Nonlinear desorption activation energy from TPD curves: Analysis of the influence of initial values for the regression procedure

摘要

Abstract > Thermal programmed desorption (TPD) is a powerful technique for materials and catalysts characterization. By analyzing TPD curves, it is possible to calculate important parameters as the desorption activation energy, type="mathematics"> <fi>E</fi> <sub> <fi>d</fi> </sub> , that depends on the surface coverage type="mathematics"> ( <fi>θ</fi> ) by a nonlinear polynomial function, ie, <mat:math display="inline" overflow="scroll" altimg="urn:x-wiley:00084034:media:cjce23700:cjce23700-math-0001" wiley:location="equation/cjce23700-math-0001.png"> <mat:msub> <mat:mi>E</mat:mi> <mat:mi>d</mat:mi> </mat:msub> <mat:mfenced open="(" close=")"> <mat:mi>θ</mat:mi> </mat:mfenced> <mat:mo>=</mat:mo> <mat:msubsup> <mat:mo>∑</mat:mo> <mat:mrow> <mat:mi>k</mat:mi> <mat:mo>=</mat:mo> <mat:mn>0</mat:mn> </mat:mrow> <mat:mi>N</mat:mi> </mat:msubsup> <mat:msub> <mat:mi>α</mat:mi> <mat:mi>k</mat:mi> </mat:msub> <mat:msup> <mat:mfenced open="(" close=")"> <mat:mrow> <mat:mn>1</mat:mn> <mat:mo>?</mat:mo> <mat:mi>θ</mat:mi> </mat:mrow> </mat:mfenced> <mat:mi>k</mat:mi> </mat:msup> </mat:math> . The Polanyi‐Wigner equation, <mat:math display="inline" overflow="scroll" altimg="urn:x-wiley:00084034:media:cjce23700:cjce23700-math-0002" wiley:location="equation/cjce23700-math-0002.png"> <mat:mo>?</mat:mo> <mat:mfrac> <mat:mi mathvariant="italic">dθ</mat:mi> <mat:mi mathvariant="italic">dT</mat:mi> </mat:mfrac> <mat:mo>=</mat:mo> <mat:mfenced open="(" close=")"> <mat:mfrac> <mat:mrow> <mat:mi>A</mat:mi> <mat:mfenced open="(" close=")"> <mat:mi>θ</mat:mi> </mat:mfenced> </mat:mrow> <mat:mi>β</mat:mi> </mat:mfrac> </mat:mfenced> <mat:msup> <mat:mi>θ</mat:mi> <mat:mi>n</mat:mi> </mat:msup> <mat:mi mathvariant="italic">exp</mat:mi> <mat:mfenced open="(" close=")"> <mat:mfrac> <mat:mrow> <mat:mo>?</mat:mo> <mat:msub> <mat:mi>E</mat:mi> <mat:mi>d</mat:mi> </mat:msub> <mat:mfenced open="(" close=")"> <mat:mi>θ</mat:mi> </mat:mfenced> </mat:mrow> <mat:mi mathvariant="italic">RT</mat:mi> </mat:mfrac> </mat:mfenced> </mat:math> , can be used as theoretical basis to calculate this parameter, by a fitting regression procedure starting from experimental TPD data. Different degrees (k) for this polynomial equation and different initial values of the frequency factor type="mathematics"> <fi>A</fi> ( <fi>θ</fi> ) were considered and discussed to obtain the univocal value of desorption energy. Three different Pt and Co based catalysts, suitable for hydrogenation reactions, have been considered as case studies for the application and validation of the proposed calculatio </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > 热编程解吸（TPD）是一种强大的材料和催化剂表征技术。通过分析TPD曲线，可以计算作为解吸激活能量的重要参数， type =“mathematics”> <fi> e </ fi> <sub> <fi> d </ fi> </ sub> </ span> ，这取决于表面覆盖范围 type =“mathematics”> （ <fi>θ</ fi> 的） </ span> 通过非线性多项式函数，即 <mat：数学显示=“内联”overflow =“滚动”Altimg =“URN：X-Wiley：00084034：媒体：Cjce23700：Cjce23700-Math-0001”Wiley：Location =“等式/ CJCE23700-Math-0001.png” > <mat：msub> <MAT：MI> E </ MAT：MI> <MAT：MI> D </ MAT：MI> </ mat：msub> <mat：mfenced open =“（”close =“）”> <mat：mi>θ</ mat：mi> </ mat：mfeced> <mat：mo> = </ mat：mo> <mat：msubsup> <mat：mo>σ</ mat：mo> <MAT：MROW> <MAT：MI> K </ MAT：MI> <mat：mo> = </ mat：mo> <MAT：MN> 0 </ MAT：MN> </ mat：MROW> <mat：mi> n </ mat：mi> </ mat：msubsup> <mat：msub> <mat：mi>α</ mat：mi> <MAT：MI> K </ MAT：MI> </ mat：msub> <mat：msup> <mat：mfenced open =“（”close =“）”> <MAT：MROW> <MAT：MN> 1 </ MAT：MN> <mat：mo>？</ mat：mo> <mat：mi>θ</ mat：mi> </ mat：MROW> </ mat：mfeced> <MAT：MI> K </ MAT：MI> </ mat：msup> </ mat：math> 。 Polanyi-Wigner方程， <mat：数学显示=“内联”overflow =“滚动”altimg =“urn：x-wiley：00084034：媒体：cjce23700：cjce23700-math-0002”wiley：location =“等式/ cjce23700-math-0002.png” > <mat：mo>？</ mat：mo> <MAT：MFRAC> <mat：mi mathvariant =“斜体”>dθ</ mat：mi> <mat：mi mathvariant =“斜体”> dt </ mat：mi> </ mat：mfrac> <mat：mo> = </ mat：mo> <mat：mfenced open =“（”close =“）”> <MAT：MFRAC> <MAT：MROW> <mat：mi> a </ mat：mi> <mat：mfenced open =“（”close =“）”> <mat：mi>θ</ mat：mi> </ mat：mfeced> </ mat：MROW> <MAT：MI>β</ MAT：MI> </ mat：mfrac> </ mat：mfeced> <mat：msup> <mat：mi>θ</ mat：mi> <mat：mi> n </ mat：mi> </ mat：msup> <mat：mi mathvariant =“斜体”> exp </ mat：mi> <mat：mfenced open =“（”close =“）”> <MAT：MFRAC> <MAT：MROW> <mat：mo>？</ mat：mo> <mat：msub> <MAT：MI> E </ MAT：MI> <MAT：MI> D </ MAT：MI> </ mat：msub> <mat：mfenced open =“（”close =“）”> <mat：mi>θ</ mat：mi> </ mat：mfeced> </ mat：MROW> <mat：mi mathvariant =“斜体”> Rt </ mat：mi> </ mat：mfrac> </ mat：mfeced> </ mat：math> ，可以用作从实验TPD数据开始的拟合回归过程来计算该参数的理论基础。这种多项式方程的不同程度（k）和频率系数的不同初始值 type =“mathematics”> <fi> a </ fi> （ <fi>θ</ fi> 的） </ span> 被考虑并讨论以获得解吸能的单一价值。适用于氢化反应的三种不同的Pt和Co基催化剂被认为是对所提出的计算的应用和验证的情况研究 </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-30631/'>《The Canadian Journal of Chemical Engineering》</a> <b style="margin: 0 2px;">|</b><span>2020年第5期</span><b style="margin: 0 2px;">|</b><span>共9页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/238.html" title="化学工业">化学工业;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=desorption energy&option=203" rel="nofollow">desorption energy;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=initial values&option=203" rel="nofollow">initial values;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Polanyi‐Wigner equation&option=203" rel="nofollow">Polanyi‐Wigner equation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=regression&option=203" rel="nofollow">regression;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=TPD&option=203" rel="nofollow">TPD;</a> </p> <div class="translation"> 机译：解吸能量;初始值;Polanyi-Wigner方程;回归;TPD; </div> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024776101.html">Nonlinear desorption activation energy from TPD curves: Analysis of the influence of initial values for the regression procedure</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> </a> <a href="/journal-foreign-30631/" target="_blank" rel="nofollow" class="tuijian_authcolor">The Canadian Journal of Chemical Engineering .</a> <span>2020</span><span>,第5期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：来自TPD曲线的非线性解吸激活能量：分析回归过程的初始值的影响</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_detail_thesis/0204119399064.html">Wheat bran reduces concentrations of digestible, metabolizable, and net energy in diets fed to pigs, but energy values in wheat bran determined by the difference procedure are not different from values estimated from a linear regression procedure</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Stein?H. 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A Linear Variation of the Activation Energy of Desorption</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Yasuo Tokoro&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Yasuo Tokoro,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Makoto Misono&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Makoto Misono,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Toshio Uchijima&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Toshio Uchijima,</a> <span>1978</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：异质表面热解吸曲线分析。 I.解吸激活能量的线性变化</span> </p> </li> <li> <div> <b>8. </b><a class="enjiyixqcontent" href="/ntis-science-report_de_thesis/020711316939.html">Application of Rigorous Nonlinear Regression for the Analysis of Complex Isothermal DSC (Differential Scanning Calorimetry) Reactivity Curves.</a> <b>[R] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Pickard, J. M.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Pickard, J. 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'98全国核仪器应用学术会议 </a> <span> <span> . 1998</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020313337613.html">混凝土裂缝扩展全过程的新G阻力曲线理论和能量转化分析</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张秀芳&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 张秀芳</a> <span> . 2006</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/061203078203.html">基于模糊曲线分析的时间差高斯过程回归软测量建模方法</a> <b>[P]</b> . <span> 中国专利： CN105205224B </span> <span> . 2018.10.30</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120107692405.html">基于模糊曲线分析的时间差高斯过程回归软测量建模方法</a> <b>[P]</b> . <span> 中国专利： CN105205224A </span> <span> . 2015-12-30</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130444693120.html">Synthesizing phoneme string of predetermined duration by adjusting initial phoneme duration on values from multiple regression by adding values based on their standard deviations</a> <b>[P]</b> . <span> 外国专利：  US6546367B2 </span> <span> . 2003-04-08</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：通过根据来自多个回归的值调整初始音素持续时间来合成预定持续时间的音素串，这些值基于标准差添加值 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130416510257.html">Method for determining correction values for control period for controlling fuel injection valve, involves determining correction values by linear regression for arbitrary values of activation period on basis of coding measurement</a> <b>[P]</b> . <span> 外国专利：  DE102012210739A1 </span> <span> . 2014-05-08</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：确定用于控制燃料喷射阀的控制周期的校正值的方法，涉及基于编码测量通过线性回归确定激活周期的任意值的校正值 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130409122617.html">REGRESSION MODELING SYSTEM USING ACTIVATION SCALE VALUES AS INPUTS TO A REGRESSION TO PREDICT HEALTHCARE UTILIZATION AND COST AND/OR CHANGES THERETO</a> <b>[P]</b> . <span> 外国专利：  CA2957767A1 </span> <span> . 2017-08-12</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用激活标度值作为回归模型的回归建模系统，可预测医疗保健利用以及成本和/或变化 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> 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