近独立子系系统的统计规律(四)——巨正则分布函数

根据吉布斯系综理论导出了由任意数目刚性粒子构成的力学系统的巨正则分布函数、化学势及粒子数和能量涨落公式.并介绍了刚球模型下,对二维和三维近独立子系系统巨正则分布的计算机模拟,结果与理论完全一致.     

Thermodynamics of graphene

The 21st century has brought a lot of new results related to graphene. Apparently, graphene has been characterized from all points of view except surface science and, especially, surface thermodynamics. This report aims to close this gap. Since graphene is the first real two-dimensional solid, a general formulation of the thermodynamics of two-dimensional solid bodies is given. The two-dimensional chemical potential tensor coupled with stress tensor is introduced, and fundamental equations are derived for energy, free energy, grand thermodynamic potential (in the classical and hybrid forms), enthalpy, and Gibbs energy. The fundamentals of linear boundary phenomena are formulated with explaining the concept of a dividing line, the mechanical and thermodynamic line tensions, line energy and other linear properties with necessary thermodynamic equations. The one-dimensional analogs of the Gibbs adsorption equation and Shuttleworth–Herring relation are presented. The general thermodynamic relationships are illustrated with calculations based on molecular theory. To make the reader sensible of the harmony of chemical and van der Waals forces in graphene, the remake of the classical graphite theory is presented with additional variable combinations of graphene sheets. The calculation of the line energy of graphene is exhibited including contributions both from chemical bonds and van der Waals forces (expectedly, the latter are considerably smaller than the former). The problem of graphene holes originating from migrating vacancies is discussed on the basis of the Gibbs–Curie principle. An important aspect of line tension is the planar sheet/nanotube transition where line tension acts as a driving force. Using the bending stiffness of graphene, the possible radius range is estimated for achiral (zigzag and armchair) nanotubes.     

Berthelot流体的热力学性质和参数解

研究了Berthelot流体的热力学性质.导出了单原子Berthelot流体Helmholtz自由能、熵、吉布斯函数、内能和焓;求得了Berthelot流体两相共存的的参数解,并用参数解讨论了Berthelot流体的相图和热力学量在临界点的行为及其相关性质.本文的研究为符合Berthelot流体的物质提供了热力学及其相变的解析理论.     

Characterization of the effects of nonspecific xenon-protein interactions on (129)Xe chemical shifts in aqueous solution: further development of xenon as a biomolecular probe

The sensitivity of (129)Xe chemical shifts to weak nonspecific xenon-protein interactions has suggested the use of xenon to probe biomolecular structure and interactions. The realization of this potential necessitates a further understanding of how different macromolecular properties influence the (129)Xe chemical shift in aqueous solution. Toward this goal, we have acquired (129)Xe NMR spectra of xenon dissolved in amino acid, peptide, and protein solutions under both native and denaturing conditions. In general, these cosolutes induce (129)Xe chemical shifts that are downfield relative to the shift in water, as they deshield the xenon nucleus through weak, diffusion-mediated interactions. Correlations between the extent of deshielding and molecular properties including chemical identity, structure, and charge are reported. Xenon deshielding was found to depend linearly on protein size under denaturing solution conditions; the denaturant itself has a characteristic effect on the (129)Xe chemical shift that likely results from a change in the xenon solvation shell structure. In native protein solutions, contributions to the overall (129)Xe chemical shift arise from the presence of weak xenon binding either in cavities or at the protein surface. Potential applications of xenon as a probe of biological systems including the detection of conformational changes and the possible quantification of buried surface area at protein-protein interfaces are discussed.     

Formal analytical solutions for the Gross-Pitaevskii equation

Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter Φ(x) and for the chemical potential μ as a function of a unique dimensionless non-linear parameter Λ. We report solutions for different ranges of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of Λ. Introducing an accumulated error function we have performed a quantitative analysis with respect to other well-established methods as: the perturbation theory, the Thomas-Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the Λ-values where each solution can be easily implemented. In particular, we showed that for Λ<−9, the bright soliton function reproduces the exact solution of GPE wave function.     

EOS for a QGP with a temperature and baryon chemical potential dependent bag pressure

We develop an equation of state (EOS) for the quark-gluon plasma (QGP) involving the temperature and baryon chemical potential dependent bag pressure arising due to the entropy and baryon number conservation at the phase boundary together with the Gibbs’ construction for an equilibrium phase transition. We show that the bag pressure thus obtained yields a decreasing behaviour with the increasing baryon chemical potential at a fixed temperature. Further consequences of the modified bag pressure are discussed.     

Mixed state in a superlattice

Presented in this paper is a theoretical calculation of the vortex solution in a chosen superlattice (Nb/NbZr) using the Gibbs free energy of an inhomogeneous superconductor. The eigenvalue obtained in this geometry from de Gennes-Werthamer proximity coupling theory is first examined according to a set of experimental data, while the correspondent eigenfunctions are then used to construct vortex solutions with either square lattice or triangle lattice symmetry. The Gibbs free energy is calculated in terms of the vortex solutions of both symmetries. The effective Ginzburg-Landau parameter,K _NS , for this superlattice is determined asK _NS =0.218 by requiring a consistency between the microscopic and macroscopic theoretical calculations. Of particular importance is a new mechanism revealed by this calculation that a highly localized state of superconducting condensate in its hosting layer, despite the spatially rapid varying characteristic of its correspondent nucleating order parameter, provides a lower eigenvalue state, which results in a dimensional crossover. A further examination of this mechanism is carried out in the mixed state calculation. Finally, a generalization of the present theoretical results to a large class of superlatices is discussed.     

Coupling of the phase-field and CALPHAD methods for predicting multicomponent,solid-state phase transformations

The development of an effective microstructure design method for multicomponent alloys is of considerable importance for improving both the design of alloys and the design of processes for producing alloys with unique properties. The coupling of the phase-field method and the calculation of phase diagrams (CALPHAD) method can be used for predicting the evolution of microstructures in multicomponent alloys. Such predictions make use of CALPHAD thermodynamic information with the chemical free energy function in the phase-field method. This article reviews several of these coupling methods, focusing on solid-state phase transformations in multicomponent systems, such as phase separation and disordered or ordered phase precipitation from a matrix. When calculating disordered phase transformations, the Gibbs energy function derived from the CALPHAD database can be used directly in the phase-field method. On the other hand, when dealing with an order/disorder transition, the degrees of freedom of the element site fraction for an ordered phase in the CALPHAD method can be reduced using the Gibbs energy single formalism for constituent phases, by using a database that stores the Gibbs energy and chemical equilibrium conditions, or by obtaining the driving force calculated using the Thermo-Calc software. The current status and future directions for further development of these coupled methods are discussed.     

Steady state solutions of master equations without detailed balance

Steady state solutions of master equations with one variable are constructed. The method of solution is based on a transformation of the original equation for the probability into one for a slowly varying function. The method is of general applicability and is particularly useful in obtaining solutions in the case where detailed balance does not hold. Examples of such systems in chemical reaction models and the two photon laser are discussed.On leave from the University of Waikato, Hamilton, New Zealand     

Cosmological string solutions in 4 dimensions from 5d black holes

We obtain cosmological four dimensional solutions of the low energy effective string theory by reducing a five dimensional black hole, and black hole-de Sitter solution of Einstein gravity down to four dimensions. The appearance of a cosmological constant in the five dimensional Einstein-Hilbert action produces special dilation potential in the four dimensional effective string action. Cosmological scenarios implemented by our solutions are discussed.     

Attainable superheating of solutions of cryogenic liquids

The kinetics of spontaneous boiling-up of superheated binary solutions of cryogenic liquids is studied. Within the framework of the Kramers-Zeldovich method, an expression is obtained for the steady state rate of homogeneous nucleation in a solution that takes into account free-molecular and diffusion regimes of the substance supply to a growing bubble. Viscous and inertial forces are also taken into account in the study of the nucleus growth dynamics. The work of critical nucleus formation is determined within the framework of the Gibbs and van der Waals capillarity theories. The dependence of the surface tension of critical bubbles in the solution on their size is investigated. The temperature of attainable superheating and nucleation rates in superheated solutions of cryogenic liquids with complete or partial solubility of the components are determined by a method of lifetime measurement. The experiments were conducted in a wide range of pressures and solution concentrations. The measurement results are compared with the theory of homogeneous nucleation taking or not taking into account the size effect in nucleation. It has been found that, by taking into account the size dependence of the surface tension of a nucleus, better agreement between the theory and experiment is obtained. The boundary of essential instability of the solution, that is, the diffusion spinodal, is computed.     

Application of the time dependent finite difference theory to the study of sound and vibration interactions in ducts

The time dependent finite difference theory is extended to the solution of the acoustic wave equation in rectangular ducts when acoustic/structural interactions are allowed at a duct wall. The treatment of the boundary condition which describes the coupling is examined, and the stability of the procedure is studied and found to depend on the nature of this coupling. The convergence of solutions is discussed as a function of the discretization of the solution domain, particularly at frequencies approaching resonance.     

The critical state and its thermodynamic stability

The Gibbs approach to study of the critical state is expanded. It is noted that the well known critical state condition D=0 was obtained by Gibbs as a necessary condition for a non-zero solution of a system of homogeneous linear equations and defines a line of spinoidal solutions. To determine the critical point on this line the explicit form of solutions of a system of homogeneous equations is considered and their relationship to the slope of the phase equilibrium line is established. For the condition D=0 four possible cases of critical system thermodynamic behavior are considered. The relationship between each of these cases and the slope of the phase equilibrium line at the critical point is established. General thermodynamic stability conditions for the critical point are considered as a function of the type of critical behavior at the point. It is shown that one of the consequences of critical point stability is a merger of the binodal line with the spinodal at the critical point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 93–98, June, 1988.     

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)⁴ . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Holographic magnetized chiral density wave

We explore the end point of the helical instability in a finite density, finite magnetic field background discussed by Kharzeev and Yee. The nonlinear solution is obtained and identified with the(magnetized) chiral density wave phase in the literature. We find there are two branches of solutions, which match the two unstable modes found before. At large chemical potential and magnetic field, the magnetized chiral density wave can be thermodynamically preferred over the chirally symmetric phase and chiral symmetry breaking phase. Interestingly, we find an exotic state with vanishing chemical potential at large magnetic field. We also attempt to clarify the role of anomalous charge in the holographic model.     

Non-Riemannian geometry of macroscopic spin distributions

The non-Riemannian geometry of macroscopic spin distributions in thermodynamics and ferromagnetism is obtained from the respective partition functions. An expression for the Cartan torsion in terms of the chemical potential is obtained. Analogies with the Einstein-Cartan theory of gravitation are discussed. From the partition function of ferromagnetism a spin-torsion relation analogous to the one obtained in Einstein-Cartan theory is given where piezomagnetic effects are taken into account.     

Benzotriazole as an inhibitor of brass corrosion in chloride solution

The current research explores the formation of protective layers on copper, zinc and copper-zinc (Cu-10Zn and Cu-40Zn) alloys in chloride solution containing benzotriazole (BTAH), by use of electrochemical techniques, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). Electrochemical reactions and surface products formed at the open circuit potential and as a function of the potential range are discussed. The addition of benzotriazole to aerated, near neutral 0.5 M NaCl solution affects the dissolution of copper, zinc, Cu-10Zn and Cu-40Zn alloys. The research also compares the inhibition efficiency and Gibbs adsorption energies of the investigated process. Benzotriazole, generally known as an inhibitor of copper corrosion is also shown to be an efficient inhibitor for copper-zinc alloys and zinc metal. The surface layer formed on alloys in BTAH-inhibited solution comprised both oxide and polymer components, namely Cu₂O and ZnO oxides, and Cu(I)-BTA and Zn(II)-BTA polymers. The formation of this mixed copper-zinc oxide polymer surface film provides an effective barrier against corrosion of both metal components in chloride solution.     

Thermodynamic analysis of lithium ion cells

The thermodynamics of ideal and non-ideal solutions has been applied to the electrochemically active lithium-based positive electrode to provide insight into the electrostatic potential as a function of the state-of-discharge. The Nernst and the Margules expressions are incorporated in the derivation for the electrostatic potential expression using the total Gibbs free energy equation. The resulting expression is applied to a lithium cell in order to study its discharge profile. These predicted results are compared with established results from the literature and a comparison is performed to validate the agreement between the predicted and the published results. Paper presented at the International Conference on Functional Materials and Devices 2005, Kuala Lumpur, Malaysia, June 6 – 8, 2005.