MINISTRY OF RESEARCH, INNOVATION AND DIGITIZATION |
Advanced methodology for the kinetic analysis of complex heterogeneous processes with application in prediction of thermal behavior of materials and their thermal lifetime,
Acronym: MET-AV
Project Registration Code: PN-III-P4-ID-PCE-2016-0088
Contract number: 112PCE/2017
Financing: Public budget
Programme: Program 4 - Fundamental and Border Research
Research domain: 4 - Eco-Nano-Technology and Advanced Materials
Project type: Exploratory Research Projects(PCE)
Total amount of the contract: 850.000 lei
Of which, by financing sources:
Source 1 – public budget: 850.000 lei
Source 2 – own budget: 0 lei
Contract duration: 12.07.2017 - 31.12.2018)
Contracting Authority: Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI)
Contractor: NATIONAL INSTITUTE FOR RESEARCH AND DEVELOPMENT IN ELECTRICAL ENGINEERING ICPE-CA BUCHAREST (INCDIE ICPE-CA)
Partner P1: NATIONAL INSTITUTE FOR RESEARCH AND DEVELOPMENT IN MICROTECHNOLOGIES IMT BUCHAREST (IMT)
Abstract:
Research teams:
Project objectives:
Project stages:
Expected results:
Contact:
Stage I:
Stage II
Stage III
Abstract:
The critical analysis of the actual used methods of kinetic analysis of heterogeneous processes by using thermal analysis data (thermogravimetry, differential thermal analysis, differential scanning calorimetry) and some physical-chemical methods (IR spectroscopy, X-Ray diffraction, etc.) will be performed, putting in evidence the following open problems that will be tried solving: improving the accuracy of isoconversional methods by suggestion of an original method, assessment of errors in the evaluation of activation energy by model-free nonlinear methods, elaboration of a general algorithm for evaluation of the kinetic scheme (mechanism) and corresponding kinetic parameters for a complex heterogeneous process. The theoretical results will be checked for the following experimental data: non-isothermal and isothermal data corresponding to decomposition and/or thermo-oxidation of some polymers and polymeric materials, and the thermal decomposition of calcium carbonate. The general algorithm for evaluation of kinetic scheme and corresponding kinetic parameters of decomposition or/and thermo-oxidation of a material will be used for improving the procedures of prediction of thermal lifetime of materials that is an important parameter in designing of devices and equipments, or the prediction of duration of decomposition in industrial conditions of a raw material in order to obtain a compound or intermediate in chemical synthesis. A procedure for rapid prediction of thermal lifetime of a material by using thermal analysis methods and based on kinetic analysis of heterogeneous processes, will be elaborated. In comparison with Standardized method (IEC 216), this procedure has the following advantages: it could be applied for materials that exhibit of single-step thermal deterioration process, and also to materials that exhibit a complex thermal deterioration process; a less time consuming.
Research teams:
Coordinator CO - INCDIE ICPE-CA Bucharest
1. PhD Chim Budrugeac Petru – IDT I, Project manager
2. PhD Chim. Cucoş Andrei – CS II, Key person
3. PhD. Chim. Ştefănescu Carmen – CSII, Research team member
4. PhD Ing. Sbârcea Beatrice Gabriela - Research team member
5. Ing. Mitrea Sorina Mitrea – IDTI, Research team member
6. Ing. Chiose Ileana Laura - Research team member
7. Masterand Dascălu Radu-Cristian - Research team member
Project objectives:
The main objectives of the project are:
a. The use of thermal analysis methods (thermogravimetry (TG or TGA), differential thermal analysis (DTA), differential scanning calorimetry (DSC)) and some physical-chemical methods (IR spectroscopy (FTIR), X-Ray diffraction (XRD), etc.) for investigation of non-isothermal decomposition and/or thermo-oxidative degradation of solid compounds or materials
b. The improving of the methods for kinetic analysis of complex heterogeneous processes by suggestion and checking of an original isoconversional method, solving the problem of assessment of errors in activation energy evaluated by isoconversional non-linear methods, elaboration and checking for simulated and experimental data of a general algorithm (methodology) for evaluation of kinetic scheme and corresponding kinetic parameters of decomposition or/and thermo-oxidation of a material.
c. The use the general algorithm (methodology) for evaluation of kinetic scheme and corresponding kinetic parameters of decomposition or/and thermo-oxidation of a material for improving the procedures of prediction of thermal lifetime of materials or the prediction of decomposition duration in industrial conditions of a raw material in order to obtain a compound or intermediate in chemical synthesis.
d. Elaboration of a procedure for rapid prediction of thermal lifetime of a material by using thermal analysis methods, which is also applicable for prediction of the duration of decomposition of a raw material.
Project stages:
Stage I
Stage name: Methods of kinetic analysis of experimental data obtained by thermal analysis of materials characterized structurally by physical-chemical methods (IR spectroscopy, X-ray diffraction, etc.)
Activity type: Fundamental research
Stage duration: 12.07.2017 – 15.12.2017
Stage II
Stage name: DSSC achievement. Solve a problem regarding non-linear isoconversional methods and elaboration of a general algorithm for kinetic analysis of non-isothermal and isothermal data corresponding to heterogeneous processes
Activity type: Fundamental research
Partners involved: CO, P1
Stage duration: 16.12.2018 – 14.12.2018
Stage III
Stage name: Improving the procedures for prediction of the thermal life of the materials and the duration of decomposition of a raw material under industrial conditions
Activity type: Fundamental research
Stage duration: 15.12.2018 – 31.12.2019
Expected results:
• Documentary study;
• Physical-chemical characterization of materials, including the determination of their thermal and thermo-oxidative stabilities
• The improving of methods of kinetic analysis of heterogeneous processes (processes with participation of a solid compound or material), including the elaboration and checking of a general algorithm (methodology) for evaluation of kinetic scheme and corresponding kinetic parameters of decomposition or/and thermo-oxidation of a material ;
• The use of the general algorithm (methodology) for evaluation of kinetic scheme and corresponding kinetic parameters of decomposition or/and thermo-oxidation of a material for improving the procedures of prediction of thermal lifetime of materials or the prediction of duration of decomposition in industrial conditions of a raw material
• Scientific works communicated at national and international scientific events;
• Scientific papers submitted for publication in ISI rated journals.
Contact:
Coordinator CO: INCDIE ICPE-CA Bucharest
Project manager: PhD Petru BUDRUGEAC
Phone: 0040213467231 / extension 129, e-mail: petru.budrugeac@icpe-ca.ro
Stage I
Abstract
A critical documentary study concerning the methods of kinetic analysis of thermo-analytical data corresponding to complex heterogeneous processes has been presented. The open problems concerning the assessment of kinetic scheme and corresponding kinetic parameters have been put in evidence.
It has been suggested a simple and precise isoconversional method applicable for evaluation of activation energy dependence on the conversion degree. For the validation of the method the data obtained by thermal analysis of calcium carbonate, PVC and HDPE were used. There was a very good concordance between the activation energy values determined by the simple method proposed with those obtained by the "advanced isoconversion" and "incremental iterative" methods, which are much more laborious.
For calcium carbonate, high density polyethylene (HDPE) and vinyl polychloride (PVC), structural characterization was determined by X-ray diffraction and X-ray photoelectron spectroscopy (XPS).
Pentru materialele carbonatului de calciu, polietilenei de înaltă densitate (HDPE) şi policlorurii de vinil (PVC) s-au determinat caracterizarea structurală prin difracţie de raze X şi spectroscopiei fotoelectronice de raze X (XPS). Also, for HDPE and PVC, TG / DTG + DTA or DSC simultaneous thermal analyses coupled with FTIR were performed both under inert atmosphere and oxidizing atmosphere, in order to determine the volatile products as result of progressive heating. The data obtained were used for the validation of the proposed isoconversion method, but will be used also in the next stages of the present project which have as main objectives the elaboration of a general algorithm of kinetic analysis of the complex heterogeneous processes and the elaboration of a procedure for rapid determination of the lifetime thermal properties of materials and the duration of heterogeneous processes.
Dissemination of the results
• Submition of the following paper to Thermochimica Acta (ISI journal): „A simple and precise differential incremental isoconversional method to kinetic analysis of heterogeneous processes under arbitrary temperature programs”, author Petru Budrugeac
• Oral communication „General algorithm for evaluation of the kinetic scheme and corresponding kinetic parameters of heterogeneous processes. Applications.” author Petru Budrugeac, presented at international conference “4th Central and Eastern European Conference on Thermal Analysis and Calorimetry (CEEC-TAC4)” , Chişinău – Republica Moldova, 28 August 2017 - 31 August 2017
• Poster „Using of TG-FTIR method for studying the thermal decomposition of some electro-insulating materials”, authors Andrei Cucos, Petru Budrugeac, presented at international conference “4th Central and Eastern European Conference on Thermal Analysis and Calorimetry (CEEC-TAC4)” , Chişinău – Republica Moldova, 28 August 2017 - 31 August 2017
• Invited conference “Non-isothermal model-free prediction for assessment of conversion vs. time curves for complex processes under arbitrary temperature programs – advantages and limitations”, author P. Budrugeac”, presented at international conference “13th Mediterranean Conference on Calorimetry and Thermal Analysis (Medicta 2017)”, Loano – Italy, 24 September 2017 – 27 September2017
Stage II
Stage name: Solve a problem regarding non-linear isoconversional methods and elaboration of a general algorithm for kinetic analysis of non-isothermal and isothermal data corresponding to heterogeneous processes
Activity type: Fundamental research
Stage duration: 16.12.2018 – 14.12.2018
Activity 2.1. Solving the problem of error determination of activation energy determination by non-linear isoconversion methods
An original method for evaluation of the error in activation energy determinated by non-linear isoconversional (model-free) methods was elaborated and checked for some non-isothermal data. For this purpose, several linear and nonlinear isoconversional methods were applied for non-isothermal data corresponding to crystallization of (GeS_{2})_{0.3}(Sb_{2}S_{3})_{0.7} (4 constant heating rates), decomposition of ammonium perchlorate (6 constant heating rates), decomposition of poly(vinyl chloride) (PVC) (5 constant heating rates) and simulated data (12 constant heating rates). For each set of non-isothermal data, the linear and nonlinear isoconversional methods were applied for evaluation of activation energy (E). It has been considered some pairs “linear isoconversional method + nonlinear isoconversional method” (“differential isoconversional method suggested by Friedman + nonlinear differential method”; each “integral pair” corresponds to a certain approximation of the temperature integral). The comparison of the errors of activation energy) evaluated by a linear method (Δ_{L}E) with the Fisher confidence intervals evaluated by the corresponding nonlinear method Δ_{F}E shows that the relation Δ_{L}E = b x Δ_{F}E + c x (Δ_{F}E)^{2} (b and c are parameters that not depend on the pair of isoconversional method) exhibits a very good accuracy of Δ_{L}E vs. Δ_{F}E fitting when Δ_{F}E is evaluated for confidence level of 95%. Consequently, the errors in E evaluation by nonlinear methods could be determined by using the above equation and Δ_{F}E values determined for the confidence level of 95%. This procedure was also checked for non-isothermal data corresponding to thermal decomposition of HDPE, which were not used for evaluation of b and c parameters.
Activity 2.2. Determination of thermal degradation curves of a kind of epoxy resin at minimum 3 constant heating rates
A “composite material based on epoxy resin (D010S+D110S cured with phtalic anhydride)” was characterized by X-ray fluorescence spectroscopy (XRF), X-ray diffraction (XRD), and differential scanning calorimetry (DSC). The thermal behavior of this material, used as electro-insulating material, was performed by the following thermal analysis methods: differential scanning calorimetry (DSC), and simultaneous thermogravimetry (TG) + differential thermogravitry (DTG) + differential thermal analysis (DTA).
The heating curves TG + DTG + DTA were recorded using STA 490C apparatus produced by Netzsch – Germany, in the following conditions: temperature range 25^{o}C – 1000^{o}C, heating rates of 2.99 K.min^{-1}, 4.98 K.min^{-1}, 10.04 K.min^{-1}, 15.42 K.min^{-1}, and 21.80 K.min^{-1}, nitrogen flow (30 ml.min^{-1}), and Pt-Rh crucible. It was obtained that the material exhibits two successive global processes characterized by mass losses, and peaks in DTG and DTA curves. The parameters of these processes depend on the heating rates.
Activity 2.3. Determination of thermal degradation isotherms of a kind of epoxy resin.
Four quasi-isothermal temperature programs (quasi-365; quasi-370; quasi-375 and quasi-380, where 365, 370, 375 and 380 are the temperatures (^{o}C) of isothermal part of temperature programs) in which the thermal degradations of composite material based on epoxy resin were determined by analyzing the non-isothermal data obtained in step 2.2. For each temperature program, the dependence of mass loss vs. time was recorded.
Activity 2.4. Applying the non-linear regression method and some physical-chemical analysis methods for finding the kinetic scheme and the kinetic parameters corresponding to the heterogeneous process of decomposition of a kind of epoxy resin
The applied kinetic analysis algorithm of data obtained by thermal analysis involves the following successive steps:
(1) application for data recorded at steady heating rates of isoconversional methods to determine the dependence of apparent activation energy on the degree of conversion;
(2) processing data recorded at constant heating rates by using a non-linear regression program (we used ‘‘Netzsch Thermokinetics” program) to determine the kinetic scheme and the corresponding kinetic parameters;
(3) verification of the results obtained in step (2) for the "conversion degree vs. time or temperature” curves recorded at certain temperature programs, other than those used for kinetic parameter evaluation.
The first two steps of this procedure (algorithm) was applied for all non-isothermal data recorded at constant heating rates and whole process of thermal degradation of “composite material based on epoxy resin (D010S+D110S cured with phtalic anhydride)”. It was obtained that this process is complex one and consists in five successive reactions. For each step, the values of corresponding kinetic parameters were determined. In the third step of algorithm, the kinetic scheme and kinetic parameters thus determined were used to calculate the quasi-isothermal degradation TG curves that were compared to the corresponding experimental curves. It follows that there is a satisfactory concordance between calculated and experimental TG curves. Thus, the mechanism of the thermal degradation process and the corresponding kinetic parameters can be used for predictions corresponding to arbitrary temperature programs.
Activity 2.5. Dissemination of results through scientific communications presented at Conferences and / or Symposia and by sending articles for publication in ISI journals
I. Published paper
1. Petru Budrugeac, A simple and precise differential incremental isoconversional method to kinetic analysis of heterogeneous processes under arbitrary temperature programs, Thermochimica Acta, 661 (2018) 116-123, doi.org/10.1016/j.tca.2018.01.025
Abstract
A simple and precise linear differential incremental isoconversional (model-free) method for kinetic analysis of heterogeneous processes using thermo-analytical data recorded at arbitrary temperature programs has been suggested. This method has been applied to simulated data corresponding to a single-step process and to a complex process consisting in two consecutive reactions, and experimental data corresponding to thermal degradation of high density polyethylene (HDPE). The obtained results are consistent with those from other isoconversional methods (advanced isoconversional method suggested by Vyazovkin, iterative method suggested by Budrugeac and differential isoconversional method suggested by Friedman).
2. P.Budrugeac, Estimating errors in the determination of activation energy by nonlinear methods applied for thermoanalytical measurements performed under constant heating rates, Thermochimica Acta, 670 (2018) 1 - 6, doi.org/10.1016/j.tca.2018.09.020
Abstract
Several linear and nonlinear isoconversional methods have been applied for following non-isothermal thermoanalytical data: simulated data for two consecutive first order reactions (12 heating rates), crystallization of (GeS_{2})_{0.3}(Sb_{2}S_{3})_{0.7} (4 heating rates), decomposition of ammonium perchlorate (6 heating rates) and decomposition of poly(vinyl chloride) (PVC) (5 heating rates). It has been considered some pairs “linear isoconversional method + nonlinear isoconversional method”. The “differential pair” is “differential isoconversional method suggested by Friedman + nonlinear differential method”, while each “integral pair” corresponds to a certain approximation of the temperature integral. The values of activation energy (E), error of E obtained by linear method (Δ_{L}E) and Fischer confidence interval obtained by nonlinear method Δ_{F}E applying the procedure suggested by Vyazovkin and Wight have been determined for each pair of methods, several conversion degrees, and the confidence levels of 68.27%, 80%, 90% and 95%. It has been obtained that, for a certain pair of methods, (a) Δ_{F}E values are substantially greater than Δ_{L}E values, and (b) the values of E determined by linear method are identical with those determined by the nonlinear method. The statement (a) is explained by the procedure for (Δ_{F}E) evaluation in which it is assumed that Δ_{F}E correspond to maximum value of Fischer distribution function. According statement (b) it is expected that is a relationship between Δ_{L}E and Δ_{F}E. Both statements suggest that the error in E determined by a nonlinear isoconversional method is equal with Δ_{L}E. Satisfactory fittings of Δ_{L}E vs. Δ_{F}E have be obtained for the relationships: (1) Δ_{L}E = a x Δ_{F}E and (2) Δ_{L}E = b x Δ_{F}E + c x (Δ_{F}E)^{2}, here a, b and c are parameters which depend on the confidence limit. These relations have been also checked for high density polyethylene (HDPE) decomposition data that were not used for their derivations. For all considered data, the best accuracy of fitting of Δ_{L}E vs. Δ_{F}E has been obtained for equation (2) and Δ_{F}E determined for confidence level of 95%. It has been conclude that the evaluation of error in E determined by a nonlinear isoconversional method involves the following two successive steps: the determination of Δ_{F}E for confidence level of 95%, and the application of relation
II. Communications presented at at “12th European Symposium on Thermal Analysis and Calorimetry (ESTAC12)”, which happened from 27th to 30th of August 2018, in Brasov –Romania
1. Petru Budrugeac, Critical study concerning the use of sinusoidal modulated thermogravimetric data (MTG) for evaluation of activation energy of heterogeneous processes. (Oral presentation)
2. Andrei Cucos, Petru Budrugeac, Thermal behaviour of some electro-insulating materials studied by coupled TG-FTIR technique (Poster)
3. Carmen Paraschiv, Gabriela Hristea, Marius Lungulescu, Beatrice-Gabriela Sbarcea, Virgil Marinescu, Investigation of thermal stability and morphology of zinc oxide-graphene oxide heterostructures obtained by hydrothermal synthesis (Poster)
4. Radu-Cristian Dascălu, Andrei Cucoş, Cătălin Maxim, Delia-Laura Popescu, Marius Andruh, Comparative Thermal Studies of Polynuclear Coordination Compounds with Organostannic Knots (Poster)
III. Communication presented at „PRIOCHEM - Priorităţile Chimiei pentru o Dezvoltare Durabilă”, 10 – 12 October, Bucureşti.
5. Radu-Cristian Dascălu, Andrei Cucoş, Cătălin Maxim, Delia-Laura Popescu, Marius Andruh, Synthesis, characterization and thermal behaviour of polynuclear coordination compounds with organostannic knots (Poster)
Each published article and communication is accompanied by the following Acknowledgements: The work was supported by the Romanian “Ministry of Research and Innovation –Executive Agency for Higher Education, Research, Development and Innovation Funding, UEFISCDI” research project MET-AV, PN-III-P4-ID-PCE Nr. 112/2017.
Stage III (in progress)
Stage name: Improvement of the processes for predicting the thermal life of the materials and the duration of decomposition in industrial conditions of a raw material used to obtain a product or an intermediate compound necessary for chemical synthesis
Activity type: Fundamental research
Stage duration: 16.12.2019 – 14.12.2019
Activity 3.1. Determination of the thermo-oxidative degradation curves of a sort of epoxy resin at least 3 constant heating rates
The thermal behavior of “composite material based on epoxy resin (D010S+D110S cured with phtalic anhydride, reinforced with quartz flour)”, used as electro-insulating material, was performed by simultaneous thermogravimetry (TG) + differential thermogravimetry (DTG) + differential thermal analysis (DTA).
The heating curves TG + DTG + DTA were recorded using STA 490C apparatus produced by Netzsch – Germany, in the following conditions: temperature range 25ºC – 1000ºC, heating rates of 4,99 K.min^{-1}; 10,04 K.min^{-1} and 20.62 K.min^{-1}, oxygen flow (30 ml.min^{-1}), and Pt-Rh crucible. It was obtained that the material exhibits four successive global processes (I, II, III and IV) characterized by mass losses, and peaks in DTG curves and exothermic peaks in DTA curves. The parameters of these processes depend on the heating rates.
Activity 3.2. Determination of the thermo-oxidative degradation isotherms of a sort of epoxy resin (in progress)
The quasi-isothermal determinations were performed with the STA 490C apparatus produced by Netzsch - Germany, in oxygen flow (30 ml.min^{-1}; oxygen purity 99.999%), the sample masses being 6.66 mg and 6.86 mg, and the isothermal portions of the temperature programs being 290ºC and 295ºC. For each temperature program, the sample mass vs. time dependence was determined.
Activity 3.3. Application of nonlinear regression method and physical-chemical methods for finding the kinetic scheme and kinetic parameters corresponding to the heterogeneous process of thermo-oxidative degradation of a sort of epoxy resin
The applied kinetic analysis of data obtained by thermal analysis corresponding to the process I + process II put in evidence in nonisothermal TG curves involves the following successive steps:
(1) application for data recorded at constant heating rates of isoconversional methods to determine the dependence of apparent activation energy on the degree of conversion;
(2) processing data recorded at constant heating rates by using a non-linear regression program (we used ‘‘Netzsch Thermokinetics” program) to determine the kinetic scheme and the corresponding kinetic parameters.
To evaluate the dependence on the degree of conversion (α) of the apparent activation energy (E) of the thermo-oxidative degradation function as a function, the Friedman (FR) and Ozawa-Flynn-Wall (OFW) isoconversional methods. It was obtained that the apparent activation energy depends on the degree of conversion, and for α ≥ 0.55, the errors of evaluation of E are large. These results show that the heterogeneous process investigated is complex.
The determination of the reaction scheme and the corresponding kinetic parameters is done by the nonlinear regression method. The non-isothermal data recorded at the 3 heating rates were used together, the differential equations are numerically solved and the kinetic parameters are numerically optimized. After running the experimental data recorded at the three heating rates used, it was obtained that the thermo-oxidation of the epoxy resin composite material is satisfactorily described by the following kinetic scheme pair - kinetic models A -1 → B-2 → C-3 → D- 4 → E - FnFnFnFn, where Fn corresponds to the model of the reaction order; A, B, C, D and E are compounds; 1, 2, 3 and 4 are stages of the mechanism).
Activity 3.4. Development and verification for experimental data of a general algorithm for evaluating the kinetic scheme and kinetic parameters corresponding to the investigated processes
Critical analysis of the procedures for evaluating kinetic parameters from non-isothermal data suggested the algorithm which consists of the following successive stages:
(1) Physical-chemical characterization of the material
(2) Application for data recorded at constant heating rates of isoconversional methods to determine the dependence of apparent activation energy on the degree of conversion
(3) Processing data recorded at constant heating rates by using a linear and/or a non-linear regression program to determine the kinetic scheme and the corresponding kinetic parameters.
(4) Verification of the validity of the kinetic scheme and the corresponding kinetic parameters for the α vs. t curves recorded at temperature programs, other than those used for kinetic analysis.
In stage (1), the material is characterized by physical-chemical methods. The results obtained by these methods help us to determine the parameters at which the thermal analyzes are performed, as well as to identify the processes that take place during the progressive heating of the material.
In stage (2), it is determined the dependence of the activation energy on the conversion degree, by applying isoconversional methods. There are two possible cases, namely Case 1. E is independent on α, and Case 2. . E is dependent on . In Case 1, with high probability, the investigated process has a single step, which is characterized from a kinetic point of view by a single kinetic triplet (activation energy (E), pre-exponential factor (A) and conversion function (f(α)).
In step 2 the dependence of the activation energy (E) on the degree of conversion (α) determined by an isoconversion method is determined. There are two distinct cases: Case 1. E is independent of α and Case 2. E is dependent on α. The procedures by which this triplet can be determined are indicated.
The dependence of the activation energy on the conversion degree (Case 2) shows that the investigated process is complex (successive, parallel, reversible reactions; diffusion of the reaction products). In this case, the determination of the reaction scheme and the corresponding kinetic parameters is performed by applying a nonlinear regression method (Stage (3)). It is known that several kinetic schemes with different kinetic parameters can very well fit the experimental data obtained at linear heating speeds. To discriminate the correct kinetic scheme, Stage (4) is performed.
The verification of this algorithm will be presented in the parts of the work corresponding to the activities 3.5 - 3.8.
Activity 3.5. Applying the nonlinear regression method and some physical-chemical methods for finding the kinetic scheme and kinetic parameters corresponding to the thermal decomposition process of a polyethylene sort
The thermal behavior of a kind of low density polyethylene (LDPE) produced by ARPECHIM Pitesti was investigated. The TG, DTG and DTA curves were recorded simultaneously with the STA 490C apparatus produced by Netzsch - Germany, under nitrogen flow (30 ml.min-1; purity of nitrogen 99.999%), in the temperature range 25 - 600ºC and at heating rates of 2.50 K.min^{-1}, 5.00 K.min-1, 9.91 K.min^{-1}, 14.89 K.min^{-1} and 19.92 K.min^{-1}. It was obtained that in the progressive heating of the polyethylene two successive processes take place, namely the melting of the polyethylene characterized in the DTA curve by an endotherm and an endothermic process with formation of volatile products.
Kinetic analysis of the volatile product formation process was performed.
The activation energy was determined by the FR and OFW methods.
Both the values of E determined by the FR method and those determined by the OFW method are dependent on the degree of conversion and the standard deviations of E from the mean value are relatively large. It follows that the process of thermal degradation of polyethylene is complex.
To determine the kinetic scheme and the corresponding kinetic parameters, the program "Netzsch-Thermokinetics" was used, which also includes a nonlinear regression method.
After running the experimental data recorded at the five heating rates used it was obtained that the thermal degradation of the polyethylene is satisfactorily described by the following pair kinetic scheme - kinetic models A -1 → B-2 → C-3 → D - FnFnFn, where Fn corresponds to the mol. reaction order; A, B, C and D are compounds; 1, 2, and 3 are stages of the mechanism).
Activity 3.6. Determination of thermal degradation isotherms of a sort of polyethylene and calcium carbonate
Determination of the thermal degradation isotherms of a polyethylene sort (in progress)
Determination of the thermal degradation isotherms of calcium carbonate
The thermal decomposition of precipitated calcium carbonate GR p.a. with a purity greater than 99% granulate (particle size of 14 μm), produced by Merck - Germany. Thermogravimetric (TG) curves were recorded with the STA 490C apparatus, produced by Netzsch - Germany, under nitrogen flow 30 mL.min^{-1}; purity 99.999%, in quasi-isothermal conditions, the sample masses being in the range 5.11 - 5.18 mg.
The quasi-isothermal determinations were performed with the STA 490C apparatus produced by Netzsch - Germany, in nitrogen flow (30 ml.min-1; nitrogen purity 99.999%), and the final isothermal portions of the temperature programs being 650ºC, 660ºC, 670ºC and 700ºC. For each temperature program, the sample mass vs. time dependence was determined.
Activity 3.7. Determination of the thermal degradation curves of calcium carbonate at least 3 constant heating rates
Non-isothermal determinations were performed at constant heating rates of 2.5; 5.0; 7.5; 10.0; 12.5 and 14.9 K.mins^{-1}, in nitrogen stream (30 mL.min-1; purity 99.999%) and temperature range 25-1000ºC. It was obtained that at the breakdown of calcium carbonate a single global endothermic process with formation of calcium oxide and carbon dioxide takes place.
Activity 3.8. Application of the general algorithm for evaluation of kinetic scheme and the corresponding kinetic parameters for calcium carbonate decomposition
The elaborated algorithm (Activity 3.4) was applied for kinetic analysis of thermoanalytical data corresponding to decomposition of calcium carbonate
The activation energy was determined by the FR and Iterative (IT) methods.
Both the values of E determined by the FR method and those determined by the IT method are dependent on the degree of conversion and the standard deviations of E from the mean value are relatively large. It follows that the process of thermal degradation of calcium carbonate is complex.
To determine the kinetic scheme and the corresponding kinetic parameters, the program "Netzsch-Thermokinetics" was used, which also includes a nonlinear regression method.
After running the experimental data recorded at the five heating rates used it was obtained that the thermal degradation of the polyethylene is satisfactorily described by the following pair kinetic scheme - kinetic models A -1→B; A←2 - B -3 →C - FnFnD3, where Fn corresponds to the model of reaction order, and D3 is the diffusion model (Jander equation: (f(α)=[3(1-α)^{2/3}]/{2[1-(1-α)^{1/3}]} ) A, B, C and D are compounds; 1, 2, and 3 are steps of the mechanism). It has been shown that the calculated quasi-isothermal curves are in very good agreement with the experimental ones.
Activity 3.9. Use of data obtained by kinetic analysis for the prediction of thermal decomposition isotherms of polyethylene and calcium carbonate by kinetic scheme method and by isoconversional methods
The “kinetic scheme” method was applied to evaluate the following thermal degradation isotherms:
- thermal decomposition isotherms of LDPE corresponding to temperatures of 400ºC, 410ºC, 420ºC, 430ºC and 440ºC;
- thermal decomposition isotherms of calcium carbonate corresponding to temperatures of 600ºC, 620ºC, 640ºC, 660ºC and 680ºC.
Applying the isoconversional method for isothermal predictions leads to correct results if the relative errors of evaluation of the activation energy by the isoconversional method are less than 2%, even for small values of the conversion degree. This condition is not met by LDPE and CaCO3, and, therefore, the isoconversional prediction method does not lead to correct α vs. time curves.
Activity 3.10. Developing a procedure for rapid prediction of the thermal life of a material by using the thermal analysis data, that is also applicable for the prediction of the decomposition time of a raw material (in progress)
Activity 3.11. Dissemination of results through scientific communications presented at Conferences and / or Symposia and by sending articles for publication in ISI journals
Published paper
Petru Budrugeac, Comparison between model-based and non-isothermal model-free computational procedures for prediction of conversion-time curves of calcium carbonate decomposition, Thermochimica Acta, 679 (2019) 178322; https://doi.org/10.1016/j.tca.2019.178322
(Impact Factor: 2,251; yellow zone )
Abstract
The model-based and non-isothermal model-free procedures have been applied for prediction of conversion-time curves of calcium carbonate decomposition. In this purpose, the thermogravimetric (TG) curves corresponding to decomposition of CaCO_{3} have been recorded in nitrogen flow in non-isothermal conditions at constant heating rates of 2.5; 5.0; 7.5; 10.0; 12.5 and 14.9 K.min^{-1}, and in other temperature programs that exhibit the following final isothermal steps: 650°C; 660°C; 670°C and 700°C.
To apply model-based procedure, the most probable kinetic schemes and corresponding kinetic parameters have been determined by using the non-isothermal data, and the isoconversional and “multivariate nonlinear regression” (“Multivar-NLR”) methods. By comparing the experimental and predicted conversion-time curves that exhibit a final isothermal step, it as been obtained that the most probable kinetic scheme consists a reversible reaction of CaCO_{3} decomposition followed by diffusion of carbon dioxide. The non-isothermal model free prediction procedure has been also used for assessment of conversion-time curves that exhibit a final isothermal step. Both model-based procedure and non-isothermal model-free procedure lead to satisfactory agreements between experimental and calculated conversion curves corresponding to temperature programs that exhibit a final isothermal step, but the curves predicted by a non-isothermal model-free procedure have a large deviation from the experimental ones than those predicted by model-based procedure.
Paper in progress that will be sent for publication to the journal Thermochimica Acta
Petru Budrugeac, Estimating errors in the determination of activation energy by nonlinear isoconversional methods applied for thermoanalytical measurements performed under arbitrary temperature programs
Abstract
In a previous paper (Thermochimica Acta, 670 (2018) 1-6) it has been obtained that for thermoanalytical measurements performed under constant heating rates, the error in determination of the activation energy by using nonlinear methods (ΔE) can be evaluated by applying the relation:
ΔE = 0.2447(±0.0005)xΔ_{F}E + 0.00037(±0.00001)x(Δ_{F}E)^{2}
where Δ_{F}E is the Fischer confidence interval obtained by nonlinear method (Δ_{F}E) for confidence level of 95% determined by the procedure suggested by Vyazovkin and Wight (Anal. Chem. 72 (2000) 3171-3175).
This relationship has been verified also for the following sets of thermoanalytical data performed under arbitrary temperature programs: simulated sinusoidal modulated data, experimental TG data obtained in investigating thermal decomposition of HDPE under quasi-isothermal conditions and experimental TG data obtained in investigating thermal decomposition of LDPE under arbitrary temperature programs.
It has been pointed out that for thermoanalytical data performed under any temperature programs, the procedure for evaluation the error of activation energy determinate by a nonlinear isoconversional method consisting in the following two successive steps: the determination of Δ_{F}E for confidence level of 95%, and the evaluation of ΔE by using the above relationship between ΔE and Δ_{F}E.
Scientific communications at conferences and / or scientific symposia
1. Oral paper communicated to “28th Symposium of Thermal Analysis and Calorimetry – Eugen Segal”, Timişoara, 9 – 10. 05. 2019.
Petru Budrugeac, On the applicability of incremental model-free methods to determine activation energy corresponding to heterogeneous processes performed under arbitrary temperature programs
Abstract
The applicability of the following isoconversional (model-free) incremental methods for determining the energy of activation of the heterogeneous processes under arbitrary temperature programs are discussed: advanced nonlinear isoconversional method (A-NL method), iterative incremental isoconversion method (IT-method) and incremental differential method (Incr-dif method).
It is justified that when a process takes place in some arbitrary temperature programs, always applying the A-NL method considering that dependence T vs. t is linear even for narrow domains of the degree of conversion leads to erroneous activation energy values.
A procedure for applying the A-NL method applicable to any temperature programs (modified A-NL method) has been suggested. This procedure has been verified for simulated sinusoidal modulated data, experimental data obtained by TG analysis of HDPE under quasi-isothermal conditions, and experimental TG data obtained in investigating thermal decomposition of LDPE under arbitrary temperature programs. For this purpose, the values of the activation energy obtained by the modified A-NL, IT and Incr-dif were compared.
Acknowledgements
The work was supported by the Romanian “Ministry of Research and Innovation –Executive Agency for Higher Education, Research, Development and Innovation Funding, UEFISCDI” research projects— Advanced methodology for the kinetic analysis of complex heterogeneous processes with application in prediction of thermal behavior of materials and their thermal lifetime (MET-AV, PN-III-P4-ID-PCE Nr. 112/2017).
2. Oral paper communicated to “2nd Journal of Thermal Analysis and Calorimetry Conference (2nd JTACC+V4 2019)”, June 18-21, 2019, Budapest, Hungary
Petru Budrugeac, Applicability of incremental isoconversional methods to determine of the dependence of activation energy on the conversion degree corresponding to heterogeneous processes performed under arbitrary temperature programs
Abstract
The following incremental isoconversional methods can be used to evaluate the dependence of activation energy on the conversion degree of heterogeneous processes occurring in arbitrary temperature programs, including programs with constant heating rates: advanced non-linear isoconversional method (A-NL) [1]; integral incremental isoconversional method (Incr-int) [2]; differential incremental isoconversional method [3]; iterative incremental isoconversional method [4].
A-NL, Incr-int and Incr-dif methods are applicable only if for small intervals of the conversion degree, the dependencies temperature (T) vs. time (t) can be approximated satisfactorily with straight lines. For example, this condition is respected when using constant heating rate programs. However, it also uses temperature programs in which this condition is not desirable, e.g. sinusoidal modulated programs. For such programs, the correct values of activation energy are obtained by the IT method in which the temperature integral is performed numerically. Also, the A-NL method could be applied in these cases if the temperature integral to a determination would be evaluated as the sum of the integers corresponding to each linear portion of the T vs. t curve own to the range of conversion. Applying the procedure involves the initial drawing of the T vs. t for delimiting linear domains. Verification of this procedure was performed for simulated sinusoidal modulated data and experimental data obtained by TG analysis of HDPE under quasi-isothermal conditions. The values of the activation energy thus obtained are compared with those obtained by applying the Incr-int, Incr-dif and IT methods.
Acknowledgements
The work was supported by the Romanian “Ministry of Research and Innovation –Executive Agency for Higher Education, Research, Development and Innovation Funding, UEFISCDI” research projects— Advanced methodology for the kinetic analysis of complex heterogeneous processes with application in prediction of thermal behavior of materials and their thermal lifetime (MET-AV, PN-III-P4-ID-PCE Nr. 112/2017).
References
[1] Vyazovkin S, Modification of the integral isoconversional method to account for variation in the activation energy. J Comput Chem. 2001; 22:178-183.
[2] Ortega A, A simple and precise linear integral method for isoconversional data. Thermochim Acta, 2008; 474: 81-86.
[3] Budrugeac P, A simple and precise differential incremental isoconversional method to kinetic analysis of heterogeneous processes under arbitrary temperature programs. Thermochim Acta, 2018; 661:116- 123.
[4] Budrugeac P, An iterative model-free method to determine the activation energy of heterogeneous processes under arbitrary temperature program. Thermochim Acta. 2011; 523: 84-89.
3. Oral paper communicated to “5th Central and Eastern European Conference on Thermal
Analysis and Calorimetry (CEEC-TAC5) and 14th Mediterranean Conference on Calorimetry and Thermal Analysis (Medicta2019)”, Roma, Italy, 27 -31 August 2019
Petru Budugeac, Estimating errors in the determination of activation energy by nonlinear isoconversional methods applied for thermoanalytical measurements
Abstract
Several linear and nonlinear isoconversional methods have been applied for following non-isothermal thermoanalytical data performed under constant heating rates: crystallization of (GeS_{2})_{0.3}(Sb_{2}S_{3})_{0.7} (4 heating rates), decomposition of ammonium perchlorate (6 heating rates) and decomposition of poly(vinyl chloride) (PVC) (5 heating rates) and simulated data for two consecutive first order reactions (12 heating rates). It has been considered some pairs “linear isoconversional method + nonlinear isoconversional method”. Each “integral pair” corresponds to a certain approximation of the temperature integral. The values of activation energy (E), error of E obtained by linear method (Δ_{L}E) and Fischer confidence interval obtained by nonlinear method (Δ_{F}E) applying the procedure suggested by Vyazovkin and Wight [1] have been determined for each pair of methods, several conversion degrees, and the confidence level of 95%. It has been obtained that, for a certain pair of methods, (a) Δ_{F}E values are substantially greater than Δ_{L}E values, and (b) the values of E determined by linear method are identical with those determined by the nonlinear method. The statement (a) is explained by the procedure for Δ_{F}E evaluation in which it is assumed that Δ_{F}E correspond to maximum value of Fischer distribution function. According statement (b) it is expected that is a relationship between Δ_{L}E and Δ_{F}E. Both statements suggest that the error in E determined by a nonlinear isoconversional method (ΔE) is equal with Δ_{L}E. It has been obtained the following correlation between Δ_{L}E and Δ_{F}E valid for all pairs of isoconversional methods and all considered processes:
ΔE = 0.2447(±0.0005)xΔ_{F}E + 0.00037(±0.00001)x(Δ_{F}E)^{2}
This relationship has been verified also for the following sets of thermoanalytical data performed under arbitrary temperature programs: simulated sinusoidal modulated data, experimental TG data obtained in investigating thermal decomposition of HDPE under quasi-isothermal conditions and experimental TG data obtained in investigating thermal decomposition of LDPE under arbitrary temperature programs.
For thermoanalytical data performed under any temperature programs, the procedure for evaluation the error of activation energy determinate by a nonlinear isoconversional method consisting in the following two successive steps: the determination of Δ_{F}E for confidence level of 95%, and the evaluation of ΔE by using the above relationship between ΔE and Δ_{F}E.
Acknowledgements
The work was supported by the Romanian “Ministry of Research and Innovation –Executive Agency for Higher Education, Research, Development and Innovation Funding, UEFISCDI” research projects— Advanced methodology for the kinetic analysis of complex heterogeneous processes with application in prediction of thermal behavior of materials and their thermal lifetime (MET-AV, PN-III-P4-ID-PCE Nr. 112/2017).
Reference
[1] S. Vyazovkin, C. A. Wight, Anal. Chem. 72 (2000) 3171-3175.