Thermochimica Acta 519 (2011) 114–124
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Thermochimica
Acta
j o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /t c
a
Thermal degradation process of the cured phenolic triazine thermot resin (Primat ®PT-30).Part I.Systematic non-isothermal kinetic analysis
Bojan Jankovi´c ∗
Depatment of Dynamics and Matters Structure,Faculty of Physical Chemistry,University of Belgrade,Studentski trg 12-16,P.O.Box 137,11001Belgrade,Serbia
a r t i c l e i n f o Article history:
Received 30December 2010
Received in revid form 8March 2011Accepted 16March 2011
Available online 31 March 2011Keywords:
Thermal degradation Primat ®PT-30
Systematic kinetic analysis Predictions Lifetime
a b s t r a c t
The non-isothermal degradation of the cured Primat ®PT-30resin in nitrogen atmosphere was exam-ined.It was found that the total mass loss of the sample strongly depends on the heating rate.Using
醉落魄咏鹰different kinetic methods,the complete kinetic triplet of investigated process was performed.It was found that process can be successfully described by the following kinetic triplet:E a =193.8kJ mol −1,A =9.82×1010min −1and f (˛)=(1−˛)3/2.Also,it was found that with single step reaction model (F n -type)with n =3/2,a complex and multi-step degradation process can be successfully approximated.Isothermal predictions of degradation were carried out at temperatures 400◦C,420◦C and 450◦C.The obrved disagreement between the prediction curves and experimental curves in terms of degradation lifetime at corresponding temperatures could lay in a very strong dependence of reaction system on the heating rate,which means on the temperature of degradation.It was concluded that due to high thermal resistance,Primat ®PT-30resin needs more temperature to pro
cess it to produce parts for usage.The lifetime parameters indicate that the rvice/process temperature has a strong influence on the degradation process of the cured Primat ®PT-30resin.
© 2011 Elvier B.V. All rights rerved.
1.Introduction
Phenolic triazine (PT)precursor resin is a reaction product of novolac resin and cyanogen halide.Phenolic triazine network is formed by the thermal cyclotrimerization of the cyanate ester of novolac [1,2].Synthesis procedure of PT resin can be con-ducted as the novolac hydroxyl groups reacted with cyanogens bromide under basic conditions to produce cyanate ester resins [2,3].Cyanate esters can thermally crosslink to form void free net-works,wherein at least some triazine rings form.The resultant networks posss high T g s (glass transition temperature),high char yield at 900◦C and high decomposition temperatures [2].
It is an ideal matrix system for composites,becau it combines the processibility convenience of epoxies and the thermal capabil-ities of poly-imides and fire resistance of phenolics.The abnce of volatile by-products during cure renders them attractive matrices for void-free moldings and composites.
PT resin offers considerable processing flexibility since their consistency ranges from low viscous liquids to mi solids,with gel temperatures that can be tuned by catalysis using a host of materials.PT resins posss better thermo-oxidative stability and char-yield than conventional phenolics,becau they are mostly cross-linked by triazine groups.The proximity of the hydroxyl
∗Tel.:+381112187133;fax:+381112187133.E-mail address:bojanjan@ffh.bg.ac.rs
groups in phenolic resin renders the methylene bridges thermo-oxidatively fragile,and the decomposition process is accelerated by the number of dihydroxy phenyl methylene groups [4].It is stated that there is always a thermo-oxidative process during degrada-tion irrespective of the atmosphere.The high oxygen content of phenol is also responsible for this.The degradation mechanism of phenolic resins was suggested by Conley [5].PT resins,on the other hand,are cross-linked mostly by triazine phenyl ether link-ages,which confer both thermo-oxidative stability and toughness to the system.The evidence for better thermo-oxidative stability is obtained from the thermal behavior of the systems in both air and the inert atmosphere [6,7].The esntially super imposable thermograms point towards a non-oxidative mechanism of degra-dation for PT systems.This implies better prospects for application of this type of resin for thermo-structural us in aerospace in place of conventional phenolics.Lar ablation studies on a ries of abla-tives inclu
ding PT resin have confirmed their potentiality for such applications [8].Ablative formulations for rocket nozzle applica-tions contain PT resin as one of the components [9].The PT resin systems have been successfully employed in filament winding of cylindrical structures such as pressure bottles which retain 83%of their room temperature properties at 288◦C [10].
Despite many claims about the superiority of PT systems over other cyanates and phenolics,there are only a few reports on its commercial utilization.One reason for this is that the resin generally shows inconsistency in cure behavior due to catalysis by the spurious impurities adsorbed on the polymer during its
0040-6031/$–e front matter © 2011 Elvier B.V. All rights rerved.doi:10.a.2011.03.014
B.Jankovi´c/Thermochimica Acta519 (2011) 114–124115
synthesis.It is not easy to purify the polymer scrupulously,to the level of monomeric dicyanates.Absorbed moisture can also cau variations in cure behavior.Unpredictable cure profiles impo pro-cessing difficulties and large property variations.It is generally found that the synthesized resins exhibit poor shelf life,particu-larly when the precursor novolac posss higher molar mass.PT resins,structurally modified with both rigid andflexible groups in their backbone were not hel
pful in improving either shelf life or thermal stability.Thus,aflexible pentadecenyl ar-danol)was introduced through copolymerization of phenol with cardanol,and subquently using the modified novolac for cyana-tion.The thermal stability decread proportional to the cardanol content and the resins exhibited poorer shelf-life[11].PT resin is commercially available under the trade name Primat®PT-15,PT-30,PT-60and PT-90,which esntially differ in their molar mass [12].The gel time can be tuned by catalyst concentration.The gen-erally recommended catalysts are zinc octoate/nonyl phenol,cobalt naphthenate,copper salts etc.
Thermoanalytical techniques(such as thermogravimetric analysis(TGA),differential thermal analysis(DTA)or differ-ential scanning calorimetry(DSC))are valuable tools for the characterization of thermotting polymers[13].Thermal tech-niques are esntial to the study of degradation process of thermotting resins under different reaction atmospheres [13,14].
The primary goal of this paper was to perform the system-atic kinetic analysis of degradation process of the cured phenolic triazine resin commercially known as Primat®PT-30.In the first part of a comprehensive study of this system,the kinetic analysis of non-isothermal degradation process under nitrogen atmosphere was carried out.By the literature survey,author did notfind the results associated with the real derivative values of‘kinetic triplet’(the apparent activation energy(E a),the pr
e-exponential factor(A)and the function of reaction mechanism f(˛);[E a,A,f(˛)]),for Primat®PT-30degradation process under dynamic conditions.Kinetic characterization of thermot resins is fundamental in understanding the structure–property–processing relationship for high performance composite processing and appli-cation.However,thermal stability and combustibility of Primat®PT-30resin was recently investigated by veral rearchers [15–18].
The corresponding‘isothermal predictions’of the investigated process,derived from the results of non-isothermal kinetic study, are also prented in this paper.This approach is important from a practical standpoint,in order to predict the thermal behavior of the tested system in different experimental conditions.
2.Experimental
2.1.Materials and methods
Primat®PT-30cyanate ester(Oligo(3-methylene-1,5-phenylenecyanate))(manufactured by Lonza Chemical Corporation Ltd.(Lonza Cologne AG,50829Cologne,Germany))(Molecular mass,M=381.39g mol−1)in this study was one-part,pure solid, commercial sample,which was ud as received without further purification and catalysts.
Primat®PT-30is a thermot resin,with65%char yield(same as phenolics),less than0.5%volatiles,no gaous by-products dur-ing cure,a low viscosity at RTM temperatures(80c.p.s.at121◦C) and post-curable[19].
The high purity tri-functional cyanate ester novolac monomer was thermally cured in convection oven without catalyst for4h at T=250◦C to more than95%conversion,in accordance with pro-cedure described elwhere[17,18].The fully cured samples were 5cm×5cm×0.65cm solid plaques that were mitransparent.
Curing the cyanate ester novolac monomer produces a tightly cross-linked thermot network of oxygen-linked triazine rings (called cyanurates)having the repeat unit atomic composition as C8H5NO.The polycyanurate samples were ud directly for ther-mogravimetric(TG)measurements.
2.2.Thermogravimetric analysis(TGA)
A thermogravimetric analyzer(TA Instruments SDT2960device capable for simultaneous TGA–DTA analysis)was ud to study the degradation process of cured samples(sample sizes of approxi-mately5mg were ud for experiments).The TGA cell was purged for15min withflowing nitrogen(99.9
98vol%purity grades)(with flow rate ofϕ=0.10L min−1)to remove residual air,after which the samples were heated from25◦C to800◦C.The non-isothermal scans were performed at lected heating rates(ˇ)in a very wide range of values,ranging from0.01to100◦C min−1(ˇ=0.01,0.10, 1,10and100◦C min−1).A wide range of heating rates is ud to a more preci determination of kinetic parameters,and values of the ont degradation temperature(T i)in accordance with ASTM E698standard[20].
In order to perform kinetic prediction,the corresponding isothermal measurements were conducted at three different oper-ating temperatures.The same instrument was ud to study the isothermal degradation process of cured samples(sample sizes of approximately between4and5mg were ud for experiments) at the following operating temperatures:T=400,420and450◦C. Reaction atmosphere is the same as in the ca of non-isothermal scans,with the same carrier gasflow.The samples were heated at a rate of200◦C min−1from the starting temperature to the temper-ature of the isothermal degradation.Before operating,the system was stabilized for1h.The actual mass loss of the samples at400, 420and450◦C were as follows: m T=8,12and15.5%,respectively.
In order to confirm the repeatability and authenticity of the gen-erated data for all considered cas,the experiments were repeated three times at every heating rate and every operating tempera
ture, where the average TG trace among them was ud as the repre-ntative thermo-analytical curve in the prent manuscript.The obrved deviations were very little.
硕士简历3.Theoretical background
In non-isothermal kinetics of heterogeneous condend pha reactions,it is usually accepted that the reaction rate is given by the following equation[21]:
d˛
d t
=ˇ·d˛
d T
=A exp
−E a
RT
f(˛)(1) where˛is the degree of conversion(˛=(m o−m)/(m o−m f)where m o,m and m f are the initial,actual and thefinal mass of the sample, respectively),T is the absolute temperature,t is the time,f(˛)is the differential conversion function(or the analytical function of reaction mechanism),R is the gas constant,ˇis the linear constant heating rate(ˇ=d T/d t),A and E a are the pre-exponential factor and the apparent activation energy given by the Arrhenius equation.
By integrating Eq.(1),the integral rate equation,so-called the temperature integral,can be expresd as:
千丈幽谷
g(˛)=
˛
[f(˛)]−1d˛=Aˇ−1
T
exp
−E a
RT
d T(2)
where g(˛)is the integral conversion function.If E a/RT is replaced by a new variable x and integration limits transformed,Eq.(2) becomes:
g(˛)=AE aˇ−1R−1
∞
x
exp(−x)x−2d x=AE aˇ−1R−1p(x)(3)
116 B.Jankovi´c /Thermochimica Acta 519 (2011) 114–124
where p (x )is the exponential integral,which has no analytic solu-tion [22].However,there are many approximations that make it
possible to obtain the kinetic parameters through the lineariza-tion of the experimental data [23–27].
There are more complex variations of p (x ),such as tho put forward by Senum and Yang [28]and Agrawal [29]who approximations of the temperature integral at an interval of x offer far higher accuracy and lower error.
3.1.Isoconversional methods
Isoconversional approach in non-isothermal experiments assumes that for a given degree of conversion,the reaction mech-anism does not depend on the heating rate.
By applying logarithms to Eq.(1),the differential isoconver-sional method suggested by Friedman (FR)[30]is obtained:ln ˇ
d ˛d T
=ln[Af (˛)]−
E a
RT
(4)
The linear plot of ln[ˇ(d ˛/d T )]versus 1/T ,obtained from DTG curves recorded for veral heating rates makes it possible to determine E a and the kinetic parameter ln[Af (˛)],for every value of ˛.
By using the Coats–Redfern [31]approximation to solve Eq.(3)and considering that 2RT /E a is much lower than unity,the Kissinger–Akahira–Suno (KAS)[25,26]equation can be written in the form:
ln
ˇT
=ln
AR g (˛)E a
−
E a RT
(5)
For each degree of conversion,the linear plot of ln(ˇ/T 2)versus 1/T enables E a and ln[AR /g (˛)E a ]t
o be determined from the slope and the intercept,respectively.If the reaction model,g (˛),is known,the corresponding pre-exponential factor can be calculated for each conversion.
If E a does not vary with ˛,the study is straightforward and one single kinetic triplet describes the degradation process.If E a changes with ˛,the process is more complex and the shape of E a –˛curve may provide the information on the reaction mechanism [32].Due to the compensatory effect,it is also necessary to study the evolution of the cond kinetic parameter,which includes the pre-exponential factor and the reaction model.Not using this cond parameter could lead to errors.3.2.Coats–Redfern method
The Coats–Redfern (CR)[31]method is bad on Eq.(5)in the following form:ln
g (˛)T 2
=ln
AR ˇE a
−
E a RT
(6)
For a given model and heating rate,the linear plot of the left-hand side of Eq.(6)versus 1/T allowed us to obtain the average
apparent activation energy and average pre-exponential factor from the slope and the intercept.Then,we can choo the reac-tion model with the apparent activation energy similar to that obtained isoconversionally and with a good linear correlation coefficient.
3.3.Composite kinetic methods
The composite kinetic methods pre-suppo one single t of kinetic parameters for all conversions and heating rates.In this way,all experimental data can be superimpod in one single master curve.
Composite integral method I [33,34]is bad on the CR equation,which is re-written as follows:ln[ˇg (˛)T
−2
]=ln
AR E a
−
E a RT
(7)
For each form of g (˛),the curve ln[ˇg (˛)T −2]versus T −1was plotted for the experimental data obtained at the different heating rates.Then,we can choo the reaction model for which the data falls in a single master straight line and which gives the best linear correlation coefficient.A single t of kinetic parameters,E a and A ,can be obtained from the slope and the intercept of the straight line,respectively.The obtained values of kinetic parameters must be similar to tho obtained for each heating rate using the CR method.
Composite differential method I [35]is bad directly on Eq.(4).In that ca,Eq.(4)can be re-written in the following form:ln
ˇ(d ˛/d T )f (˛)
=ln(A )−
E a
RT
.(8)
The data for different heating rates must be grouped together in a single master straight line,from which a single t of kinetic parameters (E a and A )is obtained.
3.4.Compensation effect (isokinetic relationship (IKR))
The apparent activation energy and the pre-exponential fac-tor can be linked due to a compensation effect or the isokinetic relationship (IKR)through the following equation [36,37]:ln A =a +bE a,
(9)
where a and b are the compensation constants and the subscript refers to a factor producing a change in the kinetic parameters (conversion,heating rate and model).
The slope b =1/RT iso is related to the isokinetic temperature (T iso )and the intercept a =ln k iso is related to the isokinetic rate constant (k iso ).
The appearance of the IKR shows that only one mechanism is prent,whereas the existence of parameters that do not agree with the IKR implies that there are multiple reaction mechanisms [37].In accordance with certain authors [36],we lected the reaction model who IKR in relation to the conversion had the best linear correlation coefficient and in which the associated T iso value was near the experimental temperature range.
Vyazovkin and Linert [36]claims that the real pre-exponential factor can be predicted by using the isoconversional apparent activation energy and the compensation effect in relation to the reaction model,at an average heating rate,without needing to know the analytical form of reaction model.The most suitable reac-tion model is that,which prents the lowest error or deviation in equation of the following form:
(%)=100
1N ˛
|ln A ˛,pred −ln A ˛,isocon |
ln A ˛,pred
(10)
where N reprents the number of elements for which the deviation is calculated,ln A ˛,pred is the predicted pre-exponential factor bad on the IKR in relation to the reaction model and ln A ˛,isocon is the pre-exponential factor calculated by applying the reaction model to the isoconversional data.
3.5.Invariant kinetic parameters method (IKP method)
In this article,the method propod by Budrugeac et al.[38]was ud for the purpo of determining the invariant kinetic param-eters (IKP).The method is bad on the experimental obrvation that the same thermoanalytical curve can be described relatively fair by the veral different conversion functions.
B.Jankovi´c/Thermochimica Acta519 (2011) 114–124117
Using an integral(Coats–Redfern(CR))method(Eq.(6)),for each
heating rate and for each conversion function,a pair of kinetic
parameters(A,E a)is established.Using the artificial compensa-
tion effect that always exists when the reaction model changes,
for each heating rate,the compensation parameters,a v and b v,are
determined in accordance with Eq.(9)(often ud for parameters
and designations as˛v*andˇv*[38]).The point of interction of
the straight lines of compensations for veral heating rates corre-
sponds to the real values of E a and A,called the invariant kinetic
parameters(E a,inv and A inv),as they are independent of the conver-
sion,the model and the heating rate[38].Since determining the
point of interction by the graphical method means is uncertain,
the invariant kinetic parameters can be defined by the correspond-
ing supercorrelation relation:
a v=ln A in v−
b v E a,in v(11)
The straight line a v versus b v allows us to determine the invariant
kinetic parameters(E a,inv and A inv)from the slope and the intercept.
Although,the IKP method aims to determine the invariant
kinetic parameters independently of the reaction model,compar-
ing them to tho obtained using the other methods(such as CR
method,isoconversional methods,etc.),also allows us to decide
which reaction model best describes the investigated degradation
process.
3.6.Integral master plot method
Using the reference point at˛=0.50,the following integral mas-
ter equation can be derived from Eq.(3):
凤山书院
g(˛) g(0.50)=p(x)
p(x0.50)
(12)
where p(x0.50)is the temperature integral at the value of˛=0.50.In this article,the fourth rational approximation of Senum and Yang [28]is ud for p(x).Recently,some authors[39,40]have given universal expression to the master plot using the concept of gener-alized time introduced by Ozawa[23].The particularization of the generalized kinetic equation for the non-isothermal experiments leads to Eq.(12).
In order to determine the reaction model,it is necessary that the conversion function f(˛),which is characteristic for the investi-gated process,should be included in the analyzed t of analytical functions.Different reaction models were studied for the purpo of determining the most suitable f(˛)(or g(˛))function,which best describes the non-isothermal degradation process of the cured Primat
®PT-30resin.The models are the follows:power law (P1,P2,P3and P4),pha-boundary-controlled reactions(R1,R2 and R3),reaction order(n)models(n=1,3/2,2and3with labels F1,F3/2,F2and F3),Avrami-Erofeev reaction models(A3/2,A2,A3 and A4)and diffusion models(D1,D2,D3and D4)[41].
4.Results and discussion
Fig.1shows the experimentally obtained non-isothermal ther-mogravimetric(TG)(a)and differential thermogravimetric(DTG) (b)curves at the different heating rates(ˇ=0.01,0.10,1,10
and Fig.1.The experimentally obtained thermogravimetric(TG)(a)and differential thermogravimetric(DTG)(b)curves at the different heating rates(ˇ=0.01,0.10, 1,10and100◦C min−1),for the degradation process of the cured Primat®PT-30 resin.
100◦C min−1),for the degradation process of the cured Primat®PT-30resin.
It can be en from Fig.1that with increasing heating rate,TG and DTG curves are shifted to higher experimental temperatures, which is a typical ca of thermally activated heterogeneous pro-cess.On the other hand,we can e that the total mass loss of the sample strongly depends on the heating rate,where this loss is very small at the lowest heating rate(0.01◦C min−1),while the biggest loss may be en at the highest heating rate of the system (100◦C min−1).As can be en,that the total mass loss ris with increasing heating rate,then this effect may be an indication of the complex process that contains at least two steps,whereas the last step consists of two concurrent process with different apparent activation energies.The total mass loss may depend on the heating rate,becau of the different apparent activation energies of the two process.However,the above hypothesis about the reaction mechanism can not be en from the corresponding DTG curves, bearing in mind that the curves are characterized by one main peak,who width and asymmetry gradually increas with the increa in the heating rate(ˇ).
英雄简笔画Table1shows the values of characteristic degradation tem-peratures(the ont(initial)degradation temperature(T i),the maximum(peak)degradation temperature(T p)and thefinal degra-dation temperature(T f)),the total mass loss values( m)and the values of degradation rates(d˛/d t),at the differentˇs.T i is taken as the point where the thermogram starts to show an inflex.T p is taken from the differential thermogravimetric(DTG)curves(Fig.1(b)) and T f,the temperature at which TG curve tends to attain a plateau region for considered process.
Table1shows that with increa in heating rates(ˇ),the val-ues of characteristic degradation temperatures(T i,T p and T f)also
Table1
The values of characteristic temperatures(T i,T p and T f),the total mass loss( m)and the rates(d˛/d t)of the degradation process of the cured Primat®PT-30resin in nitrogen atmosphere,at different heating rates(ˇ=0.01,0.10,1,10and100◦C min−1).
ˇ(◦C min−1)T i(◦C)T p(◦C)T f(◦C)Mass loss, m(%)d˛/d t(min−1)
0.01325.00435.96485.6112.00 1.654×10−4
0.10350.00474.09534.8016.000.00130
1400.00534.44589.2420.000.01114 10450.00596.46673.3826.000.10380 100525.00683.64784.3434.000.90600
西安市区旅游景点
118 B.Jankovi´c /Thermochimica Acta
519 (2011) 114–124
Fig.2.The dependence of the apparent activation energy (E a )on the degree of con-version (˛),for the non-isothermal degradation of the cured Primat ®PT-30resin,
calculated by the FR and KAS isoconversional methods (Eqs.(4)and (5)).
increa.Furthermore,the values of the total mass loss and degra-dation rate,also increas with increasing heating rate of the system.The total mass loss of the sample at ˇ=100◦C min −1is almost three times greater than the mass loss at ˇ=0.01◦C min −1(Table 1),which confirms its strong dependence on the heating rate (ˇ).不要说你不知道
It can be obrved from Table 1,that the ont degradation temperatures at all heating rates are high,which is a significant indication for the proposition that the cyanurates are the thermally stable cross-links that are responsible for the high mass loss tem-perature (>350◦C)of this thermot.The results (Table 1)confirm a proven fact that the cyanate ester resins can be ud for the high temperature applications [42].The char residues were prent at the end of each thermoanalytical experiment.It can be pointed out,that the char yield is nsitive to the chemical structure of the monomer and increas with glass transition temperature and in rough proportion to the mole fraction of unsaturated carbon-carbon bonds [43].It was shown that the nitrogen and oxygen in the cyanurate ring are incorporated into the char,but at an effi-ciency that is 2–3times higher than fud-aromatic heterocycles such as the benzimides,benzimidazoles and phenylqunioxalines [43].Alternatively,the cyanurate could be interacting with other structural groups to increa their char-forming tendency during the process of thermal degradation.
At higher heating rates (at 10and 100◦C min −1)degradation process are running faster and more vigorously (Table 1,Column 6).
In order to determine realistic and accurate kinetic triplet for non-isothermal degradation of the cured Primat ®PT-30resin,the first step in the kinetic analysis is the u of isoconversional meth-ods.The methods allow verification of the prence or abnce of the complexity of investigated process,tested from the mechanistic point of view.In this ca,we can check whether the apparent acti-vation energy shows the dependence on the degree of conversion (˛)in the whole range of ˛values,or only a part of it.
Fig.2shows the dependence of the apparent activation energy (E a )on the degree of conversion (˛),which was obtained by FR and KAS isoconversional methods (Eqs.(4)and (5)).It can be en from Fig.2that the apparent activation energy values vary very slightly around a mean value.The mean values of E a in the range 0.10≤˛≤0.90,calculated by the FR and KAS methods are equal E a FR =193.2kJ mol −1and E a KAS =192.3kJ mol −1,respectively.It may be noted that there is good agreement between the val-ues of the apparent activation energy obtained by the FR and KAS
methods.
Fig.3.The dependence of the isoconversional intercepts (ln[Af (˛)]and ln[A /g (˛)])on the degree of conversion (˛),for the non-isothermal degradation of the cured Primat ®PT-30resin,evaluated from FR and KAS isoconversional methods.
From the results prented in Fig.2,we can conclude that the degradation process of the cured Primat ®PT-30proceeds through a single reaction step,which allows us to determine the function of the kinetic model.Namely,if E a is independent of ˛,then the FR and KAS methods give practically the same values of the apparent activation energy [44].It can be said that the above condition is fulfilled in the ca of our investigated degradation pro-cess.In the ca of the cured Primat ®PT-30resin,bad on the obtained values of E a ,we can say preliminarily that the degradation process most likely involves thermolytic cleavage of the resin back-bone (usually occurred in the temperature range of 325–450◦C),which is probably accompanied by the decyclization of the triazine rings (occurred in the temperature range of 450–500◦C)with lib-eration of low molecular mass volatile compounds (for this type of reaction,the apparent activation energy values are typically rang-ing from E a =120kJ mol −1to E a =220kJ mol −1)[2,45–48].Such an assumption is made,since the high value of E a (E a =192.3kJ mol −1)can not be obtained from the reaction of aliphatic components,but from the reactions involving bridges connecting the aromatic rings,or the aromatic rings,independentl
y.This discussion should be accepted as a hypothesis,becau the preci mechanism of degra-dation can be assd only after determining the exact form of the f (˛)(or g (˛))function.
It should be noted that the isoconversional intercepts show a similar dependence on ˛(Fig.3(for the FR and KAS methods))as well as the apparent activation energy values.Also,it should be noted that the values of the pre-exponential factors (A )can be obtained,only if we know the exact analytical form of the f (˛)(or g (˛))function.
By introducing the various analytical forms of g (˛)and f (˛)func-tions for analyzed kinetic models [41]in Eqs.(7)and (8)at all heating rates (ˇ),the following best models were lected:the first order (F1)and one and a half-order (F3/2)kinetic models.Fig.4shows the results for F1and F3/2kinetic models,obtained from the composite integral and differential method I.
Table 2shows the values of the kinetic parameters (A and E a )together with results evaluated from the regression analysis (cor-responding R 2values),using the composite integral and differential method I (Eqs.(7)and (8)),for the non-isothermal degradation of the cured Primat ®PT-30resin in nitrogen atmosphere.
It can be en from Table 2,that the values of E a for the F3/2model calculated by the composite inte
gral and differential method I (E a int =193.8kJ mol −1and E a diff =196.8kJ mol −1,respectively)are clost to the value of E a ,obtained from the isoconversional analysis (E a FR =193.2kJ mol −1).On the other hand,the composite differen-tial method I give,for the F3/2model,the value of A which is for
B.Jankovi´c/Thermochimica Acta519 (2011) 114–124
119
Fig.4.Composite integral((a)and(b))and differential((c)and(d))method I analysis of the non-isothermal thermoanalytical data(ˇ=0.01,0.10,1,10and100◦C min−1) for F1and F3/2models.
Table2
Kinetic parameters(E a,A)determined using the composite integral and differential method I(Eqs.(7)and(8))for the degradation process of the cured Primat®PT-30resin in nitrogen atmosphere(R2=Adj.R-square).
Kinetic parameters Composite integral method I Composite differential method I
F1model F3/2model F1model F3/2model
E a(kJ mol−1)188.9193.8187.9196.8
ln A24.3225.3124.1625.94
A(min−1) 3.65×10109.82×1010 3.11×1010 1.84×1011
R20.993490.994030.992980.99275
one order of magnitude greater than the value of A calculated by the composite integral method I(Table2).
It should be noted,that the data does not totally overlap(Fig.4), which suggests that the methods that mix integral and differen-tial data will lead to the results that are not very preci.Using integral and differential data parately,however,allows us to establish the kinetic model reasonably well,and for the investi-gated degradation process,the best results are obtained from the integral data.In accordance with the facts,Criado et al.[35] demonstrated that for the thermal degradation of a solid sam-ple,composite methods allow us to differentiate between kinetic models,which can correctly,reproduces the thermally activated process despite having the different kinetic parameters.In accor-dance with the authors,the kinetic model in which the data are grouped together in just one straight line(Eq.(7))is the cor-rect one and the kinetic parameters obtained from this straight line are the real ones.Accepting this hypothesis as the correct, we take a kinetic model F3/2with E a and A values prented in Table2(E a int=193.8kJ mol−1;A=9.82×1010min−1),which were obtained from overlapping data to the one single master integral curve(Fig.4).
As a criterion to perform the reliable kinetic model,the existence of IKR can be ud when the conversion changes,together with the fact that the T iso is within the experimental range of temperatures.
Table3shows the results obtained using the IKR and Eq.(10) from the integral data,for the non-isothermal degradation of the cured Primat®PT-30resin in nitrogen atmosphere.
We can e from Table3that the many kinetic models have T iso in the experimental range of temperatures.However,on the other hand,the error (%)(that occurs when comparing the pre-exponential factors estimated from the IKRs when the conversion
Table3
Compensation effect in relation to conversion(Eq.(9))with corresponding values of (in%)(Eq.(10)),for non-isothermal degradation process of the cured Primat®PT-30resin in nitrogen atmosphere.
Model a(min−1)b(mol kJ−1)T iso(◦C) (%)
笔记本主板电池
P19.65988−0.61501−468.7316.7 P29.07825−0.31189−658.8115.2 P3 4.67219−0.0308−4178.3215.7 P4−4.307630.14724543.7316.9 R1−2.271510.1294656.3513.6 R2−4.
287320.14419561.019.3 R3−4.880850.1465547.867.7 F1−3.655240.14752542.180.8 F3/2−2.712790.14514555.550.2 F2−0.614050.13895592.47 5.6 F3 5.273820.12676675.71 6.1 A3/2−3.321620.14122578.55 1.8 A2−1.858820.11698755.04 1.4 A3 1.918840.0115910104.67 2.1 A4 4.88376−0.15097−1069.87 2.8 D1−4.627990.14847536.96 4.5 D2−4.094530.14539554.13 3.3 D3−3.479980.14041583.478.0 D4−4.991280.14393562.527.9
