One-dimensional α-MnO2: Trapping chemistry of tunnel structures, structural stability, and magnetic transitions

Highly crystalline one-dimensional (1D) α-MnO₂ nanostructures were synthesized by a hydrothermal method. All samples were characterized by X-ray diffraction, transmission electron microscope, thermogravimetric and differential scanning calorimeter, and infrared spectroscopy. During the formation reactions, the tunnel structure of 1D α-MnO₂ was simultaneously modified by NH₄⁺ species and water molecules. The amount of NH₄⁺ species that were trapped in the tunnels is almost independent on the reaction temperature, while the total water content increased with the reaction temperature. The average diameter of α-MnO₂ nanorods increased from 9.2 to 16.5 nm when the reaction temperature increased from 140 to 220 °C. 1D α-MnO₂ was destabilized by a subsequent high-temperature treatment in air, which is accompanied by a structural transformation to 1D Mn₂O₃ of a cubic structure. At low temperatures, all 1D α-MnO₂ nanorods showed two magnetic transitions that were characterized by a decreased Néel temperature with rod diameter reduction. According to the effective magnetic moments experimentally measured, Mn ions presented in the nanorods were determined to be in a mixed valency of high spin state Mn⁴⁺/Mn³⁺.     

Interface interactions in modulated phases,and upsilon points

Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where =0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Finite-size scaling study of a first-order temperature-driven symmetry-breaking structural phase transition

We present a study of finite-size effects in a model exhibiting a first-order temperature-driven symmetry-breaking structural phase transition in theL × cylindrical geometry in theL limit. Exact studies demonstrate the applicability of our scaling ansatz even in the one-dimensional limit, making this model ideal for studying finite-size effects. The scaling ansatz, similar to the previously developed ansatz for field-driven transitions, demonstrates that latent heat is crucial in driving these transitions. This ansatz is supported by a 2×2 phenomenological transfer matrix based upon the symmetries of the system; this produces an analytic free energy which has the scaling form. Order parameter probability distributions show that the high- and low-temperature phases coexist only in a small finite-size-affected regime near the bulk transition temperature; this regime vanishes exponentially fast asL diverges.     

Applications of Thermal Analysis and Coupled Techniques in Pharmaceutical Industry

Thermal analysis methods are well-established techniques in research laboratories of pharmaceutical industry. The robustness and sensitivity of instrumentation, the introduction of automation and of reliable software according to the industrial needs widened considerably the areas of applications in the last decade. Calibration of instruments and validation of results follow the state of the art of cGMP as for other analytical techniques. Thermal analysis techniques are especially useful for the study of the behavior of the poly-phasic systems drug substances and excipients and find a unique place for new delivery systems. Since change of temperature and moisture occur by processing and storage, changes of the solid state may have a considerable effect on activity, toxicity and stability of compounds. Current requirements of the International Conference of Harmonisation for the characterization and the quantitation of polymorphism in new entities re-enforce the position of thermal analysis techniques. This challenging task needs the use of complementary methods. Combined techniques and microcalorimetry demonstrate their advantages. This article reviews the current use of thermal analysis and combined techniques in research and development and in production. The advantage of commercially coupled techniques to thermogravimetry is emphasized with some examples. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

One-dimensional model with rotational and liquid-crystalline phase transitions

A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water.     

Synthesis and Characterization of Titanium-doped Ordered Mesoporous Alumina

Titanium-doped ordered mesoporous alumina with specific structural properties has been prepared by the evaporation induced self-assembly sol-gel method. The results show that the doped titanium helps to stabilize the ordered mesoporous alumina material without influencing the ordered mesoporosity. The textural properties of the obtained sample are related to the amount of doped titanium. When the molar ratio of aluminum to titanium(n(Al)/n(Ti)) is controlled as 10.2, the titanium-doped ordered mesoporous alumina exhibits high surface area(up to 218 m2 g-1), large pore volume(0.42 cm3 g-1) and narrow pore diameter(6.1 nm) after treating at 900 ℃, showing high thermal stability. Moreover, the obtained sample calcined at 900 ℃ still maintains ordered mesoporous structure and exhibits high thermal stability.     

Representation invariant Geometrothermodynamics: Applications to ordinary thermodynamic systems

In this work we employ a recently devised metric within the Geometrothermodynamics program to study ordinary thermodynamic systems. The new feature of this metric is that, in addition to Legendre symmetry, it exhibits invariance under a change of representation. This metric was derived in a previous work by the authors while addressing the problem of the conformal structure of the thermodynamic metrics for different representations. Here, we present a thorough analysis for the ideal gas, the van der Waals fluid, the one dimensional Ising model and some other systems of cosmological interest.