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Use of spreadsheets in thermal analysis. Part 3
Thermochimicu Acta, 143 (1989) 311-317 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
USE OF SPREADSHEETS
IN THERMAL
ANALYSIS.
311
PART 3.
LEO REICH Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 (U.S.A.) (Received 12 September 1988)
ABSTRACT
Spreadsheets have rarely been used to analyze TG and DTA (or DSC) data to obtain activation energy E and reaction order n (or mechanism). In the recent past and in this paper spreadsheet procedures have been successfully used to ascertain E and n or E and mechanism. In this paper, these procedures are applied to theoretical TG data, to TG data for calcium oxalate, calcium carbonate, teflon and sodium bicarbonate and to DTA data for benzenediazonium chloride. In addition, some of the many advantages of using such procedures are mentioned. The aim of this paper is to extend the implementation of spreadsheets in thermal analysis.
INTRODUCTION
Spreadsheet analysis of TG, DTA or DSC data to obtain activation energy E and reaction order n or mechanism has been used only rarely in the past. Thus, previous determinations of E and n generally employed graphical and/or computer methods [l]. However, recently [2-41, spreadsheet procedures have been successfully used for the determination of E and n [2,3] or of E and mechanism [4]. There are many advantages to the use of spreadsheets [5,6]. Thus, they can provide neat formats of data and results and possess many built-in functions. Some of these functions (in the case of Lotus 2) are as follows: summations (@SUM), standard deviations (@STD), maximum and minimum values (@MAX and @MIN), single and multiple linear regression analysis, graphics, sorting, etc. Furthermore, Macros allow the automatic utilization of worksheets for the estimation of the kinetic parameters E and n (and mechanism). This paper is one of a planned series whose aim is to extend the implementation of spreadsheets for the analysis of TG, DTA or DSC data to obtain values of E and n (or mechanism). 0040-6031/89/$03.50
0 1989 Elsevier Science Publishers B.V.
312 THEORETICAL
ASPECTS
For two pairs of given values of cuand T(K), i.e. cyi, T, and LYE,T2, it can be shown that [7] ln
1 - (1 - c&n I_(l_.J~)
I;
2
E 1 =&-+I
where cy= conversion at temperature T(K). From eqn (l), values of E/R can be calculated for various sets of cw-T values at arbitrarily selected values of reaction order n. However, if uniqueness is assumed, only one pair of E/R and n values will be relevant. Various values of E/R can be obtained at various n values by employing various pairs of cu-T values. However, the E/R values should not deviate (or deviate minimally} at only one unique value of n. This value can be established by utilizing the concept of the standard deviation (STD). Thus, the E/R values at a particular value of n, which afford the smallest STD value, also yield final values E(avg) and n.
RESULTS AND DISCUSSION
The spreadsheet employed in this paper was Lotus l-2-3, release 2, which can provide many advanced Macro commands. Such commands were applied in this paper to theoretical non-isothermal TG (NITG) data, to NITG data for calcium oxalate (COX), calcium carbonate (CAC), teflon (TF) and sodium bicarbonate (SB) and to DTA data for benzenediazo~um chloride (BDC). Table 1 represents a spreadsheet analysis of theoretical TG data. Final values (cf. row 29) were w = 0.50 and E = 28.0 kcal mol-’ (ref. 8, l/2 and 28). The cell contents for the worksheet in Table 1 are depicted in Table 2. From the latter table it can be seen that cells E4-E9 denote values of the left-hand-side logarithm term for various ty- T(K) values. Thus, for example, the value in cell E4 is equal to the LN(value in cell D3/value in cell D4), etc. down the Y column. The X values in cells F4-F9 represent the term in parentheses on the right-hand side of eqn. (1) (see Table 2). Finally, the E/R values in cells G4-G9 are equal to the corresponding values of the ratios of Y/X, and the average E/R value is depicted in cell Gil. The starting n value was taken as 0.10001 and was incremented initially in increments of 0.1; an initial arbitrary value of 1E + 11 was placed in cell El5 (SD2) (cf. rows 17 and 18). When E/R values yielded standard deviations in cell D15 (SDl) which were less than the values in SD2, the corresponding n values were automatically placed in cell F15 and the SD1 and E,/R(avg) values were automatically placed in cells El5 (SD2) and G15,
313
respectively (see row 20). This continued until n values up to 2 had been scanned. When n > 2, the value of n was automatically decreased by the increment value (Inc) and the Inc was decreased by a factor of 10 (cf. rows 24 and 25). The value of n was then automatic~ly incremented over a range of (n - 0.1) to (n f 0.1) using Inc = 0.01, after which the final value of tz (from cell F15) and the final value of E (from cell GlS> were automatically recorded in row 28.
Al: !!@I Alpha El: !%I "Tt%? Cl: [416! ‘H Dl: I!#!?!LHS! E!: ‘I Fl: I11101t 61: [Y9! E'R A:: I!481 i= B?: iU81:= C?: [kbl\= I)?:~IrlOl !: E?: \= F?: IWlOl\= 62: I#91\= AZ: !F5)[YBI0.1X9 83: I1133 4r?5 c3: !Ybl0.60001 D3: !S:!Ml01 111-!1-631'!1-INf1!R3~?~ A4: :FslIit31 0.:':195 84: tUEi410 D4: iS?rIW!Of~f!-(l-A4!^ll-ta!l!B4'?i E4: ~LNltD~~B4l F4: K?f tYl's! l/94-US3 64: !SZ!tU91*E4/F4 85: !F% IMSIo.swi ~5: vda141s D5: is?)[Y:Ol!il-!l-A5l*~I-tN!)/B5^;) E5: 3LNltD4:I)S) FS: is?)!YlOl!/!5-1184 65: iS?lIWPItE5m A5: lF.5) IWBI0.44165 Bb: !UBI4?0 D5: !S21IWlOli!l-i!-At!'!l-tNl!:B6'?1 Eb: JLNltlwDh) FL: 'S?)IW!Ol!iBl-::BS 66: IS?:ik191 +f*/Fi 17s IF:)!USI,f.a!Bz') 87: w1 425 D7: !SZ)IW!:'l !:f-ii-A?! :l-tNil.'B?'21 E7: jL~tt~6~D?) F7: LS?!IY!OIl:Ei-liB6 67: 152):Y9!+E?iF? A& iFSfMl1 3.81979 m: M51 470 DE: is?!IUl8!l:l-~!-AS);!i-!l)l:B8*?) EB: 3?Nl'27:18~ FB: :S?>!110!;:S8-!:B! $8: IS?)IN91'EBiF9 A9: :F5)!#I ').9x33 89: I#$!435 D9: is?)Ih!Ol!1l-'l-A9)'!!-?N)):99"?) E9: DL!IiiImP) FP: !S?1:111:1 !/BY-1!98 69: :SZ):W9!+EO!f9 MO: IbBI\= 910:Ml != no: IYL!:= Did: I!#!OJ :s El& \= FfO:
!S:!
:#I’?!
so: is21in91!= Fi!: :S11iY!bl~f/9(A%!=‘ sii: iw f#9!wGIE:Rl Al?: #$I ?= Bl?: i#eli= Cl:; '#5l il L , 012: t!4101 ',= El? c,: Fl?: iUlOI\z 512: 11191 \= AI5: !%I .Ilrl;r 813: rug1"'PC .a 813: IYlir! %Yl! E13: !S2)'%I: ~13: !%I !blO!'rctacrdr 613: !W9!^E!RL?: All: :UBJ\= 814‘ . .?#I != C14: 0461?= It:4: I11101 != El4: 1521!= F!4: tSZ1Ul131i!?!I: ul91:= a15: IYS!1
515:iWSfk6! D15: tS?lIYlOJOS?B!E/R) El% 152)0.94943m72 Fl:: (52)iYIO11).50001 Sl:: (S?l[W9113e99.934997 A17: IWfil !\a--> 817: Iwe]'(letnrkr,O:!let. inc,.I!Ilet sd?,lEtlll:let ;,.10i'01~*(paoe!:ff! Ala: IW81'\d--: BlB: [uai‘(gotoW(iet il,mtin:!* 819: N81 '(ifo:kr~l~dnd#i~-f!5i,lj(qotoja?7'!quit) r;tnordr.+n?lIet 915,91!? B?O: !#I 'Iiftsdl!sd?:!!et ;d?,sd!!(let 821: !YYl ‘(if +:3?2!ibran:t; \>I
821: [&a!
'!banKR
B?4: iY91‘igoto!n”:!et
825: E?b: GB: 829: c:s:
n,+f!S-ix:” l;iEl ‘in:*!!et iec, tln:.‘!O!* !YEI ‘{let orkr,::ibran:h !d! rw I= [if81 := [Y&Ji-
E2B: != F?9: IU!CI!= sz3: IN91!Z 129: !W81"r:tnordr= C?9: !F31IW6!*RCTNORDR X9: I!4101 'and E29; "E: FV' LIL 'WI;!1 . )INTitERZt:l G?9:,[W91'calinol ASO: !U8! \z 830: [WEI\= m: &I \= Eyy - * 11
zo: I#101\= 530: In91:= i=
id:
A?4: 143:'\k--'
315 TABLE
3.
Spraadsheet
anaiysis
of theoretical
in=l?
TG data
f (K:! Y 6-31pha LHSI PJ ________________----__1________1______1_~~~~--~~~~~_-~~-~~~~ _________________--_-------__-~~~-~~~~~~~~-~~~~~-~---~~~~~-0 _ 1’20 1
726 762 7SQ
(2.2669
l.iOO
E9 1
x
E/R
-2.OlE-09
-5.43E-_f)<)l$; -S_67E-OS -0.46757 -3.0.2X-05 0. ‘5097 79’2 -?.17E-it7 -0.30343 -1.94E-05 0. f313 ert -2. IZE-07 -0.59173 -3.71E-05 ct. @Zll; 925 -2.34E-C?7 -0.25’133 - 1.7SE-05 ====-----I--==================================~~============
1.5.3E+C>4 1.54E404 1.56E+O4 1_5$E+Ct4 1. S4E+C)4
E/R (WEi) =:>I. 57E404 f======================================~~==================~=== __“r”~____~~c_________--_~~~---__-_~~~-___~~~~~~~~__~~~~~~__ --_________________---------_--~~~~~~~~~~~~~~~~~~~~~~--~~~~-1
t-j .I\..‘71
Q. 12E+C12 4.24E+Mk
1. CtCsE+CtC> 1.51EtClY
===========================z
====z==r=2=I==========
rctnurdr= 1 .OUCH ======================
and
3X339 cdl lmol E= --_--_---~~---------____I___ -f----_-ll-----_______lt------
In order to conserve space, Macro commands (which are similar to those in Tables 1 and 2) are not included in Tables 3-6. Table 3 portrays the final results for the spreadsheet analysis of another set of theoretical TG values (a-T(K)). Final results were determined to be n = 1.00 and E = 30.2 kcal mol-’ (ref. 9, 1 and 30).
TABLE
4.
Spreadsheet
ana?ysir,
of
fG data
-Tot-COX
c71:
7” (Y.1 r.! Ai pha LHSl Y Y E/H ---_-----~----------_------_-~~~~~~-~~~~~~-~~---~--____----______---______L_---___I_-_---_---------------f__---~---.-~---0. !f2C@ 437 -_....l 7 1 -240 -1.58E-09 0.075C~ 443.2 -5_59E-C)$3 -1 .*l"Pi-_ ")L'T.3Cq$:, 47:z.z -2.33E-07 -C>.42795 -4 .5&E-05 9_3SE+QI,3 Cl*943'3 -3_&5E-Cl7 -0.4459"j -4,37E-13 1.02EtCb4 &. 483.2 0. ti::7C? 493.2 -5 .74E-07 -0 .4Es455 .-4.2C:E-C)Z;1.0~EtCt4 C2,77'ZC% 503.2 +.llE-07 -0.451663 -4.03E-05 l.i5E+O4 r=======I==================================~~=============~ E/R:AVG)=>l.G7E+04 ===l=====t==========t=====================~~==========.==_===
_"r"r____"~c____________~~~-_----_~~~----~~~~~~~~--~~~~~~---f------____--_----________I___________--~~---~--____---~~ 1 0. 01 8.21E+02 7.8EtE+CG? 1_04E+fiC1 l_Ci4Et1>4
===================== rctncrdr= 1.040 _--_------____----___ ---------~-----_-_____
========r===================
and
E=
20X30
===f========================
cdl
fmof
316
TABLE
5.
Spreadsheet
analysis
of
TG data
for
EDC
C 7 1
Alpha T!K) N Y LHSl X =========================================================== :-, .>_s '57 305. 3 1.120 -4.97E-09 0. 074 -0.65977 310.6 -?.61E-08 -4_52E-05 0. 123 -i~.5liw2 -4.4OE-05 314.9 -l.ME-07 C,. LLLl ')')c: 319.2 -0.64407 -3_05E-07 -4_2sE-05 0.336 -0.63629 323. 5 -5.7&-07 -4.1&E-05
0.575
327.8
-1. olE-06
-0.56091
-4. o5E-05
E/R
1.45Et04 1. 1.5E+04 1_5lE+04 1.53E+o4
?.3SEtO4
0.769 ?77 1 d.-.L. -1.74E-06 -Q-54643 -3.95E-05 1.38E+04 0.922 -0.59645 336.4 -3.l?E-06 -3.95E-05 1.55E+O4 =========================================================== E/R(A'JG)=>l.42E+04 =========================================================== t?rkr Il-iC SD1 SDZ rctnordtE/R(Z) =========================================================== 1
0.01
1.24E+03
__---______-_________ ---------------------
l.l4E+03
1. CQE+ix:) 1 .38E+O4
============================
rctnordr= 1.020 __----_____-_________ _______-______--_____
and
E= 27557 caI/mol ============================
A spreadsheet analysis of TG data for the dehydration of the monohydrate of COX is depicted in Table 4. Final values were determined to be n = 1.04 and E = 20.8 kcal mol-’ (ref. 7, 1.05 and 20.8). A spreadsheet analysis of DTA data for the decomposition of BDC in aqueous solution is shown in Table 5. From these a-T(K) values, the final values obtained were
TABLE
6.
Spreadsheet
analysis
of
TG data
for
CAC
L 7 1
Al ..I-,T : 9:.) N Y LHSl X ============================================================ ::i. ‘:t5(1!0 9El.2 0. 7 10 1.53E-08 0. i)75C! 1008. 2 -Q.36050 Z.ZOE-09 -2.73E-05 0. IbOC! 1cry-c X,-.J. 7 4.&,OE--OS -0.73715 -2.&.3E-05 0.5153 1064.7 -0.69028 9.17E-08 -2.63E-05 !I,. 4S50 1095. 2 -0.45507 1.46E-07 -2.tZE--05 iy”Q
E/R
1.32E64 2.SOE+:>4 2.6ZE+04 1.7SE+C)4
E/R(AVGj=>2.?3Et04 ====~====================================~=================== Pi-kr I:tc SD1 SD2 rctnordr E/R(Z) ?
- -----;Ic~mcp-=
0. C!1
----
-.---
5_42E+i!3
------0.
t1C:
5_4lE+03
6. lC)E-01 2_Ci&E+C!4
============================ and
E= 41623 cal/mo? ============================
317
n = 1.02 and E = 27.6 kcal mol-’ (ref. 7, 1.05 and 27.8). Finally, an analysis of TG data for the decomposition of CAC is depicted in Table 6. Final values were determined to be n = 0.61 and E = 41.6 kcal mol-’ (ref. 7, 0.60 and 41.5). TG data were also analyzed for TF and SB using spreadsheet analysis as previously indicated. Final values of n and E (kcal mol-‘) obtained for TF and SB were 0.98 and 65.6 and 0.82 and 24.2, respectively (ref. 8, 1.0 and 67 and 0.7 and 22). From the preceding results it can be concluded that spreadsheet analysis of TG data for the estimation of kinetic parameters, as presented here, gives final values in good agreement with corresponding theoretical and reported values. This further supports previous recommendations [3,4] that spreadsheet analysis procedures be instituted to a greater extent in the field of thermal analysis whenever possible either as primary or corroborative methods.
REFERENCES 1 2 3 4 5 6
W.W. Wendlandt, Thermal Analysis, 3rd edn., Wiley, New York, 1986. L. Reich, L.Z. Pollara and S.S. Stivala, Thermochim. Acta, 106 (1986) 379. L. Reich and S.H. Patel, Am. Lab., 19 (9) (1987) 23. L. Reich, Thermochim. Acta, Part 2, in press. R. Malloy, Spreadsheets, BYTE, 12 (7) (1987) 69. M. Adrian, C. Barr, M. Falkner, J. Taylor and W.A. Taylor, Challenging 1 2 3 on price & power, PC Magazine, 6 (18) (1987) 94. 7 L. Reich and S.S. Stivala, Thermochim. Acta, 25 (1978) 367. 8 L. Reich and S.S. Stivala, Thermocbim. Acta, 24 (1978) 9. 9 K. Bohme, S. Boy, K. Heide and W. Holand, Thermochim. Acta, 23 (1978) 17.
USE OF SPREADSHEETS
IN THERMAL
ANALYSIS.
311
PART 3.
LEO REICH Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 (U.S.A.) (Received 12 September 1988)
ABSTRACT
Spreadsheets have rarely been used to analyze TG and DTA (or DSC) data to obtain activation energy E and reaction order n (or mechanism). In the recent past and in this paper spreadsheet procedures have been successfully used to ascertain E and n or E and mechanism. In this paper, these procedures are applied to theoretical TG data, to TG data for calcium oxalate, calcium carbonate, teflon and sodium bicarbonate and to DTA data for benzenediazonium chloride. In addition, some of the many advantages of using such procedures are mentioned. The aim of this paper is to extend the implementation of spreadsheets in thermal analysis.
INTRODUCTION
Spreadsheet analysis of TG, DTA or DSC data to obtain activation energy E and reaction order n or mechanism has been used only rarely in the past. Thus, previous determinations of E and n generally employed graphical and/or computer methods [l]. However, recently [2-41, spreadsheet procedures have been successfully used for the determination of E and n [2,3] or of E and mechanism [4]. There are many advantages to the use of spreadsheets [5,6]. Thus, they can provide neat formats of data and results and possess many built-in functions. Some of these functions (in the case of Lotus 2) are as follows: summations (@SUM), standard deviations (@STD), maximum and minimum values (@MAX and @MIN), single and multiple linear regression analysis, graphics, sorting, etc. Furthermore, Macros allow the automatic utilization of worksheets for the estimation of the kinetic parameters E and n (and mechanism). This paper is one of a planned series whose aim is to extend the implementation of spreadsheets for the analysis of TG, DTA or DSC data to obtain values of E and n (or mechanism). 0040-6031/89/$03.50
0 1989 Elsevier Science Publishers B.V.
312 THEORETICAL
ASPECTS
For two pairs of given values of cuand T(K), i.e. cyi, T, and LYE,T2, it can be shown that [7] ln
1 - (1 - c&n I_(l_.J~)
I;
2
E 1 =&-+I
where cy= conversion at temperature T(K). From eqn (l), values of E/R can be calculated for various sets of cw-T values at arbitrarily selected values of reaction order n. However, if uniqueness is assumed, only one pair of E/R and n values will be relevant. Various values of E/R can be obtained at various n values by employing various pairs of cu-T values. However, the E/R values should not deviate (or deviate minimally} at only one unique value of n. This value can be established by utilizing the concept of the standard deviation (STD). Thus, the E/R values at a particular value of n, which afford the smallest STD value, also yield final values E(avg) and n.
RESULTS AND DISCUSSION
The spreadsheet employed in this paper was Lotus l-2-3, release 2, which can provide many advanced Macro commands. Such commands were applied in this paper to theoretical non-isothermal TG (NITG) data, to NITG data for calcium oxalate (COX), calcium carbonate (CAC), teflon (TF) and sodium bicarbonate (SB) and to DTA data for benzenediazo~um chloride (BDC). Table 1 represents a spreadsheet analysis of theoretical TG data. Final values (cf. row 29) were w = 0.50 and E = 28.0 kcal mol-’ (ref. 8, l/2 and 28). The cell contents for the worksheet in Table 1 are depicted in Table 2. From the latter table it can be seen that cells E4-E9 denote values of the left-hand-side logarithm term for various ty- T(K) values. Thus, for example, the value in cell E4 is equal to the LN(value in cell D3/value in cell D4), etc. down the Y column. The X values in cells F4-F9 represent the term in parentheses on the right-hand side of eqn. (1) (see Table 2). Finally, the E/R values in cells G4-G9 are equal to the corresponding values of the ratios of Y/X, and the average E/R value is depicted in cell Gil. The starting n value was taken as 0.10001 and was incremented initially in increments of 0.1; an initial arbitrary value of 1E + 11 was placed in cell El5 (SD2) (cf. rows 17 and 18). When E/R values yielded standard deviations in cell D15 (SDl) which were less than the values in SD2, the corresponding n values were automatically placed in cell F15 and the SD1 and E,/R(avg) values were automatically placed in cells El5 (SD2) and G15,
313
respectively (see row 20). This continued until n values up to 2 had been scanned. When n > 2, the value of n was automatically decreased by the increment value (Inc) and the Inc was decreased by a factor of 10 (cf. rows 24 and 25). The value of n was then automatic~ly incremented over a range of (n - 0.1) to (n f 0.1) using Inc = 0.01, after which the final value of tz (from cell F15) and the final value of E (from cell GlS> were automatically recorded in row 28.
Al: !!@I Alpha El: !%I "Tt%? Cl: [416! ‘H Dl: I!#!?!LHS! E!: ‘I Fl: I11101t 61: [Y9! E'R A:: I!481 i= B?: iU81:= C?: [kbl\= I)?:~IrlOl !: E?: \= F?: IWlOl\= 62: I#91\= AZ: !F5)[YBI0.1X9 83: I1133 4r?5 c3: !Ybl0.60001 D3: !S:!Ml01 111-!1-631'!1-INf1!R3~?~ A4: :FslIit31 0.:':195 84: tUEi410 D4: iS?rIW!Of~f!-(l-A4!^ll-ta!l!B4'?i E4: ~LNltD~~B4l F4: K?f tYl's! l/94-US3 64: !SZ!tU91*E4/F4 85: !F% IMSIo.swi ~5: vda141s D5: is?)[Y:Ol!il-!l-A5l*~I-tN!)/B5^;) E5: 3LNltD4:I)S) FS: is?)!YlOl!/!5-1184 65: iS?lIWPItE5m A5: lF.5) IWBI0.44165 Bb: !UBI4?0 D5: !S21IWlOli!l-i!-At!'!l-tNl!:B6'?1 Eb: JLNltlwDh) FL: 'S?)IW!Ol!iBl-::BS 66: IS?:ik191 +f*/Fi 17s IF:)!USI,f.a!Bz') 87: w1 425 D7: !SZ)IW!:'l !:f-ii-A?! :l-tNil.'B?'21 E7: jL~tt~6~D?) F7: LS?!IY!OIl:Ei-liB6 67: 152):Y9!+E?iF? A& iFSfMl1 3.81979 m: M51 470 DE: is?!IUl8!l:l-~!-AS);!i-!l)l:B8*?) EB: 3?Nl'27:18~ FB: :S?>!110!;:S8-!:B! $8: IS?)IN91'EBiF9 A9: :F5)!#I ').9x33 89: I#$!435 D9: is?)Ih!Ol!1l-'l-A9)'!!-?N)):99"?) E9: DL!IiiImP) FP: !S?1:111:1 !/BY-1!98 69: :SZ):W9!+EO!f9 MO: IbBI\= 910:Ml != no: IYL!:= Did: I!#!OJ :s El& \= FfO:
!S:!
:#I’?!
so: is21in91!= Fi!: :S11iY!bl~f/9(A%!=‘ sii: iw f#9!wGIE:Rl Al?: #$I ?= Bl?: i#eli= Cl:; '#5l il L , 012: t!4101 ',= El? c,: Fl?: iUlOI\z 512: 11191 \= AI5: !%I .Ilrl;r 813: rug1"'PC .a 813: IYlir! %Yl! E13: !S2)'%I: ~13: !%I !blO!'rctacrdr 613: !W9!^E!RL?: All: :UBJ\= 814‘ . .?#I != C14: 0461?= It:4: I11101 != El4: 1521!= F!4: tSZ1Ul131i!?!I: ul91:= a15: IYS!1
515:iWSfk6! D15: tS?lIYlOJOS?B!E/R) El% 152)0.94943m72 Fl:: (52)iYIO11).50001 Sl:: (S?l[W9113e99.934997 A17: IWfil !\a--> 817: Iwe]'(letnrkr,O:!let. inc,.I!Ilet sd?,lEtlll:let ;,.10i'01~*(paoe!:ff! Ala: IW81'\d--: BlB: [uai‘(gotoW(iet il,mtin:!* 819: N81 '(ifo:kr~l~dnd#i~-f!5i,lj(qotoja?7'!quit) r;tnordr.+n?lIet 915,91!? B?O: !#I 'Iiftsdl!sd?:!!et ;d?,sd!!(let 821: !YYl ‘(if +:3?2!ibran:t; \>I
821: [&a!
'!banKR
B?4: iY91‘igoto!n”:!et
825: E?b: GB: 829: c:s:
n,+f!S-ix:” l;iEl ‘
E2B: != F?9: IU!CI!= sz3: IN91!Z 129: !W81"r:tnordr= C?9: !F31IW6!*RCTNORDR X9: I!4101 'and E29; "E: FV' LIL 'WI;!1 . )INTitERZt:l G?9:,[W91'calinol ASO: !U8! \z 830: [WEI\= m: &I \= Eyy - * 11
zo: I#101\= 530: In91:= i=
id:
A?4: 143:'\k--'
315 TABLE
3.
Spraadsheet
anaiysis
of theoretical
in=l?
TG data
f (K:! Y 6-31pha LHSI PJ ________________----__1________1______1_~~~~--~~~~~_-~~-~~~~ _________________--_-------__-~~~-~~~~~~~~-~~~~~-~---~~~~~-0 _ 1’20 1
726 762 7SQ
(2.2669
l.iOO
E9 1
x
E/R
-2.OlE-09
-5.43E-_f)<)l$; -S_67E-OS -0.46757 -3.0.2X-05 0. ‘5097 79’2 -?.17E-it7 -0.30343 -1.94E-05 0. f313 ert -2. IZE-07 -0.59173 -3.71E-05 ct. @Zll; 925 -2.34E-C?7 -0.25’133 - 1.7SE-05 ====-----I--==================================~~============
1.5.3E+C>4 1.54E404 1.56E+O4 1_5$E+Ct4 1. S4E+C)4
E/R (WEi) =:>I. 57E404 f======================================~~==================~=== __“r”~____~~c_________--_~~~---__-_~~~-___~~~~~~~~__~~~~~~__ --_________________---------_--~~~~~~~~~~~~~~~~~~~~~~--~~~~-1
t-j .I\..‘71
Q. 12E+C12 4.24E+Mk
1. CtCsE+CtC> 1.51EtClY
===========================z
====z==r=2=I==========
rctnurdr= 1 .OUCH ======================
and
3X339 cdl lmol E= --_--_---~~---------____I___ -f----_-ll-----_______lt------
In order to conserve space, Macro commands (which are similar to those in Tables 1 and 2) are not included in Tables 3-6. Table 3 portrays the final results for the spreadsheet analysis of another set of theoretical TG values (a-T(K)). Final results were determined to be n = 1.00 and E = 30.2 kcal mol-’ (ref. 9, 1 and 30).
TABLE
4.
Spreadsheet
ana?ysir,
of
fG data
-Tot-COX
c71:
7” (Y.1 r.! Ai pha LHSl Y Y E/H ---_-----~----------_------_-~~~~~~-~~~~~~-~~---~--____----______---______L_---___I_-_---_---------------f__---~---.-~---0. !f2C@ 437 -_....l 7 1 -240 -1.58E-09 0.075C~ 443.2 -5_59E-C)$3 -1 .*l"Pi-_ ")L'T.3Cq$:, 47:z.z -2.33E-07 -C>.42795 -4 .5&E-05 9_3SE+QI,3 Cl*943'3 -3_&5E-Cl7 -0.4459"j -4,37E-13 1.02EtCb4 &. 483.2 0. ti::7C? 493.2 -5 .74E-07 -0 .4Es455 .-4.2C:E-C)Z;1.0~EtCt4 C2,77'ZC% 503.2 +.llE-07 -0.451663 -4.03E-05 l.i5E+O4 r=======I==================================~~=============~ E/R:AVG)=>l.G7E+04 ===l=====t==========t=====================~~==========.==_===
_"r"r____"~c____________~~~-_----_~~~----~~~~~~~~--~~~~~~---f------____--_----________I___________--~~---~--____---~~ 1 0. 01 8.21E+02 7.8EtE+CG? 1_04E+fiC1 l_Ci4Et1>4
===================== rctncrdr= 1.040 _--_------____----___ ---------~-----_-_____
========r===================
and
E=
20X30
===f========================
cdl
fmof
316
TABLE
5.
Spreadsheet
analysis
of
TG data
for
EDC
C 7 1
Alpha T!K) N Y LHSl X =========================================================== :-, .>_s '57 305. 3 1.120 -4.97E-09 0. 074 -0.65977 310.6 -?.61E-08 -4_52E-05 0. 123 -i~.5liw2 -4.4OE-05 314.9 -l.ME-07 C,. LLLl ')')c: 319.2 -0.64407 -3_05E-07 -4_2sE-05 0.336 -0.63629 323. 5 -5.7&-07 -4.1&E-05
0.575
327.8
-1. olE-06
-0.56091
-4. o5E-05
E/R
1.45Et04 1. 1.5E+04 1_5lE+04 1.53E+o4
?.3SEtO4
0.769 ?77 1 d.-.L. -1.74E-06 -Q-54643 -3.95E-05 1.38E+04 0.922 -0.59645 336.4 -3.l?E-06 -3.95E-05 1.55E+O4 =========================================================== E/R(A'JG)=>l.42E+04 =========================================================== t?rkr Il-iC SD1 SDZ rctnordtE/R(Z) =========================================================== 1
0.01
1.24E+03
__---______-_________ ---------------------
l.l4E+03
1. CQE+ix:) 1 .38E+O4
============================
rctnordr= 1.020 __----_____-_________ _______-______--_____
and
E= 27557 caI/mol ============================
A spreadsheet analysis of TG data for the dehydration of the monohydrate of COX is depicted in Table 4. Final values were determined to be n = 1.04 and E = 20.8 kcal mol-’ (ref. 7, 1.05 and 20.8). A spreadsheet analysis of DTA data for the decomposition of BDC in aqueous solution is shown in Table 5. From these a-T(K) values, the final values obtained were
TABLE
6.
Spreadsheet
analysis
of
TG data
for
CAC
L 7 1
Al ..I-,T : 9:.) N Y LHSl X ============================================================ ::i. ‘:t5(1!0 9El.2 0. 7 10 1.53E-08 0. i)75C! 1008. 2 -Q.36050 Z.ZOE-09 -2.73E-05 0. IbOC! 1cry-c X,-.J. 7 4.&,OE--OS -0.73715 -2.&.3E-05 0.5153 1064.7 -0.69028 9.17E-08 -2.63E-05 !I,. 4S50 1095. 2 -0.45507 1.46E-07 -2.tZE--05 iy”Q
E/R
1.32E64 2.SOE+:>4 2.6ZE+04 1.7SE+C)4
E/R(AVGj=>2.?3Et04 ====~====================================~=================== Pi-kr I:tc SD1 SD2 rctnordr E/R(Z) ?
- -----;Ic~mcp-=
0. C!1
----
-.---
5_42E+i!3
------0.
t1C:
5_4lE+03
6. lC)E-01 2_Ci&E+C!4
============================ and
E= 41623 cal/mo? ============================
317
n = 1.02 and E = 27.6 kcal mol-’ (ref. 7, 1.05 and 27.8). Finally, an analysis of TG data for the decomposition of CAC is depicted in Table 6. Final values were determined to be n = 0.61 and E = 41.6 kcal mol-’ (ref. 7, 0.60 and 41.5). TG data were also analyzed for TF and SB using spreadsheet analysis as previously indicated. Final values of n and E (kcal mol-‘) obtained for TF and SB were 0.98 and 65.6 and 0.82 and 24.2, respectively (ref. 8, 1.0 and 67 and 0.7 and 22). From the preceding results it can be concluded that spreadsheet analysis of TG data for the estimation of kinetic parameters, as presented here, gives final values in good agreement with corresponding theoretical and reported values. This further supports previous recommendations [3,4] that spreadsheet analysis procedures be instituted to a greater extent in the field of thermal analysis whenever possible either as primary or corroborative methods.
REFERENCES 1 2 3 4 5 6
W.W. Wendlandt, Thermal Analysis, 3rd edn., Wiley, New York, 1986. L. Reich, L.Z. Pollara and S.S. Stivala, Thermochim. Acta, 106 (1986) 379. L. Reich and S.H. Patel, Am. Lab., 19 (9) (1987) 23. L. Reich, Thermochim. Acta, Part 2, in press. R. Malloy, Spreadsheets, BYTE, 12 (7) (1987) 69. M. Adrian, C. Barr, M. Falkner, J. Taylor and W.A. Taylor, Challenging 1 2 3 on price & power, PC Magazine, 6 (18) (1987) 94. 7 L. Reich and S.S. Stivala, Thermochim. Acta, 25 (1978) 367. 8 L. Reich and S.S. Stivala, Thermocbim. Acta, 24 (1978) 9. 9 K. Bohme, S. Boy, K. Heide and W. Holand, Thermochim. Acta, 23 (1978) 17.