Chain Trajectory and Crystallization Mechanism of a Semicrystalline

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Chain Trajectory and Crystallization Mechanism of a Semicrystalline Polymer in Melt- and Solution-Grown Crystals As Studied Using 13 C−13C Double-Quantum NMR You-lee Hong,† Tadanori Koga,‡ and Toshikazu Miyoshi*,† †

Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States Department of Materials Science and Engineering, Stony Brook University, Stony Brook, New York 11794-2275, United States

‡

S Supporting Information *

ABSTRACT: The re-entrance sites, successive chain-folding number ⟨n⟩, and chain-folding fraction ⟨F⟩ of the chain-folding (CF) structure of 13C CH3-labeled isotactic poly(1-butene) (iPB1) with an weight-averaged molecular weight (⟨Mw⟩ = 37 K g/mol) in solution- and melt-grown crystals as a function of crystallization temperature (Tc) were determined using solidstate (SS) NMR. The solution- and melt-grown crystals possessed adjacent re-entry structures between the right- and left-handed stems along the (100) and (010) planes, which were invariant as a function of Tc. The adjacent re-entry structures in the former exhibited long-range order (⟨n⟩ ≥ 8) compared with that in the latter (⟨n⟩ ≥ 1.7−2). These results indicated that the concentration and entanglement of polymers play significant roles in the CF process and structural formation during the initial stage of crystallization, whereas kinetics does not. Transmission electron microscopy (TEM) revealed welldefined hexagonal and circular crystals grown from the solution state at Tc = 60 and ∼0 °C, respectively. The morphological and molecular-level structural data demonstrated that kinetics influences the structural formations of polymers differently at different length scales during crystallization. Moreover, SS-NMR, small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM) indicated that the crystallinity (χc) and lamellar thickness (⟨lc⟩) of the melt-grown crystals are highly dependent on Tc, whereas in the solution-grown crystals, these parameters are independent of Tc. The experimental results and molecular dynamics, as reported in the literature, indicated that both χc and ⟨lc⟩ are primarily determined by the molecular dynamics of the stems after deposition of the chains on the growth front (late process).

1. INTRODUCTION The crystallization of long, flexible polymer chains changes random coils in the solution and melt states into folded chains embedded in thin lamellae with a thickness of approximately 5−20 nm. To date, various theoretical models have been proposed to describe the complex crystallization mechanisms of semicrystalline polymers at the molecular level. The Lauritzen− Hoffman (LH) theory describes a single process in which stems with a length identical to the crystal thickness are deposited on the growth front while chain folding simultaneously occurs.1−3 Point and Hikosaka et al. revised the LH theory by incorporating crystal thickening after the deposition of polymer chains on the growth front.4−6 Allegra and Meille as well as Zhang and Muthukumar proposed a two-step process in which partial or whole molecules form preordered clusters via chain folding during the prestage of crystallization in which the clusters are deposited on the growth front via multiple interactions in a dilute solution.7,8 Imai et al. experimentally observed density fluctuations of poly(ethylene terephthalate) during the prestage of melt crystallization using small-angle Xray scattering (SAXS).9 This experimental result led Strobl to © XXXX American Chemical Society

propose multistage crystallization in which the random coil chains in an isotropic phase attach to mesomorphic layers that subsequently thicken and transition into granular crystal layers. When the granular layers reach critical sizes, they merge into stable crystals.10 Recent molecular dynamics (MD) simulations using the coarse-grained poly(vinyl alcohol) (PVA) model of Sommer and Luo detected chain folding during the prestage of the melt state and chain sliding and lamellae thickening during the late process.11 To properly understand polymer crystallization and to verify the validity of existing theories and simulation results, further experiments are required. An important structural parameter is the chain trajectory because this parameter preserves structural information about where, when, and how polymer chains fold during crystallization. Over the past half century, various characterization techniques, such as neutron scattering (NS)12−23 and IR16,24−26 spectroscopy combined with 2H Received: January 13, 2015 Revised: April 27, 2015

A

DOI: 10.1021/acs.macromol.5b00079 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules polymers, surface decoration on single crystals,27 and direct observations28,29 as well as force detections30 using atomic force microscopy (AFM), have been applied to elucidate the molecular-level structures of semicrystalline polymers in meltand solution-grown crystals. However, the details of the chainfolding (CF) structures in terms of the re-entrance sites, successive folding number ⟨n⟩, and adjacent re-entry fraction ⟨F⟩ of the folded chains remain under debate due to experimental limitations. We recently developed a novel strategy that employs 13C−13C double-quantum (DQ) NMR and selective 13C isotopic labeling to investigate the CF structures of semicrystalline polymers in solution- and meltgrown crystals.31,32 Our preliminary studies demonstrated that isotactic poly(1-butene) (iPB1) possesses an adjacent re-entry structure with ⟨F⟩ ≥ 80−90% in single crystals.32 Further systematic research as a function of polymer concentration (melt vs solution state) and kinetics studies are required to understand polymer crystallization at the molecular level. Another missing piece of evidence is the molecular dynamics in the crystalline (mesomorphic) states, which may play major roles in structural development during the late stage of crystallization, as indicated in several theoretical and simulation studies.4,6,7,10,11 Solid-state (SS) NMR has been applied to investigate molecular dynamics in the crystalline regions of semicrystalline polymers. Polyethylene (PE),33 and isotactic polypropylene (iPP),34,35 among others, experience discrete large-amplitude motions of whole stems around the chain axis, concomitant with translation in a slow and intermediate range of dynamics (106 Hz in disordered hexagonal packing.36 iPB1 form II also shows similar fast dynamics.37 In contrast, nylon,38 form I of iPB1,39 and syndiotactic polypropylene (sPP),40 among others, do not perform these large-amplitude motions, even at temperatures just below the melting temperature (Tm). Among the various semicrystalline polymers, the chain dynamics of iPB1 in the crystalline regions largely change depending on the polymorph (packing and conformation). When iPB1 is cooled from the melt, it crystallizes into metastable form II and spontaneously transforms into thermodynamically stable form I. However, iPB1 directly crystallizes into thermodynamically stable form I from a dilute solution. Thus, crystallization from the melt and solution states follows different pathways but ultimately leads to the same crystalline structure. It would be interesting to determine how passing the dynamic phase during crystallization influences the ⟨lc⟩ and χc of the final crystalline phase. In this study, we define two goals regarding polymer crystallization. First, we systematically investigate the CF structure of iPB1 with a relatively low Mw of 37 K g/mol in both solution- and melt-grown crystals as a function of Tc using 13 C−13C DQ NMR and spin-dynamics simulations. We demonstrate the effect of kinetics, concentration, and entanglements of the polymer on the CF structures. Second, we study the effects of Tc on the ⟨lc⟩, χc, and morphology of iPB1 grown from a dilute solution and from condensed melt states. The different crystallization pathways of iPB1 elucidate the effects of molecular dynamics on the structural evolutions during crystallization. On the basis of the chain-level structures, χc, ⟨lc⟩, and morphology, as well as the molecular dynamics

results reported in the literature, we discuss the crystallization mechanisms at the molecular level.

2. EXPERIMENTAL SECTION 2.1. Synthesis of iPB1. 13C CH3-labeled butene-1 and butene-1 were purchased from CDN isotopes, Ltd., and Matheson, Ltd., respectively. Strem Chemicals provided the rac-Me2Si(Ind)2ZrCl2 catalyst. Toluene was distilled from sodium and benzophenone under a nitrogen atmosphere. During polymerization, 20 μmol of catalyst in 1 mL of distilled toluene was dispersed in the solution. iPB1 was synthesized using rac-Me2Si(Ind)2ZrCl2 and methylaluminoxane (MAO, [Al] = 10 wt % in toluene) as a cocatalyst (commercial product from Aldrich). A 100 mL two-necked flask equipped with a magnetic stirrer was flushed for half an hour with nitrogen. Under a nitrogen atmosphere, 25 mL of toluene was introduced. After degassing the flask under vacuum, 0.74 g of gaseous butene-1 and 0.39 g of gaseous 13C CH3-labeled butene-1 were dissolved in the distilled toluene as a liquid phase below the boiling temperature. MAO was injected into this solution and stirred for 10 min. Finally, the prepared catalyst solution was added to the flask, which was maintained at −30 °C with stirring for 5 days. After removing the flask from the cooling bath, the temperature of the flask was increased to room temperature to remove the unreacted monomers. The solution was poured into methanol solvent in which the amount of solvent was approximately 3 times the volume to terminate the polymerization; a white powder immediately precipitated. Hydrochloric acid (∼36%) was added to the methanol solution to react with the remaining catalyst. The mixture was stirred overnight to fully precipitate the polymer. The precipitated pure product was filtered and washed with methanol. The product was dried at 60 °C under vacuum for approximately 4 h to evaporate the solvent, and white iPB1 powder was obtained. The weight-averaged molecular weight (⟨Mw⟩) and PDI of 13Clabeled iPB1 were 37 002 g/mol and 1.7, respectively, and those of the nonlabeled iPB1 were 36 153 g/mol and 1.8, respectively. These values were obtained by PolymerChar GPC-IR at 140 °C in 1,2,4trichlorobenzene. An INOVA 400 NMR was used to determine the tacticity of the 13C-labeled iPB1 in 1,1,2,2-tetrachloroethane-d2 at 120 °C. In the 13C NMR spectrum, the peak from the side-chain methylene of the ethyl branches defines the tacticity as mmmm = 96.6% and 96.0% for 13C-labeled and nonlabeled iPB1, respectively. The melting temperature (Tm) of form I in the melt-grown crystals was determined as 126 °C by differential scanning calorimetry (DSC). Tm was recorded by a TA Instruments Model Q2000, and the temperature was carefully calibrated. The heating and cooling rates were 10 °C/min with approximately 5 mg of sample. Liquid nitrogen was utilized for a controlled cooling process. Ar was applied to prevent thermal degradation. 2.2. Form I Bulk Crystal Preparation. The 35 wt % 13CH3labeled iPB1 was blended with nonlabeled iPB1 at different blend ratios of 10/0, 5/5, and 1/9. 13C-labeled and nonlabeled iPB1 were dissolved in toluene at 180 °C with stirring for 10 min. Then, the sample was precipitated by pouring the solution into the excess methanol at room temperature. The resulting powders were washed in methanol and dried in a vacuum oven at 60 °C for 24 h. The powder sample is form III of iPB1. A DSC scan with a heating rate of 10 °C/ min confirmed that form III undergoes a phase transition to form II at approximately 100 °C, and the Tm of form II is ca. 112 °C.41 The form III iPB1 samples were placed in glass tubes, which were sealed under vacuum to prevent decomposition. The tubes were heated in an oil bath at 130 °C for 10 min and then instantly transferred to another oil bath preset to the different crystallization temperature of 95 °C for 72 h. Polarized optical microscopy (POM) revealed that crystallization required 24 h based on observations of the impingement of the growing spherulite (data not shown). At Tc = 50 and 0 °C, the samples were melted between two cover glasses at 130 °C for 10 min and were transferred into the preset water bath at Tc = 50 °C for 24 h and 0 °C (ice water) for 2 h. All of the iPB1 samples crystallized into tetragonal form II, which spontaneously transforms into the thermodynamically B


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Macromolecules stable trigonal form I at room temperature. All of the experiments were performed after leaving the samples for more than 7 days. 2.3. Form I Single Crystal Preparation. Single crystals of form I were prepared using the above blended samples with different composition ratios of labeled to nonlabeled iPB1 (10/0, 5/5, and 1/ 9). First, 0.01 g of blend samples was placed in glass tubes, and a mixed solvent consisting of 8 mL of amyl acetate and 32 mL of n-butanol was poured into the glass tubes. The tube including a 0.03 wt % solution was heated in an oil bath at 90 °C for 30 min and then immediately transferred to another oil bath maintained at Tc = 60 °C. For the NMR experiments, the samples were crystallized isothermally for 24 h. At Tc = ∼0 °C, the mixed solvent led to mixed crystals of forms I and II. Thus, pure amyl acetate solution was used to create uniform form I crystals under rapid quenching conditions. A hot solution at 90 °C was poured into the excess amyl acetate solution maintained at ∼0 °C, and crystallization occurred immediately after mixing of the solutions. The form I single crystals were filtered and washed with methanol, followed by drying at room temperature for 24 h. 2.4. TEM. A few drops of the single crystal suspension were deposited onto a copper grid coated with carbon, and the solvent was evaporated prior to TEM analysis. A JEM-100CX II TEM operating at a voltage of 120 kV was used to examine the crystal morphology of the form I single crystals at the micrometer scale. 2.5. AFM. A few drops of the single crystal suspension were deposited onto a silicon wafer, and the solvent was evaporated at room temperature prior to AFM analysis. An Icon atomic force microscope (Bruker Nano) operating in the tapping mode under ambient conditions was used to observe the morphology and to measure the size of single crystals with a typical scan size of 50 μm, a scan rate of 1 Hz, an operating frequency between 250 and 350 kHz, and a resolution of 512 pixels. 2.6. SAXS. SAXS experiments for the iPB1 bulk samples were performed at the X27C beamline of the National Synchrotron Light Source (NSLS, Upton) at Brookhaven National Laboratory using an X-ray wavelength λ = 0.137 nm (which corresponds to an X-ray energy (E) of 9.01 keV) with an energy resolution ΔE/E = 1.1%. The scattering intensity was recorded on a two-dimensional MAR CCD detector (Rayonix, L.L.C.) with an array of 1024 × 1024 pixels. The scattering patterns were recorded as a function of the scattering vector (q = 4π sin(θ/2)/λ, where θ is the scattering angle in the medium) over a range of 0.004 < q < 0.036 nm−1. The details of the experimental setup have been described elsewhere.42 All of the SAXS measurements were conducted at room temperature (20 °C) in air. Because the SAXS scattering patterns were isotropic, the scattering profiles were integrated over the azimuthal angle after corrections for air scattering and incident beam intensity fluctuations and were converted into 1D profiles to further analyze the data. 2.7. SS-NMR. SS-NMR experiments were conducted on a BRUKER AVANCE III 300 equipped with a 4 mm double-resonance MAS probe. The carrier frequencies of 1H and 13C are 300.1 and 75.5 MHz, respectively. The MAS frequency was set to 5102 Hz. The chemical shift was referenced to the CH signal of adamantane (29.46 ppm) as an external reference. The 90° pulses for 1H and 13C were 2.5 and 4.5 μs, respectively. The recycle delay and cross-polarization (CP) times were 2 s and 1 ms, respectively. A PostC743 pulse with a field strength of 35.7 kHz was used to excite the 13C−13C DQ signals. Highpower two-pulse phase modulation (TPPM)44 and continuous wave decoupling with a field strength of 104 kHz were used during the acquisition and recoupling periods, respectively. A 1H spin-locking filter with a field strength of 62.5 kHz for 10 ms was used to suppress the amorphous contribution in the single-quantum (SQ) and DQ spectra. Numerical spin dynamics simulations were performed using SPINEVOLUTION.45

Figure 1. CF models: (a) adjacent re-entry, (b) random re-entry, and (c) intermediate model. The chains in blue include the 13C-labeling atoms described by red circles. The black chains are nonlabeled. (d) Packing of two stems of iPB1 form I along the c-axis, illustrating 13 C−13C dipolar interactions within the intrastem (blue arrow) and between interstems (red arrow).

Thus, the goal of our strategy is to evaluate only the “adjacent re-entry structure” of polymer chains among the heterogeneous structures in the melt- and solution-grown crystals. To achieve our goal, two spectral editing techniques were used in this study. The first technique is spin−lattice relaxation in the rotating frame (T1ρH) filter, which is capable of selectively suppressing the amorphous signals in the NMR spectrum due to the mobility difference of the chains between the crystalline and amorphous regions.31,32,34,35 The second technique is DQ, which selectively excites spatially interacting 13C−13C spins belonging to the closest and/or second closest neighboring stems of the same chains and the interstem at internuclear distances of less than ∼7 Å. In an ideal two-spin system, the dipolar interactions are inversely proportional to the third power of the internuclei distance ⟨r⟩. According to the X-ray diffraction (XRD) results, the chains in iPB1 form I adopt 31 helical conformations in a trigonal lattice (a = b = 17.7 ± 0.1 Å and c = 6.5 ± 0.1 Å).46 The two stems are magnified as a molecular perspective in Figure 1d. The 13C−13C closest internuclear distance between the methyl carbons in the intrastem is 6.3 Å, as shown with a blue arrow, and is considerably longer than that between interstems, as shown with a red arrow (4.2 Å). To avoid a condensed spin density, 35 wt % 13C CH3iPB1 was synthesized in our study. The spin systems were statistically analyzed under the assumption that the 13C-labeling sites were randomly inserted (see simulation in Supporting Information). Our strategy relied on 13C−13C DQ buildup curves based on spin topology, spin number, and internuclear distances determined from the chain trajectory.31,32 A comparison of the experimental and simulated buildup curves allowed us to extract the chain-folding structure of semicrystalline polymers. In order to define parameters applicable to chain folding, we choose one parameter on the scale of each adjacent re-entry event and another on the scale of the whole molecular length. Thus, we have chosen ⟨n⟩ to be the average number of adjacent re-entry folding events, whenever an adjacent re-entry event occurs. A second parameter, F, takes into account that a given molecule may incorporate multiple adjacent re-entry clusters. Thus, ⟨F⟩ is the average fraction of crystallizing stems that participate in adjacent re-entry clusters. It follows that an ith cluster of size ni will possess ni + 1 stems. Likewise, the jth molecule with mj clusters and Nj total stems, Fj = ∑mi=1j (ni + 1) ,

3. STRATEGY FOR CHAIN-FOLDING ANALYSIS Three representative chain foldings of the adjacent re-entry, random re-entry, and intermediate model are presented in Figures 1a, 1b, and 1c, respectively. Understanding the complete heterogeneous chain-level structures is difficult.

Nj

C


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Macromolecules ⟨F⟩ is then the molecular-weight-weighted average of all the Fj.32 The three structures in Figures 1a−c yield F values of 100, 0, and 60%, respectively. Our definition of Fj is slightly different from that in early NS and IR studies in which the adjacent reentry fraction, f j, was defined as ∑mi=1j ni .

transition temperature (Tg = −20 °C), and to the conformational difference between the two phases. We applied Lorentzian peaks to the experimental spectra and determined χc. In the melt-grown sample, χc remarkably decreased from 88% at Tc = 95 °C to 73% at Tc = ∼0 °C. In contrast, the solution-grown crystals resulted in a nearly invariant χc of approximately 70% at Tc = 60 and 0 °C. Table 1 summarizes the χc of the melt- and solution-grown single crystals as a function of Tc.

Nj

4. RESULTS 4.1. Morphology. Figure 2 presents the TEM images of iPB1 form I single crystals crystallized in dilute solution (0.03

Table 1. Crystallinity (χc), Long Period (⟨l0⟩), Single Crystal Thickness (⟨ls⟩), and Maximum Folding Number (⟨nmax⟩) of iPB1 with ⟨Mw⟩ = 37 002 g/mol in the Melt- and SolutionGrown Crystals as a Function of Tc melt

solution a

Figure 2. TEM images of iPB1 form I single crystals after tc = 2 h. (a) Hexagonal crystals at Tc = 60 °C. (b) Circular crystals at Tc = ∼0 °C.

Tc (°C)

tc (h)

χc (%)

⟨l0⟩ (nm)

95 50 0 60 0

72 24 2 24 2

88 81 73 73 70

24.5 17.5 13.5

⟨ls⟩ (nm)

⟨nmax⟩

6.5 6.5a

5 7 10 21 21

⟨ls⟩ at Tc = ∼0 °C was assumed to be the same as ⟨ls⟩ at Tc = 60 °C.

The long spacing ⟨l0⟩ of the melt-grown crystals and the single crystal thickness ⟨ls⟩ of the solution-grown crystals were measured using SAXS and AFM, respectively. The SAXS patterns in Figure 4a show the first- and second-order scattering peaks, which shifted to lower q values with increasing Tc. The obtained q values correspond to a ⟨l0⟩ of 13.5 nm at Tc = ∼0 °C, 17.5 nm at 50 °C, and 24.4 nm at 95 °C. The ⟨lc⟩ of the melt-grown crystals was obtained from the long spacing, and χc was determined by NMR. The crystalline thickness evidently increased from 10.0 nm at Tc = ∼0 °C to 14.2 nm at 50 °C and 21.6 nm at 95 °C. The ⟨lc⟩ values were in good agreement with the results reported in the literature.39 Figure 4b presents an AFM image of the iPB1 hexagonal single crystal and demonstrates that the thickness at tc = 2 h was approximately 6.5 nm. Using the χc and the simple assumption of the same density of the amorphous and crystalline regions, the crystalline thickness was calculated as 4.8 nm. Considering the obtained long spacing, single crystal thickness, and molecular weights (⟨Mw⟩), the maximum folding numbers ⟨nmax⟩ of the melt- and solution-grown crystals were estimated, and these values are summarized in Table 1. The reason for using ⟨Mw⟩ is that a high-molecular-weight component heavily contributes to the total 13C spin number and maximum chainfolding number (⟨nmax⟩). Notably, it was difficult to measure the monolayer thickness of single crystals at Tc = ∼0 °C using AFM due to the crystal stacking in terms of the kinetic effect. The thickness at Tc = 60 °C was highly similar to the minimum value for the reported ⟨l0⟩ of iPB1.39 Therefore, we simply assumed that ⟨ls⟩ at Tc = ∼0 °C was the same as that at Tc = 60 °C. 4.3. Chain-Packing Analysis of Form I by 13C−13C DQ NMR. The ordered crystalline signals dominated the 13C CPMAS NMR spectrum, whereas the disordered amorphous signals appeared at the bottom of the main crystalline peaks at 25 °C. Recent studies successfully suppressed the amorphous contributions using the 1H spin−lattice relaxation time in the rotating frame (T1ρH) filter.31,32,34,35 In the current study, all of the SQ and DQ NMR spectra were measured using a T1ρH filter with a spin-locking field of 62.5 kHz for 10 ms. The DQ NMR spectra were obtained using a PostC743 sequence with an

wt %) at Tc = 60 and ∼0 °C. Hexagonal single crystals with a well-defined growth front with a side length of 2−4 μm were obtained after a crystallization time tc of 2 h at Tc = 60 °C (Figure 2a). This behavior is commonly observed in the trigonal packing structure of single crystals.47 However, circular shapes with a radius of approximately 2 μm appeared at Tc = ∼0 °C (Figure 2b). The edges of the lamellae were remarkably ragged. This effect of kinetics on morphology is called kinetic roughening and has been reported in various single crystals of PE,48 poly(vinylidene fluoride),49 and isotactic polystyrene,50 among others. 4.2. Crystallinity and Crystal Thickness. Figures 3a and 3b present 13C direct polarization (DP) MAS NMR spectra of

Figure 3. 13C DPMAS NMR spectra of the CH3 region of iPB1 in (a) the melt-grown crystals at Tc = 95 (black), 50 (blue), and 0 °C (red) from bottom to top and (b) the solution-grown crystals at Tc = 60 (black) and ∼0 °C (red). These spectra were measured at 60 °C. Using Lorentzian functions, the green best-fit peaks to the crystalline and amorphous peaks were used to determine χc.

the CH3 regions of 13C CH3-labeled iPB1 form I in the meltand solution-grown crystals, respectively, as a function of Tc. These spectra were measured at 60 °C. The crystalline peak was observed at 12.3 ppm and was well separated from the amorphous signal at 10.9 ppm. The clear appearance of two separated peaks is attributed to very rapid segmental motions in the amorphous regions at 60 °C, which is well above the glass D


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Figure 4. (a) SAXS patterns of form I iPB1 crystals grown from the melt state at Tc = 95 (black), 50 (blue), and 0 °C (red) from bottom to top. AFM image and thickness of the form I single crystal crystallized at (b) Tc = 60 and (c) ∼0 °C.

function of τex. The values of ξ expressed by the black and green open circles were obtained at high and low Tc’s, respectively. The behaviors of the DQ buildup curves of the melt- and solution-grown crystals were identical, and their ξmax values were the same, with 29% at τex = 5.88 ms. These experimental results indicate that the chain-packing structure was independent of Tc in the melt- and solution-grown crystals. Figure 5b displays the crystal unit cell on the (001) plane, which includes the possible 13C-labeled sites represented by colors. Our simulations used the 11-spin system to determine the chain-packing and folding structure of iPB1 form I. The system consisted of a reference methyl carbon colored in red as well as the 10 surrounding carbons (8 carbons among interstems and 2 in an intrastem) at distances of less than 6.4 Å (Figure 5b). The projection of the 11 carbon systems on the (001) and (12̅0) planes is shown in Figures 5c and 5d, and the 10 surrounding carbons were numbered from 1 to 10. The internuclear distances between the reference carbon and the surrounding 10 carbons are listed in Table 2. The reference was fixed to detect the DQ signals in the numerical simulations performed using SPINEVOLUTION.45 Initially, the atomic coordinates determined by Natta et al. were used for the spin dynamics simulation.46 The detailed calculation steps are described in the Supporting Information. All of the possible spin interactions (the shortest 13C−13C internuclear distance of 4.2 Å) and exponential types of T2 = 10.5 ms led to one simulated DQ curve (the blue curves in Figures 5e,f). The calculated curves were slightly slower than the experimental curve. Thus, the atomic coordinates were slightly modified by shrinking the chain packing. The best-fit curve to the experimental data resulted in the shortest distance and relaxation value of 4.0 Å and T2 = 8.3 ms, respectively (red curves in Figures 5e,f). The shortest 13C−13C internuclear distance was slightly shorter than the value determined in a previous XRD study by Natta et al. in 1960.46 Notably, the packing structures and atomic coordinates of the α form of iPP have been revised by several groups since Natta et al. reported the packing structure of iPP in 1960 in which the shortest interstem CH3−CH3 distance of ⟨r⟩ was 4.2 Å.51 Subsequently, Mencik revised the distance to 4.0 Å.52 Hikosaka et al. reported ⟨r⟩ = 3.8 Å for the α form of iPP annealed at very high temperatures.53 The revised distances in iPP are highly consistent with the current NMR result on iPB1. The modified atomic coordinates and T2 = 8.3 ms are employed for the CF analysis of the melt- and solution-grown crystals diluted by blending with nonlabeled iPB1. Note that the currently obtained T2 value is shorter than that in our previous communications which was wrongly calculated due to computational errors.31,32

excitation time τex = 5.86 ms. Figure 5a presents the 13C SQ and DQ CPMAS NMR spectra of the form I iPB1 crystals grown from the melt state at Tc = 95 °C, which were measured at 25 °C. DQ efficiency (ξ) is defined as the intensity ratio of DQ/SQ. Figures 5e and 5f show the ξ of the 13C-labeled iPB1 form I of the melt- and solution-grown crystals, respectively, as a

Figure 5. (a) 13C T1ρH-filtered DQ (red) and SQ (black) CPMAS NMR spectra of 35 wt % 13CH3-labeled iPB1 form I crystallized at 95 °C from the melt, measured at 25 °C. (b) Crystalline unit-cell structure and 11-spin system of form I iPB1 on the (001). The shortest 13C−13C internuclear distances between the neighboring stems (4.2 Å) and within a stem (6.3 Å), determined by X-ray diffraction (XRD).46 The projection of the 11-spin systems on the (c) (001) and (d) (12̅0) planes. (e) Black open circles curve at Tc = 95 °C and green at ∼0 °C in the melt-grown crystals. (f) Black open circles curve at Tc = 60 °C and green at ∼0 °C in the solution-grown crystals. In (e) and (f), the red and blue curves are the calculated DQ buildup curves based on the chain-packing with the closest interstem internuclear distance ⟨r⟩ of 4.0 Å and an exponential T2 of 8.3 ms and that of interstem ⟨r⟩ = 4.2 Å and T2 = 10.5 ms, respectively, as a function of τex. E


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Table 2. Internuclear Distances Are between the Reference Carbon and the Surrounding Carbons in the 11-Spin System of Form Ia surrounding carbons internuclear distance (Å) a

1 4.1

2 4.1

3 4.0

4 4.0

5 4.0

6 4.0

7 5.7

8 5.7

9 6.3

10 6.3

The number references Figures 5c,d.

4.4. Stem Level Mixing. Most NS and IR experiments on H/1H PE systems were limited to low Tc’s due to the segregation of two components at high Tc’s.54−57 This was a considerable disadvantage for characterization of the crystalline structures driven by kinetics. We must also investigate the segregation issues of 13C-labeled and nonlabeled chains during crystallization in both melt- and solution-grown crystals. In the former, 95 °C was the highest Tc in our experiments. POM demonstrated that crystallization required 24 h based on observations of the impingement of the growing spherulite (data not shown). This slow crystallization may induce segregations, consequently leading to domain structures of the labeled chains, as schematically illustrated in Figure 6c, and leading to the DQ efficiency being independent of the composition.

10/0 to 0.22 at 5/5 and 0.19 at 1/9. The observed composition dependence of the DQ buildup curves explicitly indicated that the dipolar coupling sources change from both intra- and interchains into intrachains as the amount of 13C-labeled components decreased. Namely, the individual 13C-labeled chains (red chains) were separated from the other labeled chains and were surrounded by the nonlabeled chains (black chains), as described in Figure 6d. Therefore, the 13C selective isotopic labeling approach in both melt- and solution-grown crystals was applicable to chain-folding analysis over a wide Tc range. The higher DQ curves for the 10 wt % samples in the solution-grown crystals than those for the melt-grown crystals reflect higher adjacent re-entry fractions in the former than in the latter. 4.5. CF Structures. We considered four CF structures in a single row, which are referred to as chain-folding I (CFI), CFII, CFIII, and isolated chain (CF0). In CF0, as illustrated in Figure 7a, the spins in only the intrastem interact, which can be observed in the random re-entry model. The DQ efficiency was calculated from the 13C spin reference and the nearest surrounding six sites of intrastem within 7.8 Å, in addition to statistical interstem effects (Figure S5 in ref 31). In the 31 helix of iPB1, the shortest 13C−13C distance in the intrastem is 6.3 Å. Therefore, the statistical interstem interactions at the short distances of 4.0, 4.1, and 5.7 Å significantly affected the DQ buildup curve, which is shown as a pink curve in Figure 7e. Notably, the contribution to DQ efficiency from the remote intrastem spins of distances at 6.5 and 7.8 Å was estimated to be 0.005 in the CF0 model.31 When the DQ buildup curve is determined by multiple couplings, the weaker couplings are automatically biased against. Thereby, these long-range effects were ignored in the CFI-III models. The CF analysis included statistical interstem effects in all of the CF models considered in this study. All CF models considered here are possible to adopt alternatively crystallographic CF directions. We showed one direction of them. The chains in CFI were folded along the (110) plane, but that of CFIII was aligned along the (010) plane. In CFI and CFIII, the chains were folded as a single row, as illustrated in Figures 7b,d. The chains in CFII alternatively changed CF directions along (100) and (010), as shown in Figure 7c. Each stem contains three differently oriented methyl carbons, and each CF model assumes a specific lattice direction between adjacently folding stems. Therefore, the spatial distribution of potentially

2

Figure 6. Composition ratio dependence of the blends on ξ as a function of τex. The ratio of 13C-labeled iPB1/nonlabeled chains was 10/0 (black open circles), 5/5 (blue), and 1/9 (red), grown from (a) melt at Tc = 95 °C and (b) solution at Tc = 60 °C. Schematic illustrations of (c) segregated and (d) mixed states of 13C-labeled (red) and nonlabeled chains (black) at the molecular level.

Figures 6a and 6b present the 13C−13C DQ buildup curves of the iPB1 blends with different composition ratios of 13Clabeled/nonlabeled iPB1 in the melt-grown crystals at Tc = 95 °C and solution-grown crystals at Tc = 60 °C, respectively. In the former, ξmax decreased from 0.29 at 10/0 to 0.20 at 5/5 and 0.15 at 1/9. Similarly, ξmax in the latter decreased from 0.29 at

Figure 7. Four plausible CF structures of (a) CF0, (b) CFI, (c) CFII, and (d) CFIII and (e) corresponding DQ buildup curves of a 1:9 blending ratio of 13C-labeled and nonlabeled chains under the assumptions of infinite folding number, and ⟨F⟩ = 100%. Notably, all of the calculated DQ curves included the statistical interchain effect. The atoms in red are possible 13C-labeling sites. F


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Macromolecules proximate labeled sites around any of the three labels on a given (reference) stem will correspondingly vary and be a function of the CF model. In turn, this will allow us to make a distinction experimentally between CF models. In CFI, each 13C spin at two sites among three in each stem statistically interact with 13 C spins at 1 site (or 2) of the closest adjacently folding stem, as listed in Table 2. In the CFII and III models, all three sites of each stem statistically interact with the 13C spins of the adjacently folding stems. In the CFIII model, each 13C spin at two sites statistically interacts with those at 3 and 4 sites (or 5 and 6 sites) of the closest adjacently folding stem, and the 13C spin at one site interacts with 7 and 8 sites of the second closest adjacently folding stem. The spin density in the CFII model is the highest among the three CF models. One spin statistically interacts with four spin sites numbered as 3, 4, 5, and 6 belonging to both sides of the closest adjacently folding stems, and each 13C spin of the other two spins interacts with three sites labeled as 1, 3, and 4 (or 2, 5, and 6) belonging to the first and second closest adjacently folding stems. The DQ efficiencies calculated under the assumption that all of the chains were composed of a perfect adjacent re-entry structure (⟨F⟩ = 100%) with an infinite folding number for all three CF structures are shown in Figure 7e. The DQ efficiencies discriminated different re-entrance sites. Furthermore, the ⟨n⟩ and ⟨F⟩ values contributed to the DQ efficiency. Three parameters were used to compare the experimental results with the simulation results. Real polymer systems might include some combination of different CF structures. This effect was carefully considered in our former communication.31 Most of the cases in the CF patterns were explained using one of the structures as a monolayer CF structure. We will discuss the possibility of multilayer structures later. 4.6. Chain Trajectory in Solution-Grown Crystals. The CF pattern of iPB1 in the solution-grown crystals was analyzed into the two different morphologies of hexagonal and circular crystals at Tc = 60 and ∼0 °C, respectively, as shown in Figure 2. According to the LH theory, the smooth growth surface leads to a secondary nucleation and growth of polymer chains. Under the hypothesis of a surface nucleation process, we assumed that the CF directions are parallel to the six growth fronts of hexagon, which belong to either CFI or CFII, as shown in Figure 8a. Figure 8b presents the experimental DQ buildup curve of 10 wt % 13C-labeled chains in the blends with nonlabeled chains (black open circles) and the calculated curves of CFI and CFII under the assumption of six faces of hexagon having the same CF models, ⟨nmax⟩ = 21, and ⟨F⟩ = 100%. The values of ξmax in the CFI and CFII models were 9% at τex = 7.45 ms (green solid curve) and 21% at τex = 6.66 ms (red), respectively. The former and latter were considerably lower and slightly higher, respectively, than the experimental curve. The ξmax of CFII could be plotted to the experimental DQ efficiency by decreasing the ⟨n⟩ and ⟨F⟩ values; hence, CFI could be invalidated. Figure 8c shows the ⟨n⟩ dependence of the calculated DQ buildup curves under the assumption of ⟨F⟩ = 100%. The value of ⟨n⟩ = 8 reproduced the experimental data and corresponded to the minimum folding number (⟨nmin⟩). In the case of ⟨nmax⟩ = 21, ⟨F⟩ = 90% was in good agreement with the experimental data (Figure 8d). Thus, our simulation resulted in two limit structures. Notably, our simulation assumed that the remainder of ⟨F⟩ (100 − ⟨F⟩%) adopts the isolated structure (CF0). These experimental results clearly indicate that slow crystallization conditions generate a well-

Figure 8. Schematic drawing of (a) hexagonal crystal at Tc = 60 °C composed of CFI or CFII. The arrows in front of CFI and CFII are the growth directions of the folded chains. Black open circles represent the experimental DQ buildup curve for the blends of 13C-labeled iPB1 chains with nonlabeled chains (1/9) in the single crystals at Tc = 60 °C in (b)−(d). (b) The calculated DQ buildup curve for CFI and CFII based on ⟨nmax⟩ = 21 and ⟨FCFII⟩ = 100%. (c) ⟨n⟩ and (d) ⟨F⟩ effects of the CFII model on the DQ buildup curves based on ⟨FCFII⟩ = 100% and ⟨nmax⟩ = 21, respectively. Note that all of the calculated results include statistical interchain effects.

ordered CF structure in the single crystals under the assumption of surface nucleation. At Tc = ∼0 °C, the circular single crystals induced by a rapid crystallization no longer reflected the crystal unit-cell structure. Tanzawa previously tested the effects of supercooling on the morphology of isotactic polystyrene (iPS) single crystals.49 The results clearly showed that the crystal characteristics gradually change from hexagonal to circular crystals with increasing supercooling. The morphology of iPS under intense supercooling is similar to the morphology of iPB1. According to the LH theory, the deposition of multiple chains on the growth front interrupts the lateral spreading of preexisting chains, thereby restricting the effective niche separation. Thus, it is expected that the competition for the growth of multiple nuclei leads to the growth of a chain folding perpendicular to the growth surface and to smaller ⟨n⟩ and ⟨F⟩ values than those in the single crystals at high Tc. This condition is called regime III in which niche separations are believed to be similar to the width of a few stems. One plausible model was CFIII in which the effective CF direction was radial in the circular crystals and in which the niche separation was assumed to be similar to the width of a single stem, as illustrated in Figure 9a. The calculated DQ buildup curves of CFIII with ⟨n⟩ = 10 and ⟨F⟩ = 80% (orange solid line) and with ⟨n⟩ = 5 and ⟨F⟩ = 50% (orange dots) are shown in Figure 9b. Another model, the CFIV model, was generated by combining the CFII and CFIII models in which the niche separation corresponded to the width of two stems. The calculated DQ efficiencies of CFIV with ⟨n⟩ = 10 and ⟨F⟩ = 80% (blue solid line) and with ⟨n⟩ = 5 and ⟨F⟩ = 50% (blue dots) and of CF0 (pink solid curve) are shown in Figure 9b. The experimental result for 10 wt % 13C-labeled iPB1 at Tc = ∼ 0 °C is represented with open black circles in Figures 9b−d. Surprisingly, the DQ curve exhibited a very high ξmax value of G


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Figure 10. CFII cluster models in (a) monolayer, (b) superCFII of ⟨ns⟩ = 1, and (c) ⟨ns⟩ = 2. (a) Schematic drawings of hexagons and circles at Tc = 60 and ∼0 °C composed of CFII clusters illustrated by the red boxes on the growth surface. DQ buildup curves based on ⟨nmax⟩ = 21 with (b) ⟨FsuperCFII⟩ = 85% (blue solid line) and (c) ⟨FsuperCFII⟩ = 80% (green). Isolated stems contribute to the remaining fraction in the DQ efficiency (100 − ⟨F⟩%). Experimental DQ buildup curve for the blends of 13C-labeled iPB1 chains with nonlabeled chains (1/9) in the single crystals at Tc = 60 °C is represented as black open circles. Notably, all of the calculated results include statistical intercluster effects.

Figure 9. Schematic drawing of (a) the circular crystal at Tc = ∼0 °C composed of CF0, CFIII, and CFIV. The arrows in front of CFIII and CFIV represent the growth directions of the folded chains. The curves composed of black and green open circles are the experimental DQ buildup curves for the blends of 13C-labeled iPB1 chains with nonlabeled chains (1/9) at Tc = ∼0 and 60 °C, respectively, in (b)− (d). (b) The calculated DQ buildup curves of CFIII (orange) and CFIV (blue) with ⟨n⟩ = 10 and ⟨F⟩ = 80% (solid line) and ⟨n⟩ = 5 and ⟨F⟩ = 50% (dots) and of CF0 (pink solid curve). (c) Blue solid curve is simulated based on CFIV ⟨nmax⟩ = 21 and ⟨FCFIV⟩ = 95%, and the curve composed of sky blue crosses is simulated based on ⟨nmin⟩ = 8 and ⟨FCFIV⟩ = 100%. (d) Red crosses are the simulated curve of CFII ⟨nmax⟩ = 21 and ⟨FCFII⟩ = 90%, and the black solid curve is that of ⟨nmin⟩ = 8 and ⟨FCFII⟩ = 100%. The isolated stems contribute to the DQ efficiency as the fraction of 100 − ⟨F⟩%. Note that all of the calculated results include statistical interchain effects.

the (11̅0) plane on the original layer; this process is called superfolding, and each layer is connected by the superfolding.58 Figures 10b and 10c show superCFII models with superfolding numbers ⟨ns⟩ = 1 and 2, respectively, where only simple cluster models by superfolding under the assumption of ⟨nmax⟩ = 21 were considered and where the partial cluster structure of the single chain was ignored. The DQ buildup curves of the multilayer calculated with ⟨FsuperCFII⟩ = 85% and 80% in Figures 10b and 10c, respectively, exhibited slightly faster buildup curves than those for the monolayer and the experimental result (black open circles). However, the difference was minor. Thus, the monolayer and multiple layers were capable of explaining the experimental results. This is the current limitation of DQ analysis for the detailed CF structures. 4.8. Chain Trajectory in Melt-Grown Crystals. Figure 11a shows the DQ efficiency (black open circles) of the 10 wt % 13C-labeled iPB1 form I crystallized from the melt state at 95 °C and the calculated curves of CF0-III structures based on the assumption of ⟨F⟩ = 100% and ⟨nmax⟩ = 5. The experimental ξmax of 15% at Tc = 95 °C was considerably higher than the calculated curves of CF0, CFI, and CFIII and was lower than that of CFII. Thus, CF0, CFI, and CFIII were excluded as plausible models for the melt-grown crystals at Tc = 95 °C. Because the case of the maximum folding number and 100% fraction was extreme, ⟨F⟩ and ⟨n⟩ were adjusted downward from their upper bound to the experimental DQ efficiency. The best-fit curves were obtained in two limit structures of ⟨nmin⟩ = 2 and ⟨FCFII⟩ = 100% (blue solid curve) and ⟨nmax⟩ = 5 and ⟨FCFII⟩ = 80% (red crosses) (Figure 11a). The possible two limits of chain trajectories of the folded chains in lamellae are described at the bottom of Figure 11a. The folded chains with five folds remain in one lamella. In the case of ⟨nmin⟩ = 2, three stems connected by two folds form one building block, and two different structures are possible. The two building blocks connected by a loop could remain in one lamella, or through tie molecules, they could remain in two successive lamellae. Notably, current NMR techniques cannot discriminate among these structures.

19% and was identical to the observed DQ curve at Tc = 60 °C, expressed by green open circles in Figure 9d, and was considerably higher than the calculated curves with relatively small ⟨n⟩ and ⟨F⟩ values dominated by kinetics (Figure 9b). Two limit models of CFIV with ⟨nmax⟩ = 21 and ⟨FCFIV⟩ = 95% (blue solid curve) and ⟨nmin⟩ = 8 and ⟨FCFIV⟩ = 100% (sky blue crosses) fit to the experimental curve shown in Figure 9c. The nearly identical values of ⟨n⟩ and ⟨F⟩ at high and low Tc’s were inconsistent with the kinetic theory. Thus, the CFIV model based on kinetics can be reasonably disregarded as an appropriate CF structure at Tc = ∼0 °C. Rather, the same experimental DQ efficiency at Tc = ∼0 and 60 °C simply supports the CFII model with the same ⟨n⟩ and ⟨F⟩ values at both values of Tc’s (Figure 9d). 4.7. Cluster Models in Monolayers and Multilayers. The Tc was independent of very high DQ efficiency values, which demonstrated that the chains form the clusters via a successive adjacent re-entry structure in the solution-grown crystals. For example, ⟨nmax⟩ = 21 and ⟨F⟩ = 90% were obtained under the assumption of a monolayer of CFII. This structure corresponded to isolated clusters of single molecules, as depicted in Figure 10a. In the presence of long-range order of adjacent re-entry, not only a single layer but also multiple layers may possibly explain the experimental results. We further tested the multiple layer structures of the folded chains in a single lamella of the solution-grown crystals. The multilayer nanoclusters consist of a series of CFII monolayers in which the following layer is produced by changing the CF direction along H


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5. DISCUSSION 5.1. Kinetics, Concentration, and Entanglement Effects on the CF Structure. In the trigonal packing of form I, each right-handed 31 helix is surrounded by three lefthanded helices and vice versa. Consequently, the tight packing between the right- and left-handed chains leads to a very high density of 0.92 g/cm3.59 This ideal packing structure of form I can reasonably explain why only the form I of iPB1 does not show stem dynamics up to Tm among similar polyolefins.39 In this study, several CF models were tested to verify the CF structures of iPB1. Only the CFII model could reproduce the experimental data of iPB1 form I in both the melt- and solution-grown crystals. Considering the packing structure and re-entrance sites, it is understood that iPB1 chains select the shortest folding pathway between the right- and left-handed stems among the possible pathways and that intramolecular interactions via chain folding lead to dense packing structures. This implies that intramolecular interactions are a driving force for the nucleation and growth of polymer chains in the meltand solution-grown crystals. This nucleation and growth mechanism is in good agreement with the conclusions drawn by recent MD simulations of a model of PE beads by Hu et al.61 Notably, the CFII model determined in our study was expected to be a plausible structure in poly(L-lactide)60 and iPS single crystals.49 Another interesting feature is the considerably higher longrange order of the adjacent re-entry sequences in the solutiongrown crystals (⟨n⟩ ≥ 8 and ⟨F⟩ ≤ 100%) than that in the melt crystals (⟨n⟩ ≥ 1.7−2 and ⟨F⟩ ≤ 100%). This result clearly implies that the concentration and entanglements of polymers significantly affect the long-range order for the CF structure. The determined long-range order is consistent with the results from the observation of PE lamellar rods on the surfaces of single crystals through the decoration technique.27 However, the ⟨f⟩ values from NS studies on PE single crystals by different groups are widely distributed from 0 to 75%.15,21,22 The determined ⟨F⟩ values of iPB1 in single crystals were 80−90%, similar to the ⟨f⟩ = 75% obtained by Sadler et al.15 In the melt-grown crystals, we can obtain more detailed information through NS studies. Ballard et al. investigated the Rg of PE and iPP in melt-grown crystals as a function of Mw’s and noted that the stem length is twice the length of the lamellar thickness at a Mw less than 20K g/mol.17 The consideration of the stem length suggests that the folded chains are similar to one limit of the CF structure with ⟨nmin⟩ and ⟨F⟩ = 100% in the melt-grown crystals. Namely, the two folds of adjacent re-entry across two lamellae via tie chains (⟨nmin⟩ = 2 and ⟨F⟩ = 100% at Tc = 95 °C) rather than long-range order (⟨nmax⟩ = 5 and ⟨F⟩ = 80%) in one lamella may be preferred, as illustrated in Figure 11. The structure with ⟨F⟩ = 100% and ⟨nmin⟩ = 1.7−2.0 over a wide Tc range of 0−95 °C corresponds to ⟨f⟩ values of 64−67%. Most of the former NS and IR studies showed low adjacent re-entry fractions of PE (⟨f⟩ = 20− 46%)12,22,23,25 and iPP chains26 in the melt-grown crystals, except for PE with ⟨f⟩ = 70% by Guttman et al.18 and ⟨f⟩ = 30− 66% by Hoffman.2 Our results are similar to the early observation by Guttman et al. and deny kinetics effects on the CF process in the melt-grown crystals. On the basis of MD simulations, Hu et al. recently reported that PE bead models also showed ⟨f⟩ = 50−60% in a highly dense state (volume fraction of polymer, vf = 0.938).61 Interestingly, they reported that a higher Tc leads to a lower adjacent re-entry fraction due

Figure 11. Experimental DQ buildup curves for the blends of 13Clabeled iPB1 chains with nonlabeled chains (1/9) crystallized at (a) Tc = 95 °C (black open circles), (b) 50 °C (blue), and ∼0 °C (green). (a) The calculated DQ efficiencies are solid curves, CF0 (pink), CFI (green), CFII (red), and CFIII (orange) under the assumption of ⟨nmax⟩ = 5 and ⟨F⟩ = 100% at Tc = 95 °C. The calculated DQ efficiencies of CFII under the assumption of ⟨nmin⟩ = 2 with ⟨FCFII⟩ = 100% (blue solid curve) and ⟨nmax⟩ = 5 with ⟨FCFII⟩ = 80% (red crosses) at Tc = 95 °C. (b) The calculated DQ efficiencies of CFII under the assumption of ⟨nmin⟩ = 1.7 with ⟨FCFII⟩ = 100% (black solid) at Tc = 50 and ∼0 °C. Schematic view of probable CF structures through the lamellae: (a) ⟨nmax⟩ = 5 (red chain) and ⟨nmin⟩ = 2 (blue) on the bottom of (a) at Tc = 95 °C and ⟨nmax⟩ = 10 (green) and ⟨nmin⟩ = 1.7 (black) on the bottom of (b) at Tc = 50 and ∼0 °C.

The ξmax’s of the DQ buildup curves for 10 wt % blends at Tc = 50 and ∼0 °C were 14%, which are shown as blue and green open circles, respectively, in Figure 11b. They were nearly the same as the ξmax at Tc = 95 °C (15%) and were larger than the curves of CFI and III calculated under the extreme limit of ⟨nmax⟩ and ⟨F⟩ = 100%. The best-fit DQ buildup curves to the experimental data at Tc = 50 and ∼0 °C, respectively, were drawn using CFII in the two limit structures with ⟨nmin⟩ and ⟨nmax⟩. One of the DQ curves was based on ⟨nmin⟩ = 1.7 and ⟨F⟩ = 100%, which is shown as a black solid curve in Figure 11b. The value of ⟨nmin⟩ = 1.7 indicates that 75% of the chains adopt 2-fold adjacent re-entry, and the remainder are only 1fold in the crystalline region, as illustrated at the bottom of Figure 11b. The CF structure at Tc = ∼0 °C was highly similar to that at Tc = 95 °C. Table 3 summarizes the ⟨F⟩ and ⟨n⟩ values of the CFII model and experimental ξmax as a function of Tc in the melt- and solution-grown crystals. Table 3. Effect of Tc on CFII Structure and Experimental ξmax in the Melt- and Solution-Grown Crystals Tc (°C) solution melt

60 0 95 50 0

⟨F⟩ (%)a (⟨nmax⟩) 90 90 80 70 65

(21) (21) (5) (7) (10)

⟨nmin⟩b

exptl ξmax (%)

8 8 2 1.7 1.7

19 19 15 14 14

⟨F⟩ was simulated at ⟨nmax⟩ of each crystallization temperature under the assumption of a single layer. b⟨nmin⟩ was obtained under the assumption of ⟨F⟩ = 100%. a

I


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than those in the melt-grown crystals. The trend in our results cannot be explained in terms of entanglement and supercooling effects. DeRosa et al.65 and Miyoshi et al.39 reported that iPB1 with relatively low stereoregularity directly crystallized into thermodynamically stable form I from the melt state, and the ⟨lc⟩ of iPB1 with ⟨mmmm⟩ = 78% was approximately 5 nm across different Tcs. However, highly stereoregular samples crystallize into form I through transformation by form II and yielded a Tc dependence on ⟨lc⟩ from 10 nm at Tc = 50 °C to 28 nm at Tc = 110 °C. The latter result is consistent with the current result. Cheng et al. showed that the ⟨lc⟩ of iPP samples with different stereoregularities of 78−99% exhibited one universal line as a function of reciprocal supercooling.66 These comparisons evidently indicate that the thin lamellar thickness in form I crystallized directly from the solution state is attributed to the immobility of the crystalline chains. In contrast, the Tc dependence on ⟨lc⟩ and χc in the melt-grown crystals can be responsible for the temperature dependence of the overall chain mobility in form II.37 This concept can be applied to PE, which is also one of the mobile crystals.33 The LH and bundle theories state that ⟨lc⟩ is proportional to the inverse of supercooling. A major contribution to the reciprocal supercooling dependence of ⟨lc⟩ would be the mobility change of the crystalline chains. The multistage model mentioned that the mobility of polymer chains in transient mesomorphic states allowed their thickness to increase.10 The current study clearly showed that the mobility of chains after recognizing the crystalline phase determines the crystal thickness. Notably, Ijima et al., using in situ SAXS, demonstrated that ⟨lc⟩ in form II of iPB1 is highly dependent on Tc and is independent of the crystallization time.67 Considering our experimental results and the reported SAXS data, it is reasonably concluded that after recognizing the crystalline phase at a given temperature, the final ⟨lc⟩ is instantly determined by the mobility of the crystalline chains.

to thickening of the crystal lamellae. However, we did not observe the thickening effects on the adjacent re-entry fraction at a high Tc of 95 °C, where ⟨lc⟩ was 2-fold higher compared with that at ∼0 °C. 5.2. Crystallization Process of iPB1. In solution-grown crystals, the formation of nanoclusters at Tc = 60 and ∼0 °C cannot be explained in terms of surface nucleation dominated by kinetics. Instead, the clusters suggest that the polymer chains fold in the prestage of crystallization and that the prefolding clusters are subsequently deposited on the growth front, as shown in Figure 10a. The former process involves large structural changes from random coils to well-folded chains (nanoclusters) in a dilute solution and is not dominated by kinetics. The latter process (morphological development), however, is governed by kinetics in which individual clusters compete to deposit on the growth surface, consequently leading to the morphological difference at Tc = 60 and ∼0 °C, although we used different solvents to produce form I crystals at different Tc’s. The structural formation of polymer crystals from molecular to morphological scales in our study is in good agreement with the theoretical bundle7 and aggregation model,8 which insisted that the formation of three-dimensional preordering objects is a first step of crystallization. Furthermore, MD simulations by Muthkumar et al. confirmed that kinetically driven depositions of the nanoclusters cause markedly different crystal behaviors in the solution-grown crystals.8 The nanoclusters formed via prefolding might be three-dimensional structures that minimize the surface free energy. Unfortunately, the current DQ NMR and simulation results could not specifically discern between monolayer and multilayer clusters due to the similarities of spin topology in the former and latter. This will be a future subject for the characterization technique. Recently, Luo and Sommer conducted MD simulations on PVA coarse grain models in condensed states.11 The results indicated that most of the PVA chains folded once or twice in the prestage of crystallization for a few 10 ps and that the folded structure did not change during further crystallization processes. This result is consistent with our experiments (⟨nmin⟩ = 1.7−2 and ⟨F⟩ = 100%), implying that the CF process from the melt state is a local event without large displacements of whole chains in space. This is also supported by the invariant Rg in the melt state58 in which entanglements of polymer chains limited their rearrangement. The local process in the melt state would reasonably explain why individual chains adopt adjacent re-entry structures with only one or two folds. Furthermore, χc and ⟨lc⟩ of the iPB1 solution- and meltgrown crystals, combined with the molecular dynamics in forms I and II and comparisons with the results for other polymers, provided additional information regarding polymer crystallization in the late process. In PE crystals, experimental results and computer simulations have demonstrated that χc decreases with decreasing Tc, and χc in the solution-grown crystals is considerably higher than that in the melt.2,62 Hu et al. noted that the increase in entanglements with increasing polymer concentration significantly decreases the χc of the PE bead model.61 The ⟨lc⟩ of PE in both solution- and melt-grown crystals is highly dependent on supercooling.63,64 In iPB1, χc and ⟨lc⟩ in the melt state increased with increasing Tc but were independent of Tc in the solution state. In addition, quenching the melt to ∼0 °C yielded comparable crystallinity and a ⟨lc⟩ higher than 10 nm compared with the single crystals (4.8 nm). The ⟨lc⟩ of the single crystals was markedly lower

6. SUMMARY 13 C−13C DQ NMR combined with selective 13C isotopic labeling methods successfully determined the adjacent re-entry parameters of the re-entrance site, ⟨F⟩, and ⟨n⟩ of iPB1 in meltand solution-grown crystals as a function of Tc. It was clearly demonstrated that the chains dominantly fold between rightand left-handed chains (CFII model) in both melt- and solution-grown crystals. This result indicated that the nucleation process of polymer crystallization is dominated by the CF process. In addition, the solution-grown crystals exhibited longer range order (e.g., ⟨nmin⟩ = 8 and ⟨F⟩ = 100% under a monolayer) than that in the melt (⟨nmin⟩ = 1.7−2 and ⟨F⟩ = 100%). The long-range order was highly related to the low concentration and low entanglement density in a dilute solution that allowed the polymer chains to rearrange in space. The ⟨n⟩ and ⟨F⟩ values were nearly independent of Tc in both the solution- and melt-grown systems. Particularly, the invariant long-range order in adjacent re-entry structures at Tc = 60 and 0 °C in the solution state suggested prefolding of polymer chains in the prestage of crystallization. The morphology of the single crystals markedly changed from hexagonal at Tc = 60 °C to circular at ∼0 °C. The combined data at different length scales demonstrated that kinetics plays different roles for the structural formations from molecular to morphological levels, which supported the two-step process used in theoretical models. Furthermore, the crystallization into metastable and mobile form II (melt-grown crystals) led to Tc dependence on J


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Macromolecules the lamellar thickness (⟨lc⟩ = 10.0−21.6 nm) and crystallinity (χc = 70−88%), whereas direct crystallization into thermodynamically stable form I (solution-grown crystals) produced very thin single crystals (⟨lc⟩ = 4.8 nm) and Tc independence of low crystallinity (χc = ∼70%). These experimental results could not be explained in terms of the LH, bundle, and multistage models or by the entanglement effect but highlighted the effects of the crystalline chain dynamics after incorporation into the crystalline phase. Based on the current experimental results, the entanglements and concentrations of polymer chains significantly influenced the CF process in the initial process, and chain dynamics significantly altered the crystallinity and lamellar thickness in the late process. The molecular level structures and dynamics combined with other structural parameters provided detailed pictures for the structural evolutions during polymer crystallization.

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ASSOCIATED CONTENT

* Supporting Information S

Simulations; Figure S1. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b00079.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (T.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by the National Science Foundation (Grants DMR-1105829 and 1408855) and a UA startup fund. We are greatly indebted to Dr. Jeffrey Quinn at Bridgestone America for the GPC measurements and James Hill at the University of Akron for the AFM measurement.

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