem axis, and the RII phase can be represented as a loose hexagonal packing of parallel chain stems, which tend to orient with the in-plane projection of C-C bonds pointing between neighbors. To measure local orthorhombic, RI, or RII order, we define Potts- and Ising-like order parameters, from which global order parameters and correlation functions can be computed. We observe modest pretransitional fluctuations of local RI order in the RII phase near T(RI-RII), characteristic of this weakly first-order transition.