Non-parametric Kinetics Method Research Articles

Application of the NPK Method in the Crystallization Kinetics of High-Density Polyethylene

The Non-Parametric Kinetics (NPK) method, developed in 1998, by Serra, R., Sempere, J. and Nomen, R. has been used by them and other research groups to analyze the thermal behavior of a physical or chemical transformation and thermal stability. However, it was until 2021 that the method was applied for the first time in a cooling process for the determination of the crystallization kinetics of polypropylene, obtaining satisfactory results.
 The advantage of the NPK method is that it does not assume any model for the temperature function, nor for the conversion function to describe the crystallization kinetics. Through a mathematical process, the method provides two vectors: the vector u, which contains the information about the kinetic model, and the vector v, which contains the information about the temperature function.
 The aim of this work is to verify that the NPK method is applicable to the crystallization of high-density polyethylene by comparing the results with the most commonly used models to describe the crystallization kinetics of polymers. The fits obtained were very good and the vector u and v allow us to reproduce the original curves from DSC.

Thermal stability and kinetic degradation study for dihydroartemisinin

Dihydroartemisinin (DHA), the hydrogenated derivative of the naturally originated sesquiterpene lactone artemisinin, is a well-known antimalarial agent that is currently researched because of its potential as an anticancer medication. Because DHA has been associated with a low oral bioavailability and a short half-life, new formulations meant to overcome these shortcomings are currently under development. As such, the present paper aims to present a comprehensive physico-chemical profile of DHA containing data of great importance for the preformulation stages of the drug design process. As instrumental techniques, attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) spectroscopy and thermal analysis (TG—thermogravimetric/DTG—derivative thermogravimetric/HF—heat flow) were performed, followed by a kinetic study realized using three isoconversional methods (Friedman—Fr, Flynn–Wall–Ozawa—FWO and Kissinger–Akahira–Sunose—KAS), as well as the nonparametric kinetic method (NPK). FTIR spectroscopy confirmed the identity and purity of DHA, and thermal analysis revealed a relatively low thermal stability and a multistep thermooxidation that was proved during the performed kinetic study. The latter unveiled a two-process decomposition determined by both chemical degradations and physical transformations.

Solid-state stability and kinetic study of three glucocorticoid hormones: prednisolone, prednisone and cortisone

In the class of steroid hormones, glucocorticoids are belonging to the subclass of corticosteroids, consisting of numerous synthetic or naturally occurring compounds, widely used in medical practice either as replacement therapy in glucocorticoid deficiency or to suppress the immune system. Glucocorticoids are active pharmaceutical ingredients used in solid, semisolid or liquid formulations involved mainly in the treatment of different types of cancers, inflammatory and autoimmune disorders, but as well as allergies. Both thermal stability and heterogeneous degradation kinetics of prednisolone, prednisone and cortisone were investigated in dynamic inert atmosphere (dinitrogen), at five heating rates β = 7, 10, 12, 15 and 20 °C min−1 using isoconversional methods of Friedman, Kissinger–Akahira–Sunose and Flynn–Wall–Ozawa, and later the modified non-parametric kinetic (NPK) method. The variation of apparent activation energies versus conversion degree as revealed by isoconversional methods suggested multistep degradation, which was later confirmed by the NPK method. The NPK method disclosed that all three glucocorticoids are degraded by two parallel processes, with apparent activation energies of 171.7 kJ mol−1 for prednisolone, 78.8 kJ mol−1 for prednisone and 61.8 kJ mol−1 for cortisone, respectively. The results are in good agreement with the ones suggested by isoconversional methods, and a discussion regarding the relation between the structure and apparent activation energy is presented.

Advances in new multicomponent crystal system: structure, thermal kinetic analysis, photoluminescent, and biological activity investigations

Multicomponent organic crystals based on natural metabolites or pharmaceutical active ingredients play an important role in solid state chemistry, agriculture, and pharmaceutical industry. This study reveals the synthesis of a new luminescent alkanolammonium salt of 4-nitrobenzoic acid (MMEA4NB, methylethanolammonium 4-nitrobenzoate), together with the detailed investigation of its structural motifs, thermal stability, decomposition kinetics, and validation of its plant growth regulatory activity. The new compound was obtained at room temperature in excellent yield and shorter reaction time. Thermal stability and decomposition were studied in a dynamic air atmosphere by thermogravimetry—differential thermal analysis—derivative thermogravimetric techniques. The kinetics and mechanism of the thermal decomposition reaction were evaluated under non-isothermal conditions using three different isoconversional methods Flynn–Wall and Ozawa, Friedman, and modified nonparametric kinetics method in order to obtain the activation energy. Proton transfer and hydrogen bonding in the organic salt were elucidated and confirmed by infrared spectroscopy and single-crystal X-ray diffraction. The crystal structure revealed cation–anion heterosynthons and cation–cation homosynthon. The relation between the protonation state of the components, intermolecular interactions, and thermal stability of MMEA4NB is discussed. This study demonstrates the importance of MMEA4NB in the development of new specific luminescent plant growth regulators, possible viewers of localization and distribution in plants.

Solid State Stability and Kinetics of Degradation for Candesartan-Pure Compound and Pharmaceutical Formulation.

The aim of this work was to assess the impact of an excipient in a pharmaceutical formulation containing candesartan cilexetil over the decomposition of the active pharmaceutical ingredient and to comparatively investigate the kinetics of degradation during thermolysis in an oxidative atmosphere under controlled thermal stress. To achieve this, the samples were chosen as follows: pure candesartan cilexetil and a commercial tablet of 32 mg strength. As a first investigational tool, Universal attenuated total reflection Fourier transform infrared (UATR-FTIR) spectroscopy was chosen in order to confirm the purity and identity of the samples, as well as to check if any interactions took place in the tablet between candesartan cilexetil and excipients under ambient conditions. Later on, samples were investigated by thermal analysis, and the elucidation of the decomposition mechanism was achieved solely after performing an in-depth kinetic study, namely the use of the modified non-parametric kinetics (NPK) method, since other kinetic methods (American Society for Testing and Materials—ASTM E698, Friedman and Flynn–Wall–Ozawa) led to inadvertencies. The NPK method suggested that candesartan cilexetil and the tablet were degraded by the contribution of two steps, the main being represented by chemical degradation and the secondary being a physical transformation. The excipients chosen in the formulation seemed to have a stabilizing effect on the decomposition of the candesartan cilexetil that was incorporated into the tablet, relative to pure active pharmaceutical ingredient (API), since the apparent activation energy for the decomposition of the tablet was 192.5 kJ/mol, in comparison to 154.5 kJ/mol for the pure API.

NPK 2.0: Introducing tensor decompositions to the kinetic analysis of gas–solid reactions

AbstractA method for deriving kinetic models of gas–solid reactions for reactor and process design is presented. It is based on the nonparametric kinetics (NPK) method and resolves many of its shortcomings by applying tensor rank‐1 approximation methods. With this method, it is possible to derive kinetic models based on the general kinetic equation from any combination of experiments without additional a priori assumptions. The most notable improvements over the original method are that it is computationally much simpler and that it is not limited to two variables. Two algorithms for computing the rank‐1 approximation as well as a tailored initialization method are presented, and their performance is assessed. Formulae for the variance estimation of the solution values are derived to improve the accuracy of the model identification and to provide a tool for diagnosing the quality of the kinetic model. The methods effectiveness and performance are assessed by applying it to a simulated data set. A Matlab implementation is available as Supporting Information.

Thermal decomposition of tricyclohexylidene triperoxide

The thermal decomposition of tricyclohexylidene triperoxide both pure and in 4% w/w solution of n-dodecane to yield mainly 16-hexadecanolide is studied applying the nonparametric kinetics method to a set of scanning calorimetry records. The apparent energies of activation obtained are 148.4 ± 0.8 and 90.9 ± 0.8 kJ mol−1, respectively. Combined kinetic models are proposed (first order + Sestak–Berggren) to describe the processes. The isothermal decomposition of the pure peroxide is studied, indicating that there is no appreciable reaction after 12 h at temperatures below 103 °C and that conversion is complete at temperatures over 137 °C.

Study of solid-state degradation of prochlorperazine and promethazine

Prochlorperazine (PCP) and promethazine (PMT) are dopamine (D2) receptor antagonists with a phenothiazinic structure that used nowadays mainly for their antiemetic properties, including for the pre- and postoperative setting. In this paper, the thermal behavior of PCP and PMT was studied, including a complete kinetic analysis for the evaluation of the degradation process in heterogenous media. Samples were analyzed using Fourier transform infrared spectroscopy, thermogravimetric analysis (TG/DTG/HF) and a preliminary kinetic analysis using the ASTM E698 kinetic method, the obtained data being later completed with an in-depth kinetic analysis according to ICTAC 2000 protocol, using the isoconversional methods of Friedman, Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose, respectively, the modified nonparametric kinetics method, the latter allowing the determination of the kinetic triplet without using any approximation, but as well the separation of parallel reaction that occurs at decomposition. The results confirmed that PCP dimaleate has a better stability in comparison with PMT hydrochloride, in terms of apparent energy of activation, probably due to solid-state structure of solid and the contribution of intermolecular bondings.

Thermal degradation, kinetic analysis and evaluation of biological activity on human melanoma for artemisinin

In this paper, the bioactive compound artemisinin (ART) was evaluated by instrumental techniques, regarding its thermal stability and mechanism of decomposition, but for the biological activity as well, using in vitro techniques, namely the cytotoxic activity evaluation on two cell types (HaCaT and A375) employing the MTT proliferation method, and the antioxidant activity (AOA) using the DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging assay. The results of the isoconversional kinetic study first lead to an indication of complex decomposition mechanism, which was later confirmed by the modified nonparametric kinetics (NPK) method. According to the NPK method, it was shown that ART is mainly degraded by the involvement of two parallel processes, with different energetic contributions that are due to chemical and physical transformations. However, the estimated mean apparent activation energy yields similar results with all four kinetic methods, ranging between 61.3 and 68.7 kJ mol−1, confirming the low thermal stability of the compound, which can be explained by the presence of reactive functional groups, such as the peroxide one. Regarding the biological activity of ART, it was shown that it can be used to induce cell growth arrest on human melanoma cell line A375, but affecting in a smaller measure the viability of HaCaT cell line, while the AOA is negligible, in comparison with standard antioxidants.

Thermal behavior of entacapone, a catechol-O-methyltransferase inhibitor used in Parkinson’s disease

Entacapone, a selective and reversible inhibitor of catechol-O-methyltransferase, is used in the treatment of Parkinson’s disease in combination with levodopa/carbidopa to treat the symptoms of end-of-dose “wearing-off” effect. Considering that new formulations are researched constantly, proper knowledge of the active pharmaceutical ingredients is crucial in the preformulation stages. Kinetic analysis was performed using three methods: one integral—Flynn–Wall–Ozawa method, one differential—Friedman method, and modified nonparametric kinetics method (NPK). The thermoanalytical curves were registered at five different heating rates: β = 5, 7, 10, 12, and 15 °C min−1. Analysis was conducted in the dynamic air atmosphere to highlight potential thermooxidative processes. This paper deals with the investigation of solid-state stability and compatibility of binary mixture of entacapone with various pharmaceutical excipients by two instrumental techniques, such as universal attenuated total reflection Fourier transform infrared and thermal analysis (TG/DTG/HF). The excipients used in the mixture were: mannitol, silicon dioxide, talc, sorbitol, magnesium stearate, and povidone.

A higher-order generalization of the NPK-method

A novel algorithm to identify the full kinetic model of solid state reactions according to the General Kinetic Equation is presented. It is a higher-order generalization of the Non-Parametric Kinetics method (NPK-method) and allows for the simultaneous identification of the conversion, temperature and pressure dependency from any combination of measurements. As a model-free identification method, it does not rely on a-priori assumptions about the kinetic model. The result vectors can be used to identify the kinetic parameters by means of model fitting for each variable independently.The steps of the algorithm are described and its effectiveness is demonstrated by applying it to simulated datasets. The kinetic parameters could be recovered very accurately from the test data, also in the presence of noise.Overall the higher order NPK-method is a very promising approach to derive kinetic models from experimental data with a minimum of a-priori assumptions about the reaction.

Сравнительный кинетический анализ термической деструкции гидрогеля на основе полиметилвинилового эфира малеиновой кислоты сшитого полипропиленгликолем

Kinetic analysis was made applying TG/DTG/HF data in nitrogen and air atmospherefor thermal decomposition of hydrogel of polymethylvinyl maleic acid ester, linked with polypropylene glycol, at different heating rates. TG/DTG/HF data were processed according to the followingkinetic models: Friedman, Flynn-Wall-Ozawa, Kissinger-Akahira-Sunose, Coates-Redfern and nonparametric kinetic method (NPK) was used, to obtain the following kinetic parameters: activationenergy and pre-exponential factor.According to the attained values of activation energy, the mechanism of degradation of the hydrogel was suggested. Values of kinetic parameters attained by different methods, are compliant to eachother. Isoconversion method is one of the methods for definition of activation energy; this methoddoes not require knowledge on analytical form of conversion function, and gives the possibility todefine the activation energy against conversion degree as well.To obtain full kinetic analysis it is necessary to process the data using non-parametric kineticmethod. Non-parametric kinetics method (NPK) of Serra, Nomen and Sempere is based upon thesuggestion that reaction velocity may be expressed as multiplication of two independent functions,f (α) and k (T). Reaction model f (α) considers the dependence of conversion degree, and k (T)considers the temperature dependence.

Studies regarding the induced thermal degradation, kinetic analysis and possible interactions with various excipients of an osseointegration agent: zoledronic acid

Zoledronic acid is a nitrogen-containing bisphosphonate agent that suppresses farnesyl diphosphate synthase, i.e., inhibits bone resorption and bone remodeling activity. Our current study evaluates the thermal behavior of zoledronic acid and performs a kinetic analysis of the main degradation process and compatibility studies between the active agent and various excipients. The thermal behavior of zoledronic acid is characterized by two thermally induced events; a dehydration process with a rate maximum at 133 °C, respectively, a complex multistep process of a deep oxidative degradation that covers a range of temperature starting at 225 °C. Kinetic parameters were determined according to ICTAC 2000 Protocol recommendations and using four kinetic methods to determine the kinetic triplet: Friedman, Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and modified nonparametric kinetic method. The thermal behavior of zoledronic acid monohydrate and of its binary mixture in 1:1 mass ratio with talc, silica, mannitol, sorbitol, hydroxyethyl cellulose and magnesium stearate, respectively, were studied by thermal analysis under nonisothermal conditions. Talc and silica were used as standard inert excipients in the binary mixture. The polyhydroxylic compounds mannitol and sorbitol and the polysaccharide hydroxyethyl cellulose have similar thermal behavior, decomposing from 300 °C. Thus, they can be used in solid formulations of zoledronic acid. Magnesium stearate is recommended to be avoided in solid formulations, due to its low thermal stability.

Kinetic study for solid-state degradation of mental disorder therapeutic agents

This paper describes the thermal investigations and kinetic analysis regarding the solid-state degradation of three compounds used as mental disorder therapeutic agents (antidepressants), namely amitriptyline, desipramine and imipramine. The study was carried according to ICTAC 2000 recommendations, by using three isoconversional methods, namely Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman. The differential method of Friedman indicated multistep degradation, which was later confirmed by the nonparametric kinetic method (NPK). NPK method showed that all three tricyclic antidepressants are degraded by two processes. In terms of apparent activation energies for decomposition, the NPK method indicated 123.4 kJ mol−1 for imipramine, 112.3 kJ mol−1 for desipramine and 82.9 kJ mol−1 for amitriptyline, and the results are in good agreement with the ones suggested by isoconversional methods.

Thermal behavior of saturated phthalic-type polyesters. Influence of the branching polyol

The influence of the branching polyol on the thermal behavior of phthalic anhydride (PA)–polyol polyesters was determined under non-isothermal conditions. The polyol was glycerol, trimethylolpropane, and pentaerythritol, used in a molar ratio of 1.5:1, 1.5:1, and 2:1 in respect of anhydride, respectively. The thermal behavior of the synthesized polyesters was qualitatively estimated by the thermoanalytical curves obtained at a heating rate of 10 °C min−1. Quantitatively, the thermal behavior of the prepared polyesters was studied by a kinetic analysis using three different methods: Friedman, Flynn–Wall–Ozawa, and modified nonparametric kinetic method. By all the samples, two thermodegradation steps were observed. The beginning of the first step of degradation was considered the qualitative criterion for the thermal stability estimation: The pentaerythritol-containing polyester was the most thermostable, until 195 °C. Also the kinetic analysis the same sample presented the highest activation energy, i.e., the lowest thermodegradation rate.

Investigation of thermal-induced decomposition of iodoform

This paper presents the results obtained after the investigation of thermal-induced decomposition of tri-iodo-substituted methane (iodoform), under non-isothermal conditions in dynamic oxidative atmosphere (air flow). Iodoform was obtained in our laboratory through haloform reaction, namely the halogenation of dimethyl ketone in the presence of a base, and later purified according to literature. The kinetic study for the thermodegradation was carried out by processing the data by Friedman, Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and modified nonparametric kinetic (NPK) methods. All the results obtained by the employment of isoconversional methods are in good agreement; the mean apparent activation energy was around 330 kJ mol−1, by all three methods. However, since variation larger than 10 % of E a versus α was noticed, the NPK method was employed, and the separation of physical versus chemical transformations of the sample was possible. NPK method suggested that the degradation of iodoform occur in two parallel processes, the main step being a chemical degradation (n = 1/3), while the parallel process is a physical–chemical one (n = 3/5; m = 1/3).

Thermal degradation, kinetic analysis, and apoptosis induction in human melanoma for oleanolic and ursolic acids

This study deals with the comparative analysis of thermal degradation (including kinetic study) in dynamic air atmosphere, for two similar-structured triterpenoid acids—ursolic (URS) and oleanolic (OLE) acids. As kinetic methods, two integral methods (Kissinger–Akahira–Sunose and Flynn–Wall–Ozawa) and one differential method (Friedman) were used. The “in-depth” kinetic analysis was completed by applying the nonparametric kinetics (NPK) method, which confirmed the multiprocess degradation suggested by isoconversional methods (the observed variation in Ea vs. conversion degree). The NPK method revealed that ursolic acid is degraded solely by two parallel chemical processes, while in the case of oleanolic acid, the processes are accompanied by physical ones. The physicochemical investigation was completed with a bioactivity evaluation regarding the apoptotic process caused by the two compounds in A2058 human melanoma cell line. It was found that the similar-structured triterpenoids possess different biological effects, OLE being antiapoptotic, while URS being strong apoptotic.

Kinetic of solid-state degradation of transitional coordinative compounds containing functionalized 1,2,4-triazolic ligand

Three coordinative compounds containing Ni(II), Cd(II) and Zn(II) and functionalized 1,2,4-triazolic ligand were prepared and characterized by both thermal and non-thermal methods. The applied instrumental techniques consisted in TG/DTG/HF analysis, FTIR spectroscopy, elemental analysis and complexometric titration, while the decomposition mechanism was evaluated by evolved gas analysis. The kinetic analysis of the thermolysis of the metal complexes was achieved using the thermogravimetric data in air for the main step of decomposition under thermal treatment in non-isothermal conditions. The kinetic parameters were estimated by using three isoconversional methods (Kissinger–Akahira–Sunose, Flynn–Wall–Ozawa and Friedman) and data collected at five different heating rates, β = 5, 7, 10, 12 and 15 °C min−1. The obtained results were corroborated with the ones obtained by using a different approach of kinetic study, namely the nonparametric kinetics method, which allows a separation of the temperature, respective conversion dependence of the reaction rate. The obtained values for the kinetic parameters are in a good agreement for all the applied protocols.

Thermal decomposition, kinetic study and evolved gas analysis of 1,3,5-triazine-2,4,6-triamine

The thermal-induced thermodegradation of melamine was studied by the TG/EGA hyphenated technique. The sudden decomposition at a relative high temperature (DTGmax = 392 °C), a significant endothermic effect (81.7 kJ mol−1) and evolved gases which stop, whatever, ignition and/or burning processes (N2, CO2, H2O) are explanations for the flame retardant effect of melamine. A kinetic analysis by four different methods [FR, FWO, KAS and non-parametric kinetic (NPK)] indicates a single step process. The activation energy values obtained by this four methods are in a very closely range (119–124 kJ mol−1). The superiority of the NPK method is due to the possibility of obtaining all the kinetic parameters in an objective manner and due to the possibility of separation of the temperature, respective conversion influence on the reaction rate.

Comparative study on the thermal behavior of two similar triterpenes from birch

A comparative study on the thermal behavior of betuline and betulinic acid was performed using a TG–FTIR hyphenated technique. The comparison was focused on the kinetic of the relevant thermal-induced phenomenon. Using three different data processing strategy, that is, Friedman, Flynn–Wall–Ozawa, and nonparametric kinetic, homogeneous values for the activation energy were obtained, especially by betulinic acid. The advantages of the nonparametric kinetic method were revealed, especially by obtaining the explicit kinetic parameters of the conversion function, without any “a priori” hypothesis.