Local Structure and Dynamics of Imidazole Molecules in Proton

Oct 22, 2014 - Many proton-conducting polymers, including imidazole and its derivatives, have been developed for their applications in solid electroly...
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Local Structure and Dynamics of Imidazole Molecules in ProtonConducting Poly(vinylphosphonic acid)−Imidazole Composite Material Motohiro Mizuno,*,†,‡ Ayano Iwasaki,† Tsuyoshi Umiyama,† Ryutaro Ohashi,†,‡ and Tomonori Ida† †

Department of Chemistry, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan ‡ CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan S Supporting Information *

ABSTRACT: Many proton-conducting polymers, including imidazole and its derivatives, have been developed for their applications in solid electrolyte fuel cells. It is thought that proton conduction is caused by the Grotthuss mechanism associated with the reorientational motion of imidazole molecules in these materials. However, there are still very few analyses of the relation between proton conduction and the reorientational motion of imidazole molecules following the detailed investigation of the molecular motion of imidazole. In the present work, molecular motions and their influence on proton conductivity were investigated for poly(vinylphosphonic acid) (PVPA)−imidazole (Im) composite material (PVPA/xIm, where x is the molar ratio of Im to polymer repeat unit) by solid-state NMR. Between 20 and 50 °C, the Im molecule undergoing pseudoisotropic rotation with small anisotropy accounted for more than 90% and that undergoing rotational vibration for less than 10% for PVPA/2Im. The tight segment, where Im molecules undergo rotational vibration, prevents long-range proton conduction. Above 60 °C, efficient proton conduction accompanied by pseudoisotropic rotation of the Im molecules was confirmed in PVPA/2Im.

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INTRODUCTION Anhydrous proton-conducting polymers, which can be used stably above 100 °C, have been widely developed for their applications in solid electrolyte fuel cells. Several protonconducting polymers, including imidazole and its derivatives, have been proposed.1−12 For poly(vinylphosphonic acid) (PVPA)−imidazole (Im) composite material (PVPA/xIm, where x represents the number of moles of Im per mole of polymer repeat unit), proton conductivity increased with increasing x, and a sudden increase in proton conductivity was observed in the range from x = 1 to 2.1 A maximum value of 7 × 10−3 S/cm was obtained at 150 °C for 89 mol % Im.2 In the PVPA/xIm composite, Im molecules are intercalated into host polymer PVPA and provide a migration path for excess protons caused by dissociation of the acid functions. When proton conductivity of the PVPA/xIm composite is dominated by continuous proton transfer in the hydrogen bond network between Im molecules (Grotthuss mechanism), the reorientational motion of Im molecules is predicted to play an important role.13,14 The physical property of PVPA/xIm has been investigated by thermal analysis.1,2 The glass transition temperatures (Tg) of PVPA homopolymer, x = 1, and x = 2 were reported as −23, 5, and −36 °C, respectively. Thus, Tg increases with increasing x at a low Im concentration because segmental mobility is © 2014 American Chemical Society

suppressed due to ionic interactions and a hydrogen bond between Im and PVPA. In contrast, excess imidazole increases segmental mobility and decreases T g at a high Im concentration. Detailed analyses of the local structure and dynamics in PVPA/xIm such as the hydrogen-bonded structure around phosphonic acid and the reorientational motion of Im molecules are expected to clarify the efficient protonconducting mechanism and situation hindering proton conduction in these materials. However, such analyses have not yet been carried out. Solid-state NMR spectroscopy is an effective method for the analysis of the local structure and molecular dynamics in polymer materials. Hydrogen-bonded structures and dynamics in proton-conducting polymers have been investigated using 1H, 31P, and 13C NMR spectra.15−17 2H NMR is very useful for investigating the proton transfer mechanism associated with molecular reorientational motion, since the mode and rate of reorientational motion can be clarified from the analysis of spectral line shape.18−22 The reorientational motion of molecules related to proton conduction has been investigated by 2H NMR.23,24 Received: July 1, 2014 Revised: October 11, 2014 Published: October 22, 2014 7469

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Scheme 1. Motion of the Imidazole Molecule (Im-d3) and Used Models for the 2H NMR Spectral Simulationa

a

(a) Rotational vibration around the pseudo-5-fold axis of the Im molecule. (b) Isotropic or anisotropic rotation of the Im molecule. (c) Eight-site jump on a cone at the magic-angle model used to calculate the isotropic rotation of the Im molecule. (d) Tetrahedral four-site jump model used to calculate the isotropic and pseudoisotropic rotation of the Im molecule. For isotropic rotation, β′ = 109.4°. β′ increases with increasing anisotropy of rotation of the Im molecule. (90°)y−τ−tacq)n. n was 64. τ and tacq were 20 and 100 μs, respectively. Simulations of the 2H NMR broadline and QCPMG spectra were performed by homemade Fortran programs using double precision.25 For the spectral simulation, the 2H NMR frequency at site i (ωqi) was calculated by using the second-order Wigner rotation matrix D18−21,27

In the present work, we analyzed the changes to the local structure around phosphonic acid due to the intercalation of Im molecules in PVPA using 31P NMR. The dynamics of PVPA and Im was investigated by 13C NMR. The reorientational motion of Im molecules in the PVPA/xIm composite was investigated using 2H NMR. In polymer materials, dynamic inhomogeneity is closely related with these physical properties. In order to investigate the flexible region and the rigid region in PVPA/xIm, we measured 2H NMR broadline spectra and quadrupole Carr−Purcell−Meiboom−Gill (QCPMG) spectra in the temperature range of −80 to 100 °C. The 2H NMR QCPMG spectrum is more sensitive to slow reorientational molecular motion or small-angle liberation than the 2H NMR broadline spectrum.24,25 The relation between reorientational motion of Im molecules and proton conductivity and the ratelimiting step for proton conduction in PVPA/xIm are discussed.

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ωqi =

3 2

2

∑ D0(2)n *(ψ , θ , ϕ)Dn(2),m*(αi , βi , γi)Tm(2) n,m

2

T0(2) =

3 e qQ 8 ℏ

(1)

2

T±(2)2 =

η e qQ 4 ℏ

(2)

where (αi, βi, γi) and (ψ, θ, ϕ) are Euler angles for the transformation from the molecular axes to the principal axes of the electric field gradient tensor and from the laboratory axes to the molecular axes, respectively. e2qQ/ℏ and η are the quadrupole coupling parameters. The two-site jump model was used to calculate line shape in the presence of the rotational vibration of the Im molecule (Scheme 1a). For the calculation of the line shape due to isotropic rotation, the 8site jump on a cone at the magic-angle model (Scheme 1c) and the tetrahedral jump model with β′ = 109.4° (Scheme 1d) were used. The line shape due to the pseudoisotropic rotation of the Im molecule was calculated using the distorted tetrahedral jump model by changing β′ from 109.4° (Scheme 1d). The simulation spectrum was obtained by Fourier transformation of the calculated time-dependent NMR signal. Differential Scanning Calorimetry. For the DSC measurements, a Rigaku Thermo plus EVO DSC 8230 was used. The samples were packed into aluminum pans (17−18 mg) and measured in a temperature range of −140 to 100 °C. The midpoint in the transition region during the second heating scan was used to determine glass transition temperatures. The heating rate was 10 °C/min.

EXPERIMENTAL SECTION

Materials. Poly(vinylphosphonic acid) (PVPA) was obtained from Tokyo Chemical Industry Co., Ltd. Imidazole-d3 (Im-d3), in which only hydrogen bonded to carbon was replaced by deuterium, was prepared by repeated recrystallization of imidazole-d4 (Cambridge Isotope Laboratories, Inc.) using light water. PVPA/xIm-d3 was prepared according to a published procedure.1,2 The samples were dried under vacuum at 60 °C for 3 days. PVPA/xIm-d3 was used for 2 H NMR measurements. Deuterated samples were packed in a glass sample tube in a drybox with a nitrogen atmosphere. 13C and 31P NMR were measured using protonated PVPA/xIm. Solid-State NMR. 13C and 31P NMR spectra were measured using a JEOL ECA-300 spectrometer operating at 74.175 and 119.413 MHz, respectively. High-resolution solid-state NMR spectra were obtained using magic-angle spinning (MAS) and high-power 1H dipole decoupling (DD). Cross-polarization (CP) was used for signal enhancement. The sample was packed into a 4 mm diameter zirconia rotor. To measure 31P NMR spectra, the total suppression of sidebands (TOSS) sequence26 was used to suppress spinning sidebands. The radio frequency field strength ν1 for CP and DD was 30 and 40 kHz, respectively. The contact time for the CP process was 0.5 ms. The MAS rate was set to 4 kHz. 13C chemical shifts were expressed as values relative to tetramethylsilane (TMS) using the 29.50 ppm line of adamantane as an external reference. 31P NMR chemical shifts were expressed as values relative to phosphonic acid using the 1 ppm line of ammonium phosphate monobasic as an external reference. 2 H NMR was measured using a JEOL ECA-300 spectrometer at 45.282 MHz. The 2H NMR broadline spectra were measured using a quadrupole echo sequence (90°)x−τ−(90°)y−τ−tacq, where τ and tacq are the interval of echo and acquisition time, respectively. 90° pulse width and τ were 2.5 and 20 μs, respectively. The QCPMG spectra were observed using a sequence (90°)x−τ−(90°)y−τ−tacq/2−(τ−

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RESULTS AND DISCUSSION Local Structure in PVPA/xIm by 31P NMR. In order to discuss the change in local structure around phosphonic acid due to the insertion of Im into PVPA, solid-state 31P{1H}CP/ MAS NMR spectra for PVPA homopolymer, x = 1, and x = 2 at 34 and 100 °C are shown in Figure 1. For PVPA, the main peak at 32 ppm and shoulder at 20 ppm correspond to normal phosphonic acid and phosphonic acid anhydride, respectively.15 For x = 1 and 2, the main peak shifted to the high-field side by 4 ppm, and the shoulder was not observed. The high field shift of the main peak indicates an ionic interaction or a hydrogen bond between phosphonic acid and Im. These interactions between phosphonic acid and Im are believed to suppress the formation of phosphonic acid anhydride. The full width at half-maximum (fwhm) of the 31P NMR spectra for PVPA homopolymer, x = 1, and x = 2 was 9.1 ppm at 34 °C. At 100 °C, the fwhm of PVPA homopolymer, x = 1, and x = 2 became 6.3, 8.6, and 6.8 ppm, respectively. The large decrease in fwhm for PVPA homopolymer and x = 2 7470

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been caused by increased flexibility of PVPA at high temperatures. Heterogeneous Dynamics of Im by 2H NMR. The 2H NMR broadline spectrum at 20 °C and the QCPMG spectra in the temperature range between −80 and 20 °C for PVPA/2Imd3 are represented in Figure 3a,b. The broadline spectrum at 20 °C showed a rigid deuterium powder pattern. The red line in Figure 3a is the simulation of a rigid deuterium powder pattern with a quadrupole coupling constant e2qQ/h = 180 kHz, an asymmetry parameter η = 0.07, and the Lorentzian broadening factor of 3 kHz. The QCPMG spectrum in the rigid state consists of a row of evenly spaced sharp peaks as seen in the spectrum observed at −80 °C (Figure 3b). The increase in the line width and the decrease in the intensity of each peak in the QCPMG spectrum are caused by the slower reorientational molecular motion which does not affect the line shape of the 2H NMR broadline spectrum.24,25 For the QCPMG spectrum observed above −20 °C, the line width of each peak increased and the intensity of peaks within ±50 kHz decreased with increasing temperature. These changes in line shape of the QCPMG spectrum suggest that the Im molecules undergo rotational vibration around the pseudo 5-fold axis (Scheme 1a).24 Determination of the angle of vibration is difficult in this temperature range since the apparent angular dependence of the line shape of the QCPMG spectrum does not appear in the slow motion range. Spectral simulation was provisionally performed with a ±30°angle. The red lines in Figure 3b indicate spectral simulation assuming the rotational vibration of Im around the pseudo-5fold axis. For the simulation of QCPMG, a spin−spin relaxation time T2 value of 2.2 ms, which was estimated from the spectrum at −80 °C, was used. The rate of rotational vibration (klib) was obtained for each temperature, as shown in Figure 3. Figure 3c,d shows the 2H NMR broadline spectrum at 40 °C and the QCPMG spectra in the temperature range between −70 and 40 °C for x = 1. The red line in Figure 3c is the simulation of a rigid deuterium powder pattern of x = 1 using the same e2qQ/h, η, and broadening factor as x = 2 (Figure 3a). Changes in the line shape of the QCPMG spectrum due to the rotational vibration of Im were observed above −10 °C for x = 1. The line width of each peak of x = 2 is larger than that of x = 1 at 10 °C. klib was obtained for each temperature using spectral simulation with the same rotational angle and T2 values as those of x = 2 (red line in Figure 3d). It was found that the rotational vibration of Im in x = 2 begins at a lower temperature and becomes faster at the same temperatures than that in x = 1. The Tg of x = 1 and 2 is −19 and −30 °C, respectively (see Figure S1 in Supporting Information). These results imply that the

Figure 1. 31P{1H}CP/MAS NMR spectra for PVPA and PVPA/xIm (x = 1, 2) recorded at 4 kHz MAS: (a) 34 °C, (b) 100 °C.

indicates the enhanced mobility and homogeneity of the phosphonic acid group. For x = 1, such a large decrease in fwhm was not observed at 100 °C. The local mobility in x = 1 is predicted to be suppressed by ionic interactions and a hydrogen bond between Im and the phosphonic acid group. Local Structure and Dynamics in PVPA/xIm by 13C NMR. The structure and dynamics of Im and the backbone of PVPA in PVPA/xIm were investigated by a high-resolution solid-state 13C NMR spectrum. Figure 2 shows the temperature dependence of the solid-state 13 C{ 1 H}CP/MAS NMR spectrum for PVPA homopolymer, x = 1, and x = 2. The peak at 33 ppm corresponds to PVPA carbons.17 Two Im peaks were observed at 120 and 136 ppm for PVPA/xIm. Peak splitting of Im’s C4 and C5 was not observed. Therefore, imidazole is predicted to exist almost exclusively as an imidazolium ion due to the strong hydrogen bond between Im or between phosphonic acid and Im in PVPA/xIm. The line broadening in the 13C NMR spectrum is caused by the interference between proton decoupling and molecular motion, when the rate of the latter is comparable to the frequency of the former.28−30 Although a broadening of peaks was not observed for the main chain of PVPA, remarkable line broadening of the Im peaks was observed around 70 and 100 °C for x = 2 and x = 1, respectively. Im molecules are predicted to undergo motion at 105 Hz in these temperature ranges since the radio-frequency field strength ω1 (=2πν1) of proton decoupling was 240 kHz. The intensity of the 13C NMR spectrum of the main chain of PVPA decreased suddenly at 100 °C for x = 2. The depreciation of cross-polarization (CP) efficiency might have

Figure 2. Temperature dependence of 13C{1H}CP/MAS NMR spectrum recorded at 4 kHz MAS: (a) PVPA, (b) PVPA/1Im, and (c) PVPA/2Im. *The broad peak around 110−140 ppm is a background signal arising from rotor caps. 7471

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Figure 3. 2H NMR broadline and QCPMG spectra below 20 °C for PVPA/2Im (a, b) and below 40 °C for PVPA/1Im (c, d). The red lines in (a) and (c) are the simulation of a rigid deuterium powder pattern with e2qQ/h = 180 kHz and η = 0.07. The red lines in (b) and (d) are a simulation that considers the rotational vibration around the pseudo-5-fold axis of Im with an angle of ±30° (Scheme 1a).

rotational vibration of Im begins according to segmental relaxations due to the glass transition. The 2H NMR broadline and QCPMG spectra above 30 °C for x = 2 and those above 50 °C for x = 1 are shown in Figures 4 and 5, respectively. For the broadline spectrum, the spectral intensity around ±60 kHz decreased and that of the central portion increased with increasing temperature. These changes in the line shape of the 2H NMR broadline spectrum are observed when the rate of isotropic rotation of molecules gradually increases. For the simulation of the 2H NMR spectrum due to the isotropic rotation of molecules, the multisite jump on the cone at the magic angle (Scheme 1c) and the tetrahedral jump (Scheme 1d) are conventional models.23 In polymers, there is often a large distribution of correlation time of molecular motion.22 Simulation of the 2H NMR broadline and QCPMG spectra at 35 °C was performed using an eight-site jump on a cone at the magic angle (Scheme 1c) with a Gaussian distribution of the jumping rate krot. The observed and simulated spectra are shown in Figure 6a−d. The signal intensity was reduced by the molecular motion with the intermediate jumping rate. The reduction factor of signal intensity due to the eight-site jump on a cone at the magic angle was estimated. The distribution of the jumping rate used for the spectral simulation, the estimated reduction factor, and the resulting signal intensity are shown in Figure 6e. The line width of the central portion of the observed broadline spectrum is broad when compared with the simulation (Figure 6a,b). The line broadening of the central component of the broadline spectrum indicates that the motion of Im molecules is not perfectly isotropic. Rather, there is pseudoisotropic rotation with small anisotropy. Each peak of the observed QCPMG spectrum was broad, and the intensity of peaks within ±50 kHz was weak relative to the simulated one

Figure 4. 2H NMR broadline spectrum (a) and QCPMG spectrum (b) above 30 °C for PVPA/2Im. The red lines show a simulation that considers Im molecules undergoing isotropic rotation, pseudoisotropic rotation, and rotational vibration. krot indicates the rate of pseudoisotropic rotation. e2qQ/h = 176 kHz, η = 0, anisotropy parameter A = 0.12, and the angle of rotational vibration θ = ±30° were used for simulation.

(Figure 6c,d). These differences between observed and simulated QCPMG spectra are caused by the rotational vibration of Im. Thus, it is difficult to reproduce the broadline 7472

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the rotation of Im molecules is more strongly suppressed in x = 1 than in x = 2. For the QCPMG spectrum in Figures 4 and 5, the component of the rotational vibration of the Im molecules and the central sharp peak due to the fast isotropic rotation of the Im molecules were observed at low temperatures. The intensity of the central broad component corresponding to the pseudoisotropic rotation of the Im molecules increased with increasing temperature. This broad line shape of the central component indicates that the rate of pseudoisotropic rotation of the Im molecules is in the range of 104−105 Hz. Above 50 °C for x = 2 and 80 °C for x = 1, a decrease in the line width of the QCPMG spectrum accompanied by a decrease in anisotropy of the pseudoisotropic rotation of the Im molecules was observed. Thus, three kinds of Im molecules, namely Im undergoing pseudoisotropic rotation with small anisotropy, rotational vibration, and fast isotropic rotation, were recognized in the temperature range of 30−50 °C for x = 2 and 50−80 °C for x = 1 from the QCPMG spectrum. The Im molecules undergoing rotational vibration interact strongly with phosphonic acid, and their mobility is highly restricted in the tight segment. The Im molecules undergoing pseudoisotropic rotation do not have a strong interaction with phosphonic acid and are relatively movable in the flexible segment. The Im molecules undergoing fast isotropic rotation are predicted to be in a flexible space around the end of PVPA chains. In order to investigate the rate and anisotropy of pseudoisotropic rotation, and the ratio of three kinds of motions of the Im molecules in PVPA/xIm, simulations of the 2 H NMR broadline and QCPMG spectra were performed. Although these motions might span a wide range of jumping rates, for simplicity, a single jumping rate was used for each motion. The line shape of the 2H NMR spectrum due to the isotropic rotation and the pseudoisotropic rotation of the Im molecules was simulated by the tetrahedral jump model (Scheme 1d).32 The four deuteron sites were determined by Eular angles (β, γ) of eq 1 as (0°, 0°), (β′, 0°), (β′, 120°), and (β′, 240°). Here, the anisotropy parameter A for molecular rotation is defined as

Figure 5. 2H NMR broadline spectrum (a) and QCPMG spectrum (b) above 50 °C for PVPA/1Im. The red lines show a simulation that considers Im molecules undergoing isotropic rotation, pseudoisotropic rotation, and rotational vibration. krot indicates the rate of pseudoisotropic rotation. e2qQ/h = 176 kHz, η = 0, anisotropy parameter A = 0.14, and the angle of rotational vibration θ = ±30° were used for simulation.

A=

1 (2 + 3(3 cos2 β′ − 1)) 8

(3)

For the isotropic rotation, β′ is 109.4° and A becomes 0. In the present work, β′ changed in the range of 109.4°−180°, and the range of A was 0−1. As the A value increased, the line width of the central portion of the 2H NMR spectrum increased (see Figure S2 in Supporting Information). The observed and simulated 2H NMR broadline and QCPMG spectra of x = 2 at 35 and 45 °C are shown in Figure 7. Simulation spectra were obtained by the superposition of three components: pseudoisotropic rotation with small anisotropy, rotational vibration, and fast isotropic rotation of the Im molecules. The rate of rotational vibration (1.0 × 104 Hz), estimated by extrapolation from the rates at low temperatures, was used for the simulation. A rate of 1.0 × 108 Hz was used for fast isotropic rotation. The rate krot and anisotropy parameter A of the pseudoisotropic rotation and the ratio of each component which reproduced the 2H NMR broadline and QCPMG spectra simultaneously were determined. There was an extreme decrease in the intensity of the 2H NMR spectrum in the presence of molecular rotational motion at a rate of 104−105 Hz.19−21 Therefore, although the abundance of Im undergoing

Figure 6. 2H NMR broadline and QCPMG spectra at 35 °C for PVPA/2Im. (a) and (c) are observed broadline and QCPMG spectra, respectively. (b) and (d) are a simulation using the cone model at the magic angle (Scheme 1c) and a Gaussian distribution of the jumping rate. (e) is the distribution of the jumping rate, reduction factor, and resulting signal intensity.

and QCPMG spectra simultaneously using a single motional mode. Above 50 °C for x = 2 and 80 °C for x = 1, the line width of the broadline spectrum decreased with increasing temperature. Therefore, anisotropy of the pseudoisotropic rotation of the Im molecules decreased at high temperatures. The spectrum of x = 1 was broader than that of x = 2 at 100 °C. This implies that 7473

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Table 1. Ratios of Im Molecules Undergoing Rotational Vibration and Pseudo-Isotropic Rotation in PVPA/xIm PVPA/ xIm x=2

x=1

Figure 7. Observed and simulated 2H NMR spectra for x = 2. (a) and (b) are broadline spectra and QCPMG spectra at 35 °C, respectively. (c) and (d) are broadline spectra and QCPMG spectra at 45 °C, respectively. (i) Simulation spectra of the rotational vibration of Im with klib = 1 × 104 Hz and θlib = ±30°; (ii) simulation spectra of the pseudoisotropic rotation of Im with krot = 5 × 104 Hz (35 °C), 1 × 105 Hz (45 °C), and A = 0.12; (iii) simulation spectra of isotropic rotation of Im with kiso = 1 × 108 Hz; (iv) superposition of (i), (ii), and (iii) components; (v) observed spectra. e2qQ/h = 176 kHz and η = 0 were used for simulation. The ratio of Im molecules undergoing pseudoisotropic rotation, rotational vibration, and isotropic rotation were 96.2, 3.7, 0.09 and 98.9, 1.0, 0.07 at 35 and 45 °C, respectively.

T (°C)

rotational vibration (%)

pseudoisotropic rotation (%)

30 35 40 45 50 50 55 60 65 80

9 4 2 1 0.4 8 6 4 2 0.0

91 96 98 99 99.6 92 94 96 98 100

Figure 8. Temperature dependence of correlation time τrot of pseudoisotropic rotation of the Im molecule in PVPA/xIm. Solid and open circles are τrot of x = 2 and 1, respectively. The solid lines are the least-squares fit using the Arrhenius equation.

For PVPA/xIm, a Grotthuss mechanism was predicted to be dominant in the proton conduction process, and the reorientational motion of the Im molecules may contribute to the proton transfer between Im molecules.1,2 When proton conductivity is dominated by the proton transfer between Im molecules followed by reorientation of the Im molecule, the correlation time τ for the reorientational motion of the Im molecule obtained from 2H NMR can be related to proton conductivity σ as

pseudoisotropic rotation exceeds 90%, the contribution of this component to the spectrum is strongly suppressed. The red lines in Figures 4 and 5 show the results of the spectral simulation. krot and A for the pseudoisotropic rotation and the ratio of each component were estimated from a spectral simulation at each temperature. In the temperature range between 30 and 50 °C, the spectrum could be reproduced by A = 0.12 for x = 2. A was 0.14 in the temperature range between 50 and 80 °C for x = 1. Thus, the rotation of Im molecules was more suppressed with x = 1 than with x = 2. The ratio of Im molecules undergoing fast isotropic rotation was less than 0.2%. The ratios of Im molecules undergoing rotational vibration and pseudoisotropic rotation are shown in Table 1. The ratio of the flexible segment where Im molecules undergo pseudoisotropic rotation was greater than 90%. The ratio of the tight segment where Im molecules undergo rotational vibration decreased, and the flexible segment increased with increasing temperature. Above 60 °C for x = 2 and 80 °C for x = 1, the tight segment was not observed. Dynamics of Im and Proton Conductivity. The correlation time of pseudoisotropic rotation of the Im molecules τrot was estimated from krot using τrot = 1/(4krot). Figure 8 shows the temperature dependence of τrot. The τrot value is predicted to lie in the range of 10−7−10−8 s between 80 and 130 °C for x = 2.

σ=

nq2l 2 2τkBT

(4) 31

by assuming one-dimensional proton diffusion. Here, n, q, and l are the number density of charge carriers (the NH protons in Im), their charge, and the mean distance of proton movement by reorientation of the Im molecule, respectively. kB and T are the Boltzmann constant and temperature, respectively. Using eq 4 and the structural data of PVPA and Im,14,15 conductivities of 10−4−10−3 S/cm (similar to values observed elsewhere1) can be obtained from the correlation times τrot of the pseudoisotropic rotation of Im molecules in the temperature range of 80−130 °C for x = 2. These results suggest that an efficient proton transfer between Im molecules accompanied by the pseudoisotropic rotation of Im molecules exists in PVPA/xIm. These Im molecules provide a proton conduction path and lead to high proton conductivity for x = 2 at high temperatures. Sevil et al. interpreted the results of proton conductivity as the Vogel−Tamman−Fulcher (VTF) behavior.1 In the temperature range between 30 and 60 °C, the slope of proton 7474

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conductivity was steeper than at above 70 °C and corresponded to an activation energy of ∼90 kJ/mol.1 In this temperature range, more than 90% of Im molecules undergo pseudoisotropic rotation with an activation energy of 59 kJ/mol. The activation energies of the rotation of the Im molecule in x = 1, 2 obtained by 2H NMR and those estimated from proton conductivity are shown in Table 2.

factors when discussing the increase in proton conductivity of PVPA/xIm as the amount of Im molecule increases. The slope of temperature dependence of proton conductivity of x = 1 was steeper than that of x = 2, and its activation energy was estimated to be about 120 kJ/mol.1 This value is much larger than that of the pseudoisotropic rotation of Im molecules (64 kJ/mol). The ratio of Im molecules undergoing rotational vibration in x = 1 is higher than that in x = 2, as shown in Table 1. Therefore, compared to x = 2, the obstruction of tight segments by proton conduction becomes larger for x = 1. The temperature dependence of the full width at halfmaximum (fwhm) of the 2H NMR broadline spectrum at high temperatures, where the component undergoing rotational vibration was not observed, is represented in Figure 9. In this

Table 2. Activation Energies of Rotation of Imidazole Molecule and Proton Conduction for PVPA/xIm PVPA/ xIm

T (°C)

activation energy of rotation of imidazole (kJ/mol)

activation energy of proton conduction (kJ/mol)

x=2

60 80

59 35 64 35

∼901 21−33 (>100 °C, x > 2)2 ∼1201 ∼801

x=1

The large difference in the activation energies of proton conductivity and pseudoisotropic rotation of the Im molecules is attributed to the difference in long-range proton conduction observed by proton conductivity and short-range proton transfer associated with the reorientational motion of Im molecules. The tight segments where Im molecules strongly interact with phosphonic acid and undergo rotational vibration are predicted to prevent long-range proton conduction, as shown in Scheme 2a. The activation energy of the pseudoisotropic rotation of Im molecules was estimated to be 64 kJ/mol for x = 1. This value is higher than that of x = 2. The rate of pseudoisotropic rotation of Im molecules in x = 1 is slower than that in x = 2 at the same temperature. Moreover, the anisotropy parameter A of pseudoisotropic rotation for x = 1 was larger than that for x = 2. It is clearly seen that the mobility of the Im molecules in x = 2 is higher than that in x = 1. The excess Im molecules that intercalated with PVPA do not interact strongly with phosphonic acid and relax the packing of polymer chains and make a flexible space in PVPA. Actually, Tg of x = 2 is lower than that of x = 1 at more than 10 °C. The increase in the amount of Im molecules as a proton carrier as well as the enhanced mobility of the Im molecules are very important

Figure 9. Temperature dependence of full width at half-maximum (fwhm) of the 2H NMR broadline spectrum for PVPA/xIm (x = 1,2). Solid and open circles are fwhm of x = 2 and 1, respectively. The solid lines are the least-squares fit using the Arrhenius equation.

temperature range, the decrease in fwhm indicates that the anisotropic rotation of Im molecules approaches isotropic rotation. From the slope of the ln(fwhm) vs 1/T plot, the activation energy was estimated to be 35 kJ/mol for x = 1, 2. Similar activation energy values have been reported for the proton conductivity of PVPA/xIm above 100 °C and for other proton-conducting materials, including Im (Table 2).2,8 In this temperature range, only a flexible segment exists in PVPA/xIm.

Scheme 2. Schematic Representation of the Predicted Local Structure and Proton Conduction Process in PVPA/xIma

a

(a) Structure including a mobile segment and a tight segment at low temperatures. In the mobile segment, the Im molecules undergo pseudoisotropic rotation. In the tight segment, the Im molecules interact strongly with phosphonic acid and suppress motion. The tight segment prevents long-range proton conduction. (b) Structure without a tight segment at high temperatures. The reorientation of the Im molecules assists long-range proton conduction. 7475

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Therefore, the long-range proton conduction associated with the rotation of Im molecules is expected (Scheme 2b). Kawada et al. estimated the self-ionization energy of Im to be between 36 and 44 kJ/mol.13 The ionization of Im as well as breaking and formation of hydrogen bonds between Im molecules are important processes when assessing the Grotthuss-type proton diffusion in the hydrogen bond network of Im. The activation energy of the rotation of Im molecules in PVPA/xIm is dominated by steric hindrance and the interactions between Im molecules and PVPA in the intercalated space at low temperatures. At high temperatures, not only the mobility of Im molecules but also that of PVPA increased, as seen in 31P and 13C NMR spectra. Therefore, steric hindrance and the interactions between Im molecules and PVPA become lower and interactions in the hydrogen bond network of Im may dominate the activation energy of rotation of Im molecules. The consistency of activation energy between the molecular rotation of Im and proton conductivity suggests that the formation of the Im ion as well as breaking and forming hydrogen bonds for proton conduction are connected with the molecular rotation of Im at high temperatures.

CONCLUSIONS In the present investigation, the mode, rate, and anisotropy of the reorientational motion of Im molecules were investigated for PVPA/xIm. The enhanced mobility of Im molecules due to an increase in x was observed. Between 20 and 50 °C, there is a mobile segment where Im molecules undergo pseudoisotropic rotation with small anisotropy and a tight segment where Im molecules undergo rotational vibration in PVPA/2Im. The mobile segment accounted for more than 90% and the tight segment for less than 10%. The tight segment prevented longrange proton conduction. Above ca. 60 °C, only the mobile segment was observed. In this temperature range, formation of the Im ion and breaking and forming of hydrogen bonds for proton conduction were found to be closely related with the pseudoisotropic rotation of Im molecules. Thus, efficient proton conduction accompanied by the pseudoisotropic rotation of Im molecules exists for PVPA/2Im. The enhanced pseudoisotropic rotation of Im molecules is correlated with an increase in the proton conductivity of PVPA/xIm. ASSOCIATED CONTENT

S Supporting Information *

DSC thermodiagrams and simulation of the 2H NMR spectrum due to pseudoisotropic rotation of the imidazole molecule. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported a Grant-in-Aid for Scientific Research (No. 23310063, 26286002) from the Ministry of Education, Culture, Sports, Science and Technology, Government of Japan. 7476

dx.doi.org/10.1021/ma5013418 | Macromolecules 2014, 47, 7469−7476