非等温反应过程中新的动力学方程

对于非等温过程中的动力学方程，正确的Arrhenius方程的温度积分应该是从T₂到T₁，但是许多动力学方程中的温度积分是从T到0 K，例如Ozawa等方程。我们的研究指出对于某些反应，这些方程中的活化能存在较大的误差，因此我们提出了一个新的动力学方程。凭借等转化率法，应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能。用新方程对2个经典反应（聚酰胺的热裂解和一水草酸钙的热分解）的研究表明：Ozawa方程的活化能有时是精确的，有时偏差太大。     

A comprehensive study on the inclusion mechanism of benzophenone into supramolecular nanoassemblies prepared using two water-soluble associative polymers

In this study, the entrapment of benzophenone (BZ) into supramolecular nanoassemblies prepared by mixing two water-soluble associative polymers (i.e. polymerized β-CD (pβ–CD) and dextran grafted with lauryl-side chains (MD)) has been investigated by using isothermal titration microcalorimetry (ITC) and molecular modeling. ITC experiments have been performed at various temperatures (4 °C (277 K), 25 °C (298 K), and 37 °C (310 K)) to evaluate the interaction of BZ with pβ–CD in comparison with β-CD. The inclusion complexation for both β-CD/BZ and pβ–CD/BZ interactions was entropy-driven (|ΔH| < |TΔS|) when the temperature of the experiment was low (4 °C) and enthalpy-driven (|ΔH| > |TΔS|) with minor entropic contribution when the temperature was increased (25 and 37 °C). Using all the thermodynamic data obtained for β-CD/BZ and pβ–CD/BZ interactions when the temperature of the experiment was varied, the \Updelta H   =   f(T\Updelta S ) \Updelta H\; = \;f(T\Updelta S ) plot was perfectly linear, which reflected an enthalpy–entropy compensation process. Finally, the combination of ITC data with molecular modeling provided consistent information in regard to the location of MD side chains and BZ inside the cyclodextrin cavity, as well as concerning the stability of the nanoassemblies loaded with BZ.     

Supplement on applicability of the Kissinger equation in thermal analysis

The relative errors (e%) in the determination of the activation energy from the slope of the Kissinger straight line ln(β/βT _p²) vs. 1/T _p (β is the heating rate) are in-depth discussion. Our work shows that the relative errors is a function containing the factors of x _p and Δx _p, not only x _p (x _p = E/RT _p, E is the activation energy, T _p is the temperature corresponding to maximum process rate, R is the gas constant). The relative error between E _k and E _p will be smaller with the increase of the value of x and/or with the decrease of the value of Δx. For a set of different heating rates in thermal analysis experiments, the low and close heating rates are proposed from the kinetic theory.     

A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

Influence of the Degree of Dehydroxylation of Kaolinite on the Properties of Aluminosilicate Glasses

The degree of dehydroxylation of kaolinite, D_TG and D_IR, respectively, is characterized by thermogravimetric analysis (TG) and Fourier transform infrared spectroscopy (FTIR). The relation between DTG and DIR based on the infrared absorptions at 3600–3700, 915, 810, and 540 cm⁻¹ is established. Three regions can clearly be distinguished: the dehydroxylation region (D_TG<0.9), the metakaolinite region (0.9<D_TG<1) and the ‘spinel’ region(D_TG=1). The effect of the degree of dehydroxylation of kaolinite on the amount of reactive material is measured by the reaction enthalpy, ΔH, of the low-temperature reaction of the dehydroxylated kaolinite with a potassium silicate solution using differential scanning calorimetry (DSC). |ΔH| increases almost linearly with DTG in the dehydroxylation region. In the metakaolinite region, ΔH and thus the amount of reactive material, becomes constant. |ΔH| is sharply decreasing when metakaolinite transforms into other phases in the ‘spinel’ region. No significant differences in the reactivity of the dehydroxylates is detected with DSC. According to FTIR, the use of partially dehydroxylated kaolinite is not influencing the molecular structure of the low-temperature synthesized aluminosilicates, but residual kaolinite is retrieved as an additive. This revised version was published online in August 2006 with corrections to the Cover Date.     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001     

The Gibbs Energies of Activation of Lysozyme for Viscous Flow in Water + Dimethyl Sulfoxide Solutions at 298.15 K

Gibbs energies of activation for viscous flow of binary water (1) + dimethyl sulfoxide (2) mixtures, Δμ ₁₂^○, and of lysozyme (3) in corresponding ternary mixtures, Δμ ₃^○, were determined at 298.15 K. The binary mixtures have a maximum in the value of the excess quantity for Δμ ₁₂^○ at a dimethyl sulfoxide mole fraction of x ₂≈0.31. The values of Δμ ₃^○ are larger than Δμ ₁₂^○ at all values of x ₂, even when normalized by their molar volumes, suggesting that the solvents interact more strongly with lysozyme than with themselves. The values of Δμ ₃^○ significantly increased in the range of x ₂=0.3 to 0.4 because of an increase in solvent-lysozyme interactions, which resulted from an increase in the accessible surface area of lysozyme that was exposed by its unfolding. The mean value obtained for Δμ ₃^○ per amino acid of lysozyme at x ₂=0.2 is greater than that for hydrophobic amino acids, indicating that the solvent interacts with hydrophilic amino acids more strongly than with hydrophobic ones.     

The minimal energy conformations of o-benzosemiquinone anion radicals in the solvents containing the alkali metals and the alkali earth metals

The minimal energy conformations of o-benzosemiquinone anion radicals in the solvents containing the alkali metals and the alkali earth metals were calculated by using the INDO method and the molecular geometry adjusting method. Our previous calculations of o-benzosemiquinone anion radical in the lithium ion solution showed that the total energy of the minimal energy conformation in the case of the assignment |A₃| > |A₄| were lower by approximately 320 kcal/mol than that in the case of the assignment |A₃| > |A₄|. Therefore, the calculations of the minimal energy conformations of o-benzosemiquinone anion radicals in the metal ion solutions were carried out in the cases of the assignment |A₃| > |A₄|. The conformations in both assignments A₃ < A₄ < 0 and (A₃ < 0 < A₄ and |A₃| > |A₄|) were calculated. Although the metal ions were not explicitly contained in the molecular geometries, the minimal energy conformations are considered to be close to the real minimal energy conformations of o-benzosemiquinone anion radicals in the metal ion solutions. The C? O bond lengths has a good positive rank correlation with the stabilities of o-benzosemiquinone radicals in the divalent metal ion solutions and the bond angles ∠C₃C₄H₄ had a good negative rank correlation with those stabilities.     

Studies on Equation-of-State Parameters and Linear Polymer Dimensions of Poly(p-chlorostyrene) in Diethylene Glycol Monobutyl Ether by Intrinsic Viscosity Measurements

Summary. Intrinsic viscosities, [η], of poly(p-chlorostyrene) (PPCS) in diethylene glycol monobutyl ether (DGMBE) which exhibits an exothermic solubility behavior with the polymer were measured using an Ubbelohde type capillary viscometer between 25 and 85°C. Polymer solvent interaction parameters at infinite dilution (χ₁), exchange energy parameter , exchange enthalpy (X₁₂), and entropy parameters (Q₁₂), of the PPCS/DGMBE pair were found at studied temperature range according to equation-of-state theory. In the blob theory, dependence of [η] on temperature can be scaled by a master curve in a plot of α_η³|τ|M^1/2 versus |τ|M^1/2 as the polymer coil contracts below the Θ-point, however, it can be scaled by a master curve in a plot of α_η⁻⁵|τ|M^1/2 versus |τ|M^1/2 as the polymer coil expands above the Θ-point in an endothermic solubility behavior. Since the studied PPCS/DGMBE system represents exothermic solubility behavior, the master curves of the system were plotted in α_η³|τ|M^1/2 versus |τ|M^1/2 as the polymer coil contracts above the Θ-point and in α_η⁻⁵|τ|M^1/2 versus |τ|M^1/2 as the polymer coil expands below the Θ-point. The universal plots of α_η(N/N_c)^1/6 versus N/N_c and α_η(N/N_c)^−1/10 versus N/N_c were plotted above and below Θ-point, respectively.     

Geometric interpretation of density displacements and charge sensitivities

The “geometric” interpretation of the electronic density displacements in the Hilbert space is given and the associated projection-operator partitioning of the hardness and softness operators (kernels) is developed. The eigenvectors |?〉= |α〉 of the hardness operator define the complete (identity) projector P =Σ_α| α〉〈α | = 1 for general density displacements, including thecharge-transfer (CT) component, while the eigenvectors |i〉= |i〉 of the linear response operator determine thepolarizational P-projector, P_p = Σ_i |i〉〈i| . Their difference thus defines the complementary CT-projector: P_CT = 1-P_P. The complete vector space for density displacements can be also spanned by supplementing the P-modes with the homogeneous CT-mode. These subspaces separate the integral (normalization) and local aspects of density shifts in molecular systems.     

Non-isothermal kinetics of the thermal decomposition of sodium oxalate Na<Subscript>2</Subscript>C<Subscript>2</Subscript>O<Subscript>4</Subscript>

The thermal transformation of Na₂C₂O₄ was studied in N₂ atmosphere using thermo gravimetric (TG) analysis and differential thermal analysis (DTA). Na₂C₂O₄ and its decomposed product were characterized using a scanning electron microscope (SEM) and the X-ray diffraction technique (XRD). The non-isothermal kinetic of the decomposition was studied by the mean of Ozawa and Kissinger–Akahira–Sunose (KAS) methods. The activation energies (E _α) of Na₂C₂O₄ decomposition were found to be consistent. Decreasing E _α at increased decomposition temperature indicated the multi-step nature of the process. The possible conversion function estimated through the Liqing–Donghua method was ‘cylindrical symmetry (R₂ or F_1/2)’ of the phase boundary mechanism. Thermodynamic functions (ΔH*, ΔG* and ΔS*), calculated by the Activated complex theory and kinetic parameters, indicated that the decomposition step is a high energy pathway and revealed a very hard mechanism.     

Studies on Equation-of-State Parameters and Linear Polymer Dimensions of Poly(p-chlorostyrene) in Diethylene Glycol Monobutyl Ether by Intrinsic Viscosity Measurements

Intrinsic viscosities, [η], of poly(p-chlorostyrene) (PPCS) in diethylene glycol monobutyl ether (DGMBE) which exhibits an exothermic solubility behavior with the polymer were measured using an Ubbelohde type capillary viscometer between 25 and 85°C. Polymer solvent interaction parameters at infinite dilution (χ₁), exchange energy parameter ([`(X)]₁₂)(\bar{X}_{12}) , exchange enthalpy (X₁₂), and entropy parameters (Q₁₂), of the PPCS/DGMBE pair were found at studied temperature range according to equation-of-state theory. In the blob theory, dependence of [η] on temperature can be scaled by a master curve in a plot of α_η³|τ|M^1/2 versus |τ|M^1/2 as the polymer coil contracts below the Θ-point, however, it can be scaled by a master curve in a plot of α_η⁻⁵|τ|M^1/2 versus |τ|M^1/2 as the polymer coil expands above the Θ-point in an endothermic solubility behavior. Since the studied PPCS/DGMBE system represents exothermic solubility behavior, the master curves of the system were plotted in α_η³|τ|M^1/2 versus |τ|M^1/2 as the polymer coil contracts above the Θ-point and in α_η⁻⁵|τ|M^1/2 versus |τ|M^1/2 as the polymer coil expands below the Θ-point. The universal plots of α_η(N/N_c)^1/6 versus N/N_c and α_η(N/N_c)^−1/10 versus N/N_c were plotted above and below Θ-point, respectively.     

Kinetics of mixed-controlled oxygen reduction at nafion-impregnated Pt-alloy-dispersed carbon electrode by analysis of cathodic current transients

The effects of Co alloying to Pt catalyst and Nafion pretreatment by NaClO₄ solution on the rate-determining step (RDS) of oxygen reduction at Nafion-impregnated Pt-dispersed carbon (Pt/C) electrode were investigated as a function of the potential step ΔE employing potentiostatic current transient (PCT) technique. For this purpose, the cathodic PCTs were measured on the pure Nafion-impregnated and partially Na⁺-doped Nafion-impregnated Pt/C and PtCo/C electrodes in an oxygen-saturated 1 M H₂SO₄ solution and analyzed. From the shape of the cathodic PCTs and the dependence of the instantaneous current on the value of ΔE, it was confirmed that oxygen reduction at the pure Nafion-impregnated electrodes is controlled by charge transfer at the electrode surface mixed with oxygen diffusion in the solution below the transition potential step |ΔE _tr| in absolute value, whereas oxygen reduction is purely governed by oxygen diffusion above |ΔE _tr|. On the other hand, the RDS of oxygen reduction at the partially Na⁺-doped Nafion-impregnated electrodes below |ΔE _tr| is charge transfer coupled with proton migration, whereas above |ΔE _tr|, it becomes proton migration in the Nafion electrolyte instead of oxygen diffusion. Consequently, it is expected in real fuel cell system that the cell performance is improved by Co alloying since the electrode reaches the maximum diffusion (migration) current even at small value of |ΔE|, whereas the cell performance is aggravated by Nafion pretreatment due to the decrease in the maximum diffusion (migration) current.     

Laser-induced fluorescence study of the hydrogen atom formation dynamics in the 248 nm gas-phase photodissociation of vibrational state selected water (H<Subscript>2</Subscript>O (|04<Superscript>−</Superscript>〉))

The vibrationally-mediated H₂O gas-phase photodissociation was studied at a photolysis wavelength of 248 nm. Single rotational states of the |03⁻〉|2〉 and |04⁻〉 H₂O overtone vibrations were prepared by laser photoexcitation around 720 nm. H atoms formed in the photodissociation of the H₂O (|04⁻〉 = 3₁₃) were detected by Lyman-α laser-induced fluorescence spectroscopy with sub-Doppler resolution to determine their translational energy. The present result confirms that in the dissociation process the major part (ca. 93%) of the available energy is released as relative translational energy of the nascent H + OH photofragments, in agreement with earlier complementary measurements (R. L. Vander Wal, J. L. Scott and F. F. Crim, J. Chem. Phys. 94, 1859 (1991)), where the internal excitation of the OH product radical was investigated at different photolysis wavelengths.     

A model developed for acid dissolution thermodynamics of a Turkish bentonite

A model was proposed to calculate some thermodynamic parameters for the acid dissolution process of a bentonite containing a calcium-rich smectite as clay mineral along with quartz, opal and feldspar as impurities. The bentonite sample was treated with H₂SO₄ by applying dry method in the temperature range 50–150°C for 24 h. The acid content in the dry bentonite-sulphuric acid mixture was 45 mass%. The total content (x) of Al₂O₃, Fe₂O₃ and MgO remained in the undissolved sample after treatment was taken as an equilibrium parameter. An apparent equilibrium constant, K _a, was calculated for each temperature by assuming K _a=(x _m−x)/x where x _m is the total oxide content of the natural bentonite. Also, an apparent change in Gibbs free energy, ΔG _a^o, was calculated for each temperature by using the K _a value. The graphs of lnK _a vs. 1/T and ΔG _a^o vs. T were drawn and then the real change in both the enthalpy, ΔH ^o and the entropy, ΔS ^o, values were calculated from the slopes of the straight lines, respectively. Inversely, real ΔG ^o and K values were calculated from the real ΔH ^o and ΔS ^o values through ΔG ^o = −RT ln K = ΔH ^o − TΔS ^o equation. The best ΔH ^o and ΔS ^o fittings to this relation were found to be 65687 J mol⁻¹ and 164 J mol⁻¹K⁻¹, respectively.     

Phase transitions and ion transport in NASICON materials of composition Li1 + xZr2 ? xInx(PO4)3(x = 0–1)

NASICON materials of composition Li_{1 + x} Zr_{2 − x} In _x (PO₄)₃(x = 0–1) were synthesized. The phase constitution, particle size, and conductivity of these materials were studied as s function of synthesis temperature. High-temperature X-ray powder diffraction was used to study phase transitions in the materials synthesized. Low levels (x ≤ 0.1) partial substitution of indium for zirconium considerably increase the lithium ion conductivity and reduce the activation energy for conduction compared to the parent compound.     

Kinetics and mechanism of thermal polymerization of hexafluoropropylene under high pressures

The basic kinetic parameters of thermal polymerization of hexafluoropropylene, namely, general rate constants, degree of polymerization, and their temperature and pressure dependences in the range of 230–290 °C and 2–12 kbar (200–1200 MPa) were determined. The activation energy (E _act = 132±4 kJ mol⁻¹) and activation volume (ΔV ₀ ^≠ = −27±1 cm³ mol⁻¹) were calculated. The activation energy of thermal initiation of polymerization was estimated. The reaction scheme based on the assumption about a biradical mechanism of polymerization initiation was proposed.     

Ionization Constants of o-Phthalic Acid and Standard pH Values of Potassium Hydrogen Phthalate Buffer Solutions in Glycerol + Water Solvent Mixtures at Normal and Subzero Temperatures

Determination of primary standards for pH measurements in glycerol + water solventmixtures has been carried out based on reversible emf measurements of the cellPt|H₂|KHPh (m _PS) + KCl (m _Cl)|AgCl|Ag|Ptwhere KHPh denotes the potassium hydrogen phthalate buffer solution of molalitym _PS = 0.05 mol-kg^–1, at glycerol mass fractions w _G = 0.2 and 0.4, within thetemperature range –10 to 40°C. A multilinear regression procedure as a functionof electrolyte molality, glycerol mass fraction w _G, and temperature T has beenapplied for the data processing leading to the values of primary standards pH_PS.These can be represented by the following regression equationpH_PS = (4.007037±0.001113) + (3.55844±0.01776)x _G+(0.39622±0.01410)z + (4.3084±0.3377)z ²– (50.66±10.53)x _G z ² + (457.10±78.48)x _G ² z ²where z = (T – 298.15)/298.15. Parallel values of the first ionization constantof o-phthalic acid (H₂Ph; benzene-1,2-dicarboxylic acid, the parent acid of KHPh),which are essential for the above calculations, have been determined fromreversible emf measurements of the cellPt|H₂|H₂Ph (m ₁) + KHPh (m ₂) + KCl (m ₃)|AgCl|Ag|Ptover the range of solvent composition and temperatures mentioned above.     

Studies on temperature dependent kinetics of <Emphasis Type="Italic">Aspergillus awamori</Emphasis> feruloyl esterase in water solutions

The initial reaction rate (V ₀) for the esterification reaction of feruloyl esterase (FAE-II) at different temperatures (288, 298, 308, 318, 328, 338, 348, and 358 K) and various ethyl ferulate concentrations [(2, 4, 6, 8, 10, 12, 14, and 16) × 10⁻⁴ mol l⁻¹ of ethyl ferulate in water] were determined. The Lineweaver-Burk double reciprocal plot yielded the kinetic parameters (maximal velocity V _max, Michaelis constant K _m, and second order rate constant V/K). The effects of temperature on those 3 kinetic parameters were presented and discussed. The thermodynamic parameters ΔH* (enthalpy of activation), ΔG* (free energy of activation), ΔS* (entropy of activation), ΔG _E-S (free energy change of substrate binding), ΔG _E-T (free energy change of transition state formation), related to that biochemical process were determined and discussed from van’t Hoff plot, Arrhenius plot, and Eyring plot.     

Kinetic and thermodynamic studies of MgHPO<Subscript>4</Subscript> · 3H<Subscript>2</Subscript>O by non-isothermal decomposition data

The thermal decomposition of magnesium hydrogen phosphate trihydrate MgHPO₄ · 3H₂O was investigated in air atmosphere using TG-DTG-DTA. MgHPO₄ · 3H₂O decomposes in a single step and its final decomposition product (Mg₂P₂O₇) was obtained. The activation energies of the decomposition step of MgHPO₄ · 3H₂O were calculated through the isoconversional methods of the Ozawa, Kissinger–Akahira–Sunose (KAS) and Iterative equation, and the possible conversion function has been estimated through the Coats and Redfern integral equation. The activation energies calculated for the decomposition reaction by different techniques and methods were found to be consistent. The better kinetic model of the decomposition reaction for MgHPO₄ · 3H₂O is the F _1/3 model as a simple n-order reaction of “chemical process or mechanism no-invoking equation”. The thermodynamic functions (ΔH*, ΔG* and ΔS*) of the decomposition reaction are calculated by the activated complex theory and indicate that the process is non-spontaneous without connecting with the introduction of heat.