{"title":"积分等值转换法在数学上的正确应用","authors":"Tibor Dubaj , Zuzana Cibulková , Peter Šimon","doi":"10.1016/j.tca.2024.179739","DOIUrl":null,"url":null,"abstract":"<div><p>Here we suggest that integral isoconversional method, when applied in a mathematically correct way, can lead to satisfactory results with the least number of adjustable parameters. Differential and incremental methods are used in cases when the apparent activation energy, <em>E</em>, varies with the degree of conversion, <em>α</em>. However, in some cases the observed <em>E</em>(<em>α</em>) dependence can spuriously be induced by small variations in <em>α</em>(<em>T</em>) curves and there is only little to no benefit gained from allowing arbitrary change of <em>E</em> between adjacent conversion levels. As a result, the <em>E</em>(<em>α</em>) dependences are highly “fragile” and subject to minor variations in the experimental data. On the other hand, when the activation energy is optimized globally for all isoconversional levels, a significantly more robust estimate is obtained and the agreement between the experimental and simulated data is still plausible. The approach is demonstrated on two datasets which were evaluated with both variable <em>E</em>(<em>α</em>) dependence and with constant value of <em>E</em>.</p></div>","PeriodicalId":23058,"journal":{"name":"Thermochimica Acta","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040603124000789/pdfft?md5=a042590e5011a736cf06d9484117d291&pid=1-s2.0-S0040603124000789-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Mathematically correct application of integral isoconversional method\",\"authors\":\"Tibor Dubaj , Zuzana Cibulková , Peter Šimon\",\"doi\":\"10.1016/j.tca.2024.179739\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Here we suggest that integral isoconversional method, when applied in a mathematically correct way, can lead to satisfactory results with the least number of adjustable parameters. Differential and incremental methods are used in cases when the apparent activation energy, <em>E</em>, varies with the degree of conversion, <em>α</em>. However, in some cases the observed <em>E</em>(<em>α</em>) dependence can spuriously be induced by small variations in <em>α</em>(<em>T</em>) curves and there is only little to no benefit gained from allowing arbitrary change of <em>E</em> between adjacent conversion levels. As a result, the <em>E</em>(<em>α</em>) dependences are highly “fragile” and subject to minor variations in the experimental data. On the other hand, when the activation energy is optimized globally for all isoconversional levels, a significantly more robust estimate is obtained and the agreement between the experimental and simulated data is still plausible. The approach is demonstrated on two datasets which were evaluated with both variable <em>E</em>(<em>α</em>) dependence and with constant value of <em>E</em>.</p></div>\",\"PeriodicalId\":23058,\"journal\":{\"name\":\"Thermochimica Acta\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2024-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0040603124000789/pdfft?md5=a042590e5011a736cf06d9484117d291&pid=1-s2.0-S0040603124000789-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Thermochimica Acta\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040603124000789\",\"RegionNum\":2,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, ANALYTICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thermochimica Acta","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040603124000789","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, ANALYTICAL","Score":null,"Total":0}
引用次数: 0
摘要
在此,我们建议以正确的数学方法应用积分等值转换法,这样可以用最少的可调参数获得令人满意的结果。然而,在某些情况下,α(T) 曲线的微小变化可能会导致观察到的 E(α) 依赖性出现假象,因此在相邻转换等级之间任意改变 E 几乎没有任何益处。因此,E(α) 相关性非常 "脆弱",会受到实验数据微小变化的影响。另一方面,如果对所有等转化水平的活化能进行全局优化,就能得到明显更稳健的估计值,而且实验数据和模拟数据之间的一致性仍然可信。该方法在两个数据集上进行了演示,这两个数据集分别在 E(α) 可变依赖性和 E 值恒定的情况下进行了评估。
Mathematically correct application of integral isoconversional method
Here we suggest that integral isoconversional method, when applied in a mathematically correct way, can lead to satisfactory results with the least number of adjustable parameters. Differential and incremental methods are used in cases when the apparent activation energy, E, varies with the degree of conversion, α. However, in some cases the observed E(α) dependence can spuriously be induced by small variations in α(T) curves and there is only little to no benefit gained from allowing arbitrary change of E between adjacent conversion levels. As a result, the E(α) dependences are highly “fragile” and subject to minor variations in the experimental data. On the other hand, when the activation energy is optimized globally for all isoconversional levels, a significantly more robust estimate is obtained and the agreement between the experimental and simulated data is still plausible. The approach is demonstrated on two datasets which were evaluated with both variable E(α) dependence and with constant value of E.
期刊介绍:
Thermochimica Acta publishes original research contributions covering all aspects of thermoanalytical and calorimetric methods and their application to experimental chemistry, physics, biology and engineering. The journal aims to span the whole range from fundamental research to practical application.
The journal focuses on the research that advances physical and analytical science of thermal phenomena. Therefore, the manuscripts are expected to provide important insights into the thermal phenomena studied or to propose significant improvements of analytical or computational techniques employed in thermal studies. Manuscripts that report the results of routine thermal measurements are not suitable for publication in Thermochimica Acta.
The journal particularly welcomes papers from newly emerging areas as well as from the traditional strength areas:
- New and improved instrumentation and methods
- Thermal properties and behavior of materials
- Kinetics of thermally stimulated processes