J. Chem. SOC., Faraday Trans. 1, 1987, 83 (lo), 3207-3222 Hydrogen- 1 Nuclear Magnetic Resonance, Differential Thermal Analysis, X-Ray Powder Diffraction and Electrical Conductivity Studies on the Motion of Cations, including Self-diffusion in Crystals of Propylammonium Chloride and Bromide as well as their N-Deuterated Analogues Shin-ichi Fukada, Hideaki Y amamoto, Ryuichi Ikeda and Daiyu Nakamura" Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464, Japan 'H N.m.r. measurements and differential thermal analyses have been performed on solid propylammonium chloride and bromide, including their N-deuterated analogues. X-Ray powder diffraction and electrical con- ductivity were measured for the highest-temperature solid phase of NH,(n- C,H,)Cl. The corresponding highest-temperature solid phase of the bromide was determined. These salts have three solid phases below the respective melting temperature. In the highest-temperature phase, having a structure consisting of cation and anion layers, it was found for the chloride that the cations perform self-diffusion in two-dimensional layers.A non-linear log TI us. T1 curve observed in the room-temperature phase of propyl- ammonium chloride and bromide could be well explained by assuming a non-Arrhenius type thermal process for the random reorientation of the cation along the cationic chain axis. The broad Tl minimum of NH,(n- C,H,)Br observed in its low-temperature phase has been assigned to two closely spaced Tl minima due to the C, reorientation of the CH, and NH; groups.Motional parameters for the above cationic motions in the three phases of the present salts have been evaluated, and the features of these motions are discussed. n-Alkylammonium halides with shorter alkyl chains than C,, have been reported mostly to form tetragonal crystals belonging to space group P4/nmm around room temperature. The structure of these crystals consists of two-dimensional layers made by alkylammonium cations and halide anions stacked alternately. In this structure the cations, with regard to their orientation along the chain- or long-axis, are dynamically disordered and are packed between the layers of anions keeping their long-axes perpendicular to the layers. Previously we reported2 that methylammonium iodide, which forms the same tetragonal crystals at room temperature, transforms into CsCl- type cubic crystals with increasing temperature.In this highly symmetric phase the cations are in a more dynamically disordered state in which they perform self-diffusion through the crystalline lattice as well as isotropic rotation about their respective centres of gravity; both types of motion can be observed on an n.m.r. timescale. Tsau and Gilson, carried out measurements of differential scanning calorimetry (d.s.c.) on propylammonium chloride, NH,(n-C,H,)Cl, and found that the tetragonal crystals undergo a phase transition at 408 K with increasing temperature, with the entropy of transition AStr of 10.2 J K-l mol-l, and a high-temperature phase is formed. The value of AStr is considered to be unusually large since it is comparable to the melting entropy AS, of 13.4 J K-' mol-' obtained at 439 K by heating NH,(n-C,H,)Cl in the high-temperature phase.3 The large AStr reported suggests the onset of new cationic 32073208 Hydrogen- 1 N.M.R.of Solid Propylammonium Chloride and Bromide motions in the high-temperature phase, where a more disordered structure is possibly realized in consequence. To obtain detailed information about the dynamical behaviour of the cation in crystals of NH,(n-C,H,)Cl and NH,(n-C,H,)Br over a wide temperature range, the present investigation has been undertaken by examining lH n.m.r., differential thermal analysis (d.t.a.), X-ray powder diffraction and electrical conductivity. Experimental Crystals of NH,(n-C,H,)Cl and NH,(n-C,H,)Br were prepared by neutralizing an aqueous solution of propylamine with hydrochloric acid and hydrobromic acid, respectively, and gradually evaporating water.The crystals thus obtained were recrystallized twice from an ethanol-diethyl ether mixture. Colourless thin plates were obtained for both salts. Partially deuterated analogues, ND,(n-C,H,)Cl and ND,(n- C,H,)Br were prepared by performing repeated crystallizations of purified NH,(n-C,H,)Cl and NH,(n-C,H,)Br, respectively, from heavy water. 'H N.m.r. absorptions4 and d.t.a.5 measurements were carried out using apparatus already reported. The 'H n.m.r. spin-lattice relaxation time TI was measured at the Larmor frequencies of 10.5, 20.0 and 45.5 MHz using pulsed n.m.r. spectrometers described elsewhere.'.The 'H spin-lattice relaxation time in the rotating frame Tlp was measured at 32 MHz for NH,(n-C,H,)Cl under a spin-locking radio frequency magnetic field of 3.7 G.8 The a.c. electrical conductivity of NH,(n-C,H,)Cl was determined at various temperatures using a previously reported homemade apparatusg operating at 1 kHz. The sample pellets were prepared by pressing pulverized crystals. X-ray powder diffraction patterns of NH,(n-C,H,)Cl were recorded at ca. 400 and 420 K employing a Shimadzu model VD- 1 A diffractometer equipped with a Cu anticathode. Results D.t.a. curves recorded for NH,(n-C,H,)Cl and NH,(n-C,H,)Br between ca. 100 K and a temperature above each melting temperature (T,) are shown in fig. 1 and 2, respectively. Their partially deuterated analogues showed approximately the same curves, which were shifted to higher temperatures by deuteration.NH,(n-C,H,)Cl underwent two solid-solid phase transitions at 188 and 406 K, and melted at 436 K. These qr and T, values agree well with those of 188 and 408 K for qr and 439 K for T, reported by Tsau and Gilson3 in their d.s.c. study. As shown in fig. 1, ND,(n-C,H,)CI yielded analogous d.t.a. curves to those of NH,(n-C,H,)Cl. The higher-temperature phase of NH,(n-C,H,)Cl obtained by heating to above 406K could easily be supercooled down to ca. 350 K, while that of ND,(n-C,H,)Cl was supercooled only to ca. 390 K, around which temperature we observed a sudden exothermic transition to the room-temperature phase. When NH,(n-C,H,)Br was heated, a single solid-solid phase transition was recorded at 163 K, a temperature much higher than Tr of 138 K reported by Tsau and Gilson., T, of 457 K observed in the present study agrees well with that of 456 K reported by the same authors.When the melt of NH,(n-C,H,)Br was cooled, it solidified at 419 K. Below this temperature another exothermic peak appeared around 385 K, indicating the appearance of a new solid phase between ca. 385 and 419 K. This phase was so unstable that a sudden exothermic transition to the room-temperature phase took place at any temperature between them when any small shock was given to the sample tube. ND,(n- C,H,)Br exhibited quite similar d.t.a. curves to those of NH,(n-C,H,)Br but Kr and T, differed slightly from those of NH,(n-C,H,)Br. The three solid phases observed in these salts are referred to hereafter as phases I, I1 and 111 for the high-, room- and low- temperature phases, respectively. Temperature dependences of the second moment Mz of lH n.m.r.absorptions inS. Fukada et al. 3209 ca. 351 K (381 -403K 1 436K ( 44OK 1 188 K (188K) I I I1 liquid 1 exo I11 ca.100K - I 188 K (188K) 406K 436K (413K)(44OK) Fig. 1. The d.t.a. curve of NH,(n-C,H,)Cl recorded between ca. 100 K and ca. 470 K. Transition temperatures determined for the partially deuterated analogue, ND,(n-C,H,)Cl, are given in parentheses. 370-400K ~ 1 9 ~ (ca.409K) (421K1 162 K (161 K ) ca.100K 111 I1 liquid 163 K (168K) I 457K (470K) Fig. 2. The d.t.a. curve of NH,(n-C,H,)Br recorded between ca. 100 K and ca. 490 K. Transition temperatures determined for the partially deuterated analogue, ND,(n-C,H,)Br, are given in parentheses.NH,(n-C,H,)Cl and NH,(n-C,H,)Br along with their partially deuterated analogues are shown in fig. 3 and 4, respectively. Values of M, for NH,(n-C,H,)Cl and ND,(n-C,H,)Cl were observed between room temperature and ca. 430 K. Values of M2 for NH,(n-C,H,)Cl in phase I1 were almost constant but decreased slightly from 5.5 to 5.0 G2 on increasing the temperature to Tr = 406 K. Above 406 K M2 decreased to ca. 1 G2. With increasing temperature further, a gradual decrease in M, was observed in phase I. When phase I of NH,(n-C,H,)Cl was cooled to qr (ca. 350 K) for phase 11, M , increased slowly to ca. 2.5 G2. In phase I13210 Hydrogen- 1 N.M.R. of Solid Propylammonium Chloride and Bromide N \ 0 s 5 350 LOO o L i k o ' I I ' I T / K ' I I ' I I ' ' Fig.3. The 'H n.m.r. second moments of NH,(n-C,H,)Cl and its partially deuterated analogue, ND,(n-C,H,)Cl, determined above room temperature. The results of measurements carried out with increasing temperature for NH,(n-C,H,)Cl and ND,(n-C,H,)Cl are indicated by 0 and 0, respectively, whereas those obtained with decreasing temperature for NH,(n-C,H,)Cl are indicated by 0. q,(a) and qr (b) refer to NH,(n-C,H,)Cl, while K, (c) corresponds to ND,(n- C,H,)Cl. 15 10 5 0 100 200 300 T/K 400 Fig. 4. The 'H n.m.r. second moments of NH,(n-C,H,)Br (0) and ND,(n-C,H,)Br(n) observed with increasing temperature. Those determined for NH,(n-C,H,)Br by decreasing the temperature from the temperature of solidification, q, are shown by A.below qr, M, showed the same temperature dependence as that observed on the heating run. Tsau and Gilson" reported M, of 5.0 and 2.0 G2 for NH,(n-C,H,)Cl at 409 and 4 15 K, respectively. These values roughly agree with those observed here in each phase. M, of ND,(n-C,H,)Cl also gradually decreased from 3.8 to 3.2 G2 with increasing the temperature from 295 to 405 K. Around Kr of 413 K, M , decreased significantly to 1.0 G2. In phase I, a gradual decrease in M , was also observed on heating as in the case of NH,(n-C,H,)Cl. Temperature dependences of M, in NH,(n-C,H,)Br and ND,(n-C,H,)Br were determined in the ranges 106-441 and 114-416 K, respectively. In NH,(n-C,H,)Br,S. Fukada et al. 321 1 I I I I 1 10 1 2 4 1 0 3 ~ / ~ 5 Fig. 5.The temperature variation of 'H n.m.r. spin-lattice relaxation time observed for NH,(n- C,H,)CI at two Larmor frequencies, 20.0 (@) and 45.5 Mz (A), and its partially deuterated analogue, ND,(n-C,H,)Cl, at 20.0 MHz (0). Measurements were made mainly in phase I1 of these salts. The Solid line indicates the best fitted calculated curve by assuming non-Arrhenius type temperature dependence for the correlation time of the cationic axial reorientations (see text). M , of ca. 14 GZ was observed at 106 K. When phase 111 was warmed, M, decreased to ca. 11 G2 at ca. 160 K near qr of the transition IIT -+ IT. Around 160 K, M, decreased to 5.3 G2 upon increasing the temperature. With further heating, a gradual decrease in M, was observed in phase I1 and M, of 4.0 G2 was obtained at ca.440 K, the highest temperature attained in this phase. In phase I, prepared by cooling melted NH,(n-C,H,)Br, M , of 1.9 G2 was observed at 417 K just below the temperature of solidification. In this phase, M , increased gradually with decreasing temperature. Below Kr (I -+ TI), this sample exhibited M, values similar to those determined on the heating run. ND,(n-C,H,)Br showed an analogous temperature dependence of M, to that of NH,(n-C,H,)Br. When the temperature was raised from 180 to 416 K in phase 11, M , decreased gradually from 4.7 to 2.9 G2. M, could not be determined for phase I of ND,(n-C,H,)Br because this phase could only be obtained in a narrow temperature range and was extremely unstable. Fig. 5 shows the temperature dependence of 'H q measured for NH,(n-C,H,)Cl at 20.0 and 45.5 MHz and ND,(n-C,H,)Cl at 20.0 MHz in the range 200 K-T,.The temperature dependences of q determined at 10.5, 20.0 and 45.5 MHz are shown in fig. 6 for phase I of NH,(n-C,H,)Cl. The q data observed in phase I1 of both salts agree well with those measured at 25.3 MHz by Albert and Ripmeester.l' q values for phase I of NH,(n-C,H,)Cl increased with increasing temperature in a similar manner to those for phase 11, while the temperature gradients of log us. T1 curves obtained for phase I32 12 Hydrogen- 1 N.M. R . of Solid Propylammoniurn Chloride and Bromide 350 2.3 2.5 2.7 103 KIT Fig. 6. The temperature dependence of 'H n.m.r. spin-lattice relaxation times q and qp for phase I of NH,(n-C,H,)CI. qp was measured at 32 MHz under a radiofrequency magnetic field of 3.7 G.q was measured at 45.5 (A), 20.0 (a) or 10.5 MHz (A). The solid line on the plots indicates the relaxation time Trot originating from a cationic rotational mode and that of the cationic self-diffusion (q,,,,) determined at 10.5 MHz is shown by W and the broken line. The solid line on the qp plots is the best fitted line for the linear portion of the qp data. became steeper than those for phase 11. & values for phase I of ND,(n-C,H,)Cl were about twice those of NH,(n-C,H,)Cl. Temperature dependences of 'H q determined for NH,(n-C,H,)Br at 20.0 and 45.5 MHz and for ND,(n-C,H,)Br at 20 MHz are shown in fig. 7. Each analogue yielded a minimum in phase 111, the values of which were 24 and 35 ms observed at ca.125 K for NH,(n-C,H,)Br and at ca. 120 K for ND,(n-C,H,)Br, respectively. At qr (III+ 11), q of both salts increased discontinuously. In phase 11, almost the same q values were obtained for both analogues, which increased with increasing temperature in a similar way to those of phase I1 for NH,(n-C,H,)Cl and ND,(n-C,H,)Cl. values for phase I, observed in a narrow temperature range for each analogue, were about one fifth of those obtained for phase I1 of NH,(n-C,H,)Br and about one half of those for ND,(n-C,H,)Br. These q values for phase I showed a tendency to increase with increasing temperature. Electrical conductivity, 0, observed for phases I and I1 of NH,(n-C,H,)Cl is shown inS. Fukada et al. 3213 Fig. 7. The temperature dependence of 'H n.m.r. spin-lattice relaxation time observed for NH,(n-C,H,)Br at 20.0 (e) and 45.5 MHz (V) and its partially deuterated analogue, ND,(n- C,H,)Br, at 20.0 Mz (0).The solid line is the best fitted curve calculated by assuming a non- Arrhenius type thermal process for the correlation time of the cationic rotational motion (see text). fig. 8 . At Tr (II+I) the conductivity increased by three orders of magnitude and large values of ca. S m-l were found in phase I. Discussion Crystal Structure King and L i p s ~ o m b l ~ . ~ ~ studied phases I1 and I11 of NH,(n-C,H,)Cl and phase I1 of NH,(n-C,H,)Br by single-crystal X-ray diffraction. Phase I11 of NH,(n-C,H,)Cl forms monoclinic crystals belonging to space group Gh(C2/m) with 2 = 2, in which the carbon and nitrogen atoms of the cation can be located at fixed positions thus suggesting that the structure is not disordered.On the other hand, phase I1 of both salts form tFtragona1 crystalso [space group Dih(P4/nmrn) ; 2 = 21 haying lattice constaonts a = 6.220 A and c = 7.377 A for NH,(n-C,H,)Cl, and a = 6.497 A and c = 7.380 A for NH,(n- C,H,)Br and containing cations disordered about their long axes. The arrangement of heavy atoms in the unit cell of phase I1 can be assumed by using the lattice parameters and is shown as (a) in fig. 9. To obtain information about the structure of phase I of NH,(n-C,H,)Cl, X-ray powder diffraction experiments were carried out at higher temperatures. The powder3214 Hydrogen- 1 N.M.R. of Solid Propylammonium Chloride and Bromide I I I 0 - I E m 1 2.4 2.5 103 K/T 0 0 0 0 0 Fig.8. The temperature dependence of the electrical conductivity, 0, observed for NH,(n-C,H,)Cl at higher temperatures. Experimental results obtained with increasing and decreasing temperatures are shown by and 0, respectively. patterns observed Ft 420 & 5 K coulc be well explained as arising from a tetragonal unit cell with a = 5.23 A and c = 11.70 A. The diffraction angles observed are shown in table 1 together with those calculated using the above lattice constants and the Miller indices assigned. The agreement between observed and calculated angles is quite good. The lattice constants obtained for phase I suggest that the arrangement of ions is different from that of phase I1 because of a large difference in c values between the two phases, although the crystals of both phases have the same tetragonal symmetry.It has been reported’ that there are many alkylammonium halides with normal alkyl chains, which form tetragonal crystals around or above room temperature. All these crystals have the same space group, P4/nmm, whereas their structures can be classified into two groups with different arrangements of ions in each unit cell. As an example of one group, designated the ‘a-form,’ the structure of phase I1 of NH,(n-C,H7)C1 is shown in fig. 9. Crystals of the high-temperature phase of methylammonium bromide4 and the room-temperature phases of NH3(n-C3H,)Br,l2 NH,(n-C,H,)I’* and NH,(CH,)C1,15* l6 for example, are known to have the structure of the a-form. The structure of the other group, the ‘a’-form,’ is shown in fig.9 for butylammonium bromide as an example. The Same structure can be found for the room-temperature phases of NH,(CH,)Br,’7* l8 NH,(CH,)I,” butylammonium halides,lg and many other n-alkylammonium halides with longer n-alkyl chains.19 By comparing the lattice constants determined for phase I of NH,(n-C,H,)Cl withS. Fukada et al. 321 5 L a (a) (a‘) Fig. 9. The arrangement of heavy atoms in the unit cells of NH,(n-C,H,)Cl and NH,(n-C,H,)Br in their a- and a’-forms, respectively. All cations are orientationally disordered about their long axes. Table 1. Observed and calculated 28 values of X- ray powder diffraction patterns recorded at ca. 420 K for NH,(n-C,H,)Cl 15.15 w 18.60 m 22.87 m 24.07 vs 25.26 s 28.56 w 33.49 vw 34.30 vs 35.15 s 39.25 w 41.53 m 49.20 vw 53.10 vw 54.90 vw 15.14 18.58 22.80 24.06 25.25 28.55 33.39 34.29 35.16 39.28 41.58 49.28 53.1 1 54.96 those of the d-fqrms of NH,(CH,)Br (a = 5.09, c = 8.76 and NH,(n-C,H,)Cl (a = 5.02, c = 14.85 A),19 the structure of phase I of NH,(n-C,H,)Cl is reasonably assumed to also have the a’-form.In the a-form, both cations and anions form simple layers which are stacked alternately. On the other hand, both cations and anions form a bilayer structure in the a’-form as shown in fig. 9. The two kinds of crystallographically non-3216 Hydrogen- 1 N.M.R. of Solid Propylammonium Chloride and Bromide Table 2. Calculated second moments (G2) for three motional states of NH,(n-C,H,)+ ions in NH,(n-C,H,)Cl and NH,(n-C,H,)Br" CH,-rot. (CH, + NHi)rot. (CH, + NHi)rot.+chain rot. NH,(n-C,H,)Cl 22.0 14.5 (1 3.6) (13.6) NH,(n-C,H,)Br 21.4 13.9 (13.3) (13.3) 5.4 (4.4) 5.1 (4-2) " Values for the partially deuterated salts, ND,(n-C,H,)Cl and ND,(n-C,H,)Br, are given in parentheses. equivalent cations in a unit cell are packed with their methyl groups facing each other in a similar manner to the lamellar structure of the liquid crystal.20 Note that the ions in the a'-form are more loosely packed than those in the a. This can be proved by calculating the unit-cell volume of phase I, which is larger by % than that of phase I1 evaluated using the lattice constants (a = 6.29 A, c = 7.42 A) obtained from X-ray powder diffraction patterns recorded at ca. 400 K. N.M.R. Second Moments The motional modes of NH,(n-C,H,)+ ions activated in the present salts can be estimated by comparing the observed M, values with the theoretical ones calculated by use of Van Vleck's method.21 Values of M, evaluated for the present NH,(n-C,H,)+ salts having the cations in their several motional states are shown in table 2.These values were calculated in a similar manner to those previously calculated for the NH,(n-C,H,)+ By referring to the calculated values, M, values observed around room temperature for the all salts investigated can be well explained by the following motional model of the cations: the whole cation uniaxially rotates about the long axis together with random reorientations of both CH, and NH: groups by 120" about each C, axis. This explanation is consistent with the crystal structure determined by X-ray analysis, in which orientationally disordered cations exist." The gradual decrease in M, observed with increasing temperature for phase I1 of each salt can be attributed to an increase in the amplitude of lattice vibrations. It is noteworthy that M, values obtained for phase I (a'-form) of NH,(n-C,H,)Cl are much smaller than those of phase I1 (a-form), and that M , for phase I decreases much faster with increasing temperature than those for phase 11.Quite analogous M , behaviour to that of the present phase I was observed for NH,(n-C,H,)Br and NH,(n- C,H,)I in their tetragonal phase (a'-form). For example, NH,(n-C,H,)Br yielded M , of ca. 3 G2 at room temperature and which decreased gradually with increasing temperature to ca. 1.5 G2 at 460 K.,, These low M, values cannot be explained only through the above type of uniaxial rotation of the cations, suggesting the onset of new cationic motions.These may originate from the existence of more movable NH,(n-C,H,)+ ions in the a'-form than in the a-form. This is reasonable in view of the foregoing comparison of unit-cell volumes for these two structures. As a new motion occurring in phase I, translational self-diffusion of the cations, probably of the two-dimensional type, can be considered from the layer structure of the crystal. Experimental evidence for cationic self-diffusion taking place in this phase will be shown in subsequent sections.S. Fukada et al. 3217 Spin-Lattice Relaxation Time lH when nuclear magnetic dipolar interactions are averaged through random motions of molecules.According to this theory, q originating from a single motional process is expressed as can be analysed by the BPP c1 = C [ t / ( 1 + co2z2) + 4t/( 1 + 4c02z2)]. (1) Here, C, z and co denote the motional constant, the correlation time of the motion and the angular resonance frequency, respectively. By assuming an Arrhenius relationship for the motion, z can be written as z = zo exp(E,/RT) (2) where z, and E, are the correlation time at the limit of infinite temperature and the activation energy of the motion, respectively. Phase 111 Albert and Ripmeester" have measured 'H q of NH,(n-C,H,)Cl and ND,(n-C3H,)Cl and detected a q minimum in phase I11 of each analogue. The minimum observed for ND,(n-C,H,)Cl has been attributed to the C, reorientation of CH, groups and that of NH,(n-C,H,)Cl explained in terms of two minima due to the CH, and NH; reorientations overlapping each other.The activation energies for the C3 reorientations of the CH, and NH; groups have been determined as 10.0 and 15.5 kJ mol-l, respectively. NH,(n-C,H,)Br and ND,(n-C,H,)Br of the present study showed quite similar q curves to those of the above chlorides. The q minimum observed for ND,(n-C,H,)Br can be attributed to the C, reorientation of the CH, groups, in accord with the analysis of the results of ND3(n-C,H,)Cl.11 The motional parameters C and E, were evaluated by fitting eqn (1) and (2) to the observed q values of ND,(n-C,H,)Br using a least- squares method. The best-fit values of C and E, were 2.4 x 10' s-' and 6.9 kJ mol-l, respectively.The broad q minimum of phase I11 of NH,(n-C,H,)Br can be explained by the existence of two closely spaced q minima due to the C, reorientations of the CH, and NH; groups. When the two groups can be assumed to reorient independently, the resultant q value is expressed as where qM and qA indicate q components contributing from the CH, and NH; C, reorientations, respectively. Here, TM values were assumed to be the same as those observed for ND,(n-C,H,)Br although a correction factor arising from the difference in the numbers of protons between a ND,(n-C,H,)+ and a NH,(n-C,H,)+ cation was taken into account. The qA curve of NH,(n-C,H,)Br obtained from eqn (3) using the observed < values yielded an asymmetric & curve with a gentler gradient on the low-temperature side of the minimum.From the slope of the log qA us. T1 plots for the low-temperature side of the minimum, E, = 8.2 kJ mol-1 was roughly derived for the NH; C, reorientation by applying eqn (1) and (2) under the condition wz 9 1. The motional constant of the NH; C, reorientation was evaluated as C = 2.5 x lo9 sP2 from the qA minimum value (36 ms) obtained. The value of C for the CH, reorientation in NH,(n-C,H,)Cl can be calculated theoretically by using the equationll 2-y = c:+c; (3) C = (3/10)(9/20) )& A2r-6. (4)32 18 Hydrogen- 1 N.M.R. of Solid Propylammonium Chloride and Bromide Here, yH and r are the gyromagnetic ratio of a proton and th: interprotonic distance in a CH, group. Assuming the C-H bond distance to be 1.096 A22 and a tetrahedral angle between bonds in the -CH, moiety, the motional constant was evaluated as C = 3.34 x lo9 s - ~ .In a similar manner, C for the NH: C3 reorientation in NH,(n-C,H,)Br was calculated to be 3.1 1 x lo9 s-' using the N-H bond distance of 1.045 A.22 The theoretical C values turned out to be larger than the values obtained experimentally from the minima for both CH, and NH: C, reorientations. Another unusual result obtained for the present salts is that Ea values for the CH, and NH,+ C, reorientations are much smaller than those determined for analogous salts by lH n.m.r. measurements. For example, Ea for the CH, C3 reorientation obtained for NH,- (n-C,H,)Cl, NH,(n-C,H,)Br and NH,(n-C,H,)I was reported to be ca. 10 kJ to be in the range 16-27 kJ mol-'.It is known25 that shallower q minima and smaller Ea values than the theoretically expected ones are usually observed when the correlation time of the corresponding motional mode has a distribution over a wide range of time because of the existence of disordered atomic or molecular arrangements in crystals. In fact, analogous q data for NH,(n-C,Hg)Br obtained for its low-temperature phase, roughly equivalent to phase I11 of NH,(n-C,H,)Br, could be well explained by introducing a distribution in the correlation time of the CH, C, reorientation.22 As already described, the orientation of NH,(n-C,H,)+ ions as a whole are dynamically disordered about their long axes in phase 11. If the disordered orientations are partially frozen at Tr (I1 --f 111), it is thought that a distribution in the correlation time for the CH, and NH: C3 reorientations appears even in phase 111.9 and that for the NH,+ C3 reorientation was determined in the same salts mol-l 11,22,23 Phase II In the high-temperature limit given by CUT 6 1, eqn (1) becomes Thus q is independent of co. Combining eqn ( 5 ) and (2), it is found that log us. T1 plots increase linearly with increasing temperature provided that q is attributable to a single motional process. Both NH,(n-C,H,)Cl and NH,(n-C,H,)Br exhibited frequency independent values over the whole temperature range of phase 11. According to the analysis of M2 of this phase, 'H spin-lattice relaxation is mostly governed by a single motional process, namely the cationic reorientation about the long axis.However, the log q. plots showed a non-linear relation against & in this phase. This non-linear behaviour is marked especially for the q curve of NH,(n-C,H,)Br and unexplainable in terms of the Arrhenius type temperature dependence of the correlation time given by eqn (2). Analogous behaviour of the reorientational correlation time has been observed for the supercooled liquid state of substances easily forming glassy states such as g l y ~ e r o l . ~ ~ , ' ~ In this liquid state, the correlation time Z, of molecular reorientations can be expressed by the following non- Arrhenius- type expression : r;' = 5cz. ( 5 ) where z,, and EaR for the molecular reorientation are defined similarly as zo and E,, respectively. To denotes a reference temperature supposed to exist near the glass transition temperature.'The present salts are thought to possibly form an 'orientational glass' like state at low temperatures, if the tetragonal phases can be supercooled. This is because the reorienting low-symmetric NH,(n-C,H,)+ ions would be frozen in the supercooled state with an orientationally disordered state along the crystal axis having ' C4' symmetry. values of phase I1 of NH,(n-C,H,)Br was A fitting calculation for the observedS. Fukada et al. 3219 Table 3. Activation energies (E,) and pre-exponential factors ( T , , ~ ) for motions of NH,(n-C,H,)+ ions in NH,(n-C,H,)Cl and NH,(n-C,H,)Br _____ motional mode of cations phase E,/kJ mol-' 'RO/' G/K" chloride I 2 0 f 2 41 + 2 self-diffusion (q) 4 0 f 2 self-diffusion (qP) I1 6.4& 1 ( 2 .4 f 0 . 3 ) ~ lo-', 55f5 axial rot. bromide I1 4.8 f 1 (4.0 & 0.3) x 60 + 5 axial rot. a Temperatures appearing in eqn (6). performed using eqn ( 5 ) and (6) to estimate the unknown parameters EaR, T,, and To. In the calculation, C in eqn ( 5 ) can be given by2' C = (2/3)& AM2 (7) where AM2 is the reduction in M , due to the onset of the uniaxial reorientation of NH,(n-C,H,)+ ions and is assumed to be 8.8 G2 [( 13.9 - 5. 1)G2] for NH,(n-C,H,)Br from the calculated values given in table 2. The excellently fitted q curve selected by inspection is shown in fig. 7. The most probable values of EaR, zR0 and T, are given in table 3. A small E, value of 4.8 kJ mo1-I for the uniaxial rotation of NH,(n-C,H,)+ ions indicates the presence of cations having quite a low barrier to rotation in phase 11.If the T, values observed and the C value calculated by use of eqn (7) are substituted into eqn (9, z, values for the axial rotation of the cations can be evaluated. The T, values evaluated at 300 and 425 K were ca. 4 x s, respectively. These short correlation times of the cationic rotation also indicate that any barrier to this motion is quite small in this phase. The T, curves observed for phase TI of NH,(n-C,H,)Cl and ND,(n-C,H,)Cl also showed non-Arrhenius type temperature dependence. The same curve fitting calculation for the T, data of NH,(n-C,H,)Br was carried out also for those of NH,(n-C,H,)Cl and the unknown parameters were determined as listed in table 3. The q curve calculated by use of these parameters is shown in fig.5. and 2 x Phase I The fact that the M , values observed for phase T of NH,(n-C,H,)Cl were smaller than those of phase IT of the same salt indicates the onset of a new motion of the cation. The same expectation can be derived from the T, values of this phase, which are shorter by one order of magnitude than those of phase 11. Since increased with increasing temperature in the low-temperature region of this phase, the new motion should have short correlation times satisfying the condition u)z -+ 1. In the high-temperature region of phase I of NH,(n-C,H,)Cl, T,, which was dependent on frequency, decreased with increasing temperature. This can be explained by considering that another magnetic dipolar mechanism appreciably contributes to the value of observed in this temperature region.Self-diffusion of the cations seems to be the most reasonable candidate for the mechanism. This supposition is strongly supported from the electrical conductivity measurements of this phase described below. Consequently, & observed in this temperature region can be written by where Trot and Tdiff represent the relaxation times originating from an unknown cationic rotational mode and the cationic self-diffusion, respectively. Since Trot is I06 FAR I3220 Hydrogen- 1 N.M.R. of Solid Propylammonium Chloride and Bromide independent of w, the former mode should fulfill the condition wz 4 1. However, c d j f f is dependent on w and then the latter should satisfy the condition wz I . Therefore, we assume that Trot can be represented by the solid line shown in fig.6 because q,,,t can be expressed by eqn (5). q d i f f was evaluated by substituting the values observed at 10.5 MHz and the Trot values given above into eqn (8). These results are shown in fig. 6. Since the cation and anion layers are stacked alternately to form a layer structure in phase I, it is expected that the cationic diffusion takes place more frequently in each two- dimensional layer of the cations rather than in the direction perpendicular to the layers. It has been r e p ~ r t e d ~ ’ . ~ ~ that T due to two-dimensional diffusional motion cannot be expressed by the usual BPP relation. However, in the limit of slow motion, wz % 1, almost the same curve is predicted to be obtained as that derived from the BPP theory.,l3 32 Therefore, we determined E, for the two-dimensional self-diffusion of the cations as 41 +2 kJ mol-1 from the gradient of log qdiff us.T1 plots shown in fig. 6. Almost the same E, of 40 2 kJ mol-1 was obtained from the low-temperature gradient of the log qp us. T’ curve. This activation energy is very close to the foregoing value derived from q d i f f , indicating that the observed qp minimum is also attributable to the self-diffusion of the cations. E, for the motion of cations responsible for Trot was obtained from the slope of log Trot us. T1 as 20+2 kJ mol-’. Since the cationic reorientation about the long axis is already quite frequently excited in phase 11, this new motion activated in phase I should be a higher order motion of the cations.For example, a precessional motion of the cationic axis with NH,+ groups fixed on the anionic layer is conceivable as a possible motional model. Similar motions of the cations considered here for NH,(n-C,H,)Cl are expected to exist in phase I of NH,(n-C,H,)Br because the temperature dependences of M, and ‘H & are very similar to those of NH,(n-C,H,)Cl. No further discussion could be made on these data because phase I of NH,(n-C,H,)Br was very unstable and reliable data could be obtained only in a narrow temperature range. Electrical Conductivity in Phase I of NH,(n-C,H,)CI NH,(n-C,H,)Cl yielded a high electrical conductivity, 0, amounting to the order of lo-, S m-l which is the same order of magnitude as those observed for NH,(CH,)NO,’ and NH,(CH,)T2 in their highest-temperature solid phase.The highest-temperature solid phase of various salts of methylamm~nium,~* ’* 33--35 dimethylammonium, 36 trimethylamm~nium~~~~ and g ~ a n i d i n i u m ~ ~ studied to date are known to have similar properties to the plastic phase of molecular crystals in the sense that the constituents of crystals perform rapid self-diffusion. Ionic crystals in such a phase are expected to have a high electrical conductivity as is actually observed for some salts. In these salts, translational jumps of cations in their diffusion mechanism can occur almost isotropically because of the high crystal symmetry of the phase. In phase I of NH,(n- C,H,)CI, however, the cationic self-diffusion is thought to be a two-dimensional type as discussed before.The presence of the two-dimensional- type diffusion of alkylammonium cations in the mixed solid was reported for alkylammonium tetrachlorometallates(II), [NH,(n-C,H,,+l)],[MC14] (M = Mn or Zn) with n equal to 12 and 18.,’ These salts are known to form a layer structure similar to that of NH,(n-C,H,)Cl. The diffusion constant D for moving ions in crystals can be written by the following Nernst-Einstein equation where A, Ze and N denote the spacial correlation factor calculated in the literat~re,~’ the electronic charge of the diffusion ion and the number of ions per unit volume, D = kTAo/(Ze)2N (9)S. Fukada et al. 322 1 * I v) I 03 KIT Fig. 10. The temperature dependence of the diffusion constant defined within the layer D, evaluated from the data of the electrical conductivity measurements in the high-temperature phase of NH,(n-C,H, jCl.respectively. In the crystals of the two-dimensional layer structure, o observed for powder samples can be expressed as where oI and o,, denote electrical conductivities perpendicular to and parallel to, respectively, the cationic long axis. Assuming o, 9 oil, the diffusion constant defined within the layer D, is given by D, = kTA.o/(Ze)2N. (1 1) In the present system, the value of 3, for the two-dimensional square lattice is 0.46694.40 From the observed o values, the temperature dependence of D, can be calculated by using eqn (1 1). The results are shown in fig. 10. From the slope of logD, us. T1 plots, E, for the ionic diffusion could be calculated as 37+3 kJ mol-'.This value agrees very well with E, of 40 and 41 kJ mol-1 derived above from the Tl and TIP data, respectively. 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