Solid-State NMR Study of the Chain Trajectory and Crystallization

Aug 18, 2017 - Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States. ‡ State Key Lab of Pollution Control a...
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Solid-State NMR Study of the Chain Trajectory and Crystallization Mechanism of Poly(L‑lactic acid) in Dilute Solution Shijun Wang,† Shichen Yuan,† Wei Chen,†,‡ Qiming He,† You-lee Hong,†,∥ and Toshikazu Miyoshi*,† †

Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States State Key Lab of Pollution Control and Resource Reuse Study, College of Environmental Science and Engineering, Tongji University, Shanghai 200092, China ∥ RIKEN CLST-JEOL Collaboration Center, RIKEN, Yokohama, Kanagawa 230-0045, Japan ‡

S Supporting Information *

ABSTRACT: The nucleation and growth mechanisms of semicrystalline polymers are a controversial topic in polymer science. In this work, we investigate the chain-folding pattern, packing structure, and crystal habits of poly(L-lactic acid) (PLLA) with a relatively low molecular weight, ⟨Mw⟩ = 46K g/ mol, and PDI = 1.4 in single crystals formed from dilute amyl acetate (AA) solution (0.05 or 0.005 wt %) at a crystallization temperature (Tc) of 90, 50, or ∼0 °C. The crystal habits drastically changed from a facet lozenge shape at Tc = 90 °C to dendrites at ∼0 °C, whereas the chains adopt a thermodynamically stable α packing structure at both 90 and 0 °C. Comparing the experimental and simulated 13C−13C double quantum (DQ) buildup curves of 13C-labeled PLLA chains in crystals blended with nonlabeled chains at a mixing ratio of 1:9 indicates that the PLLA chains fold adjacently in multiple rows when the Tc ranges from 90 to ∼0 °C. The results at different length scales suggest that (i) a majority of the chains self-fold in dilute solution and form baby nuclei (intramolecular nucleation) and (ii) the intermolecular aggregation process (secondary nucleation), which is dominated by kinetics, results in morphological differences. growth front for subsequent growth. With increasing ΔT, nucleation density increases, and the secondary nucleation process competes with the growth process; thus, the extent of the subsequent growth at the growth front is limited. Alternatively, Allegra and Meille proposed the bundle model,20,21 in which long polymer chains self-fold and form baby nuclei during primary nucleation, while subsequent secondary nucleation induces their aggregation. Using computer simulations, Muthukumar22−24 and Fujiwara25,26 predicted the importance of forming three-dimensional baby nuclei via self-folding in dilute solution. From an experimental perspective, for long polymer chains in the condensed state consisting of the same repeating monomer units, it is challenging to distinguish intramolecular interactions from intermolecular ones because of the inherent folding nature of these species. To overcome this problem, neutron scattering (NS)27−42 and IR spectroscopy43−46 combined with 2H isotope labeling have been applied to investigate the radius of gyration (R g ) and chain-folding structure of polyethylene (PE)21,29,35,39,41,46 and isotactic-poly(styrene) (iPS).30,38 The Rg of PE in single crystals was demonstrated to be much smaller

1. INTRODUCTION The crystallization of long polymer chains induces drastic structural changes from random coils in the melt and solution states to folded polymer chains in thin crystalline layers with thicknesses of 5−20 nm.1−11 Under relatively low supercooling, the crystal habits of single crystals reflect the symmetry of the crystal unit cell. For example, trigonally packed isotacticpoly(styrene) (iPS)1,2,12 and isotactic-poly(1-butene)(iPB1) form I3,13 adopt hexagonal single crystals, whereas the orthorhombic form of polyethylene (PE)4−7 and poly(L-lactic acid) (PLLA) α crystals8,9 form lozenge-shaped structures. Tetragonally packed iPB1 form II10 and isotactic-poly(4-methyl1-pentene) form III11 adopt square single crystals. Under large supercooling, the crystal habits commonly show dendritic4,5,14,15 or circular12,13,16 morphologies, which have been widely accepted as a kinetics effect.14 The open questions regarding solution-grown crystals are (i) how longer polymer chains are embedded and (ii) how kinetics influence chain trajectory in single crystals. Several theoretical studies on the structural evolution of polymers during crystallization at the molecular scale have been reported.17−21 According to the Lauritzen−Hoffman (LH) theory,17−19 a part of a polymer chain, the “stem”, is deposited on the growth front (secondary nucleation). Under low supercooling (ΔT), sequential stem deposition covers the © XXXX American Chemical Society

Received: July 9, 2017 Revised: August 8, 2017

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DOI: 10.1021/acs.macromol.7b01462 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules than the Rg of random coils in the solution state and to show very weak Mw dependence.41 The result was interpreted in the following way: high densities of nuclei limit the chain-folding number in a single row and result in the superfolding of the folded chains in multiple rows. However, detailed chain-folding patterns of PE in single crystals are debatable, and the reported adjacent re-entry fraction ranges widely from 25%47,48 to 75%29,46 at ΔT = 60 °C. To avoid kinetics effects on the chainfolding events (superfolding), low ΔT and relatively low molecular weight sample would be desirable. However, 2H/1H polymer mixtures suffer from segregation at high crystallization temperature (Tc),19,49 and thus, chain-folding analysis of 2H/1H PE under very severe crystallization conditions has not been realized. Moreover, no research has focused on the very large ΔT effect on the chain-folding structure in solution-grown crystals. Therefore, kinetics effects on the chain-folding structure in solution-grown crystals have seldom been reported. Very recently, our group used solid-state (ss) NMR spectroscopy combined with 13C isotope labeling to investigate the local chain-folding patterns of iPB1 forms I13,16,50 and III,51 isotactic-poly(propylene) (iPP) α,52,53 and mesomorphic54,55 forms and PLLA/poly(D-lactic acid) stereocomplexes56 in the bulk and in solution-grown crystals.57 Selective 13C isotope labeling leads to almost no isotope effect and thus results in the cocrystallization of 13C-labeled and nonlabeled polymer chains, even at very high Tcs.46−58 Spatially sensitive magnetic dipolar interactions59 could be used to trace 13C spin networks, as determined by the chain trajectory of the 13C-labeled chains. Therefore, this 13C selective isotope labeling approach enabled the investigation of kinetics effects on chain trajectory in polymer crystals. In solution-grown iPB1 form I crystals,13 iPB1 chains with ⟨Mw⟩ = 34K g/mol were found to adopt adjacent re-entry rich structures with an adjacent re-entry fraction ≥80% in the facet hexagons formed in butanol and amyl acetate (AA) blend solution at Tc = 60 °C. Rapid quenching at ∼0 °C induced circular crystals in AA solution. The iPB1 chains also adopted adjacent re-entry rich structures in the circular crystals, a fraction of which is the same as that in the facet hexagonal crystals.16 The results clearly indicated that the experimentally accessible kinetics significantly influence morphology at the micrometer scale but does not affect local chain-folding patterns at the nanometer scale, even though different solvents were used at high and low Tcs. Moreover, iPB1 chains in form III single crystals dominantly were also reported to form threedimensional clusters in multiple rows.51 These results suggested that iPB1 chains self-fold and make baby nuclei in dilute solution and that the structural unit of the polymer during crystallization is not a “stem” but “stem clusters”.47,51 These new results further motivate us to study the chain-folding structure of different polymer systems to generalize our understanding of polymer crystallization at the molecular scale. In this work, we investigate the crystal habits, packing structure, and chain-folding structure of PLLA solution-grown crystals at varied Tcs. To investigate pure kinetics effects on polymer crystallization, AA solvent was used. Moreover, extremely low polymer concentrations of 0.05−0.005 wt % and a low ΔT of 40 °C were used to suppress kinetics effect on polymer crystallization. We have several open questions regarding PLLA solution-grown crystals: (i) What type of chain-folding pattern is adopted in facet lozenge single crystals under the extremely low polymer concentration and low ΔT? (ii) How does a large ΔT influence packing structure, morphology, and chain trajectory? (iii) How are these

structures at different length scales related to each other? (iv) When and where do polymer chains in dilute solution fold? To answer some of these questions, we synthesized a low molecular weight 13C-labeled PLLA with a weight-average molecular weight ⟨Mw⟩ = 46K g/mol and a narrow PDI of 1.4. Considering the ⟨Mw⟩, helical conformation, and crystal thickness (see Figure 1), a PLLA chain can fold up to 16

Figure 1. AFM images and height profiles of the PLLA crystals grown from a 0.05 wt % solution at (a) Tc = 90 °C and (b) Tc = ∼ 0 °C. The height profiles were obtained at the position indicated by the dashed lines.

times. This low maximum chain-folding number, nmax, along with a very low ΔT may allow us to distinguish chain-folding mechanisms driven by primary nucleation from those driven by secondary nucleation. The crystallization mechanisms of PLLA in dilute solutions will be discussed using the chain-level structure, packing, and crystal habits obtained as a function of kinetics.

2. STRATEGY 13 C−13C DQ NMR relies on dipolar interactions, the size of which is inversely proportional to the third power of internuclear distance of interacting 13C spins, spin number, and spin topology. To observe 13C−13C dipolar interactions between the neighboring stems, 30% of the carbons in the CH3 groups of PLLA were labeled with 13C. In terms of the 107 helix conformation in the α packing structure, the shortest interstem 13 C− 13 C internuclear distances are 3.4−3.8 Å. 24 The distribution of internuclear distances arises from the disordered helical conformation. The closest interstem internuclear distances are much shorter than the closest intrastem internuclear distances of 5.1−5.3 Å.60 This condition is very important to study the interstem 13C−13C dipolar interactions, which principally contribute to the DQ buildup curve. Before analyzing the 13C−13C DQ buildup curve, we briefly introduce our calculation concept at the stem levels. Scheme 1 shows schematic illustrations of the packing structure of the 13C-labeled PLLA (a) and its blends with nonlabeled PLLA with a mixing ratio of 1:9 (b and c). The latter was used for chain-folding analysis. Red circles denote 13 C-labeled stems, and purple circles represent statistically labeled stem (either 13C-labeled or nonlabeled stems with a 10% probability of being 13C labeled). In all simulations, packing and chain-folding analysis could be achieved by treatment with a seven stem cluster, including one reference stem at the center and six surrounding stems in the shape of a hexagon (bottom of Scheme 1), with only the dipolar interactions at the center stem taken into consideration. For the 13C-labeled polymer, the symmetry of the packing structure leads to only one kind of seven-stem cluster, as illustrated in the bottom of Scheme 1a. The disordered 107 helix generates five B

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with an RI detector was performed in THF (40 °C, 1 mL/min) to measure ⟨Mw⟩ and PDI. The 13C-labeled and nonlabeled PLLA had ⟨Mw⟩ = 46K g/mol with a PDI = 1.4 and ⟨Mw⟩ = 47K g/mol with a PDI = 1.7, respectively. 3.2. Preparation of Solution-Grown Crystals. PLLA (15 mg) was dissolved in 30 g of AA solution (0.05 wt %) at 130 °C. For the extremely dilute solution (0.005 wt %), 7.5 mg of PLLA was dissolved in 300 g of AA at 130 °C. After dissolution, both solutions were kept at 130 °C for at least 30 min. The hot AA solution was quickly transferred to another oil bath at preset Tcs of 90, 50, and ∼0 °C. Crystallization at all Tcs was conducted in the bath for 24 h. To ensure the crystallization at ∼0 °C, an alternative process was used, in which the hot solution was directly and slowly poured into excess cold solvent (10 times larger volume) maintained at 0 °C. Then, the precipitated crystals were collected and dried under vacuum for 1 day at room temperature. 3.3. Characterization. Atomic force microscope (AFM) in the tapping mode was used for observing the morphology for the solutiongrown crystals. An Icon AFM (Bruker Nano) was operated with a scan rate of 1 Hz and a resolution of 512 pixels. To prepare the AFM samples, several drops of the crystal suspensions were deposited onto a silicon wafer. Next, the samples were dried under vacuum prior to the measurement. All ssNMR experiments were conducted on a BRUKER AVANCE 300 equipped with a 4 mm double resonance MAS probe at 25 °C. The MAS frequency was adjusted to 5102 ± 5 Hz. The 13C CH signal of adamantane was calibrated to 29.46 ppm as an external reference of the 13C chemical shift. The 90° pulses for 1H and 13C were adjusted to 2.4 and 4.8 μs, respectively. The recycle delay and cross-polarization (CP) time were 2 s and 1 ms, respectively. A PostC762 pulse with a field strength of 35.7 kHz was applied for exciting and reconverting 13C−13C DQ signals into single quantum (SQ) signals. 1H two-pulse phase modulation (TPPM)63 and continuous wave decoupling with a field strength of 104 kHz were applied during the 13C acquisition and recoupling periods, respectively. Numerical spin-dynamics simulations were conducted using SPINEVOLUTION.64

Scheme 1. Schematic Illustrations of the Spatial Arrangement of (a) the 13C-Labeled PLLA and (b, c) Its Blend Systems Diluted with Nonlabeled PLLA at a Mixing Ratio of 1:9a

a

The latter illustration includes two examples of (b) the adjacent reentry model with a folding number of 2 and (c) an isolated stem. Red and purple circles denote 13C-labeled stems and statistically labeled stems (either 13C-labeled or nonlabeled stems with a 10% probability of being 13C-labeled), respectively.

conformationally distinguishable sites.60 Thus, spin-dynamics simulations were conducted at the five sites in one subcluster (for more details, see the Packing Analysis section). In the case of chain-folding analysis, two types of chain-folding models were represented, one of which has an adjacent re-entry structure with two folds (top of Scheme 1b). This folding structure was divided into three kinds of seven stem subclusters in the bottom of Scheme 1b, where the left and middle clusters correspond to stems at the fold ends and the right cluster represents the stem at center of the consecutive three stems connected via folding. With increasing chain-folding number, the weighting of the contribution of the last structure in simulations increases (e.g., Figure 5c,d). In the case of an isolated stem, stem connectivity can be simply represented in terms of only one kind of seven-stem cluster, as illustrated in the bottom of Scheme 1c. In this work, the mean value of the successive adjacent rej entry number ⟨n⟩ can be defined as ⟨n⟩ = ∑mj=1(∑li=1 nij)/∑mj=1lj, where nij represents the adjacent re-entry folding number of the ith cluster in the jth chain among a total of m chains and lj is the total cluster number in the jth chain. The adjacent re-entry j fraction in the jth chain is defined as Fj, where Fj = ∑li=1 (nij + 1)/Nj, Nj is the total number of crystallized stems in the jth chain, and ⟨F⟩ is an ensemble average of Fj, which can be j described in terms of ⟨F⟩ = ∑mj=1∑li=1 (nij + 1)/∑mj=1Nj (for more details, see ref 51).

4. RESULTS 4.1. Morphology and Packing Structure of the PLLA Crystals. Figures 1a and 1b show AFM images of the morphology of PLLA crystals grown from the 0.05 wt % solution at Tc = 90 and ∼0 °C. The former crystals showed a facet lozenge shape with a thickness of ∼11 nm. The structure is very similar to the one that has previously been reported.9 According to the LH theory,17−19 PLLA chains are expected to fold linearly along the facet plane, e.g., (110).8,12,65 Rapid quenching down to ∼0 °C afforded crystals with dendritic morphology and a maximum height of ca. 100 nm. The height arises from multiple stacked crystal layers. Dendritic morphology supports a kinetics effect on the morphology. Similar morphology has been observed in PE4,14 and iPS15 solutiongrown crystals under large supercooling. It is believed that kinetic roughness at the micrometer scale originates from steps on the growth front at the stem level.66,67 Figure 2b−d shows 13C CPMAS NMR spectra of the single crystals of 13C 30% CH3-labeled PLLA at Tc = 90 (red) and ∼0 °C (black). At both Tcs, the CO, CH, and CH3 groups showed four, four, and two split peaks, respectively. Such fine splitting is characteristic of the α crystals and corresponds to discrete and different conformations in the 107 helix in the α crystals.68−70 XRD analysis indicates that there are five conformationally distinguishable sites in the 107 helical backbone with torsion angles (φ, ψ, ω) of (−68.2°, 151.6°, 175.4°; A), (−63.0°, 154.5°, 165.0°; B), (−65.8°, 158.7°, 178.1°; C), (−66.0°, 163.9°, 167.3°; D), and (−58.0°, 150.0°, 168.6°; E).60 Comparing the 13C NMR spectra simulated using the gauge

3. EXPERIMENTAL SECTION 3.1. Synthesis of PLLA. 13C CH3-labeled L-lactic acid (1 g, L-LA, Sigma-Aldrich) and 2.33 g of nonlabeled L-LA were dissolved in 600 mg of water. The solution was stirred at 110 °C for 2 h to remove the water and then heated to 140 °C for 8 h under vacuum to obtain the oligomers. Al2O3/Sn(Oct)2 (80 mg) with a weight ratio of 1:4 was added to catalyze the degradation of the oligomers to obtain statistically 30% 13C CH3-labeled cyclic lactide at 200 °C under vacuum. The lactide was purified by precipitating the acetone solution in water. 13C-labeled and nonlabeled PLLA were synthesized by the ring-opening polymerization of the 13C-labeled and nonlabeled lactide, respectively, at 140 °C with 0.06 wt % Sn(Oct)2 as the catalyst.61 0.3 wt % octanol was used as the initiator to control the molecular weight. Gel permeation chromatography (GPC, Tosoh Instrument) equipped C

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Figure 3b schematically depicts a seven-stem cluster in the α crystals. DQ buildup curves at the five sites in the 107 helix at the center stem, which are circled by a dashed red line, were simulated using dipolar interactions at distances less than 6.2 Å. This cutoff distance limits the maximum spin number (max_s) up to 11−12 depending on the sites. For example, the 11 spin system at the A site was highlighted by different colors in Figure 3b, with one of the reference 13C spins colored green and the surrounding 2 intrastem and 8 interstem 13C spins colored black and red, respectively. Figure 3c displays the histogram of the distribution of the 13CH3−13CH3 internuclear distances from each reference spin at the A−E sites of the center stem in Figure 3b. The calculation procedure for the DQ buildup curve is described below. For a given m-spin system with 11−12 maximum spins, the DQ buildup subcurves am can be represented in terms of i

am(tex ) =

∑ (wm

i

1

× qm (tex )) × Pm i

where wmi represents the probability of each spin topology in the m spin system and qmi(tex) is the calculated curve for one specific spin topology i in the given m spin system (∑i1(wmi) = 1). The value of Pm, which represents the probability of m-spin system with max_s = 11 or 12, can be expressed as

Figure 2. (a) PLLA chemical structure with torsion angles along the backbone and 107 helical conformation where CO groups at five sites were highlighted by different colors. 13C CPMAS spectra of (b) CH3, (c) CO, and (d) CH groups for 13C 30% CH3-labeled PLLA in the solution-grown crystals formed in 0.05 wt % at Tc = 90 °C (red) and ∼0 °C (black). The naturally abundant CO and CH signals were vertically amplified 10- and 5-fold, respectively. The best fit-Lorentzian peaks to the 13C CH3 line shape are depicted as a blue sold line.

m−1 m−1 Pm = Cmax × (1 − x)max_s − m _s − 1 × (x)

where C is the combination sign and x equals the 13C CH3labeled ratio of 0.30. A series of Pm values can be calculated, and the sum of those values should equal 100%. Eventually, the experimental DQ results at the A−E sites were calculated based on the subcurves of am(tex) as

including projected augmented wave (GIPAW)71 method with the experimental spectra allowed the assignment of the CO signals to five different conformations (A−E).72 The assigned A−E sites were denoted in the CO group in Figure 2c. Next, we use the 13C-labeled CH3 signals for packing and chain-folding analysis. Thus, we consider the two CH3 peaks at 17.4 and 16.1 ppm. Because of the asymmetric and symmetric peaks at 17.4 and 16.1 ppm, respectively, three Lorentzian peaks were used to fit the experimental data. The area ratio of the peaks at 17.4 ppm to those at 16.1 ppm is 78:22 (ca. 4:1), which ratio is highly consistent with the ratio expected from the site number for the CO group determined by XRD. Thereby, two CH3 peaks at 17.4 and 16.1 ppm are attribute to four and one sites, respectively, among the A−E sites. A broad and minor amorphous component at the fold surface should appear at the bottom of the sharp crystalline signals. However, the amorphous peak was not included in the line shape analysis because of insufficient spectral resolution. 4.2. Chain Packing Analysis of α Phase by DQ NMR. The SQ (top) and DQ (bottom) NMR spectra of the single crystals of 30% 13C CH3-labeled PLLA grown at Tc = 90 °C are shown in Figure 3a. The latter spectrum was obtained at a DQ excitation time (tex) of 6.27 ms. The DQ efficiency (ξ) was defined as the ratio of the peak area of the DQ spectrum to that of the SQ spectrum. The maximum DQ efficiency (ξmax) values at 17.4 and 16.1 ppm were 0.25 at tex = 6.27 ms and 0.20 at 7.06 ms, respectively. The full DQ curves at 17.4 ppm (red open circle) and 16.1 ppm (black) are depicted in Figure 3e. The DQ curve at 17.4 ppm is larger in overall height than that at 16.1 ppm. The different heights of the DQ curves may reflect the disordered conformations and packing structures of the 107 helices in the α crystals.60

m

ξ(tex ) =

∑ (am(tex)) × e−t

ex / T2

1

where T2 denotes the spin−spin relaxation time and was used as an adjustable parameter. The simulation DQ curves at individual A−E sites assuming a T2 value of 9.5 ms are depicted in Figure 3d. Among the five sites, the two curves at the A and E sites showed lower and slower DQ buildup curves than those at the B−D sites. Thus, either the A or E site and the remaining four sites may be assigned to the peaks at 16.1 and 17.4 ppm, respectively. For the A−D sites, the calculated DQ single curve was obtained by equally weighting the individual DQ curves simulated at the A−D sites with T2 = 9.5 ms and was plotted as a solid red curve shown in Figure 3e. The simulated curve could well reproduce the experimental curve. For the E site, however, the DQ curve with T2 = 9.5 ms (purple solid curve) appeared slower than the experimental result. Even changing the T2 value could not reproduce the experimental curve. Similarly, the DQ curve at the A site with T2 = 9.5 ms was faster than the experimental curve. Thus, neither A nor E could reproduce the experimental data at 16.1 ppm. These inconsistencies imply that the spin density corresponding to the structure at 16.1 ppm is higher and lower than those at the E and A sites, respectively. In the NMR experiment, revising the atomic coordinates for only 1 site among the 5 sites in the 107 helix is difficult. Consequently, we simply obtained a corresponding DQ curve by averaging the DQ curves simulated at the A and E sites with T2 = 9.5 ms (black curve) instead of either A or E; D

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Figure 3. (a) 13C SQ (top) and DQ (bottom) NMR spectra of the solution-grown α crystals (from the 0.05 wt % solution) of 30% 13C CH3-labeled PLLA formed at Tc = 90 °C. (b) Illustration of an 11-spin system in the seven-stem clusters where the A site in the center stem circled by dashed line was chosen as a reference spin site. The black colored spins represent the intrachain interaction, and the red colored spins represent the interchain interaction at the A site at a distance within 6.2 Å. (c) Distribution of the internuclear distances from the A−E sites of the PLLA 107 helix to the close spins at a distance within 6.2 Å on the basis of the reported atomic coordinates of the α crystals.60 The filled black represents the intrastem 13C−13C internuclear distance between close CH3 carbons. (d) Simulated DQ buildup curves at the A−E sites with T2 = 9.5 ms. (e) DQ buildup curves of the single crystals of 30% 13C CH3-labeled PLLA formed at Tc = 90 °C at 16.1 ppm (black open circle) and 17.4 ppm (red); the calculated curves, which are the average of the simulated curves at the A and E sites and at the A−D sites with T2 = 9.5 ms; the simulated curves at the A (green) and E (purple) sites with T2 = 9.5 ms.

Figure 4. DQ buildup curves of 13C CH3-labeled PLLA blended with nonlabeled PLLA at a mixing ratio of 1:9 in crystals formed from the 0.05 wt % solution at 90 °C at (a) 16.1 and (b) 17.4 ppm. The calculated DQ curves were obtained by averaging the DQ curves simulated at (a) the A and E sites and (b) the A−D sites and were plotted as a function of the spin number included in the simulation.

corresponding DQ curves. Thus, simulated DQ curves based on various chain-folding models were used to explore possible chain-folding patterns in the single crystals. First, the isolated stem model, which is a major component of the switchboard,73 random re-entry,74 and solidification models,75 was tested (Scheme 1c). In this model, the dipolar interactions within the same stem dominate the DQ curves. Because of the absence of strong dipolar interactions between neighboring stems, dipolar interactions originating from longer internuclear distances up to 9.0 Å were considered. Figures 4a and 4b depict the simulated DQ buildup curves at 16.1 and 17.4 ppm, respectively, as a function of intrastem spin numbers of 3 up to 5.3 Å, 5 up to 7.9 Å, and 7 up to 9.0 Å. With increasing the spin number from 3 to 5, the calculated ξmax

the resulting curve could reproduce the experimental curve at 16.1 ppm. Notably, such an averaging procedure was conducted in chain-folding analysis. 4.3. Chain-Folding Models in PLLA Solution Crystallization. To understand the chain-folding structure, the 13C CH3-labeled PLLA chains were blended with nonlabeled ones with a mixing ratio of 1:9. The experimental DQ buildup curves at 17.4 and 16.1 ppm yielded ξmax = 0.18 and 0.15, respectively, at τex = 7.84 ms, as shown in Figure 4a,b, and showed a large decrease in ξmax values compared to those in pure 13C-labeled PLLA, indicating that the 13C-labeled and nonlabeled chains are cocrystallized at the stem levels, even at a very high Tc, and that the chain trajectory of the 13C-labeled chains diluted in the nonlabeled chain matrix determines the 13C spin topology and E

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Figure 5. (a) PLLA linear folding model along (110) and possible interacting spin systems, including the reference A spin at the center stem circled by the dashed line and two intrastem spins (black) and three interstem spins (red) at distances within 6.2 Å. (b) Distribution of the internuclear distances from the 13C spins at the A−E sites of the center stem circled by the dashed line to the surrounding 13C spins within 6.2 Å. The DQ experimental buildup curves (black open circles) for the 13C CH3-labeled PLLA chains in the single blended with nonlabeled PLLA in single crystals formed at Tc = 90 °C from a dilute AA solution (0.05 wt %) at 16.1 (c) and 17.4 ppm (d) and simulated curves averaged at the A and E sites (c) and A−D sites (d) were plotted as a function of ⟨n⟩ based on ⟨F⟩ = 100%.

obtained by averaging the ξmax values at the A and E sites increases slightly from 0.08 to 0.09 and 0.09 to 0.1 at the A−D sites. However, the additional two spins at 9.0 Å do not influence the DQ curves. Thereby, a five-spin system at a distance up to 7.9 Å was used to generate the DQ curves for the isolated stem model. The simulated curves are substantially lower than the experimental curves. Thus, the isolated stem model was rejected as the major structure. According to the secondary nucleation theory, the linear chain-folding pattern is expected to be the major chain-folding structure in the PLLA single crystals.42−44 One model along (110) is depicted in Figure 5a. Under the cutoff distance of 6.2 Å, this model generates either 5- or 6-spin systems at the A−E sites. The distribution histograms of internuclear distances from the reference spins at the A−E sites in the chain folding along (110) are summarized in Figure 5b. For the A site, 6-spin systems, including a reference spin colored by green and 5 surrounding spins (3 interstem spins and 2 intrastem spins colored by red and black, respectively) are illustrated in Figure 5a. The DQ buildup curves for the linear chain-folding model along (110) were simulated by averaging the curves at the A and E sites and A−D sites as a function of ⟨n⟩ assuming that ⟨F⟩ = 100%. Considering the symmetry of chain-folding structure and spin networks, DQ curves for the chain-folding structure along (1−10) were also calculated. The DQ buildup curve averaged for the two chain-folding patterns along

different directions are shown as solid curves in Figure 5c,d. As the ⟨n⟩ value increases up to 16, the heights of the DQ curves increase. However, even under the assumption of a full adjacent re-entry structure (⟨n⟩ = 16 and ⟨F⟩ = 100%), the simulated curves are much lower than the experimental curves. This comparison indicates that the simple linear folding pattern is not the major chain-folding structure in the PLLA single crystals. To replicate the experimental DQ curves, a chain-folding model with higher spin densities than those in the linear adjacent re-entry structure is necessary. Thereby, a multiple rows model was applied. For simplicity, a two rows model consisting of eight stems, as illustrated in Figure 6a, was used, where the 13C spins experience different spin networks depending on their locations: The inner spins in the two rows model interact with a larger number of spins than those in the single rows but similar to the number with which those in the packing structure interact. By contrast, the outer spins could be treated the same as those in the single-layer folding model. At the inner sites, distributions of internuclear distances at the A−E sites are represented as shown in Figure 6b. For example, a reference spin at the inner A site of the one stem circled by the dashed red line in Figure 6a spatially interacts with five interstem spins colored red in addition to two intrastem ones colored by black at distances within 6.2 Å. Compared to the single layer, higher spin density results in faster and higher DQ F

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Figure 6. (a) PLLA bilayer folding model including eight stems (⟨n⟩ = 7) closed by a lozenge box and one possible spin system that includes the reference A spin of one stem circled by a dashed line in addition to two intrastem spins (black) and five red colored interstem spins (red). (b) Distribution of the internuclear distances from the A, B, C, D, and E sites to the 13C neighboring spins at distances within 6.2 Å. Experimental DQ buildup curve for 13C−CH3-labeled PLLA blended with nonlabeled chains in single crystals formed from a 0.05 wt % AA solution at Tc = 90 °C (open circles in c and d) and simulated curves corresponding to the A and E sites (c) and A−D sites (d) as a function of ⟨n⟩ based on ⟨F⟩ = 100%.

buildup behavior (Figure 6c,d). Assuming ⟨F⟩ = 100%, the simulated curves at ⟨n⟩ = 7 could well reproduce the experimental data at both sites. Considering ⟨nmax⟩ = 16, the best-fit curve with ⟨n⟩ = 7 and ⟨F⟩ = 100% indicates that each PLLA chain participates in two clusters consisting of adjacent re-entry structures, where each cluster includes eight stems, as depicted in Figure 6a. Another model can also reproduce the experimental data. We considered the heterogeneous limit model, where it was assumed that the folded chains adopt a full adjacent re-entry ⟨n⟩ = 16 and the remaining chains (1 − ⟨F⟩) adopt an isolated stem structure (⟨n⟩ = 0). Under the assumptions of a double rows cluster, the simulated DQ curves together with the experimental results were plotted as a function of ⟨F⟩ (Figure 7a,b), and the curves corresponding to ⟨F⟩ = 90% could reproduce the experimental data at both 16.4 and 17.1 ppm. Moreover, additional rows were also considered. For example, in a quadruple rows model, the simulated curve based on curves ⟨n⟩ = 16 and ⟨F⟩ = 80% could reproduce the data (Figure S1). Because the current ⟨Mw⟩ is relatively small, the quadruple layers model provides the lowest ⟨F⟩ value. Thus, it is concluded that 80 ≤ ⟨F⟩ ≤ 90% is possible range under the assumption of the heterogeneous limit. The other possibility is the combination of the single row and the multiple rows models, where it was assumed that all chains participate in the adjacent re-entry structure (⟨n⟩ = 16

and ⟨F⟩ = 100%), and the fraction of multiple rows ⟨f⟩ was varied. In the mixed model with the double rows, ⟨f⟩ = 70% could reproduce the experimental data at both 16.1 and 17.4 ppm. With the quadruple rows, ⟨f⟩ = 60% replicated the experimental data (Figure S2). Various models, including (i) the sole multiple rows model and (ii) mixtures of the single and multiple rows models, could reproduce the experimental data. The important finding is that even with a low ⟨Mw⟩ (only nmax = 16), PLLA chains occupy multiple rows in the facet single crystals formed in dilute solution under low ΔT. 4.4. Kinetics Effects on Chain-Folding Pattern. To understand kinetics effects on the structural formation of PLLA crystals at the molecular scale, the chain-folding structure of PLLA in crystals formed at Tc = 50 and ∼0 °C was investigated using the DQ approach. Figure 8a shows the DQ buildup curves for the 13C-labeled PLLA chains blended with nonlabeled chains in single crystals formed at Tc = 50 (open square) and ∼0 °C (cross) at 17.4 ppm (red) and 16.1 ppm (black). Surprisingly, the experimental curves at Tc = 50 °C were highly consistent with those at Tc = ∼0 °C as well as those at 90 °C. The simulated solid curves used in the analysis of the DQ curves at Tc = 90 °C (Figure 6c,d) are depicted in Figure 8a and could well reproduce the experimental data at Tc = 50 and ∼0 °C. As ΔT increases, crystallization might occur before the temperature reaches ∼0 °C. Thus, we instead prepared solution crystals by pouring a hot dissolved solution at 130 °C G

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Figure 7. Experimental DQ buildup curves for the 13C CH3-labeled PLLA chains (open circles) blended with nonlabeled PLLA in single crystals grown from the 0.05 wt % AA solution at 90 °C at 16.1 ppm (a, c) and 17.4 ppm (b, d). The DQ simulation curves for the mixture of the isolated chains and bilayer folding model with ⟨nmax⟩ = 16 at the A and E sites (a) and the A−D sites (b) are plotted as a function of ⟨F⟩. The simulation curve for the mixture model of single and double row folding structures at the A and E sites (c) and A−D sites (d) are plotted as a function of the double row fraction, ⟨f⟩ assuming that ⟨nmax⟩ = 16 and ⟨F⟩ = 100%.

Figure 8. Experimental DQ buildup curve for 13C CH3-labeled PLLA blended with nonlabeled PLLA in single crystals formed (a) from the 0.05 wt % AA solution at Tc = 50 (open squares) and ∼0 (cross) °C and (b) from the 0.005 wt % AA solution at Tc = 90 °C (open circle). The black (A and E sites) and red (A−D sites) solid curves in (a) and (b) were calculated based on ⟨n⟩ = 7 and ⟨F⟩ = 100%.

into excess cold solvent preset at 0 °C. Slowly pouring the hot solution into excess cold solvent led to immediate crystallization at the cold liquid/hot liquid interface. DQ buildup curves of the 13C-labeled PLLA samples prepared by the pouring method were almost consistent with those isothermally crystallized at Tc = 90, 50, and ∼0 °C (see Figure S3). These results indicate that the experimentally accessible kinetics do not influence the chain-folding patterns of PLLA, even though the crystal habits were significantly affected. These results are highly consistent with recent results obtained for iPB1 with a low ⟨Mw⟩ = 37K g/mol.16

formation of three-dimensional baby nuclei driven by prefolding in solution state.20,21 To distinguish primary nucleation from secondary nucleation, very low ΔT and very dilute solutions were tested: the ΔT = 40 °C and polymer concentration of 0.05 wt % used in this study are much lower and more dilute than the previous conditions of ΔT = 60−110 °C and polymer concentration of 0.2−1.0 wt % in early NS works29,30,35,36,38−41 and comparable to our recent conditions.47−49 Nevertheless, our crystallization conditions still being insufficient to reach regime I may be a concern. However, crystallization from AA solution did not occur at Tc = 95 °C or higher. Thus, the temperature was not further varied. Another parameter that can control kinetics is polymer concentration.18 Therefore, we further lowered the polymer concentration to 0.005 wt % and then crystallized PLLA single crystals from this extremely dilute solution at 90 °C. The DQ buildup curves of the 13C CH3-labeled PLLA blended with nonlabeled PLLA in single crystals prepared from the 0.005 wt % AA solution at 90 °C are shown in Figure 8b and are highly consistent with those of the blended PLLA in

5. DISCUSSION 5.1. Crystallization Mechanism. According to the LH theory,17−19 chain-folding patterns would be expected to highly depend on kinetics. For example, regime I would lead to an adjacent re-entry structure in a single row along the growth front, whereas regime III might result in a less adjacent re-entry sequence. Conversely, primary nucleation might induce the H

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Figure 9. Schematic illustrations of the crystallization process of PLLA in dilute solution, including the prefolding of three-dimensional baby nuclei via intramolecular interactions and aggregation process of baby nuclei to form different morphologies via intermolecular interactions.

α′ packing.76 The striking differences in packing selections between solution- and melt-grown crystals are interesting. To further discuss kinetic effects on packing selections in the meltgrown crystals, chain-folding analysis of the melt-grown crystals is necessary. We are currently undertaking such experiments on melt-grown crystals, and the results will be reported elsewhere in the near future. After baby cluster formation (primary nucleation), the secondary step is the aggregation of individual clusters via intermolecular nucleation and growth (Figure 9). Under low ΔT, aggregations of baby nuclei induce well-ordered α-packing structure in a regular fashion and consequently leads to facet growth fronts along the (110) plane. At such a high Tc, secondary nucleation may induce an adjacent re-entry structure in single rows. With increasing ΔT, primary nucleation would predominantly induce the formation of baby nuclei. Although a kinetically dominant aggregation process still selects the ordered packing structure at the interface between baby nuclei, it also leads to steps on the growth front. The increased number of steps during the aggregation process leads to dendritic or circular morphology. This kinetics concept is similar to the LH theory.17−19 However, the structural unit of PLLA and iPB113,16 crystallization in dilute solutions is a “stem cluster”, which is much larger than the “stem” that was considered to be the structural unit in polymer crystallization in the LH theory.17−19 The formation of stem clusters process may depend on molecular weight and kinetics. Thereby, chainfolding analysis in PLLA as a function of different Mws will be a future subject in solution polymer crystallization.

single crystals prepared from the 0.05 wt % AA solution at the same and lower Tcs (Figure 6). Therefore, it is concluded that experimentally accessible low supercooling and varied concentrations in the dilute range do not influence the chain-level structure of PLLA with ⟨Mw⟩ = 47K g/mol in single crystals, where the PLLA chains adopt an adjacent re-entry structure in either multiple rows or mixed models of single and multiple layers. In the latter case, 60−70% of the chains adopt an adjacent re-entry structure in the multiple rows based on the assumption of a complete adjacent re-entry structure (⟨n⟩ = 16 and ⟨F⟩ = 100%). Because of the very low ΔT = 40 °C, extremely low polymer concentrations (0.05−0.005 wt %), and small nmax of 16, the induction an adjacent re-entry structure in the multiple rows in the single crystals by secondary nucleation would be very difficult. Naturally, primary nucleation is considered to bring about this multiple rows structure in dilute solution. However, a linear chain-folding structure induced by secondary nucleation cannot be excluded. In fact, mixed models suggest that 30−40% of the chains may be able to adopt an adjacent re-entry structure in a single row. This molecular perspective on mixed models of the chain-folding structure was predicted by Muthukumar and Liu.24 Another interesting feature is the independence of ΔT from the DQ buildup curves, indicating that the PLLA chains prefer well-folded adjacent re-entry structures, even under rapid and deep quenching conditions. This result convincingly shows that the structural units in polymer crystals are not “stems” but “stem clusters”. Similar results were obtained in the context of iPB1 solution-grown crystals.13,16,51 The combined structural results of the chain-folding pattern, molecular packing structure, and crystal morphology together provide new insights into the polymer crystallization process. Initially, primary nucleation yields three-dimensional baby nuclei consisting of a stem number of 8−17 (Figure 9). The initial formation of the baby nuclei may be related to solvent− polymer interactions as the temperature is lowered down to Tc, where the solvent property changes from good to poor, thus enabling polymer chains to expel solvent molecules and collapse via intramolecular interactions. Such a single chain event would accompany the chain-folding process, which effectively lowers the surface free energy. Single clusters comprise 8−17 stems, the sizes of which are larger than the size in the unit cell and are invariant under varied kinetics. Thereby, it is naturally considered that the Tc independence of the sizes of the folded stem clusters results in the α packing structure inside of individual baby nuclei. Conversely, the packing structure of PLLA in the melt-grown crystals shows a strong Tc dependence: Tc ≥ 120 °C leads to stable α packing, whereas Tc ≤ 90 °C leads to kinetically driven

6. CONCLUSION The chain-folding structure, packing structure, and crystal habits of PLLA in solution-grown crystals were systematically studied by varying the supercooling and polymer concentration in the dilute solution range. Crystal morphology varied from a facet lozenge shape at Tc = 90 °C to dendrites at ∼0 °C, while the packing structure adopts the stable α form at both Tcs. Sharp contrasts in kinetics effects on structures at different length scales were further explored by investigating the chainfolding patterns using the 13C−13C DQ approach. 13C CH3labeled PLLA chains were found to fold adjacently and occupy multiple rows in dilute solution in the concentration range of 0.005−0.05 wt % and Tc range of 90 to ∼0 °C. The results evidently indicate that polymer concentrations and experimentally accessible supercooling do not influence the chainfolding structure of the relatively short PLLA chains (⟨Mw⟩ = 46K g/mol) in dilute AA solution. The results support the chain-folding mechanism being dominated via self-folding (primary nucleation). Long-range order in chain-folding I

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Macromolecules patterns induces the formation of stable α crystals within the baby nuclei in the first stage. In the second stage, the aggregation process of the baby nuclei dominantly selects the thermodynamically stable packing structure, even under varied kinetics. However, amplification of kinetics effects on the aggregation process of nanoclusters (secondary nucleation and growth) leads to steps at the growth front and dendrite shape at the micrometer scale under large supercooling.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01462.

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Figures S1−S3 (PDF)

AUTHOR INFORMATION

Corresponding Author

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

Wei Chen: 0000-0001-8334-0024 Toshikazu Miyoshi: 0000-0001-8344-9687 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This study was financially supported by the National Science Foundation (Grant DMR-1408855) and Japan Society for the Promotion of Science (P16047).

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