Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Thermal Studies on Ionic Derivatives of Hafnium(IV) Involving Maltol Ligand

A number of ionic chelate complexes of maltol(A) and hafnium(IV) the type[(η₅−C₅H₅)₂HfL]⁺[MCl3]⁻ (B) [HL=maltol; M=Zn(II), Cd(II), Hg(II), Cu(II)]have been synthesized and characterized by spectral studies (IR, UV, ¹H NMR and ¹³C NMR). The stoichiometry of the complexes has been confirmed by conductance measurements. Thermogravimetric (TG) and differential thermal analytical (DTA) studies have been carried out for these complexes and from TG curves, the order, apparent activation energy and apparent activation entropy of the thermal decomposition reactions have been elucidated .The order in each case has been determined to be one and the degree of spontaneity and lability have been inferred from the apparent activation energy and entropy, respectively. Thermal parameters have been correlated with some structural aspects of the complexes concerned. From differential thermal analysis curves, the heat of reaction has been calculated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hydration heat capacities of hydrophobic solutes at 248–373 K

A new equation is suggested to define the temperature dependence of the Gibbs energy of hydration of hydrophobic substances: ΔG ⁰ = b ₀ + b ₁ T + b ₂lnT. According to this equation, the hydration heat capacity is in inverse proportion to temperature. Consistent values of hydration heat capacity of nonpolar solutes have been obtained for different temperatures using data on solubility and dissolution enthalpy. The contributions of the hydrocarbon radicals and OH group to the heat capacity of hydration of the compounds were found for the temperature range 248–373 K. The hydration heat capacity of the hydroxyl group has a weak dependence on temperature and increases by only 12 J/(mol·K) in the specified temperature interval. Changes in the hydration entropy of hydrophobic and OH groups are calculated for the temperature increasing from 248 K to 373 K.     

Excess heat capacities and orientational order in systems containing hexadecane isomers of different molecular structure

Using the Picker flow microcalorimeter, excess heat capacities have been obtained at 25°C throughout the concentration range for 2,2-dimethylbutane,n-hexane, and cyclohexane each mixed with a series of hexadecane isomers of increasing degrees of orientational order, as determined by depolarized Rayleigh scattering. The isomers are 2,2,4,4,6,8,8-heptamethylnonane, 6-, 4-, and 2-methylpentadecane, andn-hexadecane. Thec _p ^E values are negative, increasing rapidly in magnitude with increase of orientational order, and are not predicted by the Prigogine—Flory theory which neglects order. Values ofc _p ^E are obtained at 10, 25, and 55°C for cyclohexane +6-, 4-, and 2-methylpentadecane which with other literature data lead to the temperature dependence of the thermodynamic excess functions for cyclohexane solutions of the five C₁₆ isomers. The excess enthalpy and entropy vary with the C₁₆ isomer and with temperature, but the corresponding variation of the excess free energy is small, indicating a high degree of enthalpy-entropy compensation. This is consistent with a rapid decrease with temperature of orientational order in the C₁₆ isomers.     

Ionization of aqueous toluic acids: Conductance and thermodynamics

Conductivities of aqueous solutions ofortho-, meta-, andpara-toluic acids have been measured for the concentration range 0.1–2 millimolar and at 5° intervals from 5 to 100°C. At each temperature pK _a(m) andA ₀ have been calculated using the paired ion model recently described by Fuoss. Thermodynamic parameters have been calculated for the ionization of each acid, and Walden products for the anions. Results are discussed in terms of contributions to acidity by enthalpy and entropy changes as well as by hydration of the various solute species.     

Fuzzy Symmetries for Linear Molecules and their Molecular Orbitals

In this paper, the fuzzy symmetry of some prototypical linear molecules has been analyzed. The results show that some molecular orbitals (MOs) are less symmetrical but some others are more symmetrical than the molecular skeleton, which the MOs correspond to. The membership functions of space inversion for MOs are closely related to the chemical characteristics of the MOs. Sometimes, although the symmetry of a molecular skeleton is not obvious, however that of some MO is quite obvious. The membership functions of the fuzzy inversion symmetry depend on the choice of the position of the center of inversion. As compared to those of diatomic molecules and linear tri-atomic molecules, the linear polyatomic molecules in which a distinctive fuzzy symmetry of space translation may exist, and thus a significant effect on their properties can be expected.     

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.     

Thermodynamic characteristics of thermal dissociation of platinum tetrachloride

The pressure of thermal dissociation of platinum tetrachloride by the first step PtCl₄(s) = PtCl₃(s) + 0.5 Cl₂(g) was measured by the static method with a quartz membrane-gauge zero-pressure manometer. An approximating equation for the dissociation pressure vs. temperature was found. The enthalpy (52160±880 J mol⁻¹) and entropy (72.1±1.6 J mol⁻¹ K⁻¹) of dissociation were calculated. The heat of formation found for platinum tetrachloride (−246.3±1.3 kJ mol⁻¹) at 298.15 K agrees well with the value obtained by the calorimetric method (−245.6±1.9 kJ mol⁻¹).__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2028–2031, October, 2004.     

Enthalpies of mixing of <Emphasis Type="Italic">o</Emphasis>- and <Emphasis Type="Italic">m</Emphasis>-isomers at 298.15 K

Excess enthalpies (H ^E) of 17 binary mixtures of o- and m-isomers of dichlorobenzene, difluorobenzene, methoxymethylbenzene, dimethylbenzene, dimethoxybenzene, aminofluorobenzene, fluoronitrobenzene, diethylbenzene, chlorofluorobenzene, fluoroiodobenzene, bromofluorobenzene, chloromethylbenzene, fluoromethylbenzene, bromomethylbenzene, iodomethylbenzene, fluoromethoxybenzene, dibromobenzene at 298.15 K were measured. All excess enthalpies measured were very small, and those of o-+m-isomers of aminofluorobenzene, dibromobenzene and iodomethylbenzene were negative but 14 other binary mixtures of isomers were positive over the whole range of mole fractions. H ^E of o-+m-isomers of dimethoxybenzene showed the largest enthalpic instability and those of aminofluorobenzene showed the largest enthalpic stability. There was a correlation between dipole–dipole interaction, dipole–induced dipole interaction or entropies of vaporization and excess partial molar enthalpies at infinite dilution.     

"信息"到底是什么?--限于无生命、物质和科学领域的讨论

本文在无生命、物质和科学三个限制的前提下讨论“信息”到底是什么.依次论证：（1）自然科学没有能力度量信息的“质”,只能讨论信息的“量”;（2）“信息熵”只是度量信息“量”的概念;（3）在无生命的物质科学领域内,信息熵完全等价于Boltzmann熵,对应于实验中的热熵;（4）运用Occam剃刀原理,信息熵和Boltzmann熵两个名词只能留下其中的任意一个;（5）“熵”取决于体系的微观状态总数,即最终取决于热运动引起的分子核骨架的动态变化.于是,在无生命、物质和科学三个限制的领域内“信息”只是望文生义的产物.