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.     

Polyhedral ground states in clusters of asymmetric hard sphere ions

Clusters of hard sphere ions with sufficient size asymmetry to stabilize a tetrahedral structure in the bulk are found to exhibit trivalent polyhedral ground states in clusters of up to roughly 200 ions. The map of cluster ground state structures over the space of cluster size and ion asymmetry is presented.     

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e., at coexistence, where the critical nucleus becomes infinitely large.     

聚乙二醇型聚氨酯软硬段对其相变储热性能的影响

以不同分子量的聚乙二醇(PEG)为软段,MDI-BDO为硬段,采用两步法溶液聚合合成一种具有固-固相变储热性能的聚氨酯材料.通过DSC,WAXD等测试手段对体系的软硬段结晶性,微相分离,相变可逆性及循环热稳定性进行研究,结果表明,聚氨酯中硬段的存在对软段结晶有着很大的影响,当软段分子量达到2000或以上时,软段才具有较大的结晶度和熔融相变焓,且硬段含量必须高于一定值才能形成较为完善的物理交联网络以保证材料在发生相变时维持固体状态.同时符合这两个条件的试样能具有较好的固-固相变储热性能.就软段PEG含量及分子量对材料储热性能的影响进行了研究,通过调节软段含量与分子量得到一系列具有不同相变焓和相变温度的聚氨酯固-固相变储热材料.经测试还发现,该材料具备很好的相变可逆性和循环热稳定性,是一类很有开发前景的相变储热材料.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

Geometry and energy effects on the structure of hard sphere fluids

The density profile of molecules is an interesting property in the theoretical study of inhomogeneous fluids. In this work, the density profile of a hard sphere fluid around various hard and soft spheres is studied using a well-established version of the density functional theory called “modified fundamental measure theory”. The results obtained from this study show that an increase in the size of the central molecule leads to both an enhanced density profile at the contact point and an amplified layering structure. Similar effects can be observed when attraction between original and bulk molecules increases. Another finding of the present study is that increasing the size of the central molecule has a quasi-attractive role of an entropic origin called ‘depletion potential’. Since the molecule is not very large, the depletion potential can be mapped in a hard core with an attractive Yukawa tail. Increasing molecule softness, however, has an opposite effect and causes the height of the first peak of the density profile to diminish and the inhomogeneity of the structure to lighten.     

Stresses inside critical nuclei

The usual derivation of classical nucleation theory is inappropriate for crystal nucleation. In particular, it leads to a seriously flawed estimate of the pressure inside a critical nucleus. This has consequences for the prediction of possible metastable phases during the nucleation process. In this paper, we reanalyze the theory for crystal nucleation based on the thermodynamics of small crystals suspended in a liquid, due to Mullins (J. Chem. Phys. 1984, 81, 1436). As an illustration of the difference between the classical picture and the present approach, we consider a numerical study of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model.     

A study of the phase behavior of a simple model of chiral molecules and enantiomeric mixtures

We present a study of the solid-fluid and solid-solid phase equilibrium for molecular models representative of chiral molecules and enantiomeric mixtures. The models consist of four hard sphere interaction sites of different diameters in a tetrahedral arrangement with the fifth hard sphere interaction site at the center of the tetrahedron. The volumetric properties and free energies of the pure enantiomers and binary mixtures were calculated in both fluid and solid phases using isobaric Monte Carlo simulations. The models exhibit essentially ideal solution behavior in the fluid phase with little chiral discrimination. In the solid phase the effects of chirality are much greater. Solid-fluid phase behavior involving the pure enantiomer solids and also racemic compounds was calculated. The calculations indicate that, depending on the relative sizes of the hard sphere interaction sites, packing effects alone can be sufficient to stabilize a racemic compound with respect to the pure enantiomer solids.     

Mesophase formation in a system of top-shaped hard molecules: density functional theory and Monte Carlo simulation

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.     

Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study

We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.     

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.     

Crystallization kinetics of thermosensitive colloids probed by transmission spectroscopy

The kinetics of crystallization of poly-N-isopropylacrylamide (PNIPAM) particles has been investigated using the UV-visible transmission spectroscopy. Since the particle size decreases with the increase in temperature, microgel dispersions of different volume fractions have been obtained by varying the temperature of a single sample. It is found that the rates of the change in crystallinity, the average crystallite size, and the number density of crystallites at the most rapid stage over a certain time interval at various temperatures can be described by the power-law relations. At 19 degrees C, the PNIPAM system behaves as a hard sphere system under microgravity. The hard sphere theory based on Monte Carlo simulation has been used as a reference point to compare with conventional hard spheres, soft spheres, and PNIPAM spheres.     

Hollow silica capsules with well-defined asymmetric windows in the shell

A straightforward and effective approach to fabricate porous silica capsules with well-defined asymmetric windows in the shell using raspberry-like templates has been developed. This process begins with the formation of a hierarchical template by chemically coupling a large polystyrene sphere to an ensemble of small, polystyrene latex spheres. The hierarchical template in conjunction with a hard templating method and spin-coating leads to silica capsules with well-defined, asymmetric pores (windows) in the outer shell. Proof-of-principle of this approach has been demonstrated using a 1500/110 nm hierarchical template. The silica capsules thus produced were characterized with scanning electron microscopy and STEM. The diameter of the capsules was ~1400 nm, and the outer opening of the windows was ~100 nm in size, consistent with the diameters of the core and satellite spheres considering the shrinkage due to the calcination. The inner opening was ~30 nm, which gives rise to an asymmetry factor, defined as the diameter of the outer window to the diameter of the inner window, of ~3. In another example, surface-bound capsules with an asymmetry factor of ~1 were made. Collectively, these windows can provide efficient pathways to connect the inside of the capsule to the outside and have potential for asymmetric diffusion and rectification.     

Equilibrium adsorption on single and aggregated nanospheres

The mean field density functional theory has been used to explore Ar adsorption onto single and double identical carbon dioxide nanospheres. We have studied adsorption from subsaturation up to saturation at several temperatures. For the single sphere case, the adsorption excesses and density profiles approach those of plane cases as the spherical substrate size increases; at each temperature, the transition from thin-film to thick-film adsorption is strongly dependent on the size of substrate and the adsorption behavior approaches to that of a plane when the substrate size goes to a large value. For the double sphere case, the cluster formed within the region analogous to the pendular region formed by two contacting identical nanospheres of radius of 1.7 nm has also been studied. The two sphere structure favorites the cluster forming in the interstitial region but does not affect the adsorption transition.     

计算平均力势的理论方法

A universal theoretical framework is proposed for calculating potential of mean force (PMF) between two solute particles immersed in a solvent bath, the present method overcomes all of drawbacks of previous methods. The only input required to implement the recipe is solvent density distribution profile around a single solute particle. The universal framework is applied to calculate the PMF between two large spherical particles immersed in small hard sphere solvent bath. Comparison between the present predictions and existing simulation data shows reliability of the present recipe. Effects of solvent-solute interaction detail, solvent bulk density, and solute size on the excess PMF are investigated. The resultant conclusion is that depletion of solvent component by the solute particle induces attractive excess PMF, while gathering of solvent component by the solute particle induces repulsive excess PMF, high solvent bulk density and large solute size can strengthen the tendency of attraction or repulsion. Relevance of transition from depletion attraction to gathering repulsion with the biomolecular interaction, i.e. hydrophobic attraction and hydration repulsion, is discussed.     

Influence of dimerization on the nematic-isotropic phase transition in strongly polar liquid crystals

A molecular theory of the nematic-isotropic phase transition is developed for the fluid composed of rod-like particles with large longitudinal dipoles. The equilibrium between the monomers and dimers with antiparallel dipoles is explicitly taken into account and the concentration of dimers is determined self-consistently together with the nematic order parameters. We show that for small central dipole moments the nematic-isotropic transition temperature increases with the increasing dipole. This is in accordance with the results of previous approaches. By contrast, for large values of the dipole the transition temperature decreases due to the growing concentration of dimers. This result enables one to explain the results of recent computer simulations that reveal a destabilization of the nematic phase in a system of hard rods with large central longitudinal dipoles. The temperature variation of the concentration of dimers is also analysed and the sign of the concentration discontinuity at the transition point is correlated with the qualitative influence of dimers on the transition temperature.     

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.     

Equation of state and jamming density for equivalent bi- and polydisperse, smooth, hard sphere systems

We study bi- and polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid regime. A slightly improved empirical correction to Z is proposed. When the density is further increased, excluded volume becomes important, but there is still a close relationship between many-component mixtures and their binary, two-component equivalents (which are defined on basis of the first three moments of the size distribution). Furthermore, we determine the size ratios for which the liquid-solid transition exhibits crystalline, amorphous or mixed system structure. Near the jamming density, Z is independent of the size distribution and follows a -1 power law as function of the difference from the jamming density (Z → ∞). In this limit, Z depends only on one free parameter, the jamming density itself, as reported for several different size distributions with a wide range of widths.