Isoconversional Kinetics of Polymers: The Decade Past

Study on the thermal decomposition mechanism of Mg(NO3)2·6H2O from the perspective of resource utilization of magnesium slag

The magnesium slag (magnesium nitrate hydrate Mg(NO3)2·6H2O) produced in the nitric acid leaching process of laterite nickel ore can be effectively recycled by thermal decomposition. To this end, this study placed great emphasis on disclosing the thermal decomposition mechanism of Mg(NO3)2·6H2O. Firstly, thermal decomposition paths of Mg(NO3)2·6H2O were revealed through Thermogravimetry-Mass Spectrometry, Differential Scanning Calorimetry and powder X-ray diffraction. It was found that the thermal decomposition of Mg(NO3)2·6H2O was a multistep endothermic reaction involving two dehydration stages and one denitration stage. The two dehydration stages were characterized by the evolution of H2O, with the formation of magnesium nitrate dihydrate and anhydrous magnesium nitrate. The denitration stage was characterized by the simultaneous evolution of O2 and NO2, with the formation of MgO. The conventional kinetic analysis was not suitable for describing such complex multistep reaction behaviour. Thus, the kinetic rate data (dα/dt-T) for the overall reaction were separated into those for three contributing stages by mathematical peak deconvolution. Then, the complete kinetic interpretations of the separated reaction stages for Mg(NO3)2·6H2O pyrolysis were achieved by the Friedman method and the master plots method. Finally, the original experimental α-T curves were successfully simulated using the resulting kinetic triplets.

Coamorphous Systems of Valsartan: Thermal Analysis Contribution to Evaluate Intermolecular Interactions Effects on the Structural Relaxation

Coamorphous formation in binary systems of valsartan (Val) with 4,4'-bipyridine (Bipy) and trimethoprim (Tri) was investigated for mixtures with a mole fraction of 0.16~0.86 of valsartan and evaluated in terms of the glass transition temperature. The glass transition of the systems had a behavior outside the values predicted by the Gordon-Taylor equation, showing that Val-Bipy (hydrogen bonding between the components) had a lower deviation and Val-Tri (ionic bonding between the components) had a higher deviation. Mixtures of compositions 2:1 Val-Bipy and 1:1 Val-Tri were selected for further investigation and verified to be stable, as no crystallization was observed during subsequent heating and cooling programs. For these systems, the effective activation energy during glass transition was evaluated. Compared to pure valsartan, the system with the lower glass transition temperature (Val-Bipy) presented the highest effective activation energy, and the system with the higher glass transition temperature (Val-Tri) presented a lower effective activation energy. The results presented a good correlation between the data obtained from two different techniques to determine the fragility and effective activation energy: non-isothermal kinetic analysis by DSC and TSDC.

Kinetic Study of the Effective Thermal Polymerization of a Prebiotic Monomer: Aminomalononitrile

Aminomalononitrile (AMN), the HCN formal trimer, is a molecule of interest in prebiotic chemistry, in fine organic synthesis, and, currently, in materials science, mainly for bio-applications. Herein, differential scanning calorimetry (DSC) measurements by means of non-isothermal experiments of the stable AMN p-toluenesulfonate salt (AMNS) showed successful bulk AMN polymerization. The results indicated that this thermally stimulated polymerization is initiated at relatively low temperatures, and an autocatalytic kinetic model can be used to appropriately describe, determining the kinetic triplet, including the activation energy, the pre-exponential factor, and the mechanism function (E_α, A and f(α)). A preliminary structural characterization, by means of Fourier transform infrared (FTIR) spectroscopy, supported the effective generation of HCN-derived polymers prepared from AMNS. This study demonstrated the autocatalytic, highly efficient, and straightforward character of AMN polymerization, and to the best of our knowledge, it describes, for the first time, a systematic and extended kinetic analysis for gaining mechanistic insights into this process. The latter was accomplished through the help of simultaneous thermogravimetry (TG)-DSC and the in situ mass spectrometry (MS) technique for investigating the gas products generated during these polymerizations. These analyses revealed that dehydrocyanation and deamination processes must be important elimination reactions involved in the complex AMN polymerization mechanism.

Determining Preexponential Factor in Model-Free Kinetic Methods: How and Why?

The kinetics of thermally stimulated processes in the condensed phase is commonly analyzed by model-free techniques such as isoconversional methods. Oftentimes, this type of analysis is unjustifiably limited to probing the activation energy alone, whereas the preexponential factor remains unexplored. This article calls attention to the importance of determining the preexponential factor as an integral part of model-free kinetic analysis. The use of the compensation effect provides an efficient way of evaluating the preexponential factor for both single- and multi-step kinetics. Many effects observed experimentally as the reaction temperature shifts usually involve changes in both activation energy and preexponential factor and, thus, are better understood by combining both parameters into the rate constant. A technique for establishing the temperature dependence of the rate constant by utilizing the isoconversional values of the activation energy and preexponential factor is explained. It is stressed that that the experimental effects that involve changes in the preexponential factor can be traced to the activation entropy changes that may help in obtaining deeper insights into the process kinetics. The arguments are illustrated by experimental examples.

Activation Energies and Temperature Dependencies of the Rates of Crystallization and Melting of Polymers

The objective of this review paper is to survey the phase transition kinetics with a focus on the temperature dependence of the rates of crystallization and melting, as well as on the activation energies of these processes obtained via the Arrhenius kinetic treatment, including the treatment by isoconversional methods. The literature is analyzed to track the development of the basic models and their underlying concepts. The review presents both theoretical and practical considerations regarding the kinetic analysis of crystallization and melting. Both processes are demonstrated to be kinetically complex, and this is revealed in the form of nonlinear Arrhenius plots and/or the variation of the activation energy with temperature. Principles which aid one to understand and interpret such results are discussed. An emphasis is also put on identifying proper computational methods and experimental data that can lead to meaningful kinetic interpretation.

Melting Kinetics of Nascent Poly(tetrafluoroethylene) Powder

The melting behavior of nascent poly(tetrafluoroethylene) (PTFE) was investigated by way of differential scanning calorimetry (DSC). It is well known that the melting temperature of nascent PTFE is about 344 ∘ C, but reduces to 327 ∘ C for once molten material. In this study, the melting temperature of nascent PTFE crystals was found to strongly depend on heating rate, decreasing considerably for slow heating rates. In addition, during isothermal experiments in the temperature range of 327 ∘ C < T < 344 ∘ C, delayed melting of PTFE was observed, with complete melting only occurring after up to several hours. The melting kinetics of nascent PTFE were analyzed by means of the isoconversional methodology, and an apparent activation energy of melting, dependent on the conversion, was determined. The compensation effect was utilized in order to derive the pre-exponential factor of the kinetic model. The numerical reconstruction of the kinetic model was compared with literature models and an Avrami-Erofeev model was identified as best fit of the experimental data. The predictions of the kinetic model were in good agreement with the observed time-dependent melting of nascent PTFE during isothermal and constant heating-rate experiments.

Nanoconfined gelation of polyacrylonitrile, poly(vinyl alcohol), and isotactic polypropylene probed by calorimetry

Differential scanning calorimetry is used to obtain insights into the kinetics and thermodynamics of nanoconfined gelation. Gels of polyacrylonitrile in propylene carbonate, poly(vinyl alcohol) in ethylene glycol, and isotactic polypropylene in o-dichlorobenzene and decalin are studied in silica nanopores. Two major effects are observed for nanoconfined gels: a decrease in the heat of gelation and an increase in the gelation temperature. The smaller heat indicates that nanoconfinement of polymer chains results in the formation of fewer ordered crosslinks. The increased gelation temperature suggests acceleration of the gelation kinetics. The kinetics has been treated by an advanced isoconversional method and interpreted in terms of the Fisher-Turnbull model. It is found that acceleration of gelation in nanopores is associated with a decrease in the free energy barrier to nucleation, as one would expect for a change in the process mechanism from homogenous to heterogenous nucleation.

Rheological and thermal degradation properties of hyperbranched polyisoprene prepared by anionic polymerization

Hyperbranched polyisoprene was prepared by anionic copolymerization under high vacuum condition. Size exclusion chromatography was used to characterize the molecular weight and branching nature of these polymers. The characterization by differential scanning calorimetry and melt rheology indicated lower Tg and complex viscosity in the branched polymers as compared with the linear polymer. Degradation kinetics of these polymers was explored using thermogravimetric analysis via non-isothermal techniques. The polymers were heated under nitrogen from ambient temperature to 600°C using heating rates from 2 to 15°C min-1. Three kinetics methods namely Friedman, Flynn-Wall-Ozawa and Kissinger-Akahira-Sunose were used to evaluate the dependence of activation energy (Ea ) on conversion (α). The hyperbranched polyisoprene decomposed via multistep mechanism as manifested by the nonlinear relationship between α and Ea while the linear polymer exhibited a decline in Ea at higher conversions. The average Ea values range from 258 to 330 kJ mol-1 for the linear, and from 260 to 320 kJ mol-1 for the branched polymers. The thermal degradation of the polymers studied involved one-dimensional diffusion mechanism as determined by Coats-Redfern method. This study may help in understanding the effect of branching on the rheological and decomposition kinetics of polyisoprene.

All You Need to Know about the Kinetics of Thermally Stimulated Reactions Occurring on Cooling

In this tutorial overview article the authors share their original experience in studying the kinetics of thermally stimulated reactions under the conditions of continuous cooling. It is stressed that the kinetics measured on heating is similar to that measured on cooling only for single-step reactions. For multi-step reactions the respective kinetics can differ dramatically. The application of an isoconversional method to thermogravimetry (TGA) or differential scanning calorimetry (DSC) data allows one to recognize multi-step kinetics in the form of the activation energy that varies with conversion. Authors' argument is supported by theoretical considerations as well as by experimental examples that include the reactions of thermal decomposition and crosslinking polymerization (curing). The observed differences in the kinetics measured on heating and cooling ultimately manifest themselves in the Arrhenius plots of the opposite curvatures, which means that the heating kinetics cannot be used to predict the kinetics on cooling. The article provides important background knowledge necessary for conducting successful kinetic studies on cooling. It includes a practical advice on optimizing the parameters of cooling experiments as well as on proper usage of kinetic methods for analysis of obtained data.

Gelation of Poly(Vinylidene Fluoride) Solutions in Native and Organically Modified Silica Nanopores

The purpose of this study is to highlight the surface and size effects of the nanopores on the thermodynamics and kinetics of gelation. The effects have been probed by applying differential scanning calorimetry to poly(vinylidene fluoride) solutions in tetraethylene glycol dimethyl ether (tetraglyme) and γ-butyrolactone. Nanoconfinement has been accomplished by introducing gels into native and organically modified silica nanopores (4–30 nm). Nanoconfinement has produced two major effects. First, the heat of gelation has decreased three to four times compared to that for the bulk systems. Second, the temperature of gelation has increased by ~40 °C (tetraglyme based systems) and ~70 °C (γ-butyrolactone based systems), the increase being stronger in native nanopores. The effects are discussed in terms of acceleration of gelation due to heterogeneous nucleation at the confining surface, and retardation of gelation due to constricted polymer chain mobility in the middle of the pore volume. Calorimetric data have been subjected to isoconversional kinetics analysis. The obtained temperature dependencies of the activation energies of gelation have been interpreted in the frameworks of the nucleation model of Turnbull and Fisher. The results suggest that nanoconfinement leads to a lowering of both the free energy of nucleation and activation energy of diffusion.

Cationic Cyclopentadienyliron Complex as a Novel and Successful Nucleating Agent on the Crystallization Behavior of the Biodegradable PHB Polymer

Cationic cyclopentadienyliron (CpFe⁺) is one of the most fruitful organometallic moieties that has been utilized to mediate the facile synthesis of a massive number of macromolecules. However, the ability of this compound to function as a nucleating agent to improve other macromolecule properties has not been explored. This report scrutinizes the influence of the cationic complex as a novel nucleating agent on the spherulitic morphology, crystal structure, and isothermal and non-isothermal crystallization behavior of the Poly(3-hydroxybutyrate) (PHB) bacterial origin. The incorporation of the CpFe⁺ into the PHB materials caused a significant increase in its spherulitic numbers with a remarkable reduction in the spherulitic sizes. Unlike other nucleating agents, the SEM imageries exhibited a good dispersion without forming agglomerates of the CpFe⁺ moieties in the PHB matrix. Moreover, according to the FTIR analysis, the cationic organoiron complex has a strong interaction with the PHB polymeric chains via the coordination with its ester carbonyl. Yet, the XRD results revealed that this incorporation had no significant effect on the PHB crystalline structure. Though the CpFe⁺ had no effect on the polymer’s crystal structure, it accelerated outstandingly the melt crystallization of the PHB. Meanwhile, the crystallization half-times (t_0.5) of the PHB decreased dramatically with the addition of the CpFe⁺. The isothermal and non-isothermal crystallization processes were successfully described using the Avrami model and a modified Avrami model, as well as a combination of the Avrami and Ozawa methods. Finally, the effective activation energy of the PHB/CpFe⁺ nanocomposites was much lower than those of their pure counterparts, which supported the heterogeneous nucleation mechanism with the organometallic moieties, indicating that the CpFe⁺ is a superior nucleating agent for this class of polymer.

"Nothing Can Hide Itself from Thy Heat": Understanding Polymers via Unconventional Applications of Thermal Analysis

This article surveys some exciting possibilities and results offered by less common, yet essential applications of differential scanning calorimetry and thermogravimetric analysis (TGA). The applications are concerned with the most commonly studied processes of the glass transition, crystallization, melting, polymerization, and degradation. Issues related to the glass transition include the non-Arrhenius temperature dependence and fragility, kinetic complexity of physical aging, evaluation of cooperatively rearranging regions, and rigid amorphous fraction. Discussion of crystallization covers separation of heterogeneous and homogeneous nucleation, crystallization controlled by physical aging, and the use of isoconversional methods for determining the Hoffman-Lauritzen parameters. For melting, the role of reorganization and nucleation control is emphasized. For the thermal degradation and polymerization, advanced kinetic treatments as a way of obtaining mechanistic insights are discussed, and the possibility of studying both processes during continuous cooling is stressed. The possibility of using TGA for monitoring polycondensation is also highlighted.

Ring-opening copolymerization thermodynamics and kinetics of γ-valerolactone/ϵ-caprolactone

The general misconception that γ-lactones are not thermodynamically polymerizable has limited the development of all γ-lactone-based copolymers. A few studies have reported copolymerization of these five-membered cyclic esters with more reactive monomers, yet a systematic investigation of kinetics and thermodynamics is still lacking. To explore the feasibility of the reaction, we combined equilibrium and non-isothermal syntheses for the copolymerization of γ-valerolactone with ϵ-caprolactone, initiated with methoxy polyethyleneglycol and catalyzed by Tin(II) 2-ethylhexanoate. Here, we present the polymerization kinetic and thermodynamic parameters for different monomer ratios in the reaction feed. We observed the dependency of enthalpy and entropy of polymerization upon monomer ratio changes, and estimated a linear increase in the activation energy by increasing the γ-valerolactone fraction in the starting monomer mixture. Our data demonstrate that γ-valerolactone can copolymerize with ϵ-caprolactone, but only under specific conditions. The reaction parameters determined in this study will enable preparation of additional γ-valerolactone-based copolymers and development of a family of degradable materials with improved properties in respect to commonly used polyesters.

Melting kinetics of superheated crystals of glucose and fructose

Glucose and fructose crystals undergo significant superheating during melting that allows one to study the kinetics of this process. Melting of both compounds has been studied by differential scanning calorimetry (DSC). The obtained data have been subjected to isoconversional kinetic analysis. The process has been determined to have unusually large values of the activation energy and preexponential factor that indicate that melting occurs by cooperatively breaking multiple hydrogen bonds. The experimentally determined activation energy of melting demonstrates a decrease with increasing temperature. The use of the nucleation and growth models has permitted deriving theoretical dependencies of the activation energy on temperature. Testing the theoretical dependencies against the experimental ones suggests that from either the statistical or physical viewpoint the melting kinetics should be parameterized by means of the growth model. This suggests that the mechanism of melting involves the growth of the stable melt nuclei that exist on the crystal surface below the equilibrium melting temperature.

Modelling the kinetics and structural property evolution of a versatile reaction: aqueous HCN polymerization

The structural characterization and kinetics of HCN polymers were studied and the Kamal autocatalytic model can describe this aqueous precipitation polymerization.

Kinetics of Thermal Polymerization Can Be Studied during Continuous Cooling

It is demonstrated that differential scanning calorimetry can measure the kinetics of the thermally initiated polymerization during continuous cooling. The measurements are accomplished by switching from fast heating to much slower cooling. The study is exemplified by crosslinking polymerization (curing) of diglycidyl ether of bisphenol A epoxy and m-phenylenediamine taken in stoichiometric and nonstoichiometric ratios and measured under heating and cooling conditions. An advanced isoconversional method reveals that the reaction in the nonstoichiometric system follows the kinetics of the single-step type. Its activation energy is constant and the same for heating and cooling conditions. The stoichiometric system exhibits the multistep kinetics characterized by the dependencies of the activation energy on temperature that differ qualitatively for cooling and heating runs. The discovered differences emphasize the need for further systematic studies of the thermal polymerization during continuous cooling.

Phase separation of triethylamine and water in native and organically modified silica nanopores

A mixture of triethylamine and water is a lower critical solution temperature system that demixes (separates into individual phases) on heating. Differential scanning calorimetry has been applied to study the process of demixing in native and organically modified silica nanopores whose size varied from 4 to 30 nm. It has been found that in both types of nanopores, the temperature and enthalpy of demixing decrease significantly with decreasing the pore size. Isoconversional kinetic analysis has been utilized to determine the activation energy and pre-exponential factor of the process. It has been demonstrated that the depression of the transition temperature upon nanoconfinement is associated with acceleration of the process due to lowering of the activation energy. Nanoconfinement has also been found to lower the pre-exponential factor of the process that has been linked to a decrease in the molecular mobility.