Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive V_R and a density-dependent attractive V_A part.     

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Wetting of Alkanes on Water from a Cahn-Type Theory: Effects of Long-Range Forces

We apply the phenomenological wetting theory of Cahn to fluids with van der Waals forces, and in particular to the wetting of pentane on water. Taking into account explicitly the long-range substrate–adsorbate interaction allows us to reproduce the experimentally observed critical wetting transition, which arises from the vanishing of the Hamaker constant at T53°C. This transition is preceded by a first-order transition between a thin and a thick film at a (much) lower temperature. If long-range forces are neglected, this thin–thick transition is the only wetting transition and critical wetting is missed. Our study focuses on the development of useful theoretical tools, such as phase portraits and interface potentials adapted to systems with van der Waals forces.     

Mean-field theory of critical phenomenon for mutually repelling particles in complex plasmas

A mean-field theory of criticality for charged particles in complex plasmas is proposed. It is shown that the existence of the critical point and the liquid-vapor coexistence is fully consistent with a purely repulsive potential between particles; the cohesive field due to the plasma background drives these. The critical exponents, calculated by expanding the free energy near the critical point, are found to be classical. The phase coexistence curve, obtained by minimizing Gibbs potential, is similar to that of other mean-field models, e.g., van der Waals fluids, ionic fluids, etc. These results lend support to the concept of "universality" in widely different systems.     

The Classical–Quantum Passage: A van der Waals Description

We undertake a van der Waals inquiry at very low temperatures so as to find signs of a classical–quantum frontier. We investigate the relation of such signs with the celebrated van der Waals gas–liquid transition. We specialize the discussion with respect to the noble gases. For such purpose, we use rather novel thermal statistical quantifiers such as the disequilibrium, the statistical complexity, and the thermal efficiency. Fruitful insights are thereby gained.     

The role of hydrophobic interaction in phase transition and structure formation of lipid membranes and proteins

The hydrophobic interaction arises from the ordered structure of water around nonpolar groups of molecules in an aqueous solvent. Because biological systems are made of various macromolecules and amphiphiles which are suspended in aqueous solution, the hydrophobic interaction plays a very important role in the formation of higher-order structure and phase transitions in biological systems. Considering the hydrophobic interaction, the van der Waals interaction and the entropic effect, an equation of state of a lipid membrane was obtained which was analogous to the van der Waals equation. The characteristics of the lipid bilayer phase transition as well as the phase behaviors of a lipid monolayer were explained by this equation of state. Experimental evidence was obtained from ultrasonic measurements which indicated that its phase transition accompanys significant critical phenomena. Analysis of the hydrophobicity of amino acid sequences revealed that the morphology of the proteins was determined by the hydrophobicity alone. The essential role of the hydrophobic interaction in the morphogenesis of proteins could be confirmed by a denaturation experiment on a soluble protein, carbonic anhydrase B. Fluorescence measurements showed that an intermediate state, the so-called molten globule state, had a quite hydrophobic core, indicating that the globule shape of this protein is stabilized by the hydrophobic interaction.     

论范德瓦尔斯a和b参数与温度的关系

范德瓦尔斯方程中a、b参数是否与温度相关,不但不同文献中的说法互不相同,而且有同一文献前后的结论相互矛盾.本文分析了这个令人迷惑的问题.在热力学中a和b参量被处理为与温度无关,它仅仅在临界点附近有效并可以把范德瓦尔斯方程表述为对应态定律;在更加广泛的温度区间a、b参量和温度有关,但是范德瓦尔斯方程却丧失了其独特性.统计物理文献把a和b参量处理成为位力展开的一种拟合方程,发现一般情况下两个参数都依赖于温度,仅仅在特殊情况下和温度无关,以说明对应态定律成立的条件.热力学和统计物理关于a和b参量是否依赖于温度相互矛盾的表述,源于这两个理论中范德瓦尔斯状态方程适用范围不同.     

A comparison of self broadening and shift of helium,neon and argon emission lines

Self broadening (van der Waals and resonance) and shift of Ne emission lines and van der Waals broadening and shift of He emission lines have been measured using a high pressure (0.5–3.0 atom), low current discharge. These results are compared with previous measurements in Ar and He to obtain a complete comparison of self broadening and shift of He, Ne and Ar emission lines. Oscillator strengths for the resonance transitions are obtained from the resonance broadening coefficients. The trend of the van der Waals broadening coefficients for the three noble gases is correctly predicted by a theory due to HINDMARSHet al.⁽⁴⁾ in which a Lennard-Jones potential is used in the impact theory formalism. The measured line shifts cannot be accounted for by this theory and reflect the need for more accurate quantum mechanical calculations.     

Analysis of the critical line network for the van der Waals equation at the van Laar point

The density-density plot of the critical lines of the van der Waals equation at the van Laar point is analyzed through its algebraic properties. It is shown that this curve is an irreducible expression of the fifth degree of genus one. In addition, we show the topology of the second branch, i.e., theT=0 solution, which will interact with the first branch as soon as the energy parameters are slightly different from the van Laar values. Finally, we analyze the behavior of the van der Waals equation near the point at which liquid-liquid separation takes place.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

范德瓦耳斯和他的状态方程

在物理学发展史上，范德瓦耳斯对气—液流体系统做了开创性的研究工作，建立了人类历史上第一个既能反映气、液各相性质，又能描述相交和临界现象的状态方程。范德瓦耳斯的理论成就和研究方法对热力学、统计力学和低温物理学的发展产生了重要而深远的影响。文章系统探讨了范德瓦耳斯方程产生的历史背景、科学意义和局限性，讨论了范德瓦耳斯的理论和方法对当代物理学的启发意义。     

Phase coexistence and a critical point in ultracold neutral plasmas

We show the existence of the liquid-vapor phase coexistence and a critical point for strongly coupled ions in ultracold neutral (UCN) plasmas. Expressions for the free energy of UCN plasmas and an equation of state for the ions are obtained in the mean field approximation. A van der Waals-like isotherm shows the existence of a critical point in UCN plasmas. Depending on the ion temperature, the ions are shown to exist in a mixed vapor-liquid phase for a range of the ion Coulomb coupling parameter Γ(i) (defined by the ratio between the ion interaction and the ion kinetic energies), and in a strongly coupled liquid state for values of Γ(i) above this range. The estimates of critical constants show that it may be possible to observe these phenomena in the present day UCN plasmas.     

What controls the thickness of wetting layers near bulk criticality?

We study the thickness of wetting layers in the binary-liquid mixture cyclohexane methanol. Far from the bulk critical point, the wetting layer thickness is independent of temperature, resulting from the competition between van der Waals and gravitational forces. Upon approaching the bulk critical temperature [t=(T(c)-T)/T(c)-->0], we observe that the wetting layer thickness diverges as t(-beta) with effective critical exponent beta=0.23+/-0.06. This is characteristic of a broad, intermediate scaling regime for the crossover from van der Waals wetting to critical scaling. We predict beta=beta/3 approximately 0.11, with beta the usual bulk-order parameter critical exponent, showing a small but significant difference with experiment.     

Evidence for coherent collective Rydberg excitation in the strong blockade regime

We report on strong van der Waals blockade in two-photon Rydberg excitation of ultracold magnetically trapped 87Rb atoms. The excitation dynamics was investigated for a large range of densities and laser intensities and shows a full saturation and a strong suppression with respect to single-atom behavior. The observed scaling of the initial increase with density and laser intensity provides evidence for coherent collective excitation. This coherent collective behavior, that was observed for up to several thousand atoms per blockade volume, is generic for all mesoscopic systems which are able to carry only one single quantum of excitation.     

Resonance Tunneling Phenomena in Two-Dimensional Multilayer van der Waals Crystalline Systems

Works, mostly experimental, concerning the most interesting features of application of the resonant tunneling spectroscopy to a new type of heterosystems, van der Waals heterostructures, have been briefly reviewed. These heterostructures appeared after the recent discovery of two-dimensional crystals, which are a new class of materials beginning with graphene. The role of the angular matching of crystal lattices of conducting graphene electrodes of van der Waals systems in carrier tunneling between them has been analyzed together with the closely related problems of satisfaction of conservation laws in tunneling transitions. Manifestations of multiparticle correlation interactions between carriers in van der Waals systems such as Wigner crystallization of electrons in a two-dimensional electron gas in a magnetic field and Bose condensation of excitons in parallel two-dimensional electron gases have been briefly discussed.     

Study of the critical line and its double point in the intermediate model

I show that it is possible to generalise the van Laar calculation for the critical double point for the intermediate model, i.e. a model intermediate between the lattice gas and the van der Waals equation for binary mixtures. The calculation was done to investigate whether the double point is also a tricritical point, as is found both in the case of the lattice gas and in the case of the van der Waals case. Although the double point coordinates and their corresponding potential parameters can be determined, one cannot prove, by analytical means, that the point is also tricritical. Most likely the geometric-mean condition is too stringent in this case.     

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.     

Thermodynamic properties and plasma phase transition of xenon at high pressure and high temperature

By using recent Padé approximations for the Coulombic contribution and hard-core, Van der Waals and polarisation approximations for the atomic contribution, the thermodynamic functions for the nonideal xenon plasma are constructed. These formulae cover a large range of pressure and temperature. Single ionisation is studied by minimising the free energy with respect to the particle numbers. A second critical point is predicted. The coexistence line for the corresponding first order phase transition (weakly ionised plasma - strongly ionised plasma), the lines indicating the soft transition to a higher degree of ionisation at overcritical temperatures, as well as the border of the coexistence area are presented. The influence of the different interactions on the critical data is discussed.