Improved corresponding states principle for the noble gases

This paper contains the background for a complete synthesis of all the properties-equilibrium as well as transport—of the five noble gases and of the 26 mixtures that can be formed with them. The synthesis is valid for the zero-density limit only, but covers the temperature range from absolute zero to the onset of ionization.The synthesis is based on a thorough revision of the two-parameter extended law of corresponding states of Kestin, Ro and Wakeham. The paper recalls the basis for the original corresponding-states principle, identifies the places at which experiment and the theory of statistical mechanics suggest deviations, and proceeds to remove them to a point where almost perfect agreement between calculation and a very large body of diverse experimental data is achieved, in the sense that deviations of experimental data from calculation are of the same order as the uncertainty in the best contemporary measurements.The basis of the revised corresponding-states principle is a set of five parameters which characterize each pair-interaction together with a fully consistent and asymptotically correct set of universal collision integrals and functionals that appear in the rigorous theory. These are reinforced with selected quantum-mechanical calculations applied in regions where they are significant.     

Thermodynamic properties and self-diffusion coefficients of simple liquids

Pair distribution functions and thermodynamic properties for a system of 108 particles interacting with a hard-sphere modified Lennard-Jones (12, 6) potential have been calculated by the Monte Carlo technique for a range of reduced liquid densities and two reduced temperatures. It is shown that the introduction of a hard core significantly modifies the Lennard-Jones parameters for the noble gases. The friction coefficients proposed in the transport theories of Rice and Allnatt and of Palyvos and Davis have been calculated using the exact pair distribution functions. In the normal liquid range, contributions to the frictional force on a particle arising from hard sphere collisions and quasi-Brownian motion are shown always to be comparable. This result is contrary to the conditions under which the principal assumption of Brownian theory is applicable.     

利用量子对应态原理预测氦-3 p-v-T性质

利用量子对应态原理与Ne,4He的实验数据预测了3He的p-v-T性质。结果表明,在12-20K温区内,压力的计算值与Gibbons实验数据的平均相对误差是2.008%,最大误差是9.131%;在20-60K温区内,压力的计算值与Gibbons实验数据的平均相对误差是1.692%,最大误差是2.276%。获得了比较满意的预测结果。     

Perturbation theory and the excess properties of mixtures of simple liquids

One of the most successful theories of single-component simple liquids is perturbation theory which is based on the assumption that the structure of a liquid is primarily determined by the repulsive forces between its molecules, so that a liquid may be regarded as a system of hard spheres with the attractive forces providing a uniform background energy. Our earlier extension of these ideas to liquid mixtures was only partially successful. In this paper we show that this problem was due to the use of a somewhat unsatisfactory equation of state for the reference hard-sphere mixture. If a more satisfactory equation of state is used, perturbation theory yields results in close agreement with Monte Carlo and experimental results, even when the molecules of the mixture differ appreciably in size.     

Is the thermodynamic behavior of the noble fluids consistent with the principle of corresponding states?

The applicability of the Principle of Corresponding States (PCS) for the noble fluids is discussed. We give the thermodynamic evidence for the dimerization of the liquid phase in heavy noble gases like argon, krypton etc. which manifests itself in deviations from the PCS. The behavior of the diameter of the entropy and the density is analyzed. It is shown that these characteristics are very sensitive to the dimerization process which takes place in the liquid phase of heavy noble gases.     

The dynamic stabilization of the Rayleigh-Taylor instability and the corresponding dynamic equilibrium

Conditions are derived for dynamically stabilizing the Rayleigh-Taylor instability of a fluid interface and for attaining the corresponding dynamic equilibrium. These conditions could be proved in experiments using an aqueous solution of Potassium Jodide (ρ _h=1.6 g/cm³) as the heavy fluid and oil (viscosity SAE 140,ρ _ι =0.9 g/cm³) as the light one. Parametric resonances were suppressed, but could be observed using oil of lower viscosity.     

On the law of corresponding states for thermodynamic properties of a crystal

To study thermodynamic similarity of the properties of crystalline substances, we propose an approach connected with engaging of the metastable state region. Internal pressure and specific volume on the crystal’s stability boundary at T = 0 K are used as characteristic scales of thermodynamic variables. A semiempirical method of calculation of the stability boundary by the thermodynamic data related to the stable states region of a solid body is described. In the cases of argon and natrium, the stability boundary is calculated for a wide range of temperatures and pressures. Analysis of the properties of neon, argon, krypton, and xenon crystals in these variables indicates that the law of corresponding states holds for these substances.     

The extended law of corresponding states and the interaction potential

An inversion procedure is used to obtain from the extended law of corresponding states the interaction potential over a range of reduced temperature extending from 0.5 to 25. This directly determined potential is in excellent agreement with the Lee potentials in the intermediate region. The consistency between diffusion coefficients and second virial coefficients is checked.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Structure and dynamic properties of liquids confined in MCM-41 mesopores

The microscopic structure and dynamic properties of water, methanol, and acetonitrile confined in mesoporous MCM-41 materials have been investigated under monolayer and capillary-condensation conditions as a function of pore size and temperature by in situ FTIR and X-ray diffraction and quasi-elastic neutron scattering techniques. Both interfacial and confinement effects on the structure and dynamics of the liquids in hydrophilic pores are discussed at the molecular level.     

The influence of temperature and dynamic quenching on the properties of 3-hydroxyflavone excited states

The influence of temperature and dynamic quenching on the properties of excited states of the normal and tautomeric 3-hydoxyflavone forms was studied. The stationary two-band fluorescence spectra of this luminophore in acetonitrile were recorded and analyzed. The spectra were observed under excitation by electromagnetic radiation in the region of the S ₁ absorption band over the temperature range 20–80°C. TEMPO was used as a quencher of the excited state. Heating caused temperature quenching of luminescence, and the tautomer formed via the excited state of the normal form of the luminophore was quenched more strongly both in pure solvent and in the presence of the quencher. An analysis of two-band fluorescence parameters led us to conclude that solution heating over the temperature range studied increased the rate of proton transfer by 1.25 times. The introduction of the quencher also accelerated proton transfer by 1.16–1.25 times as the temperature increased from room temperature to 80°C.     

Thermodynamic properties of some ionic liquids using a simple equation of state

In this work, we have used a simple equation of state (EoS) to predict the density and other thermodynamic properties such as isobaric expansion coefficient, α_P , isothermal compressibility, κ_T, and internal pressure, P_i, for nine ionic liquids including trihexyl (tetradecyl) phosphonium chloride ([(C₆H₁₃)₃P(C₁₄H₂₉)][Cl]), trihexyl (tetradecyl) phosphonium acetate ([(C₆H₁₃)₃P(C₁₄H₂₉)][Ac]), trihexyl (tetradecyl) phosphonium bis {(trifluoromethyl) sulfonyl} amide ([(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂]), 1-butyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([bmim][NTf₂]), 1-hexyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([hmim][NTf₂]), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF₄]), 1-butyl-3-octylimidazolium tetrafluoroborate ([omim][BF₄]), 1-butyl-3-octylimidazolium hexafluorophosphate ([omim][PF₆]), and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF₆]) at different temperatures and pressures. A wide comparison with experimental and literature data has been made. The results show that this EoS can be used to reproduce and predict different thermodynamic properties of ionic liquids within experimental errors.     

A duality principle corresponding to the parabolic equations

Our principal problem consists in finding threshold values for a family of blow-up solutions of nonlinear evolution problems depending on a real parameter λ. We seek to obtain the solution of the problem in a constructive and unified approach which would provide the answer for the following general question: Is there is a constructive method for finding the threshold values? We illustrate our approach by means of an example of finding a threshold value for a family of parabolic equations with nonlinearity indefinite in sign. In the main result, the threshold value is expressed via explicitly specified dual variational principles of a new type.     

Equilibrium theories of simple liquids

In this article, the theory of equilibrium properties of simple classical fluids is reviewed. The various relationships between the pair potential φ(r) and the pair correlation function g(r) are explored, from the usual integral equations and the perturbation theories to the generalized random phase approximation proposed recently. Particular attention is devoted to the extraction of the intermolecular forces from a given experimental data on the structure and thermodynamics of fluids. In particular, the propagation of errors in these calculations arising due to uncertainties in the input data is discussed. Finally, the recent use of BGY integral equation and the vacancy-cell model in the study of solid-liquid transition and melting is discussed.     

The green function technique and the Pauli principle in intermediate states

Arguments are presented to demonstrate that in calculating higher-order transition amplitudes by the Green function technique, terms due to occupied intermediate levels need not be subtracted. The inclusion of spurious contributions exactly compensates for ignoring core excitations.     

Mode-coupling approach to the dynamics of simple liquids

Summary A new derivation of the mode-coupling theory of liquid dynamics is presented which is applicable to both quantum and classical systems. A clear distinction between the basic underlying hyphotheses and the more technical approximations has been attempted. Asymptotic corrections to the dynamics of modes due to mode-coupling effects and selfconsistent mode-coupling theories emerge from the original idea as two markedly different branches of application. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.