Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion

In the Laser-Induced Breakdown Spectroscopy (LIBS) technique, the existence of Local Thermodynamic Equilibrium (LTE) is the essential requisite for meaningful application of theoretical Boltzmann–Maxwell and Saha–Eggert expressions that relate fundamental plasma parameters and concentration of analyte species. The most popular criterion reported in the literature dealing with plasma diagnostics, and usually invoked as a proof of the existence of LTE in the plasma, is the McWhirter criterion [R.W.P. McWhirter, in: Eds. R.H. Huddlestone, S.L. Leonard, Plasma Diagnostic Techniques, Academic Press, New York, 1965, pp. 201–264]. However, as pointed out in several papers, this criterion is known to be a necessary but not a sufficient condition to insure LTE. The considerations reported here are meant to briefly review the theoretical analysis underlying the concept of thermodynamic equilibrium and the derivation of the McWhirter criterion, and to critically discuss its application to a transient and non-homogeneous plasma, like that created by a laser pulse on solid targets. Specific examples are given of theoretical expressions involving relaxation times and diffusion coefficients, as well as a discussion of different experimental approaches involving space and time-resolved measurements that could be used to complement a positive result of the calculation of the minimum electron number density required for LTE using the McWhirter formula. It is argued that these approaches will allow a more complete assessment of the existence of LTE and therefore permit a better quantitative result. It is suggested that the mere use of the McWhirter criterion to assess the existence of LTE in laser-induced plasmas should be discontinued.     

Equilibrium of ion-exchange polymeric membrane with aqueous salt solution and its thermodynamic modeling

A thermodynamic model is proposed to describe distribution of the components between a liquid solution and a swollen membrane undergoing structural transformations. Free energy contributions related to formation of solution-filled micro-cavities in the membrane interior are estimated. Formation of the cavities of different shape is accounted for by using the Helfrich expressions for the bending energy of a curved interface. Three adjustable parameters of the model are related to the hydrophobic polymer matrix of the membrane, while the electrostatic contribution is estimated explicitly. Structural changes in the membrane are described as a transition from spherical to cylindrical cavities. Predominance of cavities having definite shape (spheres, cylinders) results in a specific shift of the Donnan equilibrium, which thus, becomes dependent on the structure of the membrane on the mesoscale. The results of model calculations are compared with the experimental data on the distribution of ions (H⁺, Li⁺, Cs⁺, K⁺, Na⁺, Ca²⁺, Mg²⁺) between the aqueous solution and the membrane. Different types of predicted thermodynamic behavior of the membrane in the liquid solution, including the hysteresis of ion-exchange equilibrium curves, are discussed. The model takes into account the effect of micro-inhomogeneties and helps to establish a link between molecular characteristics of the perfluoropolymer membrane and its macroscopic behavior in the liquid solution.     

Multiperiodic multifractal martingale measures

A nonnegative 1-periodic multifractal measure on is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points.     

铁磁晶体热力学性质的稳定性分析

对铁磁晶体自旋自洽条件用斜率比较法分析发现,整个铁磁晶体系统无论有无外场的作用,只有三种可能的热力学状态.采用重正化群的分析方法分析发现,其中有一种是不稳定的,处于相变临界状态,稍有微小干扰,即可发生状态的变化,其变化的方向取决于微扰的初始条件.系统的另外两种状态是稳定状态.在没有其他强烈的相反干扰时,此状态将永远保持下去.     

Macroscale and microscale evolutions of mechanically alloyed FeZn systems

The present work aims to correlate, in time, macroscale and microscale phenomenological evolutions of the microstructure of Fe and FeZn alloys processed by mechanical milling (MM) and alloying (MA), respectively. Powders were characterized for particle size distribution (PSD), particle morphology (optical microscopy, OM, scanning electron microscopy, SEM), microhardness, crystallite size, differential scanning calometry (DSC) and transmission electron microscopy (TEM). Two macroscopic regimes of PSD behavior were distinguished: the first one dominated by the cold welding process; and, the other where both fracture and agglomeration play a significant role. Solid solubilization of Zn on bcc Fe was found to reduce the final microhardness as well as increase the lattice parameter and is very well predicted by Miedema's thermodynamical approach. Microhardness and solid solution formation kinetics were correlated in time and both could be precisely described by a logistic function. After 5 h of planetary milling, microhardness and the lattice parameter become stable as well as the PSD and particle morphology, indicating that the system has already reached steady state. Indeed, this condition can be monitored by both macroscopic and microscopic parameters. Prior to an homogeneous powder, DSC results suggest an endothermic solid-state amorphization reaction for samples processed for up to 1 h as a result of the formation of clean Fe/Zn interfaces during MA.     

Heat capacity and thermodynamic functions of nano-TiO2 rutile in relation to bulk-TiO2 rutile

Several conflicting reports have suggested that the thermodynamic properties of materials change with respect to particle size. To investigate this, we have measured the constant pressure heat capacities of three 7 nm TiO₂ rutile samples containing varying amounts of surface-adsorbed water using a combination of adiabatic and semi-adiabatic calorimetric methods. These samples have a high degree of chemical, phase, and size purity determined by rigorous characterization. Molar heat capacities were measured from T = (0.5 to 320) K, and data were fitted to a sum of theoretical functions in the low temperature (T < 15 K) range, orthogonal polynomials in the mid temperature range (10 > T/K > 75), and a combination of Debye and Einstein functions in the high temperature range (T > 35 K). These fits were used to generate $\mathit{Cp}\text{,}{\text{m}}^{\circ }$, ${\mathrm{\Delta }}_0^{\text{T}}{S}_{\text{m}}^{\circ }$, ${\mathrm{\Delta }}_0^{\text{T}}{H}_{\text{m}}^{\circ }$, and ${\phi }_{\text{m}}^{\circ }$ values at selected temperatures between (0.5 and 300) K for all samples. Standard molar entropies at T = 298.15 K were calculated to be (62.066, 59.422, and 58.035) J · K⁻¹ · mol⁻¹ all with a standard uncertainty of 0.002·${\mathrm{\Delta }}_0^{\text{T}}{S}_{\text{m}}^{\circ }$ for samples TiO₂·0.361H₂O, TiO₂·0.296H₂O, and TiO₂·0.244H₂O, respectively. These and other thermodynamic values were then corrected for water content to yield bare nano-TiO₂ thermodynamic properties at T = 298.15 K, and we show that the resultant thermodynamic properties of anhydrous TiO₂ rutile nanoparticles equal those of bulk TiO₂ rutile within experimental uncertainty. Thus we show quantitatively that the difference in thermodynamic properties between bulk and nano-TiO₂ must be attributed to surface adsorbed water.     

Experimental investigation on the dissociation conditions of methane hydrate in the presence of imidazolium-based ionic liquids

In this work, the performance of nine ionic liquids (ILs) as thermodynamic hydrate inhibitors is investigated. The dissociation temperature is determined for methane gas hydrates using a high pressure micro deferential scanning calorimeter between (3.6 and 11.2) MPa. All the aqueous IL solutions are studied at a mass fraction of 0.10. The performance of the two best ILs is further investigated at various concentrations. Electrical conductivity and pH of these aqueous IL solutions (0.10 mass fraction) are also measured. The enthalpy of gas hydrate dissociation is calculated by the Clausius–Clapeyron equation. It is found that the ILs shift the methane hydrate (liquid + vapour) equilibrium curve (HLVE) to lower temperature and higher pressure. Our results indicate 1-(2-hydroxyethyl) 3-methylimidazolium chloride is the best among the ILs studied as a thermodynamic hydrate inhibitor. A statistical analysis reveals there is a moderate correlation between electrical conductivity and the efficiency of the IL as a gas hydrate inhibitor. The average enthalpies of methane hydrate dissociation in the presence of these ILs are found to be in the range of (57.0 to 59.1) kJ ⋅ mol⁻¹. There is no significant difference between the dissociation enthalpy of methane hydrate either in the presence or in absence of ILs.