Temperature dependence of the rigid amorphous fraction of poly(butylene succinate)

In this contribution the temperature evolution of the constrained or rigid amorphous fraction (RAF) of biodegradable and biocompatible poly(butylene succinate) (PBS) was quantified, after detailed thermodynamic characterization by differential scanning calorimetry and X-ray diffraction analysis. At the glass transition temperature, around −40 °C, the rigid amorphous fraction in PBS is about 0.25. It decreases with increasing temperature and becomes zero in proximity of 25 °C. Thus, at room temperature and at the human body temperature, all the amorphous fraction is mobile. This information is important for the development of PBS products for various applications, including biomedical applications, since physical properties of the rigid amorphous fraction, for example mechanical and permeability properties, are different from those of the mobile amorphous fraction.


Introduction
Poly(butylene succinate) (PBS) is a biodegradable and biocompatible polyester produced by polycondensation of succinic acid and 1,4butanediol. Both monomers can be petrol-derived, but can be produced also from renewable resources: succinic acid via fermentation of carbohydrates, 1,2 and 1,4-butanediol through hydrogenation and reduction of succinic acid. 3 Thus, considering the growing tendency towards production of sustainable materials, PBS appears a very interesting polymer, as attested by an increasing amount of papers devoted to the properties and utilization of this polyester.
The low glass transition temperature of PBS, well below room temperature, and the relatively high melting temperature (above 100 C) are similar to those of most common polyolens. Also the mechanical properties do not differ substantially from those of polypropylene, or low-and high-density polyethylene. 4 Currently PBS is commercialized mainly as a component for compostable bags, mulching lms, nets, nonwoven sheets, beverage cups and food utensils, 5 whereas PBS-based composites are of interest for food packaging. [5][6][7] PBS is used in biomedicine, to make bone marrow stem cells, in tissue repair and engineering, to fabricate scaffolds that enhance the regeneration of bone in the dental socket, and also blended with chitosan for antimicrobial and antitumor activity, improved protein absorption and rapid cell growth. 4,[8][9][10][11][12][13][14] In addition, due to its high exibility and toughness, PBS has been widely used in blends with other biodegradable and/ or bio-based polymers, such as poly(lactic acid), poly(hydroxybutyrate), poly(propylene carbonate). [15][16][17][18][19] Although these blends are generally immiscible, materials with improved ductility and reduced brittleness can be obtained.
PBS is a semi-crystalline polymer, characterized by a quite high crystallinity degree (35-45%). Upon melt crystallization, a-crystals grow, whereas upon stretching, a different crystal modication, bform, is obtained reversibly by solid-solid transition. 20,21 Both phases are characterized by a monoclinic cell containing two repeating units, arranged with chain conformation TTTGT GTTTT in the aphase and with all chains in trans conformation in the b-form. PBS crystallization rate is high: the processes is completed in about 1 min at À10 C, and in less than 10 s in the temperature range between 10 and 80 C. 22 This means that quenched PBS cannot be maintained in the amorphous state at room temperature.
In polymers, a semi-crystalline structure necessarily implies the presence of a constrained interphase at the amorphous/ crystal boundary, due to the covalent bonds that connect the crystalline and amorphous regions. The nano-metric constrained amorphous interphase is generally called rigid amorphous fraction (RAF), because it is characterized by reduced chain mobility compared to the mobile amorphous fraction (MAF). 23 The MAF vitries/devitries at T g , whereas vitrication/ devitrication of progressively more constrained amorphous regions, i.e. RAF, occurs at progressively higher temperatures, as clearly reported in quite recent years. 23,24 RAF percentages of about 20-30 wt% have been determined for several polymers at T g , whereas its temperature dependence has been determined only for few polymers. 24 Also for PBS, RAF amount of this order of magnitude has been measured at T g . [25][26][27] Recent studies have demonstrated that the rigid amorphous fraction inuences the performance of semi-crystalline polymers, because many physical properties of the RAF are different from those of the crystalline and the mobile amorphous fractions. [28][29][30][31][32][33][34][35] Experimental evidences and theoretical modelling have demonstrated that the elastic modulus of the RAF (E RA ) is between those of the crystalline (E C ) and mobile amorphous (E MA ) fractions, in the order E MA < E RA < E C . 29,31,32 On the other hand, the density of the RAF (r RA ) is lower than that of the MAF (r MA ), due to the higher RAF vitrication temperature, 32,33 so that the order of the densities turns out to be r RA <r MA <r C , where r C is the density of the crystalline phase.
A rigid amorphous fraction is present in almost all semicrystalline polymers, 23 and can exist in nano-layered polymers, 36-38 block copolymers, 39,40 and polymer nanocomposites. [41][42][43][44][45][46][47][48][49] Since it can constitute a large fraction of the overall material, it has large impact on properties. Huge research efforts have been devoted in the latest years to a thorough understanding of the RAF, as recently reported in a review, 24 where the experimental methods used to monitor the RAF, the inuence of thermal history and crystal structure/morphology on the RAF, and the RAF inuence on material properties are summarized.
These considerations imply that quantitative information on the RAF is essential to design industrial processes for specic applications of semi-crystalline polymers. If mechanical and barrier properties have to be ne-tuned, for example in case of lms for food packaging, it needs to be taken into account that the rigid amorphous and crystalline fractions have opposite effects on barrier properties, 34,35 whereas they together contribute to the material stiffness. [28][29][30][31][32] Thus, a proper balance between crystalline and rigid amorphous fractions is essential to develop a material with specic gas/vapor permeability and exibility.
Needless to say, the above considerations on the RAF density and modulus refer to vitried RAF, since, once the RAF is mobilized, its properties become similar to the MAF. This claries the importance of knowledge on the RAF glass transition. Unfortunately literature information on RAF devitrication are available only for a few semi-crystalline polymers, including among others poly(L-lactic acid), poly(1-butene), poly [(R)-3-hydroxybutyrate], poly(ethylene terephthalate), poly(butylene terephthalate), 50-54 but to date not yet disclosed for PBS. Also the physical properties of the PBS rigid amorphous fraction (for example mechanical or permeability properties) have not yet been investigated.
With this manuscript, data on devitrication of the RAF in PBS are presented, with the aim to favor the interpretation and prediction of physical properties, in particular mechanical and barrier properties, of PBS-based materials. For an accurate quantication of the RAF evolution as a function of the temperature, a preliminary thermodynamic characterization of PBS was performed by differential scanning calorimetry and Xray diffraction analysis.

Chemicals
Additive-free poly(butylene succinate) (PBS) was kindly supplied by SIPOL (Mortara, Italy). The number-average molar mass (M n ) and the weight-average molar mass (M w ) are 27.8 Â 10 3 and 72.7 Â 10 3 g mol À1 , respectively, as determined by gel-permeation chromatography (GPC). The as received PBS chips were dried under vacuum overnight at 60 C, then compression-moulded into 200 mm thick lms. Compression-moulding was performed with a Collin Hydraulic Laboratory Forming Press P 200 E at 130 C for 3 min, then the lms were cooled to room temperature by cold water circulating into the press plates. GPC analyses revealed no sizable change of molar mass of PBS aer compression-moulding.

Thermal analysis
Differential Scanning Calorimetry (DSC) measurements were performed with a Perkin Elmer Calorimeter DSC 8500 equipped with an IntraCooler III as refrigerating system. The instrument was calibrated in temperature with high purity standards (indium, naphthalene, cyclohexane) according to the procedure for standard DSC. 55 Enthalpy calibration was performed with indium. Dry nitrogen was used as purge gas at a rate of 20 mL min À1 . To gain precise heat capacity data from the heat ow rate measurements, each scan was accompanied by a blank run with an empty pan. The sample mass was lower than 10 mg, whereas the mass of the blank and sample aluminium pans matched within 0.02 mg. The temperature of the samples upon heating was corrected for the thermal lag, determined as average by using different standard materials. This lag was 0.05 min, which, for the heating rates of 2 and 10 K min À1 , corresponds to a temperature correction of À0.1 and À0.5 K respectively, whereas for the cooling rates of 2, 5, 10 and 20 K min À1 to corrections of +0.1, +0.25, +0.5 and +1.0 K, respectively.
To measure the thermodynamic solid and liquid specic heat capacities (c p,s and c p,l ), PBS samples were heated to 150 C, and maintained at this temperature for 3 min, in order to erase the previous thermal history. 56 Then these samples were quickly removed from the DSC apparatus, quenched into liquid nitrogen, and rapidly transferred to the DSC cell maintained at À70 C. The PBS quenched samples were analysed (i) by conventional DSC from À70 C to 150 C at the heating rate of 10 K min À1 , to obtain apparent specic heat capacity (c p,app ) curves, and (ii) by TMDSC, with a saw-tooth modulation temperature program, at the average heating rate of 2 K min À1 , with a temperature amplitude (A T ) of 0.5 K and a modulation period (p) of 120 s, to obtain average specic heat capacity (c p,ave ) curve and reversing specic heat capacity (c p,rev ) curve. According to the mathematical treatment of TMDSC data, the modulated heat ow rate curve can be approximated to discrete Fourier series, and separated into average and periodic components. 57,58 The average component is equivalent to the conventional heat ow rate signal under linear temperature program. Thus, the c p,ave curve, calculated from the average heat ow rate at the average heating rate of 2 K min À1 , corresponds to c p,app upon linear heating rate of 2 K min À1 . Conversely, from the periodic component, the c p,rev curve was obtained, according to the following equation: where A HF and A T are the amplitudes of the rst harmonic of the modulated heat ow and temperature, u is the fundamental frequency of temperature modulation (u ¼ 2p/p), m the mass of the sample and K(u) the frequency-dependent calibration factor. The average K(u) values, determined by calibration with sapphire, was 1.06 AE 0.02 and 1.00 AE 0.02 for p ¼ 60 and 120 s, respectively. Non-isothermal crystallization of PBS was performed by cooling at the rate of 2, 5, 10, and 20 min À1 down to 25 C, aer fusion for 3 min at 150 C. Subsequently the samples were cooled quickly to À70 C, and reheated at 10 K min À1 up to 150 C. Aer nonisothermal crystallization at 10 K min À1 , also TMDSC runs were performed with a saw-tooth modulation temperature program, at the average heating rate of 2 K min À1 , with A T ¼ 0.5 K and p ¼ 60 and 120 s, to obtain c p,ave and c p,rev curves.
X-ray diffraction (XRD) analysis X-ray diffraction investigation was performed at room temperature (T room ) in reection mode on PBS samples nonisothermally crystallized at 2, 5, 10 and 20 K min À1 , by using a PANalytical X'PertPro diffractometer (Cu Ka radiation, l ¼ 0.15418 nm; X'Celerator detector). The crystal fraction (X C ) was calculated from the ratio A c /A tot , where A c is the integrated area of the crystalline diffraction and A tot is the integrated total scattering subtracted by the incoherent scattering. For this purpose, a scan without sample and properly scaled was used for each pattern.
In addition, a heating stage Anton Paar TTK450 allowed in situ measurements of PBS samples crystallized at 2 and 5 K min À1 , with temperature control of 0.1 K. The samples were heated from T room at 15 K min À1 . At 60, 95 and 105 C, XRD scans were recorded with acquisition time of 90 s. During the scan collection the temperature ramp was stopped. The average heating rate was about 10 K min À1 . Fig. 1 shows the apparent specic heat capacities (c p,app ) of initially amorphous PBS upon heating at 10 K min À1 , the average specic heat capacity (c p,ave ) and the reversing specic heat capacity (c p,rev ) at 2 K min À1 , together with the thermodynamic solid and liquid specic heat capacities (c p,s and c p,l ) lines, constructed by extrapolating the c p,app and c p,rev data from below the glass transition, and by connecting the region above T g to the melt, respectively. The derived c p,s and c p,l expressions are: c p,s ¼ 1.22 + 0.0031T and c p,l ¼ 1.79 + 0.0016T, with c p,s and c p,l in J g À1 K À1 and T in C. The T g value, determined at half of the c p,app increment, is À40 C at 10 K min À1 , and À42 C at 2 K min À1 . At T g , the specic heat capacity increment (Dc p,a ) is 0.63 J g À1 K À1 . According to Wunderlich's "bead theory", 59 the bead number of the PBS repeating unit is 8, which means that each bead contributes to Dc p,a with 13.5 J mol À1 K À1 . This value is in excellent agreement with the bead contribution reported for the homologue poly(trimethylene succinate) (13.3 J mol À1 K À1 ). 59 At temperatures higher than T g , the amorphous PBS sample undergoes an intense cold crystallization at temperatures increasing with the heating rate. In parallel with the cold crystallization, the c p,rev curve exhibits an irregular oscillation (red dashed line in Fig. 1), which is an artefact, oen occurring in TMDSC analyses upon fast and intense release of latent heat. 60 The expected downward step of the c p,rev curve 61 (red line in Fig. 1) has been reconstructed by interpolation. At higher temperatures, additional exothermic events occur, most likely connected to crystalline reorganization. The progressive increase in c p,rev observed in conjunction with the exothermic processes, attests that these events follow the temperature modulation, in the sense that both crystallization and fusion take place in the two different semi-periods, respectively. The intense melting peak of the c p,app and c p,ave curves is centred at 113 C. In the nal melting region, c p,rev values higher than c p,app and c p,ave indicate that recrystallization occurs extensively up to complete fusion. Fig. 2 shows the c p,app curves of PBS samples crystallized upon cooling at different rates and the c p,app curves upon subsequent heating at 10 K min À1 . As expected, non-isothermal crystallization (Fig. 2a) shis to lower temperatures with increasing the cooling rate. The inset of Fig. 2a suggests that crystallization could take place down to 25 C, although in reduced percentage with respect to the peak (less than 5%). Table 1 lists the peak temperatures of the non-isothermal crystallization process (T c ), and the measured enthalpy of crystallization (Dh c ) values, with absolute value progressively decreasing with increasing the heating rate. The c p,app curves upon heating aer cooling at different rates (Fig. 2b) exhibit an approximate constant increment at T g , which means that the solid fraction (crystalline + rigid amorphous fractions) at T g is independent of the cooling rate. The presence of endothermic and exothermic peaks in the c p,app curves in the temperature range 55-105 C proves that all the PBS samples undergo signicant reorganization/recrystallization processes before Fig. 1 Specific heat capacities of PBS after quench from the melt as a function of temperature: apparent specific heat capacity (c p,app ) at 10 K min À1 , average specific heat capacity (c p,ave ) and reversing specific heat capacity (c p,rev ) at 2 K min À1 (p ¼ 120 s, A T ¼ 0.5 K). The dotted lines are the thermodynamic solid and liquid specific heat capacities (c p,s and c p,l ) of PBS. The inset is an enlargement in the exothermic events region.

Results and discussion
nal melting, in agreement with literature data. 22,62 The shape of the c p,app curves aer cooling at the various rates is totally reproducible.
Calculation of PBS crystallinity from the c p,app curves shown in Fig. 2 requires an accurate value for the enthalpy of melting of 100% crystalline PBS ðDh m Þ. Unfortunately, largely scattered Dh m values are reported in the literature for PBS. 4,18,26,[63][64][65][66] The value of 110 J g À1 , attained with the group contribution method described by van Krevelen, 67 is oen utilized, as well as values included between 200 and 230 J g À1 . [64][65][66] To overcome this problem, the crystalline fraction (X C ) of the PBS samples cooled at different rates was quantied by XRD analysis. Then, the X C values were linked to the enthalpy of crystallization (Dh c ) derived from the c p,app curves (Fig. 2a), to attain, in combination with the temperature dependence of the thermodynamic solid and liquid specic heat capacities, the enthalpy of melting of 100% crystalline PBS as a function of temperature. Fig. 3 shows the XRD scans at T room aer cooling at different rates. The proles show the same set of reections (the main ones at 2q values: 19.6 , 21.9 , 22.6 , 26.0 , 28.8 ), all ascribable to PBS a-form, the modication that commonly grows from the melt. 20 The bell-shaped baseline, connected to the non-ordered regions of the samples, is roughly maintained with similar intensity, suggesting a limited variation of the samples crystallinity.
To conrm that the intense reorganization/recrystallization that occurs upon heating does not involve different crystalline structures, XRD analysis was performed on PBS samples aer cooling at 2 and 5 K min À1 , at selected temperatures upon heating at the average rate of 10 K min À1 . Fig. 4 shows that the XRD proles registered during heating are all due exclusively to the a-phase. The peak shi towards smaller angles observed as the temperature increases is usual for in situ measurements and it is due to thermal expansion of the unit cell, which causes an expansion of interplanar distances. These observations conrm that reorganization/recrystallization occurring upon heating concerns different crystalline populations or morphologies, without change in crystal form. However, as the transformations involve high latent heat exchanges, important  Table 1 Peak temperatures of non-isothermal crystallization (T c ), enthalpy of crystallization measured by DSC, (Dh c ), crystalline fraction measured by XRD (X C ), enthalpy of crystallization of 100% crystalline PBS at T c ðDh c Þ, mobile amorphous weight fraction at T g (w MA ) and rigid amorphous weight fraction a T g (w RA ) for PBS samples non-isothermally crystallized at different rates (estimated errors: AE0.2 C for T c , AE0.4 J g À1 for Dh c , AE0.02 for X C , AE10 J g À1 for Dh c , AE0.02 for w MA AE 0.04 for w RA )  modications of the crystalline organization are expected. This topic will be investigated in detail in a forthcoming study. The crystalline fractions X C of the PBS samples crystallized at different rates are reported in Table 1. The slightly higher crystallinity aer lower cooling rate is reected in a slightly higher T g value (T g ¼ À33 C for the sample cooled at 2 K min À1 , with respect to T g ¼ À36 C for the sample cooled at 20 K min À1 ). From the experimental Dh c values and the crystal fractions X C , the enthalpies of crystallization of 100% crystalline PBS ðDh c Þ at T c were determined as: Dh c ðT c Þ ¼ Dh c =X C , being negligible the contribution to Dh c of the crystallization at low temperature. Table 1 shows that the absolute value of Dh c ðT c Þ decreases with decreasing T c . By taking into account that the enthalpy of melting (Dh m ) is equal to ÀDh c , the temperature evolution of the enthalpy of melting of 100% crystalline PBS was determined through the relationship: with Dc p ¼ c p,lc p,s . From eqn (2), the following average expression: Dh m ðTÞ ¼ ð141 þ 0:57T À 0:0008T 2 Þ AE 10 J g À1 with T in C was obtained. According to this equation, the enthalpy of melting of 100% crystalline PBS at the melting temperature, which is centered at about 113 C, is 195 AE 10 J g À1 , which conrms the Dh m values reported in the literature close to 200 J g À1 . [64][65][66] From the c p.app increment at T g (Dc p,app ), a mobile amorphous weight fraction (w MA ) of 0.37 was calculated for all the samples, as w MA ¼ Dc p,app /Dc p,a . Consequently, the rigid amorphous weight fractions (w RA ) at T g were determined by difference, being X C + w MA + w RA ¼ 1 (see Table 1). The trends exhibited by w RA and in parallel by w C show that the PBS crystals that grow at lower temperatures are coupled with a slightly higher rigid amorphous fraction at T g .
Rigid amorphous fraction can develop during crystallization, especially at low crystallization temperatures, when the chain mobility is low and the segments arrangements in regular crystalline structures is hindered. But RAF can grow also upon the cooling subsequent to crystallization, due to the progressive reduction in chain mobility and the presence of constraints not completely released in proximity of the crystals. Upon cooling, RAF vitrication occurs in a wide temperature range, depending on the distance from the crystals surfaces and the relative mobility hindrance. The RAF formation is a true vitrication process, because generally mobilization of a RAF portion occurs at the same temperature at which it had previously vitried upon cooling. 50 The RAF evolution of PBS at temperatures higher than T g was determined by a comparison of the c p,app , c p,ave and c p,rev data aer cooling at 10 K min À1 . Fig. 5 collects the c p,app curves at 10 K min À1 , and the c p,ave and c p,rev curves at 2 K min À1 and p ¼ 60 and 120 s. Below T g and in the temperature range from T g to about 25 C, the c p,app and c p,rev curves match within the experimental error. This proves that no reversing latent heat is absorbed or released upon heating from T g to about 25 C, which means that up to about 25 C the c p,app and c p,rev correspond to the thermodynamic specic heat capacity of PBS aer cooling at 10 K min À1 . At higher temperatures, the reversing heat capacity becomes dependent on the modulation frequency, attesting the beginning of melting/recrystallization processes. From the thermodynamic specic heat capacity c p,rev , the mobile amorphous weight fraction (w MA ) was determined as: w MA ðTÞ ¼ c p;rev ðTÞ À c p;s ðTÞ c p;l ðTÞ À c p;s ðTÞ (3) Fig. 4 XRD scans collected in situ at the indicated temperature after cooling from the melt at 2 K min À1 (a) and 5 K min À1 (b).

Fig. 5
Specific heat capacities of PBS after cooling at 10 K min À1 as a function of temperature: apparent specific heat capacity (c p,app ) at 10 K min À1 , average specific heat capacity (c p,ave ) and reversing specific heat capacity (c p,rev ) at 2 K min À1 (p ¼ 60 s and p ¼ 120 s, A T ¼ 0.5 K). The dotted lines are the thermodynamic solid and liquid specific heat capacities (c p,s and c p,l ) of PBS. The inset is an enlargement of the specific heat capacity curves. Fig. 6 displays the temperature evolution of w MA and w RA up to about 25 C, with w RA calculated by difference: w RA ¼ 1 À X C À w MA . Also X C , which is constant up to about 25 C is displayed. It is worth noting that below T g the mobile amorphous fraction is vitried, w MA ¼ 0, so that (1 À X C À w MA ) corresponds to the entire amorphous fractions w MA + w RA . The rigid amorphous weight fraction in PBS is approximately 0.25 at T g , and decreases with increasing temperature, becoming zero in proximity of 25 C This means that at T room RAF is absent in PBS. This should be true also aer different crystallization conditions, because the c p,app curves aer solidication at different cooling rates were found perfectly overlapping up to about 50 C (Fig. 2b). As a consequence of the RAF devitrication, the mobile amorphous fraction in parallel increases. At temperatures higher than about 25 C, melting and recrystallization of imperfect crystals contributes to c p,rev , reversing latent heat is exchanged and, consequently, correct w MA values cannot be obtained through eqn (3). However, the beginning of the melting certainly produces a further MAF increase.

Conclusions
An accurate thermal characterization of PBS semi-crystalline samples has allowed to quantify the temperature evolution of the rigid amorphous fraction and the temperature dependence of the enthalpy of melting of 100% crystalline PBS. The rigid amorphous weight fraction in PBS is about 0.25 at T g . It decreases with increasing temperature and becomes zero around 25 C. Thus, at T room and at the human body temperature, in case of biomedical applications, RAF is absent in PBS.
This information is important for a detailed characterization of this biopolymer, by considering the peculiar physical properties of the rigid amorphous fraction, in particular mechanical and permeability properties, which are different from those of the mobile amorphous fraction. It is worth pointing out that an appropriate interpretation of the properties of semi-crystalline polymers as a function of the RAF amount has to be performed by taking into account the true rigid amorphous percentage at the temperature of interest, and not the RAF calculated at T g .
In addition, it is useful to point out that in case of chemical modication of PBS, for example through copolymerization, changes in the amorphous segments mobility are expected, not only in the MAF region, i.e. far from the crystal surface, but also in proximity of the crystals, as a consequence of inclusion or, more oen, rejection of the co-monomers from the crystal lattice. This could produce different temperature evolution of the RAF, so that the presence of rigid amorphous fraction at T room could be tuned by proper co-monomer addition.

Conflicts of interest
There are no conicts to declare. Fig. 6 Temperature dependence of crystalline (X C ), mobile amorphous (w MA ) and rigid amorphous (1 À X C À w MA ) weight fractions upon heating at 2 K min À1 after cooling at 10 K min À1 . Above T g , (1 À X C À w MA ) corresponds to w RA , below T g , (1 À X C À w MA ) corresponds to w MA + w RA (estimated errors: AE0.02 for X C , AE0.02 for w MA AE 0.04 for w RA ).