基于反卷积过程新算法分析Mn_(0.90)Co_(0.05)Mg_(0.05)HPO_4?3H_2O固相反应复杂过程的热动力学及相关热力学函数（英文）
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摘要
合成Mn_(0.90)Co_(0.05)Mg_(0.05)HPO_4?3H_2O的热固相反应过程存在3个独立的峰,分别对应于脱水Ⅰ、脱水Ⅱ和缩聚3个过程。提出一种根据单个DTG峰的峰面积计算转化率的新方法,即采用Frazer-Suzuki反卷积函数进行最优拟合。采用迭代积分等转化率方程计算3个峰的表观活化能E_α分别为65.87、78.16和119.32 k J。保证每个独立的峰都是一个具有特征动力学参数的单步骤动力学体系,通过实验曲线与模拟曲线的比较,确定反应机理函数。结果表明,第一、第二和最后的独立峰分别为球对称的二维扩散机理(D_2)、球对称的三维扩散机理(D_3)和收缩圆柱机理(圆柱对称,R_2)。根据E_α值和反应机理,计算出指数前因子分别为3.91×10~6,1.35×10~7和2.15×10~7 s。确定过渡态(活化)配合物的标准热力学函数,结果与实验数据吻合良好。
Three individual peaks of thermal solid-state reaction processes of the synthesized Mn_(0.90)Co_(0.05)Mg_(0.05)HPO_4?3H_2O were observed corresponding to dehydration I,dehydration II and polycondensation processes.An alternative method for the calculation of the extent of conversion was proposed from the peak area of the individual DTG peak after applying the best fitting deconvolution function(Frazer–Suzuki function).An iterative integral isoconversional equation was used to compute the values of the apparent activation energy E_αand they were found to be 65.87,78.16 and 119.32 kJ/mol for three peaks,respectively.Each individual peak was guaranteed to be a single-step kinetic system with its unique kinetic parameters.The reaction mechanism functions were selected by the comparison between experimental and model plots.The results show that the first,second and final individual peaks were two-dimensional diffusion of spherical symmetry(D_2),three-dimensional diffusion of spherical symmetry(D_3)and contracting cylinder(cylindrical symmetry,R_2)mechanisms.Pre-exponential factor values of 3.91×10~6,1.35×10~7 and 2.15×10~7 s~(-1) were calculated from the E_αvalues and reaction mechanisms.The corresponded standard thermodynamic functions of the transition-state(activated)complexes were determined and found to agree well with the experimental data.
Three individual peaks of thermal solid-state reaction processes of the synthesized Mn_(0.90)Co_(0.05)Mg_(0.05)HPO_4?3H_2O were observed corresponding to dehydration I,dehydration II and polycondensation processes.An alternative method for the calculation of the extent of conversion was proposed from the peak area of the individual DTG peak after applying the best fitting deconvolution function(Frazer–Suzuki function).An iterative integral isoconversional equation was used to compute the values of the apparent activation energy E_αand they were found to be 65.87,78.16 and 119.32 kJ/mol for three peaks,respectively.Each individual peak was guaranteed to be a single-step kinetic system with its unique kinetic parameters.The reaction mechanism functions were selected by the comparison between experimental and model plots.The results show that the first,second and final individual peaks were two-dimensional diffusion of spherical symmetry(D_2),three-dimensional diffusion of spherical symmetry(D_3)and contracting cylinder(cylindrical symmetry,R_2)mechanisms.Pre-exponential factor values of 3.91×10~6,1.35×10~7 and 2.15×10~7 s~(-1) were calculated from the E_αvalues and reaction mechanisms.The corresponded standard thermodynamic functions of the transition-state(activated)complexes were determined and found to agree well with the experimental data.
引文
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[22]LIU S H,SHU C M.Advanced technology of thermal decomposition for AMBN and ABVN by DSC and VSP2[J].Journal of Thermal Analysis and Calorimetry,2015,121:533-540.
[23]SATO Y.Evaluation of the hazard of heat generation by oxidation of materials using a differential-type adiabatic calorimeter[J].Journal of Thermal Analysis and Calorimetry,2016,123:1851-1859.
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[30]VYAZOVKIN S.Modification of the integral isoconversional method to account for variation in the activation energy[J].Journal of Computational Chemistry,2001,22:178-183.
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[34]SRONSRI C,NOISONG P,DANVIRUTAI C.Thermal decomposition kinetics of Mn0.9Co0.1HPO4?3H2O using experimental-model comparative and thermodynamic studies[J].Journal of Thermal Analysis and Calorimetry,2017,127:1983-1994.
[35]MáLEK J.A computer program for kinetic analysis of non-isothermal thermoanalytical data[J].Thermochimica Acta,1989,138:337-346.
[36]SRONSRI C,NOISONG P,DANVIRUTAI C.Isoconversional kinetic,mechanism and thermodynamic studies of the thermal decomposition of NH4Co0.8Zn0.1Mn0.1PO4·H2O[J].Journal of Thermal Analysis and Calorimetry,2015,120:1689-1701.
[37]ROONEY J J.Eyring transition-state theory and kinetics in catalysis[J].Journal of Molecular Catalysis A:Chemical,1995,96:L1-L3.
[2]SRONSRI C,NOISONG P,DANVIRUTAI C.Solid state reaction mechanisms of the LiMnPO4 formation using special function and thermodynamic studies[J].Industrial&Engineering Chemistry Research,2015,54:7083-7093.
[3]PANG H,WANG S,SHAO W,ZHAO S,YAN B,LI X,LI S,CHENJ,DU W.Few-layered CoHPO4·3H2O ultrathin nanosheets for high performance of electrode materials for supercapacitors[J].Nanoscale,2013,5:5752-5757.
[4]BOONCHOM B,PHUVONGPHA N.Synthesis of new binary cobalt iron pyrophosphate CoFeP2O7[J].Materials Letters,2009,63:1709-1711.
[5]BOONCHOM B,VITTAYAKORN N.Synthesis and ferromagnetic property of new binary copper iron pyrophosphate CuFeP2O7[J].Materials Letters,2010,63:275-257.
[6]SRONSRI C,NOISONG P,DANVIRUTAI C.Synthesis,non-isothermal kinetic and thermodynamic studies of the formation of LiMnPO4 from NH4MnPO4·H2O precursor[J].Solid State Sciences,2014,32:67-75.
[7]SRONSRI C,NOISONG P,DANVIRUTAI C.Synthesis,characterization and vibrational spectroscopic study of Co,Mg co-doped LiMnPO4[J].Spectrochimica Acta Part A:Molecular and Biomolecular Spectroscopy,2016,153:436-444.
[8]PEREJóN A,SáNCHEZ-JIMéNEZ P E,CRIADO J M,PéREZ-MAQUEDA L A.Kinetic analysis of complex solid-state reactions:A new deconvolution procedure[J].Journal of Physical Chemistry B,2011,115:1780-1791.
[9]FRIEDMAN H L.Kinetics of thermal degradation of char-forming plastics from thermogravimetry:Application to a phenolic plastic[J].Journal of Polymer Science:Polymer Symposia,1964,6:183-195.
[10]KHAWAM A,FLANAGAN D R.Complementary use of model-free and modelistic methods in the analysis of solid-state kinetics[J].Journal of Physical Chemistry B,2005,109:10073-10080.
[11]GOTOR F J,CRIADO J M,MáLEK J,KOGA N.Kinetic analysis of solid-state reactions:?The universality of master plots for analyzing isothermal and nonisothermal experiments[J].Journal of Physical Chemistry A,2000,104:10777-10782.
[12]SEMPERE J,NOMEN R,SERRA R,SORAVILLA J.The NPKmethod:An innovative approach for kinetic analysis of data from thermal analysis and calorimetry[J].Thermochimica Acta,2002,388:407-414.
[13]SáNCHEZ-JIMéNEZ P E,PéREZ-MAQUEDA L A,PEREJóN A,CRIADO J M.Combined kinetic analysis of thermal degradation of polymeric materials under any thermal pathway[J].Polymer Degradation and Stability,2009,94:2079-2085.
[14]VYAZOVKIN S,BURNHAM A K,CRIADO J M,PéREZ-MAQUEDA L A,POPESCU C,SBIRRAZZUOLI N.ICTAC kinetics committee recommendations for performing kinetic computations on thermal analysis data[J].Thermochimica Acta,2011,520:1-19.
[15]SRONSRI C,BOONCHOM B.Deconvolution technique for the kinetic analysis of a complex reaction and the related thermodynamic functions of the formation of LiMn0.90Co0.05Mg0.05PO4[J].Chemical Physics Letters,2017,690:116-128.
[16]SRONSRI C,BOONCHOM B.Synthesis,characterization,vibrational spectroscopy,and factor group analysis of partially metal-doped phosphate materials[J].Spectrochimica Acta Part A:Molecular and Biomolecular Spectroscopy,2018,194:230-240.
[17]CULLITY B D.Elements of X-ray diffraction[M].2nd ed.MA:Addison-Wesley Publishing,1978.
[18]BARBADILLO F,FUENTES A,NAYA S,CAO R,MIER J L,ARTIAGA R.Evaluating the logistic mixture model on real and simulated TG curves[J].Journal of Thermal Analysis and Calorimetry,2007,87:223-227.
[19]CAI J M,ALIMUJIANG S.Kinetic analysis of wheat straw oxidative pyrolysis using thermogravimetric analysis:Statistical description and isoconversional kinetic analysis[J].Industrial&Engineering Chemistry Research,2009,48:619-624.
[20]JANKOVIC B,ADNADEVIC B,KOLAR-ANIC L,SMICIKLAS I.The non-isothermal thermogravimetric tests of animal bones combustion.Part II.Statistical analysis:Application of the Weibull mixture model[J].Thermochimica Acta,2010,505:98-105.
[21]WEIBULL W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18:293-297.
[22]LIU S H,SHU C M.Advanced technology of thermal decomposition for AMBN and ABVN by DSC and VSP2[J].Journal of Thermal Analysis and Calorimetry,2015,121:533-540.
[23]SATO Y.Evaluation of the hazard of heat generation by oxidation of materials using a differential-type adiabatic calorimeter[J].Journal of Thermal Analysis and Calorimetry,2016,123:1851-1859.
[24]GALWAY A K.Solid state reaction kinetics,mechanisms and catalysis:A retrospective rational review[J].Reaction Kinetics,Mechanisms and Catalysis,2015,114:1-29.
[25]L’VOV B V.Thermal decomposition of solids and melts[M].Berlin:Springer,2007.
[26]L’VOV B V.Activation effect in heterogeneous decomposition reactions:fact or fiction?[J].Reaction Kinetics,Mechanisms and Catalysis,2014,111:415-429.
[27]L’VOV B V.On the way from the activation model of solid decomposition to the thermochemical model[J].Reaction Kinetics,Mechanisms and Catalysis,2015,116:1-18.
[28]BUDRUGEAC P,SEGAL E.Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid-gas reactions[J].International Journal of Chemical Kinetics,2001,33:564-573.
[29]BUDRUGEAC P.Some methodological problems concerning the kinetic analysis of non-isothermal data for thermal and thermooxidative degradation of polymers and polymeric materials[J].Polymer Degradation and Stability,2005,89:265-273.
[30]VYAZOVKIN S.Modification of the integral isoconversional method to account for variation in the activation energy[J].Journal of Computational Chemistry,2001,22:178-183.
[31]VYAZOVKIN S,DOLLIMORE D.Linear and nonlinear procedures in isoconversional computations of the activation energy of nonisothermal reactions in solids[J].Journal of Chemical Information and Modeling,1996,36:42-45.
[32]BUDRUGEAC P.Differential non-linear isoconversional procedure for evaluating the activation energy of non-isothermal reactions[J].Journal of Thermal Analysis and Calorimetry,2002,68:131-139.
[33]CAI J,CHEN S.A new iterative linear integral isoconversional method for the determination of the activation energy varying with the conversion degree[J].Journal of Computational Chemistry,2009,30:1986-1991.
[34]SRONSRI C,NOISONG P,DANVIRUTAI C.Thermal decomposition kinetics of Mn0.9Co0.1HPO4?3H2O using experimental-model comparative and thermodynamic studies[J].Journal of Thermal Analysis and Calorimetry,2017,127:1983-1994.
[35]MáLEK J.A computer program for kinetic analysis of non-isothermal thermoanalytical data[J].Thermochimica Acta,1989,138:337-346.
[36]SRONSRI C,NOISONG P,DANVIRUTAI C.Isoconversional kinetic,mechanism and thermodynamic studies of the thermal decomposition of NH4Co0.8Zn0.1Mn0.1PO4·H2O[J].Journal of Thermal Analysis and Calorimetry,2015,120:1689-1701.
[37]ROONEY J J.Eyring transition-state theory and kinetics in catalysis[J].Journal of Molecular Catalysis A:Chemical,1995,96:L1-L3.