Kinetics of Nucleation and Growth of Form II to I Polymorphic

Jul 14, 2016 - The phase transition was efficiently accelerated with the increase of ... II to Form I Transition in Polybutene-1 at Late Stage: A Prop...
3 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/Macromolecules

Kinetics of Nucleation and Growth of Form II to I Polymorphic Transition in Polybutene‑1 as Revealed by Stepwise Annealing Yongna Qiao, Qiao Wang, and Yongfeng Men* State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, University of Chinese Academy of Sciences, Renmin Street 5625, 130022 Changchun, P.R. China ABSTRACT: Kinetics of II to I polymorphic transformation in isotactic polybutene1 (PB-1) and its annealing temperature and time dependencies have been investigated by means of differential scanning calorimetry and in situ wide-angle X-ray diffraction techniques. The PB-1 samples were isothermally crystallized into metastable form II crystalline modification followed by annealing at a lower temperature (Tl) and at a higher temperature (Th) subsequently or at a single temperature (Ts) to promote polymorphic transition from form II to I. This solid-to-solid phase transition was shown to be a two-step process including nucleation and growth suggested by the result that more form I was obtained after being annealed at Tl and Th than annealed at Ts for the same period. Annealing at Tl benefits nucleation due to internal stress induced by unbalanced shrinkage of amorphous and crystalline phases because of their different thermal expansion coefficients, while annealing at Th is beneficial to growth owing to rapid segmental diffusion at that temperature. At a given annealing time at Tl (tl) and at Th (th), and fixing one of temperatures between Tl and Th, it shows a maximum in the transformation-temperature profile that can be correlated with the optimal temperature for nucleation or growth. The phase transition was efficiently accelerated with the increase of isothermal crystallization temperature. Such dependency can be understood as a result of higher internal stress built up during cooling from higher isothermal crystallization temperature to Tl. Our results decomposed the polymorphic transition into nucleation and growth for the first time providing a simple and effective way for rapid transition of form II to I in PB-1.

■

INTRODUCTION Isotactic polybutene-1 (PB-1) has a complex polymorphic behavior, containing twined hexagonal/trigonal form I with 3/1 helix, untwined hexagonal/trigonal form I′ with a 3/1 helix, tetragonal form II with an 11/3 helix, and orthorhombic form III with a 4/1 helix. It can crystallize into these crystalline modifications depending on preparation conditions.1−4 However, only the tetragonal form II with a 11/3 helical conformation5 and the hexagonal form I with a 3/1 helical conformation6 are of practical interest. Melt crystallization usually leads to the kinetically favored metastable form II which can transform slowly into the thermodynamically stable form I spontaneously and irreversibly with the considerable enhancement of melting points and mechanical properties such as hardness, stiffness, and strength.1,7−9 The phase transition shows a maximum rate at room temperature10−12 when annealing at a single temperature and at atmospheric pressure. And the transition can be strongly accelerated by external or thermal stress,13−16 high pressure,17 pressured CO2,18−20 and copolymerization with random 1-alkene counits less than five carbon atoms.21 Direct formation of form I has been found in butene-1/ethylene random copolymers with sufficient amount of ethylene counits.22 In some cases, formation of different crystalline forms directly from the melt can also be realized via tuning the melt structure by changing the melt temperature.23,24 In homopolymers of PB-1, form I can only be directly obtained when their ultrathin films were isothermally © XXXX American Chemical Society

crystallized at high temperature or when crystallized in stereoirregular samples.25−27 Crystal structures of form I and II of PB-1 have been confirmed that the R (right-handed helix) and L (left-handed helix) chains of (3/1) and (11/3) conformation are packed in the hexagonal and tetragonal unit cell alternately with the upward and downward directional disorder at each lattice site for form I and form II, respectively, with preservation of the helical hands during the transformation.6,28,29 The two forms are related with the common axis of [110] axis, that the (110) planes of the resultant trigonal unit cell are parallel to the (110) planes of the parent tetragonal unit cell via lateral movement of molecules.30−32 The mechanism of this solid-to-solid phase transition from form II to form I is the cooperative occurrence of chain conformational change and packing mode change so that the energy barrier to cross becomes as low as possible which can explain the formation of the twin structure of form I crystals.29 This movement results in a transient structure, in agreement with the proposal of Li et al.33 to account for the diffraction pattern during transformation. Understanding the kinetics of the II to I phase transformation in PB-1 is of great importance because of the change in physical properties, which is important commercially. This phase transition is comparatively slow, so that it is feasible to Received: April 25, 2016 Revised: July 3, 2016

A

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

(190 °C/2.16 kg). It has a weight-average molecular weight of 7.11 × 105 g/mol. Thermal analysis measurements were conducted with a DSC1 Star System (Mettler Toledo Instruments, Swiss) under nitrogen atmosphere (50 mL/min). The instrument was calibrated with high purity indium as a standard to ensure reliability of the data required. The main thermal protocols are present in Scheme 1. After

study by time-resolved observation with the in situ Fourier transform infrared spectroscopic imaging technique,33,34 microindentation hardness technique,7,8 and wide- and small-angle Xray scattering measurements.32,35 It was found that annealing conditions considerably affect the kinetics of the transition.36,37 The evolution of the content of form I with annealing time shows a typical S-shaped curve. Interestingly, a maximum rate upon annealing is at around −20 °C at the initial stage, whereas the maxima occurs at around 20 °C when transition proceeds to a later stage and the two maxima could be correlated with a nucleation and growth mechanism for the phase transition.37 It is known that nucleation shows a faster rate at low temperature where the diffusion required for growth of the new phase becomes rate-controlling, while higher temperature favors growth. Precooling to around −20 °C for minutes before annealing greatly reduced the transition time which has probably resulted in formation of form I nuclei.38 Clearly, knowledge about kinetics of the polymorphic transition in PB-1 remains fragmental and far from systematic. Actually, the form II to form I transition in PB-1 is similar to what described in the model developed by Tammann dealing with crystallization of small molecules. 39,40 It is therefore possible to apply Tammann’s two stage nuclei development approach to confirm and quantify the relative rates of low-temperature nucleation and high-temperature growth of form II to I phase transition in PB-1 as this approach has been extensively applied for analysis of polymer nucleation and crystallization.41−43 Avrami44−46 assumed that the formation of a new phase started with growth of nuclei, which has been applied to the crystallization of small molecules and polymer and solidsolid phase transition in low-molecular weight materials.47,48 Nucleation is considered to be the rate-determining step,10,49,50 which is determined by the free energy for nucleus formation and the energy of activation for diffusion across the phase boundary.51 It can also be appropriate for the crystal to crystal transition in PB-1 for the relatively slow rate in the early stage that nuclei formed, followed by a steep increase of transition ratio.8,36 In this study, we decomposed the kinetics of polymorphic transition in PB-1 from form II to form I into nucleation and growth steps via a stepwise annealing at low and high temperatures subsequently. Differential scanning calorimetry (DSC) and in situ wide-angle X-ray diffraction (WAXD) were used to investigate the degree of transformation via the observation of the weight fractions of form II and the transformed form I at the end of or during annealing. Nucleation kinetics of the phase transition at different temperatures was magnified so that observed via the following growth at higher temperature. The results show two separated processes of nucleation and growth at relatively low temperature and high temperature. The rate as a function of temperature exhibits Gaussian distribution with a maximum at about −10 °C for nucleation and 40 °C for growth. Immediately after isothermal crystallization at a certain temperature, annealing at low temperature to nucleate rapidly for about an hour before transformation at a higher temperature rather than room temperature would accelerate the rate of II to I phase transition. Moreover, it makes the transition at temperature as high as 90 °C at a considerable rate possible.

■

Scheme 1. Schematic Illustration of Thermal Treatment Applied to PB-1

melting at 160 °C for 8 min to erase the thermal history, the PB-1 samples were fast cooled to Tc to crystallize completely for 30 min and then annealed at a Tl for a time of tl followed by annealing at Th for a time of th. The cooling and heating rates in processes from Tc to Tl and then to Th were both 50 K/min. The annealed samples were heated up to 160 °C at a rate of 20 K/min to obtain the melting curve from which the contents of form II and form I were obtained via integrating each melting peak area of which the melting peaks are at around 115− 120 °C and 125−130 °C for form II and I, respectively, by using a peak fitting procedure considering exponentially modified Gaussian functions as was shown in Figure 1.37,52 The degree of the phase

Figure 1. Examples of peak fitting analysis of DSC melting curves of PB-1 to decompose the melting process of form I and form II crystallites in the samples. transition can be manifested as the content of continuous transformed form I: XI =

AI /ΔHid,I AI /ΔHid,I + AII /ΔHid,II

(1)

whereAI and AII is the area of form I and form II melting peaks, ΔHid,I and ΔHid,II are the melting enthalpy of ideal crystals in form I and form II, of which the value is 141 and 62 J g−1,9 respectively. In-situ WAXD experiments were carried out to investigate the evolution of the crystalline structure during annealing. A piece of PB-1 film with dimensions of 5, 20, and 0.5 mm in width, length, and thickness, respectively, was used for the in situ WAXD measurements. Time-resolved WAXD measurements were performed at SAXSess mc2 (Anton Paar, Austria) with monochromatic Cu−Kα radiation, of which the wavelength is 0.154 nm. The temperature-controlled sample holder and liquid nitrogen was used to control the sample temperature, which gives a temperature precision of 0.1 K. SAXSquant software system transfers the 2D diffraction image to the 1D-curve

EXPERIMENTAL SECTION

The isotactic PB-1 was produced by Lyondell Basell Industries with a trade name of PB0110M. The melt flow rate (MFR) is 0.4 g/10 min B

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules with background subtraction. The main diffraction peaks observed at 2θ of about 10.0°, 17.5°, and 20.4° correspond to crystallographic planes of (110), (300), and (220 + 211) of form I. Besides, a sequence of reflections at 11.9°, 16.9°, and 18.5° can be assigned to the (200), (220), and (213) lattice planes of form II, respectively. The fraction of form I is obtained by the following equation:22,26

XI =

I(110)I I(110)I + RI(200)II

an effective way to speed up the transition rate. Annealing at −16 °C only provided effective nucleation of the form I crystals that were not able to grow at such low temperature whereas annealing only at 20 °C would result in a less nucleation event for form I so that it limited the overall amount of form I crystals observable during the DSC melting run. A combination of first annealing at −16 °C and following annealing at 20 °C promoted extensive nucleation of the form I crystals within the crystalline lamellae of form II crystals and rapid growth of such form I nuclei simultaneously. The physical mechanism of the acceleration of the nucleation of such form I crystals within form II lamellae can be understood as a consequence of internal stress built up during cooling down to a low temperature. Indeed, the difference in thermal expansion coefficient between amorphous and form II crystalline phases can introduce strong internal stress along the normal of crystalline lamellae via tie molecules.49 Such stress along the chain direction in form II crystals is known to accelerate the form II to form I transition in PB-1. Clearly, there are four variables which would influence the final transformation degree after annealing, and they are annealing temperatures (Tl and Th) and annealing times (tl and th) at the early and later stages, respectively. First of all, the effect of annealing time at the lower temperature Tl on the PB-1 II to I phase transition has been investigated. The 50 °C isothermally crystallized PB-1 samples were annealed at −16 °C for different times from 0 to 360 min followed by annealing at 20 °C for 100 min. The last step of annealing at 20 °C for 100 min was to magnify the nucleation effect at −16 °C. Obviously, more form I crystallinity would be obtained after being annealed at 20 °C for the same period if more nuclei were developed at −16 °C prior to 20 °C annealing. The DSC melting curves of thus annealed samples were given in the top of Figure 3. It shows that more form I has been developed with the increase of tl as evidenced by the

(2)

where I(110)I and I(200)II are the integrated intensities of the (110)I and (200)II reflections, respectively, and corrected by the parameter R = 0.36 taking into account the structure factors and Lorentzpolarization factors.26 Long spacing (dac), crystalline lamellar thickness (dc), and amorphous layer thickness (da) of the isothermally crystallized samples after the form II to I transition were measured using the small-angle Xray scattering (SAXS) technique in a modified Xeuss of Xenocs, France, at a sample-to-detector distance of 2430 mm. A multilayer mirror focused Cu Kα X-ray source (GeniX3D Cu ULD, Xenocs SA, France, λ = 0.154 nm) and two sets of scatterless collimating slits 2.4 m apart from each other were used during the experiments. SAXS images were recorded with a Pilatus 100 K detector of Dectris, Swiss. Each SAXS pattern was collected within 20 min which was then background corrected and normalized using the standard procedure. Structural parameters (dac, dc, and da) of the samples in form I were obtained via the correlation function approach.53 Corresponding structural parameters in form II which were used in the discussion of this work were calculated considering a 14% elongation of the chain segments in the crystalline phase during the form transition.

■

RESULTS AND DISCUSSION Figure 2 shows the DSC results of the PB-1 sample after isothermal crystallization at 50 °C for 30 min, followed by

Figure 2. DSC melting curves of PB-1 samples after being subsequently annealed at −16 and 20 °C for different times as indicated in the plot. Inset shows an enlargement of the melting peak of transformed form I crystallites in the samples.

annealing at −16 and 20 °C individually and sequentially for the same total time. The form II crystals have a crystal-tocrystal transformation during annealing at ambient pressure to obtain form I crystals irreversibly. It shows a very tiny form I melting peak at 125 °C after annealing at 20 °C or −16 °C only, while larger amounts of form I were developed with a decrease of form II melting peak area at 115 °C when the sample was annealed sequentially at −16 °C for a short time first followed by 20 °C annealing for the remaining time. The slightly larger area of form I melting peak for sample annealed only at −16 °C than that annealed only at 20 °C may derive from transformation during heating up in the DSC run.37 This result is considered to provide a direct evidence for the twostep phase transition mechanism of nucleation and growth and

Figure 3. DSC melting curves of PB-1 annealed at −16 °C for different time followed by annealing at 20 °C for 100 min (top) and the corresponding evolution of content of form I as a function of annealing time at −16 °C (bottom). C

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules gradual increase of the melting peak area of form I crystals around 125 °C. The content of form I crystals in the samples as a function of annealing time at −16 °C was given in the bottom of Figure 3. Obviously, the content of form I crystals increased rapidly within a short annealing period at −16 °C followed by a slowdown of the transition at longer annealing time. Cooling and enlarging the undercooling led to the increase of driving force to overcome the energetic barrier for nucleation, and the internal stress relaxed gradually over time corresponding to the slowdown of the growth rate of form I fraction. Considering the results in Figure 3, 60 min was chosen as an appropriate time for annealing at Tl in the following investigations. To investigate the evolution of transformed form I fraction with increase of annealing time at 20 °C, the 50 °C isothermally crystallized samples were annealed at −16 °C for 60 min followed by 20 °C annealing for different times. The DSC melting curves of thus annealed samples, shown in the top part of Figure 4, display two endothermic peaks varying with th; that

Figure 5. DSC melting curves of 50 °C isothermally crystallized PB-1 samples annealed at a Tl for 60 min followed by annealing at 20 °C for 220 min (top) and the corresponding evolution of content of form I as a function of annealing temperature at the first stage (bottom).

top part, and the fractions of transformed form I crystals calculated via integration of the melting peaks at 115 and 125 °C of form II and form I crystals were illustrated in the bottom part as a function of Tl. A maximum appears at about −10 °C that implies the fastest nucleation rate. In the top of Figure 6, DSC melting curves of samples annealed at a fixed Tl at −10 °C and a range of Th are present. The biggest peak area around 125 °C for form I and smallest peak area at 115 °C of form II was found in the curve of the sample with Th = 40 °C showing a most rapid growth rate at this temperature than annealing at higher or lower Th, which is different from the previous reports that the fastest transformation was performed at room temperature. The Th was fixed at 40 °C to analyze Tl dependency of growth in the middle part of Figure 5. Different peak areas at 125 °C of form I in the curves indicates different amounts of form I nuclei were formed after annealing for 220 min as the following annealing at 40 °C result in a similar rate for growth. A little melting peak of form I was observed even when the Tl was −50 °C being below the glass transition temperature of −27 °C of PB-1 which was obtained from the DSC experiment during heating from −50 °C to Th. Our results therefore reveal that the nucleation and growth of form II to I polymorphic transition in PB-1 possess kinetics of different temperature dependencies with the nucleation process favored at low temperature and growth at high temperature. A prior nucleation step at Tl significantly fastens the overall transformation rate at Th. The bottom part of Figure 6 is DSC results of samples crystallized at 50 °C for 30 min and annealed at several single temperatures in which it shows notably small melting peaks of form I compared with results in the previous two parts due to slow growth in low temperature and unfavorable nucleation in high temperature. The fraction of transformed form I crystals after being annealed at different annealing conditions as described in

Figure 4. DSC melting curves of 50 °C isothermally crystallized PB-1 samples annealed at −16 °C for 60 min followed by annealing at 20 °C for different times (top) and the corresponding evolution of content of form I as a function of annealing time at 20 °C (bottom).

is, a decrease in the area of endothermic peak associated with melting of form II crystals corresponding to about a double increase in the area of melting peak of form I crystals due to the different bulk heat of fusion of the two crystalline forms. The bottom part in Figure 4 indicates that the fraction of form I increased linearly with th, for the range of time studied. On the basis of the results present in Figures 3 and 4, we fixed the annealing time tl and th at 60 and 220 min, respectively, of 50 °C isothermally crystallized samples in thermal protocols of Scheme 1 for the following DSC experiments. Annealing at −16 °C has been proven to be effective for rapid nucleation and enhance the overall phase transition rate. First, we fixed the Th at 20 °C to determine the nucleation rate at a range of Tl around −16 °C from −30 to 20 °C as shown in Figure 5. DSC melting curves after annealing of the 50 °C isothermally crystallized samples were shown in the D

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

II to I polymorphic transition in PB-1 into nucleation and growth processes as shown in the black and red lines, respectively. Clearly, this polymorphic transition can take place only when the temperature is available to nucleate and grow simultaneously as revealed by the Ts curve. The exceptional data point of Tl at −50 °C below the glass transition temperature out of the Gaussian distribution line is justified for the vitrification freezing of chain segments in the amorphous phase, and it might form a plateau in the Tl line below the glass transition temperature. It shows an almost equal amount of form I under different annealing conditions at a low temperature below Tg, from which we can deduce that there is no nucleation in the glassy state. The internal stress should be similar below Tg because the shrinkage in the glassy state can be ignored compared with that at higher temperature above Tg. Hence, the samples have no ability to form nuclei below Tg. Clearly, the observed nuclei of form I shown in Figure 7 below Tg were developed at the residence time in the temperature range where nucleation occurred during cooling and heating. Figure 8 compares the fraction of transformed form I of 50 °C crystallized PB-1 samples after being annealed at −10 °C

Figure 8. Fraction of transformed form I crystals in 50 °C isothermally crystallized PB-1 samples after being annealed at −10 °C or −25 °C for 60 min followed by annealing at different temperatures for 220 min.

Figure 6. DSC melting curves of PB-1 samples annealed at different conditions after isothermally crystallized at 50 °C: annealed at −10 °C for 60 min followed by annealing at Th for 220 min (top); annealed at Tl for 60 min followed by annealing at 40 °C for 220 min (middle) and annealed at a single temperature (Ts) for 280 min (bottom).

and −25 °C for 60 min followed by annealing at Th for 220 min. The result is in agreement with previous measurement in Figure 6 that a larger amount of form I crystals were developed in the sample nucleated at −10 °C than at −25 °C when grown at the temperature region studied in this work, corresponding to the larger number of nuclei formed at −10 °C with the same growth rate at a certain Th. One can observe that the growing temperature dependency of the transition rate showed similar behavior when the samples were nucleated at different conditions. In order to observe directly the crystalline structural transition during the annealing processes, in situ WAXD experiments were conducted. Selected WAXD data obtained at different periods during annealing were collected in Figure 9. In the top of Figure 9, selected in situ WAXD data of sample annealed at −10 °C for 60 min followed by annealing at 40 °C after isothermal crystallization at 50 °C were present. Clearly, annealing at −10 °C for 60 min did not produce any observable form I crystals as revealed by the lack of corresponding diffraction peaks for form I in the WAXD curve collected at the late stage of the annealing at that temperature. Although diffraction peaks from form I crystals were also not observed immediately after the annealing temperature was increased to 40 °C after the sample was annealed at −10 °C for 60 min,

Figure 6 as a function of annealing temperature are illustrated in Figure 7. These results provide a decomposition of the form

Figure 7. Fraction of transformed form I crystals in 50 °C isothermally crystallized PB-1 samples after being annealed at different conditions as described in Figure 5. The data represent a decomposition of the temperature dependency of form II to I transition rate (Ts curve) into nucleation (Tl curve) and growth (Th curve) rates. E

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

accelerate the phase transition rate during high temperature annealing, manifested by a significant increase of the form I fraction at the beginning of annealing, expressed in solid identifier, while it shows a flat portion for hours at the early stages of transformation for slow nucleation without the low temperature annealing, marked with a hollow identifier, as illustrated in the bottom of Figure 9. It becomes possible to develop a notable amount of form I crystals in the sample when being annealed at 60 °C with low temperature annealing for prenucleation, otherwise it can even not nucleate at all within 75 h. Compared to the three lines expressed in the solid identifier, it shows tapering off of transformed form I fractions when they reach a plateau in the later stage of annealing from 20 to 60 °C, which is because of the incomplete nucleation of the crystallites and vanishment of nuclei at such high temperature where nuclei is metastable together with the decrease of the nucleation ability of the crystals with the increase of annealing temperature for rapid relaxation of thermal stress at higher temperature,54 in agreement with the results from the Tl curve in Figure 7. In the early stage, the solid labeled line showed linear increase of form I fractions with time, in qualitative agreement with the kinetics shown in Figure 4. Quantitatively, one observes a much faster transition rate in WAXD experiments than in DSC ones. This phenomenon can be attributed to the difference in sample size and testing environments in both techniques. WAXD measurements require much larger and thicker samples than DSC measurements so that much higher internal stress could be built up in WAXD samples due to their geometrical constraint that in turn facilitates the polymorphic transition. Nevertheless, the WAXD results provide direct in situ visualization of the transition process. In situ WAXD measurements provide also an opportunity to study the mechanism of the kinetic transition in PB-1 samples using Avrami analysis which reads XI = 1 − exp⌊−kt n ⌋

(3)

where k is the transition rate coefficient and n the Avrami index. In order to derive values of k and n, eq 3 can be rewritten as follows: Figure 9. Selected in situ WAXD patterns of PB-1 samples obtained during annealing at −10 and 40 °C successively (top) and at only 40 °C (middle) after isothermal crystallization at 50 °C for 30 min. The fraction of form I crystals obtained from analysis of intensity distribution of (110)I and (200)II diffraction peaks in WAXD measurements taken during annealing at different conditions (bottom).

log[− ln(1 − XI)] = log k + n log t

(4)

Transformation of form II to form I in PB-1 was constrained by preservation of helical hands in which the (110) planes of the resultant trigonal form I of 3/1 helix are parallel to (110) planes of parent tetragonal form II crystals of 11/3 helix, as was first established by Fujiwara.32 In the nucleation stage at low temperature, it is not easy to proceed translational motion of polymer chains but possible for conformational change especially under sufficient internal stress. Tiny form I “nuclei” should be emerged within form II lamellae at positions connected with taut tie molecules where a small amount of segments with 3/1 helical conformation develop. After heating to high temperature, thermal motions of molecules lead to lateral movements of the helical chains in the invariant (110) planes with the conformational change in those sites of form I “nuclei”.29−32 Ideally, the two cases (with and without prenucleation) in our investigation would yield Avrami indexes differing by 1 corresponding to growth onto already existing nuclei and homogeneous nucleation and growth within the system, respectively. Given the fact of above-mentioned crystallographic evidence of invariant (110) plan in transformed form I with respect to the parent form II crystals, one would

clear diffraction peaks from form I crystals appeared only after 30 min annealing at 40 °C. For comparison, we included also selected in situ WAXD data for sample annealed directly at 40 °C after being isothermally crystallized at 50 °C in the middle of Figure 9. Such WAXD data shows that even after a prolonged annealing at 40 °C for 12.5 h, no observable form I crystals can be found in the system. Transformed form I crystals became visible under such single temperature annealing only at much longer annealing time. The form II to form I transformation in the PB-1 sample under more experimental conditions were also explored using in situ WAXD techniques. The results of content of transformed form I as a function of annealing time under different conditions were collected in the bottom of Figure 9. The WAXD results showed that annealing at low temperature for dozens of minutes in advance would F

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

of temperatures for 30 min except that at 95 °C where the isothermal time was 60 min to complete the crystallization. As was shown in Figure 11, such prepared samples show a slight

expect a quasi-one-dimensional growth of the form I crystals after nucleation as the transition occurs within individual form II crystalline lamellae. Figure 10 shows the Avrami plots of data present in Figure 9 according to eq 4. The Avrami indexes and transition rate

Figure 10. Avrami plots of XI present in the bottom part of Figure 9.

coefficients can thus be obtained from slopes and intercepts of the fitting lines as shown in Table 1. The Avrami index Table 1. Values of the Avrami Indexes and Transition Rate Coefficients Obtained from Slopes and Intercepts of the Fitting Lines in Figure 10 Ta /°C

20a

20

40a

40

60a

n k/h−n

0.7 0.21

1.9 2.02 × 10−3

0.7 0.22

1.86 1.95 × 10−4

0.5 0.14

The transition at the temperature with prenucleation at −10 °C for 60 min.

a

indicates the geometry growth mode of a new phase from a matrix phase. The expected values of the Avrami index for onedimensional growth are 1 and 2 for heterogeneous and homogeneous nucleation, respectively. In our investigations, the prenucleated samples represent the heterogeneous case as the nuclei have been developed at low annealing temperature whereas the nonpre-nucleated samples represent the homogeneous case. Although this expected difference in n values could be roughly confirmed by the data present in Table 1, one finds always noninteger numbers of n and values lower than unity for samples prenucleated, which cannot be explained by the Avrami model. Similar results has been reported and attributed to a stretched-exponential behavior describing the relaxation processes at temperatures near the glass-transition temperature with spatial heterogeneity, indicating a broadened distribution of transition rate.50 However, this consideration cannot apply to the current case as we are dealing with transitions at temperatures much higher than the glass transition. Failure in using the Avrami model to descibe the form II to I transtion in PB-1 indicates that the condition of using such a model is invalidated. Indeed, the Avrami model describes the behavior of ideal transitions from one phase to the other without perturbation of the rest of the system. In the current case, the form II to I transition in PB-1 introduces an increase of the chain length and a denser packing of the chain segments in the crystals which would change the surrounding environment in terms of internal stress field that in turn affects the driving force for the development of the transtion. In an effort to explore the microstructure dependency of the transition in the system, PB-1 samples with different lamellar thickness were prepared by isothermal crystallization at a series

Figure 11. Crystallinity, long spacing, lamellar and amorphous thicknesses of PB-1 samples isothermally crystallized at different temperatures (data partly taken from ref 53) (top); DSC melting curves of the isothermally crystallized samples after being subsequently annealed at −10 °C for 60 min and at 40 °C for 220 min (middle); fraction of transformed form I crystals, derived from the DSC melting curves present above) as a function of isothermal crystallization temperature (bottom).

increase in crystallinity with the increasing of the crystallization temperature but a strong increase in long spacing, lamellar, and amorphous thicknesses. The samples were then annealed sequentially at −10 °C for 60 min and 40 °C for 220 min. DSC melting curves of the annealed samples were present in the middle part of Figure 11. Clearly, for samples isothermally crystallized at different temperatures, the same stepwise annealing condition promoted different amounts of form I crystallites as was evidenced by the increase of melting peak area of form I in the DSC melting curves with the increasing of crystallization temperature. In addition, one observed also an increase in melting point with the increasing of crystallization temperature indicating an increase of lamellar thickness in the samples crystallized at higher temperatures. In the bottom part G

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules of Figure 11, we present the fraction of transformed form I, derived from integration of melting peaks shown in the middle of Figure 11, as a function of isothermal crystallization temperature. It shows a strong crystallization temperature dependency of the transition rate. High crystallization temperature is likely to promote the II to I transformation in accord with the previous work of Azzurri et al.8 Increase of crystallization temperature leads to an increase of lamellar thickness of form II crystals, further enhancing the nucleation rate due to more taut tie molecules between lamellar and bigger internal stress resulting from shrinkage upon cooling between the larger temperature difference from Tc to Tl. As a result, the overall transition rate was efficiently accelerated. This result is in agreement with the previous studies in consideration of increased rigid amorphous fraction and crystallinity.8,55 To compare the behavior of the transition between samples of different microstructure in more detail, we chose samples isothermally crystallized at 90 °C as an example. Figure 12 illustrates the melting curves of 90 °C crystallized samples after different annealing conditions for the same total annealing time as shown in Figure 6. A larger area of melting peaks at 129 °C indicates that more form I crystals have been developed in the 90 °C isothermally crystallized samples than those crystallized at 50 °C annealed under same conditions. The increased area of form I is almost double of the diminishment of form II melting peak areas due to double bulk melting enthalpy of form I compared to form II. The fractions of transformed form I after thermal protocols as described in Figure 12 as a function of annealing temperature were plotted in Figure 13. It reveals a similar tendency with the 50 °C isothermally crystallized samples in Figure 7 of the temperature dependency on nucleation and growth with an overall increase of form I fraction. Quenching to a low temperature after accomplishment of crystallization of form II is a powerful approach to nucleate instantaneously where there is almost no growth of the nuclei. The following annealing at a high temperature provides a high rate of growth of the predeveloped nuclei. On the basis of DSC and in situ WAXD measurements of the form II to form I polymorphic transformation in isothermally crystallized PB-1 samples at different annealing conditions in this work, one can conclude that (i) the crystal transformation from form II to form I is a two-step process including nucleation and growth that may occur at different temperature successively, (ii) rapid nucleation occurs at low temperature, with a maximum at around −10 °C, while the fastest growth is shown at around 40 °C, and (iii) it shows similar temperature dependency on nucleation and growth of samples isothermally crystallized at different temperatures whereas the transition rate increases with crystallization temperature. In general, the transition was performed at one certain temperature to nucleate and grow with a maximum rate at room temperature. Di Lorenzo and co-workers found two maximum transition rates at −20 and 20 °C in the early and later stages of the transition, respectively.37 The former in the early stage could be corresponding to relatively rapid nucleation at low temperature and the second maxima was related to faster growth at 20 °C in a later stage when nucleation was accomplished on most of the form II crystals. It is hard to trace the evolution of nucleation in the early stage of transition as there are even no form I diffraction patterns after nucleation at −10 °C for 1 h, because the form I nuclei with little ordered chain segments developed within form II crystals are tiny making thus the nucleation kinetics remains unclear. In this

Figure 12. DSC melting curves of PB-1 samples annealed at different conditions after isothermal crystallized at 90 °C: annealed at −10 °C for 60 min followed by annealing at different Th for 220 min (top), annealed at different Tl for 60 min followed by annealing at 50 °C for 220 min (middle) and annealed at a single temperature (Ts) for 280 min (bottom).

work, a first successful attempt has been made applying a stepwise annealing approach similar to Tammann’s two-step crystal nuclei development method for analysis of the phase transition from form II to form I in PB-1. The samples were quenched to temperatures near Tg where growth were mostly suppressed after completion of crystallization of form II from the melt to allow formation of form I nuclei in parent form II crystals as a function of time, followed by rapid heating to a relatively higher temperature to perform transition, i.e., growth on the preformed nuclei. The transition degree increased with an increase of nucleation time at low temperature, and meanwhile the transition rate slowed down over time for the relaxation of internal stress induced by the difference of the H

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

dependency of the nucleation rate of form I in form II of PB-1. The nucleation rate is dominated by the two opposing factors: the activation free energy for diffusion ({ΔE/(kt)}) and the nucleation barrier of free energy ({ΔG*/(kt)}). The later factor increases with temperature, resulting in a low rate at high temperature; while the former one decreases with temperature, leading to a low rate at low temperature. Consequently, the evolution of the nucleation rate with temperature shows a typical bell-shaped curve having a maximum at around −10 °C in the current case. In addition, when Tl reached the glass transition temperature, the diffusion of crystalline chain segments within form II crystals would be frozen too because such diffusion is strongly coupled with the amorphous phase due to constraints introduced by loop entanglements, cilia, and tie chains. The observed plateau values for the nucleation rate below the glass transition is caused by the nucleation events that occurred during cooling as well as reheating passing through the favorable nucleation temperature range above Tg due to the limited cooling/heating rate of the DSC setup. Clearly, internal stress driving the helical conformational change from 11/3 to 3/1 can be built up instantaneously with the cooling process already providing seeds for the nucleus of form I. When the cooling rate is not high enough, such as in the current case, diffusion of adjacent chain segments was possible to build up a certain amount of stable nuclei of form I. As the samples were annealed at different Tl below Tg and experiencing the same temperature protocol above Tg, they showed the same nucleation ability as indicated by the plateau value. The formed nuclei within form II crystals would grow form I crystals when the system approaches appropriate temperatures rapidly. With the prenucleation at low temperature, the kinetics and temperature dependency of growth were investigated, the fastest rate occurred at about 40 °C where the nucleation was rather slow. Thus, the transition reached a plateau of a relatively low degree in the later stage because of the incomplete nucleation and vanishment of nuclei at such high temperature where nuclei is metastable.

Figure 13. Fraction of transformed form I crystals in 90 °C isothermally crystallized PB-1 samples after being annealed at different conditions as described in Figure 10.

thermal expansion coefficient between amorphous and form II crystalline phases during cooling. The temperature dependency of the nucleation rate showed a Gaussian distribution with a maximum at around −10 °C with the combined effect of chain segment mobility and internal stress. The kinetics of nucleation of form I in parent form II crystals is similar to nucleation of crystallization from melting. During fast cooling after isothermal crystallization into form II, the amorphous phase shrinks much more than the packed crystalline phase in the lamellar normal direction, resulting in internal stress on the form II crystals via taut tie molecules in both side of the lamellae. The stress would promote a conformational change of the taut chain in lamellar crystals from 11/3 to 3/1 helix with a reduction of packed volume.49 Stable nucleus of form I crystal within the form II crystalline lamella can be formed via a diffusion of crystalline stems adjacent to the transformed segment with 3/1 helix in combination of a helical transformation from 11/3 to 3/1. Such diffusion of crystalline segments within form II crystals has been proven possible experimentally by Miyoshi et al. where crystalline stems in metastable form II perform uniaxial rotational diffusion accompanying side-chain conformational transitions while crystalline stems and side-chain conformations of the most stable form I are completely fixed.56,57 The occurrence of the nucleation of form I crystalline phase within form II crystals has its thermodynamic origin as the melt enthalpy of the form I crystals is more than twice of that of form II crystals. However, the extra surface free energy between the form II crystalline phase and the newly formed form I nucleus (the lateral surfaces) and the increased surface free energy on the lamellar normal surfaces due to more crowded chain segments in form I than in form II decided that the nucleus of form I crystal can be stable only when its size is large enough that the reduction of the free energy inside the region counteract the nucleation barrier caused by formation of new surfaces. The equation for rate of nucleation in condensed systems was derived as41,51,58,59 i=

⎡ (ΔE + ΔG*) ⎤ ⎛ NkT ⎞ ⎜ ⎟ exp⎢ − ⎥ ⎝ h ⎠ ⎣ ⎦ kT

■

CONCLUSION Kinetics of polymorphic transition from the kinetically favored form II to the thermodynamically stable form I of isothermally crystallized PB-1 as revealed by stepwise annealing was followed by DSC and in situ WAXD. The transition was decomposed into nucleation and growth steps via annealing at low temperature for dozens of minutes to promote nucleation followed by annealing at a higher temperature for growth. Stepwise-annealed samples at low and high temperatures resulted in much more transformed form I crystals than samples annealed at a single temperature for same total time. Both nucleation and growth rates as a function of temperature showed a Gaussian distribution with maxima at −10 and 40 °C corresponding to the optimum temperatures of nucleation and growth, respectively. Moreover, the transition rate was increased with the increase of crystallization temperature due to higher internal stress built up during cooling down to the nucleation temperature from higher crystallization temperature. The results provide effective means to accelerate the phase transition in polymeric systems where nucleation and growth are involved.

(5)

where k is the Plank constant, N is the number of particles participating in the nucleation process, T is the nucleation temperature, ΔG is the maximum free energy necessary for nucleus formation, and ΔE is the free energy of activation for the short-range diffusion of segments across an interface to join a new lattice. With this classical equation describing kinetics of nucleation, we are able to explain the observed temperature I

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

■

by in-situ Fourier Transform Infrared Spectroscopy. Polymer 2009, 50, 5598−5604. (20) Xu, Y.; Liu, T.; Li, L.; Li, D. C.; Yuan, W. K.; Zhao, L. Controlling Crystal Phase Transition from Form II to I in Isotactic Poly-1-butene Using CO2. Polymer 2012, 53, 6102−6111. (21) Jones, A. T. Cocrystallization in Copolymers of α-Olefins II Butene-1 Copolymers and Polybutene Type II/I Crystal Phase Transition. Polymer 1966, 7, 23−59. (22) De Rosa, C.; Ruiz de Ballesteros, O.; Auriemma, F.; Di Girolamo, R.; Scarica, C.; Giusto, G.; Esposito, S.; Guidotti, S.; Camurati, I. Polymorphic Behavior and Mechanical Properties of Isotactic 1-Butene−Ethylene Copolymers from Metallocene Catalysts. Macromolecules 2014, 47, 4317−4329. (23) Wang, Y. T.; Lu, Y.; Zhao, J. Y.; Jiang, Z. Y.; Men, Y. F. Direct Formation of Different Crystalline Forms in Butene-1/Ethylene Copolymer via Manipulating Melt Temperature. Macromolecules 2014, 47, 8653−8662. (24) Wang, Y. T.; Liu, P. R.; Lu, Y.; Men, Y. F. Mechanism of Polymorph Selection during Crystallization of Random Butene-1/ Ethylene Copolymer. Chin. J. Polym. Sci. 2016, 34, 1014−1020. (25) Zhang, B.; Yang, D. C.; Yan, S. Direct Formation of Form I Poly(1-butene) Single Crystals from Melt Crystallization in Ultrathin Films. J. Polym. Sci., Part B: Polym. Phys. 2002, 40, 2641−2645. (26) De Rosa, C.; Auriemma, F.; Ruiz de Ballesteros, O.; Esposito, F.; Laguzza, D.; Di Girolamo, R.; Resconi, L. Crystallization Properties and Polymorphic Behavior of Isotactic Poly(1-Butene) from Metallocene Catalysts: The Crystallization of Form I from the Melt. Macromolecules 2009, 42, 8286−8297. (27) De Rosa, C.; Auriemma, F.; Resconi, L. Metalloorganic Polymerization Catalysis as a Tool to Probe Crystallization Properties of Polymers: The Case of Isotactic Poly(1-butene). Angew. Chem., Int. Ed. 2009, 48, 9871−9874. (28) Natta, G.; Corradini, P.; Bassi, I. W. Uber Die Kristallstruktur Des Isotaktischen Poly-Alpha-Butens. Makromol. Chem. 1956, 21, 240−244. (29) Tashiro, K.; Hu, J.; Wang, H.; Hanesaka, M.; Saiani, A. Refinement of the Crystal Structures of Forms I and II of Isotactic Polybutene-1 and a Proposal of Phase Transition Mechanism between Them. Macromolecules 2016, 49, 1392−1404. (30) Kopp, S.; Wittmann, J. C.; Lotz, B. Phase II to Phase I Crystal Transformation in Polybutene-1 Single Crystals: a Reinvestigation. J. Mater. Sci. 1994, 29, 6159−6166. (31) Lotz, B.; Mathieu, C.; Thierry, A.; Lovinger, A. J.; De Rosa, C.; de Ballesteros, O. R.; Auriemma, F. Chirality Constraints in CrystalCrystal Transformations: Isotactic Poly(1-butene) versus Syndiotactic Polypropylene. Macromolecules 1998, 31, 9253−9257. (32) Fujiwara, Y. II-I-Phase Transformation of Melt-Crystallized Oriented Lamellae of Polybutene-1 by Shear Deformation. Polym. Bull. 1985, 13, 253−258. (33) Su, F. M.; Li, X. Y.; Zhou, W. M.; Chen, W.; Li, H. L.; Cong, Y. H.; Hong, Z. H.; Qi, Z. M.; Li, L. B. Accelerating Crystal-Crystal Transition in Poly(1-butene) with Two-Step Crystallization: An in-situ Microscopic Infrared Imaging and Microbeam X-ray Diffraction Study. Polymer 2013, 54, 3408−3416. (34) Luongo, J. P.; Salovey, R. Infrared Characterization of Polymorphism in Polybutene-1. J. Polym. Sci. A2 1966, 4, 997−1008. (35) Azzurri, F.; Gomez, M. A.; Alfonso, G. C.; Ellis, G.; Marco, C. Time-Resolved SAXS/WAXS Studies of the Polymorphic Transformation of 1-Butene/Ethylene Copolymers. J. Macromol. Sci., Part B: Phys. 2004, 43, 177−189. (36) Chvátalová, L.; Beníček, L.; Berková, K.; Č ermák, R.; Obadal, M.; Verney, V.; Commereuc, S. Effect of Annealing Temperature on Phase Composition and Tensile Properties in Isotactic Poly(1butene). J. Appl. Polym. Sci. 2012, 124, 3407−3412. (37) Di Lorenzo, M. L.; Androsch, R.; Righetti, M. C. The Irreversible Form II to Form I Transformation in Random Butene-1/ Ethylene Copolymers. Eur. Polym. J. 2015, 67, 264−273.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grants 21134006 and 51525305).

■

REFERENCES

(1) Luciani, L.; Seppala, J.; Lofgren, B. Poly-1-Butene: Its Preparation, Properties and Challenges. Prog. Polym. Sci. 1988, 13, 37−62. (2) Miller, R. L.; Holland, V. F. On Transformations in Isotactic Polybutene-1. J. Polym. Sci., Part B: Polym. Lett. 1964, 2, 519−521. (3) Jones, A. T.; Aizlewood, J. M. Crystalline Forms of Polybentene1. J. Polym. Sci., Part B: Polym. Lett. 1963, 1, 471−476. (4) Boor, J.; Youngman, E. A. Polymorphism in Poly-1-Butene: Apparent Direct Formation of Modification I. J. Polym. Sci., Part B: Polym. Lett. 1964, 2, 903−907. (5) Jones, A. T. Polybutene-1: Type II Crystalline Form. J. Polym. Sci., Part B: Polym. Lett. 1963, 1, 455−456. (6) Natta, G.; Corradini, P.; Bassi, I. W. Crystal Structure of Isotactic Poly-alpha-Butene. Nuovo Cimento 1960, 15 (Suppl), 52−67. (7) Azzurri, F.; Flores, A.; Alfonso, G. C.; Sics, I.; Hsiao, B. S.; Calleja, F. J. B. Polymorphism of Isotactic Polybutene-1 as Revealed by Microindentation Hardness. Part II: Correlations to Microstructure. Polymer 2003, 44, 1641−1645. (8) Azzurri, F.; Flores, A.; Alfonso, G. C.; Calleja, F. J. B. Polymorphism of Isotactic Poly(1-butene) as Revealed by Microindentation Hardness. 1. Kinetics of the Transformation. Macromolecules 2002, 35, 9069−9073. (9) Rubin, I. D. Relative Stabilities of Polymorphs of Polybutene-1 Obtained from Melt. J. Polym. Sci., Part B: Polym. Lett. 1964, 2, 747− 749. (10) Powers, J.; Hoffman, J. D.; Weeks, J. J.; Quinn, F. A., Jr. Crystallization Kinetics and Polymorphic Transformations in Polybutene-1. J. Res. Natl. Bur. Stand., Sect. A 1965, 69A, 335−345. (11) Danusso, F.; Gianotti, G. Isotactic Polybutene-1: Formation and Transformation of Modification 2. Makromol. Chem. 1965, 88, 149− 158. (12) Boor, J.; Mitchell, J. C. Apparent Nucleation of a Crystal-Crystal Transition in Poly-1-Butene. J. Polym. Sci. 1962, 62, S70−S73. (13) Tanaka, A.; Sugimoto, N.; Asada, T.; Onogi, S. Orientation and Crystal Transformation in Polybutene-1 under Stress Relaxation. Polym. J. 1975, 7, 529−537. (14) Liu, Y.; Cui, K.; Tian, N.; Zhou, W.; Meng, L.; Li, L.; Ma, Z.; Wang, X. Stretch-Induced Crystal−Crystal Transition of Polybutene1: An in Situ Synchrotron Radiation Wide-Angle X-ray Scattering Study. Macromolecules 2012, 45, 2764−2772. (15) Chen, W.; Li, X.; Li, H.; Su, F.; Zhou, W.; Li, L. DeformationInduced Crystal−Crystal Transition of Polybutene-1: An in Situ FTIR Imaging Study. J. Mater. Sci. 2013, 48, 4925−4933. (16) Cavallo, D.; Kanters, M. J. W.; Caelers, H. J. M.; Portale, G.; Govaert, L. E. Kinetics of the Polymorphic Transition in Isotactic Poly(1-butene) under Uniaxial Extension. New Insights From Designed Mechanical histories. Macromolecules 2014, 47, 3033−3040. (17) Nakafuku, C.; Miyaki, T. Effect of Pressure on the Melting and Crystallization Behavior of Isotactic Polybutene-1. Polymer 1983, 24, 141−148. (18) Li, L.; Liu, T.; Zhao, L.; Yuan, W. K. CO2-Induced Crystal Phase Transition from Form II to I in Isotactic Poly-1-butene. Macromolecules 2009, 42, 2286−2290. (19) Shi, J.; Wu, P.; Li, L.; Liu, T.; Zhao, L. Crystalline Transformation of Isotactic Polybutene-1 in Supercritical CO2 Studied J

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules (38) Boor, J.; Mitchell, J. C. Kinetics of Crystallization and a CrystalCrystal Transition in Poly-1-Butene. J. Polym. Sci., Part A: Gen. Pap. 1963, 1, 59−84. (39) Tammann, G. Kristallisieren und Schmelzen; Verlag Johann Ambrosius Barth: Leipzig, Germany, 1903. (40) Tammann, G.; Mehl, R. F. The States of Aggregation; Van Nostrand Co.: New York, 1925. (41) Cheng, S. Z. D. Chapter 2: Thermodynamics and Kinetics of Phase Transitions. In Phase Transitions in Polymers; Elsevier: Amsterdam, The Netherlands, 2008; pp 17−59. (42) Androsch, R.; Schick, C.; Rhoades, A. M. Application of Tammann’s Two-Stage Crystal Nuclei Development Method for Analysis of the Thermal Stability of Homogeneous Crystal Nuclei of Poly(ethylene terephthalate). Macromolecules 2015, 48, 8082−8089. (43) Zhuravlev, E.; Schmelzer, J. W. P.; Abyzov, A. S.; Fokin, V. M.; Androsch, R.; Schick, C. Experimental Test of Tammann’s Nuclei Development Approach in Crystallization of Macromolecules. Cryst. Growth Des. 2015, 15, 786−798. (44) Avrami, M. Kinetics of Phase Change. I General theory. J. Chem. Phys. 1939, 7, 1103−1112. (45) Avrami, M. Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, 212−224. (46) Avrami, M. Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III. J. Chem. Phys. 1941, 9, 177−184. (47) Burgers, W. G.; Groen, L. J. Mechanism and Kinetics of the Allotropic Transformation of Tin. Discuss. Faraday Soc. 1957, 23, 183− 195. (48) Deboer, J. H. Molecular Mechanism of Rate Processes in Solids.C. Steady-State Processes Involving Lattice Re-Arrangement Introductory Paper. Discuss. Faraday Soc. 1957, 23, 171−182. (49) Gohil, R. M.; Miles, M. J.; Petermann, J. On the Molecular Mechanism of the Crystal Transformation (Tetragonal-Hexagonal) in Polybutene-1. J. Macromol. Sci., Part B: Phys. 1982, 21, 189−201. (50) Maruyama, M.; Sakamoto, Y.; Nozaki, K.; Yamamoto, T.; Kajioka, H.; Toda, A.; Yamada, K. Kinetic Study of the II-I Phase Transition of Isotactic Polybutene-1. Polymer 2010, 51, 5532−5538. (51) Turnbull, D.; Fisher, J. C. Rate of Nucleation in Condensed Systems. J. Chem. Phys. 1949, 17, 71−73. (52) Alfonso, G. C.; Azzurri, F.; Castellano, M. Analysis of Calorimetric Curves Detected during the Polymorphic Transformation of Isotactic Polybutene-1. J. Therm. Anal. Calorim. 2001, 66, 197−207. (53) Wang, Y. T.; Lu, Y.; Jiang, Z. Y.; Men, Y. F. Molecular Weight Dependency of Crystallization Line, Recrystallization Line, and Melting Line of Polybutene-1. Macromolecules 2014, 47, 6401−6407. (54) Chau, K. W.; Yang, Y. C.; Geil, P. H. Tetragonal → Twinned Hexagonal Crystal Phase Transformation in Polybutene-1. J. Mater. Sci. 1986, 21, 3002−3014. (55) Di Lorenzo, M. L.; Righetti, M. C.; Wunderlich, B. Influence of Crystal Polymorphism on the Three-Phase Structure on the Thermal Properties of Isotactic Poly(1-butene). Macromolecules 2009, 42, 9312−9320. (56) Miyoshi, T.; Mamun, A.; Reichert, D. Fast Dynamics and Conformations of Polymer in a Conformational Disordered Crystal Characterized by 1H−13C WISE NMR. Macromolecules 2010, 43, 3986−3989. (57) Miyoshi, T.; Mamun, A. Critical Roles of Molecular Dynamics in the Superior Mechanical Properties of Isotactic-Poly(1-butene) Elucidated by Solid-State NMR. Polym. J. 2012, 44, 65−71. (58) Becker, R.; Doring, W. Kinetic Treatment of Germ Formation in Supersaturated Vapour. Ann. Phys. 1935, 416, 719−752. (59) Becker, R. Nucleation during the Precipitation of Metallic Mixed Crystals. Ann. Phys. 1938, 424, 128−140.

K

DOI: 10.1021/acs.macromol.6b00862 Macromolecules XXXX, XXX, XXX−XXX