Thermodynamics of solid surfaces

In contrast to the thermodynamics of fluid surfaces, the thermodynamics of solid surfaces was not elaborated in detail by Gibbs and other founders of surface thermodynamics. During recent decades, significant progress in this field has been achieved in both the understanding of old notions, like chemical potentials, and in formulating new areas. Applying to solid surfaces, basic relationships of classical theory of capillarity, such as the Laplace equation, the Young equation, the Gibbs adsorption equation, the Gibbs-Curie principle, the Wulff theorem and the Dupré rule, were reformulated and generalized. The thermodynamics of self-dispersion of solids and the thermodynamics of contact line phenomena were developed as well. This review provides a fresh insight into the modern state of the thermodynamics of solid surfaces. Not only a solid surface itself, both in a macroscopic body and in the system of fine particles, but also the interaction of solid surfaces with fluid phases, such as wetting phenomenon, will be analyzed. As the development of surface thermodynamics has given a powerful impetus to the creation of new experimental methods, some of these will be described as examples.     

Van der Waals forces in electrolyte solutions

In this article we study van der Waals forces in electrolyte solutions from a local point of view. It is shown for arbitrary geometry that the classical limit of the force density exerted on the ions, as found in the macroscopic theory of van der Waals forces, is identical with the force density calculated from electrostatics and thermodynamic fluctuation theory. Thus neither retardation, nor the Lorentz force affect the average force density.     

Effect of the attractive forces on the density change melting of 2D LJ fluids

The Weeks-Chandler-Andersen perturbation theory of fluids can be considered as a modern version of van der Waals'. Whereas in the old van der Waals theory the effect of the attractive forces on the thermodynamic properties is introduced through a constant, a, in Weeks-Chandler-Andersen theory this constant is replaced by a function of temperature and density α(β, ϱ). This function has been determined by means of Molecular Dynamics simulation of a two-dimensional Lennard-Jones fluid, and here is used to analyse the effect of attractive forces on the density change in melting. The influence is found to be slightly greater than the predictions of van der Waals theory.     

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...     

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.     

PETN炸药爆轰产物状态方程的理论研究

 采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小原理确定不同状态下的凝聚产物相态。对爆轰产物混合系统采用自由能最小原理,通过化学平衡方程组求解炸药爆轰产物系统的平衡组分。使用该理论计算PETN炸药Chapman-Jouguet（CJ）点的爆轰参数,其值与实验值符合得很好;同时计算了以CJ点为起始点的等熵卸载线,并与传统的Jones-Wilkins-Lee（JWL）状态方程的计算结果进行比较,发现计算的γ值是单调递减的,而JWL状态方程计算的γ值却出现了“双峰”现象。分析认为,传统的JWL状态方程给出的“双峰”变化,是由其函数形式自身决定的,并不对应实际物理过程。     

Methane molecule over the defected and rippled graphene sheet

Adsorption of a methane molecule (CH₄) onto a defected and rippled graphene sheet is studied using ab initio and molecular mechanics calculations. The optimal adsorption position and orientation of this molecule on the graphene surface (motivated by the recent realization of graphene sensors to detect individual gas molecules) is determined and the adsorption energies are calculated. In light of the density of states, we used the SIESTA code. It is found that (i) classical force field yields adsorption energy comparable with experimental result and ab initio calculation; (ii) the periodic nature of the van der Waals potential energy stored between methane and perfect sheet is altered due to the insertion vacancies and sinusoidal ripples; (iii) the van der Waals potential energy is found to be sensitive to the presence of the vacancies and the ripples so that the added molecule avoids to be around vacant cites and on top of the peaks.     

Deviations from two-dimensionality in submonolayer adsorbed films

The effects of deviations from co-planarity on the thermodynamic properties of submonolayer adsorbed films are discussed by using van der Waals type theory. According to the proposed approach, the free energy of the reference hard core fluid is approximated by the free energy of a suitably defined two-dimensional mixture of hard disks.     

二维材料及其异质结的声子物理研究

声子是固体最重要的元激发之一,是理解材料摩尔热容、德拜温度以及热膨胀系数等热力学性质的基础,同时电声子相互作用也决定了固体的电导和超导等特性。拉曼光谱是表征固体声子物理的重要实验手段,不仅能表征材料的结构和质量,还能提供材料声子性质、电子能带结构、电声耦合等信息。文章将拉曼光谱应用于二维材料及其范德瓦尔斯异质结的声子物理研究。先简单介绍二维材料的层间振动声子模式和层内振动声子模式,其中层间振动声子模式的频率可用线性链模型来计算,而强度则可用层间键极化率模型来解释;同类层内振动声子模式的Davydov劈裂峰之间的频率差异可用范德瓦尔斯模型拟合。随后,将这些模型推广到二维范德瓦尔斯异质结中,以转角多层石墨烯、MoS₂/石墨烯和hBN/WS₂为例介绍了范德瓦尔斯异质结的声子谱,阐述如何应用线性链模型和经典键极化率模型计算层间振动模的频率和强度,并由此给出二维范德瓦尔斯异质结的界面耦合强度和各层间呼吸模的电声耦合强度等重要参数。     

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.     

The surface-tension and surface-wandering problem

A zeta function renormalization scheme is applied to the van der Waals (ø⁴) theory in both the inhomogeneous and homogeneous sectors. We calculate to the one-loop level the surface tension, and suggest that in this scheme the two-dimensional surface width without stabilizing field is an intrinsic thermodynamic property.     

A Hamilton-Jacobi formalism for thermodynamics

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is 2n+1-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The ‘time’ variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

Damped Oscillators within the General Theory of Casimir and van der Waals Forces

Journal of Experimental and Theoretical Physics - It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic...     

Graphene on Ir(111): physisorption with chemical modulation

The nonlocal van der Waals density functional approach is applied to calculate the binding of graphene to Ir(111). The precise agreement of the calculated mean height h = 3.41 ? of the C atoms with their mean height h = (3.38±0.04) ? as measured by the x-ray standing wave technique provides a benchmark for the applicability of the nonlocal functional. We find bonding of graphene to Ir(111) to be due to the van der Waals interaction with an antibonding average contribution from chemical interaction. Despite its globally repulsive character, in certain areas of the large graphene moiré unit cell charge accumulation between Ir substrate and graphene C atoms is observed, signaling a weak covalent bond formation.     

Structure and tension of interfaces

This is an informal review of some of the ideas, both historical and current, in the theory of interfacial structure and tension. After recalling briefly the van der Waals theory of the late 19th century, and noting the analogy between the equations in the simplest version of that theory and those in the classical dynamics of a particle, the account goes on to consider more recent elaborations and applications of the central ideas. These include applications to three-phase equilibria, wetting and pre-wetting, line and boundary tension, and fluctuations in the structures of interfaces and three-phase lines. In the study of fluctuations there is an analogy to quantum mechanics and the Schrödinger equation, just as there is an analogy to classical mechanics in the theory of equilibrium average structures.     

In Situ Transmission Electron Microscopy Observation of Melted Germanium Encapsulated in Multilayer Graphene

Germanene is a two-dimensional germanium (Ge) analogous of graphene, and its unique topological properties are expected to make it a material for next-generation electronics. However, no germanene electronic devices have yet been reported. One of the reasons for this is that germanene is easily oxidized in air due to its lack of chemical stability. Therefore, growing germanene at solid interfaces where it is not oxidized is one of the key steps for realizing electronic devices based on germanene. In this study, the behavior of Ge at the solid interface at high temperatures is observed by transmission electron microscopy (TEM). To achieve such in situ heating TEM observation, this work fabricates a graphene/Ge/graphene encapsulated structure. In situ heating TEM experiments reveal that Ge like droplets move and coalesce with other Ge droplets, indicating that Ge remains as a liquid phase between graphene layers at temperatures higher than the Ge melting point. It is also observed that Ge droplets incorporate the surrounding amorphous Ge as Ge nuclei, thereby increasing its size (domain growth). These results indicate that Ge crystals can be grown at the interface of van der Waals materials, which will be important for future germanene growth at solid interfaces.     

Roe Linearization for the van der Waals Gas

An extension of the Roe linearization method to nonideal gases is described and applied to the particular case of the van der Waals gas. A supplementary relation connecting the thermodynamic variables is introduced to decouple the evaluation of the intermediate velocity and total specific enthalpy from the determination of the intermediate density, needed in the Jacobian matrix of the linearization due to the general thermodynamic character of the gas. The density value is obtained by solving the supplementary equation, which involves the Roe average of velocity and enthalpy, and that in the case of the polytropic van der Waals gas is a third-order algebraic equation. Numerical results are shown including classical and nonclassical behaviour in one-dimensional shock tube problems.