Thermodynamic anomalies

Since there is no reason to suspect that ol Ix) exhibits any anomalies up to and, in the thermodynamic limit, at the yield point, is a finite... 

It should be mentioned that in the last few years super-cooled water has attracted the interest of many scientists because of its exceeding properties and life at temperatures below 0 °C 1819). Speedy recently published a model which allows for the interpretation of the thermodynamic anomalies of supercooled water 20). According to this model there are hydrogen bonded pentagonal rings of water molecules which have the quality of self-replication and association with cavities. 

No matter which of the electrophilic methods of double-bond shifting is employed, the thermodynamically most stable alkene is usually formed in the largest amount in most cases, though a few anomalies are known. However, there is another, indirect, method of double-bond isomerization, by means of which migration in the other direction can often be carried out. This involves conversion of the alkene to a borane (15-16), rearrangement of the borane (18-11), oxidation and hydrolysis of the newly formed borane to the alcohol (12-28), and dehydration of the alcohol (17-1) ... 

In order to explain the above-mentioned anomalies an original model of the m-component copolymerization has been put forward [48], taking into account chemical factors along with the also thermodynamic ones. It is pertinent to dwell briefly on the key points of this model. 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

Figure 5 Relationship among loci of structural, dynamic, and thermodynamic anomalies in SPC/E water. The structurally anomalous region is bounded by the loci of q maxima (upward-pointing triangles) and t minima (downward-pointing triangles). Inside of this region, water becomes more disordered when compressed. The loci of diffusivity minima (circles) and maxima (diamonds) define the region of dynamic anomalies, where self-diffusivity increases with density. Inside of the thermodynamically anomalous region (squares), the density increases when water is heated at constant pressure. Reprinted with permission from Ref. 29.

Several anomalies in the LS determinations of molecular weight have been attributed to the presence of a stable supramolecular structure, which can persist even in thermodynamically good solvents104. Examples have been reported for solutions of... 

However, AS = — 90.4 J mol for this system. As the change occurs even though AS is negative, this reaction apparently violates the second law of thermodynamics. How do you explain this anomaly in terms of the second law ... 

Salje E. (1988). Structural phase transitions and specific heat anomalies. In Physical Properties and Thermodynamic Behaviour of Minerals, E. K. H. Salje, ed. Reidel Pnblishing Company. 

Not surprisingly, the enthalpy of reaction for cyclopropyhnagnesium bromide, —282.8 kJmol , is somewhat of an outlier, given the numerous anomalies associated with this small ring . For example, cyclopropane is the most olefinic and most acidic of the cycloalkanes—which correctly suggests that cyclopropyl forms the most polar C—Mg bond and, accordingly, is the thermodynamically most stable cycloalkylmagnesium species. 

This paper shows that the conditions of thermodynamic equilibrium in a mix-tine of chemically reacting ideal gases always have a solution for the concentrations of the mixture components and that this solution is unique. The paper has acquired special significance in the last few years in connection with the intensive study of systems in which this uniqueness does not occur. Such anomalies may be related either to nonideal components, or to treatment of stationary states, rather than truly equilibrium ones, in which the system exchanges matter or energy with the surrounding medium. 

This chapter deals with critical phenomena in simple ionic fluids. Prototypical ionic fluids, in the sense considered here, are molten salts and electrolyte solutions. Ionic states occur, however, in many other systems as well we quote, for example, metallic fluids or solutions of complex particles such as charged macromolecules, colloids, or micelles. Although for simple atomic and molecular fluids thermodynamic anomalies near critical points have been extensively studied for a century now [1], for a long time the work on ionic fluids remained scarce [2, 3]. Reviewing the rudimentary information available in 1990, Pitzer [4] noted fundamental differences in critical behavior between ionic and nonionic fluids. 

Perhaps a more decisive discrimination between Ising and mean-field behavior could be provided by the investigation of weak anomalies [6] as predicted for the specific heat. Such weak anomalies are absent in the mean-field case (cf. Table I). Except for the diameter anomalies already mentioned, no thermodynamic investigations of weak anomalies were reported so far. However, dynamical properties such as the shear viscosity and electrical conductance may show weak anomalies as well. 

Tmskett and Dill (2002) proposed a two-dimensional water-like model to interpret the thermodynamics of supercooled water. This model is consistent with model (1) for liquid water. Cage-like and dense fluid configurations correspond to transient structured and unstructured regions, observed in molecular simulations of water (Errington and Debenedetti, 2001). Truskett and Dill s model provides a microscopic theory for the global phase behavior of water, which predicts the liquid-phase anomalies and expansion upon freezing. 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

Thermodynamic (specific-heat) and transport (resisitivity) studies for the U(Pti xPdx)3 compounds have revealed magnetic transitions for x-values of 0.02 and higher, in contrast to the compounds below x = 0.01 that did not show anomalies in specific heat and resistivity that point to magnetic order. The sharpest transition in the specific heat studies is found for x = 0.05. For this compound, the resistivity v.v temperature curve exhibits a Cr-type of anomaly just below the magnetic ordering temperature suggesting the presence of a spin-density wave below TN. A few results from neutron diffraction studies are shown in fig. 6. 

These phenomena that were previously considered anomalies of the mentioned colligative properties of the solutions, have been dealt with by Arrhenius in his effort to explain such anomalies by his well known theory of electrolytic dissociation. According to this explanation the molecules of a dissolved electrolyte partly split to form smaller particles, i. e. ions, which from the thermodynamic point of view are as effective as the undissociated molecules themselves. As the number of particles of matter is thus greater, the manifestations of colligative properties are increased, compared to what they would be with an undissociated electrolyte. 

The anomalies pointed out above, including compensation effects, may be accounted for in general bases of the assumption that the chemical elementary steps on the enzyme are accompanied by the arrangement of the conformational structure of protein globules and surrounding water molecules. The kinetic and thermodynamic parameters of such structural rearrangements make a contribution to the experimentally measured and whose reflect cooperative properties of the water-protein matrix. 

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