Thermal Decomposition of Natural Fibers:Global Kinetic Modeling with Nonisothermal Thermogravimetric Analysis
Fei Yao,1Qinglin Wu,1Dingguo Zhou 2
1
School of Renewable Natural Resources,Louisiana State University Agricultural Center,Baton Rouge,Louisiana 708032
College of Wood Science and Technology,Nanjing Forestry University,Nanjing 210037,Jiangsu,China
Received 24January 2009;accepted 19March 2009DOI 10.1002/app.30439
Published online 15June 2009in Wiley InterScience (www.).ABSTRACT:The modeling of thermal decomposition process of ten natural fibers commonly ud in polymer composite industry was performed by assuming a global model occurring within the entire degradation range with
春节的诗句有哪些
consideration of fiber as one pudocomponent.Ma
´lek method with activation energy values previously obtained was applied to the modeling process.Careful calculation and evaluation indicated that,within an ac-ceptable error limit of 5%,RO(n >1)model can be ud to describe the degradation process of most lected fibers well.The other kinetic parameters ud include
activation energy range of 160–170kJ/mol;parameter n in RO(n >1)¼(1Àa )n of 3–4;and ln A between 35and 42ln s À1.Some condition limitations of the obtained model were also discusd.The model has practical sig-nificance in predicting fiber weight loss when the fiber is ud in combination with engineering thermoplastics.V
C 2009Wiley Periodicals,Inc.J Appl Polym Sci 114:834–842,2009
Key words:thermogravimetric analysis (TGA);
composites;kinetics (polym.);modeling;fibers
INTRODUCTION
Natural fiber fillers from agricultural residues and forest products processing are subjected to thermal degradation during polymer composite processing.It is,therefore,of practical significance to under-sta
nd and model the decomposition process of the fibers.Numerous kinetic schemes and models regarding to the fiber degradation process have been established.1,2However,it will be of more practical relevance to establish simplified kinetic models of the degradation of reinforcing fibers for polymer/natural fiber composite.
In our previous study,3thermal decomposition process and activation energy values of ten common natural fibers were investigated.It was found that thermal decomposition process of the lected natu-ral fibers had similar thermogravimetric (TG)and differential thermogravimetric (DTG)curves as a
result of being lignincellulosic material.The
common thermal decomposition curves of fibers showed a distinct DTG peak (cellulo)and high-temperature ‘‘tails’’(lignin).Also,the low-tempera-ture ‘‘shoulder’’can be en in some fiber decompo-sition curves.The characteristics of all lected natural fibers showed that main thermal decomposi-tion fraction (around 60%)happened in a tempera-ture range of around 100 C (i.e.,215–310Æ10 C in terms of extrapolated temperatures)for most natural fibers.The calculation result from isoconversional methods showed a stable apparent activation energy range of 160–170kJ/mol for th
e most of lected fiber throughout the polymer processing tempera-ture range.The objective of the study described in this article was to develop the practical modeling technique bad on global kinetic scheme for the thermal degradation process of the fibers.In particu-lar,the model and related kinetic parameters were developed by using a method demonstrated by Ma
´lek and coworkers.4–6Reaction mechanism and parameters of thermal decomposition process of nat-ural fibers were described in detail.
THEORETICAL APPROACH
The kinetics of solid-state process is generally com-plicated.6–8A method propod by Ma
´lek and Journal of Applied Polymer Science,Vol.114,834–842(2009)V
C 2009Wiley Periodicals,Inc.Correspondence to:Q.Wu (wuqing@lsu.edu).
Contract grant sponsor:USDA Rural Development Biomass Initiative Program;contract grant number:68-3A75-6-508.
Contract grant sponsor:Louisiana Board of Regents Industrial Tie Subprogram;contract grant number:LEQSF:2005-08-RD-B-01.
coworkers allows fairly reliable kinetic analysis and interpretation of nonisothermal TG-DTG data.This method has been described thoroughly in the cited literature.4,6A brief outline is shown below for con-sistence.Readers can refer to the original articles for details.
The fundamental expressions of analytical meth-ods to calculate thermal decomposition kinetic pa-rameters bad on nonisothermal thermogravimetric analyzer(TGA)studies are generally described as
d a dT ¼
A
b
8
>>:
9
>>;eÀx fðaÞ(1)
where T,A,b,and x are absolute temperature(K), pre-exponential factor(sÀ1),heating rate( C/min), and reduced apparent activation energy(x¼E a/ RT),respectively.E a and R are apparent activation energy(kJ/mol)and gas constant(8.314J/KÁmol), respectively.The conversion rate a has following expression:
a¼ðW0ÀW tÞ=ðW0ÀW fÞ(2) where W t,W0,and W f are the sample weights at t, initial andfinal time,respectively.Function f(a)is an analytical expression describing the kinetic model of a reaction,which depends on the actual reaction mechanism.The most frequently ud f(a)functions with their symbols are summarized in Table I.
By integration of eq.(1)in nonisothermal condi-tions,the following equation is obtained:
gðaÞ¼
Z a
1
fðaÞ
d a¼
Z T
A
b
eÀx dT¼AeÀx
T
b
pðxÞ
(3)
where p(x)is an approximation of the temperature integral,which has the following sufficiently accu-rate approximation.5
pðxÞ¼x3þ18x2þ88xþ96
(4)
Two new functions,y(a)and z(a),were then defined as below:
yðaÞ¼
d a
dt
8
>:
9
>;e x¼AfðaÞ(5)
zðaÞ¼
d a
dt
8
>:
9
>;pðxÞT
b
¼fðaÞgðaÞ%
d a
dt
8
>:
9
禁毒预防教育
>;T2(6)
One can easily transform experimental data to the y(a)and z(a)functions and then normalize them within the(0,1)interval.Obviously,this can be done without the knowledge of any kinetic parame-ter in nonisothermal conditions.Two important pa-rameters a M and a1p,at which the functions y(a)and z(a)have a maximum,respectively,are normally cal-culated by mathematical software.Then the function f(a)is determined through the schematic diagram introduced by Ma´lek and coworkers.4,6两参一改三结合
As discusd in literatures,the apparent activa-tion energy E a is vital for the determination of func-tion y(a).4Several recommended‘‘model-free’’methods(isoconversional methods)are prented in our previous article to calculate the decomposition activation energy values of lectedfibers.3Tho E a values were then ud to calculate function y(a) and z(a)in this study.The experimental data,a,T and d a/dt,were obtained from TG-DTG curves directly.
EXPERIMENTAL
Ten naturalfibers including wood,bamboo,agricul-tural residue,and bastfibers were ud in this study.All raw materials were washed with water to remove the impurity and then dried in an oven at 75 C for12h.Dried materials were then ground with a Wiley mill,and then screened.The samples with
the particle size between20and28meshes (0.9–1.3mm)were collected for test.
Thermal decomposition was obrved in terms of global mass loss by using a TA Instrument Q50 TGA.The samples were evenly and looly distrib-uted in an open sample pan with an initial sample amount of8–10mg.The temperature change was controlled from room temperature(25Æ3 C)to 800 C at six different heating rates of2,3.5,5,7.5, 10,and15 C/min in nitrogen atmosphere.The ther-mal decomposition was carried out at low or moder-ate heating rates to keep possible heat/mass-transfer intrusions at a minimum.The TG and DTG curves obtained were carefully smoothed and analyzed by using Universal Analysis2000software from TA Instruments.Relative parameters were calculated with a specially designed program in MS Excel or MATLAB software.Further details of experimental procedure were described elwhere.3
TABLE I
A Summary of Basic Thermal Kinetic Models Models Symbol f(a) Johnson-Mehl-Avrami JMA(n)n(1Àa)[Àln(1Àa)]1À1/n Reaction order law RO(n)(1Àa)n Autocatalytic
(Sˇesta´k-Berggren)
SB(m,n)(1Àa)n a m
2D-diffusion D2À1/ln(1Àa)
Jander equation D33(1Àa)(2/3)/2[1À
(1Àa)(1/3)] Ginstling-Brounshtein D43/2[(1Àa)(À1/3)À1] Prout-Tompkins PT a(1Àa)
THERMAL DECOMPOSITION OF NATURAL FIBERS835
Journal of Applied Polymer Science DOI10.1002/app
RESULTS AND DISCUSSION
Determination of kinetics model and parameters The thermogravimetric curves of 10lected fibers in nonisothermal conditions were shown in our pre-vious article along with the activation energy values.The E a value of most fibers was quite stable (ca.3%)in a conversion range of 0.1–0.6according to three isoconversional methods.Thus,the activation energy values obtained can be ud to calculate y (a )and z (a )functions.As shown in Table II,they were determined by averaging values from three isocon-versional methods prented in the previous article.The dependence of y (a )and z (a )functions on con-version rate a for various fibers is shown in Figure 1,using bagas,kenaf,rice husk,and maple fibers as examples.Obviously,each individual y (a )func-tion is c
oncave and has a clear maximum a M at a ¼0.The y (a )function curves of the other six fibers,which are not plotted here,also prent similar con-cave shapes and a M positions.Figure 1also shows that various z (a )curves from degradation process of a certain fiber are clo to each other.Each z (a )curve also exhibits a clear maximum,which is con-
sistent with the fact that z (a )function has a maxi-mum at a 1p for all kinetic models summarized in Table I.6
MATLAB software was then carefully oper-ated to fit each single [z (a )Àa ]curve to obtain the accurate values of a 1p .
All critical values of y (a )and z (a )functions are summarized in Table II.It is clearly shown from a M values (i.e.,zero)and y (a )function shape (i.e.,con-cave),as well as a 1p
values that the thermal TABLE II
The Values of Parameters a M ,a p ,and a 1p Obtained from Corresponding y (a )and z (a )Function for 10Fibers
Fiber a M a p a 1p Bagas 00.67(0.01)0.69(0.01)Bamboo 00.57(0.02)0.59(0.02)Cotton stalk 00.61(
0.02)0.62(0.02)Hemp 00.51(0.01)0.52(0.01)Jute 00.59(0.02)0.60(0.02)Kenaf 00.55(0.01)0.56(0.02)Rice husk 00.60(0.01)0.61(0.00)Rice straw 00.53(0.02)0.54(0.02)Wood-maple 00.69(0.00)0.70(0.01)Wood-pine
0.69
(0.01)
0.70
(0.01)
Figure 1Normalized y (a )and z (a )functions corresponding to fiber thermal decomposition kinetic data using bagas,
kenaf,rice husk,and maple fibers as examples.The heating rates are shown in following symbols:2 C/min (solid line);3.5 C/min (-h -);5 C/min (-*-);7.5 C/min (-D -);10 C/min (-!-);and 15 C/min (-Â-).836YAO,WU,AND ZHOU
Journal of Applied Polymer Science DOI 10.1002/app
puyi
degradation kinetic model offibers can be described using RO(n>1)model.With the knowledge of kinetic model,the equation for nonisothermal a(T) curve can be predicted from eq.(3)as
冒险造句aðTÞ¼1À1ÀT
pðxÞ
b
8
>>:
9
>>;ð1ÀnÞAeÀx
1=ð1ÀnÞ
(7)
here,the f(a)¼(1Àa)n for RO(n>1)model is ud,and conquently,
gðaÞ¼
Z a
1
fðaÞ
d a¼
1Àð1ÀaÞ1Àn祈使句语文
1Àn
(8)
The temperature dependence of the reduced acti-vation energy(x¼E a/RT)can be calculated from the average value of apparent activation energy obtained by isoconversional analysis.The key kinetic parameters A and n can be obtained by non-linear regression of experimental data using MATLAB soft-ware becau each part of an entire kinetic equation is clearly defined.The average values of the parame-ter are summarized in Table III along with standard deviations,which were calculated from six different heating rates for eachfiber type.
Comparison of experimental data(symbols)and predicted a(T)(lines)is shown in Figure2using bamboo,kenaf,rice straw,and pinefibers as exam-ples.The a(T)curves were calculated using eq.(7) for the kinetic parameters shown in Table III.The other sixfibers,which are not shown here,have sim-ilar results.There is good agreement between experi-mental data and prediction curves even though some discrepancies are obrved at both very low and very high temperature(or,a)ranges.Tho dis-crepancies were caud by the variability of activa-tion energy and the strong dependence of the Ma
第63届威尼斯国际电影节´lek method on activation energy values.However,one can expect a reasonable model if a good global agreement in the entire reaction process is reached. Therefore,the model obtained must be evaluated to quantify the goodness offit(GOF).Moreover,latent forcefitting caud by kinetic compensation effect (KCE)should also be evaluated.9,10
Evaluation of the kinetic parameters
The GOF of model is evaluated by the method of least squares(LSQ).The sum S of squared error of all picked points is defined as
S¼
X N
1
ðy obs iÀy calc
i
Þ2(9)
where y obs is the experimental data and y calc is the corresponding point of the calculated functions,sub-script i indicates the discrete values of a given y, and the parameter N is the number of the data ud in the curvefitting.Thefitness between the obrved and calculated values at the obtained parameters is given in percentage of the highest obrved y value, y obs max:
fitð%Þ¼100
ffiffiffiffiffiffiffiffiffi
S=N
p
y obs max
(10)
The method actually tests the error between obrved and calculated values.Therefore,the out-putfit(%)is also referred as deviation(%)in some literatures.11Thefitted result is shown in Table III. The good agreement,indicated by values<5%,was obrved for allfibers.As shown in parenthes,th
e very small standard deviation of eachfiber indicates the invariant GOF at different heating rates.There-fore,the error of the entirefitting was expected to be as low as5%.
GOF is necessary,but not sufficient,for the evalu-ation of a thermal model,becau it cannot evaluate
TABLE III
The Kinetic Parameters Obtained by Nonlinear Regression of Nonisothermal Data
Fiber E(kJ/mol)n ln A(ln sÀ1)fit(%)
Bagas168.6(6.3) 3.25(0.11)38.14(0.08) 4.67(0.08)
Bamboo160.9(3.2) 3.85(0.07)37.45(0.23) 3.57(0.04)
Cotton stalk171.8(4.2) 3.77(0.05)39.15(0.07) 4.32(0.13)
Hemp178.6(6.6) 3.18(0.26)40.57(0.12) 3.73(0.18)
Jute183.3(9.0) 3.75(0.26)42.17(0.10) 5.00(0.02)
Kenaf169.9(2.1) 3.23(0.17)38.76(0.07) 3.60(0.07)
Rice husk165.4(2.9) 4.03(0.19)37.78(0.10) 3.64(0.07)
Wood-maple153.3(4.8) 3.04(0.08)34.47(0.10) 4.79(0.05)
Wood-pine159.6(3.9) 3.14(0.08)35.65(0.05) 4.35(0.18)
Rice straw195.5(2.5) 5.81(0.17)46.57(0.12) 3.46(0.09)
Average I a167.9(9.4) 3.47(0.37)38.24(2.34) 4.19(0.56)
Average II b172.2(1.3.5) 3.70(0.82)39.07(3.44) 4.11(0.59)
a Exclusive of values from rice strawfiber samples.
b Including values from rice strawfiber samples.
THERMAL DECOMPOSITION OF NATURAL FIBERS837
Journal of Applied Polymer Science DOI10.1002/app
latent force fitting caud by KCE.KCE is caud by the exponent format of Arrehnius equation and r
efers to the fact that the covariability of parameter E and A makes experimental data possibly fit veral different models well with different f (a ).12–14It was reported that one might obtain extreme perfect fit-ting using F1model on artificially produced A3model curves.15An approach propod by Perez-Maqueda etc.15helps offer an evaluation in this situation.
In this technique,through algebraic transforma-tion,any function f (a )can be simplified from the
empirical S
ˇesta ´k-Berggren equation as f ða Þ¼c ð1Àa Þn a m
天空之蓝(11)
using three constants c,n,and m .A logarithm
transformation of eq.(1)(inrting b ¼dT /dt )leads to the following equation for fitting experimental data:
ln d a =dt f ða Þ
8>>:9
>>;¼ln cA À
E a RT (12)
Plotting the left hand side of eq.(12)with respect to the reciprocal of corresponding temperature,one can get a single straight line with slope (ÀE a /R )and the intercept (ln cA )if an appropriate function f (a )is chon.It is worth noting that the key to this evalua-tion is to get a single straight line even using data from different heating rates.It was pointed out in the literature 15that sometimes an inappropriate model can also lead to perfect straight lines,but tho lines are parallel to each other instead of superposing on to one single curve.
Using this method,the linear relationship between ln[(d a /dt )/f (a )]and 1/T is plotted in Figure 3after inrting obtained f (a )functions and experimental d a /dt and 1/T data into eq.(12)using bamboo,kenaf,rice husk,and maple fibers as examples.
As
Figure 2Nonisothermal TG curves for lect fibers measured at different heating rates:2 C/min (h );3.5 C/min (*);5 C/min (D );7.5 C/min (!);10 C/min (^)15 C/min (Â).Solid lines were calculated using eq.(7)for the kinetic param-eters shown in Table III.
838YAO,WU,AND ZHOU
Journal of Applied Polymer Science DOI 10.1002/app
shown in the figure,for each fiber sample,six sym-bol lines corresponding to data from six different heating rates are overlapped with each other and yield a single straight line.The expression listed in each individual plot shows detailed slope and inter-cept.Here,the value before parenthesis is the aver-age value of six slopes or intercepts while the value in parenthesis refers to standard deviation.Obvi-ously,the superposition of six scatter lines is shown by a fairly small standard deviation (within 3%in most cas).The activation energy values listed in plots are calculated from the slope.They are quite comparable (error <2%)to tho shown in Table III except that in the cas of jute (not plotted)and kenaf fibers the error reaches around 5%.In conclu-sion,the evaluation performed above shows that the model and relevant parameters obtained are appro-priate for descri
bing the degradation process of nat-ural fibers.
Comparison of kinetic parameters of different fibers
On the basis of the calculated parameters shown in Table III,one can e a general trend of the degrada-tion model for nine fibers (exclusive of rice straw fiber,which is obviously different with the others).Their degradation process has an activation energy range of 160–170kJ/mol with an average of 168kJ/mol,f (a )follows RO(n )¼(1Àa )n model,parameter n has a range of 3–4with an average of 3.5,and ln A is between 35and 42ln s À1with an average of 38ln s À1.
Tho intervals are fairly narrow ones,which may indicate the similarity of natural fiber degradation process.This obrvation was first mentioned in our previous article,where a narrow range of activation energy for most of the natural fibers was en.As the energy barrier,the activation energy itlf may provide the information of the critical energy needed to start a reaction.It implies the ‘‘difficulty’’of start-ing a reaction.The similar activation energy values of various fibers indicated that critical energy of the decomposition reaction is similar among tho fibers.However,only activation energy itlf cannot be ud to determine the ‘‘rate’’of a reaction.Once a reaction starts,the question toward how fast the reaction is should be answered by the conversion function f (a )along with its parameters and pre-expo-nential factor A .Similar to the ca of
activation
Figure 3Single linear relationship between [ln(d a /dt )Àln f (a )]and 1/T for four illustrational fibers at six heating rates:2 C/min (h );3.5 C/min (*);5 C/min (D );7.5 C/min (!);10 C/min (þ);15 C/min (Â).The value before parenthesis is the average value of six slopes or intercepts whereas the value in parenthesis refers to standard deviation.
THERMAL DECOMPOSITION OF NATURAL FIBERS 839
Journal of Applied Polymer Science DOI 10.1002/app
