Cooperativity length evolution during crystallization of poly(lactic acid)

European Polymer Journal 47 (2011) 2414–2423

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Cooperativity length evolution during crystallization of poly(lactic acid) N. Delpouve, A. Saiter, E. Dargent ⇑ AMME-LECAP EA 4528 International Laboratory, Université de Rouen, Avenue de l’Université BP 12, 76801 Saint Etienne du Rouvray, France

a r t i c l e

i n f o

Article history: Received 28 February 2011 Received in revised form 7 July 2011 Accepted 28 September 2011 Available online 5 October 2011 Keywords: Poly(lactic acid) Glass transition Crystallization Amorphous phase Three-phase model Cooperativity length

a b s t r a c t Effects of stereoregularity and crystallization mode on the amorphous phase dynamics are investigated for poly(lactic acid) PLA. An isothermal crystallization from the melt and a cold crystallization are imposed. For each PLA, the cold crystallization leads to the appearance of a less perfect crystalline phase and to an important rigid amorphous fraction RAF content (35%), although only 10% of RAF is generated after crystallization from the melt. Temperature Modulated Differential Scanning Calorimetry is used to determine the Cooperative Rearranging Regions (CRR) size at the glass transition temperature in the mobile amorphous phase MAP. It is shown that the CRR size in the MAP is not modified by the appearance and the spherulite growth. For the intra-spherulite MAP, a confining effect is evidenced, causing an amorphous phase thickness decrease during crystallization, and inducing a drastic CRR size reduction. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction During polymer crystallization, the amorphous region volume is progressively reduced and it is known that the decoupling between crystalline and amorphous phases is in general incomplete, due to the macromolecule length, that is much higher than the nanophase dimension [1]. This incomplete decoupling leads to an amorphous phase chain mobility decrease [2], and implies to describe most of the semi-crystalline polymers with a three phase model: the crystalline phase, the mobile amorphous phase MAP, and the rigid amorphous fraction RAF [3]. The RAF is the result of strong restrictions of amorphous chain segment mobility, due to the polymer chain part fixation to the crystalline lamellae [4]. Androsch [5] showed, in various annealed poly(ethylene terephthalate), that the RAF amount must be considered as a measure of the coupling between the crystalline and the amorphous phase. In the usual homogeneous stack model, the MAP is inside the lamella stack and the RAF is an interfacial nanolayer between the lamellae and the MAP [6]. Below Tg all the three fractions are solid-like. The MAP undergoes the glass transition and becomes liquid-like just ⇑ Corresponding author. Tel.: +33 2 32 95 50 80; fax: +33 2 32 95 50 82. E-mail address: [email protected] (E. Dargent). 0014-3057/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2011.09.027

above Tg, while the crystalline and rigid amorphous fractions remain solid-like within a certain temperature range above Tg [6]. The MAP glass transition phenomenon is often crystallinity-dependent and large variations of glass transition temperatures with the crystallinity degree could be observed for various polymers [7]. In this work, the crystallinity influence on the MAP is investigated through the Cooperative Rearranging Regions (CRR) concept originally introduced by Adam and Gibbs [8]. A CRR could be described as the smallest amorphous domain where a conformational rearrangement may occur without causing structural change at its boundary. Many works use the CRR concept to describe polymer amorphous phase dynamics [9–16]. One of them [10] shows the influence of geometrical confinement on the CRR size in syndiotactic poly(methyl methacrylate) system and proves that the CRR average size decreases when the polymeric matrix is more and more constrained by layers. In a previous paper [17], we showed that the CRR size in wholly amorphous and in semi-crystalline poly(lactic acid) PLA are different. The aim of this work is now to determine how the CRR size evolves during spherulite growth, and to establish the link between the CRR size and the microstructure of a semicrystalline polymer, and more particularly between the CRR size and the average interlamellar amorphous layer thickness. A wide range of crystallinity degree Xc

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must be accessible for this study. That is the main reason PLA has been chosen. Indeed, Xc can vary from zero to values higher than 75% depending on the stereoregularity and the applied thermal treatments [18]. Owing to the lactic acid chirality, PLA exists as homopolymer of L-lactic acid (PLLA), of D-lactic acid (PDLA) or as heteropolymer (PDLLA) with variable molar quantities of D-lactic acid, generally ranging between 2% and 7% [19]. Moreover, this polymer is one of the most promising bio-based polymers for packaging and commodity application [20] but its microstructure and amorphous phase dynamics remain insufficiently explored. 2. Experimental Four poly(lactic acid) (PLA) with different L/D ratio are studied in this work. Their origin and chemical characteristics are given in Table 1. PLA1 and PLA2 samples are submitted to different thermal treatments to obtain large variations of the crystallinity degree Xc, while only high Xc samples are studied for PLLA and PDLA. Before any thermal treatment, the pellets are cut, placed in DSC pans, melt in situ 10 K above their melting temperature Tf during 10 min and finally quenched at 50 K/min until room temperature. By this procedure, wholly amorphous samples are obtained (the absence of crystalline phase is controlled by Differential Scanning Calorimetry DSC and Wide angle X-ray Diffraction analyses). Semi-crystalline samples are obtained from these amorphous ones by following two different procedures: the crystallization from the melt and the cold crystallization. 2.1. Crystallization from the melt procedure for PLA1 and PLA2 The samples are melted at 458 K in a DSC TA 2920 CE apparatus during 10 min. Then, samples are cooled at 10 K/min until a crystallization temperature (Tc) 35 K lower than Tf. Tf1 = 438 K for the PLA1 and Tf2 = 428 K for the PLA2 are measured, then Tc1 = 403 K and Tc2 = 393 K are chosen. Samples are crystallized during a time tc ranging between 0 and 600 min for the PLA1 and between 0 and 2400 min for the PLA2, and cooled at 10 K/min until 293 K. Finally, each sample is analysed by Temperature Modulated Differential Scanning Calorimetry (TMDSC). 2.2. Cold crystallization procedure for PLA1 and PLA2 Samples are cold crystallized at a temperature Tc equal to 353 K (20 K above the glass transition temperature) for a duration time tc ranging between 0 and 300 min, and cooled down to 293 K at 10 K/min.

2.3. Crystallization procedures for PLLA and PDLA samples For crystallization from the melt, the samples are cooled from the melt at 10 K/min down to Tc = 423 K (Tf = 458 K), and then crystallized during tc = 1200 min. The samples are cooled at 10 K/min until 293 K before being analyzed. Regarding the cold-crystallization, melt samples are quenched to 293 K and cold crystallized at a temperature Tc equal to 353 K (20 K above Tg) during 1200 min. TMDSC analyses are performed on a TA apparatus (DSC 2920 CE). Calibration in temperature and energy is carried out using standard values of indium and zinc. The specific heat capacity for each sample is measured using sapphire as a reference. The sample masses are chosen to be similar to the sapphire sample mass, i.e. approximately 20 mg. The TMDSC experiments are performed with oscillation amplitude of ±0.318 K, an oscillation period of 60 s and with a heating rate of 2 K/min. These experimental parameters correspond to the ‘‘heat only’’ mode and give the best signal on noise ratio obtained with the apparatus used. The oscillation period number is then equal or higher than 5 in the glass transition range, depending on the sample crystallinity degree. Indeed, the greater the crystallinity degree, the wider the glass transition range. In this study, the average heat flow, the apparent complex heat capacity C⁄ with the in-phase component noted C0 and the out-of-phase component noted C00 have been analyzed. More details concerning the complex heat capacity determination and the phase angle correction are given in ref [22]. Before any TMDSC experiments, each sample is heated at 10 K/min from 293 K up to a temperature just above the glass transition range and cooled at 10 K/min down to 293 K in order to erase the thermal history.

3. Results and discussion The average heat flow vs. temperature signals are shown in Fig. 1 for some of the studied samples. For amorphous non-annealed PLA1 (Fig. 1a), four thermal phenomena are observable: an endothermic heat flow step around 326 K characterizing the glass transition, an exothermic peak around Tc = 365 K due to the cold crystallization of an amorphous phase part, a weak exothermic peak at 418 K and finally an endothermic peak around 435 K due to the crystalline phase fusion. An extensive work on PLLA samples crystallized from the glassy state in similar experimental conditions [23] shows that at temperatures just below the melting peak, melting and recrystallization of unstable crystals take place almost simultaneously [24,25]. For PLLA, Di Lorenzo has shown that at low

Table 1 L/D ratio, number-average molecular weight Mn, polydispersity, origin and related references for each poly(lactic acid). Name in this work

L/D ratio

Mn (g/mol)

Polydispersity

Origin and related references

PLLA PLA1 PLA2 PDLA

100/0 99.6/0.4 96/4 0/100

59,500 69,000 116,000 84,500

1.8 1.7 1.6 1.7

Purasorb PL24 PURAC [21] NatureworksÒ [7] 4042D NatureworksÒ Purasorb PD PURAC [21]

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endo

0.25 W/g

Average Heat Flow (W/g)

a b c d e f g h

315

335

355

375

395

415

435

455

475

Temperature (K) Fig. 1. TMDSC curves obtained for different PLA samples: (a) is the amorphous PLA1, (b) is the amorphous PLA2, (c) is a PLA1 crystallized at 353 K from the glassy state (tc = 30 min, Xc = 12%), (d) is a PLA2 crystallized at 353 K from the glassy state (tc = 650 min , Xc = 28%), (e) is the PLLA crystallized at 423 K from the melt (Xc = 76%), (f) is the PDLA crystallized at 423 K from the melt (Xc = 65%), (g) is the PLLA crystallized at 353 K from the glassy state (Xc = 46%), (h) is the PDLA crystallized at 353 K from the glassy state (Xc = 42%).

crystallization temperatures (Tc < 393 K) the very high crystallization rates lead to the achievement of low crystallinity degree values, with formation of small and/or defective crystals, having a large tendency to reorganize into more stable structures during the heating scan [26,27]. For amorphous PLA2 (Fig. 1b), the glass transition is observable in the same temperature range than for PLA1, while the cold crystallization and the fusion look different. The cold crystallization takes place on a large temperature range and Tc = 391 K. The fusion occurs at lower temperature (around 425 K) and looks bimodal. These differences are mainly attributed to the stereoregularity difference between PLA1 and PLA2. The complex peak of fusion has previously been studied [26,28,29] and is related to the crystallization temperature and rate, and to the polymer molecular weight Mw. For high-Mw PLA, as in our case, the lowest temperature endothermic peak is generally attributed to the perfect crystal melting, associated with the defective crystal transformation into more perfect crystals. The highest temperature endothermic peak corresponds to the perfect crystal melting, arisen from their fusion-recrystallization or from the defective crystal transformation. The concomitance of perfect and defective crystals in PLA2 can be explained by the wideness of the crystallization peak. At low Tc, defective crystals are formed, while more perfect crystals are generated at higher temperatures. For annealed samples, DSC curves of cold crystallized PLA1 and PLA2 with tc = 30 and 650 min respectively (Fig. 1c–d), confirm what we previously observed [17]: for a given PLA, the magnitude of the four thermal events depends on the annealing time. For PLLA and PDLA samples annealed during long times the experimental curves look different (Fig. 1e–h): the glass transition appears with a very weak magnitude and the cold crystallization peak has disappeared. Thus, the crystalline phase melting around 460 K has been generated during the annealing. However, for both homopolymers crystallized with identical crystallization times, differences are

noticed on the DSC curves depending on the crystallization mode: the cold-crystallization leads to lower melting peak temperature, and the exotherm before the melting (where defective crystals transform) is visible. The crystallinity degree Xc induced by the annealing could be deduced from the heat flow signal obtained by TMDSC using the following equation [30]:

Xc ¼

DHf  RDHc  DH f

ð1Þ 

where DHf is the measured fusion enthalpy, DHf is the calculated fusion enthalpy of a wholly crystalline material  (DHf ¼ 93 J=g [31]) and RDHc is the sum of the exothermic cold crystallization peak enthalpies obtained during the TMDSC runs. The calorimetric signal obtained for amorphous PLA2 is reported in Fig. 2 as an example. The difference between the crystallization and fusion enthalpies is negligible as expected, and a nill Xc value is obtained. The crystallinity degree values are reported in Fig. 3. The Xc variations vs. time are quasi sigmoidal for the four set of samples. After an induction time ti, Xc sharply increases to reach a maximum value Xcm. ti is higher for the cold crystallization than for crystallization from the melt, and greater for the least stereoregular PLA (PLA2 with 96/4 L/ D ratio) As expected, For example, ti is closed to 300 min for the cold crystallized PLA2 while ti = 10 min for PLA1 crystallized from the melt. The maximum crystallinity degree also depends of the L/D ratio and on the crystallization procedure: Xcmax is obtained for the most stereoregular PLA and after crystallization from the melt. Quantitative thermal analyses are performed for each sample. The in-phase components C0 are obtained and reported in Fig. 4 for the wholly amorphous PLA2 and a semi-crystalline PLA2, as examples. Typically, it is possible to calculate the MAP degree Xma from the DCp step at Tg:

X ma ¼

DC p DC p 

ð2Þ

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endo

Average Heat Flow (W/g)

0.05 W/g

ΔHc= 34.1 J/g

ΔHf = 34.0 J/g

315

335

355

375

395

415

435

455

Temperature (K) Fig. 2. TMDSC average heat flow curve obtained for the amorphous PLA2. Associated enthalpies of crystallization and fusion are reported.

70

60

Xc (%)

50

40

30

20

10

0 1

10

100

1000

10000

crystallization time (min) Fig. 3. Crystallinity degree evolution (Xc) as a function of crystallization time (tc) for different PLA. s correspond to the PLA1 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt, e correspond to the PLA2 crystallized at 353 K from the glassy state, and  correspond to the PLA2 crystallized at 393 K from the melt. From polarized light microscopy the appearance of spherulites could be observed during the isothermal procedures. The spherulite photography corresponds to the PLA1 crystallized at 403 K from the melt during 25 min (Xc = 24%). The dotted sigmoidal curves correspond to the crystallization kinetics from the glassy state and the dashed sigmoidal curves correspond to the crystallization kinetics from the melt. Uncertainty on Xc values is ±5%.

where DC p ¼ C 0liquid  C 0solid is the thermal heat capacity step at Tg for annealed and semi-crystalline samples,  and DC p that of the wholly amorphous sample (see Fig. 4: the straight lines fit the glassy state on one hand, and the liquid-like and the melt Cp data on the other hand). For the semi-crystalline sample, the slope of the straight line for T > Tg is intermediate between those of the glassy state and those of the liquid-like state. As shown in Fig. 5, Xma decreases when Xc increases. However the data are not along the line of equation X c þ X ma ¼ 100% when Xc exceeds 15%. Similar variations

have been obtained by Magon for a PLA with 1.4% D isomer [32]. As a consequence, an amorphous phase part does not participate to the glass transition. Thus, the RAF must be taken into account such as: Xma + Xc + Xra = 100% where Xra gives the RAF content. Fig. 6 displays Xra variations as a function of Xc. No difference between the four PLA is observable, but the different thermal treatments induce different crystallinity influence: Xra remains very weak and close to Xra = 10 ± 5% whatever Xc for the samples crystallized from the melt, while the RAF increases up to 35 ± 5% when Xc increases for the samples

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3 2.8 2.6

C' (J/(g.K))

2.4 2.2

ΔCp° = 0.48 J/(g.K)

2 1.8 1.6

amorphous PLA2 1.4

ΔCp = 0.18 J/(g.K)

semi-crystalline PLA2

1.2 1 300

320

340

360

380

400

420

440

460

Temperature (K) Fig. 4. TMDSC in phase components C0 of the complex heat capacity plotted against temperature for the amorphous PLA2 and a semi-crystalline PLA2 (tc = 4000 min ; Xc = 37%). The heat capacity step DC 0p is determined using baseline of solid and liquid C0 .

100 90 80 70

Xma (%)

60 50

Xma + Xc = 100% 40 30 20 10 0 0

10

20

30

40

50

60

70

80

90

100

Xc (%) Fig. 5. Mobile amorphous phase degree (Xma) evolution of each PLA as a function of crystallinity degree (Xc). s correspond to the PLA1 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt, e correspond to the PLA2 crystallized at 353 K from the glassy state,  correspond to the PLA2 crystallized at 393 K from the melt, corresponds to the PDLA crystallized at 353 K from the glassy state, N corresponds to the PDLA crystallized at 423 K from the melt, corresponds to the PLLA crystallized at 353 K from the glassy state, j corresponds to the PLLA crystallized at 423 K from the melt. Uncertainties are Xc ± 5% and Xma ± 2%.

crystallized from the glassy state. Sarasua pointed out that PLLA cold crystallization leads to higher RAF content than crystallization from the melt, when the sample is slowly cooled inside a mold [33]. Crystallization at low temperature leads to small and/or defective crystal formation, generating probably a higher tie molecule content between crystalline and amorphous phase, i.e. a higher RAF volume. Moreover, it has been shown that different crystallization procedures induce different crystal-

line microstructures for PLLA [34]: it crystallizes as the a form when the crystallization temperature Tc is higher than 393 K, while for Tc below 393 K the a0 form consisting in disordered crystal with hexagonal packing is proposed [35]. The a0 crystal is transformed into ordered a form during heating. From the three phase model, we show that a0 crystalline form generates greater RAF and that coupling between phases is stronger than for the more perfect a crystalline form.

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50 45 40 35

Xra (%)

30 25 20 15 10 5 0 0

10

20

30

40

50

60

70

80

90

100

Xc (%) Fig. 6. Rigid amorphous fraction quantity (Xra) evolution of each PLA as a function of crystallinity degree (Xc). s correspond to the PLA1 crystallized at 353 K from the glassy state, e correspond to the PLA2 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt,  correspond to the PLA2 crystallized at 393 K from the melt, corresponds to the PDLA crystallized at 353 K from the glassy state, N corresponds to the PDLA crystallized at 423 K from the melt, corresponds to the PLLA crystallized at 353 K from the glassy state, j corresponds to the PLLA crystallized at 423 K from the melt. Uncertainties are Xc ± 5% and Xra ± 6%.

In the following the discussion concerns the MAP. We focus on the molecular chain mobility study at the glass transition and more particularly on the CRR average size determination obtained from C0 and C00 TMDSC signals. According to Donth’s approach [36], the characteristic cooperativity volume at the dynamic glass transition temperature Ta noted n3Ta can be estimated from the following equation:

n3T a ¼

Dð1=C p Þ

qðdTÞ2

kB T 2a

ð3Þ

with dT the mean temperature fluctuation related to the dynamic glass transition of one CRR [37,38], kB the Boltzmann constant, q the MAP density and Cp the heat capacity at constant pressure. The D(1/Cp) is equal to (1/Cp)glass(1/ Cp)liquid and these values are estimated from C0 spectra normalized to the MAP quantity obtained from Eq. (2) [39]. Indeed, only the MAP participates to the structural relaxation process at the glass transition and is concerned by the CRR concept. The average CRR sizes are calculated by taking q = 1.25 g/cm3 for the PLA MAP. The temperature fluctuation dT is the C00 Gaussian fit standard deviation in the glass transition domain. As an example, C0 and C00 signals obtained for PLA1 sample with Xc = 35% are presented in Fig. 7. The C0 curve shows the characteristic heat capacity step at the glass transition. The C00 peak looks complex for this intermediate crystallinity degree. Indeed, the maximum is Ta = 340 K but a shoulder at higher temperature is observable. In a previous paper [17], we showed that the shape and the maxima of the C00 peaks depend of Xc. We proposed to explain these variations by the existence of two types of mobile amorphous phases in partially crystal-

lized PLA: an inter-spherulitic amorphous phase (i.e. the amorphous matrix) and an intra-spherulitic amorphous one. These two MAP parts present different C00 peaks. This model agrees with over observations obtained by Picciochi for aged PLA samples [40]: a complex relaxation phenomenon could occur at Tg and two endothermic peaks assigned to enthalpy recovery could be detected for intermediate crystallinity degrees, indicating two distinct glass transition dynamics. This behavior has been attributed to different relaxation mechanisms in the inter and intra spherulitic amorphous phases. The low temperature process is assigned to the segmental motions within interspherulitic amorphous phase and the high temperature process should be assigned to the intra-spherulitic amorphous phase presence. We must precise that the intra-spherulitic amorphous phase cannot be compared to the RAF, since the glass transition of the intra-spherulitic amorphous phase is observed in the glass transition temperature domain (5 K above the amorphous matrix glass transition). Fig. 7 gives results for a sample with spherulites immersed into the amorphous matrix (similar to the Fig. 2 picture). Thus, we suppose that the amorphous phase response is the sum of intra-spherulitic and bulklike phase responses. As a consequence, a dT value cannot be extracted directly for intermediate Xc. As shown in Fig. 7, the experimental curve is fitted by a curve P, which is the sum of two Gaussian curves called P1 and P2: P = x.P1 + y.P2 with x + y = 1. The P1 and P2 curves are fitting initially the C00 peaks for Xc = 0 or Xcmax respectively, and progressively adjusted to give the best fit for intermediate Xc. Then, the CRR size can be obtained for each sample and each part of the amorphous phase. From the P1 parameters, the CRR sizes nTa1 in the inter-spherulite amorphous-phase

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0.06

1.8

P 0.05

1.7

C'

0.03 1.5 0.02

C'' (J/(g.K))

C' (J/(g.K))

0.04

x.P1

1.6

1.4 0.01 1.3

0

C''

y.P 2 1.2

-0.01 320

325

330

335

340

345

Temperature (K) Fig. 7. C0 and C00 TMDSC curves obtained for a PLA1 crystallized during 45 min (Xc = 35%). The dashed curves are the adjusted Gaussians x.P1 and y.P2 corresponding to the contributions of the amorphous matrix and the intra-spherulitic amorphous phase respectively. The black squares correspond to P the fit of the C00 experimental curve (P = x.P1 + y.P2).

.

are estimated and reported in Fig. 8; from the P2 parameters, the CRR sizes nTa2 in the intra-spherulite amorphous phase are estimated and reported in Fig. 9. No CRR size variation is observed in the matrix during the spherulite growth whatever the crystallization procedure and whatever the PLA. An average value of nTa1 = 2.75 ± 0.25 nm can be given. Concerning the amorphous phase trapped in the spherulites, a CRR size decrease occurs when the spherulites grow: at the growth beginning, i.e. when the

spherulites are small and dispersed into the amorphous matrix (for Xc less than 20%), the CRR sizes are the same than in the matrix. So, the amorphous phase dynamics are not modified by the crystalline lamellae. When the spherulites grow enough to finally take up the whole space, the CRR sizes become smaller and smaller and reach very low values. The Donth’s [36] approach allows estimating the monomer number per CRR Na. For the amorphous matrix and for low crystallinity degree, Na reaches 293

3.5

2.5 .

Cooperativity length ξΤα (nm)

3

2

1.5

1 0

10

20

30

40

50

60

70

80

Xc (%) Fig. 8. CRR size evolution in the amorphous matrix as a function of the crystallinity degree for the different PLA. s correspond to the PLA1 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt, e correspond to the PLA2 crystallized at 353 K from the glassy state, and  correspond to the PLA2 crystallized at 393 K from the melt. The dashed line corresponds to the CRR size average value. The error bars are calculated from the generally accepted value of approximately 10% as proposed in the Ref. [51].

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Cooperativity length ξΤα (nm)

3.5

3

2.5

2

1.5

1 0

10

20

30

40

50

60

70

80

Xc (%) Fig. 9. CRR size evolution in the intra-spherulitic mobile amorphous phase as a function of the crystallinity degree for the different PLA. s correspond to the PLA1 crystallized at 353 K from the glassy state, e correspond to the PLA2 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt,  correspond to the PLA2 crystallized at 393 K from the melt, corresponds to the PDLA crystallized at 353 K from the glassy state, N corresponds to the PDLA crystallized at 423 K from the melt, corresponds to the PLLA crystallized at 353 K from the glassy state, j corresponds to the PLLA crystallized at 423 K from the melt. The error bars are calculated from the generally accepted value of approximately 10% as proposed in the Ref. [51].

while it is equal to only 23 in the intra-spherulitic amorphous phase for the highest crystallized PLLA. A correlation between an amorphous phase constrained by different factors (crystalline phase, nanoparticules. . .) and the CRR average size decrease has been already observed in different polymeric systems [41,47]. In this work, the confinement effect is associated with smaller CRR and higher Tg (or Ta). It is not a general trend but a glass transition increase with confinement has been also observed in the case of polymer-nanocomposite materials [42–45]. Other studies showed that the more constrained the amorphous phase, the smaller the CRR average size [10,13,46,47]. Thus, it is interesting to compare the CRR values with the thickness of the intra-spherulitic amorphous phase. The broader of the melting peak occurring in the DSC plots for semi-crystalline polymer is usually attributed to the crystalline lamella thickness distribution. A DSC profile, heat flow as a function of temperature, allows a lamella thickness distribution estimation by simply using the Gibbs–Thomson equation [48]: 

Tf ¼ Tf 1 

2r e  L:DHf

! ð4Þ

where Tf is the determined melting temperature of a crys talline lamella with a thickness equal to L, T f is the equilibrium melting temperature of the crystalline lamellae having an infinite thickness, re is the surface energy of  the crystalline lamella basal surface, and DHf is the calculated melting enthalpy of a fully crystalline material. It must be pointed out that Eq. (4) is only valid for lamellae with lateral dimensions larger than their thicknesses,  which is generally the case. The values of re and T f are de11 rived from literature data and are 53.6  10 J/m2 [49]

and 480 K respectively [50]. From the maximum temperature of the melting peak, a lamella thickness value Lc is obtained. Using the three phase model, the mobile amorphous phase thickness Lma ¼ ðX ma  Lc Þ=X c can be deduced and reported in Fig. 10. The Lma calculus is only made for the maximum crystallized materials i.e. when only the contribution of the intra-spherulitic amorphous phase exists. In these cases, there is no inter-spherulitic amorphous phase and it is possible to consider that Lma gives a mobile amorphous phase size estimation in the spherulites. The main problem of this method is that Lma is calculated from the melting peak while CRR size is deduced from glass transition data. For crystallized from the melt PLA, no modification of the stable a phase occurs during heating. For cold crystallized samples, a0 to a crystalline phase evolution occurs during DSC heating. In a previous work [17], a PLA1 cold crystallized sample (tc = 90 min, Xc = 42%) has been studied by small angle X-ray scattering, SAXS, using synchrotron radiation (transmission mode) at the Soft Condensed Matter A2 beamline at HASY(DESY) synchrotron facility in Hamburg (Germany). From the long period obtained by SAXS, a value of Lma ¼ L  X ma ¼ 9:2 nm has been calculated which is close to the DSC value (Lma = 8.7 nm see Fig. 10). So, even for cold crystallized samples, DSC seems to give reasonable Lma values. In a first approach we can suppose that DSC values are available and no significant evolution of the crystalline lamella thickness occurs during heating. In this context, Fig. 10 reports the MAP thickness as a function of the CRR size. This phenomenon is directly related to the crystalline lamellae and RAF dimensions, and then to the sample thermal treatment. Indeed, the lowest MAP thicknesses and the lowest CRR sizes are obtained for PLA crystallized from the melt (this procedure leading a high crystallinity degree and generating a

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3

Cooperativity length ξTα (nm)

2.8 2.6 2.4 2.2 DSC

2 1.8

SAXS

1.6 1.4 1.2 1 0

2

4

6

8

10

12

14

16

18

20

Lma (nm) Fig. 10. CRR size evolution in the intra-spherulitic mobile amorphous phase as a function of the MAP thickness Lma for the different PLA. s correspond to the PLA1 crystallized at 353 K from the glassy state, e correspond to the PLA2 crystallized at 353 K from the glassy state, d correspond to the PLA1 crystallized at 403 K from the melt, D correspond to the PDLA crystallized at 353 K from the glassy state, N corresponds to the PDLA crystallized at 423 K from the melt, h corresponds to the PLLA crystallized at 353 K from the glassy state, j corresponds to the PLLA crystallized at 423 K from the melt. The dashed line is a linear tendency curve. The results obtained respectively by SAXS [17] and DSC measurements for the PLA1 crystallized from the glassy state at 353 K during 90 min are indicated on the figure.

high crystalline lamellae thickness), while the highest MAP thicknesses and the highest CRR sizes are obtained after cold crystallization (this procedure leading a low Xc and a low crystalline lamellae thickness). Intermediate values are obtained for some cold-crystallized samples: in these cases, the Lma decrease is mainly caused by the strong RAF growth. Anyway, there is a correlation between the MAP thickness and its relaxation dynamics. We must point out that Lma is always bigger than nTa. These results suggest that the nTa decrease cannot be only associated to a pure geometrical effect. Complementary analyses using synchrotron facility must be performed to conclude without the DSC help on the CRR size evolution with the MAP dimension.

ness is progressively reduced. No L/D ratio effect is directly put in evidence: The cooperativity parameters seem to depend only of the crystallinity degree and of the RAF content, i.e. of the MAP thickness. Crystallization from the melt leads to higher Xc and consequently, to smaller CRR size. The stereoregularity effect is indirect: a lower stereoregularity implies crystallinity rate and crystallinity degree reductions: the MAP is weakly modified. It is also shown that the amorphous matrix characteristics are not modified by the appearance and growth of spherulites. Concerning the inter-spherulite CRR size, no significant differences are observable between the different PLA and between the crystallization procedures: at Tg, cooperative motions occur in the matrix with nTa = 2.75 nm whatever the L/D ratio and whatever the crystallization temperature.

4. Conclusion References During PLA sample isothermal crystallization, important molecular dynamic variations occur in the intra-spherulitic amorphous regions. First, a strong restriction of amorphous chain segment mobility occurs, due to the polymer chain part fixation to the crystalline lamellae. This phenomenon implies the RAF appearance, the RAF degree depending of the crystallization procedure. Crystallization from the melt at T equal or greater than 393 K leads to an a crystalline phase and a low RAF degree (10%), while cold crystallization at T = 353 K leads to less perfect a0 crystalline phase and to a great RAF degree (until 35%). No PLA stereoregularity effect is put in evidence from the RAF variations. Secondly, the MAP is trapped between RAF and crystalline lamellae and its molecular dynamic clearly depends of the microstructure. The CRR size and the number of monomer unit per CRR drastically decrease (from 293 for amorphous samples to 23 for the highest crystallized PLLA) when the MAP thick-

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