5分钟速览热动力学研究方法
p strong 仪器信息网讯 /strong 从20世纪30年代初开始,由Tian和Calvet等着手研究了适合于缓慢而微小热变化过程的量热装置,并且得到了满意的结果,即目前的Calvet型微热量计。Calvet 为此研究了30 年,大部分论文发表在J. Chim. Phys.、CR Acad. Sci. Paris和Bull. SocChim. Fr.等期刊中,并有相关专著介绍。 /p p 1923年,世界上第一台热导式热量计是由Tian在设计制作的,它建立在地下7米,使用大地作为恒温环境。 /p p 1948年,法国科学家E. Calvet对Tian的单池设计作了改进,提出参考的理念,并采用孪生式对称的结构。 /p p 随后,瑞典隆德大学(Lund University)的Ingemar Wadso 教授对热导式量热计的发展作了大量的贡献,许多商用热量计,都采用了他的设计思想,像瑞典Thermometric公司的LKB 和 TAM等。 /p p Calvet型微热量热计它不是直接测量出反应引起量热容器的温度变化,而是记录在每个时间所产生的热功率W与时间 t 的关系即Tian方程: /p p style=" text-align: center " strong W=f(t) /strong /p p 方程所描述的图形是一条研究过程的动力学曲线,显然,在某一时间间隔内曲线下的面积就是该过程的热效应。 /p p 在热量计中进行的变化过程称为热动力学体系。其中,热量计是一个多参数系统,是输入函数和输出函数的中间体。输入函数即热变速率与时间之间的关系方程称为热动力学方程,Ω-t曲线称为热动曲线 输出函数即温度函数Δ(表现为 t 时热谱高峰)与时间 t 之间的关系方程称为热谱方程,Δ-t 曲线称为热谱曲线。由于输入函数Ω(t)是一切动力学信息的源泉,因此,热动力学方法的关键是如何通过热谱曲线的解析而获得输入函数,这就要依赖于热量计的理论模型了。 /p p 所以,随着热量计设计和结构的不同,热量计的理论模型不同,处理的角度不同,热动力学的方法和方程也就不同。 /p p 热分析动力学处理方法是指应用各种数学方法对所得的实验数据进行分析,从而求出相应的热分解反应的 strong 活化能Ea /strong 、 strong 指前因子A /strong 等动力学参数,以及固体物质反应速率(k)与转化率(α)之间所遵循的函数关系即 strong 反应机理f (α) /strong 。动力学研究的主要任务是通过动力学处理方法设法获得表征某个反应的机理和动力学参数。 /p p 固体物质的热分解通常可用下式表示: /p p style=" text-align: center " strong A(固)→ B(固)+ C(气) /strong /p p 一般基于下列动力学方程: /p p style=" text-align: center " strong dα/dt= k (T) f (α) (等温) /strong (1) /p p style=" text-align: center " strong βdα/dT= k (T) f(α) (非等温) /strong (2) /p p 其中α,β,t ,T 分别为反应转化率,升温速率,时间和绝对温度,f (α)为与反应速率有关的函数。 /p p 机理函数f (α):反应的动力学机理函数f (α)是表示固体物质反应速率(k)与转化率(T)之间所遵循的某种函数关系,直接决定TA曲线的形状. 但由于动力学机理函数是建立在反应物颗粒具有规整的几形状和各相同性的反应活性的假设之上,再按控制反应速率的各种关键步骤推导出来的。由于动力学结果对反应界面的几何因素的依赖性很强,而实际样品颗粒的几何形状的非规整性和非均相反应本身的复杂性,虽然这些动力学机理函数能对许多固相物质的热分解反应过程作出基本描述,但也常会有实际TA曲线和理想模型不相符的情况.在绝大多数均相反应中,分解反应的整个过程遵循某一个动力学规律,但对于复相分解反应来说,分解过程可能是要由2个或者3个甚至更多的表达式来描述。 /p p 动力学参数Ea和A:对于方程(1)和(2)中k (T)一般采用Arrhenius方程: /p p style=" text-align: center " strong k ( T ) = A exp(Ea/RT ) 或 /strong /p p style=" text-align: center " strong lnk = - Ea /R T + 常数 /strong (3) /p p 此方程是在均相等温条件下推导出来的,将其用于非等温、非均相体系中的热分解动力学研究,其适用性和可靠性一直是一个有争议的问题。同时,由方程中lnk对1/T 作图,所得的直线的斜率要乘以气体常数R才得到活化能,而且公式中的指前因子也令人费解,目前还没有人对此作出很好的解释。 /p p strong 动力学处理方法 /strong /p p 对于非等温、非均相过程,将(3)式代入方程(2)中,应用不同的数学方法进行处理而得到的,其基本形式可分为2大类,即微分式和积分式,分别对应的微分法和积分法。 /p p style=" text-align: center " strong 动力学处理方法 /strong /p table border=" 1" cellspacing=" 0" cellpadding=" 0" style=" border-collapse:collapse border:none" align=" center" interlaced=" enabled" tbody tr style=" height:18px" class=" ue-table-interlace-color-single firstRow" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px word-break: break-all " height=" 18" align=" left" span style=" font-family: 宋体, SimSun " 积分法 /span /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" align=" left" p style=" line-height:150%" span style=" font-family: 宋体, SimSun " 微分法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Phadnis /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Kissinger /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 冯仰婕 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 陈炜 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 邹文樵法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 微分方程法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Coats-Redfern /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 放热速率方程法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 改良 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Coats-Redfern /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 特征点分析法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Flynn-Wall-Ozawa /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 微分修正法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Gorbatchev /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Newkrik /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Lee-Beck /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Achar-Brindley-Sharp-Wendworth /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Li & nbsp Chung-Hsiung /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Friedman-Rrich-Levi /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Agrawal /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Piloyan-Ryabchihov-Novikova-Maycock /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 冉全印 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 叶素法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Freeman-Carroll /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 冯仰婕 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 袁军 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 洪专 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 邹文樵 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 戴浩良法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Anderson-Freeman /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Zsako /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Vachuska-Voboril /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " MacCallum-Tanner /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Starink /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Satava-Sestak /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Rogers /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 一般积分法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Rogers-Smith /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 普适积分法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Rogers-Morris /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Krevelen-Heerden-Huntjens /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Borham-Olson /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Broido /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Borchardt-Daniels /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Zavkovic /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 通用 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Kissinger /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Segal /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Viswanath-Gupta /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Madhususanan-Krishnan-Ninan /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Achar-Brindley-Sharp-Wendworth /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Horowitz-Metzger /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Friedman /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " McCarty-Green /span span style=" font-family:宋体" 法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 扩展的 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Friedman /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Doyle /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Kissinger-Akahira-Sunose /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Ozawa /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" br/ /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 胡荣祖 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 高红旭 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 张海法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" br/ /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 240" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 唐万军法 /span /p /td td width=" 277" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" br/ /td /tr /tbody /table p 对于非等温过程,经过数学处理可以得到温度积分以下近似式: /p p style=" text-align: center " strong 温度积分的近似解 /strong /p table border=" 1" cellspacing=" 0" cellpadding=" 0" style=" border-collapse:collapse border:none" align=" center" interlaced=" enabled" tbody tr style=" height:18px" class=" ue-table-interlace-color-single firstRow" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Frank-Kameneskii /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Coats-Redfern /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Doyle /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Goebatchev /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Lee-Beck /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Li & nbsp Chung-Hsiung /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Agrawal /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 冉全印 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 叶素近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 冯仰婕 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 袁军 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 洪专 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 邹文樵 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 戴浩良近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Zsako /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " MacCallum-Tanner /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Krevelen-Heerden-Huntjens /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Broido /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Luke /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Senum-Yang /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Sestak-Satava-Wendlandt /span span style=" font-family:宋体" 近似式 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 307" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Tang-Liu-Zhang-Wang-Wang /span span style=" font-family:宋体" 近似式 /span /p /td /tr /tbody /table p 在非等温动力学分析中,相同条件下,不同研究者求得同一物质的动力学参数出入较大,这是由于机理函数和实际发生的动力学过程有差异,逻辑选择较合理的机理函数形式十分重要。 /p p style=" text-align: center " strong 最概然机理函数的推断方法 /strong /p table border=" 1" cellspacing=" 0" cellpadding=" 0" style=" border-collapse:collapse border:none" align=" center" interlaced=" enabled" tbody tr style=" height:18px" class=" ue-table-interlace-color-single firstRow" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Satava /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Bagchi /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 双外推法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 张同来 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 胡荣祖 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 杨正权 /span span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " - /span span style=" font-family:宋体" 李福平法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 三步判别法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Malek /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Dollimore /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Popescu /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Leyko-Maciejewski-Szuniewicz /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " Blazejowskji /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-single" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:& #39 Times New Roman& #39 ,& #39 serif& #39 " CRTA /span span style=" font-family:宋体" 法 /span /p /td /tr tr style=" height:18px" class=" ue-table-interlace-color-double" td width=" 263" nowrap=" " valign=" top" style=" border: 1px solid rgb(0, 0, 0) padding: 5px " height=" 18" p style=" line-height:150%" span style=" font-family:宋体" 双等双步法 /span /p /td /tr /tbody /table p br/ /p p strong 参考文献 /strong /p p i 沈玉芳,陈栋华, 胡小安. 热分析动力学处理方法现状及进展[J]. 中南民族大学学报自然科学版, 2002, 21(29):11-15. /i /p p i 胡荣祖,高胜利,赵凤起,史启祯,张同来,张建军. 热分析动力学.第2版[M]. 科学出版社, 2016. /i /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " span /span strong 致谢:本文由西北大学教授高胜利所提供相关资料经编辑整理撰写而成,特此致谢! /strong /span /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " strong 延伸阅读: /strong /span /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " strong a href=" https://www.instrument.com.cn/news/20190517/485442.shtml" target=" _self" 高胜利:热分析检测技术与相图构筑 /a /strong /span /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " strong a href=" https://www.instrument.com.cn/news/20190627/487852.shtml" target=" _self" DSC数据处理——基线的校正 /a /strong /span /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " strong /strong /span /p p a href=" https://www.instrument.com.cn/news/20190628/487912.shtml" target=" _self" strong 分析技术新视野——从热分析到微量热 /strong /a /p p span style=" color: rgb(68, 68, 68) font-family: 宋体, " arial=" " strong /strong /span br/ /p