Thermodynamic Limit for Polydisperse Fluids

We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice of particles. We prove that the thermodynamic limit exists with probability 1, and is independent of the choice of particles. Our proof applies to polydisperse hard-sphere fluids, colloids and ferrofluids. The existence of a thermodynamic limit implies system shape and size independence of thermodynamic properties of a system.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.     

Perturbation theory for a mixture of polarizable liquids

Thermodynamic perturbation theory developed for pure polar liquids with significant polarizability is applied to a mixture with polar and nonpolar polarizable components. Expressions for the average and unperturbed dipole moments of the components of the mixture are presented and the dipole and induced contributions to the thermodynamic functions of the mixture are calculated. The equation of state is obtained and used to calculate the excess properties of a binary mixture of particles interacting with a stockmeyer potential. It is shown that the induced dipole moments contribute significantly to the thermodynamic properties of this model solution and that their effects must be taken into account in predicting the properties of real liquid mixtures containing polar components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 69–73, March, 1985.     

Pair correlations in magnetic nanodispersed fluids

The pair distribution function of a monodisperse magnetic fluid simulated by a liquid made of dipolar hard spheres with constant magnetic moments is calculated. The anisotropy of the pair distribution function and the related structure factor of scattering in a dc uniform magnetic field are studied. The calculation is performed by diagrammatic expansion in the volume concentration of particles and the interparticle magnetic-dipole interaction intensity using a thermodynamic perturbation theory. Limitation by three-particle diagrams makes it possible to apply the results obtained to magnetic fluids with a moderate concentration. Even for low-concentration and weakly nonideal magnetic fluids, the anisotropic interparticle magnetic-dipole correlations in a magnetic field lead to the repulsion of particles in the direction normal to the field and to the formation of particle dimers along the field.     

Free energy evaluation in field-theoretic polymer simulations

We present a thermodynamic integration method for free energy evaluation in field-theoretic simulations of classical fluids and polymers. The approach employs an Einstein crystal reference state, analogous to a method developed for particle simulations of crystals by Frenkel and Ladd, but applies equally well in the present context to ordered and disordered phases. Thermodynamic averages are computed using complex Langevin sampling, which is effective against the sign problem inherent to polymer field theories. Our method is illustrated in the context of a diblock copolymer melt, where we provide a demonstration of the experimentally observed transition between the cubic gyroid and disordered phases.     

Crystal-field induced dipoles in heteropolar crystals II: Physical significance

The significance of dipole moments induced by crystal fields in heteropolar crystals is discussed with respect to some aspects of solid state physics. Experimental results from structural analyses that provide data on induced dipoles are summarized. The concept of ionic radii is reconsidered, and a new tabulation scheme is proposed in terms of deformed charge distributions. It is shown that spontaneous polarization as well as the pyro- and piezoelectric coefficients are not independent sets of crystallographic constants, but are accounted for by the structural parameters, the ionic polarizabilities and the elastic constants. The dipole concept is extended to statistically induced or random dipoles. They can account for an important part of the binding energy of substitutionally disordered and non-stoichiometric compounds and, therefore, are concluded to stabilize disorder in solids.     

Free magnetic moments in disordered metals

The screening of magnetic moments in metals, the Kondo effect, is found to be quenched with a finite probability in the presence of nonmagnetic disorder. Numerical results for a disordered electron system show that the distribution of Kondo temperatures deviates strongly from the result expected from the random matrix theory. A pronounced second peak emerges for small Kondo temperatures, showing that the probability that magnetic moments remain unscreened at low temperatures increases with disorder. Analytical calculations, taking into account the correlations between eigenfunction intensities, yield a finite width for the distribution in the thermodynamic limit. Experimental consequences for disordered mesoscopic metals are discussed. This article was submitted by the authors in English.     

Dipole-dipole minimum energy configuration for Platonic,Archimedean and Catalan solid structures

Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. In the present work, we study systems of dipoles where the particles are arranged on various types of three-dimensional structures. However, these solids are not arbitrary. They constitute the well-known Platonic, Archimedean and Catalan solids. We systematically study them in order to fill a gap in the literature that does not contemplate this interaction in the previous solids, despite the fact that they are encountered in many different physical systems. In particular, in the regime of strong dipole moments where a classical treatment is possible, we shall provide not only the minimum energy but also the precise orientations of all their dipoles. We will numerically obtain the minimum energy configuration where all vertices possess the same classic dipole, either electric or magnetic.     

Generalized Debye-Falkenhagen energy in condensed matter

The thermodynamic perturbation theory of Stell, Rasaiah and Narang is generalized to the case of multi-component Stockmayer fluids. The effects of polarization by the permanent dipoles is included to first order and the perturbation series is summed approximately to all orders in the dipole moments by means of two Padé approximants. The two-body and triplet terms in the expansion have been evaluated by Monte Carlo integration for a specific choice of the reference Lennard-Jones mixture and the results are used to study systematically the effect of dipolar interactions on excess thermodynamic properties. The utility of a one-fluid theory based on the van der Waals model is investigated and it is shown that the approach is useful for obtaining semi-quantitative information on mixtures of weakly polar fluids. The special case of mixtures of hydrogen chloride and xenon is considered and it is shown that the potential model used is inadequate to account for the large deviations from ideality which are observed for this system.     

Equation of state SAFT-CP for vapour–liquid equilibria and mutual solubility of carbon dioxide and water

ABSTRACT

The statistical associating fluid theory (SAFT) was proposed first in 1990, and has been extended to various forms for the calculation of thermodynamic properties of complex systems, such as oil reservoir fluids, polar systems, polymers, electrolytes, near-critical systems, interfacial phenomena, solids and even biomaterials. SAFT-CP (critical point) has been established for nonpolar fluids in 2001 with excellent expression of thermodynamic properties across critical points. It was extended later for polar and associating fluids with the addition of just a dipole–dipole interaction, which leads simple calculation procedure without an association term. In this article SAFT-CP is applied to carbon dioxide, water and their mixture. Vapour–liquid equilibria for pure components CO₂ and H₂O, CO₂ solubility in water and H₂O solubility in dense CO₂ are analysed. Expression of pure CO₂ properties is improved with the dipole–dipole interaction term used, while expression of pure water is a little bit improved with the non-spherical degree parameter less than 1.0. For the high asymmetry in polarity and association between CO₂ and H₂O molecules, the Stryjek–Vera combining rule is used with different temperature-dependent parameters. With the quadratic temperature-dependent parameters, the mutual solubilities in the system are calculated with good agreement with experimental ones over the wide range of temperature as 298–474 K and of pressure as 0.1–70 MPa.     

Simulation study on microstructure formations in magnetic fluids

We propose the Langevin-type microscopic equations of motion for magnetic fluids. Magnetic fluids are modeled as an ensemble of interacting ferromagnetic nanoparticles suspended in a viscous fluid. The present model is described in terms of position vectors of nanoparticles and orientation vectors of their magnetic dipole moments. In this model, forces and torques arising from the magnetic origin and the surrounding fluid flow are included. Effects of non-spherical particle shape are also taken into account. From the Brownian dynamics simulations of the model, it is found that the present model exhibits various microstructure formation processes in magnetic fluids.     

One-Dimensional Fluids with Positive Potentials

We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the thermodynamic limit of the given model.     

A theoretical study of the effect of disorder of the transition dipole moments of molecules on the shape of optical bands of molecular aggregates

Aggregates with substitutional disorder, in which molecules of different types have different transition dipole moments, are considered. The relations between the absorption spectra of aggregates with disordered and nondisordered transition dipole moments are obtained for two limiting cases: (1) the case when there is no statistical correlation between the transition energies and transition dipole moments of the molecules and (2) the case of total correlation, when the transition energies and transition dipole moments are strictly related to each other. For aggregates that are characterized by substitutional disorder along with diagonal disorder, an effective method of calculation of the optical bands is developed. Numerical calculations of the absorption bands of aggregates consisting of molecules of two types are carried out at different values of the parameters.     

Polar nano-rods under shear: From equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

Electric dipole moments: Flavor-diagonal CP violation

Searches for permanent electric dipole moments of particles, nuclei, atoms and molecules offer an extraordinary discovery potential to new mechanisms of CP violation beyond those incorporated in the standard electroweak model. The electric dipole moments induced by speculative scenarios, on different physical systems, require a complementary approach to pave the way to the fundamental CP-violating mechanisms. New avenues presently being explored in order to improve the experimental sensitivities include projects that consider the trapping of neutral particles, the confinement of charged particles in storage rings as well as the use of radioactive nuclei.     

A phenomenological theory of metastable states in disordered Ising magnets

A mechanism of the formation of an exponentially large number of metastable states in magnetic phases of disordered Ising magnets as a result of condensation of fractal delocalized modes near the localization threshold is suggested. The thermodynamic properties of metastable states are studied in the effective-field approximation in the vicinity of transitions in magnets with zero uniform magnetization in the ground state such as dilute antiferromagnets, spin glasses, and dilute ferromagnets with dipole interaction. These properties are shown to determine the parameters of nonequilibrium processes in the glassy phase, namely, the shape of the hysteresis loop, the thermodynamic values in field-cooled and zero-field-cooled regimes, and the thermoremanent and isothermal remanent magnetization values.