20 7Π8 2008 8 PROGRSS IN CHMISRY Vol. 20 No. 7Π8 Aug., 2008 3 3 3 3 3 ( 230026),,,, : O64311 ; O64213 : A : 10052281X(2008) 07Π821015206 Approimation pressions for the emperature Integral Chen Haiiang 3 3 Liu Naian 3 3 (State Key Laboratory of Fire Science, University of Science and echnology of China, Hefei 230026, China) Abstract he recent ten2year research progress in the approimation epressions for the temperature integral in the field of thermal analysis kinetics is reviewed. Some new approaches to approimate the temperature integral are introduced, and the relationship between various approimation epressions is presented. he accuracy in calculating kinetic parameters by different integral methods with different approimation epressions is commented, and the methods to avoid the problem of the temperature integral are summarized. he research tendency about the temperature integral is also suggested. Key words temperature integral ; approimation epression ; thermal analysis kinetics, ( ), [1 ],,, [2, 3 ],, : Arrhenius,,, ( ICA) Flynn 1992 30, [4 ] 1997,3 : [5 ],,,,, : 2007 9, : 2007 12 3 (No. 50576090) 3 3 e2mail :hchen @ustc. edu. cn ; liunai @ustc. edu. cn
1016 20,, 1997 Flynn [5 ], 10,,,,, 1 10,,,,, : d = k ( ) f ( )Π (1) d,, f ( ), k ( ), Arrhenius : k ( ) = Aep ( - ΠR) (2),A, R (1) (2), 0 0 ( 0 ), : 0 f ( ) d = G( ) = A e - ΠR 0 d (3) e - ΠR d 0, 0,, 0 0, e - ΠR d = ΠR, 0 e - ΠR d = 0 2 p ( ), p ( ) = R ep ( - ) d h ( ), h ( ) = p ( ) 2 e p ( ), h ( ) 0 1, [6 ], p ( ) h ( ), k ( ) : k ( ) = A m ep ( - ΠR),, I ( m, ) = m ep ( - 0 p ( m, ) ( p ( m, ) = ) ( h ( m, ) = p ( m, ) ΠR) d ep ( - ) d) m +2 h ( m, ep ( - ) m+2 m 1Π2 1 2,0 Arrhenius 2, Scholmilch MKN [7 ], Coats2Redfern [8 ] Doyle [9 ], [10, 11 ],,Heal,,,,,,, Madhusudanan [12, 13 ] MKN : ln[ p ( ) ] = - 1. 921503ln - 1. 000953-0. 297580 ln[ p ( ) ] = - 1. 920620ln - 1. 000974-0. 299963 ln[ p ( ) ] = - 1. 884318ln - 1. 001928-0. 389677 (4) MKN,MKN 2 3 ang [14 ], 9ln[ p ( ) ] ln[ p ( ) ] = c + b + aln, 9 = b + a 9ln[ p ( ) ] 9 1 b a ;
7Π8 1017 a,ln[ p ( ) ] - aln = c + b,c b: ln[ p ( ) ] = - 1. 89466100ln - 1. 00145033-0. 37773896 (5),, b, (b ), [15 ] b,, Doyle [9 ] (ln[ p ( ) ] = - 1. 0516-5. 3308 (20 60) ),, MKN,Doyle 20 60, Gao [16 ] 10 15 15 20 65 70, h ( ) = [22 ] + 0. 25403ln + 0. 36665 + 0. 24598ln + 2. 41457,( ),,,, Chen [6], h ( ): h ( ) = 1 + 2 h ( ) - 1 [23], h ( ), 0, h ( ), h ( ) = 1 + 2 h ( ) - 1 Grobachev2Lee2Beck [24,25 ] h ( ) = Doyle, 10 15 1Π 1 + 2, p ( ) = 010376ep ( - 1. 1516 ) Cai [17 ],,h ( ) = 3 2 [6 ] + 16 + 4 3 2 + 22 + 30 ( 215 %),, ( Starink [18 ] MKN Doyle Senum2Yang 4 [26 ] :, : 4 + 18 3 + 86 2 + 96 ep ( - A + B) h ( ) = p ( ) =, k A B k 4 + 20 3 + 120 2 + 240 + 120 ) Orfao [27 ] MKN Doyle (, ang Starink 2 [26 ]), ( A, B, k) : (1, - 01235,1195) (110008, - 01312, 1192),,,,,Senum2Yang 4, [26 ],, ang [19 ],Orfao, h ( ) = 1. 00198882 + 1. 87391198 :, ;,,Cai,, [20 ] + 0. 66691 h ( ) = + 2. 64943 3 [21 ] 0. 99962 + 0. 60462 h ( ) = + 2. 56879
1018 20,, ( A ),, (3) : ln G( ) = ln A R ln A R + ln[ p ( ) ] = + ln[ h ( ) ] - 2ln - (6) ln[ h ( ) ], : A ln[ h ( ) ] ln A R,, (6) ln G( ) = ln AR h 2 R - R, ;B ln[ h ( ) ] - 2ln -,ln[ h ( ) ] ln[ h ( ) ] = a ln + b + c, ln[ p ( ) ] = aln + b + c, (6) ln G( ) - a = c + ln A R R a + b R, A Coats2Redfern [8 ] Agrawal [28 ],B Doyle [9 ] MKN [12, 13 ],ang [14 ] B, A, Ortega [29 ] Coats2Redfern, 10 2 %,Coats2Redfern Liu [23 ] A B, A, [23,30 ],, [31 ] Liu B, MKN (ang [14 ] ),Doyle Perez2Maqueda [32,33 ],,A, ;B ln[ p ( ) ] = aln + b + c,,,, 4,? p ( ) = ep ( - A + B) k, [34 ] h ( ) = p ( ) 2 e, : ln[ h ( ) ] = (2 - k) ln + (1 - A) + B, h ( ) h ( ) = 2 - k h ( ) = 1 + 2 h ( ) = + (1 - A) h ( ) h ( ) - 1 [23 ], A + k : y = A + k ( y = h ( ) ) ( A, k) [15,60 ], ( A, k) = (110014452, 11891504), p ( ) = ep ( - A + B) k B, B,B, B, ang [14 ],c,,,
7Π8 1019, B,B A [23 ] 5, Singh [35 ],,ang [36 ] [19 ],, : I ( m, ) = I ( m, ) = ep - R R m+2 + ( m + 2) R ep - R R m+2 + ( m + 2) (0. 00099441 + 0. 93695599 R) 1976 [37 ] Chen [38 ] h ( ) = 1 + 2 h ( ) - 1 [6 ] h ( m, ) = 1 + m + 2 [47 h ( m, ) - 1, Serra 50 ] NPK ( non2 parametric kinetics), k ( ),, h ( m, ) = Arrhenius 1 + m + 2 1 + 2 m + 2 ( m + 1) ( m + 2) + 2, Cai [39 ],h ( m, ) a + bm + c + dm + e,,, [40 ],,,,,,, k ( ) k ( ) = A m ep ( - ΠR),,, k ( ) = A m ep ( - 6 ΠR),? Arrhenius,3 Arrhenius,,,, [2, 3, 41 43 ] Arrhenius, [44, 45 ] k ( ) Dollimore Harcourt2sson (H2) : k ( ) = B m Simon [46 ] Berthelot2Hood (B2H) [5 ] : k ( ) = Ce D, B m CD,, A k ( ) d, (1) : = dt k ( ) f ( ), 7,,,,,,,,,, Flynn [5 ] :
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