Logarithm Of Pre-exponential Factor Research Articles

Size- and Morphology-Dependent Kinetics and Thermodynamics of Adsorptions of Basic Fuchsin on Nano-TiO2

Nanoparticles have superior adsorption properties compared with corresponding bulk materials, which depends on their particle size and morphology. Herein, by introducing morphology factors, we derived the general relations of adsorption kinetic parameters and thermodynamic properties with an equivalent particle diameter of nanoparticles with different morphologies. Experimentally, we researched the adsorption kinetics and thermodynamics of basic fuchsin on nano-TiO2 with different equivalent particle diameters and morphologies. The results show that the equivalent particle diameter and morphology have significant effects on the adsorption kinetics and the adsorption thermodynamics. Within the range of the experiment, the adsorption rate constant and the equilibrium constant increase, while the activation energy, the pre-exponential factor, the Gibbs free energy, the enthalpy, and the entropy of adsorption decrease with the decrease in the equivalent particle diameter, and the logarithm of rate constant, activation energy, the logarithm of pre-exponential factor, the logarithm of equilibrium constant, molar Gibbs free energy, molar enthalpy, and molar entropy of adsorption are linearly related to the reciprocal of equivalent particle diameter, respectively. For this adsorption system, with the decrease of equivalent particle diameter, the effect of morphology on the adsorption rate constant decreases and the activation energy and the pre-exponential factor approximately remain unchanged, while the logarithm of equilibrium constant, molar Gibbs free energy, molar enthalpy, and molar entropy of adsorption increase. The experimental results are consistent with the theoretical relations. In addition, we are surprised to find a phenomenon that is contrary to the traditional concept of dynamics: compared with the three morphologies, when the adsorption rate constant of nanoparticles is larger, the adsorption activation energy is also larger and when the adsorption rate constant of nanoparticles is smaller, the adsorption activation energy is also smaller, and these can be attributed to the fact that the morphology of nanoparticles has a greater influence on pre-exponential factor than on activation energy. The theory can quantitatively describe the effect of the equivalent particle diameter and morphology on adsorption kinetics and thermodynamics of nanoparticles and better predict the adsorption behaviors of nanoparticles.

High-temperature electrical conductivity of the xNBT–(1-x)LMT ceramics: verification of Meyer-Neldel rule

Electrical conductivity behaviour of x(Na0.5Bi0.5)TiO3-(1-x)La(Mg0.5Ti0.5)O3 ceramics with x ranging from 0.95 to 0.8 was analysed in the temperature range from 300 K to 800 K at microwaves (1 MHz – 1GHz frequency region). Analysis of calculated DC conductivity parameters has shown that the activation energy changes at about 690 K which could be associated with the phase change in these materials. The logarithm of preexponential factor of DC conductivity changes linearly according to the activation energy, i.e. it follows Meyer-Neldel rule both below and above the phase transition point.

Decomposition through pyrolysis process of coconut fiber and rice husk and determination of kinetic parameters according isoconversional methods

Pyrolysis process of coconut fiber and rice husk was studied with the purpose of determining the kinetic parameters activation energy (E) and logarithm of pre-exponential factor (log A) in agreement with converted fraction (α). The determination of kinetic parameters was done through software Thermokinetics by NETZSCH, which associated ‘‘Model Free’’ package enabled the determination of these parameters by Friedman and Ozawa–Flynn–Wall isoconversion models and a probable mechanism that describes the thermal decomposition process of these materials. The thermal degradation of coconut fiber and rice husk was carried out in the range of 303–1073 K under nitrogen flow, and the heating rate used was 2.5, 5, 10, 15 and 20 K min−1. The obtained results showed that the most appropriate kinetic model to describe the thermal decomposition of coconut fiber and rice husk was the autocatalytic reactions model in two parallel reactions (F n C n model).

Size dependence of the thermal decomposition kinetics of nano- CaC2O4: A theoretical and experimental study

In the processes of preparation and application of nanomaterials, the thermal decomposition of nanoparticles is often involved. An improved general theory of thermal decomposition kinetics of nanoparticles, developed over the past 10 years, was presented in this paper where the relations between reaction kinetic parameters and particle size were derived. Experimentally, the thermal decomposition kinetics of nano-sized calcium oxalate (nano- CaC2O4 with different sizes was studied by means of Thermogravimetry Analysis (TGA) at different heating rates. The values of the apparent activation energy and the logarithm of pre-exponential factor were calculated using the equation of Iterative Kissinger-Akahira-Sunose (IKAS) and its deformations. The influence regularities of particle size on the apparent activation energy and the pre-exponential factor were summarized, which are consistent with the thermal decomposition kinetics theory of nanoparticles. Based on the theory, the method of obtaining the surface thermodynamic properties by the determination of kinetic parameters was presented. Theoretical and experimental results show that the particle size, through the effect on the surface thermodynamic properties, has notable effect on the thermal decomposition kinetics. With the particle size decreasing, the partial molar surface enthalpy and the partial molar surface entropy increases, leading to the decrease of the apparent activation energy and the pre-exponential factor, respectively. Furthermore, the apparent activation energy, the pre-exponential factor, the partial molar surface enthalpy and the partial molar surface entropy are linearly related to the reciprocal of particle diameter, respectively.

Molecular surface area based predictive models for the adsorption and diffusion of disperse dyes in polylactic acid matrix

Two predictive models were presented for the adsorption affinities and diffusion coefficients of disperse dyes in polylactic acid matrix. Quantitative structure–sorption behavior relationship would not only provide insights into sorption process, but also enable rational engineering for desired properties. The thermodynamic and kinetic parameters for three disperse dyes were measured. The predictive model for adsorption affinity was based on two linear relationships derived by interpreting the experimental measurements with molecular structural parameters and compensation effect: ΔH° vs. dye size and ΔS° vs. ΔH°. Similarly, the predictive model for diffusion coefficient was based on two derived linear relationships: activation energy of diffusion vs. dye size and logarithm of pre-exponential factor vs. activation energy of diffusion. The only required parameters for both models are temperature and solvent accessible surface area of the dye molecule. These two predictive models were validated by testing the adsorption and diffusion properties of new disperse dyes. The models offer fairly good predictive ability. The linkage between structural parameter of disperse dyes and sorption behaviors might be generalized and extended to other similar polymer–penetrant systems.

An investigation of the general regularity of size dependence of reaction kinetics of nanoparticles

In the processes of preparation and application of nanomaterials, the chemical reactions of nanoparticles are often involved, and the size of nanoparticles has dramatic influence on the reaction kinetics. Nevertheless, there are many conflicts on regularities of size dependence of reaction kinetic parameters, and these conflicts have not been explained so far. In this paper, taking the reaction of nano-ZnO (average diameter is from 20.96 to 53.31 nm) with acrylic acid solution as a system, the influence regularities of the particle size on the kinetic parameters were researched. The regularities were consistent with that in most literatures, but inconsistent with that in a few of literatures, the reasons for the conflicts were interpreted. The reasons can be attributed to two factors: one is improper data processing for fewer data points, and the other is the difference between solid particles and porous particles. A general regularity of the size dependence of reaction kinetics for solid particles was obtained. The regularity shows that with the size of nanoparticles decreasing, the rate constant and the reaction order increase, while the apparent activation energy and the pre-exponential factor decrease; and the relationships of the logarithm of rate constant, the logarithm of pre-exponential factor, and the apparent activation energy to the reciprocal of the particle size are linear, respectively.

Entropy effects in the collective dynamic behavior of alkyl monolayers tethered to Si(111).

Dynamic properties of n-alkyl monolayers covalently bonded to Si(111) were studied by broadband admittance spectroscopy as a function of the temperature and the applied voltage using rectifying Hg/C12H25/n-type Si junctions. Partial substitution of methyl end groups by polar (carboxylic acid) moieties was used to enhance the chain end relaxation response. Two thermally activated dissipation mechanisms (B1 and B2, with fB1 < fB2) are evidenced for all reverse bias values. The strong decrease of both relaxation frequencies with increasing reverse dc bias reveals increasing motional constraints, attributed to electrostatic pressure applied to the densely-packed nanometer-thick monolayer. Spectral decomposition of the frequency response shows a power-law dependence of their activation energies on |VDC|. A large reverse bias reversibly increases the B2 response attributed to the distribution of gauche defects, in contrast with the constant strength of the acid dipole loss (B1). A trans–gauche isomerization energy of 50 meV is derived from the temperature dependence of the B2 dipolar strength. For both dissipation mechanisms, the observed linear correlation between activation energy and logarithm of pre-exponential factor is consistent with a multi-excitation entropy model, in which the molecular reorientation path is strongly coupled with a large number of low energy excitations (here the n-alkyl bending vibrational mode) collected from the thermal bath. This collective dynamic behavior of alkyl chains tethered to Si is also confirmed by the asymmetric relaxation peak shape related to many-body interactions in complex systems.

Study on the Size‐Dependent Oxidation Reaction Kinetics of Nanosized Zinc Sulfide

Numerous oxidation problems of nanoparticles are often involved during the preparation and application of nanomaterials. The oxidation rate of nanomaterials is much faster than bulk materials due to nanoeffect. Nanosized zinc sulfide (nano‐ZnS) and oxygen were chosen as a reaction system. The influence regularities were discussed and the influence essence was elucidated theoretically. The results indicate that the particle size can remarkably influence the oxidation reaction kinetics. The rate constant and the reaction order increase, while the apparent activation energy and the preexponential factor decrease with the decreasing particle size. Furthermore, the logarithm of rate constant, the apparent activation energy and the logarithm of preexponential factor are linearly related to the reciprocal of particle diameter, respectively. The essence is that the rate constant is influenced by the combined effect of molar surface energy and molar surface entropy, the reaction order by the molar surface area, the apparent activation energy, by the molar surface energy, and the preexponential factor by the molar surface entropy. The influence regularities and essence can provide theoretical guidance to solve the oxidation problems involved in the process of preparation and application of nanomaterials.

Kinetic Models of Integrated Solidification and Cementation of Cementformation Interface with New Method

The isolation failure of cement-formation interface is an important and urgent problem in oil production, while an effective way to solve it is to realize the integrated solidification and cementation of cement-formation interface (ISCCFI). In order to study the kinetics of ISCCFI with MTA (Mud Cake to Agglomerated Cake) method, the Diamond Differential Scanning Calorimetry Analyzer is adopted for experiments with dynamic method and isothermal method. The results show that there is a linear relationship between the solidification reaction temperature and the heating rate of ISCCFI with MTA method. For the first exothermic peak, the initial temperature, peak tip temperature and final temperature are 53 °C, 69 °C and 83 °C respectively, and the apparent activation energy of solidification reaction is 44.39×10-3 kJ.;mol-1, the natural logarithm of preexponential factor is 7.26, the solidification reaction order is 0.88. For the second exothermic peak, the initial temperature, peak tip temperature and final temperature are 83 °C, 92 °C and 114 °C respectively, and the apparent activation energy of solidification reaction is 99.14×10-3 kJ.;mol-1, the natural logarithm of preexponential factor is 24.77, the solidification reaction order is 0.94. The maximum solidification reaction rates at 50 °C, 75 °C and 90 °C are 0.09×10-3 s-1, 0.27×10-3 s-1 and 0.51×10-3 s-1 respectively. The kinetic models of ISCCFI with MTA method under different temperatures are established. It provides a theoretical and technical support for the isolation improvement of cement-formation interface.

Study of kinetic parameters of thermal decomposition of bagasse and sugarcane straw using Friedman and Ozawa–Flynn–Wall isoconversional methods

Pyrolysis process of sugarcane bagasse and sugarcane straw was studied with the objective of determining the kinetic parameters activation energy (E), logarithm of pre-exponential factor (log A) in agreement with converted fraction (α). The determination of kinetic parameters was done through software thermokinetics by NETZSCH, which associated “Model Free” package enabled the determination of these parameters by Friedman and Ozawa–Flynn–Wall isoconversion models and a probable mechanism that describes the thermal decomposition process of these materials. The thermal degradation of sugarcane bagasse and sugarcane straw was carried out in the range of 303–1073 K under nitrogen flow and the heating rate used was 5, 10, 15, and 20 K min−1. The obtained results showed that the most appropriate kinetic model to describe the thermal decomposition of sugarcane bagasse was the autocatalytic reactions model in three parallel stages (F n C n C n model) and for sugarcane straw was also the autocatalytic reactions model for two parallels reactions (F n C n model).

Study of Dielectric Relaxation Behavior of Liquid Crystal Copolyester Vectra-A by Thermally Stimulated Discharge Current Technique

The dielectric relaxation behavior of thermotropic liquid crystal copolyester of 73% of p-hydroxy-benzoic acid (HBA) and 27% of 2-hydroxy-6-naphthoic acid (HNA) (Vectra-A) at poling temperature 80°C has been studied using thermally stimulated depolarization current (TSDC) technique in the temperature range from 15°C to 250°C. The TSD currents were obtained for different polarizing fields ranging from 3.8 kV/cm to 19.2 kV/cm. TSD current spectra in the temperature range from 15°C to 250°C show three current maxima around 25°C, 110°C, and 220°C. The maxima around 25°C and 110°C correspond to characteristic dipolar relaxations β and α, respectively. The peak around 220°C is due to space charge effects named as δ-relaxation. The various relaxation parameters like activation energy (U), relaxation strength , preexponential factor , the quantity of charge released (Q) and concentration of trap for β- and α-relaxations at polarizing temperature 80°C for different polarizing fields were evaluated using Bucci-Fieschi fit. The linear variation between activation energy and natural logarithm of preexponential factor indicates the presence of compensation effect for dipolar relaxations of Vectra-A under present poling conditions.

Kinetics of the thermal decomposition of Wangjiatan siderite

The thermal decomposition processes of Wangjiatan siderite samples were studied in nitrogen by thermogravimetric(TG) analysis. The mechanism of thermal decomposition of the siderite obeyed an Fn kinetic law and the n-order was between 1.16 and 1.29. The results from non-isothermal experiments show that the size of particles has an obvious effect on the logarithm of pre-exponential factor in kinetics parameter of the thermal decomposition of Wangjiatan siderite. A linear relationship is shown between the size of particles and the logarithm of pre-exponential factor. An F1 kinetic model containing size factor describes the thermal decomposition of Wangjiatan siderite well.

Deblocking Kinetics of Water-Solubility Blocked Isophorone Diisocyanate

The thermal decomposition process of water-solublity blocked isophorone diisocyanate(IPDI) was studied using thermal gravimetric analysis(TGA).The characteristic peaks of isocyanante groups at 40 and 140 ℃ were observed by Fourier transform infrared spectroscopy(FTIR).Results from TGA and FTIR showed that the degradation stage was a deblocking reaction of the blocked adduct.The Friedman-Reich-Levi(FRL) and Flynn-Wall-Ozawa(FWO) models were employed to investigate the apparent activation energies which were 125.0 and 124.5 kJ·mol-1,respectively.Based on the double equal-double step method,the reaction was analyzed by the apparent mechanism of the process of deblocking according to the Jander equation,which indicated that the reactive mechanism was a three-dimensional diffusion.The reaction order(n) and the logarithm of pre-exponential factor(lnA) were also determined using the FWO equation.

High-Temperature Internal Friction of Metallic Glasses with Widely Different Glass-Forming Ability

The internal friction (IF) of binary, ternary, quaternary, and quinary metallic glasses with widely different glass-forming ability (GFA) has been studied. A single-roller melt-spinning apparatus was used for preparing ribbon specimens. An inverted torsion pendulum was used in the IF measurement. The measurements were performed from room temperature, through the glass transition temperature, up to the crystallization temperature. The background IF monotonously increases with increasing temperature. The increase is of the thermal-activation type, and the activation energy E is determined. For alloys with higher GFA, the E value tends to be higher. IF is inversely proportional to the measurement frequency. The viscosity relaxation based on the Maxwell model is considered, and the relaxation time τ is determined. A linear relationship is seen between the logarithm of pre-exponential factor τ o and the activation energy E . Explanations of these results and discussions concerned are presented.

High Temperature Creep in Mechanically Alloyed Al-C-O Alloys

Parameters characterizing the creep of four mechanically alloyed aluminium alloys were compared with those of pure aluminium. It was shown that the activation energy and logarithm of preexponential factor of steady state creep rate, of inverse relaxation time of primary stage and of recovery rate are linear functions of respective stress exponents. These functions are discussed within the framework of Dorn's equation. Their existence makes a formulation of a general constitutive equation possible which describes the creep rate in the presented class of alloys as a function of only one material variable, namely the stress exponent of steady state creep rate