crystal structure, melting behaviour and equilibrium melting point of star polyesters with...

Crystal structure, melting behaviour and equilibrium melting point of star

polyesters with crystallisable poly(1-caprolactone) arms

E. Nuneza, C. Ferrandoa, E. Malmstroma, H. Claessona, P.-E. Wernerb, U.W. Geddea,*

aDepartment of Fibre and Polymer Technology, Royal Institute of Technology, SE-100 44 Stockholm, SwedenbDepartment of Inorganic, Physical and Structural Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden

Received 12 June 2003; received in revised form 1 March 2004; accepted 3 May 2004

Available online 11 June 2004

Abstract

Star polymers consisting of poly(1-caprolactone), PCL, attached to third generation dendrimer, hyperbranched and dendron cores have

been studied by differential scanning calorimetry and wide-angle X-ray scattering. The degree of polymerisation of the PCL arms of the star

polymers ranged from 14 to 81. The crystal unit cell was the same for the star polymers as for their linear PCL analogues. The star polymers

showed a lower degree of crystallinity than the linear PCL, suggesting that the dendritic cores imposed restriction on PCL crystallisation.

Slow heating of rapidly cooled samples led to crystal rearrangement—a gradual increase in melting point with decreasing heating rate and

recrystallisation followed by additional high temperature melting. The tendency for crystal rearrangement was less pronounced in star

polymers based on dendrimer or hyperbranched cores, suggesting that the dendritic cores constitute an obstacle to crystal rearrangement. The

star polymers showed higher equilibrium melting points than the linear PCL analogues. It is suggested that covalent attachment of the PCL

arms to the dendritic core reduced the positional freedom and the entropy of the melt with respect to that of linear PCL.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Star polymer; Poly(1-caprolactone); Equilibrium melting point

1. Introduction

A star polymer consists of a central core linking together

three or more linear polymer chains. The core, as in the

present study, can be a dendritic molecule based on an ABx

ðx $ 2Þ monomer to which linear polymer chains are

attached. The core may, depending on the method of

synthesis, be a dendrimer (monodisperse) or hyperbranched

polymer with vacancies in the branching. The high degree of

branching prohibits crystallisation of the core moieties. The

attachment of regular linear units, such as poly(1-capro-

lactone) (PCL), to the fully amorphous, dendritic core

molecule makes the polymer semicrystalline [1]. The

attachment of the crystallisable units to the rigid, non-

crystallisable core is expected to have profound effects on

their crystallisation and on the crystalline morphology. This

paper, which is the first of a series, reports the effect of the

molecular architecture on the crystal unit cell structure, the

melting behaviour and the equilibrium melting point. Most

studies [2–5] on semicrystalline star polymers have

reported only ‘kinetic’ melting points without any attempt

to assess the equilibrium melting point. Risch et al. [6],

however, reported that the equilibrium melting point of star-

branched polyamide-6 of finite molar mass decreased with

increasing branch-point functionality, and attributed this to

a lower enthalpy of fusion of the star-branched polymers.

Linear PCL is a highly crystalline polymer. Thermodyn-

amic data relating to the fusion of linear PCL were reported

by Crescenzi et al. [7]: the heat of fusion at the equilibrium

melting points was determined to 135 J g21 and the

equilibrium melting point of high molar mass linear PCL

by the diluent method to 336 K. The most extensive studies

on the crystallization and melting behaviour of linear PCL

are due to Phillips et al. [8,9]. They reported equilibrium

melting point data obtained by the Hoffman–Weeks method

in the range 341–343.5 K depending on molar mass (7000–

40,000 g mol21), spherulite growth rate data obeying a

single crystallization regime (Regime II) according to the

Lauritzen–Hoffman theory and yielding a fold surface free

energy of ,90 mJ m22 and isothermal data on crystal

thickening. Strobl et al. [10] recorded the small-angle X-ray

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

doi:10.1016/j.polymer.2004.05.047

Polymer 45 (2004) 5251–5263

www.elsevier.com/locate/polymer

* Corresponding author. Tel.: þ46-8-790-7640; fax: þ46-8-208-856.

E-mail address: [email protected] (U.W. Gedde).

http://www.elsevier.com/locate/polymer

scattering pattern during isothermal crystallization and at a

later stage during melting of the isothermally crystallized

samples. They found for a linear PCL with a molar mass of

42,000 g mol21, as they did for a few other polymers

(syndiotactic PP, PE), that the intersection of melting point

vs. (crystal thickness)21 and crystallization temperature vs.

(crystal thickness)21 appeared at a finite crystal thickness

and not as expected at near-infinite crystal thickness.

Extrapolation of the melting point data presented by Strobl

et al. [10] according to the Thomson–Gibbs equation

yielded an equilibrium melting point near 370 K. It should

be pointed out that the extrapolation range was very long

and that the data used for extrapolation covered only a

narrow crystal thickness range. The slope coefficient of the

melting point-reciprocal crystal thickness data presented by

the Strobl group yielded a very low fold surface free energy

ðsÞ; ,60 mJ m22. Melting point-reciprocal crystal thick-

ness data for polyethylene were presented in the same paper

and surprisingly even these corresponded to

s < 60 mJ m22, which is significantly less than the

established value, ,90 mJ m2 [11]. The Strobl group

reported in their paper [10] that no isothermal crystal

thickening occurred during crystallization and that crystal

thickening occurred only during the final stages of melting.

The crystal thickening occurring during the slow heating

used was particularly strong effect for crystals grown at

temperatures below 313 K. Nojima et al. [12] reported for a

linear PCL (degree of polymerisation < 60) a maximum

30% increase in the long period during 2 K min21 heating

from the crystallization temperature (310–319 K) to the

melting point. Phillips et al. [9] found that the melting point

increased with the logarithm of the crystallization time

according to an S-shaped curve. Crystal thickness data

calculated from melting point data using the Thomson–

Gibbs equation taken for samples crystallized at different

temperatures could be shifted along the logarithmic time

axis to obtain a master curve; the temperature dependence of

the shift factor followed the Arrhenius equation. The

heating rate used by Phillips et al. was 10 K min21 which

was higher than that used by Strobl et al.

The crystal unit cell of linear PCL resembles to some

extent that of polyethylene: the lateral packing of the chains

is very similar and the sub-cell is orthorhombic with the

space group P212121 [13,14]. Chatani et al. [13] was the first

to determine the crystal structure by X-ray diffraction of

stretched films after annealing: a ¼ 0:747 nm,

b ¼ 0:498 nm, and c ¼ 1:705 nm (orthorhombic sub-cell).

These values refer to the cell dimension at room

temperature. The crystalline stem was assumed to be

twisted slightly to account for the c spacing obtained.

Bittiger et al. [14] reported for linear PCL an orthorhombic

sub-cell with the dimensions a ¼ 0:7496 nm,

b ¼ 0:4974 nm, and c ¼ 1:7297 nm (room temperature).

They proposed that the chain conformation of the crystalline

stem was all-trans with two repeating units included in the

sub-cell along c: Later work by Hu and Dorset [15] using

electron diffraction showed that the crystalline stem had to

be twisted slightly along c: The dimensions of the

orthorhombic cell at room temperature was according to

this study: a ¼ 0:748 nm, b ¼ 0:498 nm, and c ¼ 1:726 nm.

The equilibrium melting point of a polymer is seldom

measured directly, because chain folding limits the crystal

thickness and the experimental melting points are much

lower than that of the equilibrium crystal. The equilibrium

melting point can however be determined, although often

with considerable uncertainty, by suitable extrapolation of

experimental data. The Thomson–Gibbs equation can be

used to extrapolate accurately taken melting point data of

polymers with known crystal thicknesses to infinite crystal

thickness in order to obtain the equilibrium melting point

[16]. The Hoffman–Weeks method [17] determines the

equilibrium melting point by linear extrapolation of Tm ¼

f ðTcÞ data to Tm ¼ Tc: The method is strictly applicable only

to a series of samples with crystals of a certain constant

crystal-thickening factor. Strobl et al. [10] raised serious

doubts about the validity of the Hoffman–Weeks method by

showing that the extrapolated equality Tm ¼ Tc occurred at

a finite crystal thickness of several semicrystalline poly-

mers. A third class of methods uses equilibrium melting

point data of oligomers with n repeating units with the same

crystal unit cell structure as the polymer by extrapolation to

n!1 [18–20]. The crystallisable PCL chains included in

this study are all of finite size, with maximum 117 repeating

units corresponding to a stem length of ,100 nm. The large

size of the dendritic core sets the limit for maximum crystal

thickness of the star polymers to the extended chain length

of single PCL arms. This puts the maximum crystal

thickness of the studied star polymers in the range 12–

70 nm. Different strategies were used to extrapolate thermal

analysis data to obtain the equilibrium melting point of the

finite-sized system. A theoretical discussion concerned with

this problem is presented in Section 3.

This paper reports equilibrium melting point data

obtained by analysis of melting point–crystallization

temperature data with a series of linear and star polymers

based on dendrimer, hyperbranched and dendron cores. X-

ray scattering was used to characterize the crystal structures

of the polymers and it was confirmed that the crystal

structures of the different polymers were the same. The

melting behaviour was studied at different heating rates and

it was found that the crystals in the star-branched polymers

rearranged at a lower rate than the crystals in the linear PCL

analogues. The equilibrium melting point data of the

polymers with crystallisable PCL units of finite molar

mass were finally extrapolated to infinite PCL molar mass

using the Flory–Vrij method and the Broadhurst equation.

The experimental melting point data recorded for the star

polymers were typically 3–5 K higher than those of the

linear PCL’s with corresponding PCL chain length crystal-

lized at the same temperature. The equilibrium melting

temperatures calculated for the star polymers were also

found to be higher than those of linear PCL.

E. Nunez et al. / Polymer 45 (2004) 5251–52635252

2. Experimental

Star polymers, consisting of PCL grafted to dendritic

hydroxyl-functional cores, were studied. The cores were

third-generation hyperbranched polyester with approxi-

mately 32 terminal hydroxyl groups (Boltorn, Perstorp

AB, Sweden), a third-generation dendrimer with 24

hydroxyl groups and a third-generation dendron with 8

hydroxyl groups. The dendrimer and dendron core polymers

were synthesized according to Ihre et al. [21]. The synthesis

of star polymers, i.e. the attachment of the PCL onto the

dendritic cores, was achieved according to Claesson et al.

[22]. Linear PCL’s - Tone P300, P1270 and P1241—

purchased from Union Carbide, USA were studied as

received. The structures of the star polymers studied are

displayed in Fig. 1. Molecular structure data of the polymers

studied are presented in Table 1.

The crystal unit cell structure was determined by wide-

angle X-ray scattering using a Huber Imaging Plate Guinier

Camera G670 operating at 40 kV and 30 mA using strictly

monochromatic CuKa1 radiation ðl ¼ 0:15406 nmÞ: Data

in the transmission mode were collected at 0.0058 incre-

ments in the range 4–1008 in 2u: The indexing program

TREOR [23] was used to assess the unit cell parameters.

Samples weighing 5 ^ 2 mg were encapsulated in 40 ml

aluminium pans and analysed in a temperature- and energy-

calibrated Mettler-Toledo DSC 820 purged with dry

nitrogen. Temperature calibration was performed by

recording the melting of highly pure indium at the actual

heating rates used. The samples were crystallized at

constant temperature in the range 303–321 K after 2 min

storage at 348 K and 10 K min21 cooling to the selected

crystallisation temperature. This was the maximum cooling

rate possible to use to avoid ‘over-shooting’. Calorimetric

data were recorded during both the cooling phase and during

the isothermal stage to make certain that all crystallization

occurred during the isothermal stage. The samples were

crystallized under isothermal conditions to 10% of the final

attainable degree of crystallinity at the particular tempera-

ture in an attempt to keep the crystal-thickening factor

constant at the different crystallisation temperatures. The

melting peak temperature was finally recorded at

10 K min21. The recorded melting point data were cor-

rected for the thermal lag between the sample pan and the

sample holder in accordance with Gedde and Jansson [24].

Finally, the melting curves of samples of each material were

recorded at different heating rates, after a specific crystal-

lisation procedure: cooling from 348 to 293 K at

30 K min21. The mass crystallinity of samples cooled at

10 K min21 from 353 to 250 K was assessed by the total

Fig. 1. Chemical structures of the star polymers studied: Dn—dendrimer core HBn—hyperbranched core; Donn—dendron core. The number of repeating units

in a single PCL arm is indicated by n:

E. Nunez et al. / Polymer 45 (2004) 5251–5263 5253

enthalpy method [16] using 135 J g21 [7] as the heat of

fusion of 100% crystalline PCL.

3. Theory: assessment of equilibrium melting point

The equilibrium melting point ðT0mÞ of a homopolymer is

the melting point of an infinitely thick crystal based on a

specific crystal phase with equilibrium density of internal

defects. Crystals of thicknesses in the range of micrometer

are made by high-pressure crystallisation of a few polymers,

e.g. polyethylene [25]. The melting point depression

originating from the finite crystal thickness of crystals in

the micrometer thickness range is less than 0.1 K according

to calculations based on the Thomson–Gibbs equation. In

many cases, the equilibrium melting point is obtained by

extrapolation of melting point data ðTmÞ of polymer crystals

of finite crystal thickness ðLcÞ: The negligible contribution

from the lateral surfaces to the stability of polymer crystals

is the basic assumption underlying the Thomson–Gibbs

equation:

Tm ¼ T0m 1 2

2s

Dh0Lc

� �ð1Þ

where s is the specific surface free energy of the fold

surface and Dh0 is the heat of fusion at the equilibrium

melting point. Extrapolation of Tm 2 L21c data to L21

c ¼ 0

yields the equilibrium melting point provided that the

following requirements are fulfilled: (i) the same crystal

phase must be present in the crystals of finite thickness as in

the infinitely thick, equilibrium crystal. (ii) Crystal

rearrangement (e.g., crystal thickening) has to be inhibited

during the heating and the recording of the melting point.

(iii) Superheating effects must be inhibited. (iv) The specific

fold surface free energy must be the same for all samples

used for extrapolation. (v) The concentration of defects in

the crystals must be the same for all the samples studied and

also the same as in the equilibrium crystal. In addition,

many polymer samples contain crystals with a distribution

in crystal thickness and it is difficult to select a ‘typical’

crystal thickness in a given sample.

Hoffman and Weeks [17] proposed a method based on

the assessment of melting points of crystals grown at

different crystallization temperatures ðTcÞ :

Tm ¼Tc

bþ T0

m 1 21

b

� �ð2Þ

where b is the crystal thickening factor ¼ Lc=Lpc ; where Lpc is

the thickness of the virgin crystal with the melting point

equal to the crystallization temperature. Eq. (2) is

approximately valid provided that the stability of the first

formed crystal is just slightly greater than the minimum

requirement, i.e. Lpc ¼ Lc;min þ dLc < Lc;min; where Lc;min is

the minimum crystal thickness corresponding to a melting

point equal to the crystallization temperature. The equili-

brium melting point is according to Eq. (2) obtained by

extrapolation of Tm 2 Tc data to Tm ¼ Tc; provided b is

constant between the different samples used for extrapol-

ation. More recent data on linear polyethylene [26] and

poly(ethylene oxide) [27] showed that the thickness of the

virgin crystals exceeds the minimum thickness by a more

significant dLc value, 4–5 nm. This gives the Tm 2 Tc

relationship a curvature, which is often seen in practice. The

equation that relates melting point and crystallization

temperature is:

Tm ¼ T0m 1 2

2s

Dh0b2sT0

m

Dh0ðT0m 2 TcÞ

þ dLc

" #266664

377775 ð3Þ

Table 1

Nomenclature and molecular structure of samples studied

Group Core Mcore (g mol21)a Number of PCL arms Sample code nb

Linear PCL – – 1 PCL17 17 (1.2)

PCL39 39 (1.5)

PCL117 117 (1.4)

Dendrimer-PCL 3rd-Generation dendrimer 3006 24 D14 14 (1.3)

D24 24 (1.3)

D42 42 (1.3)

D51 51 (1.3)

Hyperbranched-PCL 3rd-Generation Boltorn 3607 32 HB51 51 (1.3)

HB79 79 (1.4)

Dendron-PCL 3rd-Generation dendron 1008 8 Don15 15 (1.3)

Don46 46 (1.3)

Don81 81 (1.4)

a Molar mass of core calculated theoretically from the chemical formula.b Number average of the degree of polymerisation of the PCL arms ðnÞ; obtained by H NMR [22]. The values within parentheses show the polydispersity

ð �Mw= �MnÞ obtained by size exclusion chromatography applying the universal calibration procedure. The values presented for the star polymers are estimated

from data for linear PCL polymerized under similar conditions.


The equilibrium melting point can be obtained by implicit

solution of Eq. (3). The importance of a significant dLc term

on the Tm 2 Tc curvature and the tendency for under-

estimation of the equilibrium melting point by rectilinear

extrapolation of Tm 2 Tc curvature was recognized in the

comprehensive study of Marand et al. [28]. It was also

mentioned briefly in an earlier publication by one of the

authors of this paper [16].

The equilibrium melting point of oligomers and some

low molar mass polymers can in some cases by determined

directly by melting of extended-chain crystals grown at high

temperatures. Extrapolation of Tm 2 Tc data to Tm ¼ Tc in

order to obtain the equilibrium melting point is not strictly

valid because the relation dLc p Lc;max (Lc;max is the length

of the extended chain, i.e. maximum crystal thickness) does

not hold. However, the equilibrium melting point of the

finite sized system can be obtained by assuming that the

relationship Lc ¼ Lc;min þ dLc holds with a constant dLc

independent of crystallisation temperature. The difference

ðDTÞ between melting point and crystallisation temperature

for the equilibrium crystal with the thickness Lc;max can be

estimated from the Thomson–Gibbs equation according to:

DT ¼ T0mðnÞ2 Tc

¼ T0mðn!1Þ

2s

Dh0

1

Lc;max 2 dLc

� � 2 1

Lc;max

" #ð4Þ

where T0mðn!1Þ is the equilibrium melting point of a

polymer with infinite molar mass. The equilibrium melting

point is thus obtained at the point where the fitted curve

according to Eq. (3) deviates from Tm 2 Tc line by DT (see

the example shown in Fig. 10). The temperature at which

the curve obtained by fitting of Eq. (3) intersects the Tm ¼

Tc line is referred to as the virtual equilibrium melting point.

One of the established methods to determine the

equilibrium melting point of a polymer of infinite molar

mass is to extrapolate melting point data of extended-chain

crystals of oligomers showing the same crystal packing as

the polymer to infinite molar mass. A prerequisite of the

method is that no intermediate phases exist. Extrapolation

methods have been proposed by Broadhurst [18,19], Eq. (5),

and Flory and Vrij [20], Eq. (6):

T0mðnÞ ¼ T0

mðn!1Þðnþ aÞ

ðnþ bÞð5Þ

where a and b are constants to be adjusted in the fit of the

equation to the experimental data.

nDh0

R

!DT 2

nDCp

2R

� �DT2 2 T0

mðnÞT0mðn!1Þln n

¼T0

mðn!1Þ

R

!ðT0

mðnÞDse 2 DheÞ ð6Þ

where DCp is the difference in specific heat between the

amorphous and crystalline PCL, Dse and Dhe are the end-

group contributions to entropy and enthalpy changes at the

melting point. Hay [29] showed that Eq. (6) could be

simplified to:

Tm ¼ T0m 1 2 2RTm

ln n

nDh0

� �� ð7Þ

where Dh0 is the heat of fusion per mole repeating units. Eq.

(7) predicts that the equilibrium melting point is obtained as

the intercept in a plot of Tm vs. ln n=n:

The equilibrium melting point of linear polyethylene has

been determined by the three methods and also by direct

measurement of the melting point of extended-chain

crystals grown at elevated pressure. Extrapolation based

on the Thomson–Gibbs equation gave the values 414.7 K

[30] and 415.2 K [31]. Extrapolation of Tm 2 Tc data

according to the Hoffman–Weeks method yielded 418.2 K

[17] and 418.4 using the non-linear method (significant dLc)

[28]. Extrapolation of melting point data of extended-chain

crystals of oligomers yielded 414.3 K according to the

Broadhurst equation [18,19], 418.7 K according to Flory

and Vrij [20] and 419 K according to Hay [29]. The melting

point of crystals grown at elevated pressure gave 414.6 K

[32]. Thus, the different estimates of the equilibrium

melting point ranges from 414.3 to 419 K. Strobl et al.

[10] estimated from the their melting point–crystal thick-

ness data an equilibrium melting point data of 418–

419 K. The intersection between Tc 2 L21c and Tm 2 L21

c

occurred at finite crystal thickness at 411 K, which was

considerably lower than earlier estimates of the equilibrium

melting point obtained by the Hoffman–Weeks method.

The following data for linear PCL have been used in the

calculations: Dh0 ¼ 163 MJ m23 ¼ 135 kJ ðkgÞ21 ¼ 2:2 kJ

(mol backbone atoms)21 [7]; s ¼ 90 mJ m22 [8]. Crystal

stem length per PCL repeating unit ¼ 0.863 nm [15].

4. Results and discussion

4.1. Crystal unit cell

The X-ray diffraction patterns of the star polymers and

the linear polymers were almost identical. The recorded

diffraction patterns were in accordance with the earlier

reported data of Hu and Dorset [15] and the assessment of

the unit cell by the indexing program TREOR was

consistent with the suggested orthorhombic cell. The

positions of the two intense reflections originating from

(110) and (200) of the orthorhombic unit cell were used to

calculate the corresponding d-spacings (Table 2).

The star polymers showed the following d-spacings:

0.41615 ^ 0.00119 nm (110) and 0.37364 ^ 0.00055 nm

(200). These values are very similar to the values obtained

for the linear PCL, 0.41617 nm (110) and 0.37392 nm

(200). The percentage difference between the mean values

of the star polymers and the values obtained for the linear


PCL were: 20.4% (110) and 20.1% (200); where the

minus signs indicate that the d-spacings were larger for the

linear PCL than for the star polymers. Thus, the X-ray

diffraction data showed that the dendritic cores had no

impact on the unit cell structure of the PCL crystals.

4.2. Degree of crystallinity

The PCL crystallinity (i.e. the mass of PCL crystal phase

divided by the total PCL mass) of samples crystallized

during a 10 K min21 cooling from 353 to 273 K was larger

in linear PCL than in the star polymers (Fig. 2). The degree

of crystallinity of these samples sensitively reflects

differences between different samples with regard to their

ability to crystallize. A common feature of linear polymers

is that the degree of crystallinity decreases with increasing

molar mass. This was demonstrated by Ergoz et al. [33] for

narrow fractions of linear polyethylene covering three

orders of magnitude in molar mass. The linear PCL samples,

not fully ranging one order of magnitude in molar mass,

showed a 10% change in mass crystallinity, which is five

times greater than the standard deviation of the crystallinity

data taken (Fig. 2).

The star polymers based on dendrimer and dendron cores

showed a similar depression in PCL crystallinity with

respect to linear PCL, whereas the star polymers based on

the hyperbranched cores showed an even larger depression

in PCL crystallinity. The depression in PCL crystallinity

ðDwcðnÞÞ of the star polymers with reference to linear PCL

with a corresponding degree of polymerisation of the PCL

units is given by:

DwcðnÞ ¼ wc;PCLðnÞ2 wc;star-PCLðnÞ ð8Þ

where wc;PCLðnÞ is the mass crystallinity of linear PCL with

n repeating units and wc;star-PCLðnÞ is the PCL mass

crystallinity of the star polymer with PCL arms with n

repeating units. The mass crystallinity values for linear PCL

used in the calculations of Dwc were based on a linear

function fitted to the experimental data (Fig. 2). The number

of additional, amorphous PCL repeating ðDnÞ units per PCL

arm in the star polymers with reference to linear PCL was

calculated from:

Dn ¼ Dwcn ð9Þ

Fig. 3 shows the depression in PCL crystallinity in the star

polymers with respect to linear PCL expressed in Dn; as a

function of degree of polymerisation of the PCL arms ðnÞ:

The data obtained for the star polymers with dendrimer and

dendron cores followed a linear trend according to:

Dn ¼ Dn0 þ Cn ð10Þ

where Dn0 is the intercept, i.e., a term independent of the

PCL chain length. The data obtained for the star polymers

with dendrimer or dendron cores suggest that only one

repeating unit ðDn0 < 1Þ of PCL nearest to the core is

prohibited from crystallizing. The linear increase in Dn with

n expressed by the slope coefficient ðCÞ—equal to 0.08 for

the star polymers with dendrimer or dendron cores—

suggests that the chain folding occurring in the star

polymers with longer PCL arms was influenced by the

presence of the dendritic cores near the fold surfaces, as that

this leads to less tight folds.

The star polymers with hyperbranched core showed

an even greater crystallinity depression, corresponding to

Table 2

Crystal structure data obtained by X-ray diffraction

Sample d110 (nm) d200 (nm)

PCL117 0.41617 0.37392

D42 0.41572 0.37397

HB79 0.41523 0.37301

Don81 0.41750 0.37394

Fig. 2. Mass PCL crystallinity ðwcÞ as a function of degree of

polymerisation of a single PCL arm ðnÞ for linear PCL (B), dendrimer-

PCL (A), hyperbranched-PCL (W) and dendron-PCL (X). The crystallinity

assessments were made on samples kept at 353 K in the molten state for

1 min and then cooled at 10 K min21 to 273 K.

Fig. 3. Crystallinity depression in star polymers with reference to linear

PCL expressed as the number of PCL repeating units ðDnÞ per PCL arm

plotted against the degree of polymerisation ðnÞ of a single PCL arm:

dendrimer-PCL (A), hyperbranched-PCL (W) and dendron-PCL (X). The

standard deviation of single data was ,0.02. The continuous line is a linear

fit of the data for dendrimer-PCL and dendron-PCL. The broken line is a

linear fit of the data for hyperbranched PCL assuming the same slope

coefficient as that obtained for dendrimer-PCL and dendron-PCL.


Dn=n ¼ 0:14–0:20: Adjustment of Eq. (10) to the exper-

imental data obtained for the polymers with hyperbranched

core would lead to a very high Dn0; between 8 and 9. This in

combination with the low C-value obtained, 0.02–0.03,

indicates that the two data points available for the

hyperbranched star polymers are not sufficient for reliable

determination of Dn0 and C: It seems reasonable to assume,

however, that the irregular branching in the hyperbranched

cores makes it difficult for the ‘inner’ PCL units to

crystallize, which leads to a high Dn0: It can be argued

that the slope coefficient ðCÞ should be the same for the

hyperbranched star polymers as for dendrimer and dendron-

based star polymers. In that instance, the intercept ðDn0Þ

becomes ,5 for the hyperbranched polymers.

4.3. PCL crystal melting at different heating rates

The melting of linear PCL first crystallized during a

30 K min21 cooling from the melt may serve is a good

example showing the principal effects of varying heating

rate (Fig. 4(a)). The melting trace obtained on slow heating

(1 K min21) contained two well-resolved melting peaks.

The two peaks were shifted to lower temperatures with

increasing heating rate. The temperature difference between

the two peaks was approximately constant, 3.2 ^ 0.1 K, in

the heating rate range 1–5 K min21. The two peaks

gradually merged at the higher heating rates; the tempera-

ture difference was only 2.3 K at 10 K min21. The relative

size of the high temperature peak decreased with increasing

heating rate (Fig. 4(b)). These findings suggest that the

bimodal melting was due to the following sequence of

events: melting of the initial crystals, recrystallisation and

final melting of the crystals grown during the heating. The

same basic scheme applied to both the linear and the star

polymers. The differences between the different polymers

were only in the rate of the recrystallisation process.

The other possible cause for bimodal melting—the initial

presence of two crystal populations different in crystal phase

or crystal thickness—seems unlikely in the present case.

The X-ray diffraction patterns of the polymers studied

showed only the presence of crystals with the orthorhombic

unit cell. The relatively low polydispersity of the samples

studied and the fact that all the samples crystallized during a

constant rate cooling makes it unlikely that two crystal

populations with distinctly different crystal thickness would

be present immediately after the constant rate cooling.

The star polymers with dendrimer or hyperbranched

corers showed a significantly smaller high temperature peak

than the linear PCL at all corresponding heating rates (Fig.

4(a)–(d)). The melting merged into one melting peak at

heating rates $10 K min21 for the star polymers with

dendrimer or hyperbranched corers (Fig. 4(c) and (d)).

Linear PCL and star PCL with a dendron core given the

same thermal treatment showed bimodal melting even up to

a heating rate of 30 K min21 (Figs. 4(a), (e) and 5(a)). The

lower tendency of the star polymers with dendrimer or

hyperbranched cores to rearrange on heating with reference

to that of linear PCL is consonant with earlier data reported

by Nojima et al. [12]. They reported that the long period

associated with the PCL crystals in block copolymers based

on PCL and polybutadiene remained essentially constant

during heating from the crystallisation temperature to the

melting point. Linear PCL showed on the other hand some

increase in the long period on heating to the melting point.

The low temperature peak was due to the melting of the

crystals formed during the initial cooling phase. The heating

rate dependence of the low temperature peak for both linear

PCL and star PCL with dendrimer core suggests, however,

that this material undergoes gradual rearrangement before

final melting during the slow heating experiments (Figs.

5(a) and (b)). Heating at a rate of 10 K min21 or greater had

no further implication on the melting point. This is very

similar to the behaviour of thin polyethylene crystals that

show perfectioning and crystal thickening on slow heating

and, above a certain critical heating rate, melting occurs

essentially without previous crystal rearrangement [34].

The commonly used heating rate, 10 K min21, lead to no

significant crystal rearrangement for the rapidly cooled star

polymers with dendrimer or hyperbranched cores, but in

linear PCL and star PCL with dendron core, bimodal

melting, i.e. melting of initial crystals followed by crystal-

lisation and final melting, occurred even during faster

heating (#30 K min21). The melting point of the initial

crystals can be obtained, however, by considering only the

low temperature peak of these polymers.

4.4. Assessment of equilibrium melting point

The equilibrium melting temperatures of the different

samples were determined by extrapolation of Tm 2 Tc data.

The melting point was taken as the melting peak

temperature on samples crystallized to 10% of the final

attainable degree of crystallinity at the particular tempera-

ture. Correction was made for the thermal lag between

sample and sample holder according to Gedde and Jansson

[24]. Melting points recorded for samples crystallized at

even lower temperatures during constant rate cooling at

different heating rates approached a constant value at 5–

10 K min21 (Figs. 5(a) and (b)). No correction was thus

made for possible crystal rearrangement during heating

from the crystallisation temperature to the melting point.

The melting peaks recorded on the direct heating from the

crystallisation temperature were strictly unimodal and

narrow, observations that indicate that the orthorhombic

crystal phase is directly transformed into the molten state

without significant crystal rearrangement. Fig. 6 shows

Tm 2 Tc data for a series of samples of linear PCL. Data

reported by Phillips et al. [8] for a linear PCL with a molar

mass of 40,000 g mol21 (corresponding to DP < 350) are

included. It is evident that a linear function like the

Hoffman–Weeks equation, Eq. (2), is not in accordance

with the pronounced curvature shown by the experimental


data (Fig. 6). It was also noted that the melting point at a

given crystallisation temperature, e.g. at 316 K, increased

with increasing molar mass.

The effect of molecular architecture on the melting point

is demonstrated by the data presented in Fig. 7. The degrees

of polymerisation of the PCL units in these polymers are

approximately the same, ranging from 39 to 51. The Tm 2

Tc curves of the different samples are essentially parallel-

shifted along the melting point axis; the melting points of

the star polymers are ,2 K higher than those of linear PCL

at any given Tc within the studied temperature range. The

star polymers showed a progressive increase in melting

point with increasing PCL degree of polymerisation (Figs. 8

and 9). The data obtained for the star polymers showed a

pronounced curvature in the Tm 2 Tc diagrams (Figs. 8 and

9).

Eq. (3), which is a development of the Hoffman–Weeks

equation, considers that the crystals are more stable

(expressed by dLc) than the minimum requirement at the

particular crystallisation temperature. This equation pre-

dicts a positive second derivative of Tm with respect to Tc:

The crystal-thickening factor ðbÞ was set unity. This

supposition was made because of the short crystallisation

times and the small-angle X-ray data presented by Strobl

et al. [10] and Nojima et al. [12]. Furthermore, the goodness

of fit decreased when b set to values greater than 1. The two

adjustable parameters, the temperature at which the fitted

curve intersects Tm ¼ Tc (the virtual T0m) and dLc; were

adjusted in order to minimise the sum of square differences.

Optimum fit was achieved in most cases with dLc ¼ 5 nm:

A few of the low molar mass samples showed higher

goodness of fit with a slightly lower value, dLc ¼ 4 nm:

However, dLc was set to 5 nm as a universal value for all the

different samples.

Fig. 10 and Table 3 show the fit of Eq. (3) to the

experimental data obtained for Don81. The curvature of the

experimental data in the Tm 2 Tc diagram is stronger than

predicted by Eq. (3). This was a general feature for all the

samples studied. The positive deviation of the experimental

data with respect to the fitted line typically occurring at the

two highest crystallisation temperatures is most probably

due to a relatively small increase of the crystal thickening

factor. Crystallisation to 10% of the final degree of

crystallinity means that more time was available for crystal

Fig. 4. Melting traces recorded at different heating rates (shown adjacent to each curve; in K min21) of samples initially crystallized during a 30 K min21

cooling from the melt: (a) linear PCL (PCL39); (b) relative size of the high temperature melting peak ðAh=AtotÞ as a function of heating rate ðQÞ; star polymers

based on (c) dendrimer (D42); (d) hyperbranched (HB51); (e) dendron (Don46).


thickening at the higher crystallisation temperatures. For

Don81 the following crystallisation times were used to reach

the 10% relative level of crystallinity: 313.5 K—0.04 h;

317.5 K—0.17 h; 321.5 K—0.83 h; 325.5 K—4.03 h;

327.5 K—8.88 h.

The implication of single data points on the fitted

equation and on the ‘virtual’ T0m value obtained is however

limited (Table 3). The range in the virtual T0m obtained from

different choices of data for extrapolation was from 356.5 to

358.9 K with an average value of 357.3 K and a standard

deviation of 0.7 K. The virtual Tm0 value by fitting Eq. (3) to

the all the data taken was 357.3 K. The equilibrium melting

point of Don81 was calculated by considering the finite

thickness of the equilibrium crystal (see Section 3). The DT

value used in the assessment, see Fig. 10, was calculated

from Eq. (4) using s ¼ 40 mJ m22. This relatively low

value was used because the equilibrium crystal is lacking

Fig. 5. Effect of heating rate on melting temperature of samples crystallized

during 30 K min21 cooling from the melt of (a) PCL39 and (b) D51. The

values plotted correspond to the averages based on two individual

measurements, and the error bars represent the standard deviations. Filled

symbols indicate high-temperature peak and unfilled symbols indicate low

temperature peak.

Fig. 6. The melting point ðTmÞ as a function of crystallisation temperature

ðTcÞ for PCL17 (B), PCL39 (A), PCL117 (X) and a linear PCL with average

DP < 350 (W). The data for this polymer was reported by Phillips et al. [8].

The data shown for PCL17, PCL39 and PCL117 are averages based on three

separate measurements and they refer to samples crystallised to 10% of the

final crystallinity at each temperature. The standard deviation of the single

data points was smaller than 0.2 K. The lines are second-degree polynomial

fits to the experimental data.


ðTcÞ for PCL39 (W), D42 (X), Don46 (A) and HB51 (B). The samples

crystallised to 10% of the final, attainable crystallinity at each temperature.

The data are averages based on three separate measurements. The standard

deviation of the single data points was smaller than 0.2 K. The lines are

second-degree polynomial fits to the experimental data.


ðTcÞ for D14 (B), D24 (A), D42 (X) and D51 (W).The samples crystallised to

10% of the final, attainable crystallinity at each temperature. The data are

averages based on three separate measurements. The standard deviation of

the single data points was smaller than 0.2 K. The lines are second-degree

polynomial fits to the experimental data.


chain folds. It is important to point out, however, that

s ¼ 90 mJ m22 was used as input in Eq. (3) for the

extrapolation of the melting point data of the folded-chain

crystals grown at the crystallisation temperatures studied.

The value used for s is important since DT is strictly

proportional to s: The main emphasis, however, is to

compare equilibrium melting point data for linear and star-

branched PCL. A change in s alters the calculated

equilibrium melting point data but the qualitative con-

clusions are not influenced by any realistic alteration of s:

Fig. 11 shows data for a relatively high molar mass linear

PCL earlier reported by Phillips et al. [8]. They used a linear

extrapolation procedure in accordance with the original

Hoffman–Weeks method and obtained an equilibrium

melting point of 343.5 K [8]. The extrapolation of the

experimental data according to Eq. (3) yielded a signifi-

cantly higher value, T0m ¼ 356:7 K: The curvature of the

data in the Tm 2 Tc plot is obvious and also the difficulty to

perform a linear extrapolation of the data to determine the

equilibrium melting point.

Fig. 12 presents the results from extrapolation of the

fitted Eq. (3) using Eq. (4) to calculate DT to obtain Tm0 (n)

for the different samples. The following universal parameter

values were used: Eq. (3): s ¼ 90 mJ m22;

Dh0 ¼ 163 MJ m23; b ¼ 1; dLc ¼ 5 nm; Eq. (4):

s ¼ 40 mJ m22; Dh0 ¼ 163 MJ m23. The extrapolation

method using these parameter values produced, as it


ðTcÞ for Don15 (A), Don46 (X) and Don81 (W).The samples crystallised to

10% of the final, attainable crystallinity at each temperature. The data are

averages based on three separate measurements. The standard deviation of

the single data points was smaller than 0.2 K. The lines are second-degree

polynomial fits to the experimental data.


ðTcÞ for Don81: (a) fitted Eq. (3) using the following parameter values:

Dh0 ¼ 163 MJ m23; s ¼ 90 mJ m22; b ¼ 1; dLc ¼ 5 nm. (b) Tm ¼ Tc: (c)

the intersection between curve (a) and line (b) denoting the virtual

equilibrium melting point: (d) equilibrium melting point assuming constant

dLc ¼ 5 nm; DT denotes the difference in melting and crystallisation

temperatures calculated from the Thomson – Gibbs equation with

s ¼ 40 mJ m22.

Table 3

Virtual equilibrium melting point data for Don81 calculated from melting

point data obtained at different crystallisation temperatures

Tc (min) (K)a Tc (max) (K)a T0m (K)b

313.5 327.5 357.3

313.5 325.5 357.1

313.5 323.5 356.8

313.5 321.5 356.7

313.5 319.5 356.6

313.5 317.5 356.8

313.5 315.5 357.1

315.5 327.5 357.2

317.5 327.5 357.4

319.5 327.5 357.6

321.5 327.5 358.1

323.5 327.5 358.5

325.5 327.5 358.9

315.5 325.5 357.9

317.5 323.5 356.7

319.5 321.5 356.5

a Minimum and maximum crystallisation temperatures used for

extrapolation.b Virtual equilibrium melting point obtained by fitting of Eq. (3) to the

experimental data and using the following parameter values: Dh0 ¼ 163

MJ m23; s ¼ 90 mJ m22; b ¼ 1; dLc ¼ 5 nm:


ðTcÞ for PCL350. The experimental data are from Phillips et al. [8]. The

continuous line shows the best fit of Eq. (3) using the parameter values:

Dh0 ¼ 163 MJ m23; s ¼ 90 mJ m22; b ¼ 1; dLc ¼ 5 nm. The cross in the

right-hand upper corner indicate the estimated equilibrium melting point

using DT calculated from Eq. (4) with s ¼ 40 mJ m22.


appeared accurate results for the majority of the samples.

The results obtained by the extrapolation were not sensitive

to the choice of the data. Removal of the data points taken at

the highest crystallization temperatures (where possible

crystal thickening may have occurred) only altered the

result by a few tenths of a Kelvin. Extrapolation of the data

obtained for the lowest molar mass samples (PCL17, D14 and

Don15) gave, however, results with significant uncertainty.

This was primarily due to the large DT values shown by

these samples. The values presented in Fig. 12—marked

with arrows—should be considered as highly approximate.

The equilibrium melting point data are presented in Fig.

12 in which the data are plotted according to the Hay [29].

The equilibrium melting point data follow a linear trend

with respect to ln n=n: The following values for T0m !1

were obtained by extrapolation to ln n=n ¼ 0 : linear-PCL:

359.2 K; dendrimer-PCL: 362.0 K; dendron-PCL: 363.2 K;

hyperbranched-PCL: 363.6 K. Hence, the difference in

equilibrium melting point between the linear and the star-

branched polymers is 3–4 K. The use of a lower s-value

(10 mJ m22 was tested) in the calculation led only to small

changes in the extrapolated values of T0mðn!1Þ : 358.7 K

(linear-PCL); 363.0 K (dendrimer-PCL); 363.0 K (dendron-

PCL); 362.7 K (hyperbranched-PCL). The goodness of fit

was however lower for the data based on calculation of DT

with s ¼ 10 mJ m22.

Fig. 13 presents equilibrium melting point data plotted as

a function of n together with best fits of the Broadhurst

equation (Eq. (5)) to the experimental data. The following

values were obtained for T0mðn!1Þ : linear PCL: 358.5 K;

dendrimer PCL: 366.2 K; dendron PCL: 363.7 K; hyper-

branched PCL: 365.0 K. The determinations of the equili-

brium melting points for the low molar mass samples

PCL17, D14 and Don15 were associated with considerable

uncertainty and it was noticed from the fittings according to

the Broadhurst equation that a change of these equilibrium

melting point values by 1 K changed the extrapolated

T0mðn!1Þ-value by ,2 K. The extrapolation of the

equilibrium melting point data according the Hay equation

was less influenced by the uncertain equilibrium melting

points of the low molar mass samples. The equilibrium

melting point data obtained by using s ¼ 10 mJ m22 in the

calculation of DT were also described by the Broadhurst

equation and although the goodness of fit was not as high as

in the case of using s ¼ 40 mJ m22 essentially the same

differences in T0mðn!1Þ between linear and star polymers

were obtained: 360.6 K (linear PCL) and 363–364 K (star

polymers).

Fig. 14 shows the melting point ranges for the linear and

star polymers and the calculated crystal thickness using the

Fig. 12. The equilibrium melting point ðT0mðnÞÞ as a function of ln n=n (n is

the degree of polymerisation of PCL of a single PCL arm) for: linear PCL

(B), dendrimer-PCL (A), hyperbranched-PCL (W), and dendron-PCL (X).

The lines are best fits of Eq. (7) to the experimentally based equilibrium

melting point data. The arrows point towards data points associated with

considerable uncertainty (^2–3 K).

Fig. 13. The equilibrium melting point ðT0mðnÞÞ as a function of the degree of

polymerisation of PCL of single PCL arms ðnÞ for: linear PCL (B),

dendrimer-PCL (A), hyperbranched-PCL (W), and dendron-PCL (X). The

curves are best fits of Eq. (5) to the experimentally based equilibrium

melting point data. The arrows point towards data points associated with

considerable uncertainty (^2–3 K).

Fig. 14. Crystal thickness plotted as a function of melting point calculated

from the Thomson–Gibbs equation using the following input data:

Dh0 ¼ 163 MJ m23; s ¼ 90 mJ m22 for (curve a) linear PCL:

T0m ¼ 359 K; (curve b) star PCL: T0

m ¼ 363 K. The broken lines shows

the melting point and crystal thickness ranges included in this study. Data

for the samples with very low molar mass (PCL17, D14 and Don15) are not

included.


Thomson–Gibbs equation with the following parameter

values: Dh0 ¼ 163 MJ m23, s ¼ 90 mJ m22, Tm0 ¼ 359 K

(linear PCL), 363 K (star PCL). The crystal thickness ranges

for the higher molar mass samples (not including PCL17,

D14 and Don15) were 12–15.5 nm for linear PCL and 11–

15 nm for star-branched PCL. The extended-chain length

was between 31 and 302 nm for the linear PCL’s and 21 and

70 nm for the star polymers. The PCL chains must then be

folded at least once and in most cases twice or more times.

Hence, the presence of great many chain folds in the fold

surface of the crystals is consonant with the s value used

(90 mJ m22) in the calculation of the equilibrium melting

point according to Eq. (3) and in the calculation of the

crystal thickness according to the Thomson – Gibbs

equation. Strobl et al. [10] reported by small-angle X-ray

scattering crystal thicknesses between 7 and 9 nm corre-

sponding to melting points in the range 333–338 K. This is

considerably less than that shown in Fig. 14; 15–17 nm for

linear PCL crystals melting between 333 and 338 K. The

melting point–crystal thickness data presented by Strobl

et al. [10] yielded a unexpected low s-value, ,60 mJ m22.

A simple, qualitative analysis of these findings can be

made using the equation:

T0mðnÞ ¼

Dh0ðnÞ

Ds0ðnÞð11Þ

where Dh0 and Ds0 are the enthalpy and entropy of fusion.

The similarity in the unit cell parameters of the polymers

with different molecular architectures suggests that Dh0 is

independent of molecular architecture. However, the

depression in crystallinity of the star polymers with respect

to linear PCL indicates that a portion of the PCL arms was

hindered from crystallizing. Only the repeating PCL units

close to core should be influenced in the case of the

equilibrium extended-chain crystals. It seems reasonable, on

the basis of the data presented in Fig. 3, that only a few (,1)

repeating PCL units of each PCL arm of the dendrimer/

dendron star polymers are prohibited from crystallizing. In

hyperbranched star polymers, a larger number of PCL

repeating units (,5) are unable to crystallize. Hence, the

dendrimer/dendron star polymers would in this instance

experience a reduction in enthalpy of fusion to DH0ðn2 1Þ

and hence a lowering of the equilibrium melting point. This

effect should be more important in polymers with the short

PCL arms. More important is the reduction in Ds0ðnÞ that is

responsible for the increase in equilibrium melting point

with respect to linear PCL for the star polymers. The

attachment of the crystallisable PCL arms to the core

reduces the positional freedom of the crystallisable units in

the molten state leading to a lower Ds0ðnÞ for these polymers

than for linear PCL.

5. Conclusions

PCL star polymers based on dendritic cores showed the

same unit cell structure as linear PCL. The crystallinity of

the star polymers was lower than that of the linear PCL

analogues suggesting that a few PCL repeating units nearest

to the dendritic core were unable to crystallize and that

chain folds were less tight in the star polymers. The

crystallinity depression was particularly strong in the star

polymers with hyperbranched core. Crystal rearrangement

during the slow heating of polymers previously crystallized

during fast cooling occurred to the same extent in star

polymers based on dendron core as in the linear polymers,

but it was retarded in the star polymers based on dendrimer

or hyperbranched cores. The equilibrium melting points of

the star polymers were higher than those of the linear

analogues. This effect can be attributed to positional

restriction imposed on the PCL chains by their covalent

attachment to the dendritic cores, which lowers the melt

entropy of the star polymers with respect to their linear

analogues.

Acknowledgements

The financial support from the Swedish Research

Council (grant # 5104-20005764/20) is gratefully

acknowledged.

References

[1] Malmstrom E, Johansson M, Hult A. Macromol Chem Phys 1996;197:

3199.

[2] van Caeter P, Goethals EJ. Macromol Rapid Commun 1997;18:393.

[3] Chen E-Q, Lee S-W, Zhang A, Moon B-S, Mann I, Harris FW, Cheng

SZD, Hsiao BS, Yeh F, von Merrewell E, Grubb DT. Macromolecules

1999;32:4784.

[4] Wei HY, Shi WF, Nie KM, Shen XF. Polymer 2002;43:1969.

[5] Zhao YL, Cai Q, Jiang J, Shuai XT, Bai JZ, Chen CF, Xi F. Polymer

2002;43:5819.

[6] Risch BG, Wilkes GL, Warakomski JM. Polymer 1993;34:2330.

[7] Crescenzi V, Manzini G, Calzolari G, Borri C. Eur Polym J 1972;8:

449.

[8] Phillips PJ, Rensch GJ, Taylor KD. J Polym Sci, Polym Phys 1987;25:

1725.

[9] Phillips PJ, Rensch GJ. J Polym Sci, Polym Phys 1989;27:155.

[10] Heck B, Hugel T, Iijima M, Sadiku E, Strobl G. New J Phys 1999;1:

171.

[11] Gedde UW, Mattozzi A. Adv Polym Sci 2004;169:29.

[12] Nojima S, Kikuchi N, Rohadi A, Tanimoto S, Sasaki S. Macromol-

ecules 1999;32:3727.

[13] Chatani Y, Okita Y, Tadokoro H, Yamashita Y. Polym J 1970;1:555.

[14] Bittiger H, Marchessault RH, Niegisch WD. Acta Crystallogr 1970;

B26:1923.

[15] Hu H, Dorset DL. Macromolecules 1990;23:4604.

[16] Gedde UW. Polymer physics. London: Chapman & Hall; 1995.

[17] Hoffman JD, Weeks JJ. J Res Natl Bur Std-Phys Chem 1962;A66:13.

[18] Broadhurst MG. J Chem Phys 1962;36:2578.

[19] Broadhurst MG. J Res Natl Bur Std-Phys Chem 1966;70A:481.


[20] Flory PJ, Vrij A. J Am Chem Soc 1963;85:3548.

[21] Ihre H, Hult A, Soderlind E. J Am Chem Soc 1996;118:6388.

[22] Claesson H, Malmstrom E, Johansson M, Hult A. Polymer 2002;43:

3511.

[23] Werner P-E, Eriksson L, Westdahl M. J Appl Crystallogr 1985;18:

367.

[24] Gedde UW, Jansson J-F. Polymer 1983;24:1521.

[25] Wunderlich B. Crystal nucleation, growth, annealing. Macromolecu-

lar physics, vol. 2. New York: Academic Press; 1978.

[26] Barham PJ, Chivers RA, Keller A, Martinez-Salazar J, Organ SJ.

J Mater Sci 1985;20:1625.

[27] Cheng SZD, Chen J, Barley JS, Zhang A, Habenschuss A, Zschack

PR. Macromolecules 1992;25:1453.

[28] Marand H, Xu J, Srinivas S. Macromolecules 1998;31:8219.

[29] Hay JN. J Polym Sci, Polym Chem 1976;14:2845.

[30] Illers K-H, Hendus H. Makromol Chem 1968;113:1.

[31] Bassett DC, Hodge AM, Olley RM. Proc Roy Soc London 1981;

A377:39.

[32] Arakawa T, Wunderlich B. J Polym Sci, Polym Symp 1967;C16:653.

[33] Ergoz E, Fatou JG, Mandelkern L. Macromolecules 1972;5:127.

[34] Wunderlich B. Crystal melting. Macromolecular physics, vol. 3. New

York: Academic Press; 1980.


crystal structure, melting behaviour and equilibrium melting point of star polyesters with...

Documents