avrami

1. Introduction
• Paper offer guidelines to fit non-isothermal polymer crystallization kinetics data obtained by DSC employing the
widely used Avrami equation and other empeical equations.
• The non-isothermal crystallization behaviors of multi-walled carbon nanotubes (MWNTs)/polyamide 6 (PA6)
composites were investigated by differential scanning calorimetry (DSC).
• Paper describe effect of MWCNTs on crystallization kinetics.

2. Experiment
1. Materials
• Polyamide 6(PA6) and MWCNTs used in this study.
2.DSC procedures
• Perkin–Elmer Pyris 1 differential scanning calorimeter was used to analyse the non-isothermal crystallization.
The non-isothermal crystallization of PA6 and its composites were performed as follows:
 the samples were heated from 20 to 245 ℃ , at a heating rate of 40 ℃ /min.
 Then the samples were cooled to 50 ℃ at a constant cooling rate of 2.5, 5, 10, 20, 40 ℃ /min.
 The thermograms were recorded to estimate the non-isothermal crystallization kinetics.

3. Result and Discussion
• Tp shifts to lower temperature with increasing cooling rate. The
lower the cooling rate, the earlier the crystallization starts.
• It is noted that the MWNTs/PA6 composite has higher Tp and
broader D than the neat PA6 at all cooling rates.
• The melting PA6 macromolecule segments can be easily
attached to the surface of the rigid nanotubes, which leads to
the crystallization of PA6 molecules at higher temperature.
Fig. 1. DSC thermograms of non-isothermal crystallization at
different cooling rates for (a) PA6 and (b) PA6 composite with 1.0
wt.% MWNTs.

4. Fig. 2. Plots of amorphous fraction as a function of time for (a)
PA6 and (b) MWNTs/PA6 composite crystallized non
isothermally at various cooling rates.
Result and Discussion
• The higher the cooling rate, the lower the time range at which the
crystallization occurs, therefore, the transformation is controlled by
nucleation.
• all curves have approximately the reversed S shape.
• The values of t1/2(the crystallization half-time) are determined from Fig.
2 and summarized in Table 1. The t1/2 of the composites is larger than
those of the neat PA6. It is implied that the MWNTs actually act physical
obstacles for the crystallization of PA6 polymer chains.

5. Result and Discussion
• Fig. 4 presents plots of log [1 -ln (Xt)] versus log t for the neat PA6 and
the composites, respectively.
log [1 -ln (Xt)]=logZt + nlogt
• the linearity is poor.
• The linear line in the middle portion of the curves in Fig. 3 is adopted
to determine Avrami exponent n.
• The derived parameters are listed in Table 2. It is seen that n values
of the neat PA6 vary from 4.5 to 6.7, while those of the composite
range from 4.0 to 4.7 which means the addition of MWNTs influences
the mechanism of nucleation and the growth of PA6 crystalline.
Fig. 3. Plots of log [ln (1 -Xt)] as a function of log t for (a) PA6
and (b) PA6/MWNTs composite.

6. Result and Discussion
• Fig. 4 illustrates the plots of log [-ln(1 - Xt)] as
a function of log𝜙.
• According to ozawa eqn.
log(-ln(1 − Xt ))= logK(T) - mlog∅
• Clearly no straight lines are obtained,
indicating the failure of Ozawa model to
provide an adequate description of
crystallization in both the neat PA6 and the
composite.
Fig. 4. Plots of log [-ln (1 - Xt)] as a function of log𝜙 at indicated
temperatures for (a) PA6 and (b) MWNTs/PA6 composite.

7. Result and Discussion
• Fig. 5 presents the plots of logϕ as a function of logt.
log∅= logF(T) - ∝log𝑡
• The good linearity of the plots verifies the success of
the combined approach applied in this case.
• Meanwhile the F(T) for composites is larger than neat
PA6, which indicates that the crystallization rate of
composites is slower than that of PA6 under non-
isothermal condition.
Fig. 5. Plots of log/ as a function of log t for (a) PA6 and (b)
MWNTs/PA6 composite.

8. Conclusion
• The non-isothermal crystallization behaviour of the neat PA6 and MWNTs/PA6 composite were
investigated by DSC.
• Several equations were used to analyse the crystallization kinetic data of the samples. The kinetic
analysis indicated that the applicability of the modified Avrami equation and Ozawa equation do not
correlate satisfactory with the experimental results.
• However the combined Avrami and Ozawa equation can successfully describe the crystallization
processes of the two samples.
• The results showed that the MWNTs in PA6 acted as effective nucleation agents.
• The presence of MWNTs accelerated the nucleation of PA6, but hindered the diffusion and aligned array
of PA6 chains resulting in a slower crystallization rate of MWNTs/PA6 composite than PA6. The addition
of MWNTs influenced the mechanism of nucleation and the growth of PA6 crystallites.

9. Result and Discussion
• Fig. 4 illustrates the plots of log [-ln(1 - Xt)] as
a function of log𝜙.
• According to ozawa eqn.
log(-ln(1 − Xt ))= logK(T) - mlog∅
• Clearly no straight lines are obtained,
indicating the failure of Ozawa model to
provide an adequate description of
crystallization in both the neat PA6 and the
composite.
• Because non-isothermal crystallization is a
dynamic process in which the crystallization
rate is no longer constant but a function of
time and cooling rate, the comparison in
Ozawa analysis is to be carried out on
experimental data representing widely
varying physical states of the system, while
these differences have not been taken into
account in the model, the quasi-isothermal
treatment of Ozawa model might be
questionable.
Fig. 4. Plots of log [-ln (1 - Xt)] as a function of log𝜙 at indicated
temperatures for (a) PA6 and (b) MWNTs/PA6 composite.

10. Experiment
1. Materials
• Polyamide 6(PA6) and MWCNTs used in this study.
2. Preparation of MWNTs/PA6 composites
• The MWNTs/PA6 composites were prepared via a melt-blending process using a PRISM TSE-16-TC Brabender twin-
screw extruder.
• The temperature of the extruder was maintained at 185, 228, 238, 238, and 225 ℃ from hopper to die respectively.
The rotation speed of the twin screw was 30 rpm.
• The composite containing 1 wt.% MWNTs was used in this study. The neat PA6 was also extruded at the same
condition.
3.DSC procedures
• Perkin–Elmer Pyris 1 differential scanning calorimeter was used to analyse the non-isothermal crystallization.
The non-isothermal crystallization of PA6 and its composites were performed as follows:
 the samples were heated from 20 to 245 ℃ , at a heating rate of 40 ℃ /min.
 Then the samples were cooled to 50 ℃ at a constant cooling rate of 2.5, 5, 10, 20, 40 ℃ /min.
 The thermograms were recorded to estimate the non-isothermal crystallization kinetics.

11. Result and Discussion
• Figs. 2 and 3 present the amorphous fraction as a
function of temperature and time, respectively, for
PA6 and MWNTs/PA6 crystallized at various cooling
rates.
• The higher the cooling rate, the lower the time range
at which the crystallization occurs, therefore, the
transformation is controlled by nucleation.
• all curves have approximately the same S (or reversed
S) shape, indicating that only the retardation effect of
cooling rate on the crystallization is observed in these
curves.
• Due possibly to the spherulite impingement in the
later stage, the curves tend to flat.
Fig. 2. Plots of amorphous fraction as a function of temperature
for (a) PA6 and (b) MWNTs/PA6 composite crystallized
nonisothermally at various cooling rates.

12. Result and Discussion
• The derived parameters are listed in Table 2.
It is seen that n values of the neat PA6 vary
from 4.5 to 6.7, while those of the
composite range from 4.0 to 4.7 which
means the addition of MWNTs influences
the mechanism of nucleation and the
growth of PA6 crystalline.
• The larger the rate parameter Zc value, the
higher the crystallization rate is.
• Under the same cooling rate, the higher Zc
is obtained for PA6 than those of
MWNTs/PA6 composites.
• It is indicated that the MWNTs hinder the
growth of PA6 crystallite under non-
isothermal condition which is in accordance
with the results of t1/2. However, as
mentioned above, the addition of MWNTs
increases the onset and the peak
temperatures.