Dispersive kinetic models for isothermal solid-state conversions and their application to the thermal decomposition of oxacillin

The authors recently published works in which the use of two novel equations for modeling the dispersive kinetics observed in various solid-state conversions are described. These equations are based on the assumptions of a ‘Maxwell-Boltzmann (M-B)-like’ distribution of activation energies and a first-order rate law. In the present work, it is shown that it may be possible to expand the approach to include mechanisms other than first-order, i.e. some of those commonly encountered in the field of thermal analysis, thus obtaining ‘dispersive versions’ of these kinetic models. The application of these dispersive kinetic models to the slightly sigmoidal, isothermal conversion-time (x-t) data of Rodante and co-workers for the degradation of the antibiotic, oxacillin, is described. This is done in an effort to test the limitations of the proposed dispersive models in describing kinetic data which is not clearly sigmoidal (i.e. as shown in previous works). Finally, it is demonstrated that, using graphical analysis, the typically sigmoidal x-t plots of first-order dispersive processes are the direct result of (asymmetric) activation energy distributions that are either ‘∩-shaped’ (for heterogeneous conversions) or ‘∪-shaped’ (for homogeneous conversions) in appearance, i.e. when the activation energy is plotted as a function of conversion. This finding lends support to the founding hypothesis of the authors’ approach for modeling dispersive kinetic processes: the existence of ‘M-B-like’ distributions of activation energies.     

Semiempirical equations for modeling solid-state kinetics based on a Maxwell-Boltzmann distribution of activation energies: applications to a polymorphic transformation under crystallization slurry conditions and to the thermal decomposition of AgMnO4 crystals

Many solid-state reactions and phase transformations performed under isothermal conditions give rise to asymmetric, sigmoidally shaped conversion-time (x-t) profiles. The mathematical treatment of such curves, as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell-Boltzmann (M-B) distribution is used to describe the distribution of activation energies for the reagent solids, which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equation that may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equation is used to relate the distribution of activation energies to a corresponding distribution of rate constants for the individual molecules in the reagent solids. This distribution of molecular rate constants is then correlated to the (observable) reaction time in the derivation of the model equation. In addition to providing a versatile treatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other models is that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple, two-parameter equation to successfully model the experimental x-t data for the polymorphic transformation of a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, we use a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical (i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.     

Roles of nucleation, denucleation, coarsening, and aggregation kinetics in nanoparticle preparations and neurological disease

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k(a), is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author's dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214-225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.     

The kinetics of homogeneous and two-step nucleation during protein crystal growth from solution

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal-like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal-like behavior for the kinetics of nucleation. A two-step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two-step and homogeneous nucleation modes. We propose here that two-step solute-rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time-dependent volume of the two-step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two-step activity increases with increasing initial supersaturation or increasing salt concentration.     

Quantitative correlation of kinetic parameters and procedural factors in non-isothermal thermogravimetry-dependence of heating rate and sample mass

Dependence of kinetic parameters (activation energy and pre-exponential factor) and procedural factors (sample mass and heating rate) independent of the reversibility and the type of reactions in non-isothermal thermogravimetry have been established. Tris(ethylenediamine)nickel(II) oxalate dihydrate has been selected as a model complex and experiments were carried out at different heating rates and sample masses to study the dependence quantitatively. The kinetic parameters calculated using mechanistic and non-mechanistic equations show a systematic decrease with increase in either sample mass or heating rate for the dehydration and deamination reactions. For the decomposition reaction, the kinetic parameters are not influenced by the procedural factors. Mathematical correlations of high reliability are established between kinetic parameters and heating rate/sample mass using both mechanistic and non-mechanistic equations for dehydration and deamination reactions. The quantification follows an exponential decay of second order relation with respect to heating rate and a sigmoidal relation with regard to sample mass for both the dehydration and deamination reactions. No quantitative correlation is possible for the final decomposition stage. Thus, it is found that independent of the type of reaction (deamination or dehydration) the kinetic parameters have a particular dependence on the procedural variables. The equations for exponential decay and sigmoidal dependence can be represented as $ y = y_{0} + A_{1} {\text{e}}^{{ - x/t_{1} }} + A_{2} {\text{e}}^{{ - x/t_{2} }} $ and $ y = {\frac{{A_{1} - A_{2} }}{{1 + {\text{e}}^{{(x - x_{0} )/{\text{d}}x}} }}} + A_{2} $ respectively, where y represents kinetic parameters (E or A) and x represents the procedural variables (φ or m). Mechanism of the dehydration reaction is found to be random nucleation with the formation of one nucleus on each particle and the deamination is a phase boundary reaction. It is observed that the mechanism of these reversible reactions is not affected by the variation in sample mass and heating rate.     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

新型侧基含磷共聚酯的阻燃和热降解动力学

利用动态热重分析法(TG)研究了聚酯(PET )及侧基含磷共聚酯(FR-PET)在不同升温速率下的热稳定性及热降解动力学, 并通过极限氧指数法(LOI)考察了FR-PET的阻燃性能; 采用Flynn-Wall-Ozawa方法分析了PET和FR-PET的热降解表观活化能; 利用Coast-Redfern方法通过对不同机理模型的选取, 确定了PET和FR-PET热降解动力学机理及其模型, 得出了主降解阶段的非等温动力学方程及热降解速率曲线图. 研究结果表明, 侧基含磷单元的引入提高了聚酯的阻燃性能, 侧基上的P—C和P—O键易断裂, 从而降低了聚酯的热稳定性. PET和FR-PET的热降解表观活化能(0.1≤α≤0.85)分别为194-227和184-209 kJ/mol; PET和FR-PET热降解反应均属于受减速形α-t曲线控制的反应级数机理, 其机理函数为f(α)=3(1-α)2/3(0.1≤α≤0.85). 侧基含磷单元的引入对PET的主降解阶段的热降解速率并无实质上的影响. 侧基含磷共聚酯的凝聚相阻燃作用有限, 可能以气相阻燃机理为主发挥阻燃作用.     

Crystallization kinetics of calcium carbonate at a stoichiometric ratio of components

The formal kinetics of calcium carbonate crystallization in aqueous solutions is studied at a stoichiometric ratio of Ca²⁺ and CO₃^2- ions. The kinetics of the process was monitored by convenient and reliable methods (complexometric analysis for calcium in an aqueous solution and energy dispersive and microscopic measurement of solid particle sizes). The effect the temperature and degree of supersaturation have on the periods of induction and mass crystallization and the equilibrium concentration of calcium ions in solution is estimated at continuously controlled pH and solution ionic strength. The kinetic parameters (n, k, τ_1/2, E_a) of calcium carbonate crystallization are calculated. It is shown that calcium carbonate with a calcite structure formed at a stoichiometric ratio of reagents, and changes in the temperature (25–45°C) and the solution’s degree of supersaturation (2–6) within the considered range had no effect on the characteristics of the solid phase.     

Physico-geometric kinetics of solid-state reactions by thermal analyses

The physico-geometric kinetics for the solid-state reactions by thermoanalytical (TA) measurements were reexamined by focusing some fundamental aspects: (1) the fundamental kinetic equation, (2) the kinetic model function, (3) the fractional reaction , and (4) the apparent kinetic parameters. It was pointed out that some pitfalls in the practical kinetic study are originated by the disagreement between the kinetic information from the TA measurements and the theory of the physico-geometric kinetics. In order to increase the degree of coordination between the theory and practice, several attempts were made from both the theoretical and experimental points of views. The significance of the apparent kinetic parameters was discussed with a possible orientation for obtaining the reliable kinetic parameters.I would like to thank to Profs H. Tanaka, J. esták, J. M. Criado, A. K. Galwey and Dr. J. Malek for their kind supports.     

Laser flash photolysis of benzophenone in polymer films

With a nanosecond laser we studied flash photolysis of benzophenone (BP) dissolved in four different polymer films. We measured kinetics of decay of a triplet state of benzophenone (3)BP as well as kinetics of decay of benzophenone ketyl free radicals BPH(?). Polymer matrices have plenty of reactive C-H bonds, and the hydrogen abstraction by (3)BP leads to a formation of geminate pair which either recombines into molecular products or dissociates. Decay kinetics of (3)BP is well described by dispersive kinetics and in particular by the kinetic law suggested in Albery, W. J.; et al. J. Am. Chem. Soc. 1985, 107, 1854. We observed a broader distribution of rate constants in hard films. It was observed that the decay kinetics of transients radicals in the "hard" polymers is quite satisfactory described by the same law for dispersive kinetics. Kinetics of radicals decay in "soft" polymers is satisfactorily described as a diffusion-enhanced reaction. Effect of a hardness of polymer matrix on the measured kinetic parameters is discussed.     

Low pH acts as inhibitor of membrane damage induced by human islet amyloid polypeptide

Human islet amyloid polypeptide (IAPP) is the major component of the amyloid deposits found in the pancreatic islets of patients with type 2 diabetes mellitus. After synthesis, IAPP is stored in the β-cell granules of the pancreas at a pH of approximately 5.5 and released into the extracellular compartment at a pH of 7.4. To gain insight into the possible consequences of pH differences for properties and membrane interaction of IAPP, we here compared the aggregational and conformational behavior of IAPP as well as IAPP-membrane interactions at pH 5.5 and pH 7.4. Our data reveal that a low pH decreases the rate of fibril formation both in solution and in the presence of membranes. We observed by CD spectroscopy that these differences in kinetics are directly linked to changes in the conformational behavior of the peptide. Mechanistically, the processes that occur at pH 5.5 and pH 7.4 appear to be similar. At both pH values, we found that the kinetic profile of IAPP fibril growth matches the kinetic profile of IAPP-induced membrane damage, and that both are characterized by a lag phase and a sigmoidal transition. Furthermore, monolayer studies as well as solid-state NMR experiments indicate that the differences in kinetics and conformational behavior as function of pH are not due to a different mode of membrane insertion. Our study suggests that a low pH prevents aggregation and membrane damage of IAPP in the secretory granules, most likely by affecting the ionization properties of the peptide.     

Simple Chemical Reactions in the Solid State: Towards Elaborating a Conception

In contrast to the conventional homogeneous kinetics, there is no conception of a simple reaction in the solid-state reaction kinetics. The geometric-probabilistic phenomenology currently in use is not adequate for describing the interplay between the chemical mechanism and the observed kinetic behaviour. An attempt is made to formulate a conception of simple reaction in the solid state as a basis for constructing kinetic models of involved reactions.     

N-异丙基丙烯酰胺温度敏感性水凝胶相转变动力学研究及其应用

 研究指出表观二级动力学方程可以很好地描述N-异丙基丙烯酰胺水凝胶的溶胀和消溶胀动力学.即溶胀动力学方程为dR/dt=k₁(R_e-R)²,消溶胀动力学方程为-dR/dt=k_c(R-R_e)².把这种水凝胶用于分离高分子水溶液时可引入“单位溶张比分离循环的合理时耗”这样一个参量.它根据溶胀和消溶胀过程中的起始溶胀比、平衡溶胀比、表观溶胀动力学常数和表观消溶胀动力学常数求出.具体公式为△t₁(T_s,T_c)=2/[R_c(T_s)-R₀(T_s)]²k_s(T_s)+15/[R₀(T_c)- R_s(T_c)]²k_c(T_c)^1/2在理想情况下,分离过程的“总合理时耗”与△t_1成正比,比例系数为分离过程中的除水总量与干凝胶用量的比值,即△t_r=W_W/WG·△t₁.当根据二个动力学方程求得的总时耗计算值处于(0.9△t_r,1.1△t_r)范围内时,表明所选干凝胶用量和循环溶胀比区段均合适.     

Combined kinetic analysis of solid-state reactions: a powerful tool for the simultaneous determination of kinetic parameters and the kinetic model without previous assumptions on the reaction mechanism

The combined kinetic analysis implies a simultaneous analysis of experimental data representative of the forward solid-state reaction obtained under any experimental conditions. The analysis is based on the fact that when a solid-state reaction is described by a single activation energy, preexponetial factor and kinetic model, every experimental T-alpha-dalpha/dt triplet should fit the general differential equation independently of the experimental conditions used for recording such a triplet. Thus, only the correct kinetic model would fit all of the experimental data yielding a unique activation energy and preexponential factor. Nevertheless, a limitation of the method should be considered; thus, the proposed solid-state kinetic models have been derived by supposing ideal conditions, such as unique particle size and morphology. In real systems, deviations from such ideal conditions are expected, and therefore, experimental data might deviate from ideal equations. In this paper, we propose a modification in the combined kinetic analysis by using an empirical equation that fits every f(alpha) of the ideal kinetic models most extensively used in the literature and even their deviations produced by particle size distributions or heterogeneities in particle morphologies. The procedure here proposed allows the combined kinetic analysis of data obtained under any experimental conditions without any previous assumption about the kinetic model followed by the reaction. The procedure has been verified with simulated and experimental data.     

Thermal degradation kinetics of poly(methylphenylsiloxane) containing methacryloyl groups

The kinetics of the thermal degradation of polymethylphenylsiloxane containing methacryloyl groups (PMPS-M) were investigated by thermogravimetric analysis (TGA). Thermal degradation of PMPS-M had two different processes: “unzipping degradation” and “rearrangement degradation”. The corresponding kinetic parameters of the two degradation stages were determined by using Friedman and Flynn-Wall-Ozawa methods, respectively. Coats-Redfern and Phadnis-Deshpande methods were also used to discuss the probable degradation mechanisms of the two different stages. The results showed that the activation energy obtained from Friedman method was in good agreement with the value obtained using Flynn-Wall-Ozawa method. The solid-state decomposition mechanism followed by the first degradation stage of PMPS-M was a decelerated D₄ type (three-dimensional diffusion controlled reaction). However, as for the second degradation stage of PMPS-M, its solid-state decomposition mechanism corresponded to a sigmoidal A₃ type, a nucleation and growth mechanism.