Spherulite growth rates of in situ preparedpoly(propylene terephthalate)/SiO2 nanocomposites

George Z. Papageorgiou • Dimitrios N. Bikiaris •

Dimitris S. Achilias

Received: 30 March 2012 / Accepted: 5 December 2012 / Published online: 24 January 2013

� Akademiai Kiado, Budapest, Hungary 2013

Abstract The spherulite growth rates of in situ prepared

PPT/SiO2 nanocomposites containing 2–5 wt% nano-silica

were studied. Measurements of the spherulite growth rates

were carried out by applying non-isothermal experiments

using polarized light microscopy (PLM). Comparison with

results from isothermal PLM tests showed good agreement.

Isothermal crystallizations after self-nucleation were also

performed using differential scanning calorimetry (DSC)

and the inverse crystallization half-times were estimated.

The Lauritzen–Hoffman analysis was applied by using data

from both isothermal and non-isothermal PLM experiments

and the DSC results. Regimes II–III transition were

observed at critical breakpoint close to 195 �C. The

regimes I–II transition was not so clear, because of the

semi-rigid macromolecular chains of the polymers. Results

using DSC data were in satisfactory agreement to those

using PLM spherulite growth data.

Keywords Crystallization � Silica nanoparticles �Spherulite � Nanocomposites � Poly(propylene

terephthalate) � Poly(trimethylene terephthalate)

Introduction

Poly(propylene terephthalate) (PPT) is a relatively new and

very promising polyester of the family of terephthalates.

PPT is in fact the first and most studied polyester of 1,3-

propanediol (1,3-PDO) and it has already gained its share

in the polymer fibers market [1]. PPT fibers are charac-

terized by much better resilience and stress/recovery

properties compared to poly(ethylene terephthalate) (PET)

and poly(butylene terephthalate) (PBT). PPT chains can be

stretched up to 15 % with a reversible recovery [2].

Recently, polymer nanocomposites gained an increasing

interest from both academic and industrial viewpoint.

The formation of hybrid organic/inorganic nanocomposite

materials results in a synergetic effect of the two respective

components (i.e., polymer matrix and inorganic nanopar-

ticles) in the nanometer scale leading to considerable

improvements of various characteristics of the pristine

organic material such as mechanical, thermal, and gas-

barrier properties [3, 4]. A defining feature of polymer

nanocomposites is that the small size of the fillers leads to a

dramatic increase in interfacial area as compared with

traditional composites. Therefore, a significant volume

fraction of interfacial polymer is created with different

properties from the bulk polymer, even at low nanofiller

loadings [5].

Among the numerous inorganic/organic nanocompos-

ites, those based on polymer/silica are the most commonly

reported in the literature. They have received much atten-

tion in recent years and have been employed in a variety of

applications. Previous studies revealed that fumed silica,

due to its surface hydroxyl groups, can also participate in

some kind of reactions, probably esterification with the

carboxyl end groups of PET, during solid-state polymeri-

sation (SSP), acting as a multifunctional additive [6].

In a previous work from our group, PPT/silica nano-

composites were prepared by the in situ technique [7].

PPT and its nanocomposites form large well observable

spherulites under a polarized light microscope (PLM) and

can be used as key materials for such studies. Thus,

spherulite growth rates, G, of the nanocomposites were

G. Z. Papageorgiou (&) � D. N. Bikiaris � D. S. Achilias (&)

Laboratory of Organic Chemical Technology, Department

of Chemistry, Aristotle University of Thessaloniki,

541 24 Thessaloniki, Macedonia, Greece

e-mail: axilias@chem.auth.gr

123

J Therm Anal Calorim (2013) 114:431–440

DOI 10.1007/s10973-012-2872-7

estimated here by performing a detailed study of crystal-

lization from the melt on cooling at different cooling rates.

Generally, faster cooling allows G to be measured over a

wider range of crystallization temperatures, Tc, whereas

slower cooling allows G to be measured only at higher Tc.

Non-isothermal experiments allow estimation of the

spherulite growth rates over an expanded temperature

range by applying a fast procedure, instead of time con-

suming isothermal experiments which also are usually

limited at higher temperatures only. However, the validity

of the cooling method has to be carefully checked. So,

isothermal PLM tests were also performed at the same

temperature range as for non-isothermal experiments for

comparison. Finally, data from the overall isothermal

crystallization rates after self-nucleation were obtained

from a series of DSC experiments. The main objective of

this study was to evaluate and compare data obtained from

non-isothermal PLM, isothermal PLM experiments, and

isothermal DSC studies and calculate the Lauritzen–Hoff-

man parameters.

Theoretical background

It has been suggested that the kinetic data of isothermal

polymer crystallization can be analyzed using the spheru-

litic growth rate in the context of the Lauritzen–Hoffman

secondary nucleation theory [8, 9]. Accordingly, the

growth rate G is given as a function of the crystallization

temperature, Tc by the following bi-exponential equation

[8, 9]:

G ¼ G0 exp � U�

RðTc � T1Þ

� �exp � Kg

TcðDTÞf

� �; ð1Þ

where G0 is the pre-exponential factor, the first exponential

term contains the contribution of diffusion process to

the growth rate, while the second exponential term is the

contribution of the nucleation process; U* denotes the

activation energy which characterizes molecular diffusion

across the interfacial boundary between melt and crystals

and T? is the temperature below which diffusion stops.

Kg is a nucleation constant and DT denotes the degree of

undercooling ðDT ¼ T�m � TcÞ; f is a correction factor

which is close to unity at high temperatures and is given as

f ¼ 2Tc=ðT�m þ TcÞ:The growth rate (G) of spherulites is usually determined

before they impinge on each other by measuring the

spherulitic radii (r) from PLM micrographs that are

obtained at time (t) intervals during the isothermal crys-

tallization. At a specific temperature, the plot of spherulite

radius (r) versus isothermal time (t) is linear and the slope

G can be expressed as

G ¼ dr

dt: ð2Þ

However, isothermal measurements of spherulite growth

rates are time consuming, thus it would be better to

perform non-isothermal experiments. When a polymer melt

is cooled at a constant cooling rate (dT/dt), G can be

estimated by taking the first derivative (dr/dT) of r versus T

(temperature) at each temperature (or data point) [10]

G ¼ dr

dt¼ dr

dT

dT

dt: ð3Þ

Combining self-nucleation and non-isothermal tempera-

ture programs extends the range of temperatures over

which the growth rate can be measured.

Furthermore, it has been suggested that self-nucleation

can be combined with isothermal DSC crystallization tests,

and thus the inverse of isothermal half-times obtained from

such a procedure can also be used to approximate crys-

tallization rates replacing the spherulite growth rates in the

LH equation assuming that G & 1/t1/2 [11–13].

Experimental

Materials

Terephthalic acid (TPA) was obtained from Fluka (purity

99 %). 1,3-PDO was kindly supplied by Du Pont de

Nemours Co., Wilmington, DE. Tetrabutyl titanate (TBT)

catalyst of analytical grade and triphenylphosphate (TPP)

used as heat stabilizer were purchased from Aldrich.

Hydrophobic fumed silica (SiO2) in the form of spherical

nanoparticles, under the trade name AEROSIL� R974 was

supplied from Degussa AG (Hanau, Germany).

Preparation of the PPT/SiO2 nanocomposites by in situ

polymerization

PPT was prepared by the two-stage melt polycondensation

method (esterification and polycondensation) in a glass

batch reactor following the well-known method for poly-

ester preparation in two steps [7]. Proper amounts of TPA

and 1,3-PDO (molar ratio 1:1.2) and Ti(OBu)4 catalyst

(5 9 10-4 mol of tetrabutoxytitanium per mol of acid)

were charged into a 250-cm3 round-bottom flask of the

polycondensation apparatus. The apparatus with the

reagents was evacuated several times and filled with argon

in order to remove all oxygen. Thereupon, the mixture was

heated under a nitrogen atmosphere for 3 h at 260 �C under

constant stirring (350 rpm) and water was removed by

distillation as the reaction by-product of esterification and

collected in a graduated cylinder. In the second step of

432 G. Z. Papageorgiou et al.

123

polycondensation, TPP was added (5 9 10-4 mol TPP/mol

TPA), and vacuum (5.0 Pa) was applied slowly over a

period of time of about 30 min, to avoid excessive foaming

and to minimize oligomer sublimation. The temperature

was maintained also at 260 �C, while fresh catalyst of the

same as above quantity was added. The polycondensation

continued for about 90 min. Finally, the synthesized sam-

ple was ground in grind-mill, washed with methanol, and

dried in vacuum at 50 �C for 24 h.

For the in situ synthesis of PPT/SiO2 nanocomposites,

the same procedure was used but prior to the addition of

TPA the proper amount of SiO2 nanoparticle was added

and dispersed by ultrasonic vibration (50 W, Hielscher

UP50H) for 20 min in 1,3-PDO. The right mass of TPA

was then added and the aforementioned polycondensation

method was followed for the in situ synthesis of nano-

composites. Three different nanocomposites were prepared

containing 2, 3.5, and 5 wt% SiO2.

Characterization

Intrinsic viscosity (IV) measurement

Intrinsic viscosity measurements on the isolated polymers

were performed using an Ubbelohde viscometer cap. Oc at

25 �C in chloroform at a solution concentration of 1 wt%.

Details about molecular mass calculation can be found in

Ref. [7].

Differential scanning calorimetry (DSC)

Thermal behavior of the polymers was studied using a

Perkin-Elmer Pyris Diamond DSC differential scanning

calorimeter. A Perkin-Elmer Intracooler II was used to

allow the DSC to achieve high and constant cooling rates.

The instrument was calibrated with high purity standards.

Samples of about 5 mg were used. It is important for the

crystallization experiments to minimize the thermal lag,

so low mass samples should be used in crystallization tests.

For isothermal crystallization tests, the samples were first

melted to 280 �C for 3 min to erase any previous thermal

history and then cooled to the crystallization temperature

(Tc) at a rate 200 �C min-1. The samples were held at Tc

till the end of crystallization.

Isothermal crystallization experiments were also per-

formed after self-nucleation of the polyester sample. Self-

nucleation measurements were performed in analogy to the

procedure described by Fillon et al. [13] and Muller et al.

[14, 15].

The protocol used is very similar with that described in

our previous work [16] and can be summarized as follows:

(1) melting of the sample at 280 �C for 3 min in order to

erase any previous thermal history; (2) subsequent cooling

at a rate of 10 �C min-1 to 100 �C, which creates a

‘‘standard’’ thermal history; (3) partial melting by heating

at 10 �C min-1 up to a ‘‘self-nucleation temperature’’, Ts;

(4) thermal conditioning at Ts for 5 min. Depending on Ts,

the crystalline polyester domains will be completely mol-

ten, only self-nucleated or self-nucleated and annealed. If

Ts is sufficiently high, no self-nuclei or crystal fragments

can remain and the sample is then in the so-called domain

I, the complete melting domain. At intermediate Ts values,

the sample is almost completely molten, but some small

crystal fragments or crystal memory effects remain, which

can act as self-nuclei during a subsequent cooling from Ts

and the sample is said to be in domain II, the self-nucle-

ation domain. Finally, if Ts is too low, the crystals will only

be partially molten, and the remaining crystals will

undergo annealing during the 5 min at Ts, while the molten

crystals will be self-nucleated during the later cooling,

and the sample is in domain III, the self-nucleation

and annealing domain; (5) cooling scan from Ts at

200 �C min-1 to the crystallization temperature (Tc),

where the effects of the previous thermal treatment

will be reflected on crystallization; (6) heating scan at

20 �C min-1 to 280 �C, where the effects of the thermal

history will be apparent on the melting signal. Experiments

were performed to check that the sample did not crystallize

during the cooling to Tc and that a full crystallization

exotherm was recorded at Tc. After all, for the PPT nano-

composites of the work, it was concluded that Ts is 226 �C.

Polarizing light microscopy (PLM)

A polarizing light microscope (Nikon, Optiphot-2) equip-

ped with a Linkam THMS 600 heating stage, a Linkam TP

91 control unit and also a Jenoptic ProgRes C10 plus

camera with the Capture Pro 2.1 software was used for

PLM observations. Spherulite growth rates were measured

on freshly made films. The specimens were prepared by

placing a small amount of the polymer or nanocomposite

on a thin circular cover glass and by placing another cir-

cular cover glass on top of the material. This sandwich was

slid onto the heating stage and heated from room temper-

ature to 280 �C. A thin film was then obtained by applying

Table 1 Intrinsic viscosity, average molecular mass, insoluble con-

tent, and equilibrium melting temperature of the PPT/SiO2

nanocomposites

Sample [n]/dL g-1 Mn/Da Insoluble

content/wt%

T�m/�C

PPT 0.72 34,337 – 263.0

PPT/SiO2 2 wt% 0.70 32,623 – 276.3

PPT/SiO2 3.5 wt% 0.60 26,104 1.2 277.5

PPT/SiO2 5 wt% 0.63 28,257 7.12 278.4

Spherulite growth rates 433

123

a slight pressure on the top cover glass. Next, the specimen

was first cooled, and then heated from room temperature at

90 �C min-1 to 280 �C, at which temperature it was

maintained for 3 min to melt the crystalline residues.

In the isothermal experiments, the pre-molten specimen

of the material was cooled rapidly (90 �C min-1) to the

required isothermal crystallization temperature ranging

from 170 to 225 �C. After the heating stage reached ther-

mal equilibrium and the radius of the spherulite was larger

than 10 lm, the development of the spherulites was

recorded as a function of time during crystallization.

The growth rates of numerous spherulites in each

specimen were investigated. To save time, self-nucleation

and non-isothermal programs were combined. The pre-

molten specimen was cooled down rapidly from 250 to

190 �C, held till the radius of the spherulite was larger than

10 lm, then heated at 90 �C min-1 to 225 �C and held for

another 10 min to obtain an adequate size of spherulites.

Next, a scan from 225 to 165 �C or till spherulite

impingement at a pre-determined cooling rate was recorded

for subsequent analysis.

Results and discussion

Molecular and thermal properties

of the nanocomposites

During the formation of the PPT/SiO2 nanocomposites,

fumed silica, due to its surface hydroxyl groups, can par-

ticipate in some kind of reactions, probably esterification

with the carboxyl end groups of PPT acting as a multi-

functional additive. In fact dissolution of the nanocom-

posites in a phenol/tetrachloroethane 60/40 mixture was

tested and non-dissolved residue appeared only in case of

the higher concentrations (Table 1).

The thermal transitions of the nanocomposite were

studied using DSC. As one can see in Fig. 1a for PPT/SiO2

2 % on heating at 20 �C min-1, the particular nanocom-

posite shows a glass transition temperature of 47 �C, but

the rest samples showed negligible differences in Tg. In the

melting traces of Fig. 1b for samples crystallized at various

temperatures two melting peaks appear. However, in cases

of crystallization at even lower temperatures, in the heating

trace a low temperature melting peak, the annealing peak,

appears. The middle endothermic peak (peak I of Fig. 1a)

1 W g–1

2 % Silica

Nor

mal

ized

hea

t flo

w (

endo

up)

Temperature/°C–50 0 50 100 150 200 250

180 190 200 210 220 230 240

2 W g–1

PPT/SiO2 2 %

200 °C

196 °C

192 °C

188 °C

184 °C

Nor

mal

ized

hea

t flo

w (

endo

up)

Temperature/°C

a

b

Fig. 1 a DSC heating scan of quenched PPT/SiO2 2 wt% nanocom-

posite at 20 �C min-1. b DSC heating scans of PPT/SiO2 2 wt%

nanocomposite samples after isothermal crystallization at different

temperatures

4.0

4.4

4.8

5.2

5.6

6.0a

Tm

o = 272 °

°

°

°

°

C; βm = 1.04; a = 1.12

Tm

o = 274 C; βm = 1.02; a = 1.12

Tm

o = 276.5 C; βm = 1.00; a = 1.12

Tm

o = 278 C; βm = 0.99; a = 1.12

Tm

o = 282 C; βm = 0.96; a = 1.11

M

X2.8 3.2 3.6 4.0 4.4 4.8

180 200 220 240 260 280 300180

200

220

240

260

280

300b

Tm

o

LHW= 241.1 °C

Tm

o

NLHW= 276.5 °C

Mel

ting

poin

t/°C

Crystallization temperature/°C

Experimental LHW NLHWTm = Tc

Fig. 2 a M ¼ T�m=ðT�m � TmÞ, X ¼ T�m=ðT�m � TcÞ plots for PPT/SiO2

2 wt% nanocomposite for obtaining the equilibrium melting point by

applying the nonlinear Hoffman–Weeks method and b linear and

nonlinear Hoffman–Weeks plots

434 G. Z. Papageorgiou et al.

123

corresponding to the melting of the primary crystals gen-

erated during the isothermal stage, appears at increasing

temperature with increasing silica content.

The equilibrium melting temperature (T�m) of a polymer

is usually estimated using the Hoffman–Weeks extrapola-

tion [17]. In this procedure, the measured Tms of specimens

crystallized at different crystallization temperatures (Tcs)

are plotted against Tc and a linear extrapolation to the line

Tm = Tc, and the intercept gives T�m. In the Hoffman–

Weeks equation [18]

Tm ¼ T�m 1� 1

2b

� �þ Tc

2b; ð4Þ

Tm is the observed melting temperature of a crystal formed

at a temperature Tc, b is the thickening equal to Lc/Lc* b

indicates the ratio of the thickness of the mature crystallites

Lc to that of the initial ones Lc* [18]. The prerequisite for the

application of this theory is the isothermal thickening

process of lamellar crystals at a specific crystallization

temperature and the dependence of the thickening coeffi-

cient on the crystallization temperature.

A new extrapolative procedure to determine the T�m value

of a semi-crystalline polymer based on the observed Tm - Tc

data in which the observed Tm data is taken from samples

crystallized at different temperatures but with the same

lamellar thickening coefficient has recently been reported [19,

20]. The new mathematical derivation is based on the Gibbs–

Thomson equation [8, 21] and on the proposition of Lauritzen

and Passaglia [22] on stem length fluctuation during chain

folding. This method states a relationship between the

observed melting temperature and the corresponding crys-

tallization temperature. This equation is hereafter called the

nonlinear Hoffmann–Weeks extrapolation, and is given in the

form

T�mT�m � Tm

¼ bm r1e

rGTe

T�mT�m � Tc

þ D2DH�f2r1

e

� �; ð5Þ

where bm is the thickening coefficient, rGTe is the basal

interfacial free energy associated with nuclei of critical size

including the extra lateral surface energy due to fold pro-

trusion and the mixing entropy associated with stems of

different lengths (rGTe is the basal interfacial free energy

from the Gibbs–Thomson equation [8, 21]), r1e is the

interfacial energy associated with the formation of the

basal plane of the initial crystals which can be estimated

from the slope of a plot of the lamellar thickness versus the

inverse degree of undercooling (i.e. Lc* versus DT-1), D2 is

a constant, and all other parameters are the same as pre-

viously defined. It is worth noting that, for most cases, it is

safe to assume that r1e& rGT

e [19].

The above equation can take a simpler form

M ¼ bm r1e

rGTe

ðX þ aÞ ð6Þ

where

M ¼ T�mT�m � Tm

and X ¼ T�mT�m � Tc

: ð7Þ

In order to apply Eq. (6) to analyze the observed Tm-Tc

data in real polymer systems, it is required that the

observed Tm data be collected from samples crystallized at

various Tc’s but having the same lamellar thickening

coefficient bm for each set of the observed Tm - Tc data,

corresponding values of M and X in Eq. (6) can be

Fig. 3 Pictures of PPT/SiO2 2 wt% taken on

cooling at 10 �C min-1: a 220 �C, b 210 �C,

c 200 �C, d 190 �C

Spherulite growth rates 435

123

calculated for a given choice of T�m value. In the case where

r1e � rGT

e ; the ‘‘actual’’ equilibrium melting temperature

T�m is taken as the seed T�m value which results in the plot of

M versus X being a straight line with slope of unity (i.e.,

b = 1) and the intercept of a (i.e., a ¼ D2DH�f

2r1e

).

As was reported in previous papers for PPT, the middle

temperature melting peak is because of melting of original

crystals formed during the isothermal crystallization stage

[23, 24]. The Hoffman–Weeks plots for the nanocomposite

were constructed using the middle melting peak tempera-

tures against the crystallization temperature.

Figure 2a shows the evolution of the M versus X plots

for different choices of seed T�m value for the PPT/SiO2

2 wt% nanocomposite. According to the NLHW proce-

dure, the T�m values for neat PPT was evaluated to be ca.

276.1 �C while for the PPT/SiO2 2 wt% nanocomposite it

was found to be 276.5 �C. For the rest materials, the cal-

culated values were also very close. The T�m value for PPT

based on the NLHW procedure has previously been

reported to be ca. 273 �C [23] and 277.6 �C [24].

As was reported in previous papers for PPT, the middle

temperature melting peak is because of melting of original

crystals formed during the isothermal crystallization stage.

The Hoffman–Weeks plots for neat PPT and the nano-

composites were constructed using the middle melting

peak temperatures against the crystallization temperature.

Estimation of the spherulite growth rates using PLM

measurements

As was reported in the ‘‘Experimental’’ section, a series of

cooling experiments, after self-nucleation, were performed

during the PLM study. Photos illustrated in Fig. 3 show the

increase of the spherulites diameter of a PPT/silica 2 wt%

nanocomposite sample during cooling at 10 �C min-1.

Analysis of non-isothermal crystallization from the melt

should be performed with great care since thermal gradi-

ents within the sample and between the cooling furnace and

the sample can cause problems in monitoring of the true

sample temperature. Moreover, solidification is an exo-

thermic process, and the heat evolved during the phase

transition may cause some local heating and create addi-

tional thermal gradients within the sample, especially at

very high cooling rates. To minimize thermal lag the

samples used in this study were thinner than 10 lm.

In this non-isothermal procedure, spherulite radii were

measured during cooling from the melt at various scanning

rates to obtain G by monitoring the growth of r as a

function of temperature (T). Then, dr/dT was estimated

from the first derivative of the r versus T plot and the

growth rate from Eq. (3). dT/dt is the cooling rate as the

spherulite growth front advances [10–12].

The plots of radius versus temperature for each cooling

rate were constructed for each material. A function was

used to fit each data set as can be seen in Fig. 4a for the

PPT/SiO2 3.5 wt% nanocomposite. The derivative of the

function with reference to temperature (dr/dT) was then

obtained (Fig. 4b). This was then multiplied with the cor-

responding cooling rate (dT/dt, negative value) to result in

the growth rate for the given cooling rate (Fig. 5). The

0

50

100

150

200

250

300a

r/m

Temperature/°C

1 C min–1

3 C min–1

5 C min–1

10 C min–1

20 C min–1

170 180 190 200 210 220 230

170 180 190 200 210 220 230

–40

–30

–20

–10

0b

(dr/

dT)/

m °

C–1

Temperature/°C

1 °

°

°°

°°

°°

°°

C min–1

3 C min–1

5 C min–1

10 C min–1

20 C min–1

Fig. 4 Plots of spherulite radius versus temperature (a) and

dr/dT versus temperature (b) for PPT/SiO2 3.5 wt% nanocomposite

on cooling at different cooling rates

170 180 190 200 210 220 230

0

50

100

150

200

250

(dr/

dT)

(dT

/dt)

/m

min

–1

Temperature/°C

1 °°

°°

°

C min–1

3 C min–1

5 C min–1

10 C min–1

20 C min–1

Fig. 5 Spherulite growth rates obtained from experiments at various

cooling rates for PPT/SiO2 3.5 wt% nanocomposite

436 G. Z. Papageorgiou et al.

123

resulting growth rates match well. In any case, the average

values were finally used for fast cooling rates and low

temperatures where some small scatter was observed.

In parallel, isothermal PLM study was also performed.

Figure 6 shows PLM photos PPT/SiO2 2 wt% nanocompos-

ite, taken at different times during isothermal crystallization at

200 �C. The growth rate of spherulites at given temperature

was determined before their impingement by measuring the

spherulitic radii taken at intervals during the isothermal

crystallization. Spherulite growth rates, G, were measured as

slopes of the plots of the growing spherulite radius, r, versus

crystallization time, t, for various temperatures in the range of

175–225 �C. This was also the temperature range of interest in

non-isothermal experiments.

Figure 7 shows the spherulite growth rates for the PPT/

SiO2 2 wt% nanocomposite, measured under isothermal

and non-isothermal crystallization conditions. It should be

notified that the growth rates measured from cooling

experiments are in good agreement with those measured

under isothermal conditions for all the materials tested in

this study. It should be noticed here that similar results

with good agreement between isothermal and non-

isothermal measurements of the spherulite growth rates

determined for the poly(L-lactic acid) have been presented

by di Lorenzo [25].

Estimation of the L–H parameters using spherulite

growth rates

The above data were analyzed using the spherulitic growth

rate in the context of the Lauritzen–Hoffman secondary

nucleation theory presented in the theoretical background

Fig. 6 Pictures showing the spherulite growth

during isothermal crystallization of PPT/SiO2

2 wt% nanocomposite at 200 �C: a 30 s, b 90 s,

c 150 s, d 210 s

170 180 190 200 210 220 230

0.0

5.0x10–5

1.0x10–4

1.5x10–4

2.0x10–4

2.5x10–4

G/c

m s

ec–1

Temperature/°C

Isothermal Non–isothermal

Fig. 7 Spherulites growth rates obtained from isothermal and non-

isothermal experiments

2.0 x 10–5 2.5 x 10–5 3.0 x 10–5 3.5 x 10–5 4.0 x 10–5 4.5 x 10–5–14

–12

–10

–8

–6

–4

–2ln

( G)

+ 1

500/

[R(T

c-T

oo)]

1/(Tc T f )D

Fig. 8 Lauritzen–Hoffman plots using data from non-isothermal

PLM experiments for the PPT/SiO2 2 wt% nanocomposite

Spherulite growth rates 437

123

part [8, 9]. The nucleation parameter, Kg, is usually cal-

culated from Eq. (1) using the double logarithmic

transformation

lnðGÞ þ U�

RðTc � T1Þ¼ lnðG0Þ �

Kg

TcðDTÞf : ð8Þ

Plotting the left hand side of Eq. (8) with respect to

1/(Tc(DT)f) a straight line should appear having a slope

equal to Kg. Critical break points, identified by the change

in the slope of the line, when appear in such a plot,

have been attributed to regime transitions accompanied by

morphological changes of the crystals formed (i.e., change

from axialite-like to banded spherulite and non-banded

spherulite morphology).

Usually, the empirical ‘‘universal’’ value of U* =

6,280 J mol-1 (1,500 cal mol-1) is used and also the value

T? = Tg - 30 [8].

Growth of crystals can occur in different regimes,

depending on temperature [8]. At high temperatures (low

undercooling), formation of a surface secondary nucleus is

followed by rapid completion of the substrate. This situa-

tion is referred to as regime I. At lower temperatures, in

regime II, multiple surface nuclei form on the substrate and

spread out slowly. At even lower temperatures, when

solidification takes place in regime III, surface nuclei form

in such a large number that the distance between two nuclei

approximates the width of a stem. Regime III growth is

associated with a situation in which the frequency of sec-

ondary nucleation exceeds the rate of lateral spreading.

Thermodynamically, the rate of lateral growth should be

higher than the rate of attachment of a nucleus on the

growing surface, because of the lower energy penalty

associated with attachment to a niche on the crystal sur-

face. The general understanding is that in regime III, which

occurs at temperatures lower than regimes I and II, the

mobility of polymer chains is low.

Figure 8 shows the LH plots for PPT/SiO2 2 wt%

nanocomposites and for each case of T�m values, using data

for spherulite growth rates from cooling experiments.

Similar plots were obtained using data from isothermal

experiments.

For a secondary or heterogeneous nucleation, Kg can be

calculated from [8, 9]

Kg ¼nrreb0T�mDhfqckB

; ð9Þ

where n is a constant equal to 4 for regimes I and III and 2 for

regime II, r, re are the side surface (lateral) and fold surface

(end) free energies which measure the work required to

create a new surface, b0 is the single layer thickness,

Dhfqc = DHf is the enthalpy of melting per unit volume and

kB is the Boltzmann constant (kB = 1.38 9 10-23 J K-1).

For PPT, DH�f ¼ 28:8 kJ mol�1; q = 1.448 g cm-3, and

b0 = 0.571 nm [26].

The lateral free energy, r, can be calculated using the

empirical equation of Thomas–Stavely [27]:

r ¼ aðDHfÞða0b0Þ1=2 ð10Þ

where a0 and b0 are the molecular width and the molecular

thickness, respectively.

Hoffman has also introduced the equation [28]:

r ¼ DHfða0=2Þð1=C1Þ ð11Þ

where a0 is the molecular width (0.4637 nm for PPT),

C? is the characteristic ratio describing the unperturbed

dimension of a polymer chain.

For PPT, r, has been found to be 19.2 erg cm-2 using

the latter procedure [29]. This value was adopted in this

study.

Finally, the work of chain folding can be obtained

directly from the fold surface free energy as [8]:

q ¼ 2rea0b0 ð12Þ

q is defined as the work for chain folding by bending the

polymer chain back upon itself in the appropriate config-

uration that has been found to be a parameter most closely

correlated with molecular structure, i.e., the inherent

stiffness of the chain itself.

From Fig. 8, regime transitions were observed as critical

breakpoints close to 195 �C (regimes II–III transition).

There was also some indication for a regimes I–II transition

at about 216 �C in accordance to findings from earlier

works for neat PPT. The above analysis resulted in the

values of KgI, KgII, KgIII, rre, re, and q which are sum-

marized for non-isothermal and isothermal experiments in

case of the PPT/SiO2 2 wt% nanocomposite in Table 2.

Table 2 Results of Lauritzen–Hoffman analysis using data from non-isothermal, isothermal PLM experiments, and DSC experiments after self-

nucleation of the samples

Data T�m/oC KgIII 9 10-5/K2 KgII 9 10-5/K2 rrea/erg2 cm-4 r/erg cm-2 re/erg cm-2 q/kcal mol-1

Non-iso PLM 276.5 6.82 3.43 1,487.4 19.2 77.5 5.9

Iso PLM 276.5 6.71 3.28 1,466.4 19.2 78.4 6.0

DSC 276.5 7.25 3.68 1,400.5 19.2 72.9 5.6

a Calculated from KgII

438 G. Z. Papageorgiou et al.

123

The KgIII/KgII ratio was close to the theoretical value 2. The

KgII/KgI ratio was much lower. In fact for polymers like

PPT, having a semi-rigid backbone a regime I crystalliza-

tion is rather not anticipated. Results for the rest materials

were similar, so they are not presented in detail here for

briefness.

Estimation of the L–H parameters using DSC

measurements

The self-nucleation procedure described in the ‘‘Experi-

mental’’ section was also applied to obtain results for the

inverse of the isothermal crystallization half-times from

DSC experiments for all the samples and over almost the

whole temperature range of interest. These data were also

used in place of the spherulite growth rates and the LH

analysis was applied. Figure 9a shows the variation of

isothermal crystallization half-times with temperature for

the PPT/SiO2 2 wt% nanocomposite and Fig. 9b shows the

respective Lauritzen–Hoffman plots. The results of the LH

analysis are summarized in Table 2.

Results for Kg and also rre, re, and q are lower than the

respective values for PET (for example q = 10 kcal -

mol-1), but larger than those for PBT (q = 5 kcal mol-1)

and close to those reported for PPT in earlier works

(Kg = 3.5–8.4 9 105 K2, rre = 1,561–1,897 erg2 cm-4,

re = 81.3–98.8 erg cm-2, q = 6.2–7.5 kcal mol-1) [29–31].

Conclusions

Spherulitic morphology and crystallization rates of in situ

prepared PPT/SiO2 nanocomposites containing 2–5 wt%

inorganic nanofiller were studied. The equilibrium melting

points were estimated with the linear and nonlinear

Hoffman-Weeks methods. A significant difference was

observed between the respective values. For example the

difference was of about 35.4 �C, for the PPT/SiO2 2 wt%

nanocomposite since T�m NLHW was found 276.5 �C and that

from the linear extrapolation was T�m LHW ¼ 241:1 �C: A

new method for obtaining the spherulite growth rates from

cooling experiments was tested. The spherulite growth

rates of the nanocomposite measured from non-isothermal

experiments using PLM were in agreement with results

from isothermal PLM growth measurements. A third

method, involving isothermal crystallization after self-

nucleation using DSC, was also tested. In the latter case,

the inverse crystallization half-times were estimated as a

measure of crystallization rate. The Lauritzen–Hoffman

analysis was applied by using data sets from all the three

methods. Critical breakpoints were observed at about

195 �C (regimes II–III transition).

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