3438
J . Phys. Chem. 1990, 94. 3438-3449
Molecular Motions of Alkylenediammonium Chains in the Layer-Type Compounds (NH,-(CH,),-NH,)MnCI,, n = 3, 4, 5: An Incoherent Neutron Scattering Study F. Guillaume,”’ C. Sourisseau,+and A . J . Dianouxl Laboratoire de Spectroscopie MolPculaire et Cristalline, U R A I24 C N R S , UniversitP de Bordeaux I, 351 Cours de la Libt+ation, 33405 Talence Cedex, France. and lnstitut Laue-Langeoin, 156X, 38042 Grenoble Cedex, France (Receiued: May 26, 1989; In Final Form: October 5 , 1989)
Molecular motions of alkylenediammonium cations in manganese tetrachloride compounds (in short 2C,Mn), namely, (NH,-(CH,),-NH,)MnCI,, (ND,-(CH,),-ND,)MnCl,, and (NH3-(CD2),-NH3)MnC14 with n = 3 , 4 , 5 , have been studied in their dynamically disordered phases by means of incoherent neutron scattering (INS) over the 100-500 K temperature range in order to afford vibrational, kinetic and structural information. A detailed band assignment of the INS spectra is proposed, and the frequency softening of the torsional s(NH3)vibrations is evaluated. Quasi-elastic neutron scattering (QNS) spectra of the various derivatives under study have shown that the dynamical regimes of the -NH,+ groups and of the -(CH2),,backbones are different. QNS profiles for 2C4Mn and 2C5Mn compounds were satisfactorily fitted by the model of a conformational equilibrium between two “trans” and two “twisted” states while the -NH3: groups were performing additional independent oscillations about the -C-N axes: the corresponding correlation times and activation energies were then evaluated. A model of molecular geometry for twisted forms has been proposed in which the distortion of the molecules occurs through cooperative torsions of the -CH,- units along the main molecular axis. The dynamical regimes in the various structural phases are then discussed in connection with the already suggested crystal structures. Finally, our results are compared to recent Raman and X-ray diffraction data on the related cadmium 2C5Cd derivative and on calorimetric measurements on 2C5Mn: this leads to a consistent and unified picture of the various phase-transition mechanisms in these two-dimensional “composite” materials.
I. Introduction The perovskite-type layered compounds (NH,-(CH,),NH3)MCI4(in short 2C,M) with n = 3, 4, 5, ... and M2+ = Mn, Fe. Cu. Cd, ... crystallize in a two-dimensional structure in which parallel sheets of corner-sharing octahedra are linked together by alkylene chains bearing on both ends NH,+ groups (Figure I ) . The cations are fixed by NH-CI hydrogen bonds in the cavities between the octahedra. These compounds were initially intensively studied because of a reduced dimensionality, of magnetic ordering,’ and more recently because of their structural phase transitions.* The structural changes result from the dynamics of the alkylenediammonium chains, coupled to tilts of the octahedra occurring within the inorganic layers. The structural and physical properties of these compounds were previously studied by various techniques,’-I2 and it has been shown that the observed phase-transition sequences depend on the alkylene chain length and on the nature of the metal ion. The first models for the motions of the molecules assumed that the chains were essentially rigid (in their all-trans conformation) and that the disorder was induced by instantaneous jumps of the cations as a whole. This model appeared to be an oversimplification for chains with n > 3, in particular because of the observation of a negative thermal expansion coefficient in the crystal direction parallel to the chain axis at the order-disorder phase transition, which implies the existence of distorted molecules. A microscopic rigid-lattice model, in the mean field approximation, was thus developed to account for the phase transitions in 2C,Cd, 2C4Mn, and 2C5Cd compoundsS2 In this model, “twisted” conformations of the chains were assumed to exist in addition to “all-trans” chains. In such twisted molecular ions, the upper ammonium group -NH, would take an orientation “ I ” whereas the lower -NH, group would have another orientation “2” (Figure 2). It should be pointed out that this microscopic theory of the phase transitions is not touched by the way the molecules are twisted. The aim of the present study is to investigate by incoherent neutron scattering (INS) the high temperature phases of 2C3Mn, 2C4Mn, and 2C5Mn. We hope to discriminate between the intrinsic motions of the cations as a whole and the dynamics of the N H 3 groups by using different isotopic derivatives, namely, (NH3-(CH2),-NH3)MnC14 (in short 2C,-do), (NH,-(CD,),LiniversitE de Bordeaux 1. $institute hue-Langevin.
0022-3654/90/2094-3438$02.50/0
NH3)MnCI, (in short 2C,-cdzn), and (ND3-(CH2),-ND3)MnCI4 (in short 2C,-nd6) with n = 3, 4, 5. For the 2C3Mn derivatives, such experiments have been previously carried out, and we shall just recall the most significant results that have been already pu bi ished.
( I ) de Jongh, L. J.; Miedema, A. R. Adu. Phys. 1974, 23, 1. (2) Kind, R.; Plesko, 0. S.; Gunter, P.; Roos, J.; Fousek, J. Phys. Reu. B 1981, 23, 5301, Phys. Rev. B 1981, 24, 4910 (Erratum). (3) Tichy, K.; Benes, J.; Kind, R.; Arend, H. Acta Crystallogr. 1980, B36,
1355. (4) Negrier, P.; Couzi, M.; Chanh, N. B.; Hauw, C.; Meresse, A. In Dynamics of Molecular Crystals; Lascombe, J., Ed.; Elsevier: Amsterdam, 1987; p 231. (5) Sourisseau. C.; Guillaume, F.; Lucazeau, G.; Dianoux, A. J. Mol. Phys. 1986, 58, 413. (6) Willet, R. D.; Riedel, E. Chem. Phys. 1975, 8, 112. (7) Arend, H.; Tichy, K.; Baberschke, K.; Rys, F. Solid State Commun. 1976, 18, 999. (8) Chhor, K . ; Bocquet, J. F.; Pommier, C. J . Chem. Thermodyn. 1985, 17. 379. (9) Kind, R.; Plesko, S.; Roos, J. Phys. Stat. Solidi A 1978, 47, 233. (IO) Sourisseau, C.; Lucazeau, G. J . Raman Spectrosc. 1979, 8, 311. (11) Crowley, J. C.; Dodgen, H . W.; Willet, R. D. J . Phys. Chem. 1982, 86, 4046. (12) Chhor, K.; Abello, L.; Pommier, C.; Sourisseau, C. J . Phys. Chem. Solids 1988, 49, 1079. (13) Guillaume, F. Thesis, Bordeaux I University, 1988 (available from the author). (14) Deuterated alkylenediammonium chlorides were prepared by courtesy o f Belloc, J.; Lautie, M. F. L.A.S.I.R., C.N.R.S., Thiais, France. (15) Dianoux, A. J.; Ghosh, R.; Hervet, H.; Lechner, R. I.L.L. Technical Report, 75 DI 06 T;Institut Laue-Langevin: Grenoble, France, 1975. Bee, M. I.L.L. Technical Report, 84 BE 05 T;Institut Laue-Langevin: Grenoble, France, 1984. Guillaume, F. I.L.L. Technical Report, 88 GU 06 T; Institut Law-Langevin: Grenoble, France, 1988. ( 16) Bee, M. Application of quasi elastic neutron scattering to solid state chemistry, biology and material science; Hilger: Bristol, U.K., 1988. (17) Dianoux, A. J.; Volino, F. Mol. Phys. 1977, 34, 1263. ( 1 8 ) Chem X,developed and distributed by Chemical Design Ltd.. Oxford. England. (19) Mansfield. M.; Boyd, R. J . Polym. S i . , Polym. Phys. Ed. 1978, 16, 1227 (20) Nagle. J . F. Ann. Reu. Phys. Chem. 1980, 157. (21) Guillaume, F.; Coddens, G.; Dianoux, A. J.; Petry. W.; Rey-Lafon. M.; Sourisseau, C. Mol. Phys. 1989, 67, 665. (22) Couzi. M.; Negrier, P.: Poulet. H.: Pick, R. Croaf. Chem. Acta 1988. 61. 649
0 1990 American Chemical Society
Alkylenediammonium Motions in (NH3-(CH2),-NH3)MnCI,
Figure 1. Schematic structure of the layer-type compounds (NH3(CH2),-NH3)MCII.
a
TRANS 2
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3439
motions was evidenced. In phase 11, a change in the NH, bonding scheme involving now two equatorial and one axial chlorine atoms (orthorhombic configuration) has been p r o p o ~ e d . ~ .From ' ~ IH NMR investigations and symmetry considerations, Crowley et aLii have concluded that the chains were equally distributed over two equiprobable sites and were performing jumps with a reorientation angle of 2 P 0 = 40'. In phase I, the N H 3 bonding scheme corresponds to the monoclinic configuration, and the authors1' concluded that jumps of the chains occurred between two equivalent sites located at 2 P 0 = 80' apart. From I N S investigation^,^ we never observed equal occupation probabilities in time for the trans sites in phases I1 and I, so we have suggested that phase I1 should correspond to a monoclinic structure (a subgroup of Fmmm); meanwhile results in phase I could be interpreted assuming again the orthorhombic Pnma structure. Nevertheless, one can suggest that the idealized Imma structure, as proposed from neutron diffraction3 could only be reached at higher temperatures. This transition has never been observed due to a decomposition of the sample at 520 K. In this study, we ruled out the formation of twisted forms because of the higher energy barrier against distortion in such short chains, even though twisted conformers are not i m p ~ s s i b l e . ~ ~ In 2C4Mn, the following second-order phase transition has been observed:, phase I 1 P21la
~
1-P
m
1
j
2 -p
V -.
Figure 2. Dynamics of the (NH,-(CH,),-NH#+ cations where p is the occupation probability of a trans site: (a) trans-trans equilibrium; (b) equilibrium between two trans and two twisted chains.
In 2C,Mn, the following sequence of first-order phase transition has been
or subgroup or ~ n m a 5 of Fmmm5 In phase 111, all-trans chains are ordered in a preferential orientation below 100 K, and the NH, hydrogen bonding scheme involves two axial and one equatorial chlorine atoms (monoclinic configuration). Above 100 K. a dynamical disorder due to NH,
382 K
phase I Pnma
In phase I1 at low temperature, the chains are in their all-trans conformation, and a progressive dynamical disorder due to NH, motions was evidenced., In phase I, the dynamical disorder originates from motions of both -(CH2)4- and NH, groups. For this compound, the existence of twisted forms was postulated in addition to all-trans chains, and their existence has been evidenced in 2C4Mn from a neutron diffraction determination., According to symmetry considerations, a model including two equiprobable trans states and two equiprobable twisted states was proposed. In 2C5Mn, the following second-order phase transition has been reported:',' * phase I1 Pnma
P
-
301
K
phase I lmma
The dynamical behavior of the chains is expected to be very similar to that observed in 2C4Mn derivatives in both phases. Indeed twisted molecules were evidenced in a very recent study of 2C5Cd by Raman scattering.22 It comes out from this short literature overview that two kinds of motions are effective in the high temperature phases of 2C,Mn compounds: ( 1 ) dynamics of the cations about their main molecular axis; (2) dynamics of the polar NH,' groups about the internal C-N axes. For compounds with n I 3, the cations keep an all-trans conformation and the whole chains reorient over two equilibrium sites (not necessarily equiprobable) located at 2 P 0 apart (Figure 2a). For compounds with n I 4, the cations can be distorted so that each chain can accommodate four different states, two all-trans and two twisted states (Figure 2b). Little is known about the NH3+ reorientations about the C-N axis so that the N-H protons are usually supposed to jump on a circle over three equivalent sites.5 We report here experimental evidences for such motions in the various structural phases of 2C,Mn, 2C4Mn, and 2C5Mn. More specifically, we are interested in a detailed evaluation in the motions of both the cations (as a whole) and the NH,+ polar heads, as a function of the phase-transition sequences and the chain lengths. The experimental method consists firstly of studying the inelastic part of the incoherent neutron scattering spectra (0-500 cm-') in order to follow the temperature dependence of some characteristic vibrational modes. Secondly, the theoretical models for rotational motions will be examined in details and fitted to the experimental profiles recorded in the quasi-elastic spectral (23) Willet, R. D.;Halvorson, K. Acto Crystdlogr. 1988, 44, 2071.
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The Journal of Physical Chemistry, Vol. 94, No. 9, I990
region. The parameters thus obtained will be discussed and compared to literature data. 11. Experimental Section Polycrystalline samples of 2C,-do, 2C,-cd2,, and 2C,-nd6 ( n = 4, 5) were prepared according to literature p r o ~ e d u r e s ~and ~J~ monitored by infrared and ‘HNMR spectroscopic techniques.I0J3 The samples were contained in flat aluminum containers, and their thickness was chosen in order to get an experimental transmission coefficient typically of the order of 0.9 (to avoid excessive multiple scattering). I t is worth recalling that former experiment^^^ on several deuterated samples of 2C3Mn using a very high instru1000 ps) demonstrated that mental resolution (IN 10, 1 peV, T no tunneling could be observed at low temperature (4 K ) . Furthermore, it was shown that the IN6 resolution fitted well with the broadening of the quasi-elastic spectra due to rotational motions. All the neutron scattering spectra were accordingly recorded on the time of flight IN6 spectrometer at the ILL (Institut Laue-Langevin, Grenoble, France) with an incident wavelength of 5.9 A (5.1 A) and a mean resolution of 70 peV (100 peV). In these experiments, the Q momentum transfer range was of about 0-2 A-l. The spectra were corrected by standard programs available at the ILL.I5
-
111. Inelastic Neutron Scattering On the inelastic part of the spectra, one expects to observe peaks due to internal vibrations and to lattice modes. The corresponding frequency distribution function can be written as follows:’6
k4
Guillaume et al.
2CL- do
I72
35 E NE RG Y m c V
70
Figure 3. I N S spectra of (NH,-(CH2),-NH3)MnCI4 and (ND3-(CH2),-ND3)MnCI, at 100 K (band wavenumbers are in cm-I). 100 K
where W, is the Debye-Waller factor,
kB is the Boltzmann constant and S(a,P) = exp
(
--
2trT)
Svib(Q,w)
(4)
In order to compare INS results with optical data (infrared and Raman), it is useful to calculate the extrapolated frequency distribution function: P(@) = a-0 lim P(a,@)
(5)
This extrapolation implies an averaging over all the possible orientations of Q (isotropic approximation) and consequently a polycristalline powdered sample. Very detailed studies of the Raman, infrared, and INS spectra for the 2C3Mn compound have been already p u b l i ~ h e d . ~We J~~~~ have performed similar experiments on 2C4Mn and 2C5Mn compounds, and the complete results can be found in ref 13. Let us now draw the more significant and interesting features: On the infrared spectra, the internal NH3 (- 1600-I“’) and ~) modes are very sensitive upon temCH, ( - 1 5 0 0 - ~ m - bending perature changes and exhibit pronounced frequency variations near I 8 ENEROY/m.~ the phase transitions; in particular, these modes present variations with large thermal hysteresis (characteristic of first-order-type Figure 4. INS spectra of three isotopic derivatives of 2C,Mn at 100 K. phase transitions) in 2C3Mn. We have also noted large variations with increasing temperature on the far-infrared spectra (60-300 space groups indicated in the Introduction. As the temperature cm-I). In this spectral region, some characteristic modes are due increases, many bands are strongly broadened, and we have noted to librations of the MnCI,2- anions, and these variations indicate a wide “Rayleigh wing” on the (ZX) spectra. Drastic frequency distorsions of the octahedra layers in conjunction with a dynamical and intensity changes are observed for the bands due to the (NH,) disorder due to the organic cations. torsional modes. For the 2C,Mn derivative, this effect is so In the low-temperature phases of these compounds, the number pronounced that this mode, the more intense one at 120 K (-325 of observed bands on the polarized Raman spectra for the diagonal cm-l), could no more be detected at 310 K.5 components of the Raman tensor is always consistent with the Additional information is obtained from the INS experiments using the isotopic derivatives 2C,-d0, 2C,-cdzn, and 2C,-nd6. The low-frequency parts (ho< 160 cm-I) of the spectra for the various (24) Sourisseau, C.; Lucazeau. G.: Dianoux, A . J . Phys. (Les Ulis, Fr.) 1983. 44, 967. derivatives are displayed in Figure 3 for 2C4Mn and Figure 4 for
Alkylenediammonium Motions in (NH3-(CH2),,-NH3)MnCl4
,
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3441 p ITNH’J),“’
300 280, 260.
240.
1
1
0
J
35
100
500
300
’TA
Figure 7. Frequency variations of the r(NH,) torsional vibration in the different phases of 2C4-d,, and 2C4-cd8as function of the temperature.
ie
ENERGY /meV
Figure 5. INS spectra of 2C4-d0 from 100 up to 440 K.
2
1
100 200 300 400 T/K Figure 8. Frequency variations of the r(NH,) torsional vibration in the different phases of 2C5-d0 and 2C5-dloas function of the temperature.
coherent neutron scattering law in the quasi-elastic region can be written as follows: S(Q,u) = exp(-Q2(u2))(sro‘(Q,w,, + WQ) (6) The first term is the Debye-Waller factor, B(Q) is the inelastic background contribution, and S r o ‘ ( Q , ~=) Ao(Q) a(u) + EAi(Q)U w )
(7)
I
Figure 6. INS spectra of the isotopic derivatives of 2CSMn at 31 3 and 373 K.
2C5Mn and can be found in ref 5 for 2C3Mn. They do not exhibit significant changes upon deuteration, and the signals are assigned to the librational motions of the layers probably coupled with external modes of the chains. The torsional (NH,) mode gives rise now to intense INS peaks at high temperature (Figure 5 for 2C4Mn and Figure 6 for 2C5Mn), and its frequency “softening” can be followed as a function of the temperature (Figures 7 and 8). This shows that there is a significant relaxation of the hydrogen bond strengths and of the potential barrier against the N H 3 torsion. Under these conditions, assuming that the potential has a simple cosine form, we estimate in the harmonic oscillator approximation the 3-fold torsional barriers V3to be, for all compounds, in the 1 I < V3(NH3) < 20 kJ-mo1-l range. We have also observed a very significant broadening of all bands corresponding to vibrations in which the hydrocarbon -(CH2)n- chains are involved. This is probably due to large amplitude motions of the chains in all phases I 1 and 1. The complete band assignments and band wavenumber maxima are reported in Tables I and 11. IV. Quasi-Elastic Neutron Scattering The general formulation for the incoherent neutron scattering by molecular crystals is now very well-known.I6 Assuming no correlation between rotational and vibrational motions, the in-
where the first term is the amplitude of the elastic component, called the elastic incoherent structure factor (EISF), and the Ai(Q) factors are the amplitudes of the Lorentzian functions Li(w). The ElSF characterizes the geometry of the motions (and therefore the conformations of the chains) while the second term in eq 7 is characteristic of the kinetics of the motions. The experimental profiles will be fitted by means of eq 6, and then the relevant parameters of the theoretical models (eq 7) will be evaluated. The ElSF (Ao(Q)) can be estimated from the experimental spectra by fitting procedures:
where IeI is the total elastic intensity and Iqc is the total intensity of the quasi-elastic scattering profile. As mentioned in the Introduction, the molecular motions of the (NH3-(CH2)n-NH,)2+ cations must be considered as follows: ( 1 ) If the chains are “rigid” in their all-trans conformation, they can perform instantaneous jumps over two equilibrium sites about the main molecular axis. (2) If the chains are allowed to be distorted, the rotational process will correspond to instantaneous jumps of the chains among four sites corresponding to two equiprobable trans states and to two equiprobable twisted states. (3) Finally, the NH, groups can perform, in addition to the above motions, independent rotations about the C-N internal axis. Thus, we shall now examine the various theoretical models that can be postulated by analyzing the motional processes for a single N-H or C-H proton and then generalizing the equations for the
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
3442
Guillaume et al.
TABLE I: Raman (R) and Inelastic Neutron Scattering (INS) Band Maxima (em-’) Observed in the Low-Frequency Spectra of Three Isotopic Derivatives of the Butylenediammonium Manganese Tetrachloride Compound at Various Temperatures and Proposed Assignments
2C4-dO INS
R 100 K 19 vu 29 w
35
120 K 293 K
2C,-nd6 IkS
R
363 K 440 K
100 K
363 K
120 K 333 K
2C4-cdS
19 vw 27 vw 34 vw 48 vs 62
40 sh
40 sh
40 s h
66 vs
69 vs
74%
VT
73 vs 83 sh
85 sh
I27 s
126vs 1 1 7 s
48 vs
40 sh
40 sh
65 vs
68 vs
120s
119s
45 m 51 w 60 m 69 vs 65 w 71 m 75 w 82 sh 87 m 100 m 113 m Illm
141 s
137s
137s
61 vs 72vs
85sh
87 m IO0 m 112 m 126s
85 sh
40 sh
131 u 139 s
150sh 141 s
363 K 423 K
159 s 166 s 189 m I78 m 1 7 8 s h
182s 198 s 240 w 230 sh
assignments
338 m 346 s
282s
254s
335 ah 350 sh 383 w
242s
233 270 305 314 334 345 365 381 401
I77 w
I
R’ layers 70m
68 m
66 m
100 m
99m
90m
+ AMnC12-
T; chains [u(NH:CI)] 194m 194m 218s u( Mn-CI)
193vw 1 9 0 s h 308 sh 314 vs
T(NH,) 6(CCN)
324 s
m
vw vw 345 w 339 w
31Ovs 2 8 8 v s 2 7 0 v s
348 vw 359 s 381 m 380 sh
340 w
w w
z
T
40 sh
155 m 153 m 161 m R’x,z and T’x,zchains
187 s 198 s
vs w m
m
42 sh
R’, chains
156 s 165 s
226 m I98 w 311 s
40 m
136 s
145vs
161 s 171 s
374s 382 m 400 w
41 vw 45 vs 53 m 60m 68 vw 72 m
115sh
131 v w 142 s
300 w 317 vs
293 K
36 vw
115 w
191 s 199 s 240 M
100 K
19 vu 27 vw
VH
44 V H 53 m 6I m 68 sh 73 m 78 vw 88 m 105 m
INS
R 433 K
6(CCC)
p is the occupation probability in site 1, d is the jump distance,
and
molooulrr r x l s
= 1 - Ao(Q) 7 ’ L
( 1 1)
The mean residence time in site 1 is
-N a x i s T
= pD-’
(12)
Jumps ouer Four Sires ( J A I P ) . The following schematic diagram can be drawn for this process: twist 1
trans
-
c- trans 2
P X
P
twist 2
Figure 9. Spherical coordinates relative to the motions occurring about two different axes Z and Z’. The scatterer is located at P.
case of a complete chain. Finally, we shall also discuss the models for the conformations of the chains. A . Dynamics of a Single C-H Proton. Jumps among Two Sites (JAZP). The scattering law for such a motion can be written as follow^:^.'^
The corresponding Lorentzian’s width is D, = k’/p A2(Q) = P - pjo(Qdii) with D2 = 2k
+ 2h
Alkylenediammonium Motions in (NH3-(CH2),-NH3)MnC14
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3443 A3(Q) =
( X - P ) - CY2 - p)jo(Qdw)
(16)
with D3 = 2k'+ 2u, where d,, is the jump distance between two trans sites, d,, is the jump distance between a trans site and a twisted site; and dw is the jump distance between two twisted sites. If trans-trans jumps are hindered, the structure factors are now Ao(Q) = 4p2 + 2(Y2 - pI2 + 8 ~ ( % - p)jdQd,,) + 2(!h - p)2jdQd,,) (17) 4
~m
%
o s E
~m
E
0
s
E o
E m
0
s
-2 VI
cVI V I >
E
"
4 P
m
m o aIN N
E
4,
c
OIO N OI-
2 E m
2
1115 m 52"
N
Ai(Q) =
~ P ( Y -* P ) - W Y 2 - p ) j d Q ~ t , )+ 2p(Y2 - p)jo(Qd,,)
w m -N N w
(18)
with Dl = k ' / p AdQ) =
CY2
- P)
- (72 - p ) j d Q d w )
(19)
with D2 = 2 k ' + 2u. B. Dynamics of a Single N-H Proton. The dynamics of a single N-H proton can be effective about two different axes (Figure 9): this means that, in addition to the motions described in section IVA, we must consider motions about the C-N axis. Jumps among Three Equivalent Sites (JA3P). The incoherent neutron scattering law is53I6
111
I-
R
with EP
& 2 mm
The residence time of the proton in a site is 5
P
111
m
-
4
P
111
N
N
m
W
m
w
w
V I P m
d
N
w
T
W
N
-
I=
(23)
Oscillations around the C-N Axis (FAIP). I f now we consider large amplitude oscillations around the C-N axis, the corresponding EISF is given by1'
N VI
= 2/,D-'
E
3
W
I=
-
I-
N
AgAIP(Q)= L 1 ) 0 ( 2 Q r
sin x ) f 0 ( 2 ycos x ) dx
afo(r) 0
where Iois the special Bessel function, r is the gyration radius, and y is the relative barrier height of the potential: y = V/2kBT
eo VI VI N
E
3 N
(25)
The mean angle of the oscillations can be calculated from the following expression:
"N 4N
6
(24)
9 = c0s-l (I,(y)/fo(y))
(26)
The A,(Q) factors are complicated expressions, and it is cumbersome to fit the exact scattering function to the experimental data. However, for y > 2, it can be assumed that the diffusional process is dominated by Lorentzian functions displaying an uniform rotational-type behavior of amplitude such that ~ ; d i f ( Q=)
VI
1
jo( 2Qr sin
Np- I
wN I
for N
(z)) (7)
(27)
COS
> 6. We then make the following approximation:
VI
w N W
and T,
=
T~
(
sin2 :)/sin2
j(
5)
with
TI
=
sin2
(i)
(29)
3444
Guillaume et al.
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
TABLE 111: Gyration Radii
(A) for C-H
C8
Protons about the Main
c4
Molecular Axis
2C,Mn NH3
trans 2C4Mn trans C4 C, 2C5Mn trans 0.202 0.365 N H , 0.477 0.841 0.478 NH, 1.173 1.208 1.073 1.161 1.329 1.173 1.208 0.975 1.161 1.329 C’H, 1.393 C’H, 1.640 1.572 1.683 CIH, 1.483 1.593 C2H2 1.255 C2H2 1.451 1.819 1.592 C2H2 1.349 1.837 C3H2 1.571
TABLE IV: Gyration Radii
(A) for N-H
Protons about the C-N
2C,Mn 0.964
2C5Mn 0.998
Axis
2C3Mn 0.942
In order to give a complete picture of the N H 3 motions, it is now necessary to combine both motions around the molecular and the internal C-N axis. The EISF, taking account for the notations given in Figure 9, is now i l ’ d B [ &2n&2rd$ d$’exp(iQOP) p ( $ ) ~ 2
0
( $ 9 1sin~ 0
Top v i e w
Figure 10. Representation of the models of conformations C 4 and C8 proposed in the literature for the 2C4Mn compound (ref 1 1 ) . TRANS
(30)
TWIST
n
with
+
Q O P = Q[r’ cos $’sin 8 sin (d - a ) r’sin 4’sin 8 X cos (4 - a ) - r’sin X sin $’cos 8 + r sin 8 cos (4 - a ) ] ( 3 1 ) This calculus (30) does not reduce into a simple expression so that the desired functions are estimated by performing the simple product of the respective structure factors. We have checked this assumption by performing the numerical integration of eq 30 for the combination of jumps over two equiprobable sites around the main molecular axis and oscillations around the C-N axis. The ElSF evaluated from the numerical calculation was then compared to the simple product of the structure factors of both models: the estimated error was less than 3%.13 C. Molecular Models. In this section, we shall elaborate models to describe the motions of the whole cations (assemblies of protons). Generally, the contribution considered as for each individual proton is taken into account in the total scattering function. For rigid all-trans molecules, the structure factors depend only on the values of the gyration radii (Tables 111 and IV). Thus, the jump distance di for the proton Hi is
P
di = 2ri sin 2
(32)
where p is the jump angle around the molecular axis. For distorted molecules, a geometrical model must be considered in order to calculate the individual protonic displacements. Two models of twisted molecules have been postulated in the literature: ( I ) Tichy et aL3 have suggested, from their neutron diffraction experiments on 2C4Mn samples, twisted conformations in which most of the torsion was considered to occur on the central C-C bond (Figure IO), so that the configuration of the molecule was nearly an eclipsed one. Calculation of the variation of intramolecular energy for an isolated distorted cation, as compared to the trans conformer, has been performed with a commercial software package,’* and it is found to be of about 54 kJmol-I. (2) P. Negrier et aL4 have proposed another model from X-ray diffraction experiments on 2C5Cd compounds. In this model, the distortion of the molecule is produced by a progressive and cooperative torsion of the C H 2 units running along the main chain axis (Figure 1 I ) . Such conformation was already postulated in several works on the molecular dynamics of long-chain molecules (polyethylene for exampleI9) and has been proposed from molecular dynamics simulationsZoand INS experiments2’ on models of lipid membranes. For the isolated (NH3-(CH2)4-NH,)Z+ cation, the variation of intramolecular energy, as compared to the
U
Top view
Figure 11. Representation of the trans and twisted molecules proposed
in this study.
trans form, for such a conformer is equal to about 13 kJmol-I. So in the following, we have made use of the model of twisted molecules in which the torsions are progressive and cooperative. The displacements of the protons resulting from the elementary torsion A of the - ( C H 2 ) r or NH, groups are assumed to be proportional to ‘1,so that d, = Kid\
(33)
where d, is the jump distance and K, an empirical parameter (extracted from the geometrical modelsI3) for the Hi proton. D. Experimental Results. First of all, in this study, we have extracted the experimental ElSF (eq 8) by fitting proceduresL5 in order to select the best models. Thus, the characteristic parameters were estimated by fitting simultaneously all the spectra recorded at various elastic momentum transfers. Initially, the results were analyzed for the deuterated samples, and we have checked that there was a satisfactory agreement in between observed and calculated spectra for the fully hydrogenated compounds when using the same parameters as those previously determined for the deuterated samples. More details about the experimental procedure can be found in ref 5. In our previous study, on the 2C3Mn derivative^,^ we have obtained satisfactory results by fitting the experimental profiles for the 2C3-nd6compound with the JA2P model (eq 9-1 I ) . Chain motions were detected only in phases I 1 and I, and the fitted
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3445
Alkylenediammonium Motions in (NH,-(CH2),-NH,)MnCI,
TABLE V: Best Fit Parameters for the Three 2C3-dm 2C3-nd6, and 2C3-cd6 Compounds in Their Three Structural Phases
compd 2C3-nd6
phase I I
phase I l l 270 K
JA2PT
no quasi-elastic broadening
2C3-Cd6
2C3-dO
FAlP 288 K 9 = 47O T., = 5.06 ps FAlP 296 K 9 = 470 Tc Tf
phase I
298 K p = 1100 p = 0.94 i C= 2.05 ps
JA2PT 321 K
p=
p = 0.92 T~ = 1.93 ps
473 K
p = lloo p = 0.78 i C= 1.29 ps
FAlP
FAlP
311 K 9 = 47O T., = 6.03 ps
373 K 0 = 440 T., = 3.46 ps
JA2PT*FAIP 328 K p = 1100 p = I100 p = 0.93 p = 0.90 i C= 1.85 ps T~ = 2.04 ps T? = 4.83 ps T., = 5.53 PS
373 K p = lloo p = 0.84 T C = 2.01 ps T? = 2.75 ps
311 K
=m = 4.95 ps
1100
373 K p = 1100 p = 0.80 i C= 1.88 ps
473 K 9 = 53O i f = 2.05 ps JA2PTIFAIP 427 K
p = lloo p = 0.82
= 1.57 ps
iC T.,
= 2.06 ps
493 K
p = 1100 p = 0.78 rC = 1.18 ps T., = 1.46 ps
TABLE VI: Best Fit Parameters for the Three 2C4-dm 2C4-nd6, and 2C4-cd8 Compounds in Their Two Structural Phases phase I 1 phase 1 compd
- .
2CA-ndA
JA2PT
JA2PW
JA2PW X F A l P
2Cd-cds
2C4-d0 (2C,-nd6 and 2C4-cd8 models combined)
333 K P(CH2) = 105' p = 0.92 i C= 1.50 ps A = 30' pl = 0.90 i C= 1.40 ps
363 K P(CH2) = 105' p = 0.86 T C = 2.00 ps I = 31' pl = 0.82 rC = 1.53 ps
JA4Cb
433 K A = 29,6O pl = 0.323 T c = 1.22 ps
473 K A = 31,6' pl = 0.302 T c = 1 . 1 1 ps
336 K P(NH3) = 90' p , = 0.88 i C= 1.40 ps 9 = 53O it.= 6.92 ps
363 K P(NH3) = 90' pl = 0.79 i C= 1.53 ps 9 = 52O T? = 4.70 ps
JA4Cb X F A l P
433 K p(NH3) = 90' p, = 0.35 TC = 1.22 ps 9 = 52' T? = 1.88 ps
473 K P(NH3) = 90' p , = 0.33 T C = 1.11 ps 9 = 52' T? = 1.31 ps
333 K A = 30' P(NH3) = 90° pl = 0.91 9 = 55O i C= 1.83 ps T., = 7.00 ps
363 K A = 31' P(NH,) = 100' pl = 0:80 9 = 56O i C= 1.92 ps T., = 5.06 ps
440 K A = 31° P(NH,) = 90' pl = 0134 9 = 53' i C= 1.29 ps T., = 1.34 ps
493 K A = 31° P(NH3) = 90' p , = 0:25 0 = 52' iC = 0.94 ps T., = 0.91 ps
parameters were the jump angle (?about the main chain axis, the 1 occupation probability p , of the trans 1 site, and the mean residence time ic of the chains in the trans 1 state. In the present study, the experimental profiles for the 2C3-cd6 derivative were fitted by the FA1 P model combined to the JA2P one (see section 1V.B) in order to evaluate the mean angle of the oscillations of the NH, groups (+) and also the characteristic time of this process. It was noteworthy that NH3+motions were effective in all the structural phases. The best fit parameters are reported for the first time in Table V . For the longer chain compounds with n = 4 and 5 , we were unable to obtain satisfactory fits assuming only reorientational motions of trans chains. In phase 11, it was thus necessary to assume a jump process between two equiprobable trans states and two equiprobable twisted states. The relevant parameters in such models are, for the hydrocarbon chain motions, the elementary torsion angle A, the occupation probability pl of a trans site, and the corresponding residence time iC (eqs 13-16, 17-19); for NH, motions, the relevant parameters are P(NH3), the reorientation angle about the main chain axis, the mean angle of oscillations about the internal C-N axis the related characteristic time iY, and also the p , and i Cparameters previously described. Satisfactory results obtained for both 2C,Mn and 2C5Mn samples are shown in Figures I2 and 13, where theoretical and experimental EISF can be nicely compared. A good agreement between the experience and the theory is also evidenced in the various structural I 1 Q/A" 2 phases (Figures 14 and 15) and in all the consistent results obtained as a function of the elastic momentum transfer Q (Figures Figure 12. Experimental (symbols) and theoretical (lines) elastic inco16 and 17). herent structure factors (EISF) in the two structural phases of 2C4-d0.
+,
3446
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
assumption of infinite barriers in the effective potential. This simplified model probably induces also some unreliability on the determination of the torsional A angles. However, the whole set of the data suggest an uncertainty factor of * l o . Even though we cannot get very precise values for the reorientational and torsional angles from fitting procedures, the variations of all the parameters as a function of temperature are significant and meaningful. In particular, as expected, we note a pronounced decrease of the pt parameter when the temperature raises, because the proportion of less stable twisted forms becomes more important.
a293 K
0
Guillaume et a].
1
c 1
Q/k'
2
Figure 13. Experimental (symbols) and theoretical (lines) elastic incoherent structure factors (EISF) in the two structural phases of 2C5-d0.
The best fit parameters are reported in Tables VI and VII, and the values deserve some comments. We conclude to a reorientational angle fl of 1 IO"; this value seems too large as compared to that expected for 90" reorientations of the ammonium groups in their cavities. This is probably due to an oversimplification of the jump model, in which the motional process implies the
V. Discussion The inspection of Tables V, VI, and VI1 deserves some comments. First of all, the chains are rigid and in their all-trans conformation for n = 3 only because of the higher energy needed to distort such short chains. When n > 3, stabilized twisted forms are evidenced, the mean elementary torsion being on average 31" for 2C,Mn derivatives and 26" for 2C5Mn compounds. The jump angles of the N H 3 groups around the main molecular axis are always large enough (90 < P(NH3) < 110") to allow the rearrangements of the polar heads within the MnCI6*-cavities. The NH3+protons perform also independent oscillations around the C-N axis. It is worth noting that the mean angle of fluctuations (47O < Q < 5 6 O ) is neither temperature nor chain length dependent. It is thus likely than motions of the NH3+groups are correlated to those of the inorganic matrix. Variations of the correlation times T, and r7 are characteristic of thermally activated processes. In particular, the residence time in the twisted sites increases markedly as the temperature increases. Assuming an Arrhenius law, the activation energies can be calculated from the following relation: (34) The corresponding Arrhenius plots In T = f( 1/ r ) are reported in Figures 18 and 19 for 2C4Mn and 2C,Mn samples, respectively, I
1
1 -C
I
i
i i
' ?
ti
I t
I' D
'I I!
it
t i
-1
2
-1
ENelKiY/
moV
Figure 14. Experimental spectra and fitted profiles for the 2 C 4 compound at Q = 1.4 A-' and in the two structural phases I1 ( ( A ) 333; ( B ) 363 K) and 1 ((C) 440; (D) 493 K ) .
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3447
Alkylenediammonium Motions in (NH3-(CH2),-NH3)MnC14 I
1
'
1
C
A € ,
80
I I
'
D
c n
t
4
0
II -1.5
ENEWY/mrV
2
-1.5
2
ENERG\C/mrV
Figure IS. Experimental spectra and fitted profiles for the 2C,-d0 compound at Q = 1.4 A-' and in the two structural phases I1 ((A) 293 K) and I ((B) 313; (C) 373; (D) 473 K).
TABLE VII: Best Fit Parameters for the Three 2C5-dm2C5-nd, and 2C5-cdloCompounds in Their Two Structural Phases phase I1 2C5-nd,
2Cycdlo
JA2PW
JA2PW X FAlP
phase I
249 K A = 25' p , = 0.94 T, = 26.30 ps
JA4Cb
293 K P(NH3) = 100' p t = 0% 9 = 53' T , = 3.10 ps T., = 4.70 ps
JA4Cb
313 K
X
293 K A = 25.3' P(NH3) = 90' p , = 0.83 Q = 53' rC = 2.79 ps T., = 4.70 ps
and all the values obtained in the high-temperature phases can be compared: 2C3Mn
AHINH,= 8 kJ-mo1-I
PHICHz 2C4Mn
10 kJ.mol-l
AHINH, N 13 kJ.mol-'
PHICHzN 7 kJ.mol-l
2C5Mn
AHINHI= 6 kJ-mol-' AHICH1 4 kJ.mol-l
The effective potentials V., calculated from eq 25 for the NH3+ oscillations around the C-N axis are in the 7-9 kJ.mol-' range.
FAlP
A = 25.4' pl = 0.384 T, = 2.36 ps
373 K A = 25.7' pl = 0.368 T, = 1.86 ps
473 K A = 26.3' pl = 0.325 7, = 1.59 ps
313 K P(NH3) = 100' pl = 0.384 = 53' T, = 2.41 ps T? = 4.11 ps
373 K P(NH3) = 100' pt = 0.365 Q = 52' T , = 2.14 ps T~ = 2.63 ps
473 K P(NH3) = 100' pt = 0.325 Q = 52' T, = 1.58 ps T., = 1.83 ps
313 K A = 25.4' P ( N H J = 100' Q = 53' pl = 0.378 7, = 2.12 ps T., = 4.1 1 ps
373 K A = 25.7' P(NH3) = 100 ' Q = 52' pt = 0.351 T, = 1.42 ps T? = 2.74 ps
473 K A = 26.3' P(NH3) = 105' 0 = 52' p, = 0.303 T~ = 1.03 ps T~ = 1.83 ps
Also, it is worth recalling the values estimated from the inelastic spectra for the V3 torsional components, 11-20 kJ.mol-I. From all these values, one notes a consistency between V7 and AHact and also a dependence of the dynamics of the polar heads upon the parity and the length of the hydrocarbon chains. These results indicate that the activation energies cannot be simply related to the V3 potential barriers for the -NH3+ torsional motions. The potential barriers against the CH2 motions decrease significantly as n increases. For 2C4Mn compounds, our results are in good agreement with literature data and confirm the stabilization of twisted conformers. However, we ruled out, in agreement with calculations of the intramolecular energies for isolated conformers, the geometrical model already proposed by Tichy et aL3 from neutron diffraction, in which the distortion of the molecule was mainly localized on the central C-C bond. Supporting our assumptions, the model of the cooperative torsion running along the molecular axis has
3448
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
Guillaume et ai. 1.42 I
4
1.27
1
1
*
0.83
S(0
9
! ~
-
w)
I
01 0 . 7 0 2 '
4
1
-1 1 ENERGY 1 m V Figure 16. Experimental spectra of 2C4-d0 at 493 K for different values of the elastic momentum transfer ( 5 times amplified).
1.42
2%- do 1.21
1.ll
1
0.97 I
14
I
473 K
-
1
-1
1
ENERGY1 nwV
Figure 17. Experimental spectra of 2 C 4 , at 473 K for different values of the elastic momentum transfer ( 5 times amplified).
been also successfully used in X-ray diffraction on 2C5Cd4and also in a calorimetric study on 2C5Mn.I2 For 2C5Mn compounds, we find a good agreement with literature data and confirm the existence of twisted forms of the chains. In 2CsCd, the phase-transition sequence is different and displays an additional monoclinic phase at above 417 K (phasetransition temperature). From Raman scattering experiments, Couzi et have shown that the proportion of twisted chains was about 70%) at 417 K. In the manganese derivative, this
proportion is 40% at the highest temperature investigated. By analogy with 2C5Cd,one could expect the existence of a monoclinic modification containing twisted chains only at higher temperatures. Finally, our results agree also with the values of the entropy variations as measured by calorimetry: ( 1 ) For 2C,Mn,* A S = R In (1.33) at the 111 IJ I I phase transition and A S = R In ( I .26) for the 11 I transition. This agrees quite well with our model in which the dynamical disorder of the chains is effective over two unequivalent sites.
Alkylenediammonium Motions in (NH3-(CH2),,-NH,)MnCI4
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3449
t
In
xlo”
I
1 I
1 1
2.5
0
I
1
3
,, 102 F *!‘?I 3:s
,I
I
\y) i
1
1 -.
13.1
ZI
1
I
0.5
2.5
yl’ lI
I
I
,
I
lox
I I
2
--
I
I
0 *.
.-
5
3k
Figure 18. Arrhenius plot of the different correlation times in the various structural phases of 2C4Mn compounds: (A) -(CH,)- motions for 2C4-d0 (0)and 2C4-nd, ( 0 ) ;(B) -NH, motions for 2C4-do (0) and 2C4-cd8 ( 0 ) .
+
(2) For 2C5Mn,I2AS = R In (2.7) AS,, where ASexis the excess entropy arising from the disorder between two trans and two twisted configurations.
VI. Conclusion In this study by incoherent inelastic and quasi-elastic neutron scattering about the various dynamical processes responsible for the phase transition in (NH3-(CH2),-NH3)MnC14 compounds, selectively deuterated samples were used in order to discriminate the intrinsic N-H and C-H motions. We have thus evidenced a dynamics effective around the main chain axis and an independent process around the C-N axis. For short chains with n = 3, slight distortions of the molecules take place. In the low-temperature phase, the chains are immobile, meanwhile the N-H protons oscillate around the C-N axis. The reorientational model for the whole cations in phases I1 and I corresponds to jumps about two trans equilibrium states. We thus proposed a new phase-transition sequence in which the symmetry of phase I I is likely to correspond to a monoclinic structure (a subgroup of Fmmm) and the symmetry of phase I corresponds to the Pnma orthorhombic structure. The idealized Imma structure could then be reached at higher temperature but has not yet been observed because the sample decomposes at 520 K. In phase 11, a change in the hydrogen bonding scheme, as clearly observed on the Raman s p e ~ t r a , Iis~ responsible *~~ for the unusual
behavior (slackening) of the dynamics of the NH3+ groups. For chains with n = 4, our results are in agreement with the already proposed phase-transition sequence: uncorrelated motions of both the polar NH3+heads in a cation are probably inducing the formation of distorted forms, and our results are in good agreement with a progressive torsion running along the chain. Simple intramolecular energy calculations confirm this model. For chains with n = 5, we also confirm the suggested phasetransition sequence. By analogy with 2CSCd,4,22 one could expect at higher temperature a monoclinic modification containing only twisted forms, but this phase is not detected due to a lower content of distorted forms. The proposed geometry for these conformers is similar to that found in 2C4Mn, and our results are in agreement with recent X-ray experiments on 2C5Cd4 and calorimetric measurements on 2C5Mn.12 In all these compounds, the amplitude of the oscillations of the NH, groups is nearly the same, indicating that there is a coupling via the hydrogen bonds between the deformations of the octahedra and the internal dynamics of the cations. This shows that the inorganic matrix, the chain length, as well as its parity, are important factors in stabilizing twisted conformers. In particular, the formation of twisted chains seems to be less hindered within the cadmium lattices than in the manganese ones.
Acknowledgment. We express sincere thanks to Professor M. Bee (University of Grenoble, France), J. C. Cornut and Dr. M. Couzi (CNRS, University of Bordeaux, France), and Professor G. Lucazeau (University of Grenoble, France) for helpful discussions and experimental assistance. Registry No. (NH3-(CHJ3-NH3)MnC14, 59683-1 8-0; (NH3-(CH2)-NH3)MnCI4,59683-19- 1 ; (NH3-(CH2)5-NH3)MnC14,59890-70-9.
