Polymer Communication

Model of cold crystallization of uniaxially oriented

poly(ethylene terephthalate) fibers

Zhiying Zhang*, Shizhen Wu, Minqiao Ren, Changfa Xiao

School of Materials Science and Chemical Engineering, Tianjin Polytechnic University, 63 Chenglinzhuang Road, Tianjin 300160, People’s Republic of China

Received 4 October 2003; received in revised form 9 April 2004; accepted 26 April 2004

Abstract

The differential scanning calorimeter heating curves of uniaxially oriented poly(ethylene terephthalate) (PET) fibers with three peaks were

analyzed by using a newly proposed equation. The diffusion-controlled crystallization theory is suitable for describing cold crystallization of

uniaxially oriented PET fibers. A crystallization model was proposed based on the kinetic parameters obtained. The model embraces the three

sub-processes of crystallization corresponding to different growth geometries. The first sub-process corresponds to the nucleation of ordered

molecular segments or the radial growth of preformed nucleus, resulting in the shorter bundle-like entities. The second sub-process

corresponds to further growth of the bundle-like crystallites along chain direction, resulting in the longer bundle-like entities. The third sub-

process corresponds to the three-dimensional growth of crystallites relating to the random segments, resulting in the spherical entities.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Non-isothermal crystallization; Crystallization model; Orientation

1. Introduction

There are two aspects of significance to investigate the

cold crystallization of uniaxially oriented poly(ethylene

terephthalate) (PET) fibers. First, it is of important

technological interest. The reasons are that in traditional

fiber processing, the as-spun fibers, except high-speed

spinning, are basically non-crystalline and the crystal-

lization and orientation are accomplished in the subsequent

processing, such as drawing and annealing. Secondly, it is

also of great importance from a scientific point of view

because PET can easily turn into the oriented non-crystal-

line state under some conditions. Therefore, the research is

helpful to discover the mechanism of crystallization and

structure reorganization. Many researches have been made

on the orientation, the structure formation, and the cold

crystallization of the oriented PET samples. Main results

include (1) PET chains undergo ordering process in the

induction period of crystallization [1–3]; (2) the initial

structural differences cause differences in crystallization

rate from the glass state [4], originating from the nucleation

density [5,6]; (3) oriented PET fibers undergo the crystal-

lization and orientation relaxation processes at a tempera-

ture above or below glass transition temperature [7,8]; (4)

the orientation of amorphous phase promotes a substantial

increase in crystallization rate [9]; (5) the cold drawing

causes a depression of the glass transition temperature [10,

11]; (6) the multi-processes of crystallization are related to

the different growth geometries [12,13].

Most of the previous researches on cold crystallization of

PET fibers have neglected the analysis of the multi-

crystallization processes. Here, we present our preliminary

model obtained by analyzing the cold crystallization curves

of PET fibers determined by using differential scanning

calorimeter (DSC). The model involves different structures,

such as precursors, bundle-like and spherical entities, and

the relationship between them.

2. Experimental

As-spun fibers of PET with intrinsic viscosity of

0.643 dL/g were drawn in water bath at 40 8C at a rate of

4 cm/s. The draw ratios were 2.314 and 2.771, respectively.

The wide angle X-ray diffraction measurements were

performed on the drawn PET fibers by using a Ragaku

0032-3861/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.polymer.2004.04.046

Polymer 45 (2004) 4361–4365

www.elsevier.com/locate/polymer

* Corresponding author. Tel.: þ86-22-24528463; fax: þ86-22-

24528054.

E-mail address: zhangz@public.tpt.tj.cn (Z. Zhang).

D/max-r A X-ray diffractometer, showing no obvious

degree of crystallinity. The overall birefringence measure-

ments were carried out with an Opton polarized optical

microscope equipped with a Na lamp and a tilting

compensator. The orientation factor of the non-crystalline

PET fibers is calculated from

fb ¼Dn

Dn0a

ð1Þ

where Dn is the birefringence of the samples; Dn0a ; the

intrinsic birefringence of the amorphous phase, 0.20 for

PET fibers [14]. The sonic velocities of PET fibers were

measured by using a SSY-1 sonic velocity apparatus. The

sonic orientation factor can be expressed by

fs ¼ 1 2C2

u

C2ð2Þ

where C is the sonic velocity of PET fibers under

investigation; Cu is equal to 1.35 km/s, the sonic velocity

of the unoriented PET fibers. The crystallization process

was traced by a Perkin–Elmer DSC, model DSC-7. The

fibers with 5 ^ 0.2 mg in weight and 0.5 mm in length were

encapsulated in an aluminium pan and heated under a

nitrogen atmosphere at a heating rate of 20 K/min.

The whole relative degree of crystallinity at temperature

T can be fitted by [12]

aðTÞ ¼Xk

i

viaiðTÞ ð3Þ

where k is an integer determined by the number of

crystallization peaks in the DSC curve; vi; the mass fraction

of crystallites formed by sub-process i; thus,Pk

i vi ¼ 1; the

relative degree of crystallinity of sub-process i at tempera-

ture T can be written as

aiðTÞ ¼ 1 2

exp 2K0i

nib

RT2

Edi

exp 2Edi

RT

� �1 2

2RT

Edi

� �" #ni( )

ð4Þ

where K0 is approximate to a constant; Ed; the activation

energy of diffusion of crystallizing segments across the

phase boundary; n; the Avrami exponent, related to the

mechanism of crystallization; b; the heating rate; R; the gas

constant.

3. Results and discussion

3.1. Effects of drawing on crystallization peaks of PET fibers

The crystallization peaks of PET fibers in the DSC curves

are shown in Fig. 1.

Compared with the undrawn fibers, the cold crystal-

lization peaks are broadened and composed of several

overlapped single peaks. The peak at relatively higher

temperatures is sharp and narrow and its area trends to

decrease with increasing draw ratio. The peaks at relatively

lower temperatures are flat and wide and their area trends to

increase with increasing draw ratio. The reasons will be

explained in the following section. Also, it can be found that

the onset temperature at which the crystallization begins to

occur gets down with increasing draw ratio, while the end

temperature at which the crystallization is ceased rises

slightly with increasing draw ratio. The reasons are stated

below. The orientation factors of the samples with draw

ratios of 1, 2.314 and 2.771, determined by using

birefringence method, are 0.049, 0.796 and 0.798, respect-

ively and those, determined by using sonic method, are

0.125, 0.702 and 0.765, respectively. The increase of

orientation factors with increasing draw ratio means that

drawing gives rise to the more ordered structure although

the orientation factors obtained by different methods are

somewhat different. The ordered segments are easily

arranged into the crystal lattice, making the onset tempera-

ture of crystallization shift to lower direction. Generally, the

crystallites formed at relative lower temperature are small

and further crystallization is affected to different extents by

the small crystallites, making the end temperature shift to

higher direction.

The difference in values of orientation factor obtained by

different methods comes from the difference in structure

scale characterized by different methods. The orientation

factor measured by birefringence method is sensitive to the

orientation of segments, but that determined by sonic

velocity method is sensitive to that of whole macromol-

ecules. The segments are shorter than the macromolecules

in length and easier to orient with drawing. Therefore, the

values of orientation factor determined by birefringence

method rise more rapidly than those got by sonic velocity

one in the initial stage with increasing draw ratio.

Fig. 1. DSC non-isothermal crystallization curves of PET fibers at different

draw ratios.

Z. Zhang et al. / Polymer 45 (2004) 4361–43654362

3.2. Parameters of crystallization kinetics

The relative degrees of crystallinity at different tempera-

tures were fitted with Eqs. (3) and (4), as shown in Fig. 2.

The kinetic parameters obtained from the fitting are listed in

Table 1.

It is clearly shown that the oriented PET fibers can

crystallize at relative lower temperatures. And the predicted

curves are consistent with experimental data obtained from

DSC crystallization curves.

3.3. Crystallization mechanism

The crystallization mechanism can be inferred from the

kinetic parameters, such as the Avrami exponent. Generally,

crystallite growth is controlled by a process which occurs at

the crystallite-liquid interface and the front of crystal varies

linearly with time. In the case of the instantaneous

nucleation, the values of the Avrami exponent for one-

dimensional or rodlike growth, two-dimensional or platelike

growth, and three-dimensional growth have been deter-

mined to be 1, 2, and 3, respectively and in the case of the

sporadic nucleation, to be 2, 3, and 4, respectively. The

crystallization process is controlled either by the formation

of the nuclei or by the diffusion of the molecular segments.

If the crystallite growth is controlled by the diffusion of the

molecular segments in the non-crystalline regions, then the

front of crystallite growth should be proportional to

the square root of time [15]. By taking the relation between

crystallite volume and time into account, the physical

significance of the Avrami exponent, n; can be obtained, as

listed in Table 2.

Some experiments have shown that the values of the

Avrami exponent are less than unity [5,16,17] for the cold

crystallization of highly oriented PET fibers. In Table 1, one

of the Avrami exponents is also less than unity that is out of

the range predicted by the mechanism of nucleation-

controlled growth, suggesting the crystallite growth is

controlled by the diffusion of polymer segments. As seen

in Table 1, the values of the Avrami exponent for the first

peak are close to 1.6 which can be denoted to be either the

three-dimensional or two-dimensional growth geometry

since the Avrami exponents can be considered to lie

between the range of 1.5–2.5 or the range of 1–2, as

shown in Table 2. By taking the increase of the area of the

first peak with draw ratio into account, it is impossible that

the spherical entities are formed. Therefore, the three-

dimensional nucleation which is induced by the molecular

orientation or the two-dimensional growth geometry which

is involved in the radial growth of bundle-like entities is the

possible growth mode. The values of the Avrami exponent

for the second peak are equal to or less than 1, suggesting

the one-dimensional growth geometry, that is, the rodlike

entities grow along the direction of molecular chain inferred

in terms of Table 2. The values of the Avrami exponent for

the third peak are close to or less than two, which can be

considered as one of the three growth geometries.

Considering the positions of the peak are consistent with

that of undrawn sample and the mass fractions of the peak

decrease with increasing draw ratio, it is reasonable to

consider that this peak corresponds to the three-dimensional

growth geometry. As to why the sample with draw ratios of

2.771 has lower Avrami exponent than that predicted by

Table 2, it can be explained as the three-dimensional growth

geometry is confined to large extent by the crystallites

formed in the previous two sub-processes.

3.4. Model of crystallization

Based on the mechanism inferred above, we propose a

Fig. 2. The temperature dependence of the relative degree of crystallinity;

the symbols are experimental data; solid lines were predicted by fitting

parameters in terms of Eqs. (3) and (4).

Table 1

Parameters of crystallization kinetics of PET fibers

Samples Ed (kJ/mol) n K0 (min21) v

PET fibers(DRa ¼ 2.314)

Peak 1a 144.5 1.61 4.19 £ 1021 0.12

Peak 2a 115.7 1.00 2.48 £ 1016 0.50

Peak 3a 109.5 2.11 2.95 £ 1014 0.38

PET fibers(DR ¼ 2.771)

Peak 1 144.1 1.55 1.66 £ 1021 0.18

Peak 2 111.3 0.75 4.33 £ 1015 0.62

Peak 3 141.2 1.37 2.20 £ 1018 0.20

a DR refers to draw ratio; peak 1: at relatively low temperature; peak 2: at

middle temperature; peak 3: at relatively high temperature.

Table 2

The physical significance of the Avrami exponent

Growth geometry Instantaneous nucleation Sporadic nucleation

Three-dimensions 3/2 5/2

Two-dimensions 1 2

One-dimension 1/2 3/2

Z. Zhang et al. / Polymer 45 (2004) 4361–4365 4363

model that describes the cold crystallization of the

uniaxially oriented PET fibers, as illustrated in Fig. 3,

where the state (a) denotes the oriented segments,

precursors [18], or mesophase [2], which exists in drawn

PET samples. The state (a) can crystallize into state (b) or

disorient into state (d) under heating scanning. The

transition from (a) to (d) is not a phase change and has

little heat response. The transition from (a) to (b) represents

that the oriented segments develop into a crystallite (three-

dimensional nucleation) or a small nucleus grows in the

radial direction (two-dimensional growth). We refer to this

process as sub-process 1. The Avrami exponent of this

process should be in the range of 1–2.5, which is in

agreement with the values of the Avrami exponent for peak

1. The transition from (b) to (c) corresponds to bundle-like

crystallite growth along the molecular chain direction (one-

dimensional growth). We refer to this process as sub-

process 2. The Avrami exponent for this process should be

in the range of 0.5–1.5, being consistent with the values of

the Avrami exponent for peak 2. The transition from (d) to

(e) corresponds to growth of spheric entities including

folded-chain lamellae (three-dimensional growth). We refer

to this process as sub-process 3. Theoretically, the values of

the Avrami exponent for this process should be in the range

of 1.5–2.5, approximately being consistent with that for

peak 3. The value of the Avrami exponent of the oriented

PET fibers with draw ratios of 2.771 (1.37) is somewhat

lower than the lowest theoretical value for the three-

dimensional growth geometry (1.5). The reason is that

drawing makes the amount of isotropic segments reduce and

the three-dimensional growth of spherulites is blocked by

the preformed entities. The reduction of the dimensional

number of real crystallite growth gives rise to a depression

of the Avrami exponent. The model of crystallization is also

supported by the peak positions, the change of mass fraction

of the peaks with draw ratio, and the rate parameters of

crystallization shown in the next paragraph.

3.5. Crystallization rate constant and activation energy

By assuming that diffusion of polymer segments

predominate over crystallization rate in the DSC heating

process, the crystallization rate constant at temperature T

can be given by [19,20]

KðTÞ ¼ K0 exp 2Ed

RT

� �ð5Þ

which can be estimated in terms of the parameters listed in

Table 1, as shown in Fig. 4.

Compared with the undrawn fibers, the crystallization

rates of sub-processes 1 and 2 are higher than those of

undrawn fibers, while the rates of sub-process 3 are lower

than those of undrawn fibers. It is easily understood that

drawing results in a more ordered structure that can

crystallize in a faster mode. As the temperature rises, the

increase of disorientation or the decrease of the ordered

segments reduces the crystallization rate. The reason that

why the crystallization rate of sub-process 3 is lower than

that of undrawn fibers is that this sub-process is located at

the ending stage of crystallization and considerably affected

by crystallites formed in the previous sub-processes.

The activation energy, Ed; of PET sample in the literature

is widely varied. Several different values of Ed were

reported, such as 58.5–246.6 kJ/mol by Sun et al. [21],

184 kJ/mol by Miller [22], 163.4 kJ/mol by Okui [23],

154.7 kJ/mol by Mayhan et al. [24], 80–86 kJ/mol by Kim

et al. [25], and 96.6–109.7 kJ/mol by Zhang et al. [12]. The

values of Ed for peaks 1 and 2 decrease slightly with

increasing draw ratio, implying that drawing is beneficial to

sub-processes 1 and 2. The values of Ed for peak 3 increase

with increasing draw ratio, suggesting that drawing is

unfavorable to crystallization of sub-process 3. The reason

is that drawing leads to more ordered segments, which are

not beneficial to the crystallization of the isotropic

segments. Therefore, analysis of the crystallization rate

Fig. 3. Illustration of model of cold crystallization of uniaxially oriented

PET fibers; (a) oriented molecular chain segments or precursor; (b) short

bundle-like crystallite; (c) long bundle-like crystallite; (d) random

molecular coil; (e) chain folded crystallite.

Fig. 4. The temperature dependence of crystallization rate constant of

different sub-processes during cold crystallization of PET fibers.

Z. Zhang et al. / Polymer 45 (2004) 4361–43654364

and the activation energy of the crystallization also supports

the model proposed above.

4. Conclusions

Three cold crystallization peaks emerged in the DSC

heating curves of PET fibers and two of them were induced

by the orientation. The values of the Avrami exponent of the

first peak at relatively low temperature are close to 1.6,

those of the second peak, at middle temperature, equal to or

less than 1, and those of the third peak, at relatively high

temperature, close to or less than 2. With increasing draw

ratio, the mass fractions of the first and second peaks

increase, but those of the third peak decrease. The analysis

suggests that the first peak corresponds to the nucleation

procedure induced by the orientation or the two-dimen-

sional growth in the radial direction, the second peak

corresponds to the one-dimensional growth of bundle-like

crystallites along the molecular chain direction, and the

third peak corresponds to the crystallization of isotropic

chain in the confined condition. The results support that the

non-isothermal cold crystallization of uniaxially oriented

PET fibers belongs to the diffusion-controlled growth

process.

Acknowledgements

The authors are grateful for financial support granted by

Tianjin Municipal High Education Commission for the

Developing Fund of Science and Technology.

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