Kinetic study of non-isothermal degradation of PA6
composites containing flame retardant additives
Sweety Monga, J. B.
Dahiya*
Department of Chemistry, Guru Jambheshwar University of Science &
Technology,
Hisar-125001, Haryana, India
*Corresponding Author
E-mail: jbdic@yahoo.com
ABSTRACT:
The kinetics of thermal degradation of PA6
composites containing intumescent flame retardant and inorganic additive was
studied by using various model-free methods such as Flynn-Wall-Ozawa,
Kissinger, Coats-Redfern Modified and model-based Coats-Redfern method at three
heating rates 5, 10 and 20 oC/min under nitrogen atmosphere.
Model-free methods suggested the simple reaction mechanism for pure PA6 and
complex multistep mechanism for flame retarded PA6 composites. The activation
energy values obtained from three model-free methods were comparable to each
other. Model-based Coats-Redfern method suggested the random nucleation and
growth mechanism for both PA6 and PA6/AP760 samples but the degradation
mechanism is changed to phase boundary controlled mechanism on further addition
of inorganic additives. The change of activation energy values indicated that
inorganic additives acted as catalyst during major degradation stage but at
later stage of charring they acted as strong barriers to prevent escaping of
volatile materials.
KEYWORDS: Polyamide 6, Degradation mechanism, Flame retardants, Coats-Redfern
method.
Polyamide 6 (PA6) is widely used polymer and meets great demand in
electrical and engineering applications where resistance to degradation and
fire is essential1. But PA6 is easily ignitable and sustains flaming
combustion upon ignition. In recent years, the intumescent flame-retardants (FRs) have been explored extensively in PA6 due to their halogen-free, low
smoke and low toxicity during combustion2-5.
The studies has revealed that the thermal stability is not the sole
criterion for flame-retardancy but it also depends on decomposition rate, char
forming rate and the amount of char formed. Thus, for applications in fire
safety materials, it is very important to investigate thermal decomposition
behaviour and kinetics of the material as it influences the flame retardancy to
a considerable extent. The kinetic parameters obtained from thermogravimetric
(TG) data are very helpful to postulate thermal degradation mechanism of
polymeric materials6 and to identify the
changes observed after addition of flame retardant additives. The kinetic information
from TG data can be obtained by various model-based and model-free methods.
Model-based methods involve the fitting of different function models to TG data
to obtain the best statistical fit model, which is further used to calculate the
kinetic parameters. The model-free methods or isoconversional methods involve
numerous TG curves for performing the analysis without considering any
assumptions about the reaction function model and order. There are many
publications7-9 involved in the study of the thermal degradation
kinetics to develop the flame-retarded polymeric materials. Dabrowski et al1
have studied thermal degradation of polyamide 6/clay nanocomposite by kinetic
analysis and reported that the enhanced thermal stability of the polyamide/clay
nanocomposite is associated with an increase in the activation energy of the
degradation coupled with the barrier effect of clay layers.
In the present paper, the kinetics of thermal degradation of PA6
composites containing intumescent flame retardant and inorganic additive was
studied as an extension of our previous published work10. One
model-based integral method i.e. Coats-Redfern method11 and three
different model-free methods such as Kissinger12, Flynn-Wall-Ozawa13,14
and Coats-Redfern Modified11 methods were employed to study the
degradation mechanism by determining the kinetic parameters of PA6 and its
composites.
KINETIC METHODS:
Model-free methods
Flynn-Wall-Ozawa (OFW) method13,14: OFW is an integral
isoconversional method derived by using Doyle’s approximation using TG data of
multiple heating rates. The mathematical expression is given by
Where, T = temperature; A = pre-exponential factor; R = gas
constant; Ea = energy of
activation; β = heating rate;
and α (W0-Wt/W0-Wf) is the degree of conversion (W0 =
initial weight of the sample; Wt = residual weight of the sample at
the temperature T; Wf = final weight of the sample).
The plot of log β vs.
1000/T gives a series of straight lines for different values of degree of
conversion (α) taken at suitable regular intervals. The slope of
the line (-0.4567 Ea/R)
gives the activation energy (kJ/mol) corresponding to each value of α. The parameter A is calculated from the intercept (log(AEa/Rg(α))
by assuming g(α) corresponding to a particular reaction model.
Coats-Redfern Modified (CRM) method11: The Coats-Redfern
Modified method is a multiple-heating rate application of the Coats-Redfern
method. The mathematical expression is given by:
Plotting ln(β/T2)
against 1000/T for each heating rate
gives a family of straight lines of slope (-Ea/R)
corresponding to different degree of conversion.
Kissinger method12: This is a maximum
rate method and applicable only to the multiple heating rate TG data. The
temperature (Tm) corresponds to the DTG peak temperature is used to
calculate the single values of activation energy (Ea) for a series of experiments at different heating
rates. The mathematical expression for this model is
The plot of ln(β/Tm2) vs. 1000/Tm
gives a straight line with slope equal to (-Ea/R)
and the intercept is given by ln(AR/Ea).
Model-based method:
Coats Redfern method11: There are various non-isothermal model-fitting
methods including the most popular Coats-Redfern method. This method is an
integral method using single heating
rate TG data to evaluate the
degradation kinetics. The mathematical expression is:
By inserting
various expression for g(α) already reported15-17 (Table 1)
into eq. (4), kinetic parameters are determined from the plot of ln(g(α)/T2)
against 1000/T. The parameters Ea and A are obtained from the slope = –Ea/R and
intercept = ln(AR/β Ea).
Table 1: Algebraic
expressions for g(α) for the most commonly
used mechanisms of solid state processes15-17
|
Symbol |
Model |
Form of G(α) |
|
|
Diffusion controlled
models (deceleratory curves) |
|
|
D1 |
One-dimensional diffusion |
α2 |
|
D2 |
Two-dimensional diffusion |
α + (1-α) ln (1-α) |
|
D3 |
Jander Equation; Three-dimensional diffusion; spherical
symmetry |
[1-(1-α)
1/3 ]2 |
|
D4 |
Ginstling
Brounshtein Equation; Three-dimensional diffusion; spherical symmetry |
1-2/3α-(1-α) 2/3 |
|
|
Geometrical
contraction models (deceleratory
curves) |
|
|
R1 |
Phase boundary
reaction; plate symmetry; one dimensional contraction |
1-(1-α) |
|
R2 |
Phase boundary
reaction; cylindrical symmetry; contracting area |
1-(1-α)
1/2 |
|
R3 |
Phase boundary
reaction; spherical symmetry; contracting volume |
1-(1-α)
1/3 |
|
|
Nucleation and growth
models (sigmoidal curves) |
|
|
A2 |
Avrami equation I;
two-dimensional growth of nuclei |
[-ln (1-α)]
1/2 |
|
A3 |
Avrami equation II;
three-dimensional growth of nuclei |
[-ln (1-α)]
1/3 |
|
A4 |
Avrami equation III |
[-ln (1-α)]
1/4 |
|
|
Rreaction order models
(deceleratory curves) |
|
|
F1 |
Mample equation
(first order reaction); Random nucleation with one nucleus on each particle |
-ln (1-α) |
EXPERIMENTAL:
Materials and methods used:
Polyamide 6 (PA6) was purchased from Sigma Aldrich Co., India. Sodium
montmorillonite (clay) was supplied by Southern Clay Products Inc., Germany.
Exolit AP760 (a blend of ammonium polyphosphate and tris(2-hydroxyethyl)
isocyanurate) (AP760) was obtained from Clariant Inc., US. Zinc borate (ZB) was
purchased from Himedia Chemicals Co., India. These chemicals were used as
received. The detailed description of preparation PA6 composites (PA6/AP760 and
PA6/clay/AP760/ZB) has been reported in our previous publication10.
Thermal
characterization:
Non-isothermal thermogravimetric (TG)
measurements were performed on Perkin Elmer Pyris thermogravimetric analyzer
instrument at three different heating rates (β) 5, 10 and 20 °C min−1 from room
temperature to 600 °C under nitrogen atmosphere at a flow rate of 20 mL/min.
RESULTS AND DISCUSSIONS:
Thermal
degradation analysis:
(Fig. 1a-c) shows the TG curves of
PA6, PA6/AP760 and PA6/clay/AP760/ZB composites at different heating rates (5,
10 and 20 o C/min) under nitrogen atmosphere.
Fig. 1: TG curves of (a) PA6, (b) PA6/AP760 and (c)
PA6/clay/AP760/ZB at different heating rates.
It can be seen from Fig. 1a-c that at all
heating rates, the degradation of the flame-retarded PA6 composites starts at
lower temperature relative to pure PA6. This is attributed to the
destabilization caused by release of phosphoric acid from decomposition of
AP760 added as a flame retardant to PA6. The thermal analysis of these samples
under air atmosphere at only one heating rate has already been reported in our
previous work15. In this study, the samples are analyzed under
nitrogen atmosphere at three different heating rates with the aim to study
degradation mechanism by employing different kinetic methods. Table 2 gives the
onset temperature (Tonset) and the temperature at maximum rate of
degradation (Tm) at three heating rates (5, 10 and 20 oC/min)
as well as composition for PA6 composites. On addition of 5 wt% of clay and 5
wt% of zinc borate (ZB), both the onset temperature and temperature at maximum
rate of degradation are increased at all heating rates. Thus, the thermal
stability has been improved for PA6/clay/AP760/ZB sample in comparison to
PA6/AP760 due to barrier effect of inorganic additives. Further, it can be
observed from Fig. (1a-c) that all the TG curves are shifted to higher
temperatures with the increase of the heating rates i.e. Tonset, and
Tm are also increased on increasing the heat rate. These shifts can
be attributed to the difference in the rate of heat transfer with the change in
the heating rate and the less exposure time to a particular temperature at
higher heating rates in addition to the effect of the decomposition kinetics18.
Table 2: Composition and important degradation
temperatures of PA6 and its composites.
|
Sample/ (Composition in %) |
Degradation temperatures at different heating rate |
|||||
|
5 oC/min |
10 oC/min |
20 oC/min |
||||
|
Tonset (oC) |
Tm (oC) |
Tonset (oC) |
Tm (oC) |
Tonset (oC) |
Tm (oC) |
|
|
PA6 (100) |
386 |
443 |
412 |
461 |
435 |
492 |
|
PA6/AP760 (80+20) |
303 |
372 |
322 |
387 |
334 |
400 |
|
PA6/clay/ AP760/ZB (80+5+10+5) |
349 |
395 |
375 |
420 |
390 |
435 |
Model-free
methods:
Thermal degradation mechanism of PA6
and effects of AP760 and ZB is studied by model-free as well as model based
kinetic methods. It is convenient to carry out the kinetic analysis with the
model-free or isoconversional methods which determine the activation energy (Ea) and dependence of Ea
with degree of conversion (α)
directly from experimental α-T data of TG curve obtained at
various heating rates without the knowledge of reaction model function g(α). In this study, Flynn-Wall-Ozawa13-14,
Coats-Redfern modified11 and Kissinger12 methods have
been used to determine the kinetic parameters of PA6 and its composites at
three heating rates i.e. 5, 10 and 20 °C min−1.
Fig. 2:
Iso-conversion plots for (a) PA6, (b) PA6/AP760, (c) PA6/clay/AP760/ZB,
and (d) Ea-α curve using OFW method.
Flynn-Wall-Ozawa
(OFW) method: The isoconversional plots
obtained by OFW method corresponding
to different conversion values are shown in Fig. 2a-c (α = 0.1 –
0.9). It is seen from (Fig. 2a) that the fitted straight lines obtained at
different α values for pure PA6 are almost parallel over the
complete range of conversion (α = 0.1 – 0.9). This suggests that
the degradation process of PA6 follows simple reaction mechanism19.
Whereas, in case of composites (Fig. 2b,c), the slopes of lines fluctuate at
very high and very low conversion which indicates the possibility of complex
multistep mechanism for composites20,21.
Dependence of activation energy (Ea) on α: Fig. 2d
shows the plots of calculated activation energy Ea as a function of degree of conversion (α) using OFW method. It is observed
that for pure PA6, the Ea
values do not vary much with α suggesting
that the thermal degradation of pure PA6 obeys a simple reaction mechanism19.
In case of PA6/AP760 composite, the case is completely different. The Ea values are continuously
increasing with the increase of α up to α=0.8, but beyond that the activation
energy decreased which supports the idea that the thermal degradation of
PA6/AP760 composite occurs via complex reaction mechanism. In case of
PA6/clay/AP760/ZB composite, the Ea
values are increased up to α=0.3,
then the values remain almost constant for the range (α=0.4 – 0.7). At higher conversion, the Ea values are significantly
increased making the curve chaotic at the end. It indicates that the
degradation mechanism is entirely different by the addition of ZB along with
clay at the later stage of charring of the polymer due to the formation of a
barrier layer.
Coats-Redfern
Modified method (CRM): The plots of Coats-Redfern Modified method for PA6 and
its composites at multiple heating rates were found to follow the same trend as
that of OFW plots. From the slopes of the fitted straight lines at different
conversion degrees, the corresponding activation energy (Ea) values were calculated over a range of conversion (α=0.1
– 0.9). These activation energy (Ea)
values are comparable to the values obtained by OFW method. Analogous to OFW
method, the fitted straight lines at different conversions possess same slope
for pure PA6 over the whole range of conversion but in case of composites, the
slope of lines diverge at very low and very high conversions. This again
suggests the possibility of a simple reaction mechanism for pure PA6 and
complex multistep mechanism for composites.
The average activation energy values (α=0.4 – 0.8) calculated by using the Coats
Redfern Modified method for PA6, PA6/AP760 and PA6/clay/AP760/ZB were 114.5,
162.5 and 120.0 kJ/mol, respectively (Table 3). The activation energy followed
the same order as in the case of the OFW method. However, the average
activation energy values were slightly higher in the OFW method compared to the
CRM method. The differences observed between the values of Ea can be assigned to the different approximations of
the temperature integral in different methods22. The dependence of
activation energy (Ea) on α obtained using Coats-Redfern
Modified method was found to be similar to that observed by using OFW method.
Kissinger
method:
The kinetic parameters for thermal degradation of PA6 and its composites were
also calculated using Kissinger method and are listed in Table 3. The
activation energy followed the same order as in the case of the OFW and CRM
methods. The apparent activation energy (Ea) of PA6, PA6/AP760 and
PA6/clay/AP760/ZB were found to be 114.2, 167.2 and 121.5 kJ/mol, respectively.
These values were found to be in good agreement with the values evaluated from
OFW and CRM methods.
Table 3: The activation energies obtained by
OFW, CRM and Kissinger methods.
|
Samples |
Ea (average value over α = (0.4 – 0.8)
(kJ/mol) |
Ea (kJ/mol) |
|
|
OFW |
CRM |
Kissinger |
|
|
PA6 |
120.4 |
114.5 |
114.2 |
|
PA6/AP760 |
164.9 |
162.5 |
167.2 |
|
PA6/clay/AP760/ZB |
125.0 |
120.0 |
121.5 |
Model-based
method:
Coats-Redfern
method (CR): To predict the degradation mechanism i.e. appropriate kinetic model of
thermal degradation process, the conventional model fitting CR method was
employed assuming first order reaction in the range α=0.4 – 0.8. The range (α=0.4
– 0.8), was selected for CR method because the activation energy values were found nearly
constant in this range on applying Model-free methods23. The values
of activation energies (Ea)
evaluated for PA6 and its composites from CR method using several reaction
models at three heating rates 5, 10 and 20 oC/min, are summarized in
Table 4. The data obtained from the linear plots of CR method over the range α=0.4 to 0.8 resulted in very high
correlation coefficients (R2)
for all the models. So, the linear correlation coefficient has a drawback for
verifying the accuracy of a reaction mechanism as it is not sure whether the
slight differences between correlation coefficients are due to improper choice
of g(α) or any experimental
error involved in TG measurements24. Therefore, the accuracy
of a mechanism was assumed on the basis of comparing activation energy values
to those obtained from model-free methods25.
Table 4 shows that, the activation
energy values corresponding to A2 type mechanism (Avrami
equation I;
two-dimensional growth of nuclei, Table 1) for pure PA6 at all heating rates obtained
by model based method are in agreement with the values obtained using
Model-free methods. Thus, from kinetic data it seems that the degradation
kinetic process of pure PA6 follows sigmoidal degradation mechanism (A2) i.e. nucleation and growth at all three heating rates 5, 10 and 20 oC/min.
For PA6/AP760 composite at all heating rates, the activation energy
corresponding to F1 type mechanism (random nucleation having one nucleus on
individual particle, Mample equation I) is comparable to the values obtained by
model-free methods. This suggests that the addition of 20 wt% of AP760 an
intumescent flame retardant changes the degradation mechanism from A2 to F1
type mechanism. Further, for PA6/clay/AP760/ZB composite at all heating rates (Table
4), the activation energy corresponding to R1 type mechanism (phase boundary
controlled reaction with one-dimensional contraction) is in good agreement with
the values obtained by model-free methods. Thus, the addition of clay (5 wt%)
and zinc borate (5 wt%) to PA6/AP760 transforms the degradation process from
random nucleation (F1) to phase boundary controlled reaction (R1)
(one-dimensional contraction).
Table 4:
The activation energy obtained using Coats-Redfern method at different heating
rates.
|
Model |
PA6 |
PA6/AP760 |
PA6/clay/AP760/ZB |
||||||
|
G(α) |
Heating rate (oC/min) |
Heating rate (oC/min) |
Heating rate (oC/min) |
||||||
|
5 |
10 |
20 |
5 |
10 |
20 |
5 |
10 |
20 |
|
|
F1 |
236.0 |
223.0 |
262.5 |
152.2 |
161.0 |
172.3 |
179.3 |
202.3 |
217.0 |
|
D1 |
288.6 |
271.5 |
320.7 |
176.5 |
197.6 |
212.1 |
217.3 |
281.8 |
264.3 |
|
D2 |
341.6 |
322.0 |
379.6 |
209.3 |
234.3 |
251.1 |
258.5 |
316.3 |
313.5 |
|
D3 |
410.0 |
387.4 |
455.5 |
251.6 |
281.7 |
301.4 |
312.0 |
358.6 |
377.1 |
|
D4 |
364.2 |
343.6 |
404.6 |
223.3 |
249.9 |
267.7 |
276.1 |
330.3 |
334.4 |
|
R1 |
138.4 |
129.7 |
154.1 |
82.9 |
93.4 |
100.5 |
103.1 |
117.5 |
126.2 |
|
R2 |
182.4 |
171.6 |
202.8 |
110.1 |
123.8 |
132.8 |
137.3 |
155.6 |
167.0 |
|
R3 |
199.1 |
187.6 |
221.5 |
120.5 |
135.4 |
145.2 |
150.4 |
170.2 |
182.6 |
|
A2 |
112.1 |
105.4 |
124.9 |
66.4 |
75.1 |
80.6 |
84.1 |
95.4 |
102.6 |
|
A3 |
70.8 |
66.2 |
79.1 |
40.7 |
46.4 |
50.0 |
52.4 |
59.8 |
64.5 |
|
A4 |
50.2 |
46.6 |
56.2 |
27.9 |
32.1 |
34.8 |
36.5 |
42.0 |
45.4 |
CONCLUSIONS:
The thermal degradation of the
flame-retarded PA6 composites started at lower temperature relative to pure PA6
due to catalytic effect of phosphoric acid released from the used flame
retardant AP760. The onset temperature and temperature at maximum rate of
degradation were increased for PA6/clay/AP760/ZB in comparison to PA6/AP760 due
to the formation of a barrier layer of inorganic additives. Model-free methods
suggested the simple degradation mechanism for pure PA6 and complex multistep
mechanism for flame retarded PA6 composites. Model-based Coats-Redfern method
suggested the random nucleation and growth mechanism for both PA6 and PA6/AP760
samples but the degradation mechanism is changed to phase boundary controlled
mechanism on further addition of inorganic additives. The change of activation
energy values indicated that inorganic additives acted as catalyst during major
degradation stage but at later stage of charring they acted as strong barriers
to prevent escaping of volatile materials.
REFERENCES:
1.
Dabrowski F, Bourbigot S, Delobel R
and Bras ML. Kinetic modelling of the thermal degradation of Polyamide-6
nanocomposite. European Polymer Journal.
36; 2000: 273-284.
2.
Levchik SV, Costa L and Camino G.
Effect of the fire-retardant, ammonium polyphosphate, on the thermal
decomposition of aliphatic polyamides: Part II--polyamide 6. Polymer Degradation and Stability. 36;
1992: 229-237.
3.
Levchik GF, Levchik SV and Lesnikovich
AI. Mechanisms of action in flame retardant reinforced nylon 6. Polymer Degradation and Stability. 54;
1996: 361-363.
4.
Levchik SV, Levchik GF, Camino G,
Costa L and Lesnikovich AI. Mechanism of Action of Phosphorus-based
Flame Retardants in Nylon 6.III. Ammonium Polyphosphate/Manganese Dioxide. Fire and Materials. 20; 1996: 183-190.
5.
Dahiya JB,
Rathi S, Bockhorn H, Haußmann M and Kandola BK. The combined effect of organic
phoshphinate/ ammonium polyphosphate and pentaerythritol on thermal and fire
properties of polyamide 6-clay nanocomposites. Polymer Degradation and
Stability. 97; 2012: 1458-1465.
6.
Cones JA,
Marcilla A, Caballero JA and Font R. Comments on the validity and utility of
the different methods for kinetic analysis of thermogravimetric data. Journal
of Analytical and Applied Pyrolysis. 58; 2001: 617−633.
7.
Zhao H, Wang
YZ, Wang DY, Wu B, Chen DQ, Wang XL and Yang KK. Kinetics of thermal
degradation of flame retardant copolyesters containing phosphorus linked
pendent groups. Polymer Degradation and Stability. 80; 2003: 135-140.
8.
Chen Y and Wang
Q. Thermal oxidative degradation kinetics of flame-retarded polypropylene with
intumescent flame-retardant master batches in situ prepared in twin-screw
extruder. Polymer Degradation and Stability. 92; 2007: 280-291.
9.
Kumar N and Dahiya
JB. Polypropylene-nanoclay composites containing flame retardant additive:
Thermal stability and kinetic study in inert atmosphere. Advanced Material
Letters. 4; 2013: 708-713.
10. Monga S and Dahiya JB. Effect of Ammonium
Polyphosphate in Combination with Zinc Phosphate and Zinc Borate on Thermal
Degradation and Flame Retardation of Polyamide 6/Clay Nanocomposites. Asian Journal of Research in Chemistry. 8; 2015: 39-44.
11.
Coats AW and
Redfern JP. Kinetic parameters from Thermogravimetric data. Nature. 201;
1964: 68-69.
12.
Kissinger
HE. Reaction Kinetics in Differential Thermal Analysis. Analytical Chemistry.
29; 1957: 1702-1706.
13.
Flynn JH and
Wall LA. General treatment of the thermogravimetry of polymers. Journal of
Research of the National Bureau of Standards, Section A: Physics and Chemistry.
70; 1966: 487-489.
14.
Ozawa T. A
new method of analyzing thermogravimetric data. Bulletin of the Chemical
Society of Japan. 38; 1965: 1881-86.
15. Avrami M. Kinetics of phase change. I. General Theory. Journal
of Chemical Physics. 7; 1939:
1103-1112.
16. Sestak J and Berggren G. Study of the kinetics of the mechanism of solid-state
reactions at increasing temperatures. Thermochimica Acta. 3; 1971: 1-12.
17. Wendlandt WW. Thermal Analysis.
3rd edition. Wiley, New York. 1986.
18. Jaber JO and Probert
SD. Pyrolysis and gasification kinetics
of Jordanian oil shales. Applied Energy.
63; 1999: 269-286.
19. Bourbigot S, Gilman JW and
Wilki CA. Kinetic analysis of the thermal degradation of
polystyrene-montmorillonite nanocomposite. Polymer
Degradation and Stability. 84; 2004: 483-492.
20. Flynn JH. Degradation kinetics applied to lifetime predictions of
polymers. Polymer Engineering Science.
20; 1980: 675-677.
21. Flynn JH. Thermal analysis kinetic-problems, pitfalls and how ot deal
with them. Journal of Thermal Analysis
and Calorimetry. 34; 1988: 367-381.
22. Jankovic B. Kinetic analysis of the nonisothermal decomposition of
potassium metabisulfite using the model-fitting and isoconversional
(model-free) methods. Chemical
Engineering Journal. 139; 2008: 128–135.
23. Jankovic B, Adnadevic B and
Jovavovic J. Application of
model-fitting and model free kinetics to the study of dehydration of
equilibrium swollen poly(acrylic acid) hydrogel: Thermogravimetric analysis. Thermochimica Acta, 452, 2007, 106-115.
24. Dahiya JB, Kumar K, Muller-Hagedorn M and Bockhorn H. Kinetics of
isothermal and non-isothermal degradation of cellulose: model-based and
model-free methods. Polymer International. 57; 2008: 722–729.
25. Khawam A and Flanagan DR,
Complementary use of Model-free and Modelistic methods in the Analysis of
Solid-State Kinetics. Journal of Physical Chemistry B,
109; 2005: 10073-10080.
Received on 05.10.2015 Modified on 09.11.2015
Accepted on 14.11.2015 © AJRC All right reserved
Asian J. Research
Chem. 8(11): November 2015; Page 683-689
DOI: 10.5958/0974-4150.2015.00109.1