Ring-Puckering Motion of Azetidinium Cations in a MetalâOrganic

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Ring-Puckering Motion of Azetidinium Cation in a Metal-Organic Perovskite [(CH)NH][M(HCOO)] (M = Zn, Mg) - A Thermal and H NMR Relaxation Study 2

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Tetsuo Asaji, Yoshiharu Ito, Hiroki Fujimori, and Biao Zhou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11789 • Publication Date (Web): 25 Jan 2019 Downloaded from http://pubs.acs.org on January 25, 2019

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The Journal of Physical Chemistry

Ring-Puckering Motion of Azetidinium Cation in a Metal-Organic Perovskite [(CH2)3NH2][M(HCOO)3] (M = Zn, Mg) − A Thermal and 1H NMR Relaxation Study − Tetsuo Asajia,*, Yoshiharu Itob†, Hiroki Fujimoria,b, and Biao Zhoua,b a Department

of Chemistry, College of Humanities and Sciences,

Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan b

Department of Correlative Study in Physics and Chemistry, Graduate School of Integrated Basic Sciences,

Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan † Present

address: Department of Material Science and Engineering, Tokyo Institute of

Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan

ABSTRACT A metal-organic perovskite which consists of four-membered-ring ammonium (azetidinium), magnesium, and formate ions, [(CH2)3NH2][Mg(HCOO)3] was synthesized. Differential scanning calorimetry revealed a first-order phase transition at Tc = 288 K. Beside a sharp anomaly at Tc, a broad Schottky-type anomaly was observed at 273 K. Temperature dependences of spin-lattice and dipolar spin-lattice relaxation times T1 and T1D were determined. In the low-temperature phase, short and long T1values were observed. T1D showed a minimum of 0.15 ms at around 220 K, which can be assigned to the ring-puckering motion of azetidinium cation. Comparing with the previously reported zinc analogue [(CH2)3NH2][Zn(HCOO)3], energy separation between the two molecular conformations associated with the ring-puckering motion and inhomogeneity occurred in the crystals at low-temperatures are discussed.

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* Tel: +81 3 5317 9739. E-mail: [email protected]

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1. INTRODUCTION Recently, the formate-based metal-organic frameworks of general chemical formula A[M(HCOO)3] (M=Mn, Fe, Co, Ni, Cu, Zn, Mg) have attracted significant scientific attention.1-3 The organic cation A+ in these compounds is included in the cavity of the anionic NaCl-type metal-formate-frame. Since the structure can be regarded as CaTiO3 (mineral perovskite)-like structure, this type of compound is called a metal-organic perovskite. These compounds show interesting physical properties such as ferro- or antiferroelectricity. The onset of these properties is expected to be related to the excitation of the molecular motion of the organic cations in the cavity. Therefore, the dynamics of the cations have been extensively studied by use of various experimental techniques including nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and quasielastic neutron scattering.4-9 Azetidinium (AzH+), (CH2)3NH2+, is a four-membered-ring ammonium cation, which has a degree of freedom of the ring-puckering motion. Utilizing the freezing of the ring-puckering motion of AzH+, Zhou et al.10,11 have successfully obtained a series of interesting compounds AzHM(HCOO)3 (M = Cu, Mn, Zn) having an extremely large and broad dielectric anomaly at around 280 K. It was speculated from the strong thermal cycle dependence of the dielectric behavior that small ferroelectric domains gradually develop in the non-polar crystal during the thermal cycles, like the famous metal-oxide perovskite relaxor Pb(Mg1/3Nb2/3)O3 (PMN) with polar domains embedded in a non-polar matrix.11 Although the origin of giant dielectric anomalies is not clear yet, an evolution of a kind of “dipole cluster”, in which the sum of molecular electric dipole moments survives, is strongly suggested.

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If that is the case, a development of inhomogeneity in the crystal should be detected. It has been reported that in 207Pb NMR spin-lattice relaxation time T1 measurements of PMN, the 207Pb magnetization recovery curves become definitely nonexponential below the relaxor transition temperature suggesting an existence of polar nanoregions embedded in a nonpolar cubic matrix.12 Previously, we have reported 1H NMR T1 study of AzHZn(HCOO)3, in which the ring-puckering motion of AzH+ cation was revealed above the phase transition temperature Tc1 = 299 K and another first-order phase transition was detected at Tc2 = 254 K.13 On the other hand, the molecular motion below Tc1 was discussed only on the basis of speculation, and furthermore 1H magnetization recovery curves were not examined with enough attention whether it becomes nonexponential below Tc1. Therefore, in the present study we reinvestigated 1H T1 at several temperatures as well as checked the previously obtained data, and in order to reveal the ring-puckering motion below Tc1, proton dipolar spin-lattice relaxation time T1D was measured. It is known that T1D is sensitive to slow molecular motion with frequency of the order of the resonance frequency in the local field ( ~10 kHz).14-17 For getting a deeper understanding of nature, it is sometimes useful to extend measurements to similar substances. So, we have prepared an analogous compound AzHMg(HCOO)3 by replacing the metal ion from Zn to Mg, which is also diamagnetic so that molecular motion is expected to be able to be investigated by use of 1H NMR relaxation measurements.

2. EXPERIMENTAL 2.1. Sample

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The sample crystals of AzHZn(HCOO)3 used in the preceding study13 was used for the present measurements. AzHMg(HCOO)3 was prepared by a similar solutiondiffusion-method as the Zn analogue. A typical procedure is as follows. A 30 mL of a 0.5 mol L−1 solution of HCOOH in methanol added 1 mL of azetidine was placed at the bottom of a glass tube (30 mm diameter and 40 cm long). Then, 12 mL of methanol and 50 mL of a 0.1 mol L−1 solution of MgCl2∙6H2O in methanol were carefully layered in sequence. The glass tube was sealed with a silicone rubber stopper and kept undisturbed. After several days of crystallization, the colorless block-like crystals were collected. The sample was identified by chemical analysis conducted by Center for Organic Elemental Microanalysis, Kyoto University. Anal. Calcd. for [(CH2)3NH2][Mg(HCOO)3]: C, 33.14; H, 5.10; N, 6.44 %. Found: C, 33.07; H, 5.14; N, 6.32 %.

2.2. Powder and single crystal X-ray measurements X-ray powder diffraction measurements were conducted using a diffractometer (Rigaku, Rint 2100) with monochromated Cu (Kα) radiation ( λ = 1.5418 Å ). Single crystal X-ray measurements were performed using a Rigaku AFC-8 diffractometer equipped with a Mercury CCD detector using monochromated Mo (Kα) radiation (λ = 0.71075 Å).

2.3. 1H NMR A pulsed NMR system consisting of an in-house-built probe, a flow-cryostat (Cryo Industries RC 152), a superconducting magnet (Cryomagnetics), and a spectrometer (Thamway PROT 3100MR) was used at a Larmor frequency of 47.35 or 45.08 MHz. For the measurements, the pulverized crystals were sealed in a glass tube

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along with ca. 5 kPa helium gas to heat-exchange. The spin-lattice relaxation time T1 was determined using a comb−−90°(x) −e−90°(y) pulse sequence. The 90° pulsewidth was 4.5 s and the pulse delay time e for solid-echo pulses was set at 5.5 s. The intensity of solid echo was measured as a function of the delay time τ after comb pulses. The delay time τ was varied usually up to about 102 times longer than the expected T1 value. For the measurements of the dipolar spin-lattice relaxation time T1D, 90°(x)−−45°(y) −e−45°(y) pulse sequence with  = 10 μs was used. The intensity of Jeener echo observed after the last 45°(y) pulse was measured as a function of the pulse separation time e to determine T1D.18, 19 The spin-spin relaxation time T2 was determined by measuring the intensity of solid echo as a function of the pulse separation time e using 90°(x) −e−90°(y) pulse sequence. For echo intensity, a small offset voltage was corrected in the all above measurements of relaxation times. 2.4. DSC Differential scanning calorimetry (DSC) measurement was conducted by use of PerkinElmer DSC8500 employing heating and cooling rate of 10 K min-1. 7.25 mg of AzHMg(HCOO)3 was used.

3. RESULTS AND DISCUSSION 3.1. Spin-lattice relaxation time T1 Elemental analysis of the Mg analogue AzHMg(HCOO)3 described in the experimental section and X-ray powder diffraction pattern shown in Figure 1 suggest that a similar compound with AzHZn(HCOO)3 structure can be prepared, in which the

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metal ion is replaced from Zn to Mg. The structural similarity of the Mg analogue with the Zn analogue was confirmed also by a preliminary single crystal analysis, although it was recognized that a complete structure analysis is not easy due to evolution of crystalline twin structure.

(CH2)3NH2Zn(HCOO) 3

(CH2)3NH2Mg(HCOO) 3

20

2

40

Figure 1. Comparison of X-ray powder diffraction patterns of the Mg and Zn analogues.

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T/K

400 10

1

280

250

(CH2)3NH2Mg(HCOO) 3 1

H NMR T1

47.35 MHz T1 / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10

0

288 K −1

24 kJ mol

10

270 K

−1

3

3

10 K / T

4

Figure 2. Temperature dependence of spin-lattice relaxation time T1 of AzHMg(HCOO)3. The T1 values measured with increasing and decreasing temperature are shown by black and blue symbols, respectively. In case of nonexponential recovery, short and long T1 values are shown by inverted-triangles and triangles, respectively. Temperatures at which heat anomalies were observed in DSC measurements are indicated by arrows.

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Figure 2 shows the temperature dependence of spin-lattice relaxation time T1 of the Mg analogue. The overall feature is similar to that of the Zn analogue except for that the Mg analogue shows only single phase transition instead of two observed in the Zn analogue. Phase transition temperature was located at 270 K and 288 K, respectively, with decreasing and increasing temperature by DSC measurements. This indicates this phase transition is of first-order. The T1 observed in 260-290 K with increasing temperature from low-temperature below 260 K, showed slightly longer values than that observed with decreasing temperature from high-temperature above 290 K. The T1 minimum of 0.11 s, observed at around 350 K using Larmor frequency of 47.35 MHz, can be assigned to ring-puckering motion of AzH+ cations as discussed in the previous paper.13 From the fitting calculations by use of Bloembergen-Purcell-Pound formula,13, 20, 21

the activation energy of 24 kJ mol−1 was obtained. The correlation time of the ring-

puckering motion becomes about 10 ns at around 300 K. With decreasing temperature, it was found that proton magnetization recovery showed an appreciable deflection from a single exponential law below about 260 K. The recovery could be interpreted by assuming the magnetization which consists of the two components with short- and long-T1. Figure 3 shows the magnetization recovery curves obtained at 294 K (high-temperature phase), 244 K, 150 K, and 76.0 K. The recovery function is defined by S() = (M0 – M())/M0 using the solid echo intensity M() measured with the delay time  after comb pulses and the equilibrium intensity M0 of the echo signal in thermal equilibrium. In Figure 3, ln S() is plotted as a function of . The plots of high-temperature phase (294 K) result in a straight line showing a single exponential law is well established. While, in order to explain the data of lowtemperature phase, it is necessary to introduce at least two, short and long, spin-lattice

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relaxation times T1S and T1L. In this case, the signal intensity was assumed to be explained by a bi-exponential function (1).

M ( )  M 0S [1  exp( / T1S )]  M 0 L [1  exp( / T1L )] .

(1)

Here, M0S and M0L denote amplitudes of the magnetization with short and long spinlattice relaxation times, respectively.

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0

ln S ( )

0

AzHMg(HCOO) 3 T = 294 K

−1


−2

−2

−4 0

0.4

0

0.8

/s


−2

−4

0

0

ln S ( )

−3

ln S ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ln S ( )

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40

/s

80

AzHMg(HCOO) 3 T = 76.0 K

−2

−4 0

4

8

/s

12

0

40

/s

80

Figure 3. Magnetization recovery curves of AzHMg(HCOO)3 at several temperatures. Recovery function S() is defined by S() = (M0 – M())/M0 using the solid echo intensity M() measured with the delay time  after comb pulses and the equilibrium intensity M0 of the echo signal in thermal equilibrium. The data at 244, 150, and 76.0 K were fitted by a bi-exponential function with short and long spin-lattice relaxation times T1S and T1L; (T1S, T1L) were obtained as (1.4 s, 5 s), (6 s, 30 s), and (6 s, 43 s), respectively.

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We have also tried to explain the nonexponential recovery by the stretched exponential model22-25 which is often applied to a glassy state. However, the stretched exponential model failed to explain the recovery at 76 K as shown in the Supporting Information (SI). Taking these results of AzHMg(HCOO)3, we reanalyzed the magnetization recovery in the low-temperature phase of AzHZn(HCOO)3. Since this compound has two phase transitions at Tc1 = 299 K and Tc2 = 254 K, the three phases are called as the high-, intermediate-, and low-temperature phases in this paper. In the case of the Zn analogue, the deflection from a single exponential law was not so appreciable as compared with the Mg analogue that we have analyzed the magnetization recovery by the stretched exponential model.22-25 In Figure 4(a), as an example of data, ln S() obtained at 301 K, 200 K, 100 K, and 76.4 K are plotted as a function of . For comparison, the same quantities are also plotted as a function of β in Figure 4(b). In the stretched exponential model, the recovery function S() decays according to the following equation.

     S ( )  exp       T1  

0   1

.

(2)

So, ln S(τ) vs τβ plots result in a straight line with the slope of -T1-β. As shown in Figure 4(b), assuming β = 0.8, almost satisfactory results can be obtained, while the plot of Figure 4(a) is appreciably convex downward for the low-temperature phase (LTP). For the high-temperature phase (HTP) at 301 K, on the other hand, the stretched exponential plots with β = 0.8 result in a curve slightly convex upward showing the agreement with

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a single exponential law is better. As for the intermediate-temperature phase (ITP), the recovery function was observed at 267 K to obey a single exponential law, too.

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ln S ( )

0

AzHZn(HCOO) 3 T = 301 K

−1

0.4


−1

T = 301 K

 = 0.8 0

0

0


−2

−3

40

/s

0

200

/s

AzHZn(HCOO) 3

0

T = 76.4 K

−2

−2 80

/s

20

40

( / s)



80

AzHZn(HCOO) 3 T = 76.4 K

−1

40



 = 0.8

0

−1

0

( / s)

T = 100 K

0

ln S ( )

100

10

AzHZn(HCOO) 3

−4 0

0.8

 = 0.8

−2

−4



T = 200 K

0

ln S ( )

20

( / s)

AzHZn(HCOO) 3

−2 0

0.4

−1

−2

ln S ( )

AzHZn(HCOO) 3

−3

0.8

/s

ln S ( )

ln S ( )

0

0

−3

0

−2

−3

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−1

−2

ln S ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ln S ( )


120

 = 0.8 0

(a)

20

( / s)



40

(b)

Figure 4. Magnetization recovery curves of AzHZn(HCOO)3 at several temperatures. Decay of the recovery function S() = (M0 – M())/M0 is compared by assuming (a) a single exponential law and (b) stretched exponential model. - 14 -


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3.2. Schottky-type thermal anomaly As reported in our previous study,13 AzHZn(HCOO)3 shows two endothermic peaks at Tc2 = 254 K and Tc1 = 299 K in the DSC measurements with increasing temperature. Here, it is noteworthy that a broad endothermic peak is accompanied in between the two temperatures. DSC measurements of AzHMg(HCOO)3 also showed a Schottky-type anomaly26, 27 below a sharp thermal anomaly at Tc = 288 K assigned to phase transition as shown in Figure 5. In this case, however, only single phase transition was observed. The lower-temperature phase transition corresponding to that observed at Tc2 in the Zn analogue with increasing temperature was not detected. The phase transitions at Tc1 and Tc2 of the Zn analogue seem to be of second- and first-order, respectively, judging from the continuous and thermal-history-dependent temperature dependences of 1H T1 through Tc1 and Tc2, respectively.13 On the other hand, the phase transition of the Mg analogue is of first-order as shown by the large thermal hysteresis observed in DSC measurements (Figure 5). The transition entropy was calculated as ΔS = 5.6 J K−1 mol−1 including the Schottky-type anomaly on the low-temperature side. This value is comparable with ΔS = 4.3 J K−1 mol−1 observed in the Zn analogue13 as well as the theoretical value of R ln 2 = 5.8 J K−1 mol−1, which suggests phase transitions of these compounds are related to the order-disorder of the AzH+ cation between the two molecular conformations associated with the ring-puckering motion. This Schottky-type anomaly is attributable to the thermal equilibrium between the two molecular conformations. The Schottky heat capacity for a two-level system is given by Csch 

E 2 g1 exp(E / RT ) , 2 RT g 0 1  ( g1 / g 0 ) exp(E / RT )2

(3)

where g0, g1, and ΔE are degeneracies of the ground and excited states, respectively, and a molar energy separation between the two states.26, 27 Putting g0 = g1 = 1 for the - 15 -



energetically favorable and unfavorable conformations of the AzH+ cation, the maximum heat capacity occurs at Tm = 0.417 ΔE / R. In the following, we assume that the broad DSC peak is in principle corresponding to the above heat capacity maximum, although some cooperative effect may have to be considered.27 Then, the energy separation ΔE between the two molecular conformations can be derived from the broad DSC peaks observed at 284 K and 273 K, respectively, in AzHZn(HCOO)3 and AzHMg(HCOO)3. ΔE = 5.7 kJ mol−1 and 5.4 kJ mol−1 were obtained for the LTP of the respective compound.

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288 K

endo 0.4 Net heat flow / mW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-0.4 200

exo

270 K 240

280

320 T/K

Figure 5. DSC curves of AzHMg(HCOO)3 after baseline correction. The heating (red curve) and cooling (blue curve) rate was set to 10 K min-1.

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3.3. Dipolar spin-lattice relaxation time T1D Freezing of the ring-puckering motion of AzH+ cation at low-temperatures is suggested from X-ray crystal structure analysis10, 11 and the present DSC measurements. In order to elucidate a slow molecular motion of the cation in an asymmetric potential well, we have measured proton dipolar spin-lattice relaxation time T1D. Temperature dependences of T1D of AzHZn(HCOO)3 and AzHMg(HCOO)3 are shown in Figures 6 and 7, respectively, along with those of spin-lattice and spin-spin relaxation times T1 and T2. At the temperature where T1 shows a minimum, a shoulder was observed in the temperature dependence of T1D. This is due to the contribution which is proportional to the spectral density at the angular Larmor frequency of 0 or at 20 , to the dipolar spin-lattice relaxation rate in the short correlation time limit.14 The T1D minimum corresponding to the T1 minimum observed at HTP was observed at around 230 K and 220 K in the Zn and Mg analogues, respectively. The maximum dipolar relaxation rate T1D-1 occurs at temperature where the resonance line motionally narrows. The stepwise change of T2 observed at around the T1D minimum temperature in the Zn analogue is consistent with this prediction. On the other hand, the description of the spin system by a spin temperature becomes very dubious in this temperature region since the approach to internal equilibrium after the preparation pulses is also of the order of T2 which is a measure of time required for the spin system to reach its equilibrium. Therefore, any theory based on a density matrix formalism cannot be applied.14-16 In spite of this fact, the expression (4) derived by an extrapolation may be used to get rough justification of the experimental behavior.14, 17

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    T1D1  C  2 2   1   RL 

,

(4)

where  RL and τ denote the rigid lattice line-width in the unit of angular frequency and correlation time of a motion, respectively, and C is a motional constant. In the present case, however, the potential asymmetry should be taken into account. Therefore, the expression will be modified as (5) - (7) referring to the spin-lattice relaxation rate equation for molecular motion in asymmetric double well potential.28

T1D1  C

a 1  a 2

     2 2   1   RL 

,

(5)

where a  exp(E / RT )  pA / pB denotes the ratio of probabilities of occupation of the stable (pA) and metastable (pB) conformations associated with ring-puckering motion, which are separated by ΔE. And the correlation time τ of the motion will be given by (6) and (7).



W

1 W 1 a

1

1

.

(6)

V  1  W exp 0   RT 

(7)

Here, V0 and W are, respectively, the activation energy required to jump and the transition probability per unit time of a transfer, from stable to metastable molecular conformations. W corresponds to W at infinite temperature.

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Using equations (5) - (7), we have tried to explain the temperature dependence of T1D in the LTP. In this approach, the energy separation ΔE was fixed to the estimated value obtained from the broad maximum of heat anomaly observed in DSC measurements: ΔE = 5.7 kJ mol-1 and 5.4 kJ mol-1 for the Zn and Mg analogues, 2 respectively. Further, as the rigid lattice line-width parameter, RL = 7.6×1010 s-2 and

5.7×1010 s-2 were used, which was calculated by putting  RL  2 1 / 2 from the observed half-widths  1 / 2  44 kHz and 38 kHz of the resonance lines at 69 K of the Zn and Mg analogues, respectively. The solid lines in Figures 6 and 7 were obtained by adjusting the parameters 1

V0, W , and C so as for the experimental values to be reproduced. 1

V0 = 41 kJ mol-1,

1

W  1.7 10 14 s , C = 1.2×1011 s-2 and V0 = 31 kJ mol-1, W  3.4 10 12 s , C = 7.2×1010 s-2 were obtained for the Zn and Mg analogues, respectively. These results show that a slow ring-puckering motion is still taking place in the asymmetric potential well in the LTP. The ratio of T1/T1D at around the T1 minimum temperature was estimated to be about 5.4 and 8.5 in the Zn and Mg analogues, respectively. These values are much larger than the theoretical expectation 2 ≤ T1/T1D ≤ 3 15 and suggest that a new motional mode other than the ring-puckering motion is excited at higher temperatures.

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500

T/K

200

80

299 K 1

T1, T1D , T2 / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H NMR T1

10

10

47.35 MHz

(CH2)3NH2Zn(HCOO) 3

0

25 kJ mol

−1

254 K −2 1

H NMR T1D −1

41 kJ mol , E = 5.7 kJ mol 10

−1

−4 1

H NMR T2

4

8

12 10 K / T 3

Figure 6. Temperature dependence of proton dipolar spin-lattice relaxation time T1D along with those of spin-lattice and spin-spin relaxation times T1 and T2 of AzHZn(HCOO)3.

- 21 -



500

T/K

200

80

(CH2)3NH2Mg(HCOO) 3 288 K 10

10

1

0

T1, T1D / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 45

24 kJ mol

H NMR T1 47.35 MHz

−1

270 K −2 1

H NMR T1D

−1

31 kJ mol , E = 5.4 kJ mol 10

−1

−4

4

8

3

12

10 K / T Figure 7. Temperature dependence of proton dipolar spin-lattice relaxation time T1D along with that of spin-lattice relaxation time T1 of AzHMg(HCOO)3.

- 22 -


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3.4. Correlation time of ring-puckering motion and transition probability between two molecular conformations Using motional parameters obtained from spin-lattice as well as dipolar spinlattice relaxation times measurements, temperature dependence of the correlation time of ring-puckering motion of the AzH+ cation is examined in this section. Table 1 summarizes the obtained motional parameters. For the LTP, the correlation time τ is given by (6) and (7), while it is by

 Ea    RT 

    exp

(8)

for the HTP. Figure 8 illustrates the definition of each parameter and double-minimum potentials for ring-puckering motion in the high- and low-temperature phases. In Figure 9, temperature dependence of the correlation time τ was depicted for the both compounds. Reflecting first-order nature of the phase transition, τ of the Mg analogue shows a discontinuity at the transition temperature. The τ of the Zn analogue in the intermediate-temperature phase (ITP) is not clear in the present study. In Figure 9, extrapolations from the HTP and LTP are shown by dotted lines in the temperature 5 5 range of ITP. At 200 K, τ are about 2.4 10 s and 1.4 10 s in the Zn and Mg

analogues, respectively. The transition probabilities W per unit time of a transfer from 3 -1 stable to metastable conformations are calculated at 200 K as 1.3 10 s and

2.6 10 3 s -1 , respectively, using the relation W  (1  a) 1 1 . On the other hand, the 4 -1 4 -1 reverse transition probabilities aW are calculated as 4.0 10 s and 6.9 10 s at

200 K, respectively. Such values of the transition probabilities will be enough to ensure for a “dipole cluster” to follow the alternating electric field of 1 kHz applied in the - 23 -



Page 24 of 45

dielectric measurements, by which frequency an extremely large dielectric anomaly was observed above about 200 K.

Table 1. Motional parameters of ring-puckering motion of azetidinium cation in the high- and low-temperature phases (HTP and LTP, respectively) of AzHZn(HCOO)3 and AzHMg(HCOO)3. Compound

 / s

HTP

E a / kJ mol

1

W

1

/s

LTP V0 / kJ mol 1 E / kJ mol 1

AzHZn(HCOO)3

4.110 13 a)

25a)

1.7 10 14

41

5.7

AzHMg(HCOO)3

7.2 10 13

24

3.4 10 12

31

5.4

a) Reference (13)

Figure 8. Double-minimum potential for ring-puckering motion in high- and lowtemperature phase (HTP and LTP, respectively) and definition of motional parameters.

- 24 -


Page 25 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

0

AzHZn(HCOO) 3

/s

10

−4

AzHMg(HCOO) 3

254 K 288 K

10

−8

270 K 299 K

2

4

6

8

3

10 K / T Figure 9. Temperature dependences of the correlation time τ of ring-puckering motion of azetidinium cation in AzHZn(HCOO)3 and AzHMg(HCOO)3.

- 25 -



3.5. Development of conformational order of azetidinium cations through the crystals The broad heat anomaly observed below Tc1 = 299 K or Tc = 288 K of the Zn or Mg analogues, respectively, suggests that one of molecular conformation becomes more stable than the other. In Figure 10, according to the single crystal X-ray analysis of AzHZn(HCOO)3,11 the ordering of the molecular conformation of AzH+ cation in a cage constructed by metal-formate framework is shown schematically by black and white arrows, by which direction and color the dipole moment component of the cation in the projection plane and the molecular conformation are represented, respectively. Since the two conformation occur with equal probability in the HTP, the conformation is represented by gray color in the HTP. In all phases, the dipole moment components are arranged so as for the total moment to be canceled in the projection plane, that is, there exist equal number of the arrows with opposite orientation in the unit cell. The number of the cation with opposite conformation is also equal to each other, in the LTP as well as HTP resulting in no net dipole moment also in the direction perpendicular to the projection plane. However, all the cations have the same conformation in the ITP resulting in the polar structure with space group of Pna21. A structural inhomogeneity of the LTP was suggested by a distribution of the T1 value which can be described by the stretched exponential model and by the biexponential model in the Zn and Mg analogues, respectively. The origin of the inhomogeneity is not clear yet. However, a collective inversion of the conformation of the cations on a plane perpendicular to the crystal a-axis in LTP will produce a “dipole cluster” having a similar structure with ITP. Mączka et al. reported IR and Raman studies of phase transitions in the Zn analogue.29 The presence of conformational disorder and formation of hydrogen bonds between the cation and the metal-formate

- 26 -


Page 26 of 45

Page 27 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


framework were confirmed by very large bandwidth of the lattice modes. However, a clear evidence of the existence of inhomogeneity has not been reported. The structural details as well as dielectric properties of the Mg analogue are not yet known. These are the subjects of future studies.

- 27 -



Figure 10. Schematic representation of ordering of the azetidinium cations through phase transitions of AzHZn(HCOO)3. The direction of arrows represents the dipole moment component of the cation in the projection plane. Black and white colors show the different molecular conformations and gray color means equal distribution between the two conformations.

- 28 -


Page 28 of 45

Page 29 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4. CONCLUSIONS The energy separation between the stable and metastable molecular conformations of AzH+ cation associated with the ring-puckering motion could be estimated in the low-temperature phase as 5.7 kJ mol-1 and 5.4 kJ mol-1, respectively, for AzHZn(HCOO)3 and AzHMg(HCOO)3, from Schottky-type thermal anomaly observed in DSC measurements. 1H

NMR spin-lattice relaxation time T1 of the Mg analogue was observed to

consist of short and long T1-values in the low-temperature phase, while that of the Zn analogue showed a distribution of the T1 values which is described by the stretched exponential model23 with the stretching exponent β = 0.8. These results suggest a development of inhomogeneity in the crystal and are consistent with the assumption that an evolution of a kind of “dipole cluster” in a nonpolar matrix is a cause of giant dielectric anomalies. Temperature dependence of dipolar spin-lattice relaxation time T1D revealed a slow ring-puckering motion of AzH+ cations in an asymmetric potential at low temperatures. The transition probabilities per unit time of a transfer from stable to 3 -1 3 -1 metastable conformations are estimated to be 1.3 10 s and 2.6 10 s at 200 K in

the Zn and Mg analogues, respectively

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.******* The Stretched Exponential Model Applied for the Nonexponential Recovery of Proton Magnetization of AzHMg(HCOO)3 at 76 K (PDF)

- 29 -



ACKNOWLEDGMENTS Thanks are due to Ms. Ikumi Miyaki for sample preparation and identification. This work was partially supported by the Japan Ministry of Education, Culture, Sports, Science, and Technology (MEXT)-Supported Program for the Strategic Research Foundation at Private Universities, 2009-2013.

- 30 -


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References (1) Wang, Z.; Hu, K.; Gao, S.; Kobayashi, H. Formate-Based Magnetic Metal-Organic Frameworks Templated by Protonated Amines, Adv. Mater. 2010, 22, 1526-1533. https://doi.org /10.1002/adma.200904438 (2) Zhang, N.; Xiong, R. G. Ferroelectric Metal-Organic Framework, Chem. Rev. 2012, 112, 1163-1195. https://doi.org /10.1021/cr200174w (3) Li, W.; Wang, Z.; Deschler, F.; Gao, S.; Friend, R. H.; Cheetham, A. K. Chemically Diverse and Multifunctional Hybrid Organic-Inorganic Perovskites, Nature Reviews Materials 2017, 2, 16099. https://doi.org /10.1038/natrevmats.2016.99 (4) Besara, T.; Jain, P.; Dalal, N. S.; Kuhns, P. L.; Reyes, A. P.; Kroto, H. W.; Cheetham, A. K. Mechanism of the Order-Disorder Phase Transition and Glassy Behavior in the Metal-Organic Framework [(CH3)2NH2]Zn(HCOO)3, Proc. Natl. Acad. Sci. Unit. States Am. 2011, 108, 6828-6832. https://doi.org /10.1073/pnas.1102079108 (5) Asaji, T.; Ashitomi, K. Phase Transition and Cationic Motion in a Metal-Organic Perovskite, Dimethylammonium Zinc Formate [(CH3)2NH2][Zn(HCOO)3], J. Phys. Chem. C 2013, 117, 10185-10190. https://doi.org /10.1021/jp402148y (6) Šimėnas, M.; Balčiūnas, S.; Trzebiatowska, M.; Ptak, M.; Mączka, M.; Völkel, G.; Pöppl, A.; Banys, J. Electron Paramagnetic Resonance and Electric Characterization of a [CH3NH2NH2][Zn(HCOO)3] Perovskite Metal Formate Framework, J. Mater. Chem. C 2017, 5, 4526-4536. https://doi.org/10.1039/C7TC01140G (7) Šimėnas, M.; Ciupa, A.; Usevičius, G.; Aidas, K.; Klose, D.; Jeschke, G.; Mączka, M.; Völkel, G.; Pöppl, A.; Banys, J. Electron Paramagnetic Resonance of a Copper Doped [(CH3)2NH2][Zn(HCOO)3] Hybrid Perovskite Framework, Phys. Chem. Chem. Phys. 2018, 20, 12097-12105. https://doi.org/10.1039/c8cp01426d (8) Šimėnas, M.; Ptak, M.; Khan, A. H.; Dagys, L.; Balevičius, V.; Bertmer, M.; Völkel,

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G.; Mączka, M.; Pöppl, A.; Banys, J. Spectroscopic Study of [(CH3)2NH2][Zn(HCOO)3] Hybrid Perovskite Containing Different Nitrogen Isotopes, J. Phys. Chem. C. 2018, 122, 10284-10292. https://doi.org/10.1021/acs.jpcc.8b02734 (9) Rok, M.; Bator, G.; Medycki, W.; Zamponi, M.; Balčiūnas, S.; Šimėnas, M.; Banys, J. Reorientational Dynamics of Organic Cations in Perovskite-like Coordination Polymers, Dalton Trans. 2018, 47, 17329-17341. https://doi.org/10.1039/C8DT03372B (10) Zhou, B.; Imai, Y.; Kobayashi, A.; Wang, Z-M.; Kobayashi, H. Giant Dielectric Anomaly of a Metal-Organic Perovskite with Four-membered Ring Ammonium Cations, Angew. Chem. Int. Ed. 2011, 50, 11441-11445. https://doi.org /10.1002/anie.201105111 (11) Imai, Y.; Zhou, B.; Ito, Y.; Fujimori, H.; Kobayashi, A.; Wang, Z-M.; Kobayashi, H. Freezing of Ring-Puckering Molecular Motion and Giant Dielectric Anomalies in Metal-Organic Perovskites, Chem.−Asian J. 2012, 7, 2786-2790. https://doi.org/10.1002/asia.201200673 (12) Blinc, R.; Gregorovič, A.; Zalar, B.; Pirc, R.; Laguta, V. V.; Glinchuk, M. D. 207Pb NMR Study of the Relaxor Behavior in PbMg1/3Nb2/3O3, Phys. Rev. B 2000, 63, 024104. https://doi.org/10.1103/PhysRevB.63.024104 (13) Asaji, T.; Ito, Y.; Seliger, J.; Žagar, V.; Gradišek, A.; Apih, T. Phase Transition and Ring-Puckering Motion in a Metal-Organic Perovskite [(CH2)3NH2][Zn(HCOO)3], J. Phys. Chem. A 2012, 116, 12422-12428. https://doi.org/10.1021/jp310132a (14) Van Steenwinkel, R. The Spin Lattice Relaxation of the Nuclear Dipolar Energy in Some Organic Crystals with Slow Molecular Motions, Z. Naturforsch. A 1969, 24, 1526-1531. https://doi.org/10.1515/zna-1969-1010 (15) Goldman, M. Spin Temperature and Nuclear Magnetic Resonance in Solids; Clarendon Press: Oxford, U. K., 1970.

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(16) Lauer, O.; Stehlik, D.; Hausser, K. H. Nuclear Zeeman and Dipolar Relaxation due to Slow Motion in Aromatic Single Crystals, J. Magn. Reson. 1972, 6, 524-532. http://doi.org/10.1016/0022-2364(72)90162-X (17) Paczwa, M.; Sapiga, A. A.; Olszewski, M.; Sergeev, N. A.; Sapiga, A. V. Proton Dipolar Spin-Lattice Relaxation in Nano-Channels of Natrolite, Appl. Magn. Reson. 2016, 47, 895-902. https://doi.org/10.1007/s00723-016-0806-5 (18) Jeener, J.; Broekaert, P. Nuclear Magnetic Resonance in Solids: Thermodynamic Effects of a Pair of RF Pulses, Phys. Rev. 1967, 157, 232-240. https://doi.org/10.1103/PhysRev.157.232 (19) Yang, H.; Schleich, T. Modified Jeener Solid-Echo Pulse Sequences for the Measurements of the Proton Dipolar Spin-Lattice Relaxation Time (T1D) of Tissue Solid-like Macromolecular Components, J. Magn. Reson. Ser. B, 1994, 105, 205-210. https://doi.org/10.1006/jmrb.1994.1126 (20) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Relaxation Effects in Nuclear Magnetic Resonance Absorption, Phys. Rev. 1948, 73, 679-712. https://doi.org/10.1103/PhysRev.73.679 (21) Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: London, U. K., 1961. (22) Sobol, W. T.; Cameron, I. G.; Pintar, M. M.; Blinc, R. Stretched-Exponential Nuclear Magnetization Recovery in the Proton Pseudo-Spin-Glass Rb1-x(NH4)xH2AsO4, Phys. Rev. B 1987, 35, 7299-7302. https://doi.org/10.1103/PhysRevB.35.7299 (23) Johnston, D. C. Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays, Phys. Rev. B 2006, 74, 184430. https://doi.org/10.1103/PhysRevB.74.184430

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(24) Phillips, J. C. Stretched Exponential Relaxation in Molecular and Electronic Glasses, Rep. Prog. Phys. 1996, 59, 1133-1207. https://doi.org/10.1088/00344885/5919/003 (25) Asaji, T. Glassy Behavior in a Metal-Organic Perovskite, Dimethylammonium Zinc Formate [(CH3)2NH2][Zn(HCOO)3], Solid State Commun. 2018, 284-286, 31-34. https://doi.org/10.1016/j.ssc.2018.08.016 (26) Gopal, E. S. R. Specific Heats at Low Temperatures; Plenum Press: New York, 1966, p. 102. (27) Fujimori, H.; Asaji, T.; Hanaya, M.; Oguni, M. Orientational Ordering of Pyridinium ion in its Tetrabromoaurate(III) Salt − Intermediate Situation between Schottky Anomaly and Phase Transition −, J. Therm. Anal. Cal. 2002, 69, 985-996. https://doi.org/10.1023/A:1020640930186 (28) Andrew, E. R.; Latanowicz, L. Solid-State Proton Transfer Dynamics and the Proton NMR Second Moment and Proton Relaxation Rates, J. Magn. Reson. 1986, 68, 232-239. http://doi.org/10.1016/0022-2364(86)90240-4 (29) Mączka, M.; Almeida da Silva, T.; Paraguassu, W.; Ptak, M.; Hermanowicz, K. Raman and IR Studies of Pressure- and Temperature-Induced Phase Transitions in [(CH2)3NH2][Zn(HCOO)3], Inorg. Chem. 2014, 53, 12650-12657. https://doi.org/10.1021/ic502426

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Page 34 of 45

Page 35 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1.

(CH2)3NH2Zn(HCOO) 3

(CH2)3NH2Mg(HCOO) 3

20

2


40


Figure 2.

T/K

400 10

1

280

250

(CH2)3NH2Mg(HCOO) 3 1

H NMR T1

47.35 MHz

T1 / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 45

10

0

288 K

24 kJ mol

10

−1

270 K

−1

3

3

10 K / T


4

Page 37 of 45

0

ln S ( )

ln S ( )

Figure 3.


−1

0


−2

−2

−4 0

0.4

0

0.8

/s


−2

−4

0

ln S ( )

−3

ln S ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

40

/s

80

AzHMg(HCOO) 3 T = 76.0 K

−2

−4 0

4

8

/s

12

0


40

/s

80


0

ln S ( )

ln S ( )

Figure 4.


−1

0.4

T = 301 K

0

/s


 = 0.8

−3

0.8

ln S ( )

ln S ( )

0

−1

0

0

0

/s


−2

−3

40

ln S ( )

20

0

AzHZn(HCOO) 3

0

T = 76.4 K

−2

/s

120

20

 = 0.8 40

( / s)



80

AzHZn(HCOO) 3 T = 76.4 K

−2 80



T = 100 K

0 −1

40

( / s)

AzHZn(HCOO) 3

0

−1

0

10

0

200

/s

ln S ( )

100

0.8

 = 0.8

−4

0



T = 200 K

−2

−4

( / s)

AzHZn(HCOO) 3

−2

0

0.4

−1

−2

ln S ( )

AzHZn(HCOO) 3

−2

−3

−3

0 −1

−2

ln S ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 45

 = 0.8 0


20

( / s)



40

Page 39 of 45

Figure 5.

288 K

endo 0.4

Net heat flow / mW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-0.4 200

exo

270 K 240

280

320 T/K



Figure 6.

500

T/K

200

80

299 K 1

T1, T1D , T2 / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 45

H NMR T1

10

10

47.35 MHz

(CH2)3NH2Zn(HCOO) 3

0

25 kJ mol

-1

254 K -2 1

H NMR T1D -1

41 kJ mol , E = 5.7 kJ mol 10

-4 1

H NMR T2

4

8


12 10 K / T 3

-1

Page 41 of 45

Figure 7.

500

T/K

200

80

(CH2)3NH2Mg(HCOO) 3 288 K 10

10

1

0

T1, T1D / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


24 kJ mol

H NMR T1 47.35 MHz

-1

270 K -2 1

H NMR T1D

-1

31 kJ mol , E = 5.4 kJ mol 10

-4

4

8

3

10 K / T


12

-1


Page 42 of 45

Figure 8.

aW W V0

Ea

E

LTP

HTP


Page 43 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9.

10

0

AzHZn(HCOO) 3

/ s

10

−4

AzHMg(HCOO) 3

254 K 288 K

10

−8

270 K 299 K

2

4

6 3

10 K / T


8


Figure 10.

b

c

a

HTP (Pnma)

c a

b

ITP (Pna21)

a c

b

LTP (P21/c)


Page 44 of 45

Page 45 of 45

500 1

10

−2

10

T/K

200 H NMR T1D

80

AzHMg(HCOO)3 DSC

T1D / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


200

240

T/K

280

320

−4

ΔE = 5.4 kJ mol−1

4

8

3

10 K / T

12


Ring-Puckering Motion of Azetidinium Cations in a MetalâOrganic

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