Research Article Thermal Decomposition Study of Ferrocene ...Research Article Thermal Decomposition Study of Ferrocene [(C 5 H 5)2 Fe] AshisBhattacharjee, 1 AmlanRooj, 1 DebasisRoy,

Research ArticleThermal Decomposition Study of Ferrocene [(C5H5)2Fe]

Ashis Bhattacharjee1 Amlan Rooj1 Debasis Roy1 and Madhusudan Roy2

1 Department of Physics Visva-Bharati University Santiniketan 731235 India2 Surface Physics and Material Science Division Saha Institute of Nuclear Physics Kolkata 700064 India

Correspondence should be addressed to Ashis Bhattacharjee ashisbhattacharjeevisva-bharatiacin

Received 19 December 2013 Accepted 14 March 2014 Published 27 April 2014

Academic Editor Ahmad Ibrahim

Copyright copy 2014 Ashis Bhattacharjee et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A single-step thermal decomposition of ferrocene [(C5H5)2Fe] using nonisothermal thermogravimetry (TG) has been studied using

single- as well as multiple-heating rate programs Both mechanistic and nonmechanistic methods have been used to analyze theTG data to estimate the kinetic parameters for the solid state reaction Two different isoconversional methods (improved iterativemethod and model-free method) have been employed to analyze the TG results to find out whether the activation energy of thereaction depends on the extent of decomposition and to predict themost probable reactionmechanismof thermal decomposition aswell A comparison of the activation energy values for the single-step thermal reaction of ferrocene estimated by different methodshas been made in this work An appraisal on the applicability of single-heating rate data for the analysis of single-step thermaldecompositions over the recommendations by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) ismade to look beyond the choice

1 Introduction

In recent times the organometallic compound ferrocene[(C5H5)2Fe] has become an important precursor mate-

rial for preparing iron oxide nanostructures through ther-mal decomposition for example ferromagnetic micronanoparticles [1ndash3] iron oxide thin films [4] and single-walledferromagnetic-filled carbon nanotube [5 6] Takingleaf out of these works we undertake to study the thermaldecomposition of ferrocenematerials in the presence of guestmolecules of various kinds leading to iron oxides and toinvestigate the correlation among the thermal decompositionreaction kinetics morphologyphysical characteristics of thereaction products and the nature of the guest molecules Asa prerequisite we undertake to study the kinetics of thermaldecomposition reaction of one such precursor materialferrocene in order to find the reaction kinetic parametersas well as the most probable mechanism To the best ofour knowledge there is only one report on the thermaldecomposition study of ferrocene [7] which however doesnot discuss the reaction mechanism

There are two basic approaches to determine the reactionkinetic parameters or kinetic triplets (activation energyfrequency factor or rate of reaction and most proba-ble reaction mechanism function 119892(120572)) related to thermaldecomposition using the thermogravimetry (TG) datamdash(a)mechanistic and (b) nonmechanistic [8] At the beginningof the present TG data analysis we have utilized the well-known classic equations of Freeman-Carroll [9] Kissinger[10] and Lozano et al [11] to estimate kinetic parame-ters related to the thermal decomposition of ferroceneIn addition Arrhenius equation [12] has been used toidentify the most probable reaction mechanism functionBesides the Kissinger method [10] all other methods requiresingle-heating rate-based TG data Most importantly thebasic assumption for these methods is that the activationenergy of decomposition reaction is unique and it doesnot depend on the extent of thermal decomposition atany instant of time But as per the recommendation ofthe kinetics committee of the International Confedera-tion for Thermal Analysis and Calorimetry (ICTAC) themultiple temperature program methods should be used

Hindawi Publishing CorporationJournal of Experimental PhysicsVolume 2014 Article ID 513268 8 pageshttpdxdoiorg1011552014513268

2 Journal of Experimental Physics

to evaluate the reaction kinetic parameters reliably [13]Accordingly two multiheating rate methods called isocon-versional methods namely improved iterative method [14]and model-free method [15] are also employed to analyzethe present TG data The modern kinetics investigationprocedure using multiheating rates is used to find out themost probable reaction mechanism function as well [16]

In the present paper we have reported the thermaldecomposition study of ferrocene by thermogravimetry Ouraim is on one hand to estimate the reaction kinetic parame-ters based on themathematical analysis of thermogravimetricprofiles of ferrocene and on the other hand to discuss thevariation of activation energy values (estimated by variousmethods) with the extent of thermal decomposition to revealthe applicability of the methods based on single-heating rateover the ICTAC recommendation for single-step solid statethermal reactions

2 Experimental

21 Materials andMeasurement Thematerial for the presentstudy is ferrocene [(C

5H5)2Fe]The high quality material was

procured from Sigma and used without further purificationNonisothermal thermogravimetry (TG) measurements werecarried out using a thermogravimetry analyzer (NetzschGermany model STA 449C) The sample and referencecrucibles used for measurements are made of alumina Thesample of sim4mg mass was scanned at constant heatingrates (5 10 15 and 20Kminminus1) in (room) air environmentUHP nitrogen (99999) was used as protective gas in theinstrument

22 Kinetic Calculations To determine the activation energyof solid state thermal decomposition reaction of ferroceneusing nonmechanistic methods two equations proposedby Freeman-Carroll [9] and Kissinger [10] are used firstFreeman-Carroll equation is given by

ln119882 =119864lowast

119877119879+ ln(

119903119889

119860) (1)

where 119882 is the remaining mass fraction in a TG curve thatrepresents the thermal decomposition at a constant heatingrate at any instant of time 119864lowast is the activation energy 119877 is theuniversal gas constant 119879 is the temperature in absolute scale119903119889is thermal decomposition rate and119860 is the preexponential

factor Using (1) the activation energy value of the thermaldecomposition can be estimated from the slope of the ln119882

versus 1119879 plotThe nonmechanistic Kissinger equation [10] is given by

ln(120573

1198792119875

) = minus119864lowast

119877119879+ ln(

119860119877

119864lowast) (2)

where 120573 is the linear heating rate 119879119901is the differential

thermogravimetry peak temperature in absolute scale andother symbols have their usual meaning To apply Kissingerrsquosmethod the TG profiles with different heating rates arerequired Employing (2) the activation energy values of the

thermal decomposition process can be calculated from theslope of the ln(1205731198792

119875) versus minus1119879 plot

In order to find out the nonisothermal reaction kineticmodel describing the thermal decomposition process thefollowing mechanistic equation is used to identify the mech-anism of reaction according to Lozano et al [11]

Δ ln1205721015840

Δ ln (1 minus 120572)= minus

119864lowast

119877

Δ (1119879)

Δ ln (1 minus 120572)+

Δ ln119891 (120572)

Δ ln (1 minus 120572) (3)

where 120572 = (119898119894minus 119898119905)(119898119894minus 119898119891) is the extent of reaction

or conversion that is the fraction of material reacted intime 119905 with 119898

119894and 119898

119891being the initial and final masses

respectively 119898119905is the mass at any instant of reaction

1205721015840= 119889120572119889119879 and 119891(120572) is the kinetic differential mechanism

function which determines the actual reactionmechanism Aseries of proposed forms of 119891(120572) are available in [17] A plotof ((Δ ln120572

1015840minus Δ ln119891(120572))Δ ln(1 minus 120572)) versus Δ(1119879)Δ ln(1 minus

120572) will be a straight line with a slope minus119864lowast119877 irrespective

of the form of 119891(120572) employed The form of the function119891(120572) is selected in such a way that it best fits the actualmechanism of the reaction corresponding to the interceptvalue and the correlation coefficient close to zero and unityrespectively The reaction kinetic parameters for the thermaldecomposition are thus estimated To identify the actualmechanism of the reaction kinetic process and to test thecorrectness of the validity of conclusions drawn using (3) theArrhenius equation of the following type is used [12]

ln1205721015840minus ln119891 (120572) = ln(

119860

120573) minus

119864lowast

119877119879 (4)

where 1205721015840

= 119889120572119889119879 119860 is the Arrhenius parameter andthe remaining symbols have their usual meaning The plotof [ln120572

1015840minus ln119891(120572)] versus 1119879 is expected to be a straight

line when the Arrhenius equation is applicable and from itsslope and intercept the values of 119864

lowast

120572and 119860 are estimated

respectively Now if the proposed mechanism on the basisof (3) is correct the activation energy values estimated from(4) should in principle be the same or close to those obtainedusing (3) [12] According to this paradigm the most probablemechanism function 119891(120572) using TG data can be determined[17]

To describe the reaction kinetics and mechanism of ther-mal decomposition of solids most reliably isoconversional(model-free) methods are presently often used In isocon-versional method the reaction rate at constant extent ofconversion is supposed to be a function of temperature onlyTwo simplifying assumptions are mostly used in this regard(i) the temperature at any point in the solid remains the sameand (ii) the controlling step in the reaction rate does notalter throughout the transformation of a solid state chemicalprocess [18 19] In order to study the kinetics of solidstate reaction under nonisothermal conditions with linearheating rates (120573) two early basic equations used as regardsthermal decomposition are Flynn-Wall-Ozawa (FWO) [20

Journal of Experimental Physics 3

21] and Kissinger-Akahira-Sunose (KAS) [10 22] equationsThe FWO equation is expressed as

ln120573119894= ln

00048119860120572119864lowast

120572

119892 (120572) 119877minus 1052

119864lowast

120572119860120572

119877119879120572119894

(5)

and the KAS equation is written as

ln120573119894

1198792120572119894

= ln119860120572119877

119892 (120572) 119864lowast120572

minus119864lowast

120572

119877119879120572119894

(6)

where the subscript ldquo119894rdquo denotes different heating rates and119879120572119894

is the temperature at which an extent of reaction (120572) isreached at constant heating rate (120573

119894) and 119864

lowast

120572is the activation

energy for a given120572 and119892(120572) = int120572

0[119891(120572)]

minus1119889120572The activation

energy values obtained by (5) and (6) are often found lessaccurate To calculate the activation energy more accuratelythe iterative procedure approximating the exact value ofactivation energy is used [14] according to the followingequations

ln120573119894

ℎ (119909) 1198792

120572119894

= ln119860120572119877

119892 (120572) 119864lowast120572

minus119864lowast

120572

119877119879120572119894

(7)

ln120573119894

119867(119909)= ln

00048119860120572119864lowast

120572

119892 (120572) 119877minus 10516

119864lowast

120572119860120572

119877119879120572119894

(8)

where ℎ(119909) is expressed as [23]

ℎ (119909) =1199094+ 18119909

3+ 88119909

2+ 96119909

1199094 + 201199093 + 1201199092 + 240119909 + 120(9)

and119867(119909) is expressed as [16]

119867(119909) =exp (minus119909) ℎ (119909) 119909

2

00048 exp (minus10516119909) (10)

where 119909 = 119864lowast

120572119877119879120572119894

In performing the iterative procedure the following stepsare often used step 1mdashthe initial value of the activationenergy (119864

lowast

120572)1is estimated by assuming ℎ(119909) = 1 or 119867(119909) =

1 (generally the conventional isoconversional methods stopcalculating at this step) step 2mdashusing 119864

lowast

120572= (119864

lowast

120572)1the

new value of activation energy another value of 119864lowast

120572=

(119864lowast

120572)2is calculated from the plot ln(120573

119894119867(119909)) versus 1119879

120572119894

or ln (120573119894ℎ(119909)119879

2

120572119894) versus 1119879

120572119894 step 3mdashrepeat of step 2

replacing (119864lowast

120572)1with (119864

lowast

120572)2resulting 119864

lowast

120572= (119864lowast

120572)3 and so on

until the absolute difference of [(119864lowast120572)119894minus (119864lowast

120572)119894minus1

] becomes lessthan 01 kJmoleminus1 [17]The last value of (119864lowast

120572)1thus obtained is

considered to be themore exact value of the activation energyof the thermal decomposition reactionThe activation energyevaluated by this method is reaction-model independent andusually regarded as more reliable [14]

In the model-free isoconversional method for non-isothermal thermogravimetry experiments the activationenergy 119864

lowast

120572can be evaluated at any particular value of 120572 by

minimizing the following objective function [15 24]

Ω(119864lowast

120572) =

119899

sum

119894=1

119899

sum

119895=1

119894 = 119895

119868 (119864lowast

120572 119879120572119894) 120573119895

119868 (119864lowast120572 119879120572119895

) 120573119894

(11)

where 119868(119864lowast120572 119879120572119894) the temperature integral is given as

119868 (119864lowast

120572 119879120572119894) = int

119879120572119894

0

exp(minus119864lowast

120572

119877119879)119889119879 (12)

There are several methods and popular approximationsto evaluate this temperature integral Approximation ofCai et al [25] which is proved to be superior to any otherapproximations is mostly used for evaluation of activationenergy 119864

lowast

120572and other kinetic parameters from nonisothermal

kinetic analysis of the TG data According to this approxima-tion the temperature integral is given as

int

119879120572119894

0

exp(minus119864lowast

120572

119877119879)119889119879

=1198771198792

120572119894

119864lowast120572

[(119864lowast

120572119877119879120572119894) + 066691

(119864lowast120572119877119879120572119894) + 264943

] exp(minus119864lowast

120572

119877119879120572119894

)

(13)

The equation which is mostly used to estimate the mostprobable reaction mechanism that is 119892(120572) function is givenas [16]

ln119892 (120572) = [ln119860120572119864lowast

120572

119877+ ln 119890

minus119909

1199092+ ln ℎ (119909)] minus ln120573

119894 (14)

where 119892(120572) = int120572

0[119891(120572)]

minus1119889120572 = (119860120573) int

119879

0exp(119864lowast119877119879)119889119879

is the integral form of the reaction model describing thereaction mechanism [17 18] and the other symbols havetheir usual meaning For the determination of the mostprobablemechanism function the slope of the straight line ofln119892(120572) versus ln120573

119894plot using linear regression of least square

method should be nearly equal to minus10000 and the linearcorrelation coefficient 119877

2 should be nearly equal to unity[17] While finding the most probable reaction mechanismfunction 119892(120572) involved in the present thermal decompositionreaction the 35 types of mechanism function given in [17]have been used If incidentally a number of 119892(120572) functionssatisfy the conditions specified above the values of the extentof reaction 120572 corresponding to multiple-heating rates at atemperature but other than the previous one along the 120572

versus 119879 plots are applied to confirm the most probablereaction mechanism function by the same way

Using the estimated value of the activation energy andthe most probable reaction mechanism function the preex-ponential or frequency factor (119860) value can be evaluated fromthe following equation [17 26]

119860 = minus120573119909119901

1198791198911015840 (120572119901)exp (119909

119901) (15)

where 119909119901

= 119864lowast119877119879119901(119879119901is the peak temperature on corre-

sponding differential thermogravimetry curve) and 1198911015840(120572119901) is

the first derivative of the reaction mechanism function

23 Thermodynamic Parameters From the theory of theactivated complex (transition state) of Eyring [27ndash30] thefollowing general equation may be written

119860 =119890120594119896119861119879119901

ℎ exp (Δ119878lowast119877) (16)

4 Journal of Experimental Physics

where 119890 = 27183 (base of natural logarithms) 120594 is thetransition factor (=1 for monomolecular reactions) 119896

119861is

the Boltzmann constant ℎ is Plankrsquos constant and 119879119901is the

peak temperature of the differential thermogravimetry curveat the corresponding stepThe change of the entropyΔ119878lowastmaybe calculated according to the following formula

Δ119878lowast= 119877 ln(

119860ℎ

119890120594119896119861119879119901

) (17)

Since

Δ119867 = 119864lowastminus 119877119879119901 (18)

the changes of the enthalpy Δ119867lowast and Gibbs free energy

Δ119866lowast for the activated complex formation from the precursor

can be calculated using the well-known thermodynamicalequation

Δ119866lowast= Δ119867

lowastminus 119879119901Δ119878lowast (19)

The values of Δ119878lowast Δ119867lowast and Δ119866lowast are calculated at 119879

119901 since

this temperature characterizes the highest rate of decomposi-tion

The calculations of reaction kinetic parameters using theabove-stated equations were based on a program compiledin MATLAB

3 Results and Discussion

Figure 1 shows the TG profiles of ferrocene obtained underfour different heating rates (5 10 15 and 20Kminminus1) EachTG profile confirms a one-step decomposition process forthis material and represents the relationship of the resid-ual mass with temperature during thermal decompositionHowever this decomposition takes place in temperatureranges 349ndash465K 345ndash485K 356ndash498K and 385ndash511 K for5 10 15 and 20Kminminus1 heating rates respectively and thethermal reaction becomes maximum at sim448K in all casesof heating rates and is completed with almost sim100 massloss beyond sim510K Melting point of ferrocene is 448KFerrocene (C

5H5)2Fe has a ldquosandwich structurerdquo of two

parallel cyclopentadienyl rings with an iron in the centerbetween these rings It is solid at room temperature andthermally decomposes at 448K and its boiling point is 522KIn the temperature range from sim870K to sim1420K ferrocenefurther decomposes [31] According to Leonhardt et al [6] attemperatures above sim770K gaseous ferrocene decomposesspontaneously to form metallic iron according to the follow-ing reaction

(C5H5)2Fe 997888rarr Fe +H

2+ CH

4+ C5H6+ sdot sdot sdot (20)

This means that in this temperature range solid or liquid-like Fe particles and different kinds of hydrocarbons mayexist in the reaction medium Thus the presently observedthermal decomposition indicates that the sublimation offerrocene which takes place during solid state reaction andno further conversion to liquid or solid Fe has been observedas no increase in mass has been recorded in the TG profile

350 400 450 500 5500

20

40

60

80

100

(iv)

(iii)

(ii)(i)

m(

)

T (K)

Figure 1 Thermogravimetric profiles of ferrocene obtained underdifferent heating rates (i) 5 Kminminus1 (ii) 10 Kminminus1 (iii) 15 Kminminus1and (iv) 20Kminminus1

At this point it has to be noted that TG deals with a verysmall amount of sample mass At higher temperatures whenthe further conversion of sublimated ferrocene to liquid orsolid Fe takes place it is quite unlikely to be detected by theTG considering the converted sample mass as well as thepresently used sample cell geometry

Utilizing the TG data of the thermal decomposition offerrocene the activation energy values for the single-stepreaction process were calculated from the slope of (i) the ln119882

versus 1119879 plot using (1) and of (ii) the ln (1205731198792

119875) versus minus1119879

plot using (2) and are shown in Table 1 Again combining(3) and (4) the kinetic parameters for the decompositionof ferrocene were estimated and are presented in Table 1According to (3) and (4) the most probable mechanismfunction 119891(120572) using the TG data of ferrocene has beendetermined to be three-dimensional diffusion type which canbe represented by 119891(120572) = 32[(1 minus 120572)

minus13minus 1]minus1

[17] The 119864lowast

120572

values obtained from the multiheating rate TG data using(7) and (8) are also compared in Table 1 The temperaturevariations of the extent of reaction 120572 = (119898

119894minus 119898119905)(119898119894minus 119898119891)

during thermal decomposition of ferrocene under differentheating rates are illustrated in Figure 2 The minimizationprocedure according to (11)ndash(13) was repeated for each valueof 120572 for 01 to 09 taking data from Figure 2 to find out thedependency of 119864

lowast

120572on 120572 The 120572-dependent 119864

lowast

120572values thus

obtained are presented in Table 1The activation energy 119864

lowast

120572values for the single-step ther-

mal decomposition of ferrocene obtained by all methodsdiscussed so far are shown as a function of the extent ofconversion 120572 in Figure 3 It is noticeable that the 119864

lowast

120572values

thus calculated by the three different methods given by (7)(8) and (13) are remarkably identical and are also closeto that obtained by (1) At this point it should be recalledthat de Souza et al [7] observed three activation ener-gies for the single-step thermal decomposition of ferroceneusing Freeman-Carroll method which are 667 712 and

Journal of Experimental Physics 5

Table 1 Values of the activation energy (119864) estimated following different equations and the frequency factor (119860) for different heating rates(120573) for thermal decomposition of ferrocene

120572 Activation energy 119864kJsdotmoleminus1 Frequency factor 119860minminus1

(1) (2) (3) (4) (7) (8) (13) 120573 = 5Kminminus1 120573 = 10Kminminus1 120573 = 15Kminminus1 120573 = 20Kminminus1

01

6418 886 776 877

6801 6801 6802 23 times 104 229 times 104 241 times 104 233 times 104

02 6766 6766 6768 811 times 104 809 times 104 854 times 104 825 times 104

03 6634 6634 6636 124 times 105 125 times 105 133 times 105 128 times 105

04 6642 6642 6644 222 times 105 224 times 105 237 times 105 228 times 105

05 6642 6642 6644 343 times 105 345 times 105 366 times 105 351 times 105

06 6721 6721 6723 606 times 105 604 times 105 639 times 105 616 times 105

07 6740 6740 6740 855 times 105 851 times 105 900 times 105 869 times 105

08 6941 6941 6942 192 times 106 188 times 106 197 times 106 193 times 106

09 6834 6834 6835 180 times 106 177 times 106 187 times 106 181 times 106120572 extent of conversionNote A = 187 times 105 from (1) and 105 times 108 from (4)

360 400 440 480 520

00

02

04

06

08

10

(iv)

(iii)(ii)(i)

120572

T (K)

Figure 2 Variation of the extent of conversion of mass (120572)with temperature during thermal decomposition of ferrocene fordifferent heating rates (i) 5 Kminminus1 (ii) 10 Kminminus1 (iii) 15 Kminminus1and (iv) 20Kminminus1

865 kJmoleminus1 It has to be noted that the 119864lowast120572= 667 kJ moleminus1

value is the same as the one determined using (1) (7) (8)and (13) whereas the 119864

lowast

120572= 712 kJmoleminus1 is close to that

obtained using (3) and the other 119864lowast

120572= 865 kJmoleminus1 value

is close to that obtained from (2) and (4) The analysis basedon the isoconversional methods could successfully detect anydependence of 119864lowast

120572on 120572 in the present studies

Some of the frequently used reactionmechanisms operat-ing in solid state reactions are given in [17 23] Equation (14)is used to estimate the most probable reaction mechanismfunction 119892(120572) using the multiheating rate-dependent TGdata for ferrocene The 119892(120572) value thus obtained for thethermal decomposition of ferrocene is three-dimensionaldiffusion type given by 119892(120572) = 1 + 21205723 minus (1 + 120572)

23 or119891(120572) = 32[(1 + 120572)

minus13minus 1]minus1

It is interesting to note thataccording to (3) a three-dimensional diffusion has also been

000 025 050 075 10060

70

80

90

100

Elowast 120572

(kJmiddotm

oleminus

1)

120572

Equation (1)Equation (2)Equation (3)Equation (4)

Equation (7)Equation (8)Equation (13)

Figure 3 Dependence of activation energy (119864lowast120572) on the extent of

conversion (120572) of ferrocene obtained using different methods

held responsible as the reaction mechanism for the thermaldecomposition of ferrocene but represented by a differentfunction 119891(120572) = 32[(1 minus 120572)

minus13minus 1]minus1

Using the values of the activation energy and the most

probable reaction mechanism function estimated for fer-rocene in (15) the value of frequency factor (119860) for differentvalues of 120572 as well as for different heating rates has beenestimated (see Table 1) The variation of the average values of119860 estimated for different heating rates is shown in Figure 4The effect of heating rate on the 119860 value is found not to beremarkable However the dependence of 119860 on the 120572 valuesis quite appreciable It is noted that the rate of reaction forthe decomposition of ferrocene varies in the range of 104 sim

106minminus1 Interestingly the observed dependence of 119860 value

6 Journal of Experimental Physics

00 02 04 06 08 100

5

10

15

20

120572

(105minminus1)

Aav

Figure 4 Dependence of the frequency factor (119860av) averaged fordifferent heating rates on the extent of conversion (120572) of ferrocene

with 120572 indicates that the reaction rate cannot be assumed asa constant for the nonisothermal decomposition process offerrocene From Table 1 one can also note that the 119860 valuedetermined by using (1) is sim105minminus1 while that from (4)is sim108minminus1 where the former lies well within the rangedetermined by (15)

Figure 5 shows the variation of 119860 values as a function of119864lowast

120572where one can see that compensation effect holds between

119860 and 119864lowast

120572values for a narrow range of 119864lowast

120572[664 kJmolminus1 le

119864lowast

120572le 694 kJmolminus1] The appearance of the compensation

effect indicates that only one reaction model may be heldresponsible for the solid state reaction mechanism [32] Thevalues of119860 in solid state reactions are expected to be in a widerange [17]The low119860 values often indicate a surface reactionIf the thermal reactions are not dependent on surface areathe low 119860 value indicates a ldquotightrdquo complex while the higher119860 value indicates a ldquolooserdquo complexTherefore in the presentcase the thermal decomposition reaction of ferrocene dealswith a ldquolooserdquo complex

The observed 119879119901values correspond to 120572 = sim09 in the 120572

versus119879 plots (Figure 2) Based on the estimated values of theactivation energy 119864

lowastand frequency factor 119860 for 120572 = 09 forthermal decomposition of ferrocene under different heatingrates (see Table 1) the thermodynamic parametersΔ119878lowastΔ119867lowastand Δ119866

lowast for the formation of an activated complex fromthe precursor were calculated according to (16)ndash(19) and arepresented in Table 2 These values are calculated at the peaktemperature 119879

119901in the differential thermogravimetry curve

for the corresponding heating rates since this temperaturecharacterizes the highest rate of the reaction during thesingle-step thermal decomposition

As can be seen from Table 2 the values of Δ119878 Δ119867 andΔ119866 obtained under different heating rates are independent ofheating rates and thus we discuss the average values of theseparameters only The value of Δ119878 for ferrocene is negative Itmeans that the corresponding activated complex had lowerentropy or a higher degree of ordering than the precursor

66 67 68 69 70

0

5

10

15

20

Elowast

120572(kJmiddotmoleminus1)

(105

mminus1

)A

av

Figure 5 Dependence of the frequency factor (119860av) averaged fordifferent heating rates on the activation energy (119864lowast

120572) of ferrocene

state Thus if we denote the entropy of the precursor andthe activated complex as 119878

0and 119878

119868 respectively then 119878

0gt

119878119868for thermal decomposition of ferrocene In the terms of

the theory of an activated complex [27ndash30] the thermaldecomposition of ferrocene may be further classified intoldquoslowrdquo stage with negative entropy change

4 Conclusion

The nonisothermal thermal decomposition of ferrocene hasbeen represented by a single-step solid state reaction Bothmechanistic and nonmechanistic methods including single-and multiple-heating rate approaches have been utilized toanalyze the TG data to estimate the reaction kinetic param-eters and to identify the most probable mechanism involvedin the solid state reaction Ferrocene undergoes 100 thermaldecomposition A comparison of the kinetic parameters forthe single-step thermal decomposition reaction of ferroceneestimated here by different methods has been made Theactivation energy values determined are in conformity withpreviously reported values The activation energy values arefound to be independent of the extent of conversion whereasthe reaction rate strongly depends on the same

From the present analysis it has to be noted that theactivation energy and the frequency factor values deter-mined by Freeman-Carroll equation are quite similar to thatobtained by multiheating rate-dependent isoconversionalmethods as recommended by ICTAC On the other handthe reaction mechanism-three-dimensional diffusion reac-tion for the thermal decomposition of ferrocene predictedby Lozano et alrsquos method [11] is basically similar to thatobtained by using isoconversional methods following ICTACrecommendation Thus it seems that for single-step thermaldecomposition reactions like the present one the methodsbased on single-heating rate program may provide reliablekinetic parameters as obtained by multiple-heating rateprograms and thus single-heating rate-based methods could

Journal of Experimental Physics 7

Table 2 Values of the thermodynamic parameters for thermal decomposition of ferrocene for different heating rates

120573Ksdotminminus1 119879119875K Δ119878Jsdotmoleminus1sdotKminus1 Average value of

Δ119878Jsdotmoleminus1sdotKminus1 Δ119867kJsdotmoleminus1 Average value ofΔ119867kJsdotmoleminus1 Δ119866kJsdotmoleminus1 Average value of

Δ119866kJsdotmoleminus1

5 462 minus17112

minus17145

6449

6434

14356

1468110 479 minus17142 6436 1464715 488 minus17157 6428 1480120 495 minus17169 6422 14901

be applicable for such single-step thermal decompositionreactions However this is an open question which needs tobe verified for good number of such thermal decompositionreactions It is our conjecture that the activation energy ofsolid state reaction in such a case is either unique or nearlyindependent of the extent of thermal decomposition

Ferrocene when heated alone above sim770K does notproduce any traceable solid material detectable in the TGprofile but when it is heated together with oxalic acid thesolid hematite product is formed at sim450K [33] This mayimply that oxalic acid catalyzes the thermal decomposition offerrocene With the above results in hand our next interestwill be to control the thermal decomposition reaction offerrocene in the presence of suitable guest molecules leadingto the formation of interesting ferrite materials which are inprogress

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] N Koprinarov M Konstantinova and M Marinov ldquoFerro-magnetic nanomaterials obtained by thermal decomposition offerrocenerdquo Solid State Phenomena vol 159 pp 105ndash108 2010

[2] K Elihn L LandstromO AlmM Boman and PHeszler ldquoSizeand structure of nanoparticles formed via ultraviolet photolysisof ferrocenerdquo Journal of Applied Physics vol 101 no 3 ArticleID 034311 2007

[3] E P Sajitha V Prasad S V Subramanyam A K Mishra SSarkar and C Bansal ldquoStructural magnetic and Mossbauerstudies of iron inclusions in a carbon matrixrdquo Journal ofMagnetism and Magnetic Materials vol 313 no 2 pp 329ndash3362007

[4] M Rooth A Johansson K Kukli J Aarik M Boman and AHarsta ldquoAtomic layer deposition of iron oxide thin films andnanotubes using ferrocene and oxygen as precursorsrdquoChemicalVapor Deposition vol 14 no 3-4 pp 67ndash70 2008

[5] A Barreiro S Hampel M H Rummeli et al ldquoThermal decom-position of ferrocene as a method for production of single-walled carbon nanotubes without additional carbon sourcesrdquoThe Journal of Physical Chemistry B vol 110 no 42 pp 20973ndash20977 2006

[6] A Leonhardt S Hampel CMuller et al ldquoSynthesis propertiesand applications of ferromagnetic-filled carbon nanotubesrdquoChemical Vapor Deposition vol 12 no 6 pp 380ndash387 2006

[7] A C de Souza A T N Pires and V Soldi ldquoThermal stabilityof ferrocene derivatives and ferrocene-containing polyamidesrdquo

Journal of Thermal Analysis and Calorimetry vol 70 no 2 pp405ndash414 2002

[8] M E Brown D Dollimore and A K Galwey ldquoTheory of solidstate reaction kineticsrdquo in Comprehensive Chemical KineticsReactions in the Solid State C H Bamford and C H TipperEds p 41 Elsevier Amsterdam The Netherlands 1980

[9] E S Freeman and B Carroll ldquoThe application of thermoana-lytical techniques to reaction kinetics The thermogravimetricevaluation of the kinetics of the decomposition of calciumoxalatemonohydraterdquo Journal of Physical Chemistry vol 62 no4 pp 394ndash397 1958

[10] H E Kissinger ldquoReaction kinetics in differential thermalanalysisrdquo Analytical Chemistry vol 29 no 11 pp 1702ndash17061957

[11] R Lozano J Roman J C Aviles A Moragues A Jerezand E Ramos ldquoThermal decomposition of molybdenum(IV)dialkyldithiocarbamates application of a newmethod to kineticstudiesrdquo Transition Metal Chemistry vol 12 no 4 pp 289ndash2911987

[12] N Deb ldquoAn investigation on the solid state pyrolytic decom-position of bimetallic oxalate precursors of Ca Sr and Bawith cobalt a mechanistic approachrdquo Journal of Analytical andApplied Pyrolysis vol 80 no 2 pp 389ndash399 2007

[13] S Vyazovkin A K Burnham J M Criado L A Perez-Maqueda C Popescu and N Sbirrazzuoli ldquoICTAC KineticsCommittee recommendations for performing kinetic compu-tations on thermal analysis datardquoThermochimica Acta vol 520no 1-2 pp 1ndash19 2011

[14] Z Gao M Nakada and I Amasaki ldquoA consideration of errorsand accuracy in the isoconversional methodsrdquo ThermochimicaActa vol 369 no 1-2 pp 137ndash142 2001

[15] S Vyazovkin and D Dollimore ldquoLinear and nonlinear proce-dures in isoconversional computations of the activation energyof nonisothermal reactions in solidsrdquo Journal of ChemicalInformation and Computer Sciences vol 36 no 1 pp 42ndash451996

[16] L Liqing and C Donghua ldquoApplication of ISO-temperaturemethod of multiple rate to kinetic analysis dehydration forcalcium oxalate monohydraterdquo Journal of Thermal Analysis andCalorimetry vol 78 no 1 pp 283ndash293 2004

[17] L Vlaev N Nedelchev K Gyurova and M Zagorcheva ldquoAcomparative study of non-isothermal kinetics of decompositionof calcium oxalate monohydraterdquo Journal of Analytical andApplied Pyrolysis vol 81 no 2 pp 253ndash262 2008

[18] J Farjas and P Roura ldquoIsoconversional analysis of solid statetransformations a critical reviewmdashpart II complex transfor-mationsrdquo Journal of Thermal Analysis and Calorimetry vol 105no 3 pp 767ndash773 2011

[19] E Ruiz-Agudo J DMartın-Ramos andC Rodriguez-NavarroldquoMechanism and kinetics of dehydration of epsomite crystals

8 Journal of Experimental Physics

formed in the presence of organic additivesrdquo Journal of PhysicalChemistry B vol 111 no 1 pp 41ndash52 2007

[20] T Ozawa ldquoA new method of analyzing thermogravimetricdatardquo Bulletin of the Chemical Society of Japan vol 38 pp 1881ndash1886 1965

[21] J H Flynn and L A Wall ldquoA quick direct method for thedetermination of activation energy from thermogravimetricdatardquo Journal of Polymer Science Part B Polymer Letters vol 4no 5 pp 323ndash328 1966

[22] T Akahira and T Sunose ldquoTrans joint convention of fourelectrical institutes paper no 246 1969 research reportrdquo Scienceand Technology vol 16 pp 22ndash31 1971

[23] G I Senum and R T Yang ldquoRational approximations of theintegral of the Arrhenius functionrdquo Journal ofThermal Analysisvol 11 no 3 pp 445ndash447 1977

[24] S Vyazovkin ldquoIsoconversional kineticsrdquo in Handbook of Ther-mal Analysis and Calorimetry M E Brown and P K GallagherEds Recent Advances Techniques and Applications pp 503ndash538 Elsevier AmsterdumThe Netherlands 2008

[25] J Cai F Yao W Yi and F He ldquoNew temperature integralapproximation for nonisothermal kineticsrdquo AIChE Journal vol52 no 4 pp 1554ndash1557 2006

[26] J Malek ldquoThe kinetic analysis of non-isothermal datardquo Ther-mochimica Acta vol 200 pp 257ndash269 1992

[27] D Young Decomposition of Solids Pergamon Press OxfordUK 1966

[28] H F Cordes ldquoThepreexponential factors for solid-state thermaldecompositionrdquo Journal of Physical Chemistry vol 72 no 6 pp2185ndash2189 1968

[29] J SestakThermophysical Properties of Solids Academia PragueCzech Republic 1984

[30] J M Criado L A Perez-Maqueda and P E Sanchez-JimenezldquoDependence of the preexponential factor on temperaturerdquoJournal of Thermal Analysis and Calorimetry vol 82 no 3 pp671ndash675 2005

[31] L M Dyagileva V P Marrsquoin E I Tsyganova and G ARazuvaev ldquoReactivity of the first transition row metallocenesin thermal decomposition reactionrdquo Journal of OrganometallicChemistry vol 175 no 1 pp 63ndash72 1979

[32] B Jankovic S Mentus and M Jankovic ldquoA kinetic study ofthe thermal decomposition process of potassium metabisulfiteestimation of distributed reactivity modelrdquo The Journal ofPhysical Chemistry Solids vol 69 no 8 pp 1923ndash1933 2008

[33] A Bhattacharjee A Rooj M Roy J Kusz and P Gutlich ldquoSol-ventless synthesis of hematite nanoparticles using ferrocenerdquoJournal of Materials Science vol 48 no 7 pp 2961ndash2968 2013

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