Application of different macrokinetic models to the isothermal crystallization of PP/talc blends

Composite Structures 62 (2003) 291–302

www.elsevier.com/locate/compstruct

Application of different macrokinetic modelsto the isothermal crystallization of PP/talc blends

Carmen Albano a,b,*, Jos�ee Papa b, Miren Ichazo c, Jeanette Gonz�aalez c,Carmen Ustariz b

a Lab. De Pol�ıımeros, Centro de Qu�ıımica, Instituto Venezolano de Investigaciones Cient�ııficas (IVIC), Apartado. 21827,Caracas 1020-A, Venezuela

b Facultad de Ingenier�ııa, Universidad Central de Venezuela, Escuela de Ingenier�ııa Qu�ıımica, Caracas, Venezuelac Departamento de Mec�aanica, Universidad Sim�oon Bol�ııvar, Caracas, Venezuela

Abstract

The crystallization kinetics of neat polypropylene (PP) and of PP composites containing 2, 5, 10 and 30 wt% of talc was studied.

Various kinetic equations, namely the Avrami, Velisaris–Seferis, Dietz, Khanna, Malkin models, have been applied to describe the

kinetics of crystallization from the melt state under isothermal conditions. The results suggested that experimental data of the

Avrami’s exponent, ‘‘n’’, is approximately 2, meaning that the crystallization of PP alone and of its composites with talc is a two-

dimensional growth process. Experimental data of PP alone can be best described by the Avrami, Velisaris–Seferis, Dietz and

Malkin models; whereas the models that in the case of composites better correlate their behavior are those of Velisaris–Seferis,

followed by Avrami’s.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: Polypropylene; Solidification process; Crystallinity; Kinetic models; Crystallization profiles

1. Introduction

Isotactic polypropylene (PP) is becoming the most

important commodity polymer widely used in techni-

cal applications. Thanks to its good mechanical

properties, its easy processability, its versatility to ac-cept numerous types of filler, and its relatively low

cost, PP has found a wide range of applications in the

house ware, packaging, and automotive industries. Its

mechanical properties depend on the supermolecular

structure arrangement achieved in the crystalline state.

Isotactic PP is known to exhibit three different crys-

talline forms: the monoclinic a-form, the hexagonal

b-form, and triclinic c-form [1]. Under normal pro-cessing conditions, a-PP is the principal constituent,

which may be accompanied by a relatively low

amount of the b modification.

The incorporation of calcium carbonate, mica or

talc as a filler in thermoplastics is a common practice

in the plastics industry with the purpose of reducing

*Corresponding author. Tel.: +58-2-504-1320; fax: +58-2-504-1350.

E-mail addresses: [email protected], [email protected]

(C. Albano).

0263-8223/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2003.09.028

the production cost of molded products. It is well

known that mineral fillers improve the rigidity of the

polymers, but they also decrease ductility and tough-

ness. The use of PP composites in the automotive

sector has been increasing in recent years, mainly be-

cause of its high stiffness, which enables it to replaceconventional materials in structural engineering appli-

cations [2].

On the other hand, the crystallization process affects

polymer properties through the crystal structure and

morphology established during the solidification pro-

cess. An important aspect of the crystallization process

is its kinetics, both from the fundamental view of

polymer physics and the modeling and control of poly-mer processing operations.

The goal of the present work was to study the effect of

talc in blends with PP on the crystallization kinetics

under isothermal conditions. A number of macrokinetic

models have been proposed [3–7] in order to describe the

macroscopic evolution of the crystallinity during the

crystallization process. In addition, the purpose of this

study was to compare the quality of these models, basedon the correlation index (r2), which suggest applicability

of each model.

mail to: [email protected],

292 C. Albano et al. / Composite Structures 62 (2003) 291–302

2. Models of crystallization kinetics

2.1. Avrami’s model

The Avrami’s equation [3], when used to describe

isothermal crystallization kinetics of polymers, is ex-

pressed as follows:

X ðtÞX1

¼ 1� eð�ktnÞ ð1Þ

where X is the crystallinity developed by the polymer in

a time t, at a constant temperature T , k is the Avrami

kinetic constant and n is the Avrami exponent.

2.2. Khanna’s model

Khanna [4] modifies the Avrami’s equation as fol-

lows:

X ðtÞX1

¼ 1� eð�ktÞn ð2Þ

where n is the Avrami exponent and k the Avrami

constant.

2.3. Dietz’s model

To consider secondary crystallization (post-Avrami),

this model [5] incorporates an additional term into the

crystallization rate equation proposed by Avrami. Thisnew parameter, a, can range between 0 and 1. When

there is no post-Avrami crystallization, this parameter

equals zero; otherwise it is different from zero. The

equation used in isothermal processes is

dhdt

¼ nkð1� hÞtðn�1Þe�ah1�hð Þ ð3Þ

where h ¼ X ðtÞX1

and ‘‘n’’ and ‘‘k’’ continues to be theAvrami’s parameters under conditions of isothermal

crystallization.

2.4. Velisaris–Seferis’ model

These authors [6] present two equations, which are a

series and/or parallel linear combination of Avrami’s or

Kamal–Chu’s equations, to model and simulate crys-tallization kinetics where two physically differentiable

crystalline structures are developed, that is, a dual

crystallization process. However, according to Cebe [8],

these arrangements can also be used to determine if

there is an extensive secondary crystallization.

The equations involved in isothermal processes are

the following:

• Series:

X1

X ðtÞ ¼ W1

1

1� eð�k1tn1 Þ

� �þ W2

1

1� eð�k2tn2 Þ

� �ð4Þ

• Parallel:

X ðtÞX1

¼ W1 1�

� eð�k1tn1 Þ�þ W2 1

�� eð�k2t

n2 Þ� ð5Þ

where W1 and W2 are weight factors describing the

extension of each crystallization process; therefore the

following must occur: W1 þ W2 ¼ 1

2.5. Malkin’s model

Malkin [7] develops a model comprising both primary

as well as secondary crystallization.

The kinetic expression is as follows:

X ðtÞX1

¼ 1� C0 þ 1

C0 þ expðC1tÞ

� �ð6Þ

where

C0 ¼ 4n � 4

C1 ¼ lnð4n � 2Þ kln 2

� �1=n

where n and k are the Avrami kinetics parameters.

3. Experimental

The polymer object of study was commercial PP

[MFI: 6.5 g/10 min], supplied by Pro-Fax. The talc used

was supplied by Key Venezolana de Talco.

The blends of PP with talc were prepared with weight

concentrations of 2, 5, 10 and 30% w/w. The blends

obtained were extruded in a W & P intermeshing co-rotating twin extruder, under the following temperature

profile: 150, 190, 190, 190 and 170 �C and a screw ve-

locity of 80 rpm. Then the samples were placed in a

stove and dried at 80� for 30 min.

A Mettler Toledo Differential Scanning Calorimeter

(DSC), model DSC821, was used for the analysis of the

isothermal crystallization kinetics of this polymer and its

blends with talc. Standard flat-surface aluminum cap-sules were used and the dragging gas was nitrogen. For

isothermal tests, samples of PP and PP with different

contents of talc were first melted over their fusion tem-

perature, and maintained at this temperature for 10 min

to erase previous thermal history of the polymer. Then,

to analyze isothermal crystallization kinetics, samples

were cooled at the maximum speed allowed by the

equipment to the desired crystallization temperature.This temperature was maintained during the period of

time required to complete the crystallization process.

The crystallization temperatures studied were six: 110,

117, 121, 125, 127, and 131 �C. The analysis of experi-

mental data was carried out using a software appro-

priate for characterization and analysis, whose general

working logic is described by Albano et al. [9,10].

Fig. 2. DSC thermograms of PP with talc at different compositions

and different crystallization temperatures.

C. Albano et al. / Composite Structures 62 (2003) 291–302 293

4. Results and discussion

4.1. Analysis of the thermograms

Isothermal thermograms obtained by cooling at dif-

ferent temperatures the melted PP and blend of PP with

different concentrations of talc (2, 5, 10, 30), are pre-

sented in Figs. 1 and 2, respectively.

The delay in the DSC signal, observed in tests per-

formed under isothermal conditions, cannot simply be

attributed to an effect of the induction time (tn) resultingfrom nucleation. Nucleation is typically heterogeneousin most polymers used for commercial applications and

is the result of the presence of impurities and catalyst

residues together with the presence of nucleating agents

(talc), which are usually added to accelerate the overall

crystallization process [11]. In Tables 1–5, the apparent

increase in induction time (tn) with the increase in the

crystallization temperature (Tc) may well be simply due

to the slowing-down of the overall crystallization pro-cess (nucleation and growth) that affects the instanta-

neous value of the rate of heat release. Patkar and

Jabarin [12] report that this behavior of tn is due to the

decrease in the nucleation rate at temperatures near

melting point. On the other hand, Kenny and Maffezzoli

[13] report that this delay is only representative of the

induction time associated with the crystal nucleation.

The effect of temperature on the crystallization rate ofPP is clearly observed in the isothermal thermograms

obtained from neat PP, at the different temperatures

reported in Fig. 1. According to this, crystallization ki-

netics of PP is strongly affected by temperature. A

similar behavior is observed in Fig. 2 for PP with dif-

ferent concentrations of talc. This effect is still more

evident in the degree of the crystallization curves ob-

tained by integration of the thermograms in Figs. 1 and2, which are reported in Figs. 3 and 4.

With increasing crystallization temperature (Figs. 1

and 2), the crystallization exothermic shifts to longer

time and becomes flatter. This implies that the total

crystallization time is lengthened and crystallization rate

decreases with increasing Tc which is in line with the

Fig. 1. DSC thermograms of the neat PP at different crystallization

temperatures.

kinetic theory of crystallization according to which an

increase in the crystallization temperature will result in a

decrease in supercooling (DT ) and hence in a decrease ofthe growth rate [14].

Peak (tmax-exp), crystallization (tc) times and t1=2 (half

time) are reported for neat PP and for nucleated PP in

Tables 1–5. In these tables, tmax represents the time re-

quired to reach the maximum rate of heat flow, and

corresponds to the changeover to a slower kinetic pro-

cess due to impingement of adjacent spherulites. In the

meantime, since tmax is the solution of dH=dt ¼ 0, we canuse the Avrami’s equation (1) to derive tmax-theoretical in

terms of n and k:

tmax-theoretical ¼n� 1

nk

� �1=n

ð7Þ

Table 1

Summary of the nucleation times (tn), experimental and theoretical (theo.) peak times (tmax), crystallization time (Tc) and experimental and theoretical

crystallization rate (G) for the neat PP

Temperature (�C) tn (seg) tmax-exp (seg) tmax-theo (seg) tc (seg) t1=2 exp (seg) t1=2theo (seg) Gtheo (seg�1) Gexp. (seg�1)

110 785 13 12 47 15.0 15.5 0.0645 0.0670

117 788 22 24 70 25.0 29.0 0.0344 0.0400

121 790 42 38 104 49.0 46.4 0.0216 0.0200

125 794 49 65 134 53.0 71.9 0.0141 0.190

127 801 103 78 219 135.0 83.3 0.0120 0.0074

131 818 110 112 – – – – –

Table 2

Summary of the nucleation times (tn), experimental and theoretical peak times (tmax), crystallization time (Tc) and experimental and theoretical

crystallization rate (G) for PPwith 2 wt% of talc

Temperature (�C) tn (seg) tmax-exp (seg) tmax-theo (seg) tc (seg) t1=2 exp (seg) t1=2theo (seg) Gtheo (seg�1) Gexp (seg�1)

110 777 8.0 7.4 38.0 13.0 9.96 0.1004 0.0769

117 777 13.0 11.5 14.4 0.0694 0.0769

121 782 10.0 21.4 46.0 21.0 25.9 0.0386 0.0476

125 786 24.0 41.1 72.0 37.0 45.4 0.0220 0.0270

127 786 35.0 53.8 96.0 50.0 57.0 0.0175 0.0200

131 792 90.0 80.3 192.0 132.0 84.9 0.0118 0.0076

Table 3


crystallization rate (G) for PP with 5 wt% of talc


110 777 7 6.1 38 9.9 8.3 0.1207 0.0100

117 – – – – – – – –

121 783 9 20.1 42.0 16.0 24.7 0.0441 0.0624

125 787 21 27.8 67.0 25.0 33.9 0.0295 0.0400

127 785 35 38.9 94.0 37.0 41.7 0.0239 0.0270

131 793 87 46.9 186.0 96.0 49.8 0.0201 0.0104

Table 4


crystallization rate (G) for PPwith 10 wt% of talc


110 775 11 5.4 35 10.9 7.6 0.1316 0.0917

117 775 10 9.6 40 13.9 12.6 0.0792 0.0714

121 777 13 15.2 44 13.9 19.1 0.0523 0.0714

125 781 20 20.6 63 22.9 25.8 0.0388 0.0430

127 784 32 29.2 91 33.9 32.9 0.0304 0.0294

131 784 54 40.7 116 96.0 43.8 0.0228 0.0104

Table 5


crystallization rate (G) for PP with 30 wt% of talc


110 771 10 4.8 36 9.0 7.1 0.1417 0.1110

117 771 12 7.0 36 10.9 9.7 0.1036 0.0909

121 772 13 10.3 35 12.0 13.2 0.0757 0.0833

125 772 21 13.1 51 17.0 16.6 0.0604 0.0588

127 774 23 16.4 62 23.0 19.6 0.0511 0.044434

131 780 31 22.2 77 34.0 25.3 0.0395 0.0294


Fig. 3. Relative crystallinity versus time for the neat PP.

Fig. 4. Relative crystallinity versus time for the PP with different

concentration of talc.


The values estimated for tmax-theoretical can be compared

with the tmax-exp values obtained directly from the plot of

H vs. t, both listed in Tables 1–5. The two sets of tmax

values are relatively similar at low crystallization tem-peratures, both for the neat PP as well as for the used PP

blends with the talc, but they become to be very different

as the crystallization temperature and the talc concen-

tration increase (P 10%). At the same time, tmax ex-

perimental and theoretical values increase as a function

of crystallization temperature both for neat PP as for the

blends with talc, but are lower for a higher talc con-

centration.At the same temperature, the values of the peak

(tmax-exp and tmax-theoretical) and the crystallization (tc) times

measured for neat PP are higher than those of the talc

composites, being this behavior more pronounced at

higher temperatures (>127 �C).In addition, tmax-exp, tmax-theoretical and tc can also be used

to describe the crystallization rate, which decreases with

increasing crystallization temperatures, and at a giventemperature increases with the addition of talc, being this

effect more pronounced as talc concentration is higher.

From the comparison of the induction times (tn)measured for neat PP and PP with different concentra-

tions of talc, it is possible to conclude that the nucle-

ation process in the composites is faster than in neat PP,

since tn decreases as talc concentration increases in the

composites. This is due to an increase in the nucleationrate, which implies an increase in the number of nuclei

per unit PP volume, and a subsequent reduction in the

spherulite size distribution, which is observed in the Dwin Figs. 1 and 2 (Dw represents width at half-height of

the crystallization peak). Kenny and Maffezzoli [13]

found that carbon fiber in blends with polyphenylene

sulfide (PPS) has the opposite effect, which implies that

the carbon fiber delays the PPS crystallization process.In addition, the behavior in tn can be attributed to the

decrease in the nucleation rate as the temperatures gets

closer to the melting point.

The decrease in the nucleation process considerably

influences the behavior of tn and tmax for PP and for the

composites at high temperatures; consequently, the

values of tn and tmax obtained through the Avrami

equation deviate from the experimental values. On theother hand, when talc concentration is high, although

nucleation rate is controlling the process, the number of

nuclei is larger and thus spherulites are smaller and the

development of a secondary crystallization might not be

extensive. Consequently, values are lower for a higher

talc concentration, both for experimental values and for

those calculated by Avrami.

L�oopez et al. [15] also studied the effect of glass fiber,sisal fiber and polyethylenterephtalate (PET) on the PP

crystallization process. They detected that crystalliza-

tion rate was faster when fibers were incorporated into

the polymer matrix, independently of the Tc selected.

Fig. 5. DSC thermograms and relative crystallinity of PP with differ-

ent amounts of talc at a temperature of 125 �C.


Binsbergen [16] reported that the effect of nucleating

agents consists in diminishing the spherulites size and

increasing their number as compared with neat polymer.

Therefore, nucleation density in PP increases as afunction of the talc content, resulting in a faster crys-

tallization process and smaller spherulites.

Crystallization isotherms with a similar behavior to

that observed in this research were found by Avalos et

al. [17] in their studies on blend of polymer matrices, PP/

PEAD with 5% and 10% of HDPE, filled with 20% of

glass fiber. This means that PP crystallization in the

composite was considerably influenced by temperature.The same trend was found by Lee et al. [18] in their

study on the polybutylenterephtalate crystallization ki-

netics, and Li et al. [19] who worked with samples of

nylon 1012.

The effects of different concentration of talc on the PP

crystallization are visible in Figs. 3 and 4, where crys-

tallization and the evolution of the crystallization degree

are depicted for different temperatures. For all thecomposites analyzed, all isotherms exhibited a sigmoid

dependence upon time. According to these results, the

PP crystallization rate increases in the presence of talc,

being this effect more marked for lower crystallization

temperatures (110 �C). It can be concluded that the

relative amount of crystallinity developed at a definite

time t decreases as crystallization temperature increases,

and that talc acts as a nucleating agent for PP, inde-pendently of crystallization temperature. Xu and He [20]

found similar results in their studies on blends of poly-

oxymethylene with attapulgite.

The trend observed in Figs. 3 and 4 was also reported

by other researchers, such as Patel and Spruiell [21] in

works with nylon 6, Li et al. [19], who studied nylon

1012, Chan and Isayev [22], who worked with PET, and

L�oopez et al. [15] who analyzed PP with or without glassfiber, sisal fiber, etc. Lee et al. [18] also demonstrated a

decrease in nucleation rate at temperatures close to

melting point.

Crystallization isotherms are shown in Fig. 5, as

well as curves representing the variation of the relative

crystallinity as a function of time, for different talc

concentrations and at a crystallization temperature of

125 �C. It can be noticed that the crystallization rateof PP composites increases with increasing talc con-

tent, possibly attributable to a nucleating effect of the

filler.

The behavior observed in the curves in Fig. 5 gives

reasons to infer that when talc concentration in the

blend is higher, nuclei density increases, crystal size is

smaller and spherulite size distribution decreases (ob-

served in Dw). The start of the secondary crystallizationcorresponds to the collision between spherulites. When

these are smaller, the time required to fill the interstices

is shorter and the secondary crystallization process, if

any, is reduced.

The crystallization half-time (t1=2) is defined as the

time at which the extent of crystallization is 50%. As

shown in Tables 1–5, a 20 �C increase in the crystalli-

zation temperature implies an increase in more than 10times of the half time of crystallization (t1=2) of PP. Thesame behavior can be seen with blends of PP with dif-

ferent talc concentrations; this increase is smaller for

higher talc concentrations (Tables 4 and 5). According

to values of t1=2, its increase is assumingly exponential

with increasing crystallization temperature Tc, at least

within the temperature range studied.

The half time of PP crystallization is, in general, moreinfluenced by the crystallization temperature than by the

talc content in the composites, with a noticeable increase

up to about 131 �C in Tc, both for neat PP as well as for

the PP/talc blends.

This behavior in the half time of crystallization (t1=2)influences the PP crystallization rate (s1=2 ¼ 1=t1=2). Thes1=2ðGÞ can also be determined from measured kinetics

parameters (k, n of Avrami’s equation) using the fol-lowing expression:

s1=2 ¼1

t1=2¼ 1

ln 2k

� �1=n ¼ G ð8Þ

The values of G and t1=2, derived from two methods, are

listed in Tables 1–5. According to their analysis, these

values are relatively similar at low temperatures and low

Fig. 6. Rate of crystallization versus temperature for PP with different

amounts of talc.

Fig. 7. Simple and double linearization of the isothermal melt crys-

tallization data of neat PP at 127 �C. Regression index¼ 0.999.


talc concentrations, resulting G for PP with talc faster

than in neat PP.

In addition, the dependence of the overall crystalli-

zation rate on temperature can be seen from G in Fig. 6

for neat PP and their blends with talc. According to this

figure, crystallization rate is slower with increasing

temperature, and an increase in G is detected when talc

concentration is higher. This is consistent with the nu-cleation control of crystallization at low degrees of

undercooling, i.e., DT ¼ Tm�� Tc [11,23]. This figure

also reflects that an increase in the talc concentration

results in an increase in G, meaning that G is strongly

dependent on composition and crystallization tempera-

ture.

In the region of melting temperature, the growth rate

is easily comparable to the nucleation rate so thatcrystallization rate is governed by the nucleation process

and hence strongly depends on crystallization tempera-

ture. Additionally, the decrease in G with increasing Tc(Fig. 6) suggests that a nucleation-controlled process

occurred.

Table 6 shows the values of the crystallization en-

thalpy for PP in the blend, which decrease as the tem-

perature selected for isothermal crystallization increases,meaning that PP crystallinity also decreases. According

to this table, as talc content in PP is higher for the same

crystallization temperature, crystallization enthalpy in-

creases as a result of the nucleating action of talc. Ma-

cauley et al. [24] reported similar results with PP with

white titanium dioxide pigment.

Table 6

Enthalpy crystallization (J/g) for the PP with different composition of

talc at different crystallization temperature

Crystallization

temperature (�C)Talc concentration

0 2 5 10 30

110 97 101 103 106 110

117 91 98 99 100 103

121 86 83 93 97 99

125 83 83 86 89 96

127 76 80 82 84 87

131 73 76 80 82 84

4.2. Kinetic parameters

The values of the kinetic parameters of the PP/talc

blend were obtained through the crystallization kineticssimulation and modeling program [9], which develops a

linear regression per isotherm. Theoretically, when the

experimental values of each isotherm are plotted at a

logarithmical scale, Avrami’s equation adjusts to a

straight line whose slope is the Avrami’s exponent ‘‘n’’,and the intercept with the abscise is the rate constant

‘‘k’’. According to Velisaris and Seferis [6], in turn, ex-

perimental values of each isotherm should be adjusted totwo straight lines, representing primary and secondary

crystallization, and also to the possible presence of a

double crystallization mechanism, from which the ki-

netic parameters n1, n2, k1, k2 are obtained (Figs. 7–9).

Plot of log½� lnð1� X ðtÞ=X ð1Þ� versus log t is shownin Fig. 7 for neat PP. A pretty good linear relationship

for the melt crystallization appears. Unlike most semi-

crystalline polymers, no roll-off at longer times can beobserved, indicating that the secondary crystallization of

PP does not occur under the experimental conditions.

These results are in line with studies conducted by Av-

alos et al. [17], L�oopez et al. [15] and Supaphol [23] on

neat PP.

Regarding to the curves of log½� lnð1� X ðtÞ=X ð1Þ�versus log t for PP with different talc concentrations

(Figs. 8 and 9), the straight line at lower conversions

Fig. 8. Simple and double linearization of the isothermal melt crys-

tallization data of PP with 2% talc at 127 �C. Regression index¼ 0.999.

Fig. 9. Simple and double linearization of the isothermal melt

crystallization data of PP with 30% talc at 127 �C. Regression

index¼ 0.999.


represents primary crystallization and the one at higher

conversions represents secondary crystallization, being

this latter more marked at high temperatures. Similar

results were reported by Patkan and Jabarin [12] in PET

composites within the temperature range they studied.The results of linearization of experimental values

obtained from the thermograms can be seen on Figs. 10

and 11. Based on these values, the Avrami’s exponent

‘‘n’’ (Fig. 10) for constant talc concentration increases as

a function of the temperature selected for crystallization.

The kinetic parameter ‘‘n’’ was found to decrease

slightly when talc content in PP increases for the same

crystallization temperature (Fig. 10).

Fig. 10. Variation of Avrami exponent with crystallization tempera-

ture for the PP with different amounts of talc.

Fig. 11. Variation of Avrami’s rate constant with the crystallization

temperature for PP with different amounts of talc.

The Avrami’s parameter ‘‘n’’ varies within the range

1.9–2.5 for the neat PP and within the range 1.7–2.4 for

PP composites, depending on the crystallization tem-

perature. According to the definition of the Avrami’sexponent [11], when the value of ‘‘n’’ is around of 2.0,

the nucleation process is simultaneous and the growth of

crystals is probably two-dimensional under the experi-

mental conditions, with a combination of the thermal

and athermal nucleation mechanisms that explain the

fractional values observed for the Avrami’s exponent.

Intuitively, the temperature dependence of the Avrami’s

exponent ‘‘n’’, within the nucleation control region,should be such that ‘‘n’’ increases with increasing Tc.This results from the fact that the number of the

athermal nuclei is found to increase tremendously with

decreasing crystallization temperature [25,26], causing

the nucleation mechanism to be more instantaneous in

time, which, in turn, decreases the values of the Av-

rami’s exponent ‘‘n’’.Interpretation of n is complex; for example, values of

n between 2 and 4 are reported in the literature, for the

crystallization of polymers from the melt state. The

Avrami’s exponent, ‘‘n’’, is defined as: n ¼ cþ k, where crepresents the nucleation step, n is 0 for constant nu-

cleation, i.e., density of the nucleation site remains

constant, and 1 for sporadic nucleation. The term krepresents the growth step. It is 1 for lineal development,

2 for discs and 3 for spheres. If n ranges between 2 and 3,the growth mechanism is expected to be the same in

both, the formation of lamellae and their radial growth

into spherulitic structures. According to Khanna and

Taylor [4] the differences in n reflect variations in the

mechanism of nucleation.

Most of the real crystallization processes do not pro-

ceed with a unique mode of nucleation. Tobin [27,28]

reports that a sample containing a number of heteroge-neous nuclei per unit area (or volume), once nuclei start

to grow, two phenomena can take place: (1) the rate of

radial growth is constant and it is supposed that as soon

as growth site initiation starts, all of the heterogeneous

nuclei present in the sample start to grow simultaneously,

and fresh homogeneous nuclei start to initiate the growth

site in untransformed regions of the sample; or (2) the

rate of radial growth of the site growth is not constant; ifcurves of X versus t are sigmoid, nucleation is simulta-

neously initiated. For the mixed nucleation, Kim and

Kim [29] report that mixed nucleation (EmðtÞ) is the sumof thermal nucleation (EðtÞ) and athermal nucleation

(EðaÞ). In the case of the two-dimensional growth:

EmðtÞ ¼ ½KtF ðtÞ þ Ka�f ðtÞ2 where Kt and Ka are constants

of the thermal and athermal nucleation.

In addition, heterogeneous nucleation is generallyinstantaneous [30]. The activity of a particle depends on

its size, which should be large enough to accommodate a

heterogeneous nucleus able to initiate on its surface a

stable lamella.

Fig. 12. Activation energy of crystallization vs. talc concentration.


In all cases, fractional values of n were obtained,

which can be explained in terms of a partial overlapping

of the primary nucleation with the crystal growth. Ad-

ditionally, at the same Tc, the Avrami’s exponent chan-ges with the talc content of composites, at least within

the range studied.

According to Fig. 11, the Avrami’s rate constant ‘‘k’’is found to decrease monotically with increasing crys-

tallization temperature Tc. According to Supaphol [23],

this remark is only valid when the Tc of interest is withinthe range where nucleation mechanism is the rate-

determining step. Additionally, ‘‘k’’ decrease as a func-tion of temperature results from the fact that the

experimental crystallization temperature is higher than

the temperature of the maximum crystallization rate.

Moreover, the addition of a nucleating agent leads to an

increase in the kinetic constant k, and as analyzed, a

shortening of the crystallization half-time (t1=2).The rate constant, ‘‘k’’, which controls crystallization

of the sample and is extremely sensitive to temperature,determines both nucleation rate and growth processes.

The value of ‘‘k’’ is dependent on the molecular weight

and structure of the polymer, molecular weight distri-

bution, presence of impurities and nucleating agent.

The Avrami’s parameter ‘‘k’’ is assumed to be ther-

mally activated and can be used to determine crystalli-

zation activation energy (DEc). This crystallization rate

can be described by an Arrhenius equation [31]:

k1=n ¼ k0 expð�DEc=RT Þ ð9Þwhere k0 is a pre-exponential constant, R is the gas

constant, T is the absolute crystallization temperature,

and DEc is total activation value, which consists of thetransport activation energy DE� and the nucleation ac-

tivation energy DF . DE� refers to the activation energy

required to transport molecular segments across the

phase boundary to the crystallization surface. DF is the

free energy of formation of the critical size crystalliza-

tion nuclei at the crystallization temperature (Tc).A similar approach has been reported for the crys-

tallization of Poly (phenylene sulfide, PPS) and Nylon1012 [19].

The lineal regression of the experimental data of ln kagainst 1=T determines DEc=R. Fig. 12 shows the vari-

ation of activation energy as a function of talc concen-

tration, which decreases with the talc content in the

composites. The presence of some nuclei would result in

a decrease in crystallization free energy barrier and thus

a decrease in crystallization activation energy. Accord-ing to Beck [32] interfacial surface free (re) energy could

be reduced by the addition of an effective nucleating

agent. Thus, the decrease in the re value of PP with a

nucleating agent suggests that the addition of talc in-

creases crystallization growth rate of PP. This implies a

decrease in the energy required for the crystallization

process to take place.

With regard to the kinetic parameters obtained

through the double linearization, values for ‘‘n’’ and

‘‘n2’’ and ‘‘k’’ and ‘‘k2’’ (Fig. 10 and Table 7) are similar,and ‘‘k1’’ value is very small. On the other hand, the

average values of ‘‘n1’’ for secondary crystallization

range between 1.0 and 2.0 (Table 7). These values are

lower than those for primary crystallization. This is

consistent with the lower values of n for secondary

crystallization reported by Yu et al. [33]. The ‘‘n1’’ av-erage values suggest that the one-dimensional crystalli-

zation growth is occurring at the final stage ofcrystallization. Additionally, the rate growth decreased

with increasing temperature, which is consistent with

nucleation control of crystallization. The k1 values

(Table 7) are very low, implying a predominance of

primary crystallization in the blends under study. When

crystallization process is a simple mechanism, one of the

weight factors in the V–S equation equals one (W1 tends

to 0).

4.3. Comparison between the different macrokinetic

equations

The quality of each kinetic equation for describing

segmental data is quantitatively represented by the val-

ues of r2 (correlation index) obtained along with the best

fit, where the closer to 1 the better the quality of the fit.

Comparison of the values of the r2 parameters are

summarized in Tables 8 and 11 for neat PP and for PP/talc blends at different concentrations respectively. In

the case of neat PP (Fig. 13), these r2 values indicate thatAvrami’s, Velisaris–Seferis, Dietz’ and Malkin’s models

offer the best description based on experimental data at

the different crystallization temperatures analyzed,

meaning that crystallization process is a simple one.

Graphically, deviation of the fits (Fig. 13) from the

experimental data using Khanna is obvious, while thatbased on the other models (Avrami, serial and parallel

Velisaris–Seferis, Malkin, Dietz) is much less pro-

nounced.

Specifically the Khanna model appears to overesti-

mate the experimental data at low crystallization tem-

perature, while it appears to underestimate them at

higher crystallization temperature.

Table 7

Kinetic parameters using Velisaris–Seferis equations in isothermal processes

Temperature (�C) 110 117 121 125 117 131

PP Avrami’s exponent, n1 (–) 1.0606 1.2478 1.2972 2.4299 2.2781 2.5417

Kinetic constant, k1 (min�1) 1.3779 0.6511 0.4242 0.2764 0.2231 0.1453

Regression coefficient, r2 (–) 1.0000 0.9974 0.9892 0.9996 0.9996 0.9999

Average of n1 (–) 1.8092

Avrami’s exponent, n2 (–) 2.0199 2.1913 2.2050 2.2882 2.4980 2.6054




PP/2 wt% talc Avrami’s exponent, n1 (–) 1.0812 1.0964 1.2080 1.2231 2.2256 2.8655








PP/10 wt% talc Avrami’s exponent, n1 (–) 1.0602 1.0643 1.1048 1.1394 1.2933 2.2941








Table 8

The r2 parameter suggests the quality of the fit for PP alone

Temperature (�C) Avrami V–S parallel V–S series Malkin Khanna Dietz

110 0.9930 0.9999 0.9995 0.9945 0.0104 0.9895

117 0.9240 0.9741 0.9744 0.9229 0.0860 0.9276

121 0.9795 0.9790 0.9801 0.9782 0.0240 0.9861

131 0.9939 0.9992 0.9992 0.9912 0.0093 0.9940


The r2 values for the blends of PP with different talc

concentrations are shown in Tables 9–11. It can be seen

that for the blend of PP with 2 wt% of talc and at low

crystallization temperatures, all models, except Khan-

na, are close to the experimental data, being Avrami,

serial and parallel Velisaris–Seferis and Malkin (Fig.

14) the best. All of them underestimate the experi-

mental data at the early stage of crystallization whereasthey appear to overestimate the experimental data at

the final stage of crystallization (Fig. 14). As crystalli-

zation temperature is increased, all of the models, ex-

cept for V–S, deviate from the experimental data,

which is detected by the values of the correlation in-

dices (Table 9). This can be seen in Fig. 14(b) at a

temperature of 117 �C. The adjustment of the models

for the PP blends with 5% of talc follows the sametrend as the blend of PP with 2% of talc. When talc

concentration is increased to 10%, and for the whole

range of crystallization temperatures, the kinetic mod-

els that better fit experimental data are the serial and

parallel V–S (Table 10), but with some underestimate

at the final stage of crystallization. The other models

report higher or lower values and correlation indices

are shown in Table 10.

Finally, at high talc concentrations (30 wt%) a similar

behavior is detected (Table 11); that is, this composite

exhibits a similar behavior to that of PP with low talc

concentrations and at low crystallization temperatures.

The models that best fit are Avrami, series and parallelV–S, with a correlation index close to the unity, and

then the others follow with different indices; moreover,

with increasing temperature, the models deviate more

and more from the behavior of the experimental data.

In addition, at all temperatures analyzed and at the

different concentrations, the Khanna model is found not

to fit to the data.

The behavior exhibited by the Malkin model can beexplained because there is not any direct analytical

procedure for determining the Malkin kinetic parame-

ters, since the Malkin parameters C0 and C1 are esti-

mated based on a previous knowledge of the Avrami’s

parameters.

Fig. 13. Comparison of experimental data for the neat PP with those

predicted by different models at two temperatures: (a) 110 �C, (b)

131 �C.Fig. 14. Comparison of experimental data for PP mixed with 2% by

weight of talc with those predicted by different models at two crys-

tallization temperatures: (a) 110 �C, (b) 117 �C.


Regarding the results obtained in modeling with the

Dietz equation, in several cases the curve developed

through this equation adjusts itself to experimental data.

In addition, Dietz factor ‘‘a’’ reported a value ap-

Table 9

The r2 parameter suggests the quality of the fit for PP with 2 wt% of talc

Temperature (�C) Avrami V–S parallel V–S se

110 0.9946 0.9980 0.9960

117 0.8962 0.9747 0.9970

121 0.8978 0.9813 0.9812

131 0.8728 0.9088 0.9090

Table 10



110 0.9305 0.9086 0.9212

117 0.9554 0.9882 0.9878

125 0.8903 0.9772 0.9884

127 0.8800 0.9974 0.9987

131 0.8991 0.9210 0.9222

Table 11



110 0.9505 0.9985 0.9986

117 0.9736 0.9797 0.9960

121 0.8995 0.9497 0.9899

131 0.8839 0.9258 0.8965

proaching to zero for all the composites studied,

meaning that in our case the crystallization process

mainly consist in a primary crystallization.

ries Malkin Khanna Dietz

0.9954 0.2906 0.8905

0.8649 0.3670 0.8905

0.8747 0.4225 0.8820

0.7679 0.6775 0.8242


0.8263 0.2650 0.8448

0.8594 0.3643 0.8575

0.8368 0.6353 0.8268

0.8874 0.7115 0.7921

0.7998 0.5971 0.8483


0.8465 0.1900 0.8593

0.8944 0.1087 0.8937

0.8405 0.5084 0.8367

0.8316 0.1384 0.8662


5. Conclusions

The addition of talc results in an improvement in

nucleation rate and in a reduction of the spherulite sizedistribution (Dw). According to these results, talc has a

nucleating ability. All the crystallization rate parameters

(tn, tmax, t1=2, G, tc) were found to be very sensitive to

changes in the crystallization temperature within the

explored range. The values of crystallization rate (G)were found to increase with decreasing temperatures.

The Avrami’s kinetic parameter ‘‘n’’ was found to

vary within the range 1.9–2.5 for neat PP and within therange 1.7–2.3 for blends with talc, depending on crys-

tallization temperature. This reflects a two-dimension

crystal growth from a combination of thermal and

athermal nuclei.

The crystallization rate of PP was found to be faster

with talc than that of a neat PP, meaning that talc is an

effective nucleating agent what increases then the kinetic

constant ‘‘k’’ and decreases the half-time (t1=2).Experimental results suggested that, within the range

of temperatures studied, the crystallization process falls

within the region where the nucleation mechanism is the

rate-determining step and that experimental data of neat

PP can be better described by the Avrami, V–S, Dietz

and Malkin models, whereas for blends with talc the

best correlations were obtained with Velisaris–Seferis

models, followed by Avrami’s.

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Application of different macrokinetic models to the isothermal crystallization of PP/talc blends