materials

Review Crystallization of Polymers Investigated by Temperature-Modulated DSC

Maria Cristina Righetti

National Research Council of Italy—Institute for Chemical and Physical Processes (CNR-IPCF), Via Moruzzi 1, 56124 Pisa, Italy; [email protected]; Tel.: +39-050-315-2068

Academic Editor: Ming Hu Received: 6 March 2017; Accepted: 10 April 2017; Published: 24 April 2017

Abstract: The aim of this review is to summarize studies conducted by temperature-modulated differential scanning calorimetry (TMDSC) on polymer crystallization. This technique can provide several advantages for the analysis of polymers with respect to conventional differential scanning calorimetry. Crystallizations conducted by TMDSC in different experimental conditions are analysed and discussed, in order to illustrate the type of information that can be deduced. Isothermal and non-isothermal crystallizations upon heating and cooling are examined separately, together with the relevant mathematical treatments that allow the evolution of the crystalline, mobile amorphous and rigid amorphous fractions to be determined. The phenomena of ‘reversing’ and ‘reversible‘ melting are explicated through the analysis of the thermal response of various semi-crystalline polymers to temperature modulation.

Keywords: polymer; crystallization; differential scanning calorimetry; temperature-modulated differential scanning calorimetry; reversing melting; reversible melting; crystalline fraction; mobile amorphous fraction; rigid amorphous fraction

1. Introduction Temperature-modulated differential scanning calorimetry (TMDSC), in which a periodic temperature perturbation is superimposed on a linear heating or cooling or takes place around a fixed temperature, has become, in recent years, a technique extensively used for the characterization of polymeric materials [1,2]. TMDSC, which was introduced commercially in the 1990s [3], has been proven to provide several advantages for the analysis of polymers with respect to standard differential scanning calorimetry (DSC), allowing the clarification of important aspects of polymer transitions. As regards crystallization and melting, TMDSC has allowed the reversibility of latent heats contribution to be proven also in the case of polymers. In principle, melting and crystallization of polymers should be irreversible processes, as crystallization needs considerable undercooling, and the temperature modulation is generally only fractions of degrees or few degrees [1,2]. Actually, it has been demonstrated that melting and crystallization of polymers can also be reversed by small temperature modulations, and, in some cases, exhibit reversible features [1,2]. For this reason, the term ‘reversing melting’ was introduced [4,5]. Reversing melting identifies a situation in which the modulation amplitude connects the temperature intervals in which melting and crystallization take place. Only processes that are reversing on the timescale of the temperature modulation contribute to the reversing signal. This seems in contrast with the requirement of an undercooling, which is generally of the order of 10 K for the crystallization of high molar mass polymers [2,5]. The phenomenon has been imagined and rationalized by considering the particular organization of the chains in a semi-crystalline polymer. A macromolecule, due to its length, may be partially in the crystal and partially in the melt. Detachment of segments and subsequent attachment can take place without the need of molecular

Materials 2017, 10, 442; doi:10.3390/ma10040442 www.mdpi.com/journal/materials Materials 2017, 10, 442 2 of 22 nucleation, with the result that the difference between the crystallization and melting temperatures becomes smaller [2,5]. This could be the mechanism of reversing melting in polymers that do not exhibit sliding diffusion. In this case, the phenomenon could take place at the lateral surfaces [2,6,7], whereas polymers characterized by sliding diffusion could undergo reversing melting at the fold surfaces, as changes in the fold-length can occur without melting [8,9]. The specific heat capacity that is derived from TMDSC experiments, which is connected to the heat flow that follows temperature modulation, is called reversing specific heat capacity (cp,rev). According to the mathematical treatment generally applied to TMDSC data, the modulated heat flow rate curve is expressed as a Fourier series [10–13]. If linear condition is fulfilled (i.e., if the perturbation amplitude is doubled, the resulting response amplitude is doubled too) and stationarity holds (i.e., the relationship between the perturbation and the response does not change during one modulation period) [14], the first harmonic is able to describe the response of the sample to modulation. Thus, cp,rev can be obtained from the ratio between the amplitudes of the first harmonic of the modulated heat flow rate (AHF) and the temperature modulation (AT)[10–13]:

AHF(t, T) K(ω) cp,rev(ω, t, T) = (1) AT(t, T) mω where ω is the frequency of temperature modulation (ω = 2π/p with p representing the modulation period), m the mass of the sample and K(ω) the frequency-dependent calibration factor. The most commonly used temperature modulations have sinusoidal shape or sawtooth profile: in the latter case, the temperature is also described with a Fourier series, and AT corresponds to the amplitude of the first harmonic [13]. The sawtooth temperature modulation appears more appropriate for the investigation of polymer melting and crystallization, if steady state is reached in each semi-period [7]. Appropriate measurement conditions must be chosen in order to obtain correct cp,rev data. Linear and stationary conditions are generally achieved by using temperature perturbation as small as possible: the modulation amplitude must be small enough to avoid important changes of specific heat capacity during a single period, and the average scanning rate (q) and the modulation period also have to be low, so that the average temperature change during one modulation period is smaller than the temperature amplitude [14,15]. The correct operative conditions depend on the sample and thermal transition under investigation. To improve linearity in the melting region, heating only condition has to be used (ωAT < q)[14]. This requisite, which hinders recrystallization, can conversely be inappropriate for the study of a crystallization process. Non-linearity and non-stationarity cause the presence of higher harmonics in the heat flow rate signal, which influences the accuracy of cp,rev determined by Equation (1). Therefore, correctness of the reversing specific heat capacity should be verified by checking the potential presence of higher even harmonics in the measured modulated heat flow rate [14,15]. With the conventional TMDSC instruments, the modulation period ranges approximately from 40 s to 200 s, the amplitude is comprised between 0.1 K and 2 K, and the average scanning rate is not higher than 3 K min−1 [1,2]. Modulation of temperature can be obtained also by combining short heating or cooling steps with isotherms [1,16]. The mathematical treatment of these ’step-scan’ experiments is different, but the information derived on the reversibility of the processes is similar [1,16]. The temperature-time profile in the temperature-modulated experiment can however be any periodic function. If non-harmonic temperature perturbations are applied, the response is a multi-frequency signal. Simultaneous multi-frequency measurements can thus be performed [17,18]. Temperature-modulated measurements can also be performed by using fast scanning nano-calorimeters [19,20], which allow the accessible frequency range to be extended to higher frequencies (0.1–100 Hz) [21]. In this review, however, only experiments carried out with conventional TMDSC instruments (sinusoidal or sawtooth temperature-modulation) will be reported and discussed. In the crystallization and melting region, the reversing specific heat capacity is generally a superposition of the baseline specific heat capacity (cp,base), which corresponds to the specific Materials 2017, 10, 442 3 of 22 heat capacity needed to increase the temperature of the sample without changing crystallinity [22], and an excess specific heat capacity (cp,exc), which in turn originates from the latent heats of the melting and crystallization processes that occur during the two modulation semi-periods, respectively [1,2]. When cp,exc is zero, the reversing specific heat capacity corresponds to cp,base, which means that crystallization or melting take place irreversibly with the same rate during the two semi-periods. Conversely, when cp,exc is higher than zero, reversing processes, i.e. melting and crystallization, occur in the two semi-periods, respectively. If the exothermic and endothermic contributions are symmetric, the reversing-specific heat capacity can be considered reversible within the chosen modulation amplitude and frequency. Conversely, when the exothermic and endothermic latent heats are asymmetric, cp,rev depends on the progress of the phase transition, which can occur partially or completely in an irreversible way. For this reason, cp,rev is designated as ‘reversing’, in order to distinguish it from a true reversible situation. As better detailed in Section3, after sufficiently long time in quasi-isothermal conditions, the irreversible events are completed, and the reversing-specific heat capacity tends to the reversible cp,rev value [12,23]. The crystallization process of polymers has been widely investigated by TMDSC [7,22,24–38]. An accurate investigation of the crystallization process is a fundamental step for a full comprehension of the polymer structure, which in turn strongly influences the material properties. In this review, studies conducted by TMDSC on various polymers in different crystallization conditions will be reported and discussed, with the aim of illustrating the type of information that can be deduced. Crystallizations occurring in different experimental conditions will be examined and discussed in different sections. The novelty of the results that this technique can provide about the crystallization process of polymers will be thus identified and highlighted.

2. Non-Isothermal Crystallization and Stepwise Quasi-Isothermal Crystallization upon Heating

Polymer crystallization that takes place above the glass transition temperature (Tg) upon heating, in the presence of nuclei grown during the previous cooling step or during a permanence of the sample at temperatures below Tg, is the so-called ‘cold-crystallization’ process [39]. This type of crystallization occurs at temperatures well below the melting region, far from equilibrium, and due to high nucleation density, it is generally fast. For these reasons this process may not be modulated, and commonly it is observed as a fully irreversible phenomenon in TMDSC curves [1,2]. An example is reported in Figure1, which shows the comparison between the cp,app curve from standard DSC and the cp,rev curves at two different frequencies of temperature modulation for an initially amorphous poly(3-hydroxybutyrate) (PHB) sample. Above the glass transition temperature, ◦ ◦ which is located around 0 C, in the temperature range 25–45 C, the cp,rev curves overlap the apparent specific heat capacity (cp,app) data, as well as the thermodynamic specific heat capacity of liquid PHB, attesting that in this interval no processes involving latent heat take place. Around 30–45 ◦C, simultaneously with the appearance of the cold crystallization peak in the cp,app curve, the cp,rev value ◦ suddenly decreases. The cp,rev curves overlap in the interval 45–75 C, which proves that the reversing specific heat capacity is independent of the modulation frequency in this temperature range, and that no reversing latent heat is exchanged. This means that, in this temperature range, crystallization and melting do not take place consecutively in the two semi-periods, respectively, and that the cp,rev curve corresponds to the baseline specific heat capacity. In fact, the general rule for the interpretation of the TMDSC curves is that when crystallization and melting latent heats do not contribute to the reversing specific heat capacity, i.e., when the excess specific heat capacity is zero, cp,rev is independent of the modulation frequency and corresponds to the baseline specific heat capacity of the crystallization process. The evolution of crystallinity can be thus followed by changes in cp,rev [22,31], and the ◦ rapid decrease in cp,rev around 30–45 C has to be ascribed to an increased solid fraction of PHB, which develops during an irreversible process that occurs continuously both in the heating and cooling ◦ semi-periods with the same rate. In contrast, above 75 C, the frequency dependence of the cp,rev Materials 2017, 10, 442 4 of 22 curves attestes that thermal processes involving reversing exchanges of latent heat, typical of polymer melting,Materials take 2017 place, 10, 442 in this temperature range [1,2]. 4 of 22 Materials 2017, 10, 442 4 of 22 10 ) 10

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Specific heat capacity capacity Specific heat 0 cp,rev p= 60s 0 50 100 150 cp,rev p=120s Specific heat capacity capacity Specific heat Temperature (°C)

0 50 100 150 Figure 1. Apparent specific heat capacity (cp,app) by standard differential scanning calorimetry (DSC) Figure 1. Apparent specific heat capacity (cp,app) by standard differential scanning calorimetry (DSC) and reversing-specific heat capacity (cTemperaturep,rev) of poly(3-hydroxybutyrate) (°C) (PHB) measured after cooling −1 −1 and reversing-specificfrom the melt heat at 200 capacity K min at (modulationcp,rev) of poly(3-hydroxybutyrate)periods p = 60 s and 120 s (AT = 1.0 (PHB) K, q = 2 measured K min ). The after cooling −1 −1 fromFigure the melt 1. thinApparent at solid 200 lines K specific min are the heat atsolid modulation capacity- and liquid (c-p,appspecific periods) by heatstandard pcapacities,= 60 differential s andas taken 120 from scanning s ( A[22].T =The calorimetry 1.0 inset K, isq an= 2(DSC K min) ). enlargement of the Figure in the cold crystallization region. (Reprinted (adapted) with permission The thinand reversing solid lines-specific are the heat solid- capacity and (c liquid-specificp,rev) of poly(3-hydroxybutyrate) heat capacities, (PHB as taken) measured from after [22]. cooling The inset is from [35]. Copyright (2012) American Chemical Society). an enlargementfrom the melt of at the 200 Figure K min− in1 at the modulation cold crystallization periods p = 60 region. s and 120 (Reprinted s (AT = 1.0 (adapted) K, q = 2 K withmin−1 permission). The fromthin [35 ].solid CopyrightA lines second are (2012) examplethe solid American of- andcold liquidcrystallization Chemical-specific Society).studied heat capacities, by TMDSC as is taken illustrated from in[22]. Figure The 2. inset In this is an enlargementcase, the ofcold the crystallization Figure in the was cold monitored crystallization during region.heating (throughReprinted a stepwise (adapted) ‘quasi with-isothermal’ permission from method.[35]. Copyright Every 2 (2012) K, a quasi Ameri-isothermalcan Chemical experiment Society of). 20 min was performed, by oscillating the A secondtemperature example around of cold a fixed crystallization value. Also in Figure studied 2, as in byFigure TMDSC 1, the cp,rev is curve illustrated of a melt-quenched, in Figure 2. In this case, theA cold secondamorphous crystallization example sample of of cold waspoly(ethylene crystallization monitored terephthalate) during studied (PET) heating by exhibitsTMDSC through a sharpis illustrated decrease a stepwise around in Figure ‘quasi-isothermal’100 °C, 2. In this simultaneously with the cold-crystallization process. After cold crystallization, the crystallinity case, the cold crystallization was monitored during heating through a stepwise ‘quasi-isothermal’ method. Everyamount, 2 K, determined a quasi-isothermal by standard DSC, experimentwas 40%. For a comparison, of 20 min Figure was 2 also performed, shows the cp,rev by curve oscillating the temperaturemethod. aroundEveryof a semicrystalline 2 a K, fixed a quasi value.PET-isothermal sample Also with in expsimilar Figureeriment crystallinity2, as of in 20 Figure degree, min 1 wasobtained, the performed,c p,revwith curvethe same by of oscillatingTMDSC a melt-quenched, the amorphoustemperature sampleexperimental around of poly(ethyleneprocedure.a fixed value. Also terephthalate) in Figure 2, as (PET) in Figure exhibits 1, the acp,rev sharp curve decrease of a melt- aroundquenched, 100 ◦C, simultaneouslyamorphous withsample the of cold-crystallization poly(ethylene terephthalate) process. (PET) After coldexhibits crystallization, a sharp decrease the crystallinityaround 100 °C, amount, simultaneously with the cold-crystallization process. After cold crystallization, the crystallinity determined by standard DSC, was 40%. For a comparison, Figure2 also shows the cp,rev curve of amount, determined by standard DSC, was 40%. For a comparison, Figure 2 also shows the cp,rev curve a semicrystallineof a semicrystalline PET PET sample sample with with similar similar crystallinity crystallinity degree, obtained obtained with with the thesame same TMDSC TMDSC experimentalexperimental procedure. procedure.

Figure 2. Reversing-specific heat capacity (cp,rev) of a melt-quenched amorphous poly(ethylene terephthalate) (PET) sample (filled circles) and a melt-crystallized PET sample (open circles) with crystallinity degree of 44%, measured by quasi-isothermal temperature-modulated differential

scanning calorimetry (TMDSC) upon stepwise heating (p = 60 s and AT = 1.0 K, oscillation time around each temperature: 20 min). The thin solid lines are the solid and liquid specific heat capacities, as taken from [40]. The broken line is the calculated specific heat capacity for a 40% crystalline PET. (Reprinted (adapted) with permission from [5]. Copyright (1997) American Chemical Society).

Figure 2. Reversing-specific heat capacity (cp,rev) of a melt-quenched amorphous poly(ethylene Figure 2. Reversing-specific heat capacity (cp,rev) of a melt-quenched amorphous poly(ethylene terephthalate) (PET) sample (filled circles) and a melt-crystallized PET sample (open circles) with terephthalate) (PET) sample (filled circles) and a melt-crystallized PET sample (open circles) with crystallinity degree of 44%, measured by quasi-isothermal temperature-modulated differential crystallinity degree of 44%, measured by quasi-isothermal temperature-modulated differential scanning scanning calorimetry (TMDSC) upon stepwise heating (p = 60 s and AT = 1.0 K, oscillation time around calorimetryeach temperature: (TMDSC) 20 upon min). stepwiseThe thin solid heating lines (arep = the 60 solid s and andA Tliquid= 1.0 specific K, oscillation heat capacities, time aroundas eachtaken temperature: from [40]. 20The min). broken The line thinis the solid calculated lines specific are the heat solid capacity and liquid for a 40% specific crystalline heat capacities,PET. as taken(Reprinted from [(adapted)40]. The brokenwith permission line is the from calculated [5]. Copyright specific (1997) heat American capacity Chemical for a 40% Society crystalline). PET. (Reprinted (adapted) with permission from [5]. Copyright (1997) American Chemical Society).

Materials 2017, 10, 442 5 of 22

3. Quasi-Isothermal Crystallization The isothermal crystallization of several polymers has been investigated by TMDSC [9,22Materials,24– 322017,34, 10, 36442 ,38]. Crystallization is monitored with this technique5 by of 22 oscillating the temperature3. Quasi around-Isothermal a Crystallization predefined crystallization temperature, with amplitude ranging from fractions of degreesThe isothermal to few degrees crystallization [1,2]. of several polymers has been investigated by TMDSC [9,22,24– For polycarbonate32,34,36,38]. Crystallization (PC) and is PHBmonitored [22 ,with29,31 this], technique no contribution by oscillating of the latent temperature heat around to the a measured reversing-specificpredefined heat crystallization capacity was temperature, detected with during amplitude crystallization ranging from fractions at low temperature, of degrees to few i.e., slightly degrees [1,2]. above the respective glass transition temperatures. For polycarbonate (PC) and PHB [22,29,31], no contribution of latent heat to the measured Figure3reversing shows-specific the timeheat capacity evolution was detected of the during reversing-specific crystallization at low heat temperature, capacity i.e., ofslightly PHB during quasi-isothermalabove the crystallization respective glass at transition 23 ◦C[ temperatures.22,31]. At very low crystallization temperature, the dynamics of the crystallizationFigure 3 is shows slow, the and time theevolution conditions of the reversing of linearity-specific and heat stationaritycapacity of PHB of during the heat quasi flow- signal isothermal crystallization at 23 °C [22,31]. At very low crystallization temperature, the dynamics of are better satisfiedthe crystallization [14,15 ].is slow, The and reversing the conditions specific of linearity heat and capacity stationarity decays of the withheat flow time signal from are the liquid specific heatbetter capacity satisfied value [14,15]. atThe the reversing crystallization specific heat temperature,capacity decays with to antime approximately from the liquid specific constant final heat capacity value at the crystallization temperature, to an approximately constant final value. The value. The frequency independence was checked by measuring cp,rev at the end of crystallization with frequency independence was checked by measuring cp,rev at the end of crystallization with different different modulation periods. modulation periods.

Figure 3. Time evolution of reversing specific heat capacity (cp,rev) during quasi-isothermal Figure 3. Time evolution of reversing specific heat capacity (cp,rev) during quasi-isothermal crystallization of PHB◦ at 23 °C (p = 100 s and AT= 0.4 K), curve a. Curves b and c correspond to the crystallization of PHB at 23 C(p = 100 s and AT= 0.4 K), curve a. Curves b and c correspond to the solid solid and liquid specific heat capacities (cp,solid and cp,liquid), respectively, as taken from [22]. Curve d was and liquid specificestimated heatfrom a capacities two-phase model, (cp,solid Equationand c (3),p,liquid and ),curve respectively, e from a three as-phas takene model, from Equation [22]. (5). Curve d was estimated fromThe squares a two-phase represent model,measurements Equation at modulation (3), and periods curve ranging e from from a three-phase240 to 1200 s. Curve model, f (thick Equation (5). The squaresdashed represent line) is measurementsthe expected cp,rev curve at modulation from model calculations, periods rangingsee text. At from the bottom, 240 to HF 1200 is thes. Curve f average heat flow rate (Reprinted (adapted) with permission from [31]. Copyright (2003) Elsevier). (thick dashed line) is the expected cp,rev curve from model calculations, see text. At the bottom, HF is

the averageThe heat final flow crystalline rate (Reprinted weight fraction (adapted) (wC), with equal permission to 0.64, was from obtained [31]. from Copyright integration (2003) of Elsevier).the complete average heat flow rate curve, divided by the enthalpy of fusion of th24]: The final crystalline weight fraction (w ), equalt to 0.64, was obtained from integration of the C  HFt' ,Tc dt' 0 (1) complete average heat flow rate curve, dividedwC t,Tc   by the enthalpy of fusion of the 100% crystalline o o hm Tc  polymer at the crystallization temperature, ∆hm(Tc), according to Equation (2) [24]: At the end of the crystallization, the measured cp,rev was smaller than the value of the two-phase baseline, calculated according to the following equationt [22,31]: R 0 0 HF(t , Tc)dt c p,base,2phase  wC c p,solid  1wC c p,liquid (2) 0 wC(t, Tc) = (2) where cp,solid and cp,liquid are the solid and liquid specific oheat capacities of PHB at the crystallization ∆hm(Tc) temperature. This indicated that an additional solid fraction developed during the crystallization process. This solid non-crystalline fraction is the ‘rigid amorphous’ (RA) fraction [2]. As the length of At the end of the crystallization, the measured cp,rev was smaller than the value of the two-phase baseline, calculated according to the following equation [22,31]:

cp,base,2phase = wCcp,solid + (1 − wC)cp,liquid (3) where cp,solid and cp,liquid are the solid and liquid specific heat capacities of PHB at the crystallization temperature. This indicated that an additional solid fraction developed during the crystallization Materials 2017, 10, 442 6 of 22 process. This solid non-crystalline fraction is the ‘rigid amorphous’ (RA) fraction [2]. As the length of the polymer molecules is much higher than the dimensions of the crystalline phase, at least in one direction, a frequent crossing of chains occurs at the amorphous/crystal interface. This interface, with nano-metric dimensions, constituted by amorphous chain segments with mobility hindered by the near crystalline structures, is the RA fraction. The mobility of the RA fraction is lower than that of the unconstrained amorphous phase, which, for this reason, is usually named ‘mobile amorphous’ (MA) fraction. The total solid fraction (wS), after completion of crystallization, was estimated at Tg from the relationship [22]: ∆cp wS = wC + wRA = (1 − wMA) = 1 − (4) ∆cp,a where ∆cp and ∆cp,a are the specific heat capacity increments at Tg for the semi-crystalline and the fully amorphous polymer, respectively. The wS value at Tg was 0.88, which means that the RA weight fraction (wRA) was 0.24. The three-phase baseline was thus calculated [22,31]:

cp,base,3phase = wCcp,solid + wRAcp,solid + wMAcp,liquid (5) being cp,solid = cp,crystal = cp,rigid amorphous = cp glass [41]. For most polymers, the thermodynamic cp,solid and cp,liquid are available from [40]. The proof that the evolution of the cp,rev curve corresponds to the evolution of the baseline specific heat capacity during the entire crystallization process was achieved by simulating the time dependence of cp,base according to the following equation [31]:

wC(t)   cp,base = cp,liquid − cp,liquid − cp,base(∞) (6) wC(∞) where cp,base(∞) was assumed equal to [wS(∞) cp,solid + (1 − wS(∞)) cp,liquid] with wS(∞) = 0.88. The dashed line in Figure3 shows that the agreement between the experiment and the predicted data is perfect. This proves that the rigid amorphous fraction in PHB at 23 ◦C is formed during the whole crystallization process, simultaneously with the crystal growth. The rigid amorphous fraction evolution does not always parallel the crystalline development. In order to highlight how the crystallization temperature can influence the RA fraction development, quasi-isothermal crystallization of poly(L-lactic acid) (PLLA) was performed at different temperatures. Also, PLLA is a polymer that, like PC and PHB, does not exhibit dependence of the reversing-specific ◦ heat capacity on the modulation frequency [34,38]. The sample was crystallized at Tc = 90 C, 0 ◦ a temperature at which the slightly distorted and disordered α -form grows, and at Tc = 130 C and 135 ◦C, which allows crystallization of the more stable α-form [42–44]. The time evolution of the reversing specific heat capacity (cp,rev) of PLLA at two different modulation periods (p = 60 s and 120 s), during quasi-isothermal crystallization at various Tcs, is displayed in Figure4. The cp,rev curves at p = 60 s and 120 s fully overlap, within the experimental noise, at the three Tcs investigated, which proves that cp,rev corresponds to the baseline specific heat capacity of the crystallization process and that crystallization of PLLA occurs irreversibly in a wide temperature range. Figure4 shows the decay of the reversing specific heat capacity curves during crystallization from the liquid specific heat capacity values at the respective Tcs, to an approximately constant final value. From these cp,rev curves, the time evolution of the mobile amorphous weight fraction (wMA) during quasi-isothermal crystallization was calculated according to the following equation [31]: cp,rev(t, T) − cp,solid(T) wMA(t, T) = (7) cp,liquid(t, T) − cp,solid(T)

For PLLA, cp,solid and cp,liquid were taken from [45]. Materials 2017, 10, 442 7 of 22

MaterialsFrom the2017 average, 10, 442 heat flow rate, the growth kinetics of the crystalline weight fraction7 (ofw 22C ) was obtained. An example is shown in Figure5. From the partial areas of the average heat flow rate ( HF), o ◦ whichcurve is drawnMaterials was derived 2017 superimposed, 10, 442according to on Equation the experimental (2). For crystallization modulated at HFTc =mod 90 °C,signal the athTm cT=c  1357 of 22 the C, α the- wC ◦ o curveform was was derived used, whereas according for crystallization to Equation (2).at Tc For = 130 crystallization °C, and 135 °C, at theTc = 90 C, values the ∆ referringh (Tc) of the o m 0 curve was derived according to Equation (2). For crystallization◦ at Tc = 90 ◦°C, the hm oTc  of the α- α -formto the was α-form used, were whereas applied for [4 crystallization6]. Finally, the atrigidTc =amorphous 130 C, and weight 135 fractionC, the ∆ (hwmRA()T evolutionc) values was referring form was used, whereas for crystallization at Tc = 130 °C, and 135 °C, the values referring to thedeterminedα-form were by difference, applied [being46]. Finally,(wC + wMA the + w rigidRA) =1. amorphous weight fraction (wRA) evolution was to the α-form were applied [46]. Finally, the rigid amorphous weight fraction (wRA) evolution was determineddetermined by difference, by difference, being being (wC (w+C w+ MAwMA + wwRARA) =1.) =1.

T =130 °C T =135 °C 2.1 Tc=90 °C c c T =130 °C T =135 °C 2.1 Tc=90 °C c c

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1.71.7 0 0 5050 100100 00 5050 1001000 0 5050100100150150 t (min) tc (min) c Figure 4. Crystallization time (tc) evolution of the reversing specific heat capacities (cp,rev) of poly(L- FigureFigure 4. 4.Crystallization Crystallization time time (t (c)t cevolution) evolution of the of reversing the reversing specific specificheat capacities heat capacities(cp,rev) of poly( (cp,revL- ) of lactic acid) (PLLA) during quasi-isothermal crystallization from the melt at Tc = 90 °C, 130 °C, and◦ ◦ poly(lacticL-lactic acid) acid) (PLLA (PLLA)) during during quasi quasi-isothermal-isothermal crystallization crystallization from the from melt theat T meltc = 90 at °C,Tc 130= 90 °C,C, and 130 C, 135 °C, respectively (p = 60 s: thick line, p = 120 s: thin line, AT = 0.4 K). (Reprinted (adapted) with ◦ and 135135 °C,C,permission respectively from ([3p (4 p=].= Copyright60 60 s: s:thick thick (2011) line, line, Elsevierp =p 120= 120). s: thin s: thin line, line, AT A= T0.4= K). 0.4 ( K).Reprinted (Reprinted (adapted) (adapted) with with permissionpermission from from [34 ].[34 Copyright]. Copyright (2011) (2011) Elsevier). Elsevier).

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0 50 100 150 t (min) T =135°C -0.08 c c Heat flow rate (W/g) exo

Figure 5. Crystallization time0 (tc) evolution of50 the modulated100 heat flow rate 150(HFmod: grey line) and average heat flow rate (HF: black line) during quasit-isothermal (min) crystallization of PLLA (p = 60 s, AT = c 0.4 K) at Tc = 135 °C. (Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier). Figure 5. Crystallization time (tc) evolution of the modulated heat flow rate (HFmod: grey line) and Figure 5. Crystallization time (tc) evolution of the modulated heat flow rate (HFmod: grey line) and averageThe heat time flow evolution rate (HF of: theblack crystalline, line) during mobile quasi amorphous-isothermal and crystallization rigid amorphous of PLLA weight (p = fractions60 s, AT = average heat flow rate (HF: black line) during quasi-isothermal crystallization of PLLA (p = 60 s, of PLLA during quasi-isothermal TMDSC analyses is illustrated in Figure 6. As expected, the final 0.4 K) at Tc = 135 °C. ◦(Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier). AT = 0.4crystalline K) at T cdegree= 135 increasesC. (Reprinted with the (adapted) crystallization with permissiontemperature. fromAlso,[ 34the]. w CopyrightRA evolution (2011) is found Elsevier). Thedependent time evolution on the crystallization of the crystalline, temperature. mobile The amorphous rigid amorphous and rigid fraction amorphous grows in parallel weight with fractions ofThe PLLA timewC from during evolution the beginningquasi of-isothermal the of the crystalline, crystallization TMDSC mobile analyses process amorphous during is illustrated the entire and in solidification Figure rigid amorphous 6. As process expected, at weightlow the Tc. final fractions During crystallization at intermediate temperature (Tc = 130 °C), the RA fraction starts to appear at crystalline degree increases with the crystallization temperature. Also, the wRA evolution is found of PLLA duringlonger times, quasi-isothermal approximately simultaneouslyTMDSC analyses with the is illustratedsecondary crystallization in Figure6. process, As expected, which the final dependent on the crystallization temperature. The rigid amorphous fraction grows in parallel with crystallinegenerally degree increasestakes place with in geometrically the crystallization restricted temperature. regions, after Also, spherulite the w RA impingement,evolution is found wC from the beginning of the crystallization process during the entire solidification process at low Tc. dependentapproximately on the crystallization connected with temperature.the inflection point The of the rigid wC curve amorphous [47]. At higher fraction Tcs, RA grows fraction in parallel Duringdoes crystallization not form. at intermediate temperature (Tc = 130 °C), the RA fraction starts to appear at with wC from the beginning of the crystallization process during the entire solidification process longer times, approximately simultaneously with the secondary crystallization◦ process, which at low T . During crystallization at intermediate temperature (T = 130 C), the RA fraction generallyc takes place in geometrically restricted regions, after c spherulite impingement, starts to appear at longer times, approximately simultaneously with the secondary crystallization approximately connected with the inflection point of the wC curve [47]. At higher Tcs, RA fraction process,does which not form. generally takes place in geometrically restricted regions, after spherulite impingement, approximately connected with the inflection point of the wC curve [47]. At higher Tcs, RA fraction does not form. Materials 2017, 10, 442 8 of 22 Materials 2017, 10 , 442 8 of 22

1.0

Tc=90 °C Tc=130 °C Tc=135 °C

0.8

0.6 w wMA MA wMA

0.4 w wC

Weight fractions C wC 0.2 w RA wRA wRA 0.0 0 50 100 0 50 100 0 50 100 150 t (min) c

Figure 6. Time evolution of crystallinew (wC), mobile amorphous (wMA) and rigid amorphous (wRA) Figure 6. Time evolution of crystallineMA (wC), mobile amorphous (wMA) and rigid amorphous (wRA) weight fractions during quasi-isothermal crystallization from the melt of PLLA at Tc = 90 °C, 130◦ °C, ◦ weight fractions during quasi-isothermal crystallization from the melt of PLLA at Tc = 90 C, 130 C, and 135 °C (p = 60 s: thick line, p = 120 s: thin line, AT = 0.4 K). Estimated errors: ±0.02 for wC and wMA, and 135 ◦C(p = 60 s: thick line, p = 120 s: thin line, A = 0.4 K). Estimated errors: ±0.02 for w and ±0.04 for wRA. (Reprinted (adapted) with permission fromT [34]. Copyright (2011) Elsevier). C wMA, ±0.04 for wRA. (Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier). These trends prove the existence of a crystallization temperature limit for the formation of RA fractionThese trends in PLLA, prove as already the existence proven for of other a crystallization different semi- temperaturecrystalline polymers limitfor [34,3 the6,3 formation7,48,49]. The of RA fractiondissimilar in PLLA, evolution as already of the RA proven fraction for at other different different Tcs can semi-crystalline originate from different polymers mobility [34,36 of,37 the,48 ,49]. chains and different crystalline organizations and morphologies [34,36,37,48,49]. At high The dissimilar evolution of the RA fraction at different T s can originate from different mobility of the crystallization temperature, the macromolecules havec high mobility, which facilitates the chainsorganization and different of the crystalline polymeric organizations segments into and ordered morphologies crystal structures, [34,36,37 with,48 ,minor49]. At or high no fraction crystallization of temperature,amorphous the segments macromolecules at the amorphous/crystal have high interface mobility, subjected which to facilitates geometrical the constraints. organization At high of the polymericTc, the segmentscrystallization into rate ordered is lower, crystal and structures,this condition with can minor also allow or no the fraction growth of of amorphous regular lamellae segments at thecharacterized amorphous/crystal by adjacent interface regular subjected re-entry to folding. geometrical Conversely, constraints. the low At chain high T mobilityc, the crystallization at low rate iscr lower,ystallization and this temperatures condition implies can also a allowmore difficult the growth organization of regular of lamellae the entangled characterized chain segments by adjacent regularinto re-entry ordered folding. crystal Conversely, structures, which the low can chain lead mobility to the development at low crystallization of irregular temperatures chain cluster implies a morestructures, difficult and organization large rigid ofamorphous the entangled fraction chain at the segments amorphous/c into orderedrystal boundaries. crystal structures, which can lead to theAs development regards the mobile of irregular amorphous chain fraction cluster of structures, PLLA, a higher and large glass rigidtransition amorphous temperature fraction was at the observed after crystallization at low Tcs, and a lower glass transition temperature after crystallization amorphous/crystal boundaries. at high Tcs [50,51], as also shown in Figure 7. The glass transition temperature of the PLLA sample As regards the mobile amorphous fraction of PLLA, a higher glass transition temperature was crystallized at Tc = 145 °C is close to the Tg of the completely amorphous PLLA, whereas the Tg of the observedsample after crystallized crystallization at Tc = 85 at °C low is Taboutcs, and ten a degrees lower glassabove. transition The lower temperature glass transition after temperature crystallization at high(Tg,unconstTcs [)50 was,51 ], connected as also shown to the devitrification in Figure7. The of anglass unconstrained transition temperature mobile amorphous of the (MA PLLAunconstr sample) ◦ crystallizedfraction atwhereasTc = 145 the glassC is transition close to the at higherTg of thetemperature completely (Tg,constr amorphous) was associated PLLA, to whereas the mobilization the Tg of the ◦ sampleof a crystallizedslightly constrained at Tc = mobile 85 C isamor aboutphous ten (MA degreesconstr) fraction above. [3 The8,52 lower,53]. glass transition temperature (Tg,unconstA) wasdetailed connected analysis to of the the devitrificationevolution of the ofcrystalline an unconstrained and the different mobile amorphous amorphous fractions (MA unconstrat ) different Tcs (85 °C and 145 °C) proved that during crystallization at low temperature, both MAconstr fraction whereas the glass transition at higher temperature (Tg,constr) was associated to the mobilization and RA fractions develop together with the crystal phase [38]. The RA fraction vitrification occurs of a slightly constrained mobile amorphous (MAconstr) fraction [38,52,53]. during the entire crystallization process, whereas the transformation from unconstrained to A detailed analysis of the evolution of the crystalline and the different amorphous fractions at constrained mobile◦ amorphous◦ fraction seems connected with the secondary crystallization process. different Tcs (85 C and 145 C) proved that during crystallization at low temperature, both MAconstr During crystallization at Tc = 145 °C, RA fraction formation is not detected. Only upon cooling from and145 RA °C fractions to room temperature, develop together some mobile with amorphous the crystal segments phase undergo [38]. Thestiffening RA fractionand restriction vitrification of occursmobility, during but the with entire the peculiarity crystallization that onl process,y the most whereas constrained the transformationfraction, the RA fraction, from unconstrained develops to constrainedupon cooling, mobile whereas amorphous the residual fractionMA fraction seems remains connected practically with unconstrained the secondary also near crystallization Tg. The ◦ process.analysis During of the crystallization evolution of the at T RAc = fraction 145 C, and RA the fraction different formation constrained is not MA detected. fractions during Only upon cooling from 145 ◦C to room temperature, some mobile amorphous segments undergo stiffening and restriction of mobility, but with the peculiarity that only the most constrained fraction, the RA fraction, develops upon cooling, whereas the residual MA fraction remains practically unconstrained Materials 2017, 10, 442 9 of 22

also nearMaterialsT g2017. The, 10, 442 analysis of the evolution of the RA fraction and the different constrained9 of 22 MA fractions during crystallization at different temperatures and after cooling to below Tg, led to assume crystallization at different temperatures and after cooling to below Tg, led to assume a possible a possible distribution of the amorphous regions [38]. The development of the RA and the MAunconstr distribution of the amorphous regions [38]. The development of the RA and the MAunconstr fractions in fractions in the PLLA samples crystallized at high Tcs appeared not linked, probably because these the PLLA samples crystallized at high Tcs appeared not linked, probably because these fractions are fractions are placed in regions different with respect to the crystal lamellae position. Thus, it was placed in regions different with respect to the crystal lamellae position. Thus, it was supposed that supposedthe RA that fraction the RA develops, fraction afterdevelops, crystallization after crystallization at high temperature, at high temperature, in the inter-lamellar in the inter-lamellar regions, regions,whereas whereas the unconstrained the unconstrained MA fractions MA fractions remains remainslocated in located the larger in theinter larger-stack inter-stackgaps [38], as gaps also [38], as alsodemonstrated demonstrated by by different different techniques techniques for for other other polymers polymers [54– [56].54– 56 For]. For crystallizations crystallizations at low at low temperatures,temperatures, which which lead lead to αto0 -formα-form growth, growth, this this typetype of of a analysisnalysis did did not not allow allow to identify to identify univocally univocally if RAif fraction RA fraction develops develops exclusively exclusively in in the the inter-lamellar inter-lamellar regions regions or or also also at at the the crystal/amorphous crystal/amorphous interfaceinterface [38]. [38].

12 2.5

10 2.0

)

-1

K 1.5

-1 8

J g 1.0

(

6 40 60 80 100

p,app

c 4

2

50 100 150 200 Temperature (°C)

FigureFigure 7. Apparent 7. Apparent specific specific heat heat capacity capacity (cp,app (cp,app) of) of an an amorphous amorphous PLLA PLLA samplesample (thickest(thickest solidsolid line line)) and ◦ ◦ after completeand after complete isothermal isothermal crystallization crystallization at Tc = 85at TcC = (dotted85 °C (dotted line) andline)T andc = 145Tc = 145C (solid °C (solid line) line) (heating −1 rate 10(heating K min rate−1). 10 The K thinmin solid). Thelines thin solid are the lines solid are andthe solid liquid and thermodynamic liquid thermodynamic specific specific heat capacities, heat capacities, as taken from the literature [45]. The inset is an enlargement of the Tg region. (Reprinted as taken from the literature [45]. The inset is an enlargement of the Tg region. (Reprinted (adapted) (adapted) with permission from [46]. Copyright (2015) Elsevier). with permission from [46]. Copyright (2015) Elsevier). Unlike PHB, which exhibits frequency independence of the reversing specific heat capacity Unlikewhen crystallized PHB, which at low exhibits temperature, frequency and PLLA, independence for which the of frequency the reversing independence specific holds heat capacityin a whenwide crystallized temperature at lowrange, temperature, for most polymers and PLLA, the value for of which cp,rev depends the frequency on the modulation independence frequency. holds in a wideIn temperaturethis case, cp,rev range,is the result for most of the polymers superposition the value of the ofbaselinecp,rev depends specific heat on thecapacity modulation and an excess frequency. specific heat capacity, originating from the latent heat contributions of the melting and crystallization In this case, cp,rev is the result of the superposition of the baseline specific heat capacity and an excess processes that occur during the two modulation semi-periods, respectively. For these polymers, specific heat capacity, originating from the latent heat contributions of the melting and crystallization isothermal crystallization is a reversing process. processes that occur during the two modulation semi-periods, respectively. For these polymers, The dependence of cp,rev on the modulation frequency during quasi-isothermal crystallization isothermalwas widely crystallization investigated is for a reversing polycaprolactone process. (PCL) [7,24,25]. Figure 8 shows the reversing specific Theheat dependence capacity of of PCLcp,rev duringon the quasi modulation-isothermal frequency crystallization during at quasi-isothermal 55 °C. The amplitude crystallization of the was widelytemperature investigated modulation for polycaprolactone was 0.5 K, and the (PCL) period [7, 24ranged,25]. Figurefrom 208 to shows 1200 s. the The reversing Figure displays specific the heat ◦ capacitydecrease of PCL in c duringp,rev from quasi-isothermal the value of the thermodynamic crystallization cp,liquid at 55, in comparisonC. The amplitude with the of cp,base,2phase the temperature trend modulationcalculated was according 0.5 K, and to theEquation period (3). ranged Through from the 20 entire to 1200 crystallization s. The Figure process, displays except the decrease at the in beginning, during the induction time, cp,rev remains higher than the calculated cp,base,2phase which at the cp,rev from the value of the thermodynamic cp,liquid, in comparison with the cp,base,2phase trend calculated accordingend of to the Equation process (3).corresponds Through to the a crystalli entire crystallizationne weight fraction process, of 0.5. exceptThe difference at the beginning, between the during cp,rev the and cp,base,2phase is the excess specific heat capacity (cp,exc) connected to the latent heat exchanges that take induction time, cp,rev remains higher than the calculated c which at the end of the process place during the two modulation semi-periods. p,base,2phase corresponds to a crystalline weight fraction of 0.5. The difference between the cp,rev and cp,base,2phase is the excess specific heat capacity (cp,exc) connected to the latent heat exchanges that take place during the two modulation semi-periods.

Materials 2017, 10, 442 10 of 22 Materials 2017, 10, 442 10 of 22

Materials 2017, 10, 442 10 of 22

◦ FigureFigure 8. 8.Reversing-specific Reversing-specific heat heat capacity capacity (cp,rev) (duringcp,rev) crystallization during crystallization of PCL at 55 of°C as PCL a function at 55 of C as a functioncrystallization of crystallization time (AT = time 0.5 K). (A Tcp,base,2phase= 0.5 K). wascp,base,2phase calculatedwas according calculated to Equation according (3). to(Reprinted Equation (3). Figure 8. Reversing-specific heat capacity (cp,rev) during crystallization of PCL at 55 °C as a function of (Reprinted(adapted) (adapted) with permission with permission from [7]. Copyright from [7]. (2000) Copyright Springer (2000)). Springer). crystallization time (AT = 0.5 K). cp,base,2phase was calculated according to Equation (3). (Reprinted (adapted) with permission from [7]. Copyright (2000) Springer). The frequency dependence of cp,exc for PCL, after 2000 min of crystallization at 55 °C is detailed ◦ Thein Figure frequency 9: only dependence at high modulation of cp,exc frequency,for PCL, the after reversing 2000 min-specific of crystallization heat capacity atcorresponds 55 C is detailed to The frequency dependence of cp,exc for PCL, after 2000 min of crystallization at 55 °C is detailed in Figurethe baseline9: only capacity at high modulationof the crystallization frequency, process, the bec reversing-specificause the fraction heatof crystalline capacity material corresponds that to in Figure 9: only at high modulation frequency, the reversing-specific heat capacity corresponds to the baselinecan follow capacity temperature of the modulation crystallization decreases process, with increasing because the frequency fraction [57 of–59 crystalline]. At infinitely material high that the baseline capacity of the crystallization process, because the fraction of crystalline material that modulation frequency, the reversing process is inhibited, and the baseline-specific heat capacity is can followcan follow temperature temperature modulation modulation decreases decreases withwith increasing increasing frequency frequency [57 [–5759–].59 At]. i Atnfinitely infinitely high high generally achieved. modulationmodulation frequency, frequency, the the reversing reversing process process isis inhibited, and and the the baseline baseline-specific-specific heat heat capacity capacity is is generallygenerally achieved. achieved.

Figure 9. Excess specific heat capacity of PCL (cp,exc) after 2000 min of crystallization at 55 °C as a function of the modulation frequency. (Reprinted (adapted) with permission from [7]. Copyright Figure 9. Excess specific heat capacity of PCL (cp,exc) after 2000 min of crystallization at 55 °C as a ◦ Figure(2000) 9. SpringerExcess specific). heat capacity of PCL (cp,exc) after 2000 min of crystallization at 55 C as afunction function of of the the modulation modulation frequency. frequency. (Reprinted (Reprinted (adapted) with (adapted) permission with from permission [7]. Copyright from [7]. (2000) Springer). CopyrightSignificant (2000) cp,exc Springer). values during crystallization have been reported also for polyether ether ketone (PEEK) [24,31], PET [5,37], and polyethylene (PE) [8,9,26,60–62]. Figure 10 exhibits the reversing Significant cp,exc values during crystallization have been reported also for polyether ether ketone specific heat capacity curve during quasi-isothermal crystallization at 126 °C of a linear polyethylene Significant(PEEK) [24,31cp,exc], PETvalues [5,37 during], and polyethylene crystallization (PE) have [8,9, been26,60– reported62]. Figure also 10 for exhibits polyether the reversing ether ketone sample [8]. The cp,rev curve progressively increases with time, up to an almost constant value, then (PEEK)specific [24, 31heat], PETcapacity [5,37 curve], and during polyethylene quasi-isothermal (PE) [crystallization8,9,26,60–62]. at Figure126 °C of 10 a linearexhibits polyethylene the reversing slightly decreases, whereas the baseline specific heat capacity, as expected, decreases◦ progressively, specificsample heat [8]. capacity The cp,rev curve curve during progressively quasi-isothermal increases with crystallization time, up to an at 126almostC constant of a linear value, polyethylene then because the specific heat capacity of the crystalline phase is smaller than that of the amorphous phase. sampleslightly [8]. decreases, The c whereascurve the progressively baseline specific increases heat capacity, with time, as expected, up to decreases an almost progressively, constant value, The trend of cp,revp,rev is different from that reported in Figure 8 for PCL: for PE, the reversing specific heat because the specific heat capacity of the crystalline phase is smaller than that of the amorphous phase. then slightlycapacity decreases,increases and whereas remains the higher baseline than the specific thermodynamic heat capacity, cp,liquid as du expected,ring the whole decreases crystallization progressively, The trend of cp,rev is different from that reported in Figure 8 for PCL: for PE, the reversing specific heat becauseprocess the at specific 126 °C. heat Figure capacity 10 also ofshows the crystalline the evolution phase of the is crystalline smaller than weight that fraction of the (w amorphousC). The capacity increases and remains higher than the thermodynamic cp,liquid during the whole crystallization phase. The trend of cp,rev is different from that reported in Figure8 for PCL: for PE, the reversing process at 126 °C. Figure 10 also shows the evolution of the crystalline weight fraction (wC). The specific heat capacity increases and remains higher than the thermodynamic cp,liquid during the whole crystallization process at 126 ◦C. Figure 10 also shows the evolution of the crystalline weight fraction (wC). The inflection points of the cp,rev and wC curves are located approximately at the same Materials 2017, 10, 442 11 of 22 MaterialsMaterials 2017 2017, 10, ,10 442, 442 11 of11 22 of 22 crystallizationinflectioninflection points points time, of whichof the the c p,revc meansp,rev and and w thatwCC curves curves the excess areare locatedlocated specific approximately heat capacity at at the mirrorsthe same same crystallization the crystallization crystallinity time, time, degree duringwhichwhich the means initialmeans that stagethat the the ofexcess excess isothermal specific specific crystallization, heat heat capacitycapacity mirrors as also the reportedthe crystallinity crystallinity elsewhere degree degree [61 during ],during up tothe the completion initial initial of primarystagestage of of isothermalcrystallization, isothermal crystallization, crystallization, as the inflection as as also also point reportedreported roughly elsewhere corresponds [61 [61],], up up to to tothe completio completio beginningn n of of primary secondaryprimary crystallizationcrystallization,crystallization, [47 ]. as as the the inflection inflection point point roughly roughly corresponds to to the the beginning beginning of of secondary secondary crystallizationcrystallization [47 [47]. ]. The dependence of cp,rev on the temperature modulation amplitude is detailed in Figure 11 for TheThe dependence dependence of of c p,revcp,rev on on the the temperature temperature modulation amplitudeamplitude is is detailed detailed in in Figure Figure 11 11for for quasi-isothermal crystallization of linear polyethylene at 128.5 ◦C. Both the reversing specific heat quasiquasi-isothermal-isothermal crystallization crystallization of of linear linear polyethylenepolyethylene atat 128.5128.5 °C.°C. Both Both the the reversing reversing specific specific heat heat capacity and the heat flow rate curve shift to smaller time-scale with increasing the temperature capacitycapacity and and the the heat heat flow flow rate rate curve curve shift shift to to smaller time time--scalescale with with increasing increasing the the temperature temperature amplitude, because of the larger temperature window covered by modulation. The result is that the amplitude,amplitude, because because of of the the larger larger temperature temperature window coveredcovered by by modulation. modulation. The The result result is this atth atthe the crystallizationcrystallizationcrystallization rate rate rate decreases decreases decreases with with with reducing reducing reducing the thethe amplitude.amplitude.

p,rev FigureFigure 10. 10.(A ()A) Reversing Reversing specific specific heat heat capacity capacity (c ()c p,rev of a) linear of a polyethylene linear polyethylene (PE) during (PE) quasi during- isothermal crystallization at 126 °C◦ (solid line). A sinusoidal temperature modulation was applied quasi-isothermalFigure 10. (A) crystallizationReversing specific at 126 heatC (solid capacity line). (cp,rev A sinusoidal) of a linear temperature polyethylene modulation (PE) during was quasi applied- with AT = 1.0 K and p = 60 s. The linear solid line is the liquid thermodynamic specific heat capacity withisothermalAT = 1.0 crystallization K and p = 60 s. at The 126 linear °C (solid solid line). line isA thesinusoidal liquid thermodynamic temperature modulation specific heat was capacity applied of of PE◦ at 126 °C [63]. The cp,base curve (dotted line) was calculated according to Equation (3), on the basis PEwith at 126 AT =C[ 1.063 K]. and The pc p,base= 60 curves. The (dottedlinear solid line) line was is calculatedthe liquid thermodynamic according to Equation specific (3),heat on capacity the basis of the variation of the crystalline weight fraction (wC) with time. At the bottom, HF (dashed line) is of PE at 126 °C [63]. The cp,base curve (dotted line) was calculated according to Equation (3), on the basis of the variation of the crystalline weight fraction (wC) with time. At the bottom, HF (dashed line) is the the average heat flow rate. (B) Time evolution of the crystalline weight fraction (wC), calculated as the of the variation of the crystalline weight fraction (wC) with time. At the bottom, HF (dashed line) is averageratio heat between flow rate.the integrat (B) Timeed average evolution heat of flow the rate crystalline (HF) and weight the literature fraction value (wC for), calculated the heat of asfusion the ratio the average heat flow rate. (B) Time evolution of the crystalline weight fraction (wC), calculated as the betweenof 100% the crystalline integrated polyethylene average heat [63]. flow (Reprinted rate (HF (adapted)) and the with literature permission value from for [8]. the Copyright heat of (2001) fusion of ratio between the integrated average heat flow rate (HF) and the literature value for the heat of fusion 100%American crystalline Chemical polyethylene Society). [ 63]. (Reprinted (adapted) with permission from [8]. Copyright (2001) Americanof 100% Chemicalcrystalline Society).polyethylene [63]. (Reprinted (adapted) with permission from [8]. Copyright (2001) AmericanA detailed Chemical study Societyon the). connection between the excess specific heat capacity and the evolution of the crystallinity degree and melting temperature during isothermal crystallization of a linear PE A detailedA detailed study study on on the the connection connection between between the the excess excess specific specific heat heat capacity capacity andand thethe evolutionevolution of was conducted by Marand et al. [60]. The cp,exc curves determined during quasi-isothermal the crystallinity degree and melting temperature during isothermal crystallization of a linear PE was of crystallizationsthe crystallinity in degree a wide andtemperature melting rangetemperature are shown during in Figure isothermal 12. crystallization of a linear PE conductedwas conducted by Marand by et Marand al. [60 ]. et The al.c p,exc [60].curves The determinedcp,exc curves during determined quasi-isothermal during quasi crystallizations-isothermal in acrystallizations wide temperature in a wide range temperature are shown range in Figure are shown 12. in Figure 12.

Figure 11. The effect of the modulation amplitude on the quasi-isothermal crystallization of linear PE at 128.5 °C : top: reversing-specific heat capacities (cp,rev) curves, bottom: average heat flow rate (HF) curves. (Reprinted (adapted) with permission from [26]. Copyright (1999) Elsevier). Figure Figure 11. 11.The The effect effect of of the the modulation modulation amplitudeamplitude on the quasi quasi-isothermal-isothermal crystallization crystallization of oflinear linear PE PE at 128.5◦ °C : top: reversing-specific heat capacities (cp,rev) curves, bottom: average heat flow rate (HF) at 128.5 C: top: reversing-specific heat capacities (cp,rev) curves, bottom: average heat flow rate (HF) curves. (Reprinted (adapted) with permission from [26]. Copyright (1999) Elsevier). curves. (Reprinted (adapted) with permission from [26]. Copyright (1999) Elsevier).

Materials 2017, 10, 442 12 of 22

Materials 2017, 10, 442 12 of 22

Materials 2017, 10, 442 12 of 22

Figure 12. Evolution of the excess specific heat capacity (cp,exc) with time during quasi-isothermal Figure 12. Evolution of the excess specific heat capacity (cp,exc) with time during quasi-isothermal crystallization of a linear PE at the indicated temperatures (AT = 0.8 K and p = 48 s). (Reprinted A p crystallization(adapted) of with a linear permission PE at the from indicated [60]. Copyright temperatures (2004) American ( T = 0.8 Chemical K and Society= 48 s).). (Reprinted (adapted) with permission from [60]. Copyright (2004) American Chemical Society). At high crystallization temperature, as also shown in Figure 10, the excess specific heat capacity increases during the initial stage of the process, and after reaching a maximum, decays slowly. At At highFigure crystallization 12. Evolution temperature, of the excess specific as also heat shown capacity in (c Figurep,exc) with 10 time, the during excess quasi specific-isothermal heat capacity lower temperatures, when primary crystallization is completed during the previous cooling step, increases duringcrystallization the initial of a linear stage PE ofat the the indicated process, temperatures and after (AT reaching= 0.8 K and a p maximum,= 48 s). (Reprinted decays slowly. only the(adapted) decay with is observed permission (Figure from [ 6012)]. .Copyright The peak (2004) melting American temperature Chemical was Society found). to shift to higher At lowervalues temperatures, with increasing when the primary crystallization crystallization time (Figure is 13). completed The time evolution during the of the previous melting cooling step, onlytemperature theAt high decay hadcrystallization isa sigmoidal observed temperature, shape, (Figure thus asthe12 also). entire Theshown crystallization peak in Figure melting 10, process the temperature excess was roughlyspecific was heatdivided foundcapacity into to shift to higherthreeincreases values stages: during with the increasing firstthe ini andtial thirdstage the crystallization stagesof the wereprocess, pu tand time into after relation (Figure reaching with 13). a pure Themaximum, time primary evolution decays and secondaryslowly. of the At melting temperaturecrystallizationlower temperatures, had a processes sigmoidal when respectively, shape,primary thuscrystallization whereas the the entire middle is completed crystallization step was during associated processthe previous to a wasmixed cooling roughly regime step, of divided into threeprimaryonly stages: the and decay thesecondary is first observed and crystallization. third(Figure stages 12) Figure. The were peak 13 putexhibits melting into the relationtemperature correlation with betweenwas pure found the primary to evolution shift to and higher of secondarythe excess specific heat capacity during quasi-isothermal crystallization at high temperatures and the crystallizationvalues with processes increasing respectively, the crystallization whereas time the (Figure middle 13). step The was time associated evolution to of a the mixed melting regime of correspondingtemperature had melting a sigmoidal temperature shape, progression.thus the entire The crystallization onset of the processdecay of was the roughly excess specificdivided heat into primarycapacitythree and stages: secondary was found the first crystallization.to correspond and third stages approximately Figure were pu13t toexhibits into the relationbeginning the with correlation of the pure third primary betweenstage andof the the secondary melting evolution of the excesstemperaturecrystallization specific heatevolution, processes capacity i.e., respectively, to during the secondary quasi-isothermal whereas crystallization the middle crystallization step event, was which associated in at PE high to takes a mixed temperatures place regime mainly of and the correspondingthroughprimary lamellarand melting secondary thickening temperature crystallization. [64]. This progression. proceFiguress 13 in exhibits PE The is connected onset the correlation of theto a decaycrystal between ofαc therelaxation the evolution excess process, specificof the heat capacitywhichexces wass involves foundspecific toheat cooperative correspond capacity chainduring approximately sliding quasi - inisothermal the crystalline to the crystallization beginning regions [at65 of ].high the The temperatures third decay stage of the ofand excess the the melting specific heat capacity in PE at high crystallization temperature was thus connected with lamellar temperaturecorresponding evolution, melting i.e., temperature to the secondary progression. crystallization The onset of event,the decay which of the in excess PE takes specific place heat mainly thcapacityickening, was and found therefore to correspond associated approximately with molecular to motionsthe beginning occurring of the in thirdthe fold stage interface of the regionsmelting through lamellar thickening [64]. This process in PE is connected to a crystal α relaxation process, [temperature60]. Conversely, evolution, reversing i.e., crystallization/meltingto the secondary crystallization that takes event, place whichin PE atin lowPE takestemperaturesc place mainly was which involves cooperative chain sliding in the crystalline regions [65]. The decay of the excess attributedthrough lamellar to lateral thickening crystal surface [64]. This activity, proce basedss in onPE pais rtialconnected melting to anda crystal crystallization αc relaxation without process, the specificneedwhich heat of capacity involvesmolecular cooperative in nucleation, PE at high chain according crystallization sliding to inthe the mechanism crystalline temperature typical regions of was [polymers65]. thus The connected decaythat do of not the withexhibit excess lamellar thickening,slidingspecific and diffusion heat therefore capacity [66, associated67 ].in PE at high with crystallization molecular motions temperature occurring was thus in theconnected fold interface with lamellar regions [60]. Conversely,thickening, reversing and crystallization/meltingtherefore associated with molecular that takes motions place occurring in PE atlow in the temperatures fold interface wasregions attributed to lateral[60 crystal]. Conversely, surface reversing activity, crystallization/melting based on partial meltingthat takes andplace crystallization in PE at low temperatures without the was need of attributed to lateral crystal surface activity, based on partial melting and crystallization without the molecular nucleation, according to the mechanism typical of polymers that do not exhibit sliding need of molecular nucleation, according to the mechanism typical of polymers that do not exhibit diffusionsliding [66,67 diffusion]. [66,67].

Figure 13. Correspondence between the three stages of the melting temperature (Tm) evolution,

plotted as the difference between the melting temperature and the crystallization temperature (Tc), and the decay of the excess heat capacity at the indicated crystallization temperature. (Reprinted (adapted) with permission from [60]. Copyright (2004) American Chemical Society).

Figure 13. Correspondence between the three stages of the melting temperature (Tm) evolution, Figure 13. Correspondence between the three stages of the melting temperature (Tm) evolution, plotted as the difference between the melting temperature and the crystallization temperature (Tc), plottedand as the the difference decay of the between excess heat the capacity melting at temperature the indicated crystallization and the crystallization temperature. temperature(Reprinted (Tc), and the(adapted) decay of with the permission excess heat from capacity [60]. Copyright at the (2004) indicated American crystallization Chemical Society temperature.). (Reprinted (adapted) with permission from [60]. Copyright (2004) American Chemical Society). MaterialsMaterials2017 2017,,10 10,, 442 442 1313 ofof 2222

To summarize, for some polymers, for example PCL and PE, the dynamics of the reversing To summarize, for some polymers, for example PCL and PE, the dynamics of the reversing melting melting is fast, and, as a consequence, considerable cp,exc values are measured and cp,rev might iscorrespond fast, and, asto the a consequence, baseline specific considerable heat capacitycp,exc onlyvalues if the are modulation measured and periodcp,rev ismight very short. correspond When, toon the the baselinecontrary, specific the dynamics heat capacity of the reversing only if the melting modulation is sufficiently period isslow, very for short. example When, for PHB on the at contrary,low crystallization the dynamics temperature, of the reversing or for melting PLLA, the issufficiently high-frequency slow, limit for example is reached for PHBat standard at low crystallization temperature, or for PLLA, the high-frequency limit is reached at standard frequencies frequencies of TMDSC, and cp,rev provides the thermodynamic baseline specific heat capacity during ofthe TMDSC, entire the and crystallizationcp,rev provides process. the thermodynamic baseline specific heat capacity during the entire the crystallizationThe study process. of the time dependence of the reversing specific heat capacity during quasi-isothermal The study of the time dependence of the reversing specific heat capacity during quasi-isothermal experiments has demonstrated that when cp,exc is not zero, cp,rev can tend to a constant value, higher experiments has demonstrated that when c is not zero, c can tend to a constant value, than the expected thermodynamic cp,base. This conditionp,exc identifies p,reva reversible melting process, i.e., the higheroccurrence than theof a expected true local thermodynamic equilibrium at cthep,base crystal. This/amorphous condition identifies interface a reversible[2]. The phenomenon melting process, has i.e.,been the studied occurrence mainly of a in true the local melting equilibrium region at of the various crystal/amorphous polymers, for interface example [2 ]. PET, The poly(butylene phenomenon hasterephthalate) been studied (PBT), mainly poly(trimethylene in the melting regionterephthalate) of various (PTT), polymers, PS, nylon12, for example cis-1,4- PET,polybutadiene poly(butylene [68– terephthalate) (PBT), poly(trimethylene terephthalate) (PTT), PS, nylon12, cis-1,4-polybutadiene [68–75]. 75]. During a quasi-isothermal annealing around a given temperature (To) in the melting region, cp,rev Duringdecreases a quasi-isothermalprogressively towards annealing a constant around value, a given as illustrated temperature in Figure (To) 14 in for the a meltingsemi-crystalline region, cPBTp,rev decreasessample [73 progressively]. These relaxation towards curves a constant are generally value, as fitted illustrated with ina Figuresum of 14 two for exponential a semi-crystalline decay PBTfunctions sample [2]: [73 ]. These relaxation curves are generally fitted with a sum of two exponential decay functions [2]: t /1 t /2 c p,rev t  c p, C1e−t/τ1 C2 e −t/τ 2 (7) cp,rev(t) = cp,∞ + C1e + C2e (8)

   wherewherec pc,∞p, is is the the final final equilibrium equilibrium reversible reversible specific specific heat heat capacity, capacity, and andτ1 and 1 τand2 the relaxation2 the relaxation times associatedtimes associated to irreversible to irreversible events that events occur that during occur the during quasi-isothermal the quasi- analysis,isothermal as partial analysis, melting as partial and fastmelting recrystallization, and fast recrystallization, which are connected which with are connectedthe lower relaxation with the time,lower and relaxation slow crystal time, perfection, and slow relatedcrystal toperfection, the higher related relaxation to the timehigher [71 relaxa,72].tion Partial time melting [71,72]. leads Partial to melting the removal leads of to fully the removal melted moleculesof fully melted from themolecules reversing from melting, the reversing because these melting, molecules because would these need molecules a new molecular would need nucleation a new tomolecular recrystallize. nucleation Recrystallization to recrystallize. and crystal Recrystallization perfection also produce and crystal a reduction perfection in cp,rev also, because produce more a perfectreduction crystals, in cp,rev with, because higher more melting perfect temperature, crystals, with are higher removed melting from temperature, the reversing are cycle. removed After longfrom times,the reversing all these cycle. irreversible After long events times, disappear, all these and irreversible a steady stateevents is disappear, reached, which and a corresponds steady state tois areached, situation which of local corresponds equilibrium. to a Insituation Figure of14 local, the equilibrium occurrence of. In a Figure true reversible 14, the occurrence local equilibrium of a true atreversible the crystal/amorphous local equilibrium interface at the crystal/amorphous is attested by the finalinterfacecp,rev isvalues, attested which by the are final higher cp,rev than values, the correspondingwhich are highercp,base,2phase than thedata corresponding calculated bycp,base,2phase Equation data (3) calculated from the by values Equation of the (3) crystallinity from the values degrees of measuredthe crystallinity at the enddegrees of the measured quasi-isothermal at the end measurements of the quasi-isothermal [73]. measurements [73].

2.6

To = 225.2 °C

) -t/12.5 -t/88.2

-1 2.4 cp,rev(t) = 2.28 + 0.24 e + 0.14 e

K

-1

J g J To = 216.5 °C

(

2.2

p,rev

c -t/10.1 -t/55.2 cp,rev(t) = 2.16 + 0.15 e + 0.14 e 2.0

0 100 200 300 time (min)

Figure 14. Time dependence of the reversing specific heat capacity (cp,rev) of PBT isothermally Figure 14. Time dependence of the reversing specific heat capacity (cp,rev) of PBT isothermally crystallizedcrystallized atat 200 ◦°CC for 30 30 min, min, during during quasi quasi-isothermal-isothermal measurements measurements over over long long time time periods periods in the melting region at To = 216.5 °C◦ (□) and 225.2 °C◦ (○) (p = 120 s, AT = 0.2 K). The dashed lines with in the melting region at To = 216.5 C() and 225.2 C( )(p = 120 s, AT = 0.2 K). The dashed lines with squares and circles are the cp,base,2phase values calculated by Equation (3) from the crystallinity degrees squares and circles are the cp,base,2phase values calculated# by Equation (3) from the crystallinity degrees measured at the end of the quasi-isothermal annealing at To = 216.5 °C◦ and 225.2 °C,◦ respectively, by measured at the end of the quasi-isothermal annealing at To = 216.5 C and 225.2 C, respectively, byusing using the the solid solid and and liquid liquid specific specific heat heat capacities capacities of PBT of PBT as taken as taken from from [40].[ (40Reprinted]. (Reprinted (adapted) (adapted) with withpermission permission from from [73]. [Copyright73]. Copyright (2004) (2004) American American Chemical Chemical Society Society).).

Materials 2017, 10, 442 14 of 22

The time evolution of the reversing specific heat capacity during quasi-isothermal annealing Materials 2017, 10, 442 14 of 22 depends on To. Figure 15 illustrates the results of quasi-isothermal analyses performed for 6 h at ◦ differentTheTos ,time chosen evolution in the of melting the reversing range specific of a PBT heat sample capacity isothermally during quasi crystallized-isothermal annealing at 200 C[ 73]. −1 The cdependsp,app and oncp,rev To. Figurecurves 15 registered illustratesimmediately the results of afterquasi crystallization-isothermal analyses upon performed heating atfor 0.5 6 h K at min , ◦ are showndifferent in Tos the, chosen graph in the on melting the left. range For of Ta oPBT< 227sampleC, isothermally the cp,rev curves crystallized registered at 200 °C during [73]. the quasi-isothermalThe cp,app and cp,rev annealing curves registered (plot on immediately the right) after display crystallization the common upon observedheating at 0.5 decay. K min When−1, are PBT is analyzedshown in at the 227 graph◦C, the on reversingthe left. For specific To < 227 heat °C, the capacity cp,rev curves remains registered practically during constant the quasi during-isothermal theentire experiment.annealing For (plot quasi-isothermal on the right) display analyses the common performed observed at higherdecay. When temperatures PBT is analyzed (228 ◦ Cat and227 °C, 230 ◦C), the reversing specific heat capacity remains practically constant during the entire experiment. For cp,rev shows a different trend, increasing with the measurement time. These last experiments start quasi-isothermal analyses performed at higher temperatures (228 °C and 230 °C), cp,rev shows a fromdifferent an almost trend, completely increasing melted with the sample, measurement which partiallytime. These recrystallizes last experimen duringts start the from quasi-isothermal an almost measurements.completely melted This recrystallization sample, which partially progressively recrystallizes add newduring crystals the quasi to- theisothermal reversing measurements. melting process: the effectThis recrystallization is a continuous progressively increase add in thenew measured crystals to thecp,rev reversing. At the melting intermediate process: the temperature effect is a of ◦ 227 continuousC, fusion, increase recrystallization in the me andasured crystal cp,rev. perfection At the intermediate are clearly temperature counterbalanced, of 227 °C, which fusion, results in a constantrecrystallizationcp,rev value. and crystal Also, perfection in Figure are 15 clearly, the comparison counterbalanced, between which the resultscp,rev invalues a constant at the cp,rev end of value. Also, in Figure 15, the comparison between the cp,rev values at the end of the quasi-isothermal the quasi-isothermal annealing and the corresponding calculated cp,base,2phase data prove that a local reversibleannealing melting/crystallization and the corresponding process calculated is established cp,base,2phase in PBTdata after prove long that times a of local annealing. reversible melting/crystallization process is established in PBT after long times of annealing.

14

) 2.5

-1 A 225 °C B K cp,rev

-1 226 °C J g cp,app 222 °C ( 10

)

-1 2.3 217 °C 218 °C

K

-1 227 °C

6 228 °C

(J g 230 °C p,rev 2.1 220 °C c 215 °C 2

Specific heat capacity cp,base,2phase 200 210 220 230 1.9 Temperature (°C) time 360 min

FigureFigure 15. (15.A) ( ApparentA) Apparent specific specific heat heat capacity capacity (cp,app, dashed, dashed line) line) and and reversing reversing specific specific heat capacity heat capacity ◦ (cp,rev(c,p,rev solid, solid line) line) of of PBT PBT isothermally isothermally crystallizedcrystallized at at 200 200 °C Cfor for 30 30min min as a as function a function of temperature of temperature duringduring heating heating (heating (heating rate: rate: 0.5 0.5 K K min min−−1,, modulation modulation period: period: 120 120 s, temperature s, temperature modulation modulation amplitude: 0.2 K); (B) time dependence of the reversing specific heat capacity (cp,rev) of PBT during amplitude: 0.2 K); (B) time dependence of the reversing specific heat capacity (cp,rev) of PBT during quasi-isothermal measurements of 6 h at the indicted Tos. The data are from separate measurements quasi-isothermal measurements of 6 h at the indicted Tos. The data are from separate measurements and and are collected in a single graph in order to compare the cp,rev trend at different temperatures. The are collected in a single graph in order to compare the cp,rev trend at different temperatures. The dashed dashed lines are the cp,base,2phase values calculated by Equation (3) from the values of the crystallinity lines are the c values calculated by Equation (3) from the values of the crystallinity degrees degrees measuredp,base,2phase at the end of the quasi-isothermal annealing, by using the solid and liquid specific measured at the end of the quasi-isothermal annealing, by using the solid and liquid specific heat heat capacities of PBT as taken from [40]. (Reprinted (adapted) with permission from [73]. Copyright capacities(2004) ofAmerican PBT as takenChemical from Society [40].). (Reprinted (adapted) with permission from [73]. Copyright (2004) American Chemical Society). 4. Non-Isothermal Crystallization and Stepwise Quasi-Isothermal Crystallization upon Cooling 4. Non-Isothermal Crystallization and Stepwise Quasi-Isothermal Crystallization upon Cooling Non-isothermal crystallization that takes place upon cooling from the melt, sometimes named ‘hotNon-isothermal crystallization’, crystallization usually exhibits that a reversing takes place response upon in cooling TMDSC from analyses. the melt, The amount sometimes of the named ‘hot crystallization’,reversing melting usuallygenerally exhibits increases a reversingwith increasing response temperature, in TMDSC and analyses.it is higher Thein the amount melting of the region with respect to the crystallization region [2]. At the low average cooling rates used with the reversing melting generally increases with increasing temperature, and it is higher in the melting TMDSC technique (generally 1–2 K min−1), non-isothermal crystallizations occur at temperature far region with respect to the crystallization region [2]. At the low average cooling rates used with the above the glass transition temperature. For this reason, the excess specific heat capacity largely TMDSC technique (generally 1–2 K min−1), non-isothermal crystallizations occur at temperature contributes to cp,rev, with the result that it is impossible to attain the baseline specific heat capacity of far abovethe non the-isothermal glass transition crystallization temperature. by TMDSC, For as this prove reason,n, for theexample excess, inspecific the case heatof PET capacity and PHB largely contributes[36,37]. to cp,rev, with the result that it is impossible to attain the baseline specific heat capacity of the non-isothermalAn example crystallization of non-isothermal by TMDSC, crystallization as proven, monitored for example, during in TMDSC the case cooling of PET run and is PHBshown [36 ,37]. inAn Figure example 16. The ofnon-isothermal apparent specific crystallization heat capacity (c monitoredp,app) of PET duringmeasured TMDSC by conventional cooling run DSC is at shown in Figure 16. The apparent specific heat capacity (cp,app) of PET measured by conventional DSC at Materials 2017, 10, 442 15 of 22

−1 cooling rate of 2 K min , is compared in Figure 16 with the corresponding cp,rev curves by TMDSC −1 with pMaterials= 60 s 2017and, 10 120, 442 s (average cooling rate: 2 K min ). On the same graph, the specific heat15 of capacity 22 data in the liquid and solid state of PET, as taken from the literature, are also indicated. cooling rate of 2 K min−1, is compared in Figure 16 with the corresponding cp,rev curves by TMDSC The cp,app curve depicted in Figure 16 reveals that the crystallization process extends from with p = 60 s and 120 s (average cooling rate: 2 K min−1). On the same graph, the specific heat capacity about 240 ◦C down to approximately 120 ◦C, with the peak centered at 218 ◦C. The glass transition, data in the liquid and solid state of PET, as taken from the literature, are also indicated. related to vitrification of the MA fraction, is centered approximately at 80 ◦C. At temperatures below ◦ The cp,app curve depicted in Figure 16 reveals that the crystallization process extends from about 140 C,240 the °C overlappingdown to approximately of the cp,rev 120curves, °C, with which the peak are centered independent at 218 °C of. The the glass frequency transition, of modulation, related atteststothat vitrification no reversing of the MA latent fraction, heatis is exchangedcentered approximately in this temperature at 80 °C. At range tempe uponratures cooling. below 140 As a°C, result, ◦ betweenthe overlapping approximately of the 140 cp,rev curves,C and which the glass are independent transition temperature, of the frequency the ofc modulation,p,rev curves attests correspond that to ◦ cp,basenoof reversing the crystallization latent heat process. is exchanged Conversely, in this temperature at temperatures range higher upon cooling. than 140 As C,a result, the cp,rev betweencurves do not defineapproximately the baseline 140 specific°C and the heat glass capacity, transition because temperature, they exhibit the cp,rev a peakcurves that correspond originates to fromcp,base of reversing the crystallization/meltingcrystallization process. or Conversely, change in theat temperatures crystallization higher rate than between 140 °C, thethe twocp,rev curves semi-periods. do not define The fast releasethe of baseline latent heat specific that occurs heat capacity, during crystallization because they exhibit can cause a peak false that effects origi innates the calculated from reversing reversing crystallization/melting or change in the crystallization rate between the two semi-periods. The fast specific heat curve [76]. The irregular shape of the cp,rev curves, which becomes more wrinkled in release of latent heat that occurs during crystallization can cause false effects in the calculated the crystallization temperature range with increasing the modulation period, is an example of these reversing specific heat curve [76]. The irregular shape of the cp,rev curves, which becomes more possiblewrinkled artifacts. in the As crystallization a first approximation, temperature a baseline-specificrange with increasing heat the capacity modulation can be period, constructed is an by ◦ ◦ extrapolatingexample of up these to melt possible the artifacts. linear trend As a displayedfirst approximation, from 100 a baselineC to about-specific 140 heatC bycapacity the cp,rev can curves.be The linearconstructed baseline by allowsextrapolating the cp,app up tocurve melt tothe be linear integrated, trend displayed to determine from 100 the °C crystalline to about 140 weight °C by fractionthe evolution,cp,rev curves. according The linear to Equation baseline (9) allows [37]: the cp,app curve to be integrated, to determine the crystalline weight fraction evolution, according to Equation (9) [37]: 0 0 Z To c (T ) − c (T ) p,app  p,base 0 wC(T) = To c p,app (T' ) c p,base (T' ) dT (9) wC (T)   o 0 dT' T T ∆ho m(T ) (8) hm (T' ) where T is a reference temperature in the melt. whereo To is a reference temperature in the melt.

)

-1 c cooling K 2.0 p,app

-1 cp,rev p=60s

J g J ( cp,rev p=120s 1.8

1.6

6

heat capacity in in capacity heat 4 1.4

2

40 80 120 160 200 240

Specific 1.2 40 80 120 160 200 240

Temperature (°C)

Figure 16. Apparent specific heat capacity (cp,app) by standard DSC and reversing specific heat capacity Figure 16. Apparent specific heat capacity (cp,app) by standard DSC and reversing specific heat capacity −1 (cp,rev) of PET at modulation period of 60 s and 120 s, measured upon cooling from the melt at 2 K min −1 (cp,rev) of PET at modulation period of 60 s and 120 s, measured upon cooling from the melt at 2 K min (AT = 1.0 K). The black solid line with circles is the approximate linear baseline, whereas the solid grey (AT = 1.0 K). The black solid line with circles is the approximate linear baseline, whereas the solid grey line is the two-phase baseline (cp,base,2phase). The black thin solid lines are the solid and liquid specific line is the two-phase baseline (c ). The black thin solid lines are the solid and liquid specific heat capacities of PET, as takenp,base,2phase from [40]. The inset shows the entire cp,app curve. (Reprinted (adapted) heat capacitieswith permission of PET, from as taken[37]. Copyright from [40 ].(2014) The Elsevier inset shows). the entire cp,app curve. (Reprinted (adapted) with permission from [37]. Copyright (2014) Elsevier). The calculated temperature-dependence of the crystalline weigh fraction wC is presented in Figure 17. The final wC is 0.42, a value quite high due to the slow cooling rate used in the TMDSC The calculated temperature-dependence of the crystalline weigh fraction wC is presented in measurements [77,78]. From this wC curve, a two-phase approximate baseline specific heat capacity Figure 17. The final wC is 0.42, a value quite high due to the slow cooling rate used in the (cp,base,2phase), which neglects vitrification of the rigid amorphous fraction, can be determined, according TMDSC measurements [77,78]. From this w curve, a two-phase approximate baseline specific heat to Equation (3). Figure 16 shows that cp,base,2phaseC crosses the approximate linear baseline around 190 °C. capacityThis ( cfindingp,base,2phase suggests), which that neglects part of the vitrification amorphous of chains the rigid might amorphous start to vitrify fraction, during can crystallization be determined, accordingat 2 K to min Equation−1 approximately (3). Figure at 190 16 °C.shows A more that correctcp,base, 2sigmoidalphase crosses cp,base the curve approximate can be constructed linear baseline by ◦ aroundmerging 190 C. the This cp,base, finding2phase curve suggests from the thatbeginning part of of thethe crystallization amorphous chains to 190 °C, might to the start linear to c vitrifyp,base curve during −1 ◦ crystallizationfrom 190 °C at down2 K min to the approximatelyglassy state. The atresultant 190 C. wC A, determined more correct by Equation sigmoidal (9)c p,baseusingcurve the new can be

Materials 2017, 10, 442 16 of 22

◦ constructedMaterials 2017, 10 by, 442 merging the cp,base,2phase curve from the beginning of the crystallization to 19016 ofC, 22 Materials 2017, 10, 442 ◦ 16 of 22 to the linear cp,base curve from 190 C down to the glassy state. The resultant wC, determined bybaseline, Equation is practically (9) using coincident the new baseline, with that is determined practically with coincident the linea withr baseline that determined(∆wC = 0.001 withat 40 the°C). baseline, is practically coincident with◦ that determined with the linear baseline (∆wC = 0.001 at 40 °C). linearThis type baseline of analysis, (∆wC =which 0.001 combinesat 40 C). conventional This type ofand analysis, temperature which-modulated combines DSC conventional measurements, and This type of analysis, which combines conventional and temperature-modulated DSC measurements, temperature-modulatedcan thus allow an approximate DSC measurements, identification canof the thus temperature allow an approximateat which the identificationRA fraction starts of the to can thus allow an approximate identification of the temperature at which the RA fraction starts to temperaturedevelop during at which non-isotherm the RA fractional crystallization. starts to develop during non-isothermal crystallization. develop during non-isothermal crystallization. SimilarSimilarc cp,revp,rev curves were registered forfor PETPET duringduring stepwisestepwise quasi-isothermalquasi-isothermal coolingcooling fromfrom thethe Similar cp,rev curves were registered for PET during stepwise quasi-isothermal cooling from the meltmelt (see(see FigureFigure 1818).). After After crystallization, crystallization, the the crystallinity crystallinity percentage, percentage, determined determined on on re- re-heatingheating by melt (see Figure 18). After crystallization, the crystallinity percentage, determined on re-heating by bystandard standard DSC, DSC, was was 0.49, 0.49, a a value value slig slightlyhtly higher higher than than the the final final wwCC determineddetermined at at the end end of of the the standard DSC, was 0.49, a value slightly higher than the final wC determined at the end of the experimentexperiment describeddescribed inin FiguresFigures 1616 andand 1717.. TheThe reasonreason isis ascribableascribable toto thethe muchmuch smallersmaller averageaverage experiment described in Figures 16 and 17. The reason is ascribable to the much smaller average coolingcooling raterate ofof the the stepwise stepwise quasi-isothermal quasi-isothermal run run (0.1 (0.1 K K min min−−11).). ForFor aa comparison,comparison, FigureFigure 1818 shows shows cooling rate of the stepwise quasi-isothermal run (0.1 K min−1). For a comparison, Figure 18 shows alsoalso thethec cp,revp,rev curvecurve of a a semicrystalline semicrystalline PET sample with similar crystallinity degree,degree, obtainedobtained throughthrough also the cp,rev curve of a semicrystalline PET sample with similar crystallinity degree, obtained through aa stepwisestepwise quasi-isothermalquasi-isothermalheating heating experimental experimental procedure. procedure. a stepwise quasi-isothermal heating experimental procedure.

0.6 0.6 cooling rate: 2 K min-1 cooling rate: 2 K min-1

0.4 0.4

C

C

w

w 0.2 0.2

0.0 0.0 40 80 120 160 200 240 40 80 120 160 200 240 Temperature (°C) Temperature (°C) Figure 17. Temperature evolution of the crystalline weight fraction (wC) of PET during non-isothermal Figure 17. 17. TemperatureTemperature evolution evolution of the crystalline of the crystalline weight fraction weight (wC fraction) of PET during (wC) of non PET-isothermal during −1 crystallization at 2 K min . (Reprinted (adapted)−1 with permission from [37]. Copyright (2014) crystallizationnon-isothermal at crystallization 2 K min−1. (Reprinted at 2 K min (adapted). (Reprinted with permission (adapted) from with [37 permission]. Copyright from (2014) [37]. Elsevier). Elsevier)Copyright. (2014) Elsevier).

Figure 18. Reversing-specific heat capacity (cp,rev) of PET (filled circles) during stepwise quasi- Figure 18. 18. ReversingReversing-specific-specific heat heat capacity capacity (cp,rev ()c p,rev of PET) of (filled PET (filled circles) circles) during during stepwise stepwise quasi- isothermal TMDSC cooling from the melt (p = 60 s and AT = 1.0 K, oscillation time around each isothermal TMDSC cooling from the melt (p = 60 s and AT = 1.0 K, oscillation time around each quasi-isothermaltemperature: 20 min) TMDSC. The cooling thin solid from lines the are melt the (p solid= 60 and s and liquidAT = specific 1.0 K, oscillationheat capacities, time as around taken temperature: 20 min). The thin solid lines are the solid and liquid specific heat capacities, as taken eachfrom temperature:[40]. The broken 20 min).line is the The calculated thin solid specific lines are heat the capacity solidand for a liquid 49% crystalline specific heat PET. capacities, The open fromas taken [40]. from The [broken40]. The line broken is the linecalculated is the calculated specific heat specific capacity heat for capacity a 49% crystalline for a 49% crystallinePET. The open PET. circles describe the cp,rev curve of a melt-crystallized PET sample (crystallinity degree: 44%). (Reprinted circlesThe open describe circles the describe cp,rev curve the cof a meltcurve-crystallized of a melt-crystallized PET sample PET (crystallinity sample (crystallinity degree: 44%). degree: (Reprinted 44%). (adapted) with permission fromp,rev [5]. Copyright (1997) American Chemical Society). (adapted)(Reprinted with (adapted) permission with permissionfrom [5]. Copyright from [5]. (1997) Copyright American (1997) Chemical American Society) Chemical. Society). Up to now, only the reversing specific heat capacity of PLLA has been found to be independent Up to now, only the reversing specific heat capacity of PLLA has been found to be independent of frequency modulation during non-isothermal crystallization from the melt. Figure 19 shows the of frequency modulation during non-isothermal crystallization from the melt. Figure 19 shows the c,app curve of a PLLA sample obtained by conventional DSC during cooling from the melt at 2 K min−1 c,app curve of a PLLA sample obtained by conventional DSC during cooling from the melt at 2 K min−1 together with the corresponding cp,rev curves by temperature-modulated DSC (average cooling rate: 2 together with the corresponding cp,rev curves by temperature-modulated DSC (average cooling rate: 2

Materials 2017, 10, 442 17 of 22

Up to now, only the reversing specific heat capacity of PLLA has been found to be independent of frequency modulation during non-isothermal crystallization from the melt. Figure 19 shows the c,app −1 curveMaterials of 2017 a PLLA, 10, 442 sample obtained by conventional DSC during cooling from the melt at 2 K min17 of 22 together with the corresponding cp,rev curves by temperature-modulated DSC (average cooling rate: 2K K min min−1,− temperature1, temperature amplitude amplitude:: 1.0 1.0K, modulation K, modulation periods periods:: p = 60p = s 60and s and120 s, 120 respectively) s, respectively) [79]. [The79]. Thecrystallization crystallization peak peak extends extends from from about about 130 130 °C◦ C to to approximately approximately 90 90 °C,◦C, and and appears slightly slightly asymmetric.asymmetric. This irregular shape, already reported in the literature [80],], hashas beenbeen attributedattributed toto thethe growthgrowth ofof thethe twotwo differentdifferent crystalcrystal forms,forms, thethe αα-form-form atat higherhigher temperatures,temperatures, andand thethe αα0-form-form atat lowerlower temperaturestemperatures [[4242––4444].]. In allall thethe samples,samples, thethe reversingreversing specificspecific heatheat capacitycapacity uponupon coolingcooling appearsappears frequencyfrequency independentindependent (within(within thethe experimentalexperimental errorerror andand noise)noise) inin thethe wholewhole crystallization range, whichwhich meansmeans thatthat reversingreversing latentlatent heatheat isis notnot exchanged duringduring thethe temperature modulationmodulation andand thatthat thethe ccp,revp,rev curvescurves correspond correspond to to the the baselines baselines of of the the crystallization crystallization process. process. TheThe reductionreduction inin thethe MA MA fraction fraction during during non-isothermal non-isothermal crystallization crystallization was was derived derived according according to Equationto Equation (7), and(7), the and growth the growth of the crystalline of the crystalline weight fraction weight from fraction the integration from the of integration the crystallization of the o o peak,crystallization according peak, to Equation according (9), byto usingEquation for ∆(9),hm (byT) theusing average for  ofhm theT the enthalpy average of fusionsof the enthalpy of the 100% of crystallinefusions of αthe0- and100%α-forms crystalline [46]. Finally,α- and theα-forms RA fraction [46]. Finally, evolution the upon RA non-isothermalfraction evolution crystallization upon non- wasisothermal determined crystallization by difference. was determined by difference. FigureFigure 20 displaysdisplays the the temperature temperature evolution evolution of of crystalline crystalline (w (Cw), Cmobile), mobile amorphous amorphous (wMA (w) andMA) andrigid rigid amorphous amorphous (wRA) (weightwRA) weight fractions fractions during non during-isothermal non-isothermal crystallization crystallization of PLLA at of 2 PLLA K min at−1. −1 2During K min the. During non-isothermal the non-isothermal crystallization, crystallization, simultaneously simultaneously with the increase with the in increase wC, the in MAwC, fraction the MA fractiondecreases decreases progressively, progressively, as evidenced as evidenced by the marked by the first marked step firstin the step temperatur in the temperaturee range 130 range °C ÷ ◦ ◦ 130100 °C.C ÷ A100 secondC. A step second is observed step is observedin the wMA in curve the w inMA thecurve glass in transition the glass transitionregion between region 80 between °C and 8060 ◦°C,C andwhen 60 all◦C, mobile when allamorphous mobile amorphous fraction becomes fraction vitrified. becomes vitrified.

6

)

-1 cp,app

K

-1 cp,rev p= 60s

J g ( cp,rev p=120s 4

2

Specific heat capacity

20 60 100 140 Temperature (°C)

Figure 19. Apparent specific heat capacity (cp,app: solid lines) of PLLA and reversing specific heat Figure 19. Apparent specific heat capacity (cp,app: solid lines) of PLLA and reversing specific heat capacity (cp,rev) on cooling at 2 K min−11 as a function of temperature (p = 60 s: dashed line; p = 120 s: capacity (cp,rev) on cooling at 2 K min as a function of temperature (p = 60 s: dashed line; p = 120 s: dasheddashed dotted dotted line). line). The The thin thin solid lines are the thermodynamic solid and liquid liquid specificspecific heat heat capacitiescapacities ofof PLLAPLLA asas takentaken fromfrom thethe literatureliterature [[4545].]. (Reprinted(Reprinted (adapted) with permission from [ 79]. CopyrightCopyright (2017)(2017) Springer).Springer).

The RA fraction develops in parallel with the crystal phase, starting from approximately 130 °C. The RA fraction develops in parallel with the crystal phase, starting from approximately 130 ◦C. This further validates the hypothesis that 130 °C is likely the upper limit temperature for the RA This further validates the hypothesis that 130 ◦C is likely the upper limit temperature for the RA fraction in PLLA [34,38]. The development of the rigid amorphous fraction occurs simultaneously fraction in PLLA [34,38]. The development of the rigid amorphous fraction occurs simultaneously with crystal growth, both during primary and secondary crystallizations. Between the apparent end with crystal growth, both during primary and secondary crystallizations. Between the apparent end of the crystallization, approximately 90 °C, and the beginning of the glass transition, the RA fraction of the crystallization, approximately 90 ◦C, and the beginning of the glass transition, the RA fraction continues to increase. This could be due to a minor and undetectable increase in wC, which, occurring continues to increase. This could be due to a minor and undetectable increase in w , which, occurring in in geometrically restricted areas, could induce stiffening of an additional fractionC of amorphous geometrically restricted areas, could induce stiffening of an additional fraction of amorphous segments. segments. Otherwise, since RA fraction originates from amorphous segments that are constrained Otherwise, since RA fraction originates from amorphous segments that are constrained above Tg, it is above Tg, it is probable that internal stresses, which are not released during crystal growth, and are concentrated at the amorphous/crystal interface, can produce some amorphous segments vitrification upon cooling, as a consequence of the reduced mobility of the chains [81]. In addition, rigid crystalline domains could produce, through a friction or “wall” effect, an elevation of the glass transition temperature of the amorphous segments located in proximity of the rigid crystal surfaces [82,83]. The

Materials 2017, 10, 442 18 of 22 probable that internal stresses, which are not released during crystal growth, and are concentrated at the amorphous/crystal interface, can produce some amorphous segments vitrification upon cooling, as a consequence of the reduced mobility of the chains [81]. In addition, rigid crystalline domains couldMaterials produce, 2017, 10, 442 through a friction or “wall” effect, an elevation of the glass transition temperature18 of of22 the amorphous segments located in proximity of the rigid crystal surfaces [82,83]. The final increase in thefinal RA increase fraction, in observedthe RA fraction, at Tg, reflects observed vitrification at Tg, reflects of the MAvitrification fraction, of because the MA at fraction, temperatures because lower at than T , all the material is solid.g temperaturesg lower than T , all the material is solid.

1.0

0.8

wMA 0.6

0.4

Weight fractions wC 0.2

wRA 0.0 20 60 100 140 Temperature (°C)

Figure 20. Temperature evolution of the mobile amorphous (wMA: dashed line), crystalline (wC: solid Figure 20. Temperature evolution of the mobile amorphous (wMA: dashed line), crystalline line), and rigid amorphous (wRA: dotted line) weight fractions during non-isothermal crystallization (wC: solid line), and rigid amorphous (wRA: dotted line) weight fractions during non-isothermal of PLLA at 2 K min−1. Estimated errors:−1 ±0.02 for wC and wMA, ±0.04 for wRA. (Reprinted (adapted) with crystallization of PLLA at 2 K min . Estimated errors: ±0.02 for wC and wMA, ±0.04 for wRA. (Reprintedpermission (adapted)from [79]. with Copyright permission (2017) from Springer [79].) Copyright. (2017) Springer).

5. Conclusions At the end of this review,review, itit isis worthworth emphasizingemphasizing furtherfurther thatthat thethe combinationcombination ofof conventionalconventional DSC and TMDSC is a useful useful path path that that can can allow allow thethe obtainment obtainment of of muchmuch information information on the crystallization andand thermal thermal behavior behavior of of polymeric polymeric materials. materials. Although Although TMDSC TMDSC measurements measurements are slow are andslow quite and time-consuming, quite time-consuming, the calorimetric the calorimetric data that data can that be derived can be derived are crucial are for crucial a more for detailed a more descriptiondetailed description of the thermal of the properties thermal properties of polymeric of polymeric materials. materials. By means ofBy themeans temperature-modulated of the temperature- calorimetricmodulated calorimetric technique, technique, evolution ofevolution the baseline of the specificbaseline heat specific capacity heat capacity can be assessedcan be assessed during polymerduring polymer crystallization, crystallization, which makes which the makes calculation the calculation of the crystallinity of the crystallinity degree much degree more much accurate. more Thisaccurate. possibility This possibility is offered especiallyis offered atespecially low crystallization at low crystallization temperatures, temperatures, when the amount when ofthe reversing amount meltingof reversing is smaller. melting Particularly is smaller. interesting Particularly is the interesti case ofng PLLA, is the which case doesof PLLA, not exhibit which dependence does not exhibit of the reversingdependence specific of theheat reversingcapacity on specific the modulation heat capacity frequency, on so the that modulation crystallization frequency occurs irreversibly, so that incrystallization a wide temperature occurs irreversibly range. This in favorable a wide temperature situation has range. allowed This the favorable accurate situation determination has allowed of the evolutionthe accurate of the determ crystalline,ination mobile of the amorphous evolution and of rigid the amorphous crystalline, fractions mobile amorphousduring solidification and rigid in differentamorphous experimental fractions during conditions, solidification and has in allowed different the experimental distribution conditions, of the amorphous and has regions allowed with the respectdistribution to the of crystalline the amorphous areas to beregions supposed. with The respect description to the crystalline of the micro- areas and to nano-phase be supposed structure. The ofdescription PLLA was of thus the attained. micro- and This typenano of-phase investigation, structure detailed of PLLA in this was review thus attained. in particular This for type PLLA, of isinvestigation, a procedure detailed advantageous in this review and very in usefulparticular for thefor PLLA, assessment is a procedure and prediction advantageous of many and physical very characteristics,useful for the assessment because it and has beenprediction proven of thatmany many phys propertiesical characteristics, of polymeric because materials, it has been for example proven mechanicalthat many properties and gas permeability, of polymeric depend materials, not only for example on the crystallinity, mechanical but and also gas on permeability, the rigid amorphous depend fraction,not only andon the on itscrystallinity, evolution duringbut also solidification on the rigid [amorphous84–91]. fraction, and on its evolution during solidification [84–91].

Conflicts of Interest: The author declares no conflict of interest.

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Materials 2017, 10, 442 19 of 22

Conflicts of Interest: The author declares no conflict of interest.

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