全 文 ：物理化学学报(Wuli Huaxue Xuebao)
Acta Phys. -Chim. Sin., 2008, 24(12)：2214-2220
Received: August 4, 2008; Revised: September 22, 2008; Published on Web: October 29, 2008.
*Corresponding author. Email: solexin@ustc.edu.cn; Tel: +86551-3601804
鬁 Editorial office of Acta Physico-Chimica Sinica
[Article] www.whxb.pku.edu.cn
December
丁香油-β-环糊精包合物中残存态环糊精的热分解动力学
徐 鹏 宋乐新*
(中国科学技术大学化学系,合肥 230026)
摘要：采用双外推法确定了丁香油-β-环糊精(CD)包合物中残存态 β-CD最可能的热分解机制.基于 Flynn-Wall-
Ozawa方法对残存态 β-CD热分解反应过程的计算结果发现,活化能(Ea)变化曲线可划分为三个阶段.第一和第
三阶段的曲线轮廓近似平行,并且都被推定为按照 Avrami-Erofe′ev A1.5模型发生热分解反应.但是在曲线的第
二阶段,出现了一个 Ea值近似相等的平台.为此,采用确定反应级数的方法考察了该阶段的热分解过程.研究表
明,反应级数随着温度升高呈现规律性的降低,表明在这个阶段残存态 β-CD分解反应的复杂性.最后,比较了
游离态 β-CD和残存态 β-CD在分解过程中红外光谱的变化情况.结果显示,它们在 1000 cm-1以下的谱图轮廓
存在明显差异,这与计算给出的二者具有不同 Ea值的结果是一致的.
关键词： 环糊精; 包合物; 双外推法; 热分解动力学
中图分类号： O643
Thermal Decomposition Kinetics of Survived β-Cyclodextrin from an
Inclusion Complex of β-Cyclodextrin with Clove Oil
XU Peng SONG Le-Xin*
(Department of Chemistry, University of Science and Technology of China, Hefei 230026, P. R. China)
Abstract： A double extrapolation method was employed to determine the most probable mechanism for the thermal
decomposition reaction of the survived β-cyclodextrin (β-CD) from the inclusion complex of β-CD with clove oil. The
activation energy (Ea) curve calculated by Flynn-Wall-Ozawa method was clearly divided into three stages for the thermal
decomposition process of the survived β-CD. The nearly parallel linear relationship between first and last stages was
assessed as an Avrami-Erofe′ev A1.5 model. Furthermore, the platform in the second stage of the decomposition of the
survived β-CD in which each point has approximately equivalent Ea was carefully investigated using the reaction order
(n) method. A regular decline in n as the temperature increased implied a complicated decomposition reaction mechanism
for the survived β-CD in this stage. Infrared spectroscopic profiles from the thermal decomposition of free β-CD and
survived β-CD were also compared. The changes in IR spectra below 1000 cm-1 between free β-CD and survived β-CD
in the decomposition process were quite different which agreed with the calculated Ea values.
Key Words： β-Cyclodextrin; Inclusion complex; Double extrapolation; Thermal decomposition kinetics
Connected with seven α-1,4-glucoses, β-cyclodextrin (β-CD)
possesses both a hydrophobic cavity and a hydrophilic surface.
This special structure makes it possible to interact with many
kinds of organic molecules to form stable inclusion complexes[1-3],
so it has been widely used in many industries such as food,
spice, drug, and agriculture[4-7]. The preparation method, spectral
characterization, and thermal stability of β-CD inclusion com-
plexes have been studied a lot[8,9], but there is a conceptual con-
fusion, i.e., to confuse one thing with another, in description and
interpretation of the thermal stability, especially the thermal de-
composition kinetics, between the inclusion complex of β-CD
with an organic guest and the survived β-CD from the inclusion
complex of β-CD with the guest[10,11].
So far, the reports on the thermal decomposition kinetics of
2214
No.12 XU Peng et al.：Thermal Decomposition Kinetics of Survived β-Cyclodextrin from an Inclusion Complex
the survived β-CD from inclusion complexes of β-CD have not
been found. Clearly, the thermal stability of β-CD inclusion
complexes should be considered as that of the molecular aggre-
gate of β-CD and an included guest. Once the guest extricated it-
self from an inclusion complex, the inclusion complex will be
simultaneously destroyed and superseded in favor of the sur-
vived β-CD. Most of the guests are usually small organic
molecules with low boiling point. During the heating process of
sample, guest molecules will melt down and volatilize before the
melting/decomposition of β-CD. In view of the intermolecular
interaction between β-CD and a guest, it may be reasonable to
guess tentatively that the thermal decomposition behaviors of β-
CD as a host before and after inclusion would be different.
In one recent paper, we showed that an organic guest, clove
oil, released from its inclusion complex of β-CD far before de-
composition of β-CD[12]. So it is necessary to find out whether
physical and chemical properties of β-CD have changed be-
tween before inclusion and after exclusion of clove oil. The pre-
sent research makes an effort to answer the following questions:
what are the differences in TG profiles at five heating rates, as
well as in IR curves at different temperatures between free β-CD
and the survived β-CD? How to exert double extrapolation
method on the decomposition process of the survived β-CD from
the inclusion complex of β-CD with clove oil.
Clove oil has been extensively used as a natural flavoring
agent in food industry. In consideration of the volatility and in-
stability, it may be feasible to use a molecular envelope against
oxygen and other diffusion, with the aid of forming its inclusion
complex of β-CD. After they are released from the inclusion
complex at a moderate temperature, how the residue, i.e., the
survived β-CD from the inclusion complex of β-CD with clove
oil, behaves in even hotter surroundings? How to comprehend
completely and correctly the fastest and largest mass loss pro-
cess of the survived β-CD is the focus of our present work. So
the thermal decomposition kinetics of the survived β-CD is esti-
mated by a double extrapolation method under nonisothermal
condition[13,14]. The structures of β-CD and the main component of
clove oil are presented in Scheme 1.
On one hand, when the model free methods of Flynn-Wall-
Ozawa and Friedman are employed to calculate activation ener-
gy (Ea), the value of Ea differs depending on the change of con-
version degree (α). And the regulation of such change relates to
different reaction type. α represents the develop stage of the
crystal nucleus for new particles. Thus the calculated Ea is the
value for different develop stage of the new crystal nucleus. On-
ly when α is extrapolated to zero, the value of Ea, α→0 would be
nucleation formation activation energy of the new particles.
On the other hand, if the thermal process of a sample is dealt
with the method of model function fitting, the calculated Ea and
α varied with the heating rate for a certain function. The thermal
conduction between the sample and the surroundings, the en-
dothermic and exothermic of the sample, as well as the deviation
of sample heating rate from programmed heating rate all have
influences on the assessment of reaction mechanism. Neverthe-
less, if heating rate (ζ) is extrapolated to zero, the sample would
be at the ideal thermal equilibrium state and the calculated Ea, ζ→0
would be close to the real value.
According to these views, the double extrapolation method is
employed to determine the most probable mechanism function
for the thermal decomposition reaction of the survived β-CD at
both thermal equilibrium and original state.
1 Experimental
1.1 Materials
β-CD is purchased from Shanghai Chemical Reagent Compa-
ny and recrystallized twice from deionized distilled water. Clove
oil, a seminatural and semisynthetic product, is purchased from
Shanghai Feixiang Chemical Company and used without further
purification. All other chemicals are of analytical-reagent grade
unless otherwise stated.
1.2 Preparation of β-CD inclusion complex of clove oil
Inclusion complex of β-CD with clove oil is prepared by mix-
ing clove oil with β-CD and stirring for 48 h at 298.2 K. The ini-
tial molar ratio of clove oil to β-CD (1 mmol) is about 10:1 in
deionized water.
The separated crude product is washed using small amounts
of deionized water (3×5 mL) and alcohol (95%, 3×3 mL) to re-
move the unreacted β-CD and clove oil. The obtained sample is
dried for 24 h at 383.2 K in vacuo, and then stored in a vacuum
desiccator over silica gel[12]. In aqueous solution, the chemical sto-
ichiometry and formation constant of the inclusion complex of
β-CD with the main component of clove oil of β-CD were deter-
mined to be one-to-one and 3.55×104 mol-1·L, respectively[15].
1.3 Instrument and method
TG curves are recorded on a Shimadzu TGA-50 (Shimadzu
Co., Ltd., Japan) thermogravimetric analyzer at the heating rates
Scheme 1 Chemical structure of β-CD and main component of clove oil
2215
Acta Phys. -Chim. Sin., 2008 Vol.24
of 5.0, 10.0, 15.0, 20.0, 25.0 K·min-1 under a nitrogen gas flow
of 25 mL·min-1. The crystallite powder is about 5.5 mg for the
various TG measurements.
The samples are heated byMTI GSL1600X (Hefei Kejing Ma-
terials Technology Co., Ltd., China) in vacuo under the heating
rate of 10.0 K·min-1 to 573.2 and 623.2 K, respectively. Fourier
transform infrared (FT-IR) spectra are recorded on a Bruker
EQUINOX55 spectrometer with KBr pellets.
2 Results and discussion
2.1 A comparison in the TG profiles between free
β-CD and the survived β-CD
The TG profiles of the thermal decomposition process of the
survived β-CD from the inclusion complex of β-CD with clove
oil are displayed in Fig.1A, corresponding to the residual mass
fraction (w) range from 70% to 30%. At this stage, the guest,
clove oil, has already been released from its inclusion complex
of β-CD, and the fastest mass loss process is caused by the ther-
mal decomposition of the survived β-CD[12]. After the w of less than
30%, it is reckoned as the carbonization and cineration process-
es of the survived β-CD. In order to evaluate the effect of clove
oil on the thermal decomposition behavior of β-CD, the TG pro-
files of free β-CD in the same w range are given in Fig.1B.
Obviously, the thermal decomposition temperature of the sur-
vived β-CD in Fig.1A rises accompanying the increase of the
heating rate. A very similar situation is observed in Fig.1B. On
the other hand, although all guest molecules should have es-
caped after mass loss of more than 30%, the effect of the guest
molecules on the thermal behavior of β-CD can still be seen from
the distinction of the TG profiles between Fig.1A and Fig.1B.
The influence, resulting from the released clove oil, makes a
smaller temperature span of 58.5 K (577.9-636.4 K in Fig.1A)
for the survived β-CD than 82.4 K (578.1-660.5 K in Fig.1B) for
free β-CD during the decomposition process in w from 70% to
30%. The difference in temperature interval between any two of
the five heating rates is also apparently different from each other
between free β-CD and the survived β-CD. For example, when
the w value of the sample is 50%, the temperature differences
between the heating rates of 5.0 and 10.0, 10.0 and 15.0, 15.0
and 20.0, 20.0 and 25.0 K·min-1 are 13.20, 9.20, 9.83, and 6.48
K for the survived β-CD, whereas they are 13.64, 9.66, 9.16, and
4.28 K for free β-CD, respectively.
These observations give a strong impression on the influence
of the existence and disappearance of clove oil on the thermal
decomposition process of β-CD. In the following sections, we
will undertake to determine thermal decomposition kinetic pa-
rameters and kinetic mechanism functions for the survived β-
CD.
2.2 Basic theory of thermal decomposition kinetics
Continuous distribution kinetics can be employed to analyze
the thermal decomposition processes of β-CD and β-CD com-
plexes on the basis of many analysis methods, such as integral
Flynn-Wall-Ozawa [16,17], Coats-Redfern [18,19], and differential iso-
conversional Friedman methods[20,21]. Eq.(1) represents the kinet-
ics of thermal decomposition reactions of the survived β-CD:
dα
dt =ζ
dα
dT =k·f(α)=Aexp(
-Ea
RT )·f(α) (1)
where α is the degree of conversion at heating time t, ζ is the
heating rate, and k is the rate constant. Ea is the apparent activa-
tion energy. A, R, and T are the frequency factor, molar gas con-
stant, and absolute temperature, respectively. And f(α) relating
to the reaction mechanism described in this paper only depends
on the value of α. It should be noted that Eq.(1) has been pro-
posed as the beginning to deal with the kinetics process by many
kinds of analysis methods. The methods can be classified ac-
cording to either the experimental conditions selected (isother-
mal or nonisothermal condition) or the mathematical analysis
performed (model-fitting or isoconversional model-free
method) [22-24]. In the present work, the values of Ea for the de-
composition processes of survived β-CD are calculated both by
the isoconversional model-free and model-fitting methods under
the nonisothermal condition.
2.3 Evaluation of the activation energy of thermal
decomposition reaction
One of the most popular integral methods to calculate the Ea
values is Flynn-Wall-Ozawa method [25]. This method involves
isoconversional type analysis and multiple heating rates. It has
the presentation form as follows:
lgζ=lg( AEaR )-lgF(α)-2.315-0.4567
Ea
RT (2)
Fig.1 TG profiles of (A) the survived β-CD and (B) free β-CD inw range from 70% to 30% at different heating rates (ζ)
ζ/(K·min-1): (a) 5.0, (b) 10.0, (c) 15.0, (d) 20.0, (e) 25.0
2216
No.12 XU Peng et al.：Thermal Decomposition Kinetics of Survived β-Cyclodextrin from an Inclusion Complex
where F(α) is a power series expansion for the integration of the
exponential term of Eq.(1). At the same value of α, F(α) will be
a constant, and Ea can be determined from the slope (0.4567Ea/
R) of a plot of lgζ versus (-1/T).
The Ea values are related to α values. The variations of Ea in
the α range from 0.30 to 0.70 for both the survived β-CD and
free β-CD are presented in Fig.2. The varied curves of Ea for the
survived β-CD and free β-CD are just coincident with the fastest
mass loss processes of their respective thermal decomposition
reactions.
There are three stages in Fig.2A for the thermal decomposi-
tion process of the survived β-CD. An approximate platform ap-
pears in stage b, and the Ea values fluctuate around a mean of
135.1 kJ·mol-1 in the α range from 0.40 to 0.60. Stages a and c,
respectively corresponding to the α range from 0.30 to 0.40 and
from 0.60 to 0.70, relate to the linear parts of the Ea curve.
The curve in Fig.2B can also be divided into three stages, i.e.,
a descent stage e, an approximate platform stage f, and an ascent
stage g. The former two are somewhat similar to stages a and b
in Fig.2A except for the difference of α range and the detailed
values of Ea. However, there exists a significant difference be-
tween stage g and stage c. The reverse trend might indicate the
different decomposition mechanism between free β-CD and the
survived β-CD. Otherwise, the values of Ea differ between the
two curves even at the same value of α, and the difference esca-
lates as α is increased.
The linear relationships in stage a and stage c are rather good,
with the correlation coefficients (r) of 0.999 and 0.993, respec-
tively. Furthermore, it is very interesting that the slopes (-58.92
in stage a and -63.52 in stage c) of the two straight lines are al-
so quite close. The approximately parallel relationship suggests
that there might be a similar reaction mechanism in the two
stages, because the decrease trend of Ea in the two stages seems
to obey a similar rule. Consequently, it is very important to fur-
ther elucidate the thermal behavior of the survived β-CD in
stages a and c. So the isoconversional type analysis and model-
fitting method are employed to investigate the two processes.
The differential isoconversional method suggested by Fried-
man is based on the general form of rate Eq.(3)[21]. It can be writ-
ten in the natural logarithmic form as follows:
ln dαdt =lnAf(α)-
Ea
RT (3)
When α keeps constant, the plot of ln(dα/dt) versus 1/T, which is
obtained from TG analysis results recorded at several heating
rates, should be a straight line whose slope allows an evaluation
of Ea. The calculated values of Ea for the survived β-CD under
five heating rates with varied α, according to Friedman method,
are listed in Table 1.
Also, the values of Ea, when α are extrapolated to 0 for stages
a and c based on Friedman method, are exhibited in Table 1. It
is 135.2 kJ·mol-1 for stage a and 69.9 kJ·mol-1 for stage c. It
should be noted that the calculated values of Ea (Table 1), as well
as the extrapolation data, from Friedman method are, to a certain
degree, different from those (Fig.2) calculated by the modified
Ozawa method.
Although the mathematical analyses for two methods are of
the same basic form, i.e., Eq.(1), the detailed operation process,
such as integral, differential and application of approximation,
differs slightly under different methods, which causes the differ-
ence in the calculated or extrapolated results between the meth-
ods. In order to strictly assess the extrapolation results from
Friedman method, a double extrapolation procedure, i.e., Coats-
Redfern method, is also employed to further inspect the kinetic
mechanism function of the thermal decomposition in stages a
and c.
Model-fitting methods involve fitting different model func-
tions to temperature integral process and simultaneously deter-
mining the value of Ea. There are many nonisothermal model-fit-
ting methods, and the most popular one is Coats-Redfern
method[19].
Applying a first order integration to Eq.(1) gives Eq.(4) as fol-
Fig.2 Ea profiles of the thermal decomposition processes of
(A) the survived β-CD and (B) free β-CD in the α range from
0.30 to 0.70 based on Flynn-Wall-Ozawa method
α Ea r α Ea r
0.300 121.7±5.3 0.997 0.600 110.8±21.9 0.946
0.325 121.3±6.1 0.996 0.625 112.0±25.1 0.932
0.350 120.4±6.9 0.995 0.650 112.8±27.3 0.922
0.375 119.0±7.7 0.994 0.675 113.8±32.5 0.896
0.400 117.4±8.9 0.991 0.700 118.3±41.9 0.852
extrapolate 135.2±3.7 0.986 extrapolate 69.9±16.3 0.922
Table 1 Calculated results of Ea (in kJ·mol-1) for the
survived β-CD from Friedman method
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Acta Phys. -Chim. Sin., 2008 Vol.24
lows:
G(α)=Aζ
T
0乙exp(-Ea/RT)dT (4)
Then utilizing an asymptotic series expansion for approximat-
ing the exponential integral in Eq.(4) gives Coats-Redfern repre-
sentation in Eq.(5):
ln G(α)T2乙 乙=ln(AR/ζEa)-Ea/RT (5)
At a constant heating rate of ζ, plotting the left side of Eq.(5)
with varied α, which includes the model function G(α) versus
1/T gives the value of Ea in the light of the slope of the fitted line
in the plot. The most common model functions are listed in Table
2[26].
By replacing, in turn, the expression of G(α) in Eq.(5) with the
listed 18 model functions, based on the original data of T and α,
we obtain the calculated Ea values from these functions at five
heating rates and their respective extrapolation results. These da-
ta in the α ranges from 0.30 to 0.40 and from 0.60 to 0.70 are
listed in Table 3 and Table 4, respectively. The model function
that gives the closest value of Ea in stage a or stage c to those
from Friedman method is selected as the chosen model.
The obtained values of Ea by extrapolating ζ to 0 in Coats-
Redfern method are carefully compared with those by extrapo-
lating α to 0 in Friedman method. It is found that the calculat-
ed and extrapolated values of Ea from the function A1.5, i.e.,
[-ln(1-α)]2/3 in both stages are the closest to those from the
Friedman method. And among the 18 functions, the function A1.5
displays the best linear correlation coefficients under five heat-
ing rates at the two stages. Thus, both of the two stages (a and c)
in Fig.2A are of the same kind of the decomposition mechanism,
i.e., Avrami-Erofe′ev (m=1.5). This result is also in good accor-
dance with the parallel relationship of the straight lines in Fig.
2A.
2.4 Reaction order of thermal decomposition of the
survived β-CD in stage b
Stages a and c in Fig.2A studied above, indicating that the
changes of the Ea values involve in the same regulation. Stage b
Model symbol Model Function G(α)
P1 Power law α3/2
P2 Power law α1/2
P3 Power law α1/3
P4 Power law α1/4
A1.5 Avrami-Erofe′ev (m=1.5) [-ln(1-α)]2/3
A2 Avrami-Erofe′ev (m=2) [-ln(1-α)]1/2
A3 Avrami-Erofe′ev (m=3) [-ln(1-α)]1/3
A4 Avrami-Erofe′ev (m=4) [-ln(1-α)]1/4
R2 phase-boundary controlled reaction
(contracting area)
[1-(1-α)1/2]
R3 phase-boundary controlled reaction
(contracting area)
[1-(1-α)1/3]
D1 one-dimensional diffusion α2
D2 two-dimensional diffusion Valensi Eq. [(1-α)ln(1-α)]+α
D3 three-dimensional diffusion Jander Eq. [1-(1-α)1/3]2
D4 three-dimensional diffusion
Ginsthing-Brounshtein
1-(2/3)α-(1-α)2/3
F0 zero-order α
F1 first-order -ln(1-α)
F2 second-order (1-α)-1-1
F3 third-order 0.5[(1-α)-2-1]
Table 2 Expression of the model functions G(α) for some of
the common mechanism in the solid reaction[26]
Model
symbol
Ea/(kJ·mol-1) Extrapolate
to ζ→05.0
K·min-1
10.0
K·min-1
15.0
K·min-1
20.0
K·min-1
25.0
K·min-1
P1 251.5±4.1 209.7±3.6 203.6±3.4 215.4±5.2 182.5±5.3 252.2±6.7
P2 78.4±1.7 62.8±0.8 61.1±1.2 65.1±1.7 54.2±1.8 78.2±6.1
P3 48.5±0.9 38.6±0.5 37.4±0.8 40.1±1.1 32.7±1.2 48.5±3.8
P4 34.0±0.7 26.6±0.3 25.6±0.5 26.6±1.2 21.9±0.8 34.1±2.6
A1.5 135.0±3.0 110.8±1.1 108.5±2.5 114.5±2.2 96.6±2.3 134.9±9.6
A2 99.2±2.3 80.6±0.9 78.7±2.1 83.7±1.7 70.1±1.8 99.0±7.3
A3 62.9±1.5 50.4±0.6 49.0±1.5 52.4±1.1 43.4±1.2 62.8±4.9
A4 44.8±1.1 35.5±0.3 34.4±1.0 36.8±0.8 30.0±0.9 44.9±3.6
R2 185.6±3.5 152.7±1.6 149.2±3.2 158.3±3.5 133.9±3.6 185.3±13.1
R3 192.9±3.9 158.8±1.5 155.1±3.6 164.6±3.5 139.3±3.6 192.5±13.6
D1 339.2±5.6 280.3±3.6 274.6±4.9 290.7±7.0 247.1±7.2 338.5±23.4
D2 365.8±6.6 302.6±3.4 296.3±6.0 313.8±7.0 266.9±7.3 365.1±25.2
D3 395.3±7.8 327.1±3.1 320.3±7.2 339.3±7.0 288.7±7.4 394.5±27.2
D4 375.5±6.9 310.7±3.4 304.3±6.3 322.2±7.1 273.6±3.6 375.0±25.9
F0 164.7±2.8 135.3±1.7 132.3±2.4 140.4±3.5 118.8±3.3 164.4±11.7
F1 208.0±4.5 171.4±1.5 167.5±4.2 177.7±3.4 150.5±3.7 207.7±14.6
F2 256.8±7.4 213.0±1.9 208.2±6.5 220.9±3.6 187.5±3.8 256.5±17.6
F3 314.4±9.9 260.0±3.1 254.3±9.2 270.2±4.5 229.3±4.1 313.7±21.9
Table 3 Calculated and extrapolated Ea for the survived β-
CD in the α range from 0.30 to 0.40 under five heating rates
Model
symbol
Ea/(kJ·mol-1) Extrapolate
to ζ→05.0
K·min-1
10.0
K·min-1
15.0
K·min-1
20.0
K·min-1
25.0
K·min-1
P1 98.3±6.8 73.9±5.2 64.1±5.8 98.2±5.2 76.0±3.7 88.2±18.2
P2 26.3±2.3 15.3±2.9 14.3±1.9 25.8±1.9 13.8±1.7 23.5±7.1
P3 14.3±1.5 8.7±1.1 6.1±1.2 13.7±1.3 8.7±0.8 12.2±4.1
P4 8.2±1.1 4.0±0.8 2.0±0.9 7.7±1.0 4.0±0.5 6.6±3.0
A1.5 75.4±4.1 56.2±3.2 48.4±3.8 75.2±3.1 57.7±2.1 67.5±14.3
A2 54.3±3.1 39.8±2.3 33.6±2.7 53.8±2.5 40.6±1.5 48.4±10.8
A3 32.9±2.1 23.2±1.4 18.9±1.8 4.0±0.5 23.6±1.0 28.9±7.8
A4 22.3±1.6 14.9±1.1 11.6±1.4 21.7±1.3 15.1±0.7 19.4±5.4
R2 87.4±5.4 65.6±4.0 56.4±4.6 87.1±4.2 67.2±2.7 78.4±16.4
R3 97.0±5.7 73.0±4.3 63.1±4.9 96.6±5.8 74.9±2.9 87.2±17.9
D1 134.5±9.1 102.2±6.8 88.8±7.7 134.5±7.1 104.9±4.9 121.1±24.3
D2 164.6±10.2 125.5±7.8 109.5±8.8 164.6±7.9 128.9±5.3 148.3±29.3
D3 203.8±11.3 156.1±8.7 136.7±10.0 203.9±8.7 160.2±5.8 184.0±35.9
D4 177.5±10.6 135.6±8.1 118.4±9.2 177.5±8.1 139.2±5.5 160.0±31.5
F0 62.4±4.6 46.1±3.4 39.2±3.8 62.0±3.6 47.2±2.4 55.7±12.2
F1 120.0±6.8 88.2±4.3 77.7±5.6 118.0±4.8 91.8±3.1 107.1±22.2
F2 197.7±7.5 151.3±6.0 132.4±7.7 197.5±6.4 155.0±4.0 178.5±34.8
F3 298.0±10.4 229.4±7.5 201.7±10.1 177.5±8.1 235.1±5.4 281.7±42.9
Table 4 Calculated and extrapolation Ea in the α range from
0.60 to 0.70 under five heating rates
2218
No.12 XU Peng et al.：Thermal Decomposition Kinetics of Survived β-Cyclodextrin from an Inclusion Complex
in Fig.2A can be approximately considered as a platform be-
cause all of the nine points in the shadowed area in Fig.2A have
very close values of Ea, i.e., these Ea values are within a narrow
range of (135.1±3.2) kJ·mol-1. An evaluation method of reaction
order is utilized to investigate whether the stage is a simple ther-
mal decomposition process. According to the extended theory of
Avrami[27] under nonisothermal condition, the variation of α with
temperature and heating rate can be described in Eq.(6) as fol-
lows:
α(T)=1-exp(-k/ζn) (6)
where, k and n are the reaction rate and reaction order, respec-
tively. And k can be defined based on Arrhenius Equation, i.e.,
Eq.(7):
k=Aexp(-Ea/RT) (7)
Substituting it into Eq.(6), then taking double natural logarithm
for both sides in Eq.(6) gives Eq.(8) as follows:
ln{-ln[1-α(T)]}=lnA- EaRT -nlnζ (8)
Plotting the left side in Eq.(8) against lnζ under isothermal con-
dition[26], we can obtain a figure, in which the slope of the straight
line is just the reaction order of the survived β-CD. It should be
emphasized that the value of n is changed with temperature. A
plot describing the n values for the thermal decomposition of the
survived β-CD in stage b as a function of temperature is shown
in Fig.3.
A survived β-CD should be also composed of seven glucose
units joined by α-1,4-glucosidic bonds, and the scission of the
chemical bonds would not be occurred at a single location. From
our recent work with gas chromatography coupled to time-of-
flight mass spectrometry to make tracks for the thermal decom-
position behavior of β-CD inclusion complexes, it is found that
many small fragment ions from the loop backbone of the sur-
vived β-CD could be produced, and the small fragments could
still form some larger fragments. These complicated the decom-
position process of the survived β-CD.
The considered temperature range in Fig.3 just corresponds to
the center area of the thermal decomposition of the survived β-
CD under five heating rates (Fig.1A). The continuously decreas-
ing trend of n implies the complexity of the thermal decomposi-
tion process of the survived β-CD in stage b, even with an ap-
proximately constant value of Ea in the stage.
For the four black points in Fig.3, the fit to a linear relation-
ship between n and T from 603.2 to 633.2 K is quite good, with
correlation coefficient (r) value of 0.998. Combined with the TG
profiles in Fig.1A, the value of α from 0.40 to 0.60 is included in
this temperature range except for the heating rate of 5.0 K·min-1.
Then fitting this area to Fig.2A, it is found that Ea is kept ap-
proximately constant in stage b. This phenomenon is abnormal
but very interesting. Because a continuously varying value of n
suggests that there should exist changing reaction mechanisms
with the escalation of the decomposition process. The approxi-
mate invariability of Ea in Fig.2A may result from the superposi-
tion result supplied by the different decomposition mechanism
functions.
The varied mechanism could be attributed to the different
thermal behaviors of the sample at different stages. One of our
recent studies[12] described the detailed decomposition process of
the survived β-CD from its inclusion complex of clove oil. First,
at stage a, a few fragments of the survived β-CD were observed,
implying that its main component was still left in the sample.
Second, the survived β-CD began to decompose rapidly at stage
b, since there was a very large mass loss in TG curve corre-
sponding to the stage. Then it is the carbonization process of the
survived β-CD with a few fragments released which related to
stage c. The different decomposition behaviors in different
stages resulted in the variation of the thermal decomposition ki-
netics of the survived β-CD.
2.5 Difference in FT-IR spectra between free β-CD
and the survived β-CD
FT-IR spectra of free β-CD and the survived β-CD at 573.2
and 623.2 K, as well as IR spectrum of free β-CD at 298.2 K, are
displayed in Fig.4, aiming to give a direct comparison of the
structural difference between them.
The absorptions at about 3390, 2298, and 1200-1000 cm-1 for
free β-CD at 298.2 K are due to the vibration of —OH group,
—CH2 group, and C—O bond, respectively. The absorption at
943 cm-1 is the breathing vibration of β-CD backbone, and 854
cm-1 is the characteristic absorption of glucose.
On the whole, many fine absorption peaks at finger print re-
gion between 1300-700 cm-1 for free β-CD at 298.2 K disappear
both at 573.2 K and at 623.2 K for free β-CD and the survived
β-CD. And the two IR curves of the survived β-CD show more
similarity than those of free β-CD. In other words, the IR curve
of free β-CD at 623.2 K is simpler than that at 573.2 K. For ex-
ample, the single peak at 1639.8 cm-1 for free β-CD at 298.2 K
has been split into two peaks at 1705.3 and 1612.6 cm-1 at 573.2
K, however, only a single peak at 1598.6 cm -1 is observed at
623.2 K. As for the survived β-CD, the single peak appears at
1642.7 cm-1 at 623.2 K and 1631.9 cm-1 at 573.2 K. Moreover,
the vibration absorptions of —OH and —CH2 groups are not
readily observable for both free β-CD and the survived β-CD at
higher temperatures. It should be noted that at 623.2 K, the ab-
Fig.3 Changing trend of n with enhanced temperature for
the thermal decomposition of the survived β-CD in stage b
2219
Acta Phys. -Chim. Sin., 2008 Vol.24
Fig.4 FT-IR spectra of free β-CD and the survived β-CD at
different temperatures
sorption curve trend of free β-CD below 1000 cm-1 is quite dif-
ferent with that of the survived β-CD.
These observations mean that there exists a difference in ther-
mal decomposition mechanisms or rates between free β-CD and
the survived β-CD from the inclusion complex of β-CD with
clove oil. In other words, clove oil as guest affects the decompo-
sition rates of β-CD as host to a certain extent, which are in good
accordance with the calculated results of Ea values.
3 Conclusions
The calculation method of double extrapolation was employed
and the obtained results from both isoconversional model-free
and model-fitting methods under the nonisothermal condition
displayed the complexity of thermal decomposition process of
the survived β-CD from its inclusion complex of clove oil. The
difference of the thermal decomposition behaviors of the sur-
vived β-CD in different stages was discussed. It was interesting
that the initial stage and the final stage of the decomposition pro-
cess for the survived β-CD were of the same reaction model
while the platform stage in the middle presented a regular de-
cline value of reaction order (n). Different methods were used to
calculate the activation energy and the method of Coats -Redfern
with the model function of Avrami-Erofe′ev(m=1.5) was found
to be the best to explain the whole process of the thermal de-
composition reaction.
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