Hierarchy of equations for the surface tension of solids

Of the four main equations in thermodynamics for the surface tension of condensed matter, i.e. the generalized and classical Lippmann equations and the Shuttleworth and Gokhshtein equations, only the classical Lippmann and Gokhshtein equations have been confirmed experimentally. The generalized Lippmann (Couchman–Davidson) equation is considered to be more universal, since three other equations could be derived from it. Although this fact has been widely accepted, it was recently reevaluated in two opposite ways. In the first approach, the experimental verification of the Gokhshtein equation should support the correctness of the generalized Lippmann and Shuttleworth equations. In the second approach, the incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics throws doubts upon all its corollaries, including the generalized Lippmann and Gokhshtein equations. However, both of these approaches are here shown to be erroneous, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations, and the opposite is also true: neither the generalized Lippmann nor Shuttleworth equations could be derived from the Gokhshtein equation.     

The surface tension of polymer liquids

An experimental and theoretical review of the surface tension of polymer liquids is presented. New experimental methods for polymer surface tension measurement are reviewed. Numerous theoretical and empirical approaches are briefly described. Strong emphasis is placed on the accuracy and limitations of the thermodynamic information which are used as input to many of if not all these theories. It is shown that, by using accurate thermodynamic bulk properties for these liquids including polar polymers, one can use a simple corresponding states principle to describe the temperature and molecular weight dependences of the surface tension with no adjustable parameters to within a few per cent, even though the actual surface tensions may vary by a few hundred per cent. Any small inaccuracies in the predictions arise from conformational entropic effects or because one cannot accurately compute the 'real' cohesive energy density of a polymer liquid from thermodynamic properties alone. The results of recent measurements on high molecular weight polymers are compared with previous work on lower molecular weight liquids. We use the polyethylene and polytetrafluoroethylene oligomeric series to illustrate the uses and limitations of thermodynamicdata for the prediction of surfacetension. The temperature and molecular weightdependences of the surface tensions of these polymers are dominated by the dependence of the bulk thermodynamic properties on temperature and molecular weight. Limited discussion is also given to studies of copolymers and blends using surface tension and complementary techniques.     

Structure-mechanical approach to surface tension of solids

Some problems of applying the Lippmann equation to adsorption studies on solid electrodes are shortly reviewed. A novel nonthermodynamic approach to consider the role of elastic and plastic deformation of electrode surfaces during adsorption is proposed. The extremely thin electrode surface layers affected electrically and mechanically by adsorbate are supposed to be free of dislocations because of volume discrepancy. The nearest structure-mechanical analogs of such layers are the whisker crystals whose side surface could have one- and two-dimensional defects, but have no active dislocations. Like whiskers, surface metal layers should possess a high ultimate strength close to the theoretical one and a purely elastic deformation. Affected only by adsorbate, the surface electrode layer should be considered as absolutely elastic body, whose plastic deformation is impossible, i.e. the Lippmann equation and other equations containing terms of plastic deformation cannot be used in thermodynamics of the solid metal surface.     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.     

Corresponding states theory for the prediction of surface tension of ionic liquids

The surface tension of ionic liquids is studied according to phenomenological scaling and the law of corresponding states. The reduced coordinates γ*–T*, where γ* represents the reduced surface tension and T* is the reduced temperature, are introduced for the prediction of the surface tension from the melting point up to boiling point. It has been shown that the correlation can be expressed as a unique straight-line plot with a linear correlation coefficient of 0.984 that requires only the melting and boiling point parameters and can predict the surface tension accurately.     

用力敏传感器测量液体表面张力系数

利用力敏传感器测量液体表面张力系数，既改进了传统的实验方法和仪器，提高了实验的准确度和稳定性，同时因实现了非电量电测，也有助于测量过程中学生对物理过程的观察和规律的理解。     

用力敏传感器测液体表面张力系数的误差分析

分析了采用力敏传感器测量液体表面张力系数实验误差的主要来源，给出了计算公式和测量结果，并提出了改进建议．     

Assessing the equation of state and comparing it with other relationships used for determining the surface tension of solids

Some facts regarding the equation of state (EQS) in calculating the surface tension of solids by means of contact angle measurements were manifested. In the present investigation, it was mathematically proved that the surface tension of a solid as estimated by the EQS is in fact equivalent to the Zisman critical surface tension for that same solid. Additionally, the applicability of the EQS's approach in attaining the surface tension of powdered solids by the aid of the capillary rise procedure is also discussed and its limitations are clarified. Furthermore, a methodology was devised so that the surface tension of solids as determined by the EQS could be compared with those calculated by approaches using components of surface tension. This methodology revealed that the applications of approaches based on the geometric mean (i.e. Owens/Wendt and van Oss et al. relationships) are restricted to achieving only high surface tensions of solids.     

Isochoric temperature coefficient of surface tension andS o-parameter of quasi-spherical molecular liquids

The Sharma parameterS _o which is characteristic of molten alkali halides and polymers has also been shown to be characteristic of a wide variety of liquids. Calculated data using the volume expansivity of the liquid establish the constancy of theS _o-parameter which retains, on an average, a constant value of 1·11 for quasi-spherical molecular liquids. It is shown thatS _o-parameter is also related to volume expansivity of the surface layer of the liquid, temperature coefficient of surface tension of liquids and describes the temperature and volume or pressure dependence of thermodynamic Grüneisen parameter and isochoric heat capacity with significant contribution for influencing the thermoacoustic and surface tension properties of liquids.     

Electron transport in solids and liquids

We review our recent experimental studies of the excess electron states in insulating solids and liquids. We use a muon spin relaxation technique to explore the phenomenon of delayed muonium formation: excess electrons liberated in the μ⁺ ionization track converge upon the positive muons and form Mu (μ⁺e^?) atoms in which the μ⁺ polarization is partially lost. The spatial distribution of such electrons with respect to the muon is shown to be highly anisotropic: the μ⁺ thermalizes well “downstream” from the center of the electron distribution. Measurements in electric fields up to 30 kV/cm allow one to estimate the characteristic muon-electron distance in different insulators: the results range from 10^?6 to 10^?4 cm. Such a microscopic length scale enables the electron to sometimes spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. This circumstance illustrates the potential of μ⁺SR techniques in studies of electron transport in matter. The muonium formation process in condensed matter is shown to depend critically upon whether the excess electron forms a polaron or remains in a delocalized state. Different mechanisms of electron transport in insulators are discussed.     

Empirical equations of state for solids

A comparison of three one-parameter empirical equations of state due to Lennard-Jones, Bardeen, and Birch using Bridgman's experimental compression data shows that they do not generally fit the data within experimental error. Heuristic arguments are used to derive a well known three-parameter equation of state which includes these equations as special cases. Several simple two-parameter equations of state, including the Murnaghan equation, can be obtained as special cases of the general form. All of these two-parameter equations are shown to fit Bridgman's data within experimental error with about equal success. It is also shown that the general three-parameter equation, and hence its special cases, is consistent with the observation of Grover, Getting, and Kennedy that the log of the bulk modulus of solids is a linear function of compression. Several of the two-parameter special cases are shown to give satisfactory extrapolations.     

Elastic modulus,surface tension,adhesion, and ideal and real strengths of solids

Formulas for the surface tension coefficient, adhesion energy, elastic modulus, and strength of solids versus the atomic density have been derived. The theoretical values of these parameters have been confirmed by experimental data gathered from many metals, insulators, and semiconductors.     

Surface tension of the restrictive primitive model for ionic liquids

Hybrid molecular dynamics and Monte Carlo simulations are performed to study the liquid-vapor interface of the restricted primitive model (RPM) of ionic fluids. We report for the first time simulation results of the surface tension associated to this interface. The RPM accurately predicts experimental surface tensions of ionic salts and good agreement with theoretical predictions that include the idea of ion association is found. The simulation results indicate that the structure of an ionic liquid-vapor interface is rather rough. This is reflected in the interfacial thickness, larger than that observed in simple fluids and water.     

任意维固体的热力学性质的研究

精确地计算了n维固体的热力学函数、热容,讨论了极端高、低温近似时的结果;并将不同维数的热力学性质统一地由一组公式表达了出来.     

Experimental equations of state for the rare gas solids

Piston-displacement equations of state (EOS) for the rare gas solids neon, argon, krypton and xenon have been determined to 20 kbar at temperatures from 4.2 K to the triple point in each case, with V(P,T) relations which are believed to be accurate to roughly 0.1 per cent. The present paper describes the results for the three heavier solids, argon, krypton and xenon, and indicates consistency between these results and other low pressure experiments at all temperatures. In particular, the individual isotherms can be represented by P(V) relations which are suggested by the form of the Lennard-Jones potential, the bulk moduli are only slightly temperature dependent at constant volume, and the data for the three solids appear to obey a reduced EOS both at T = 0 and near the triple point.     

Nonlinear transport equations and invariance principles for solids

The nonlinear hydrodynamic equations of motion for simple solids are derived. They are shown to be invariant under arbitrary homogeneous displacements, rotations, and deformations of the reference lattice. This leads to transport equations that are independent of a reference state. Galilean invariance is investigated too.