Effects of Chemical Modification on the Molecular Dynamics of

Aug 26, 2013 - Two-dimensional 1H–13C wide-line separation (WISE) NMR spectra of three samples demonstrated that the PEG chains provide two componen...
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Effects of Chemical Modification on the Molecular Dynamics of Complex Polyrotaxanes Investigated by Solid-State NMR Chuan Tang,† Aoi Inomata,‡ Yasuhiro Sakai,‡ Hideaki Yokoyama,‡ Toshikazu Miyoshi,*,† and Kohzo Ito‡ †

Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States Department of Advanced Materials Science, Graduate School of Frontier Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan

‡

ABSTRACT: The chemical modification of the pendant hydroxyl functional groups on cyclodextrins (CDs) significantly suppresses the hydrogen-bonding interactions between the cyclodextrin molecules and leads to the unique viscoelastic properties of hydroxypropylated polyrotaxane (HyPR) [Inomata et al. Macromolecules 2010, 43, 4660−4666]. HyPR consists of poly(ethylene glycol) (PEG) and α-CDs that are partially modified with a hydroxypropyl (Hy) group, setting them apart from other polyrotaxanes (PRs). The molecular dynamics of PR and HyPR with 25% (HyPR25) and 78% (HyPR78) modification ratios were investigated using various solid-state NMR techniques. Two-dimensional 1H−13C wideline separation (WISE) NMR spectra of three samples demonstrated that the PEG chains provide two components of the restricted and the near-isotropic components in a fast motion limit at 329 K. The fraction of restricted dynamics of the threaded PEG chains was found to depend on the chemical modification ratio. In addition, WISE experiments proved that the CD side chains exhibit enhanced mobility when the modification fraction is increased. Centerband-only detection of exchange (CODEX) NMR was used to characterize the slow dynamics of both CD and PEG molecules with frequencies directly comparable to those used in viscoelastic measurements. The CD molecules undergo slow main-chain dynamics in HyPR78 in the mechanicalrelaxation temperature range, whereas the other two systems do not. The temperature dependence of the correlation time ⟨τc⟩ determined by CODEX revealed Arrhenius behavior with a high activation energy (163 ± 16 kJ/mol), which is consistent with the previous viscoelastic result. The high activation energy for the dynamics of the CDs was interpreted in terms of cooperative motions with the threading PEG chains. The dependence of the evolution time of the CODEX data and simulation results indicated that the CD dynamics match random-jump and uniaxial rotation diffusion models. These results indicate that chemical modifications of the side groups can dramatically affect not only the molecular dynamics of both the CD main and side chains but also the threading of PEG chains across wide time scales.

I. INTRODUCTION In the 1990s, Harada found that poly(ethylene glycol) (PEG) and cyclodextrins (CDs) generate unique complexes in water1 and subsequently capped both ends of this complex with bulky groups.2 These types of supramolecular complex, in which cyclic molecules are threaded on to a linear polymer capped with bulky end groups, are called polyrotaxanes (PRs). Since the publication of that initial report, the preparation, characterization, and application of PRs have been widely reported and are summarized in recent reviews.3−7 Numerous PRs with sophisticated structures have been developed. Although PRs consisting of other cyclic molecules can be successfully constructed,8−10 CDs are the most interesting. They are biocompatible, inexpensive, and readily available; CDs also have pendant functional groups that are amenable to further chemical or biological functionalization.11−13 The 18 hydroxyl groups of α-CDs can be substituted with various functional groups, such as methyl, hydroxypropyl, acetyl, or ethyl groups. Chemically modified CDs provide access to a series of PR © 2013 American Chemical Society

derivatives with unprecedented macroscopic properties, such as thermal reponsiveness,14,15 improved elasticity,16 photoresponsivity,17 and solubility in organic solvents;18 in addition, the chemical modifications allow further cross-linking. The crosslinking of PRs is a commercially promising technique. The cross-linked product, which is a novel material called slide-ring gel, provides unique mechanical properties that differ completely from those of conventional chemical gels.19 In recent years, the fundamental issues in PR and its derivatives, e.g., the molecular structure and dynamics of PR and its components, have garnered increasing research interest. The basic research on PR generates a deeper understanding of PR’s macroscopic properties within a microscopic view. Notably, Inomata et al. investigated the crystallinity and viscoelastic properties of PR and chemically modified PRs in Received: July 13, 2013 Revised: August 15, 2013 Published: August 26, 2013 6898

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the solid state.16 Their DSC and XRD results indicated that the chemical modification of CDs dramatically changes the crystallinity of the PR components. Without modification, the CDs in PR form a columnar crystalline structure, whereas the PEG guest is amorphous. However, the CDs with appended hydroxypropyl (Hy) groups in PR demonstrate more disordered arrangements, and the PEG guest becomes slightly crystalline. Dynamic mechanical analysis (DMA) results revealed that PR and hydroxypropylated PR (HyPR) with a lower modification ratio (25%) do not exhibit apparent relaxation over the experimental angular frequency (0.06−100 rad/s) at temperature range (303−403 K). In contrast, HyPRs with modification ratios greater than 38% clearly demonstrate a one-relaxation process in the same frequency and temperature ranges. In particular, HyPR with greater modification ratios (78%) have a 327 K relaxation temperature, which is 59 K lower than the PR with a low, 38% modification ratio. The relaxation process obeys a Williams−Landel−Ferry (WLF) temperature dependence. In addition, both PR and HyPR exhibit a low storage modulus (∼107 Pa) over the entire temperature range. Typical polymers in glassy states are known to exhibit storage moduli of approximately 109 Pa. The storage modulus is lower by 2 orders of magnitude, which is also one of the unique features of PR. Chemical modification affects the viscoelastic properties of PRs and HyPRs, which is intriguing. For researchers attempting to confirm the origin of these notable changes in macroscopic properties, the collection of detailed microscopic information is essential. Studies of how chemical modification affects molecular dynamics may provide information about solid-state PR systems and lead to the design of new classes of materials. Solid-state NMR spectroscopy is a versatile tool used to investigate the molecular dynamics of glassy and semicrystalline polymers20−26 as well as heterogeneous systems such as polymer blends27−29 and inclusion compounds.30−34 Solidstate NMR spectroscopy offers a variety of methods and spans a frequency range covering more than 10 orders of magnitude to enable the investigation of molecular motion. In particular, anisotropic interactions, such as 2H quadrupole interactions, chemical shift anisotropy (CSA), and homo- and heteronuclear dipole−dipole interactions provide detailed dynamic geometric and kinetic parameters.35,36 Beckham et al. investigated the molecular dynamics of deuterated PEG included in α-CD and the geometry of its motion using solid-state 2H NMR.32 Tonelli et al. have also studied the molecular dynamics of polycarbonate (PC),37 polycaprolactone (PCL),38 and block copolymers31,39 in α- and γ-CDs using various solid-state NMR techniques. Dipolar shift correlation NMR provides the geometry of the local motions of the benzene ring flip on the PC in CDs. WISE provides site-specific dynamics of PCL, both in CDs and in bulk. Recently, Miyoshi et al. indicated that the dynamic geometry of the PEG chains in supramolecules with UREA is highly restricted compared to the natural bulk dynamics in natural abuandance.33 Most of former NMR investigations have been focused on polymer dynamics threaded in host molecules. In this work, the molecular dynamics of both the PEG chain and CDs in chemically modified and unmodified PR systems are systematically investigated using several NMR techniques in natural abundance. 13C cross-polarization and magic angle spinning (CP/MAS) NMR identifies chemical modification effects on the CD side groups according to their different chemical shifts. WISE experiments prove that a dynamic

difference exists between the CDs and PEG chains and that dynamic heterogeneity exists in the PEG chains themselves; they also prove the effects of chemical modification on the sidechain dynamics. Finally, the centerband-only detection of exchange (CODEX) depicts a direct image of the geometric and kinetic parameters of CDs with and without chemical modifications. These investigations allow conclusions about how chemical modifications affect the molecular dynamics of CD and PEG molecules on various time scales to be drawn.

II. EXPERIMENTS AND MATERIALS Materials. PR and HyPRs were prepared using previously reported methods.12,40,41 The PRs consist of PEG with an average molecular weight (M̅ w) of 35 000 and α-CD with adamantylamine capping the end of the chain (Figure 1a). The HyPRs consist of PEG with an M̅ w

Figure 1. Chemical structures of (a) PR and (b) α-CD and hydroxypropylated α-CD. of 35 000 and chemically modified α-CDs functionalized with different amounts (25 and 78%, Table 1) of hydroxypropyl (Hy) groups (Figure 1b). The values describing the CD coverage were estimated from the 1H NMR spectra. The samples were dried under vacuum at 323 K.

Table 1. Chemical Structures of PR and HyPRs samples

M̅ w (PEG) (g/mol)

coveragea (%)

functional group (−R)

modification ratiob (%)

PR HyPR25 HyPR78

35 000 35 000 35 000

28 28 21

H CH2CH(CH3)OH CH2CH(CH3)OH

0 25 78

a

Coverage = CD molecules per chain/maximum number of CD molecules per PEG chain assuming that two PEG repeat units are covered by one CD molecule at most. bModification ratio determined by solution-state 1H NMR. Solid-State NMR. All experiments were performed with a Bruker Avance III 300 NMR spectrometer (Bruker Biospin; Rheinstetten, Germany). The 1H and 13C frequencies were 300.1 and 75.5 MHz, respectively. CP/MAS and 1H−13C wide-line separation (WISE) experiments were performed using a 4 mm double resonance CP/ MAS NMR probe and a 6000 ± 3 Hz MAS frequency. The CP time was 200 μs for the WISE experiments and 1.5 ms for all other experiments. The recycle delay was 2 s. 1H two-pulse phase modulation (TPPM) decoupling with a 60 kHz field strength was applied during 13C signal acquisition. The WISE NMR experiments were performed using time-proportional phase incrementation (TPPI)42,43 in the t1 dimension with 512 scans. A total of 128 sampling points at 10 μs increments along t1 were obtained. To analyze the main and side chains of the CDs, the time domain size along t1 was truncated to 32. The proton chemical shifts were externally referenced to the CH signal of adamantine (29.5 ppm). The temperature inside the NMR probe was calibrated using the 207Pb chemical shift from Pb(NO3)2.44 Spectra analysis was performed using the Igor Pro 6.0 software package (Wavemetrics). 6899

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The CODEX experiments were performed using a 7 mm probe with a 4000 ± 3 Hz MAS spinning frequency. The 90° pulse lengths for the 1H and 13C channels were 4 and 3.75 μs, respectively. During the CODEX experiments, the chemical shift anisotropy (CSA) was recoupled by applying rotor-synchronized 180° pulses at every half rotor period (1/2tr). In the pulse sequence (Figure 2) used to obtain

Figure 2. Pulse sequence of the CODEX experiments. exchange spectrum S, the mixing time tm was sandwiched between two evolution periods. The magnetization evolved under the recoupled CSA during the first evolution time. The magnetization was then stored using a 90° pulse along the z-direction. If no reorientations of CSA occurred during tm, magnetization evolved under the same CSA orientation during the second evolution time and was completely refocused, resulting in a lack of signal decay. When a reorientation dynamics process occurred during tm, the magnetic dephasing led to signal decay. In addition to the molecular reorientation dynamics, T1 and T2 relaxations also resulted in signal decay. To remove the relaxation effect, a reference spectrum (S0) was necessary. We generated S0 by simply interchanging z filter time tz with tm in the exchange experiment. In our experiment, tz was set to one rotation period, tr. In the reference spectrum, only T1 and T2 relaxations, in addition to the pulse errors, contribute to the intensities. Therefore, the normalized ratio S/S0 includes only pure dynamic information used to characterize the correlation function and dynamic geometry; S/S0 was plotted as a function of tm and evolution time (Ntr). The dynamic geometry of the CDs was analyzed using custom-written FORTRAN software. For the axial symmetric tensor, the CODEX intensity was expressed as the reorientation angle βR weighted by distribution R(βR,tm)45 E(tm , δNtr) =

∫0

Figure 3. 13C CP/MAS NMR spectra of PR, HyPR25, and HyPR78 at 296 K and chemical structures and signal assignments of CD and HyCD.

at 19 and 66 ppm are assigned to the methyl (C9) and overlapped signals (C6,7,8) of the CH2 (C7 and C8) and CH (C6) groups, respectively, of the Hy groups. The PEG signals are not clearly observed in the spectra of PR and HyPR25; however, they are detected at 70 ppm in the spectrum of HyPR78. At ambient temperature, the 13C line widths of signals associated with the CDs in PR and HyPR samples are different. An increase in the chemical modification leads to 13C line broadening. For example, the line width of the C1 signals in PR, HyPR25, and HyPR78 are 100, 170, and 250 Hz, respectively. Among the three samples, only PR adopts hexagonal packing structures in the crystalline state. An increase in chemical disorder induces 13C line broadening for the CDs, which is attributed to the structural disorder of CDs caused by the interruption of intermolecular hydrogen bonding (see the discussion about motional broadening). Figure 4 presents the 13C CP/MAS NMR spectra of three samples at 329, 344, and 359 K. The 13C line widths of the CDs in PR and HyPR25 decrease slightly with increasing temperature. The line widths of the C1 signals are plotted in Figure 5a. For example, the line widths in PR are ca. 140 Hz at 296 K to 100 Hz at 359 K. This slight narrowing process is attributed to the fast side-chain dynamics of CDs. However, the 13C line widths of the CDs in HyPR78 exhibit broadening in the same temperature range. Specifically, the C1 line width increases from 240 Hz at 296 K to 350 Hz at 359 K. The observed line broadening is caused by the onset of molecular dynamics in the frequency of several 10 kHz. When a motional frequency approaches the 1H decoupling frequency (60 kHz in our case), interference between 1H decoupling and molecular dynamics occurs, leading to maximum broadening.27 Dynamics that are faster than the decoupling lead to motional narrowing. Therefore, the motional frequency of CDs in HyPR78 is close to 60 kHz at 359 K. The methylene carbons on the side chains of all three samples narrow with increasing temperature (Figure 5b). At 273 K, their line widths are approximately 240−420 Hz, whereas they decrease to 90−150 Hz at 359 K. Of the three samples, HyPR78 clearly demonstrates the narrowing of the line width with increasing temperature, which is opposite to the broadening observed in the backbone signals. This result indicates that at least two dynamic processes occur in HyPR78 and that motional frequency of the side chain exceeds 60 kHz,

90 °

R(βR , tm)ε(δNtr ; βR ) dβR

ε(δNtr ; βR ) = 1 − cos(N

∫0

t r /2

(ω2(t ) − ω1(t )) dt )

(1) (2)

where the reorientation is described with a single reorientation angle βR between the unique principal axis before and after tm, ε(δNtr;βR) is the normalized exchange intensity for the reorientation angle βR with a powder average and anisotropy parameter δ = σ33 − σiso, and ω1(t) and ω2(t) are the orientation-dependent 13C frequencies before and after molecular motion (the difference in their frequencies is related to the difference chemical shift tensor ωΔij ).

III. RESULTS 13 C CP/MAS NMR Spectra. Figure 3 presents the 13C CP/ MAS spectra of the PR, HyPR25, and HyPR78 samples at 296 K. The signal assignments are based on those in previous reports.4,46 The signals at approximately 101 and 82 ppm are attributed to the CD backbone carbons (C1 and C4) connected to the linking oxygen atoms, respectively. The other backbone signals (C2, C3, and C5) are assigned to one overlapped resonance between 67 and 78 ppm (C2,3,5). The resonance signal between 58 and 65 ppm is attributed to the methylene groups on the unmodified pendant side chain, C6. With increasing chemical modification ratios, new signals appear at approximately 19 and 66 ppm, and the intensities of these two signals increase relative to the modification ratio. Correspondingly, the intensity of C6 decreases. The newly observed signals 6900

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Figure 4. 13C CP/MAS NMR spectra of (a) PR, (b) HyPR25, and (c) HyPR78 at 329, 344, and 359 K.

Figure 5. Temperature dependence of 13C line widths for (a) the backbone (C1 signal) of all three samples as well as for (b) the unmodified side chain (C6) for PR (black open circle) and HyPR25 (orange) and the modified side chain (C6,7,8) for HyPR25 (red) and HyPR78 (green).

Figure 6. 1H WISE slice spectra of the backbone and side chains of CDs and PEG chains in (a) PR, (b) HyPR25, and (c) HyPR78 at 329 K.

ca. Tg + 30 K.27 In the spectra of all three samples, the line widths of PEG remain almost constant at 329−359 K. The consistently narrow line widths indicate that the PEG dynamics reach the fast motional limit (⟨τc⟩ < 10−5 s) at 329 K. 1 H−13C WISE Spectra. In the spectra of organic polymers, the 1H full-line-width at half-height (flwhh) is typically limited to ca. 40−60 kHz depending on the 1H density. When the motional frequency exceeds the static line width, the 1H line width narrows relative to the dynamic geometry. The WISE spectra qualitatively provide site-specific information about the molecular dynamics in complex molecules when the 13C signals are highly resolved. In complex molecules, different 1H spins interact with each other via dipole−dipole interactions. This interaction leads to 1H spin diffusion, which averages the intrinsic 1H line widths of different molecules and functional

even at 276 K. The narrowing of the side-chain and backbone signals in the spectra of PR and HyPR25 also imply the existence of rapid side-chain dynamics. These dynamics will be validated by the WISE experiments. The 13C signals from the PEG in all the three samples overlap with the CD backbone resonances at temperatures less than 313 K and subsequently resolve at temperatures greater than 329 K. Earlier DSC measurements indicated that the PEG in PR adopts an amorphous structure with very low crystallinity in HyPR, with a melting range of 323−333 K. The observed narrow component corresponds to the amorphous/melt states.47 The reported glass-transition temperature (Tg) of pure amorphous PEG is 158−200 K.47 For a low Tg, the 13C line width exhibits maximum broadening at 188−238 K because typical polymers exhibit 13C maximum broadening at 6901

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Figure 7. CODEX exchange spectra (S), reference spectra (S0), and difference spectra (S0 − S) of (a) PR, (b) HyPR25, and (c) HyPR78 with tm = 200 ms and Ntr = 1.50 ms at 337 K.

dynamic heterogeneity. The second possible explanation is that the 1H line shapes overlap in the CDs with broad line widths caused by the incomplete separation of their 13C signals. Third, the spin diffusion process transfers the polarization from the 1H spins of rigid CD molecules to the 1H spins of the more flexible PEG. Even within the same molecule, the side and main chains on the CDs in HyPR exhibit vastly different 1H line widths. Therefore, intermolecular spin diffusion between the highly mobile PEG and the CDs is unlikely. In addition, in the spectrum of PR, the broad portions of the PEG chains’ 1H line shapes (22.4 kHz) are much narrower than the analogous line shapes of the signals associated with the CD backbone (43 kHz). Furthermore, the 1H signal of PEG exhibits a Lorentzian shape, which is quite different from the Gaussian shape of the CD main chain. Therefore, the second and third possibilities are excluded as the main sources of broadening. Similar discussions can be extrapolated to HyPR25 and 78. Therefore, dynamic heterogeneity exists within the PEG chains in the PR and HyPR systems. This conclusion is supported by the results of a recent 2H NMR investigation by Beckham et al., who investigated the detailed molecular dynamics of the threaded PEG chains in pseudo PR using CDs (coverage ratio of 83%).32 The 2H line shape of PEG in the pseudo PR exhibited two components: a partially averaged Pake-type line shape and an isotropic single peak at temperatures greater than 290 K. The partially averaged line shape was assigned to the threaded PEG chains, which undergo trans−gauche conformational changes in limited space with a rapid motional limit (⟨τc⟩ < 10−5); meanwhile, the isotropic component is attributed to the uncovered region. Notably, the apparently rigid portions of the PEG chains assigned by the WISE data are much larger than the actual coverage ratios (28 and 21%). This large discrepancy originates from the CP efficiency. Nearly isotropic dynamics lead to a lower CP efficiency than do anisotropic dynamics. Therefore, the CP step largely enhances the apparently restricted components in their dynamic geometry. In HyPR systems, even a modification ratio of 25% reduces both fractions as well as the 1H line width of the broad component of PEG. The modification’s effect on the molecular dynamics of the PEG chains is more clearly observed in the spectrum of HyPR78, even though the coverage ratio (21%) is slightly lower than the other two (28%). According to the observed 1H line widths of the CDs and PEG relative to the modification ratio, the degree of interruption to the hydrogen bonding of the CDs significantly influences the molecular dynamics of the CDs and threaded PEG chains.

groups when the CP time is increased. Several ways to quench spin diffusions, including WIM-24,48 off-resonance CP using the Lee−Goldburg sequence,49 and short CP,50 have been developed. In this work, a short CP (200 μs) was applied to suppress the spin-diffusion effects. Figure 6 presents the 1H slice data of the two-dimensional 1 H−13C WISE spectra of PR, HyPR25, and HyPR78 at 329 K. The different molecules and different functional groups within the CD provide characteristic 1H line shapes and widths. For the CD backbone, the 1H line widths through C1 are 43.9, 40.7, and 38.4 kHz for PR, HyPR25, and HyPR78, respectively. The 1 H line width decreases with increasing modification ratios. The observed reductions are attributed to the motion of the CD backbone and/or dynamics of the spatially close lateral groups. The 13C line widths of PR and HyPR25 reveal small reductions when the temperature is increased to 359 K. Therefore, dynamics with frequencies close to or greater than ca. 50 kHz are absent from PR and HyPR25. In addition, the side groups in PR exhibit a 33 kHz 1H line width. After chemical modification, the 1H line widths of the modified and unmodified side groups are 25.0 and 36.9 kHz, respectively, for HyPR25. For HyPR78, only the modified signals exhibit a highly narrowed 1H line width (14.2 kHz). An increase in the degree of chemical modification causes the lateral groups to become highly mobile, which is direct evidence for the interruption of the hydrogen bonding in CDs. This enhanced mobility reduces the long-range coupling between the 1H spins in the backbone and those in the side chain. For HyPR78, the backbone dynamics are also confirmed by the 13C motional broadening at temperatures greater than 329 K. Therefore, the side-chain dynamics are the major cause of the reduced 1H line widths in the CD backbones of HyPR25 and HyPR78. The 1H line shapes of the PEG signals in the spectrum of PR clearly reveal two components. The narrowed line widths of the PEG signals in the spectra of PR, HyPR25, and 78 are 1.9, 2.0, and 1.2 kHz, respectively. The narrowed line width is almost invariable, even when the chemical modification ratios are changed. However, the broad line widths in the spectra of PR, HyPR25, and 78 are 22.4, 18.1, and 13.1 kHz, respectively. The fractions of the broad components are 92, 78, and 48% for PR, HyPR25, and 78, respectively. The narrowed line shape is attributed to the nearly isotropic motions of the PEG chains in PR and HyPR. The broad components of the PEG line shape can be explained several ways. The constrained dynamic geometry of the PEG molecules is one possibility. The PEG chains are covered by CDs with ratios of 28 and 21%. Therefore, structural heterogeneity may reasonably explain 6902

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Figure 8. Temperature dependence of the ΔS/S0 intensity ratios of the backbone (C2,3,5, filled circles) as well as the modified (open circles) and unmodified side chains (open squares) (C6,7,8) of the CDs in (a) PR, (b) HyPR25, and (c) HyPR78 with tm = 200 ms and Ntr = 1.5 ms.

Figure 9. (a) Temperature dependence of the CODEX tm dependence on the (S/S0) intensity ratios of the C2,3,5 signals in HyPR78 at various temperatures: 298 K (black filled circles), 314 K (blue circles), 329 K (green circles), 337 K (purple circles), and 344 K (red circles). (b) Arrhenius plot of ⟨τc⟩ obtained from the CODEX tm dependence experiments (filled circles) and former DMA (open red circles) as functions of temperature. The solid black and dashed red lines represent the best results, where the experimental data indicated an activation energy of 163 kJ/mol and were fitted with a WLF curve, respectively, with c1 = 18.1 and c2 = 117.0.16

ΔS/S0 values of less than 0.1 over the entire temperature range. For the side chains, some points give (ΔS/S0) ≈ 0.2 with large errors caused by the low intensities of the signals. The large errors induced the scattering of data from the side chains. Because of the noise levels and temperature independence of the (ΔS/S0) ratios, the observed small reductions of (S/S0) are not attributed to molecular dynamics; they are instead ascribed to the spin-diffusion effects at natural abundance. Spin-diffusion effects have been similarly observed in polymer systems at natural abundance.24 However, the ΔS/S0 intensities for both the main- and side-chain signals in HyPR78 are strongly dependent upon the temperature. For the C2,3,5 signal, the ΔS/ S0 intensity reaches its maximum of 0.6 at 344 K. For the side chain, the intensity ratio reaches a maximum of 0.32 at 329 K. Differences between the CODEX (S/S0) ratios of the backbone and side-chain signals are attributed to the motional average of the CSA size of the lateral group. The side-chain signals are influenced by both overall and lateral dynamics. According to the 1H line shapes, the dynamics of the lateral group are much faster than the overall dynamics. Specifically, the fast side-chain dynamics partially averages the CSA size of the side-chain carbons to reach a certain size in the current temperature range. Only motions that are overall slow can be probed via partially averaged CSA of the side chains. The small anisotropy leads to a small reduction in the CODEX intensity at one fixed Ntr. Additionally, the tm dependence of the (S/S0) intensity ratios of the CDs in HyPR78 was investigated. Figure 9a presents the tm dependence for the (S/S0) intensity ratios of the C2,3,5 signals from HyPR78 at different temperatures. The tm dependence for the (S/S0) ratios was analyzed using the equation (S/S0) = 1 − a exp(−(tmix/⟨τc⟩)β), where a is related to the available number

Slow Dynamics of CD in HyPR78. In the earlier DMA work with PR and HyPR, tan δ was investigated in the angular frequency range of 10−2−102 rad/s.16 One- and two-dimensional exchange NMR51 is a powerful tool for analyzing the dynamic geometries and kinetic parameters in the slow dynamic range (10−3−102 s).24,52,53 Among the various techniques, CODEX is a versatile tool for evaluating the slow dynamics of complex molecules at the atomic level in natural abundance. Figures 7a−c display the 13C CODEX exchange (S), reference (S0), and difference spectra (S0 − S) for the PR, HyPR25, and HyPR78 samples, respectively, with a tm of 200 ms and a Ntr of 1.50 ms at 337 K. As previously mentioned, the PEG dynamics are very fast at 329 K (⟨τc⟩ < 10−5 s). All of the difference spectra indicate the absence of slow dynamics for the PEG chains within 200 ms at 337 K. For PR and HyPR25, the difference spectra for both the CD main- and side-chain components exhibited signal intensities less than 10% of those in S0. However, the difference spectrum of HyPR78 exhibits features that differ substantially from the spectra of PR and HyPR25. All of the CD signals clearly demonstrate significant intensities in the difference spectra. For example, the C2,3,5, signals in the main chain and C6,7,8 ones in the modified side chain give a ΔS/S0 of approximately 0.6 and 0.3, respectively. The CODEX experiments were performed using a temperature range from 286 to 359 K. Figure 8 illustrates the normalized exchange intensity ΔS/S0 as a function of temperature, where the C2,3,5 and C6,7,8 peaks were used as the main-chain and side-chain signals, respectively. In the spectra of PR and HyPR25, the CD main-chain signals exhibit 6903

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Figure 10. (a) Ntr dependence of CODEX (S/S0) intensities of C2,3,5 (filled circles) with a tm of 200 ms at 337 K and a simulated average curve for C2,3,5 at various rotation angles (ψ) in a uniaxial rotation model. (b) Normalized Gaussian distribution of the rotation angle (ψ) with various widths σ = (2tm/⟨τc⟩)1/2 in a uniaxially rotational diffusion model. (c) Averaged simulated intensities of C2,3,5 under the assumptions of full (black line) and 70% (red line) participation in the dynamics of uniaxial rotational diffusion.

of sites p by the relation a = (p − 1)/(p) in the dynamic process, 0 < a ≤ 1, and β is the distribution width parameter, 0 < β ≤ 1. The solid red curve shows the best fit with the experimental data (red filled circles) at 344 K; the best-fit parameters are a = 0.70 ± 0.02, β = 0.50 ± 0.04, and ⟨τc⟩ = 22.1 ± 3.9 ms. In the crystalline region, molecules perform discrete jumping motions at conformationally determined finite sites, whereas the segmental motions related to the glass transition have infinite sites due to the continuous dynamics.36 Therefore, the infinitely available sites (a = 1.0) can be used for the CD dynamics in HyR78. The obtained apparent value of a at 0.7 means that 70% of the segments participate in the molecular dynamics within the CODEX dynamic window of tm = 1 s. Specifically, the dynamics of the remaining 30% of the CDs are much slower or faster than the dynamic window. The fitted distribution parameter (β = 0.50) corresponds to a distribution width of ca. 1.7 decades at the half-height of a log-Gaussian distribution.54 This wide distribution can reasonably explain the apparent value of a in the limited dynamic window. At lower temperatures, the plateau value was not obtained within the available tm up to 1 s. Assuming that a = 0.7, we obtained the ⟨τc⟩ values at the lower temperatures, which are plotted in Figure 9b. The temperature dependence of the ⟨τc⟩ values (filled circles) simply follows an Arrhenius-type curve, with a best-fit activation energy of 163 ± 16 kJ/mol. In the recent DMA work with HyPR78, macroscopic relaxation was investigated in the temperature range from 324 to 349 K.16 The corresponding angular frequency (ω) ranged from 2.5 × 10−1 to 6.3 × 102 rad/s. Using a simple relationship of ⟨τc⟩ = 2π/ω, we determined the temperature dependence of ⟨τc⟩ (red open circles) obtained via the earlier DMA results; the results are also plotted in Figure 9b. At first, the DMA results appeared consistent with the current NMR data in that, at low temperatures, the discrepancy between the CODEX and DMA fitted lines becomes large. However, the maximum difference between DMA (⟨τc⟩ = 25.0 s) and NMR (⟨τc⟩ = 1.7 s) is approximately 1 order of magnitude at 323 K. These facts indicate that local dynamics probed by the NMR cause the macroscopic relaxation detected by DMA. The current NMR results clearly indicate that the CDs dynamics do not follow WLF-type relaxation but instead exhibit simple Arrhenius behavior in the case of HyPR78. The WLF behaviors observed in the previous DMA work can be attributed to the small dynamic window of the experiment. Dynamic Geometry of CD in HyPR78. The CODEX decay curve as a function of Ntr can probe the reorientational angles of molecular motions.45 Ntr dependence of the CODEX

(S/S0) intensity ratio of the C2,3,5 signals of HyPR78 is obtained with tm = 200 ms at 337 K and is shown in Figure 10. The (S/ S0) ratios (filled circles) gradually decay with increasing Ntr. To examine the dynamic effects on the decaying CODEX curve, three possible dynamic models of the CDs in HyPR78 are considered and illustrated in Figure 11. Figure 11a depicts the

Figure 11. Possible dynamics and reorientations of the CSA principal axes of the C5 carbon in HyPR78: (a) rotation around the PEG chain axis, (b) tilting of the CDs relative to the PEG axis, and (c) sliding of CDs along the PEG chains.

rotations of the CD molecules around the threaded PEG chain. Figures 11b and 11c illustrate the tilting motions of the CD rings relative to the PEG chain and the sliding motions along the PEG chains, respectively. If the chains adopt a straight, extended structure, simple sliding does not include the reorientation of the CDs relative to the magnetic field. However, real sliding motions along the PEG chains are not simple because the PEG chains undergo liquid-like motions: individual chains are not straight and adopt highly disordered conformations to perform conformational transitions. Therefore, the translations of the CD molecules accompany their reorientations along the threaded PEG chains. In actual simulations, it is difficult to treat all of the dynamics separately. Here, we utilize two different dynamics for simple rotations around the PEG chains and the combined dynamics of all three. The former is treated as a uniaxial rotation around the PEG chains. The latter is approximated using a random jump model. For the simulation, the principal values and the orientations of the shielding tensor of carbon during this study are necessary. The principal values of the shielding tensor of C2,3,5 are (σ11, σ22, σ33) = (91, 82, 45 ppm), which are obtained by separation of undistorted powder patterns with an effortless 6904

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recoupling (SUPER) experiment.55 The asymmetry parameter, η = (σ22 − σ11)/(σ33 − σiso), is 0.29 for the C2,3,5 of the CDs. This small η value of ≤0.3 may be approximated as the symmetric tensor. In this case, the reorientations due to the molecular dynamics may be described using one of three Euler angles, βR. The chemical environment of the CH2 carbon of the CDs is similar to the carbon atoms in PEG. Therefore, it is simply assumed that the PAS orientation of the 13C shielding tensor for the CD molecules adopts the same orientation as the PAS orientation of the shielding tensor for the CH2 carbon of PEG as follows: the σ11 direction is perpendicular to the −C− C−O− plane, the σ22 direction is on the −C−C−O− plane and 30° away from the −H−C−H− bisector, and the σ33 direction is perpendicular to both the σ11 and σ22 directions.56 First, the rotation of CDs around the PEG chains is considered; the CD ring planes are perpendicular to the rotational axis of the PEG chains. The rotation may be described by the precession of the σ33 axis on a cone (Figure 11a). The expression of the reorientation angle βR is more conveniently expressed using the rotation angle ψ around the PEG chain. The rotation angle ψ is between the tensor axes σ33 before and after rotation and is projected to the CDs bottom plane. The reorientation angle βR is also related to the semicone angle βPM, which is between the tensor axis of σ33 and the rotational axis. The reorientation angle βR may be obtained using the equation cos βR = cos2 βPM + sin 2 βPM cos ψ

correlates to no motion or reorientation back to the original, and a wide sin distribution that includes all of the possible βR angles, which is a sphere-like distribution. The ratio between the two distributions is related to the ⟨τc⟩ of molecular dynamics. The components at 0° are assumed to decay as a function of exp(−tm/⟨τc⟩), and exchanged ones are assumed to increase according to 1 − exp(−tm/⟨τc⟩). In the simulation, this distribution is approximated using 18 sites between 0° and 90° at 5° intervals. The normalized distribution of βR in the random-jump model at tm/⟨τc⟩ = 4.6 is illustrated in Figure 12a.

Figure 12. (a) Normalized distribution of βR with tm/⟨τc⟩ = 4.6 under the assumption of a sin distribution in the random-jump model. (b) Experimental (filled circles) and simulated intensities of C2,3,5 using the random-jump model assuming the full (black line) and 65% of the mobile fraction (blue line) are within the CODEX dynamic window.

The averaged CODEX Ntr dependence of all of the C2,3,5 signals are calculated as functions of mobile CD fractions using the distribution of βR. Figure 12b depicts the simulated curves with 100% (black) and 65% (blue) CD mobile fractions in the CODEX dynamic window. The latter curve is quite consistent with the experimental results (filled circles). Both the random-jump and uniaxial rotational diffusion models agree with the experimental results of CDs when 65 and 70% of CDs are assumed to participate in the molecular dynamics within the CODEX dynamic window, respectively. These portions of the mobile segments are consistent with the CODEX tm dependence (70%).

(3)

where βPM for C2, C3, and C5 can be calculated to be 83°, 88°, and 48°, respectively, on the basis of the atomic coordinates of the CD crystalline structures.57 The simulated Ntr dependence of the decaying CODEX curves for C2 and C3 reproduce similar CODEX curves, which are slightly different from that for C5. Figure 10a shows the Ntr-dependent CODEX intensities and the simulated average curves for C2,3,5 with different rotation angles ψ. The intensity decay is normalized and rescaled to 65% to reflect the existence of the 35% fraction outside the dynamic window. The initial decay is roughly consistent with the rotation angles of 50°−90°. However, this single angle cannot describe the experimental results. The CDs rotation is more reasonably described using a uniaxially rotating diffusion model, in which a Gaussian distribution of rotation angle ψ (with a distribution width σ = (2tm/⟨τc⟩)1/2) is assumed. Under this assumption, the normalized distributions of the rotation angles ψ are calculated and displayed as a function of tm/⟨τc⟩ in Figure 10b. With small tm/⟨τc⟩ values and using 0.5 as an example, the majority of ψ is less than 90°. An increase in the tm/⟨τc⟩ value causes a broader distribution of rotation angles ψ. As previously mentioned, the CODEX results’ tm dependence causes the tm/⟨τc⟩ to be 4.6 at 337 K. Using the distributions of ψ based on tm/⟨τc⟩ = 4.6, we calculated the averaged CODEX decay curves for all of the C2,3,5 signals, where this distribution is approximated using 36 sites between 0° and 360° with a 10° step. The black and red solid lines illustrated in Figure 10c represent the calculated curves with full and 70% CDs participating in uniaxially rotational diffusions, respectively. Simulated intensities reproduce the experimental data well when 30% of the components are assumed to be out of the range of our dynamic windows (red curve). In the random-jump model, the reorientational angles of βR adopt two distributions: a single distribution at 0°, which

IV. DISCUSSION Hydrogen Bonding and Molecular Dynamics of CD and PEG. The chemical modifications’ effect on the PR dynamics is well described using NMR techniques, WISE, and CODEX in combination with the former XRD and DMA results.16 The previous XRD data indicate that PR has a hexagonal crystalline structure, as illustrated in Figure 13. The NMR data reveal that both the overall and side-chain dynamics

Figure 13. Schematic illustrations of the chemical modifications’ effects on the structure and dynamics in PR systems. 6905

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another source for the high activation energy of CDs dynamics in HyPR78. Finally, we give comments on structural difference between HyPR78 in solid state and PR in solution state. Beckham et al. measured the self-diffusion coefficient (D) of PRs consisting of PEG and CDs with various coverage ratios of 20−70% and individual components in dilute dimethyl sulfoxide (DMSO-d6) solutions using diffusion ordered NMR spectroscopy and found that D of guest PEG in PR is completely consistent with D of CDs in PR and is much smaller than those of pure components.58 Using Einstein−Stokes laws59 and D values, they estimated hydrodynamic radius of PR (RPR) and PEG (RPEG). From these results, it was suggested that various PR systems behave as random coil chains in solution state. On the basis of statistical conformational calculations and RPR/RPEG, Tonelli suggested that PR is consisting of locally blocky structures of covered and uncovered PEG regions even in diluted solution, where several CDs are stacking via intermolecular hydrogen bonds.60 Such PR structure in solution state is essentially the same as the structure of PR in solid state and is different from the homogenously distributed structure of CDs of HyPR78 in the solid state. Through these discussions, it is reasonably understood that the spatial distributions of CDs (the stacking structure at certain length vs the isolated structure) play important roles for molecular dynamics of the PEG chains as well as CDs themselves. Chemical modifications on CDs can control not only hydrogen-bonding structures but also local structures and molecular dynamics of both the CDs and PEG chains in complex PRs and resultantly influence bulk viscoelastic property.

of the CD are highly restricted because the CDs exhibit intermolecular hydrogen bonding within the studied temperature range. Therefore, PR does not exhibit any relaxation at temperatures from 303 to 403 K. In addition, the WISE results clearly indicate that the PEG dynamics generate two components at 329 K. The restricted and near-isotropic components are assigned to the PEG chains covered and uncovered by CDs, respectively. When the two dynamic components and crystallinity are combined, the covered and uncovered regions form domain structures similar to block copolymers (Figure 13). The fast dynamics of the PEG in all of the PR and HyPR samples explain why all PR systems exhibit a lower storage modulus at temperatures far below the relaxation temperature of HyPR. In HyPR25, the crystalline structure of the CDs is destroyed. The WISE data indicate that the modified side chain exhibits enhanced mobility and that the restricted components of the PEG chains are diminished. However, these small modifications are not sufficient to induce cooperative CDs dynamics via major hydrogen-bonding structures, even in disordered states. Therefore, the majority of the CDs remain stacked, even in disordered states, and maintain the domain structure in HyPR25, as illustrated in Figure 13. When the modification ratio is 78%, the CP/MAS and CODEX results clearly detect the overall CD motion in the mechanical relaxation window. The CODEX tm- and Ntrdependent experiments indicate that ca. 70% of the CDs participate in cooperative motions in the limited dynamic window. In simulations, both uniaxial rotational diffusion and random-jump models successfully reproduce the CODEX data. Two different topologies of CD dynamics depend strongly on the spaces available around the CD molecules. For the stacked case, limited spaces might allow the individual CDs to prefer uniaxially rotational diffusions. However, if the CDs are homogeneously dispersed along the PEG chains, complex dynamics such as rotations, tilting, and sliding motions would be preferred, even in solid state. Unfortunately, CODEX angular resolution is not sufficient to specify either uniaxially rotational diffusion or random jump model. However, the WISE data clearly indicate that the liquid-like component in the PEG chains significantly increases and that the modified side chains perform enhanced dynamics. These experimental results imply that the CDs without intermolecular hydrogen bonds are not stacked and are therefore likely to be more homogeneously distributed along the PEG chain (Figure 13). As a consequence, complex dynamics, rotations, tilting, and sliding motions, might be preferred, even in the solid state. The observed temperature dependence of ⟨τc⟩ of CD backbone dynamics gives a very high activation energy of 163 kJ/mol. There are several possible sources for the very high activation energy. One is complex dynamics including translation, rotations, and tilting in condensed solid states, where the intermolecular interactions (CD−CD and CD−PEG) might lead to a higher barrier for apparent CD dynamics. Another possible source is cooperative dynamics of CDs with the physically threaded PEG chains. As shown above, the PEG chains perform near-isotropic motions in a fast motional limit (⟨τc⟩ < 10−5 s), while CDs gives much slower dynamics ⟨τc⟩ of 0.3 s at 329 K. This fact indicates that very fast motion of the threaded PEG chains does not influence CD dynamics at the same time scale. Namely, very fast PEG dynamics is really local event and does not induce displacement of CDs at the same time scale. On the other hand, slow dynamics of CDs is possible to accompany displacement of the threaded PEG chains performing a fast dynamics. This may be

V. CONCLUSIONS Our NMR experiments have successfully characterized the molecular dynamics in the components, as well as in the different functional groups, of complex PR and HyPR. Control of the hydrogen-bonding interactions with chemical modifications significantly influenced both the structures and dynamics of the CDs and PEG chains at different length and time scales. Chemical modifications led to greater mobility in the side chains and slower dynamics of the backbone of the CDs in addition to changes in the dynamics of the threaded PEG chains from heterogeneous to homogeneous. The confirmed slow dynamics of the CD backbone was assigned to the same origins as the mechanical relaxation in HyPR78. Understanding the unique microscopic dynamics of chemically modified PR helps us to understand the nature of macroscopic relaxation and is useful in the design of new PR materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Science Foundation. (Grant DMR-1105829) and UA startup funds REFERENCES

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