Article pubs.acs.org/Macromolecules
13
C MAS NMR Study of Poly(methacrylic acid)−Polyether Complexes and Multilayers
Blythe Fortier-McGill, Violeta Toader, and Linda Reven* Centre for Self-Assembled Chemical Structures (CSACS-CRMAA), Department of Chemistry, McGill University, 801 Sherbrooke St. W., Montreal, QC H3A 0B8, Canada S Supporting Information *
ABSTRACT: Hydrogen-bonded interpolymer complexes are widely used as stimuli-responsive materials. This solid-state 13 C MAS NMR spectroscopy study examines the influence of water and temperature on the hydrogen bond structures of 13 C-labeled poly(methacrylic acid) (PMAA) complexes with poly(ethylene oxide) (PEO) and poly(vinyl methyl ether) (PVME). The spatial variation of the inter- and intrapolymer hydrogen bonds in the dried bulk complexes and supported multilayers was measured by 2D 13C exchange (EXSY) NMR. In contrast to earlier studies of PAA complexes, the cross-peak intensities of the PMAA complexes are primarily due to 13C spin exchange rather than H-bond exchange due to the use of 13Clabeled PMAA and slower dynamics. The 13C−13C spin diffusion between the carbonyl groups with intra- versus interpolymer hydrogen bonds indicates interatomic distances of PVME complex > PEO supported multilayers > PVME supported multilayers. For the multilayer films, there are fewer of the stronger, more ordered cyclic dimer hydrogen bonds due to the disordering effect of the interfaces.
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INTRODUCTION The layer-by-layer (LBL) method, applied to both polyelectrolyte and hydrogen-bonded polymers, is an attractive approach for producing polymer thin films due to the range of the materials that can be incorporated and the nanometer thickness control.1 Hydrogen bonds are highly cooperative and offer the possibility for designing systems that respond to external stimuli, such as temperature, humidity, pH, and solvents. The hydrogen bond interactions in LBL films, polymer blends, polymer complexes, and block copolymers can be systematically modulated through variation of the components.2 The response of hydrogen-bonded polymeric materials to environmental stimuli will depend on the quantity and stability of both the inter- and intrapolymer hydrogen bonds. We previously characterized the hydrogen bond structures within a series of poly(methacrylic acid) (PMAA) complexes by solidstate 1H NMR.3 The role of the different types of PMAA hydrogen bonds was assessed and compared to the relative pH and temperature stabilities of these complexes. The following hydrogen bond acceptor polymers, in order of increasing pH stability of their complex with PMAA, were studied: poly(ethylene oxide) (PEO), polyacrylamide (PAAM), poly(vinyl methyl ether) (PVME), poly(vinylpyrrolidone) (PVPon), and poly(vinyl caprolactam) (PVCL). The pH value can be changed to induce charges in the material, thereby reducing the number of hydrogen bonds while introducing repulsive © XXXX American Chemical Society
forces. Thus, erasable multilayers can be designed that disintegrate at specific pH values determined by the particular combination of poly(carboxylic acid) and hydrogen bond acceptor polymer.4 Temperature is the most widely used parameter to modify the hydrogen bond strength for responsive properties such as conductivity and volume transitions. The inclusion of low glass transition (Tg) polymers such as the polyethers, PEO or PVME, allows the formation of flexible free-standing films for sensor and device applications.5 PEO is known to induce order within the hydrogen bond structure of the poly(carboxylic acids).6−8 This order can be detected in the solid-state 13C NMR spectra where the broad 13C carbonyl NMR resonance of the poly(carboxylic acid)6,9 splits into two or three distinct resonances upon complexation to PEO.6,8,10,11 We have correlated this spectroscopic resolution to the stabilization and weakening of PMAA’s cyclic and open type dimers, respectively.3 This change in the intra-PMAA hydrogen bonding was also proposed to explain why PMAA−polyether bilayers are relatively thick and permeable12 relative to the other PMAA complexes. Adsorbed water is another environmental parameter to alter the properties of hydrogen-bonded multilayers. The imporReceived: August 8, 2013 Revised: June 11, 2014
A
dx.doi.org/10.1021/ma401673n | Macromolecules XXXX, XXX, XXX−XXX
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Multilayers. First 0.94 mL of the Snowtex suspension, which is equivalent to 0.5 g of the colloidal silica, was diluted with 10 mL of Milli-Q water with a pH value of 1.2. This suspension was centrifuged at 10 krpm for 5 min, decanted, and resuspended 3 times to ensure that the surface was sufficiently protonated. For the first layer, the hydrogen accepting polymer, either PEO or PVME, was added as a 5 mL aliquot with a concentration of 2 mg/mL and a pH value of 1.2 and mixed overnight at 800 rpm. The suspension was washed with Milli-Q water with a pH value of 1.2 by decanting the supernatant after the suspension had settled (20 min) and resuspending in low pH water, a total of three times. This was followed by the addition of the second layer, a 5 mL aliquot of the 2 mg/mL PMAA-13C in Milli-Q water with a pH value of 1.2, mixed overnight at 800 rpm. The above washing procedure was repeated before and after the addition of the third layer, a 5 mL aliquot of the 2 mg/mL, pH 1.2 solution of either PEO or PVME. These three-layer multilayers were dried under vacuum for 48 h at 50 °C. Characterization. A Bruker AVANCE 600 WB spectrometer operating at the Larmour frequency of 600.14 MHz for 1H and 150.92 MHz for 13C was used for acquisitions of all the spectra. A double resonance probe that supports 4 mm outer diameter rotors at a spinning speed of 14 kHz was used for the acquisition of all 13C CPMAS and 2D 13C CP-EXSY spectra, unless otherwise specified. The exact temperature at low spinning speeds was calibrated using the relation T = (4.637 − Δ (ppm))/0.009967 (K), where Δ is the 1H chemical shift difference between ethylene glycol’s methylene and OH protons. The change in temperature at elevated spinning speeds was monitored by the 207Pb chemical shift within Pb(NO3)2 where the temperature dependence of the chemical shift has been calibrated by Beckmann and Dybowski.16 The 13C spectra were referenced to glycine (176.03 ppm, carbonyl, 13 C). The 2D 13C CP-EXSY spectra were acquired with a typical 1H 90° excitation pulse length of 3.5 μs, 13C 90° pulse length of 4.5 μs, a contact time of 1.5 ms, a recycle delay of 2 s, with 16−32 scans for each of the 80−60 slices, and a spectral width of 20 kHz and 1K of data points. The excitation time t1 was varied by 50 μs intervals. Phase sensitive detection in t1 was achieved through States-TPPI. The series of 2D 13C CP-EXSY experiments with mixing times between 1 ms and 27 s were collected at the corrected sample temperatures of −15, 45, and 60 °C. For the 1D 13C CP spectra the typical 1H 90° excitation pulse length was 3.5 μs, with a contact time of 1.5 ms, a recycle delay of 2 s, and 8−256 scans, with a spectral width of 38 kHz and 1K of data points. 1H spectra were initially acquired to center its offset frequency, with a typical 90° pulse of 4.5 μs and a delay time of 2 s for 1 scan. The maximum CP B1 (1H) value was either 60 kHz (bulk complex) or 87 kHz (supported multilayers) with a ramp that descends to half this maximum value, and the B1 (13C) was 55 kHz for both the CP and the CP-EXSY 13C experiments. The B1 of the decoupling pulse was 71 kHz. The 13C T1 values were extracted from the cumulative data of eight Torchia 13C T1 inversion recovery experiments with different times between pulses, τ. The τ values were varied to exponentially increase from 0.5 to 64 s, typically using a 1H 90° excitation pulse of 3.5 μs, a 13 C 90° pulse length of 4.5 μs, a contact time of 1.5 ms, recycle delay time of 2 s, and 8 scans, with a 38 kHz spectral width and 1k of data points. The maximum B1 (1H) value was either 60 kHz (bulk complex) or 87 kHz (supported multilayers) while the B1 (13C) value was fixed at 55 kHz. The 13C T1 relaxation values were extracted by fitting, using Bruker’s analysis software, a plot of the integrated carbonyl region versus the τ times to an exponential decay of the form I(t) = I(0) + Pe−τ/T1. The standard deviation values of the fits ranged between 5 and 25 ms, giving a 99.9% confidence interval within ±0.1 s. The 2D 1H−13C HETCOR spectra were acquired using the frequency-switched Lee−Goldberg (FS-LG) applied during the evolution time t1, using an 8 step phase cycle, with a typical 1H 90° excitation pulse of 2.5 μs, a contact time of 1.5 ms, a recycle delay of 2 s, and typically 16 transients for each of the 128 increments, using a spectral width of 30 kHz with 1K of data points. The 2D HETCOR spectra were acquired using the double resonance probe that supports
tance of adsorbed water is highlighted by the humidified PAA− PEO multilayer films that have been proposed as being competitive with Nafion as a proton exchange membrane (PEM).13 PAA−PEO multilayer films can be made at a lower cost, thinner, and function at lower relative humidities.1,13 As the clusters of water are considered to facilitate the proton transfer, the hydroscopic nature of the PEO−PAA multilayer film is advantageous. The focus of this paper is on the distribution of the hydrogen bonds, for the purpose of providing a more comprehensive understanding of the packing arrangement. In addition, we were interested in relating the dynamic exchange process of the hydrated complexes to our previous variable temperature 2H NMR study of PMAA’s backbone motion within water saturated complexes, and supported multilayers.14 The 2D exchange (EXSY) NMR experiment is well suited for slow dynamics in the range of millisecond to second correlation times; however, there is no distinction between chemical and 13 C−13C spin exchange processes.15 The spectroscopic resolution of the PEO−PAA system mentioned above was used by Miyoshi et al. to evaluate the rate of exchange between hydrogen-bonded states.11 Here we apply the 2D 13C EXSY experiment to the dry PMAA complexes with either PEO or PVME and to their respective supported multilayer films. The proton resonances assigned to the different types of hydrogen-bonded carboxylic acid groups are first related to the 13 C carbonyl resonances. The variation of the intensities of the three resolved carbonyl peaks of the dried and rehydrated complexes are then compared to those of the supported multilayer films. For the rehydrated samples the reversibility of the line shape was evaluated. Whether any hydrogen bond exchange occurs on the NMR time scale was first assessed, followed by a comparison of the 13C spin diffusion between the different hydrogen bonds for the complexes and the multilayers to determine their spatial distribution.
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MATERIALS AND METHODS
Materials. Poly(ethylene oxide) (PEO; Mw 300 kDa) and poly(vinyl methyl ether) (PVME 1.5 kDa, independently determined by electrospray and MALDI-TOF, mass spectrometry experiments) as a 50 wt % solution were all purchased from Sigma-Aldrich and were used as received. The Snowtex colloidal silica (70−100 nm, 40−41 wt %, d = 1.29−1.32 g/mL, pH 8.5) was provided by Nissan Chemical. The 48 wt % HCl, NaOH (pellets), glacial acetic acid, and sodium acetate were all purchased from Fisher Sci. and used as received. The Milli-Q water used in all sample preparation had a measured resistivity of 18.2 MΩ·cm. The method used to synthesize the 13C-labeled poly(methacrylic acid) (PMAA; Mw 14 kDa) has been reported previously.3 Sample Preparation. Bulk Complexes. The typical concentration of the initial polymer solution was 6 mg/mL dissolved in Milli-Q water. The pH of these solutions was adjusted using 1 M HCl to obtain a final measured value of pH 1.2. The complex suspensions were formed upon the addition of 10 mL of the PMAA solution to 10 mL of the hydrogen accepting polymer solution, from which a white precipitate was formed immediately. The complex suspensions were concentrated by centrifuging at 7 krpm for 2 min. The supernatant was decanted and the complexes were dried under vacuum for 24 h at 50 °C. Humidified Bulk Complex. The complex was placed in a Milli-Q water saturated environment for 48 h, then removed and wrapped in Teflon tape, and stored in a closed vial. The samples were weighed before and after placing in the humidification chamber. The final water content was found to be ∼12 and ∼6 wt % for the PEO− and PVME− PMAA-13C complexes, respectively. B
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that reported by either Sun et al.18 or Akbey et al.20 in their 1H MAS NMR studies of poly(acrylic acid) (PAA). Sun et al.18 assigned the 10.7 ppm protons to a combination of free isolated COOH and those associated with open dimers that survive a DQF, whereas Akbey et al.20 attribute this resonance to COOH groups in exchange between the free and hydrogen-bonded states. In addition, the 1H signal that appeared in the 7−9 ppm range for PAA was labeled as water exchanging with the acid protons, rather than the free acid.18 We agree that water shifts the resonance of the free COOH groups of PMAA but assign the non-hydrogen-bonded PMAA to the 9.5 ppm peak and the lower frequencies to free COOH groups associated with water. Next the 13C signals in the HETCOR spectra of the PMAA complexes are considered. In earlier 13C MAS NMR studies, three carbonyl resonances have been assigned as the intraPMAA dimer, disordered PMAA, and PMAA−polyether complex. These labels are a combination of those used by Miyoshi et al.8 for the PEO−PMAA complex and Asano9 for the noncomplexed PMAA. The HETCOR spectra show that the dimer carbonyl at 187 ppm is correlated with the 1H signal at 13 ppm assigned to the intra-PMAA cyclic dimers, for both polyether complexes (Figure 3a,b). The carbonyl peak at 179 ppm (Figure 3a,b) includes both the interpolymer hydrogen bonds of the complex (10.5 ppm) and the free COOH proton signals (9.5 ppm). This is not surprising as the 13C peak at 180 ppm previously assigned as the complex8 overlaps with that assigned as the free carbonyl (178 ppm).9 The broad 13C resonance at 182.5 ppm for disordered Hbonded carbonyls of the noncomplexed PMAA (Figure 3c) correlates with the broad proton resonance centered around 10.5 ppm, assigned to the more weakly hydrogen bonded protons of the open dimer sequences. The broadness of these spectral frequencies is possibly associated with a different number of consecutive hydrogen bonds, where shorter hydrogen bonded segments with more terminal groups would resonate at lower frequencies. This scenario agrees with Asano’s description of the disordered resonance as including irregular weak hydrogen bonds that disassociated into more ordered hydrogen bonds upon heating.9 In the case of the PAA−PEO complex, Miyoshi assigned this middle carbonyl peak (180 ppm) as the “free non-hydrogen bonded” PAA, as it is similar to that of the noncomplexed PAA.10 However, in an earlier study they do clearly stipulate that they do not mean that it is totally free of any hydrogen bonds. Additionally, the 181 ppm signal found for the noncomplexed PAA was observed at a temperature (37 °C) below the glass transition (Tg) of the noncomplexed PAA (100 °C); thus, the line shape was attributed to a static superposition of the free (176 ppm) and intra-PAA hydrogen bonds (183
Figure 1. Pulse sequence for the T1ρ (1H) measurements. 2.5 mm outer diameter rotors, at a spinning speed of 15 kHz, a corrected sample temperature of 30 °C, a B1 (1H) = 85 kHz, and a B1 (13C) = 55 kHz. The T1ρ (1H) measurements were acquired using the same probe, spinning conditions, CP B1 field strengths, and sample temperature as was used for the CP and CP-EXSY experiments described above. A 3.5 μs 1H 90° excitation pulse with a contact time of 1500 μs, a recycle delay of 2 s, with 8−64 scans was used. Typically 12 spectra with distinct variable pulse duration times, τ, were acquired to extract the T1ρ (1H) values. The duration of the variable pulse, τ, ranged between 0.1 and 12 ms. The B1 (1H) field for the variable pulse was 60, 69, 87, or 88 kHz. The T1ρ (1H) values were extracted by plotting the integration of the 12 variable pulse spectra as a function of the τ values and fitting to an exponential decay function. The standard deviation of the fits was less than 0.05 ms. A table of the values can be found in the Supporting Information.
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RESULTS AND DISCUSSION H−13C HETCOR. In Figure 3, the HETCOR spectra of the PMAA−polyether complexes, first presented in the earlier 1H MAS study,3 are reproduced here and discussed in more detail. The suggested structures for the 1H−13C correlations of the HETCOR spectra are based on our previous assignment of the PMAA dimers within the polyether complexes,3 Diez-Pena’s assignment of the free PMAA protons,19 and Nakashima’s proposed forms of hydrogen-bonded PAA.17 We first describe the proton signals. In PMAA it has been shown that two different types of dimers are formed with chemical shifts of 10.5 and 13 ppm. Rather than relating the two forms specifically to the tacticity of the polymer chains as suggested by Diez-Pena, we proposed that these resonances are due to the stable cyclic type dimers (13 ppm) and metastable open dimer chains (10.5 ppm) as shown in Figure 2. This new assignment is based on the lack of correlation between the tacticities and the intensities of the 1H double quantum coherences (DQCs) for different PMAA samples.3 This proposed assignment also differs from 1
Figure 2. Possible hydrogen-bonded structures of PMAA including the stable cyclic dimer and metastable chains of hydrogen bonds formed through open dimers,17,18 where the terminal carboxyl group is proposed to be able the H-bond to water. In addition, the interpolymer complex H-bonds with either PEO or PVME along with a free non-H-bonded PMAA unit are illustrated. C
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Figure 4. 13C−CP MAS spectra acquired at a spinning speed of 14 kHz, a sample temperature of 45 °C, a contact time of 1.5 ms, and a maximum CP B1 (1H) value of 60 kHz, of the (left) PMAA−PEO and (right) PMAA−PVME complexes that were (a) dried under vacuum and (b) rehydrated, while (c) and (d) are the vacuum-dried supported multilayer films with either 3 or 2 layers, respectively, for (left) SiO 2 (PEO/PMAA/PEO) or SiO 2 (PEO/PMAA) and (right) SiO2(PVME/PMAA/PVME) or SiO2(PVME/PMAA). The relative integrations ±5%, are presented as % values below each spectrum.
Figure 3. Displays the 1H−13C HETCOR spectra of the PMAA13C complexes with (a) PVME and (b) PEO while (c) is the noncomplexed PMAA13C. The spectra were acquired at 30 °C with a spinning speed of 15 kHz, a contact time of 1.5 ms, and a 1H B1 = 85 kHz/13C B1 = 55 kHz.
quantitative data, but in view of the very long carbon T1 values, we decided to look at the population trends by assuming that the cross-polarization parameters to not vary much for the different types of carbonyl carbons. The PMAA−PEO complex and films have a larger intra-PMAA dimer (187 ppm) and disordered (182.5 ppm) components in comparison with the PMAA−PVME complex, reflecting a weaker complexation capacity. The rehydrated complexes have larger disordered components as compared to the dried complexes (Figure 4a,b), showing the disruption of the hydrogen bonds by adsorbed water. The supported multilayers have fewer cyclic dimers, due in part to the disordering effect of the two interfaces (polymer− air and polymer−substrate). For example the spectrum of the supported two-layer film (Figure 4d) contains more of the disordered H-bonds compared to the three-layer films (Figure 4c), demonstrating that the disordering effect of the PMAA−air
ppm) signals, rather than a motional average of the two peaks.10 We assigned the middle signal of PMAA (182.5 ppm) to chains of open dimers, based on our previous 1H double quantum (DQ) NMR study.3 For the PEO−PMAA complex (Figure 3b) the middle (182.5 ppm) signal is not as broad as it is in the noncomplexed PMAA (Figure 3c), suggesting that the chains of hydrogen bonds are equivalent in size and relatively short, including the possibility of isolated single intra-PMAA hydrogen bonds. 1D 13C NMR: Effect of Water and Interfaces on Hydrogen Bonds. Figure 4 compares the 13C carbonyl signal integrations, based on Gaussian line shape fits, of the three different types of carbonyls of the dried and rehydrated bulk complexes to the dried supported multilayer films with either 2 or 3 layers. Fully relaxed 13C spectra would ensure accurate D
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dimers, in addition to the water loss, as a contributing factor to the observed decrease in the local chain dynamics after heating. A detailed study of the combined effect of temperature and water on the populations of the different types of carbonyls was carried out, taking care to consider the effect of sample spinning which can cause a spatial redistribution and loss of water (see Supporting Information, Figures S1−S5). Upon heating the hydrated complexes, the population of cyclic dimers significantly increases relative to the disordered component while the interpolymer peak only decreased slightly, comparable to the dried complexes. Although there was no measurable loss of water, the lack of a tight seal and/or centrifuging of the water by sample spinning could not be ruled out. The 13C spectra of the heated hydrated samples returned to their initial states after sitting at room temperature overnight. 2D 13C EXSY: Distribution of the Hydrogen Bonds from 13C−13C Spin Diffusion. The 13C CP-EXSY NMR spectra of the dry polyether−PMAA13C complexes carbonyl region for different mixing times are presented in Figure 6. As the dry complex has a minimal contribution from the disordered carbonyl resonance (182.5 ppm), the spectra are dominated by cross peaks between the complex (179 ppm) and dimer (187 ppm) resonances. The relative intensities of the cross-peaks compared to the diagonal peaks represent the population that has changed its chemical environment during the indicated mixing time, either by chemical exchange or by spin diffusion. We also attempted to study the effect of water on the exchange; however, we could not prevent the gradual loss of water during the long 2D NMR experiments due to the sample spinning (for more details see Supporting Information). Plots of the mixing time dependence, τmix/s, of the sum of the two cross-peak integrations, Icross(pair), relative to the sum of the diagonal-peaks, Idiagonal(all), were fit to a general expression for 2D exchange spectra:
interface is diminished by the additional PEO or PVME layer in the three-layer samples. As the T1ρ (1H) values for PMAA’s COOH involved in the complex H-bond (3.45 ms (PEO), 8.45 ms (PVME)) and PMAA’s COOH involved in a cyclic dimer H-bond (3.65 ms (PEO), 8.56 ms (PVME)) resonances were found to differ by less than 1 ms, the 13C relative integration are considered representative to within ±5%. 1D 13C NMR: Effect of Temperature on Hydrogen Bonds. The spectra in Figure 5 illustrate that the equilibrium
[Icross/Idiagonal ](τmix ) = A[1 − exp( −(kτmix )β )]
(1)
where A, k, and β are the fractional population that participates in the exchange, the rate of exchange, and the distribution exponent, respectively. The distribution exponent, 0 < β ≤ 1, takes into account the possibility that the system is better described by a distribution of exchange rates, as commonly encountered for amorphous polymers. The Supporting Information shows that the rates of exchange and distribution exponent values obtained from a more detailed function are similar to those obtained with eq 1. Whereas spin diffusion was ruled out for the previous study of a natural abundance PAA−PEO complex by Miyoshi,11 we find that the exchange in the 13C-enriched PMAA complexes is dominated by 13C−13C spin diffusion. Spin diffusion and chemical exchange are commonly differentiated by using natural abundance 13C samples and/or by subtracting low temperature data, where no exchange is expected, from high temperature data. The natural abundance method assumes that because of isotopic dilution, the average 13C−13C internuclear distance is significantly greater than the optimal distance required for exchange via spin diffusion. 13C spin exchange for natural abundance samples, which becomes observable for mix times longer than ∼10 s, can only be studied in samples with very long carbon spin−lattice relaxation times.21 The subtraction method is based on the approximation that the rate of spin diffusion is temperature independent within a reasonable temperature range (e.g., −15 to 100 °C), while
Figure 5. 13C−CP MAS spectra acquired with a contact time of 1.5 ms and with a maximum B1(1H) = 60 kHz, of the dried (a−c) PMAA13C− PEO complex and the dried (d−f) PMAA13C−PVME complex at (c, f) −15 °C, (b, e) 45 °C, and (a, d) 60 °C. The indicated percentages were calculated from the relative integration values of the corresponding peak used to fit the line shape.
state at elevated temperatures shifts toward the formation of the more stable intra-PMAA cyclic dimers, as was found previously.8 It is important to note that in the earlier studies the solid PMAA−PEO8 and PAA−PEO11 complexes were probably not completely dry. More recent 1H NMR and FTIR studies of PAA used more extreme drying conditions: under vacuum at 50 or 60 °C for 3−5 days.17,18,20 In earlier NMR studies, Diez-Pena19 and Miyoshi8,11 dried their samples under vacuum for 1−2 days with no additional heating. Our samples were dried at 50 °C for 1−2 days under vacuum. In our previous 2H NMR studies of water-saturated PMAA complexes, it was found that the PMAA backbone motion decreased after one heating cycle.14 We believe it is reasonable to suggest a structural rearrangement to form more of the stable cyclic E
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Figure 6. 13C CP EXSY spectra acquired at 45 °C with a spinning speed of 14 kHz, at a contact time of 1.5 ms and a CP B1(1H) = 60 kHz. The dried (left) PEO−PMAA13C and (right) PVME−PMAA13C complexes, with a mixing time of (a, d) 1.5 s, (b, e) 3 s, or (c, f) 6 s.
Figure 7. Plot of the mixing time dependence, τmix/s, of the sum of the two cross-peak integrations, Icross(pair), relative to the sum of the diagonal peaks, Idiagonal(all), for (A) the PMAA complex with either (red) PVME or (blue) PEO and (B) the three-layer supported PMAA multilayers; (red) SiO2(PVME/PMAA/PVME) or (blue) SiO2(PEO/PMAA/PEO), at (square, solid line) −15 °C, (triangle, long dashed line) 45 °C and (diamond, short dashed line) 60 °C. The “best fit” line was obtained using [Icross/Idiagonal](τmix) = A[1 − exp(−(kτmix)β)], where A, k (s−1), and β are the fractional population that participates in the exchange, the rate of exchange, and a distribution exponent, respectively.
chemical exchange is thermally activated.9,22 Using this approximation, we subtracted the normalized absolute crosspeak integrations values obtained at −15 °C where no chemical exchange was expected, from those at 45 and 60 °C and fit the resulting values, for the dry PEO−PMAA complex (Supporting
Information, Figure S7 and Table S3). The residual rate of exchange at 60 °C was found to be 0.64 s−1, which is lower than the rate found for the PAA−PEO complex at 65 °C, 1.08 s−1.11 Furthermore, the maximum normalized cross-peak integration is less than 0.1, as opposed to the 0.5 observed for the PAA− F
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PEO complex.11The β exponent was 0.92 for PMAA−PEO, close to single exponential, as compared to 0.29 for PAA−PEO, which implies that the k value is distributed over several orders of magnitude.11 For a rough comparison with the previous exchange study of the 13C natural abundance PAA−PEO complex by Miyoshi, an EXSY spectrum at a mixing time of 3 s at 60 °C for a natural abundance dry PMAA−PEO complex was acquired (data not shown). The normalized cross-peak intensity of 0.035 is consistent with the values obtained from the spin diffusion corrected 13C-enriched sample data. Given that any chemical exchange occurs at a very low rate and only involves a small fraction of the population even at 60 °C, we conclude that proton driven 13C spin diffusion (PDSD), enhanced by 13C enrichment, is the dominant mechanism. Since the initial intention was to use the EXSY solid state NMR experiment to detect any dynamics of the hydrogen-bonded network, we had opted to perform the experiments at 14 kHz, a relatively high spinning speed, which provides increased signalto-noise ratios but should also attenuate spin diffusion. As shown in Table 1, the exchange rate was significantly reduced at 14 kHz as compared to 5 kHz due to the decrease in spin diffusion efficiency.
describing the probability of spin exchange between two carbon, i and j, is proportional to the square of the dipolar coupling, ωij, and the zero quantum line shape, f ij(0), which is the Fourier transform of the free-induction decay of a transverse two-carbon zero-quantum correlation under the influence of the surrounding protons. f ij(0) is a measure of the probability that single quantum transitions will occur at identical frequencies for spins i and j and is basically the amount of overlap between the NMR signals for the two types of carbons in the presence of proton coupling. kij ∝ ωij 2fij (0)
ωij =
k (s−1 )
A
β
% cyclic dimer k (s−1 ) A β % cyclic dimer
0.18 ± 0.02 0.67 (νrot = 5 kHz) 0.97 ± 0.06 0.98 (νrot = 5 kHz) 0.97 ± 0.05 0.83 (νrot = 5 kHz) 35 ± 1 0.15 ± 0.01 0.88 ± 0.2 1.00 ± 0.06 30 ± 4
PVME− PMAA
SiO2/PEO/ PMAA/PEO
SiO2/PVME/ PMAA/PVME
T = 45 °C 0.14 ± 0.04
0.17 ± 0.18
0.12 ± 0.29
0.71 ± 0.09
0.68 ± 0.34
0.44 ± 0.64
1.0 ± 0.17
0.88 ± 0.25
1.00 ± 0.66
31 ± 1
25 ± 5
22 ± 3
T = −15 °C 0.11 ± 0.05 0.67 ± 0.09 1.00 ± 0.28 32 ± 1
0.29 ± 0.12 0.50 ± 0.09 1.00 ± 0.28 24 ± 5
0.1 ± 1.3 0.4 ± 5.8 1.0 ± 1.9 21 ± 5
μ0 γC 2h 4πrij 3
(3)
However, accurate distances cannot be easily obtained due the difficulty of estimating f ij(0) which contains the contribution of the proton bath to the polarization transfer. Given the widespread use of proton driven 13C spin diffusion (PDSD) to provide distance constraints in biomolecules, recent efforts to extract quantitative information have appeared using the master equation approach combined with numerical simulations of the zero-quantum line shapes26 and comparing spin diffusion constants calculated from PDSD relaxation theory with direct simulations.27 In practice, the distance scale can be calibrated using a pair of static chemically distinct carbons separated by a known distance. Linder et al.28 used doubly labeled poly(ethylene terephthalate) (PET) to study its miscibility with bisphenol A polycarbonate (BPAPC) by 13C spin diffusion. The k value of 19.0 s−1 for the 13C−13C distance of 0.235 nm between the CH2 and the carbonyl carbon of the PET was used to calibrate the intermolecular exchange rates, which indicated mixing of PET and BPAPC within distances of 0.45−0.6 nm.28,29 Asano scaled this k value to estimate a distance of 0.37 nm between the ester carbonyls of the poly(vinyl acetate) and the carboxylic acids of the PMAA.30 He justified this comparison based on the glassy state of both systems and attributed the short distance to the formation of strong hydrogen bonds. A more qualitative approach was used by Heinen et al. to study the effect of crosslinking on 13C-enriched polymer blends.31,32 The two polymers were found to be intimately mixed with an average interpolymer distance of ∼0.6 nm, based on the measured diffusion rate for a known intramolecular distance in a doubly labeled polymer.31 The interpolymer cross-peaks in the 2D 13C spin diffusion experiments disappeared after cross-linking due to phase separation into domains ranging from 1 to 100 nm as determined by proton spin diffusion measurements.32 On the basis of these prior 13C spin diffusion studies of selectively 13C-enriched glassy polymers, we estimate that the intra-PMAA and interpolymer hydrogen bonds are within a distance range of 0.3−0.7 nm. This range is based on the distribution of dipolar couplings expected for an amorphous polymer, the minimum intramolecular distances between the PMAA carbonyl groups and the rate constants estimated by Linder et al.28 which become very small (
