From a Three-Phase Model to a Continuous Description of Molecular

Article pubs.acs.org/Macromolecules

From a Three-Phase Model to a Continuous Description of Molecular Mobility in Semicrystalline Poly(hydroxybutyrate-cohydroxyvalerate) Antonella Esposito,*,† Nicolas Delpouve,† Valerio Causin,‡ Alexandre Dhotel,† Laurent Delbreilh,† and Eric Dargent† †

LECAP, Normandie Université-UNIROUEN, Rouen 76000, France Dipartimento di Scienze Chimiche, Università degli Studi di Padova, 35131 Padova, Italy

‡

S Supporting Information *

ABSTRACT: In most cases, a three-phase model consisting of crystalline domains surrounded by rigid amorphous areas dispersed in the mobile amorphous phase is required and eventually sufficient to accurately describe the microstructure of semicrystalline polymers. This work shows that the microstructure developed by poly(hydroxybutyrate-co-hydroxyvalerate) by cold crystallization is better described by a complex two-phase model in which the boundaries of the crystalline domains and the surrounding amorphous environment form a “continuum of mobility”. This concept can be extended to a wide range of semicrystalline polymers. When the crystalline and the amorphous phases are strongly coupled, the rigid and mobile amorphous fractions are hardly fractionated, and the whole noncrystalline phase should be rather depicted as continuum with a broad distribution of the relaxation times associated with the glass transition. Such a depiction of the amorphous phase allows taking into account any modification of the mobility landscape with time, which can be evidenced as the progressive spreading of the relaxation functions. From a practical point of view, the rigidification of the “continuum of mobility” upon storage in conditions of cold crystallization could be considered as a cause of the progressive embrittlement sometimes observed in semicrystalline materials during physical aging and would be explained by a redistribution of the relaxation times translated in terms of relaxation temperatures.

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INTRODUCTION The structural representation of semicrystalline polymers as constituted by an amorphous phase separated from a crystalline phase (two-phase model) is generally better replaced by a three-phase model1−3 including an additional fraction that connects the amorphous to the crystalline phase. The incomplete decoupling between the portions of random coils in the amorphous phase and the surface of the crystals is due to the length of the polymer molecules that is much higher than the dimensions of the crystalline phase.4,5 When the coupling is strong enough, the domain of involved molecular segments may be sufficiently large to produce an intermediate phase in which the mobility of the amorphous portions of chains is restricted by the interfacial geometrical constraints imposed by the neighboring crystalline portions.6 This intermediate nanophase is called rigid amorphous fraction (RAF) and is defined by opposition to the theoretically unconstrained mobile amorphous fraction (MAF) as the portion of amorphous phase that does not contribute to the heat capacity increment at the glass transition.7,8 The devitrification of the RAF requires more energy and therefore occurs at higher temperatures. As a consequence, when investigating the molecular dynamics at the © XXXX American Chemical Society

glass transition by techniques such as differential scanning calorimetry,9 dielectric spectroscopy10 or solid-state NMR,11 the RAF is typically revealed by a value of the relaxation strength that is lower than expected from the fraction of noncrystalline phase.12 Many studies have highlighted the complexity behind the development of the RAF. Depending on both the polymer and the conditions of crystallization, the RAF can either establish during the final stages of the crystallization, i.e., after spherulites’ impingement,13 or concomitantly with crystals’ growth.5 Once established, the RAF can devitrify in a very wide temperature range,14 possibly overlapping cold crystallization or melting, under the form of either a welldefined second glass transition15 or a gradual variation of the heat capacity, indicating that several possible macromolecular organizations may coexist.8 Singular diffusion properties have recently been reported in semicrystalline polymers16,17 in connection with the high free volume attributed to the RAF,18 which makes it interesting to clarify the influence of thermal Received: February 22, 2016 Revised: June 13, 2016

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DOI: 10.1021/acs.macromol.6b00384 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

involved in the vitrification and devitrification of the RAF at temperatures spanning the whole crystallization domain (lower and upper boundaries, that is to say, the closest and the farthest with respect to the glass transition) would allow predicting the possible outcomes in other semicrystalline PHA systems. In this work, new results are presented to get a deeper understanding of the consequences of the crystallization conditions (temperature, time) on the vitrification and devitrification of amorphous fractions. The molecular mobility of a PHBV random copolymer with 3% HV and 97% HB repeating units was investigated as a function of the microstructure developed through different thermal treatments (quenching from the melt, isothermal crystallization after cooling from the melt, and isothermal cold crystallization after heating from the glassy state). Whereas quenching from the melt is the most efficient and common way to obtain a totally amorphous polymer, the choice of the crystallization procedure is crucial to the development of a well-controlled microstructure. In this work, two crystallization pathways were chosen to access different forms of RAF and therefore observe different α relaxations, as reported by Righetti and Di Lorenzo’s research group42 about PHB. The obtained microstructures were investigated by wide-angle X-ray diffraction (WAXD), small-angle X-ray scattering (SAXS), and Flash DSC. The molecular mobility was investigated by performing temperature-modulated differential scanning calorimetry (MT-DSC) and broadband dielectric spectroscopy (BDS) measurements.

history on the dynamics of devitrification of the RAF. Obviously, the investigation of the molecular mobility in semicrystalline polymers also includes the behavior of the MAF. Broadband dielectric spectroscopy is a performing tool to investigate the molecular mobility in small fractions of amorphous phases relaxing in complex systems. It may be the case of semicrystalline polymers with high degrees of crystallinity19 but also of systems where a confinement effect is induced either by the presence of nanoparticles20,21 and multiphase polymers22 or by geometrical restrictions.23−29 Although the effects of a geometrical constraint are definitely lower in the MAF, it has been evidenced that its relaxation dynamics can also be strongly affected by the crystallinity degree in consequence of both the confinement effect induced by the crystalline phase directly on the RAF and the subsequent confinement effect of the latter on the MAF.30,31 When the MAF splits into intra- and interspherulitic amorphous regions, calorimetric measurements can even show two separate signatures within the glass transition temperature range.32,33 To overcome the issues related to such a complex molecular mobility landscape, one can limit the investigation of the relaxation dynamics in the amorphous phase of a semicrystalline polymer to the extreme cases, i.e., in the absence of crystals and when the crystallization is performed to its maximum extent. Among the emergent semicrystalline polymers, polyhydroxyalkanoates (PHAs) have been the object of recent investigations concerning the development of the RAF during crystallization and cooling.34−36 PHAs are linear biopolyesters produced by bacteria via the fermentation of sugars and/or lipids to store energy in conditions of physiological stress.37,38 The most common and simplest bacterial PHA is poly(hydroxybutyrate) (PHB), but hydroxybutyrate (HB) repeating units can be associated with other repeating units such as hydroxyvalerate (HV) or hydroxyhexanoate (HHx) to obtain PHBV or PHBHHx copolymers with different microstructures. It is possible to control PHAs microstructure by producing copolymers with variable ratios of different repeating units, and/or by adding nucleating agents such as boron nitride,39,40 and/or by performing different thermal treatments. One possible technique to correlate the coupling of the amorphous and crystalline domains to the macroscopic properties of semicrystalline polymers consists in measuring the change in wide-angle X-ray diffraction angle with load.41 Nonetheless, most of the investigations concerning the impact of the RAF on the macroscopic properties presently reported in the literature are based on the quantification of each fraction involved in the three-phase model and the subsequent comparison with the results of other characterizations. Quantifying each fraction in a three-phase model implicitly suggests that (1) the RAF and the MAF can be easily fractionated, (2) both the RAF and the MAF are homogeneous, and (3) one can predict a given property by knowing their respective contents. However, sometimes this vision leads to unsatisfying outcomes, essentially because it does not take into account the peculiar properties of the RAF and the MAF, in particular their macromolecular arrangement and their molecular mobility. Besides, although investigating the molecular mobility at the glass transition in the MAF of semicrystalline polymers is very common, the molecular dynamics of the RAF are mostly unknown. Since the physical nature of the RAF is directly depending on the crystallization conditions, its organization can dramatically vary from one thermal treatment to another. Investigating the mechanisms

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MATERIALS AND METHODS

A commercial grade of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) having a weight-average molecular weight of 350 000 g mol−1 and a content of hydroxyvalerate (HV) monomer units of 3% (ENMAT Y1000 P) was supplied by TianAn Biopolymer, China. The polymer was submitted to different thermal treatments as illustrated in Figure 1. Quenching. Melting (190 °C), annealing (2 min at 190 °C), and quenching in liquid nitrogen to get the polymer in its fully amorphous glassy state. Melt isoT Cryst (Isothermal Crystallization from the Melt). Melting (190 °C), annealing (2 min at 190 °C), cooling down to 110 °C at a rate of 20 K min−1, crystallizing to the highest possible extent

Figure 1. Thermal treatments: Quenching, Melt isoT Cryst (isothermal crystallization from the melt), and Cold isoT Cryst (isothermal crystallization from the glassy state). The temperature ranges expected for glass transition (−10 to 10 °C), cold crystallization (20 to 50 °C), crystallization from the melt (120 to 70 °C), and melting (130 to 180 °C) are also represented.40 B


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Novocontrol Technologies GmbH (accuracy in tan δ ∼ 0.001, sensor diameter 20 mm, combs-gold plated copper). The comb fingers are 150 μm in width and 35 μm in thickness and are spaced by 150 μm. Each electrode was calibrated prior to sample deposition by determining their respective geometric (empty) capacity (C0) and substrate capacity (Csu) through measurements of a reference material (mineral B-oil from Vacuubrand) of known permittivity. Measurements were carried out in a frequency range of 10−2−106 Hz by an Alpha-A analyzer from Novocontrol Technologies GmbH. A Quatro Cryosystem (Novocontrol Technologies GmbH) was used to control the temperature with a stability of ±0.2 °C. The temperature was increased from −150 to −10 °C by successive steps of 10 °C and then from −9 to 60 °C by successive steps of 1 °C to improve the resolution in the glass transition’s temperature range. The Havriliak− Negami (HN) complex function was used to analyze the dielectric relaxation curves:

in isothermal conditions (110 °C for a duration of 120 min), and quenching in liquid nitrogen to freeze the microstructure. Cold isoT Cryst (Isothermal Crystallization from the Glassy State). Quenching, crystallizing to the highest possible extent in isothermal conditions (25 °C for a duration of 1000 min), and quenching again in liquid nitrogen to freeze the microstructure. Thermal treatment (c) was also prolonged to 1 week and 1 month because storing polymers at room temperature is a common procedure, and it is therefore interesting to monitor the possible evolutions of their microstructure. However, in most of the text, the duration of Cold isoT Cryst has to be considered of 1000 min (unless otherwise stated). Wide-angle X-ray diffractometry (WAXD) and small-angle X-ray scattering (SAXS) measurements were performed on all the treated samples. WAXD patterns were recorded in the diffraction angular range 2θ = 10°−45° (step 0.10° and counting time 10 s/step) by a Philips X’Pert PRO diffractometer working in reflection mode and equipped with a graphite monochromator on the diffracted beam (Cu Kα radiation, λ = 0.154 nm). SAXS patterns were recorded by a MBraun system with a Cu Kα radiation from a Philips PW 1830 X-ray generator. The data were collected, corrected for blank scattering, desmeared, and Lorentz-corrected. The degree of crystallinity induced by each thermal treatment was evaluated at room temperature (25 °C) from both the wide-angle diffraction (XC WAXD) and the small-angle scattering (XC SAXS) traces. WAXD experimental curves were classically fitted with a two-phase model, and XC WAXD was obtained by comparing coherent scattering (crystalline diffraction area) to the total area (including the underlying amorphous halo). The average size of the crystalline domains was estimated by Scherrer’s equation43,44 applied to the two main coherently scattering peaks, i.e., to the (020) and the (110) crystallographic planes. A fitting method for SAXS patterns was used as previously developed on the basis of a theoretical model45,46 referring to the Hosemann’s model,47 which assumes the presence of lamellar stacks having an infinite side dimension. The position of the peaks in the SAXS patterns directly provided the values of the long period (S Z), allowing calculating the amorphous (S A) and crystalline (S C) lengths. XC SAXS was then evaluated as the ratio between the thickness of the crystalline lamellae over the long period (SZ = SA + SC )48 (Supporting Information #1). Samples with mass comprised between 5 and 10 mg were enclosed in standard aluminum pans and thermally treated. Temperaturemodulated differential scanning calorimetry (MT-DSC) could be performed right after each thermal treatment, without delay, by Discovery DSC (TA Instruments). Prior to measurement, indium and sapphire standards were used for energy, temperature, and thermal capacity calibrations. All the thermal treatments and the characterizations were performed under N2 (50 mL/min) to prevent oxidative degradation. A fresh sample was used any time a new thermal treatment and/or measurement was started. Each measurement was performed at least twice to ensure repeatability and good accuracy. MT-DSC ramps were performed in heat-iso conditions (heating from −50 to 190 °C at a rate of 2 K min−1 and modulating ±0.32 °C every 60 s) because previous works proved that such experimental parameters are suited to investigate the evolution of the microstructure in semicrystalline polymers.49 The C* = f(T) signal resolved for the real component was exploited according to the two-phase and threephase models previously reported by Righetti and Di Lorenzo’s research group34,35,50 and used to estimate the fractions of crystalline (C), rigid amorphous (RA), and mobile amorphous (MA) phases (XC, XRA, and XMA, respectively). Flash DSC (Flash DSC1, Mettler Toledo) was also used to characterize the microstructures. Right after performing each thermal treatment, a tiny fragment of the sample (tens of nanograms) was collected, placed on the MultiSTAR chip sensor, and analyzed within the shortest delay by heating it up to 200 °C at a rate of 1000 K s−1. More information about the experimental protocol and temperature corrections used for Flash DSC measurements are available in Dhotel et al.51 Broadband dielectric spectroscopy (BDS) experiments were performed using interdigitated electrodes (BDS1410-20-150) from

ε*(ω) = ε∞ +

ΔεHN [1 + (iωτHN)αHN ]βHN

(1)

This formalism allows fitting the real (ε′(ω)) and imaginary components (ε″(ω)) of the complex dielectric permittivity (ε*(ω)), from which it is possible to evaluate the relaxation strength ΔεHN, the relaxation time τHN, and the symmetric and asymmetric broadening factors αHN and βHN.52,53 The HN function can be expressed as a superposition of individual Debye relaxation phenomena correlated to each other by a function in the frequency domain f(τ). As such, the inverse Fourier transform of the HN function can be numerically calculated to obtain the corresponding time-domain correlation function ϕ(t), which informs about the distribution of the relaxation times. Because the linear superposition of simple exponential decays results in a stretched exponential behavior, the ϕ(t) function was fitted by the Kohlrausch− Williams−Watts (KWW) function54,55 to obtain the βKWW stretching exponent. The HN fitting parameters (αHN and βHN) are correlated with the βKWW stretching exponent.56 The equations are available in Supporting Information #2.

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RESULTS AND DISCUSSION Figure 2 shows the WAXD spectra recorded at room temperature (25 °C) on the PHBV samples right after each thermal treatment. The amorphous halo obtained after Quenching proves that the thermal treatment was effective.

Figure 2. WAXD patterns recorded at room temperature (25 °C) after the thermal treatments Quenching, Melt isoT Cryst (isothermal crystallization from the melt), and Cold isoT Cryst (isothermal crystallization from the glassy state). C


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Table 1. Crystallinity Degrees (XC) Obtained by WAXD and SAXS on PHBV Samples Treated by Quenching, Melt isoT Cryst (Isothermal Crystallization from the Melt), and Cold isoT Cryst (Isothermal Crystallization from the Glassy State)a WAXD Quenching Melt isoT Cryst Cold isoT Cryst

SAXS

XC WAXD (%)

size(020) (nm)

size(110) (nm)

XC SAXS (%)

S Z (nm)

S C (nm)

S A (nm)

0 66 44

n.a. 37 15

n.a. 26 13

0 66 50

n.a. 6.7 5.0

n.a. 4.4 2.5

n.a. 2.3 2.5

a The average size of the crystalline domains was estimated by Scherrer’s equation43 perpendicularly to the (020) and (110) crystallographic planes. SAXS traces were fitted for the long period (S Z), the thickness of the crystalline lamellae (S C), and the thickness of interlamellar amorphous regions (S A).

Two main peaks are observed in both Melt and Cold isoT Cryst samples; the literature reports that the first peak (2θ ≈ 13.3°) corresponds to the (020) crystallographic plane and the second peak (2θ ≈ 16.7°) corresponds to the (110) crystallographic plane57−59 of the orthorhombic crystal lattice of PHB.60,61 These two peaks were used to estimate the average size of the crystalline domains responsible for coherent scattering perpendicularly to each crystallographic plane. The values obtained by Scherrer’s equation43 are reported in Table 1 along with the degrees of crystallinity assessed by fitting WAXD patterns (XC WAXD).62 It appears that Melt isoT Cryst leads to higher overall crystallinity degrees as compared to Cold isoT Cryst and that the sample crystallized from the melt developed larger crystalline domains (the peaks are more defined and much sharper) with respect to the sample crystallized from the glassy state, whatever the crystallographic direction considered. Cold isoT Cryst samples stored at 25 °C for longer times (up to 1 month) were also characterized by WAXD and showed no increase in the crystallinity degree (Supporting Information #3).

lamellar stacks, with a smaller average long period. The values obtained for the long period (S Z), along with the average thicknesses of the amorphous layers (S A) and the crystalline lamellae (S C), confirm that melt crystallization is the most efficient approach for maximizing the degree of order within the material. Melt isoT Cryst induces a longer periodicity in the layered structures within the spherulites (6.7 nm vs 5.0 nm), which appears to be beneficial only to the crystalline lamellae, as the interlamellar amorphous regions have the same average thickness whatever the thermal treatment (2.3 nm vs 2.5 nm). Table 1 compares the degrees of crystallinity assessed by fitting WAXD patterns (XC WAXD)62 to the values obtained from the SAXS traces (XC SAXS). In general, the degree of crystallinity assessed by SAXS is equal to (or larger than) the degree of crystallinity estimated by WAXD.63 Any divergence can be explained considering the difference between the two techniques; SAXS is only sensitive to the crystalline and amorphous regions organized in lamellar stacks, whereas WAXD allows the detection of all the regions contributing to the semicrystalline framework, eventually including the amorphous regions located outside the lamellar stacks64 or less-regularly alternating to crystalline lamellae. WAXD and SAXS provide exactly the same degree of crystallinity for Melt isoT Cryst sample, suggesting that the spatial distribution of the amorphous and crystalline domains is regular throughout the entire volume of the sample with no areas completely devoid of crystalline structures. (One may describe this microstructure as a regular percolating network of crystalline domains.) On the contrary, SAXS slightly overestimates the degree of crystallinity of Cold isoT Cryst sample with respect to WAXD, but the difference is only about 6%. The difference is small enough to consider that most of the amorphous phase is trapped between the crystalline lamellae, even though with a less regular repartition. Crystalline reorganization was observed when performing heating ramps at 10 K min−1 (results previously reported in the literature40). Flash DSC was then used to obtain unbiased information about the nature of the crystalline phases generated before the measurement step because any possible crystalline reorganization induced by the temperature increase is drastically reduced if not completely suppressed. The glass transition temperature appears at approximately 25 °C, which is a value higher than expected for amorphous PHA.65 Such a dependence of the glass transition temperature on the heating (and cooling) rate has been recently observed and investigated over a wide range of heating and cooling rates.51,66,67 Melt and Cold isoT Cryst samples both show an endothermic signal corresponding to melting. The maxima were found to be at 160 °C for Melt isoT Cryst and at approximately 120 °C for Cold isoT Cryst; this confirms that Cold isoT Cryst induced thinner and less stable crystals,68 as revealed by SAXS results

Figure 3. SAXS patterns recorded at room temperature (25 °C) after the thermal treatments Quenching, Melt isoT Cryst (isothermal crystallization from the melt), and Cold isoT Cryst (isothermal crystallization from the glassy state).

The SAXS trace for Melt isoT Cryst sample displays a rather sharp peak, located at lower angles with respect to Cold isoT Cryst sample; this is the evidence for a lamellar organization with a larger average long period and a narrower distribution of the lamellae thicknesses. On the other hand, the Cold isoT Cryst sample, which shows a broader peak shifted toward larger angles, is made of a much less homogeneous population of D


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isoT Cryst (1000 min, 1 week and 1 month). In a first approach, the reference values of heat capacity in the solid and liquid states for PHB69 are used to predict the repartition of crystalline (XC) and mobile amorphous (XMA = 1 − XC) fractions on the basis of a two-phase model. These reference values, experimentally obtained by linear regression, were proven valid since Czerniecka et al.70 provided evidence that they are in good agreement both below and above the glass transition temperature with the heat capacity computed by a quantum design physical property measurement system (PPMS). Using the values of solid and liquid heat capacity of PHB to make calculations about PHBV is a reasonable approximation due to the low content of HV units (the error induced on the calculations of the crystalline and amorphous fractions is estimated at ±3%). The glass transition (Tg ≈ 0 °C) and the subsequent cold crystallization (appearing as a sudden change in the Rev-Cp curve between 30 and 40 °C) for the quenched sample were recorded in the expected temperature ranges.40 The experimental curve perfectly superimposes with the reference Cp solid and Cp liquid lines respectively below and above the glass transition. The sample in the glassy state contains only mobile (i.e., unconstrained) amorphous polymer chain, and the whole sample relaxes in a single-step process corresponding to the glass transition. In other words, after Quenching the whole amorphous solid fraction is given by the mobile amorphous fraction (XMA = 1 and XC = 0 at T < Tg), which is then entirely converted from solid to rubbery through glass transition. Under the assumption of equal heat capacities for crystalline and glassy polymers below the glass transition temperature, and because heat capacities are additive, the expected two-phase repartition of crystalline (XC) and mobile amorphous (XMA = 1 − XC) mass fractions can be obtained with a simple mixing rule.12 Calculating XC as a ratio of enthalpy values extracted from DSC curves is trouble because of the crystalline reorganization occurring at slow heating rates;40 therefore, the values used for XC were the ones obtained by WAXD after each thermal treatment (Table 1). The gray dotted lines reported in Figure 5 represent the repartition of crystalline and amorphous fractions expected under the assumptions of a twomodel phase for Melt isoT Cryst (XC WAXD = 66%) and Cold isoT Cryst (XC WAXD = 44%) samples. As expected in the case of a semicrystalline microstructure, ΔCp (Tg) for Melt and Cold isoT Cryst samples is much lower with respect to the quenched samples because their microstructures in the glassy state include lower fractions of amorphous phase (XMA < 1 and XC ≠ 0 at T < Tg). The corresponding glass transition appears broadened and shifted to higher temperatures (Tg ≈ 12 °C for Melt isoT Cryst sample, and even higher for Cold isoT Cryst sample). According to the literature, this observation can be ascribed to a confinement effect, as reported for other semicrystalline polymers.32,69,71 Rev-Cp curves in Figure 5 also point out that the predictions made on the basis of a simple two-phase model (XMA 2ph = 0.34 for Melt isoT Cryst sample and XMA 2ph = 0.56 for Cold isoT Cryst sample) are unfulfilled in the region of the glass transition and that the RAF must be considered. For example, according to the ΔCp (Tg) values estimated from Figure 5, the Melt isoT Cryst sample seems to have a fraction of amorphous chains relaxing at the glass transition (XMA) which barely corresponds to 0.22, as illustrated by the corresponding red dotted line. The formation of RAF has already been investigated in various polyesters, including poly(ethylene terephthalate) (PET),2,9,72,73 poly(lactic acid) (PLA),34,74

Figure 4. Heating ramps recorded by Flash DSC at 1000 K s−1 on the polymer samples previously enclosed in standard aluminum pans and thermally treated by isothermal crystallization from the melt (Melt isoT Cryst) and isothermal crystallization from the glassy state (Cold isoT Cryst). Quenching was performed in situ on the chip sensor, and then the sample was heated at the same rate for comparison. The mass of the samples was estimated by comparing the values of ΔCp (Tg) obtained by Flash DSC and conventional MT-DSC on quenched PHBV, following a procedure already reported elsewhere.51,66 The heat flow signals were normalized to the sample mass (11, 44, and 36 ng, respectively) and evenly shifted for the sake of clarity.

reported in Table 1 (S C = 2.5 nm for Cold isoT Cryst as compared to S C = 4.4 nm for Melt isoT Cryst). Figure 5 shows the reversing heat capacity (Rev-Cp) signals recorded after Quenching, Melt isoT Cryst (120 min), and Cold

Figure 5. Reversing heat capacity extracted from MT-DSC signals in heat-iso conditions (heating ramp from −50 to 190 °C at a rate of 2 K min−1 modulating ±0.32 °C every 60 s) obtained after the thermal treatments: Quenching, Melt isoT Cryst (isothermal crystallization from the melt), and Cold isoT Cryst (isothermal crystallization from the glassy state) eventually prolonged to longer crystallization times. The reference values of heat capacity in the solid and liquid states for PHB are reported from the literature70 and used to predict the repartition of crystalline (XC) and mobile amorphous (XMA = 1 − XC) fractions on the basis of a two-phase model (gray dotted lines). The red dotted line represents the actual repartition of crystalline and mobile amorphous fractions after Melt isoT Cryst (lower than the predicted 66% XC WAXD dotted line). E


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Macromolecules poly(butylene succinate) (PBS),75 poly(trimethylene terephthalate) (PTT),8 and poly(3-hydroxybutyrate) (P3HB).35,50 Melt and Cold isoT Cryst samples both developed a complex microstructure that requires a three-phase model to be fully described. The temperature dependence of the total amorphous fraction (XA = XMA + XRA) within their microstructure is presented in Figure 6 as compared to the quenched sample (for which XRA = 0 because XC = 0). The comparison is also made with Cold isoT Cryst performed over longer crystallization times.

Melt and Cold isoT Cryst thermal treatments induced a different repartition of the amorphous regions in mobile and rigid. The temperature dependence of (XMA + XRA) for the sample isothermally crystallized from the melt (Melt isoT Cryst) is typical of semicrystalline polymers, as previously reported:73,74,76 a broader glass transition occurring at higher temperatures (as compared to the quenched sample) and involving a smaller fraction of amorphous polymer chains (XMA ≈ 0.25) followed by a very weak devitrification of the residual fraction of polymer chains (XRA ≈ 0.1), which in this case occurs over a temperature range of about 50 °C (from 30 to 80 °C). Evidences that high-temperature crystallization limits the development of the RAF have already been reported in the literature: higher temperatures reduce the overall crystal growth rate, promote the formation of regularly fold surfaces, and reduce the coupling between crystalline and amorphous regions.77 More generally, the RAF only establishes after spherulites’ impingement or when any other topological constraints in geometrically restricted areas are there to inhibit the motions and hinder the organization of the polymeric segments.34 The temperature dependence of (XMA + XRA) for the samples isothermally crystallized from the glassy state (Cold isoT Cryst) is totally different. Almost all the amorphous polymer chains are constrained (XMA < 0.1) and the glass transition is hardly noticeable from Figure 5, but a gradual devitrification of a significant fraction of amorphous polymer chains with lower mobility starts right above the expected glass transition temperature range and progresses at a steady rate as temperature increases, relaxing 4 times faster, because less stable, with respect to the RAF in the Melt isoT Cryst sample. Figure 6 shows how the RAF induced by Cold isoT Cryst (XRA ≈ 0.5 at 5 °C) relaxes over a temperature range of about 80 °C, whereas the RAF induced by Melt isoT Cryst (XRA ≈ 0.1 at 35 °C) relaxes over a temperature range of approximately 50 °C. Ma et al.8 recently submitted another polyester, poly(trimethylene terephthalate) (PTT), to a stepwise temperature program deliberately designed to induce a discrete gradient of microstructural heterogeneity. Then they used a three-phase model to correlate the devitrification of the RAF to the layered structure previously created. Analogously to the description given by Ma et al.,8 the gradual devitrification of the amorphous fractions during a DSC scan would reflect a “continuum of mobility” whose gradient is found when moving from the crystalline phase (where the mobility is at its lowest) throughout the RAF and finally reaching the MAF. The macromolecules directly neighboring the crystalline lamellae are strongly tied to their surfaces and devitrify at higher temperatures because of the subsequent condition of hindered mobility. However, the farther the macromolecules are from the surfaces of a crystalline lamella, the less they sense the interfacial geometrical constraints and the closer their mobility gets to that of the mobile (i.e., totally unconstrained) fraction of amorphous polymer chains. This means that even if a structural representation of Cold isoT Cryst samples with XMA ≈ 0 appears reasonable, distinguishing the RAF from the MAF is quite subtle when it comes to the amorphous layers that are the farthest from the crystals. In this kind of situation, the concept of a “continuum of mobility” with a qualitative description of the amorphous phase provides a more convincing depiction of the microstructure compared to a quantitative three-phase model. Similarly to the coupling observed between the crystalline lamellae and the surrounding amorphous phase

Figure 6. Temperature dependence of the amorphous solid fraction (XMA + XRA) obtained by MT-DSC (heating ramp from −50 to 190 °C at a rate of 2 K min−1 modulating ±0.32 °C every 60 s) after the thermal treatments Quenching, Melt isoT Cryst (isothermal crystallization from the melt), and Cold isoT Cryst (isothermal crystallization from the glassy state) eventually prolonged to longer crystallization times. XC WAXD values for Melt isoT Cryst and Cold isoT Cryst samples are also reported.

The curves (XMA + XRA)solid = f(T) in Figure 6 were obtained as (XMA + XRA )solid = 1 − XC WAXD −

Rev‐Cp(T ) − Cp solid(T ) Cp liquid(T ) − Cp solid(T ) (2)

where the XC WAXD values are those reported in Table 1, the Rev-Cp(T) data are extracted from the curves in Figure 5, and the reference data for heat capacity, i.e., Cp solid(T) and Cp liquid(T), are issued from the literature.70 XC WAXD values are represented in Figure 6 by the arrows indicating 66% CR and 44% CR and are assumed as constant as long as the temperature remains below the melting temperature range. Flash DSC showed that Cold isoT Cryst samples start melting around 80 °C (Figure 4). However, the curves in Figure 6 can be rigorously derived from MT-DSC data only up to 50 °C, i.e., in the temperature range where no reversing melting occurs. Schick and co-workers70 previously showed that no excess heat capacity can be detected for semicrystalline polymers such as bisphenol A polycarbonate (PC) and poly(3-hydroxybutyrate) (PHB)12,70 at temperatures above the glass transition and below the lowest endotherm detected on the total heat capacity signal. The lowest endotherm for semicrystalline PHB (isothermally crystallized at 23 °C) was found to be at 47 °C, which is the reason why in Figure 6 the area between 50 and 80 °C is shaded. F


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⎛ DT0 ⎞ τ = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠

through tie macromolecules and loops, RAF and MAF can be more or less coupled, with devitrification signatures more or less superposed. A better decoupling between the amorphous fractions in Melt isoT Cryst sample with respect to Cold isoT Cryst samples is observed; this indicates that not only the crystalline phase depends on the crystallization conditions but also the mobility landscape described by Ma et al.8 In both Melt and Cold isoT Cryst samples, the RAF starts devitrifying at temperatures above the glass transition of the MAF (T ≥ 5 °C) and below the crystallization temperature and completes its devitrification slightly above 80 °C, when crystalline reorganization starts for Cold isoT Cryst samples and probably contributing to it. These results seem to be in agreement with previous observations made by Righetti et al.42 about PHB after different thermal treatments: that there is a critical temperature for both the formation and the disappearance of the RAF which does not depend on the thermal treatment and that situates at a temperature of about 70 °C. It is worth pointing out that longer crystallization times in Cold isoT Cryst conditions shift the devitrification of the RAF to increasingly high temperatures, considerably reducing the global molecular mobility over a broader temperature range (up to 50 °C). In other words, prolonging Cold isoT Cryst does not increase either XC or XRA but progressively increases the thermal stability of the RAF. This phenomenon could explain the progressive embrittlement of PHA samples stored at room temperature, even if already crystallized to the maximum extent. Figure 7 shows the Arrhenius plots, i.e., log[τ (s)] as a function of temperature (1000/T), obtained by BDS in the

(3)

where τ0 is a pre-exponential factor, D is a dimensionless parameter related to the slope variation (steepness strength), and T0 is a reference temperature. The method consisting in plotting the relaxation times was first introduced by Oldekop,78 fully exploited by Laughlin and Uhlmann,79 and further developed by Angell80 to classify glassformer liquids on the basis of how the temperature dependence of their structural relaxation deviates from the Arrhenius behavior. The fragility index (or steepness index) m was expressed by Angell80 as m=

d log(τmax ) d(T /Tg)

T = Tg

(4)

where τmax is the relaxation time corresponding to the maximum of the α-relaxation peak and T/Tg is the temperature reduced with respect to the dielectric glass transition temperature Tg (average relaxation time of 100 s). The values of both Tg (100 s) and the fragility index m are reported in Figure 7. Similarly to the dynamic glass transition extrapolated to a relaxation time of 100 s, the fragility index is also known to be sensitive to different microstructures. Recent investigations showed that m is a key parameter to evaluate the molecular arrangement and the relaxation dynamics of amorphous phases81,82 because it is supposed to be strongly dependent on the packing efficiency of the macromolecules as well as to the stiffness of their backbone.83−86 In the case of semicrystalline polymers, the discussion about the influence of the crystalline phase on the fragility value is still intense. For instance, Ngai and Roland87 showed that for a variety of materials the parameter m of the MAF is unchanged with respect to the one measured in the completely amorphous state. More recently, some authors associated the variations of m in semicrystalline polymers to the establishment of the RAF;88 others suggested that the less flexible the polymer backbone is the more m is affected by the fact that the amorphous phase is confined.83,89 No universal law has been established so far, as the variations of m with the crystallization conditions depend on the considered polymer.30,73,90 As for PHBV, the presence of crystals (and the subsequent establishment of a rigid amorphous fraction) reduces the m value by approximately 30% (m ≈ 79 for both Melt and Cold isoT Cryst vs m = 113 after Quenching). Melt and Cold isoT Cryst thermal treatments induce totally different microstructures, with only one shared feature: the average thickness of the amorphous regions trapped within the lamellar stacks (Table 1). This shared feature of the microstructure could possibly correlate with the shared value of the fragility index. It is also quite interesting to stress that the fragility index stays unchanged even after Cold isoT Cryst is prolonged to longer crystallization and/or storage times, as the VTF extrapolation of the corresponding Arrhenius plots to a relaxation time of 100 s appears perfectly superimposed to the one obtained after Cold isoT Cryst 1000 min (Figure 7). This suggests that the progressive rigidification of the “continuum of mobility” affects the thermal stability of the RAF (the devitrification is observed at higher temperature) but has no consequences on the relaxation time of the MAF. Whatever the thermal stability of the RAF, i.e., the temperature at which its devitrification occurs,

Figure 7. Arrhenius plots obtained after all the considered thermal treatments (Quenching, Melt isoT Cryst 120 min, and Cold isoT Cryst 1000 min). The glass transition temperature Tg is the value extrapolated to a relaxation time of 100 s. The fragility index m is obtained according to Angell’s approach (eq 4).80

temperature range close to the glass transition (the corresponding experimental data are available in the Supporting Information #4). As expected, the samples exhibit a nonlinear dependence of the relaxation time with temperature, which is typical of the α-relaxation process associated with the glass transition. The Arrhenius plots were fitted with the Vogel− Tamman−Fulcher (VTF) law: G


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where ε0 is the vacuum permittivity, g is the Kirkwood correlation factor, μ2 is the time-correlation function of the total dipole moment, kB is Boltzmans’s constant, T is the temperature, and N/V is the volume density of dipoles. Equation 5 shows how Δε is directly proportional to the number of dipoles relaxing in the amorphous phase and inversely proportional to the temperature. In spite of its intrinsic temperature dependence, an overall increase in Δε is recorded for both Melt and Cold isoT Cryst samples that according to eq 5 could be due to several reasons, including (i) an increase in the correlation factor g (which is rather known to be inversely proportional to temperature91), (ii) an increase in the dipole moment μ2 (to be excluded because the comparison is made between samples of the same polymer), and/or (iii) an increase in the density of dipoles N/V. It is reasonable to assume that the increase in Δε, i.e., the increase in the N/V ratio, is associated with the increasing amount of relaxing amorphous phase due to the devitrification of the RAF. This result confirms that Cold isoT Cryst induces large fractions of rigid amorphous polymer chains that are initially unstable, but whose thermal stability is increased during storage at room temperature. When Cold isoT Cryst is prolonged to even longer crystallization times (1 month vs 1000 min), Δε does not significantly increase, yet the devitrification of the RAF begins at higher temperature. To summarize, (1) the development of the RAF in PHBV occurs in concomitance with the formation of the crystalline domains, and (2) when the polymer is stored at room temperature, the RAF becomes more and more “rigid”. Previous works showed that the RAF established during and/ or right after cold crystallization eventually slows down its kinetics until no more crystals can be formed and then starts to get denser;8,92 this work shows that its thermal stability increases (the manifestation of molecular mobility requires increasingly higher temperatures) as the polymer is stored in the same conditions as crystallization. Similarly to the crystalline domains, which constraint the surrounding polymer chains and freeze them in a disordered arrangement with reduced molecular mobility as they grow, the portions of RAF whose relaxation dynamics is slower gradually constraints the rest of the RAF and progressively shifts the “continuum of mobility” toward longer relaxation times, that is to say, toward higher relaxation temperatures. In other words, the progressive “rigidification” of the already vitrified amorphous phase can be described as a “thermal stabilization” of its molecular arrangement or, equivalently, as a modification of the map of relaxation times within the “continuum of mobility”. This scenario, which confirms and extend the results reported by Ma et al.,8 may dramatically help explaining phenomena such as the progressive embrittlement affecting PHA samples upon storage at room temperature. The BDS signals obtained for the αrelaxation peaks can be fitted with the HN complex function (Supporting Information #2) and properly shifted with respect to the maximum of the peak (ε/εmax) at the corresponding frequency (ν/νHN) to obtain the superimposition shown in Figure 9a, which compares the distributions of frequencies associated with the relaxation phenomena at the glass transition. The inverse Fourier transform of the obtained HN functions, which gives a sigmoid centered in τα (the average relaxation time at the dynamic glass transition), Figure 9b, can then be fitted by the KWW function56 to obtain the stretching exponent βKWW. This parameter is commonly used to discuss the heterogeneity of the relaxation dynamics in the amorphous

the relaxation occurring in the amorphous phase requires the same average relaxation time. Figure 7 also points out that the value of Tg (100 s) differs by one degree after Quenching (−1 °C) and Melt isoT Cryst (0 °C) and that the time−temperature dependences of the corresponding relaxation processes are different. The Arrhenius plots illustrate that for any given temperature in the region T > Tg (100 s) the relaxation process after Melt isoT Cryst requires longer times with respect to Quenching. This behavior is the signature of a restricted mobility in the amorphous phase. The value of Tg (100 s) is significantly shifted in the case of Cold isoT Cryst sample (5 °C). This result is interesting if compared to the devitrification processes shown in Figure 6. The Cold isoT Cryst sample has a lower crystallinity degree with respect to the Melt isoT Cryst sample (44% vs 66%), yet a dramatically higher amount of rigid amorphous phase (XRA ≈ 0.5 vs XRA ≈ 0.1) if a three-phase model is used to describe the microstructure. It is therefore reasonable to assume that the amorphous phase left after Cold isoT Cryst is considerably slowed down in its relaxation kinetics. The evolution in intensity of the α-relaxation peak (the experimental data are available in Supporting Information #4) is given in Figure 8, where the variation of the dielectric

Figure 8. Dielectric strength obtained as a function of temperature by BDS measurements after all the considered thermal treatments (Quenching, Melt isoT Cryst 120 min and Cold isoT Cryst 1000 min, 1 week and 1 month). Δεamorphous and Δεsemicrystalline (parallel dotted lines) represent the temperature dependence of the dielectric strength in the reference states (totally amorphous and crystallized to the maximum extent, respectively).

strength (Δε) associated with the α-relaxation is shown as a function of temperature for all the considered thermal treatments. The temperature dependence of the dielectric strength in the reference states (totally amorphous and crystallized to the maximum extent) is also represented by graphically extrapolating the values recorded after Quenching from below and above the temperature at which coldcrystallization occurs (parallel dotted lines, Δεamorphous and Δεsemicrystalline, respectively). Δε can be expressed using the Kirkwood−Fröhlich equation Δε =

1 μ2 N g 3ε0 kBT V

(5) H


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Figure 9. (a) Relaxation curves obtained after fitting BDS experimental data sets with the HN complex function (Supporting Information #2). The best set of fitting parameters (αHN and βHN) is reported for each relaxation peak: α = 0.84 and β = 0.58 for Quenching (9 °C), α = 0.36 and β = 1 for Melt isoT Cryst 120 min (30 °C), α = 0.33 and β = 1 for Cold isoT Cryst 1000 min (30 °C) and Quenching (30 °C), and α = 0.27 and β = 1 for Cold isoT Cryst 1 week (30 °C) and Cold isoT Cryst 1 month (30 °C). (b) Time-domain correlation function obtained by fitting the inverse Fourier transform of HN fitting curves shown in (a) with the KWW function.56 The value of the stretching parameter (βKWW) are reported for each correlation function: 0.54 for Quenching (9 °C), 0.27 for Melt isoT Cryst 120 min (30 °C), 0.25 for Quenching (30 °C) and Cold isoT Cryst 1000 min (30 °C), and 0.20 for Cold isoT Cryst 1 week (30 °C) and Cold isoT Cryst 1 month (30 °C).

from 0.58 to 1) and widely spread (αHN decreases from 0.84 to 0.33), indicating that the formerly abrupt change in the molecular dynamics at the glass transition converts into a gradual evolution of the molecular mobility and that the distribution of the relaxation times in the residual amorphous phase becomes increasingly heterogeneous. The same behavior is observed when the initially quenched glass is completely crystallized in isothermal conditions at 25 °C for 1000 min. Among all the semicrystalline microstructures considered, Melt isoT Cryst provides the highest value of the αHN fitting parameter (αHN = 0.36); this means that the sample crystallized from the melt is not only the one with the highest degree of crystallinity and the most regularly arranged crystalline phase but also the one with the less heterogeneous mobility landscape. This seems to be linked to a decreased coupling between the amorphous fractions. On the other hand, prolonging storage at room temperature further increases the dynamical heterogeneity of the “continuum of mobility”, as the curve becomes even wider; the minimum values of αHN = 0.27 and βKWW = 0.20 are reached after 1 month storage. This suggests that a decreased value of βKWW means an increased coupling between phases. It is reasonable to assume that the amorphous areas being the closest to the crystalline domains are the most impacted by the reorganization and that this process slowly diffuses to the areas having a higher molecular mobility, therefore enhancing the gradient of mobility throughout the amorphous phase and the heterogeneity of the relaxation process. Here again it is worth pointing out that depicting the microstructure as a simple juxtaposition of three amorphous fractions without investigating their molecular mobility is insufficient to understand phenomena such as the progressive embrittlement of PHA upon storage, since no evolution in the amount of RAF was evidenced when prolonging Cold isoT Cryst. A cross-comparison on the different thermal treatments from both the BDS and MT-DSC points of view confirms that dielectric spectroscopy can be successfully used to evaluate the relaxation of both mobile and rigid amorphous fractions in semicrystalline polymers and proves that its extremely low detection threshold allows measuring fractions of polymer chains with different mobility that would be otherwise quite difficult to indentify exclusively on the basis of calorimetric measurements. A depiction of the microstructure based on the discussion of the molecular dynamics allows giving both a quantitative and a qualitative estimation of the degree of coupling between phases, especially when the systems appears as a heterogeneous “continuum of mobility” rather than a clearly quantifiable three-phase model.

phases at the glass transition; the more stretched are the ϕ sigmoids, the more heterogeneous is the distribution of the relaxation times at the glass transition. Being respectively the frequential and temporal representation of the same relaxation phenomena, Figures 9a and 9b are worth a joint discussion. The distribution of frequencies obtained at 9 °C right after Quenching illustrates the typical behavior of a glass just above its α-relaxation, that is to say, solid-like at ν > νHN and liquid-like at ν < νHN; the inverse Fourier transform of the corresponding HN function, fitted by the KWW function, gives a stretching exponent βKWW = 0.54. As the temperature increases well above the glass transition (30 °C) and the polymeric glass undergoes cold crystallization upon heating, the curves become symmetrical (βHN increases

CONCLUSIONS While the three-phase model is generally considered as the most relevant approach to describe the microstructure of semicrystalline polymers, its representation cannot be considered equally appropriate for any microstructure because it depends on the mobility provided to the system during crystallization. Because of a relatively high molecular mobility, isothermal crystallization from the melt (Melt isoT Cryst) performed to its maximum extent (120 min at 110 °C) on a PHBV random copolymer produces a network of crystalline domains perfectly percolating throughout the entire volume of the sample, with the highest degrees of crystallinity, the largest crystalline domains (37 nm in the (020) direction), the thickest crystalline lamellae (4.4 nm), and the highest thermal stability

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of the crystalline phase (its reorganization only starts when melting temperature is approached, i.e., T > 110 °C). Melt isoT Cryst also induces a relatively weak coupling between the crystalline domains and the residual amorphous phase, establishing only a small fraction of rigid amorphous polymer chains (≈ 10%); as a consequence, the glass transition of the MAF and the devitrification of the RAF are sufficiently well differentiated to adopt a microstructural representation including three distinct fractions. On the other hand, isothermal crystallization from the glassy state (Cold isoT Cryst) performed to its maximum extent (1000 min at 25 °C, i.e., in a condition of relatively low molecular mobility) produces a less regular semicrystalline structure, with significantly lower crystallinity degrees, much smaller crystalline domains (15 nm in the (020) direction), much thinner crystalline lamellae (2.5 nm), and a dramatically lower thermal stability of the crystalline phase (its reorganization starts at 80 °C and biases calorimetric characterizations performed at conventional heating rates). Cold isoT Cryst also induces a much stronger coupling between the irregular crystalline domains and the surrounding amorphous phase, which is almost entirely rigid (≈50%) and whose glass transition is hardly noticeable by MT-DSC. The rigidification of the amorphous phase during Cold isoT Cryst is particularly complex because of such a strong coupling between the crystalline phase and the nearest-neighboring amorphous phase. During crystallization, a RAF is established that is thermally unstable; after 1 week storage at 25 °C, the initial RAF becomes thermally more stable and induces the progressive rigidification of what should better be considered as a “continuum of mobility”. This is, the consequence of a strong coupling between the crystalline phase and the surrounding amorphous layers, and in this case the concept of a two-phase model (crystalline domains embedded in an amorphous environment, the “continuum of mobility”) appears more suitable to describe the microstructure obtained after Cold isoT Cryst. With the measurement of the dynamic glass transition temperature Tg (100 s), the characterization of the temperature dependence of the relaxation time (VTF fits on the Arrhenius plots), and the evaluation of the relaxation dynamics and the fragility index, this study shows that any amorphous phase (mobile, rigid, constrained, confined) can be successfully quantified and monitored via its devitrification. By comparing the results obtained on Melt and Cold isoT Cryst semicrystalline samples with their purely amorphous counterpart, two major effects have been highlighted. The first one is a confinement effect exerted on the amorphous polymer chains within the lamellar stacks and revealed by the same decrease in the fragility index. This result illustrates the existence of a volume contribution to fragility because the amorphous phase is geometrically confined to the same dimension (2.5 nm) independently of the crystallization procedure. The second effect is related to the degree of coupling between the crystalline and amorphous phases and is revealed by a shift of the α-relaxation of glass transition to higher temperatures along with an increased heterogeneity of the molecular dynamics for structures better described by the “continuum of mobility”. In the continuum, no distinction is made between the relaxation rates associated with the devitrification of the amorphous areas far off and adjacent to the crystals. This means that however large and thermally stable, the dynamics of devitrification of the RAF is the same as that of the unconstrained MAF.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00384.

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Methods and results; Figures S1 and S2 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +33 2 32 95 50 83; Fax +33 2 32 95 50 82 (A.E.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Clément Fosse for helping with preparing MT-DSC samples as well as exporting and plotting data. The authors also thank Prof. Peter Mallon (University of Stellenbosch, South Africa) for proof-reading the paper. The authors acknowledge the financial support by Rég ion Normandie to acquire the BDS equipment, the Discovery DSC, and the Flash DSC.

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REFERENCES

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