Chiral mononuclear lanthanide complexes derived from chiral Schiff bases: Structural and magnetic studies

Article abstract of DOI:10.1016/j.poly.2019.05.051

A new family of mononuclear lanthanide complexes with formula [Ln^III(L)Cl₃] (Ln = Eu (1), Tb (2), Dy (3), Er (4), Yb (5)) and L = N,N′-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-(R,R/S,S)-ethane-1,2-diamine has been obtained employi

Full text of DOI:10.1016/j.poly.2019.05.051

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Chiral mononuclear lanthanide complexes derived from chiral Schiff bases:
structural and magnetic studies
J. Mayans, L. Sorace, M. Font-Bardia, A. Escuer
PII:
S0277-5387(19)30389-4
https://doi.org/10.1016/j.poly.2019.05.051
POLY 13976
DOI:
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Polyhedron
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28 May 2019
Please cite this article as: J. Mayans, L. Sorace, M. Font-Bardia, A. Escuer, Chiral mononuclear lanthanide
complexes derived from chiral Schiff bases: structural and magnetic studies, Polyhedron (2019), doi: https://doi.org/
10.1016/j.poly.2019.05.051
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Chiral mononuclear lanthanide complexes derived from chiral Schiff bases: structural and
magnetic studies.
J. Mayans,a* L. Sorace,b* M. Font-Bardia,c A. Escuera
a
Departament de Química Inorgànica i Orgànica, Secció Inorgànica and Institut de
Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Martí i Franqués 1-11,
Barcelona-08028, Spain.
b Dipartimento di Chimica “Ugo Schiff” & INSTM RU, Università degli Studi di Firenze,
Via della Lastruccia 3, 50019, Sesto Fiorentino (Firenze), Italy.
c
Departament de Mineralogia, Cristal·lografia i Dipòsits Minerals, Universitat de
Barcelona, Martí Franqués s/n, Barcelona-08028, and Unitat de Difracció de R-X. Centre
Científic i Tecnològic de la Universitat de Barcelona (CCiTUB), Solé i Sabarís 1-3,
Barcelona-08028, Spain.
Dedicated to Prof. Miquel Julve. Great chemist and friend.
A new family of mononuclear lanthanide complexes with formula [LnIII(L)Cl3] (Ln=Eu (1),
Tb (2), Dy (3), Er (4), Yb (5)) and L= N, N’-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-
(R,R/S,S)-ethane-1,2-diamine has been obtained employing enantiomerically pure Schiff
bases. The complexes have been structurally characterized using X-Ray single crystal and
powder diffraction. Their dynamic magnetic properties have been studied showing that this
family presents slow relaxation of the magnetization under certain conditions and confirms
the different behavior of each LnIII cations in isostructural complexes: only the Er one
possibly relaxing via an overbarrier Orbach process, while Raman process dominates for
Dy and Yb derivative.
Keywords: lanthanide, Schiff base, magnetism, chirality.
1. Introduction
Coordination chemistry related with lanthanide cations has been experiencing an increasing
impact since the discovery in 2003 by Ishikawa and co-workers [1] that a terbium-
phthalocyaninate complex is magnetically bistable up to 30 K. This potentially opened new
way to molecular-based magnetic memory unit and spurred a large wealth of studies. It was
soon realized that this somehow surprising magnetic behavior is due to the large magnetic
moment of TbIII (7F6) and to the strong easy axis type single ion anisotropy which it
assumes in the specific coordination environment. [2-5] This results in a large barrier to the
reorientation of the magnetization which can be overcome by an Orbach-type thermally
activated process, with a relaxation time that obeys the Arrhenius law. Following this first
report, hundreds of lanthanide-based complexes have been reported to show slow relaxation
of the magnetization, as probed by ac susceptometry, either with or without an external

applied field.[6-11] Among this, DyIII based complexes have been by large the most studied
lanthanide ones due to the large magnetic moment of DyIII and to its Kramers ion nature,
which ensures a strict degeneracy of the two lowest lying levels and reduce the possibility
of magnetization relaxation via Quantum Tunneling of the Magnetization. It is however
clear, that any lanthanide ions (with the obvious exception of EuIII) can show slow
relaxation of the magnetization in specific cases. Theoretical and experimental studies have
shown that a key role is played by the symmetry of the crystal fields around the lanthanide
cation which could effectively enhance the ion anisotropy. [12-13] In the past few years,
however, many reports pointed out that the presence of a large anisotropy barrier is not
enough to increase the relaxation time in all the temperature range, due to the competing
relaxation mechanisms, such as Raman and direct one. [14-15]
Lanthanide based complexes are specifically interesting in luminescence investigations due
to their characteristic narrow line-like emissions, long lifetimes and high quantum yields.
When this luminescence is mixed with chirality by using enantiopure organic ligands new
optical properties can be found in the synthesized systems, related to absorption and to
emission, which can be studied spectroscopically with Electronic Circular Dichroism
(ECD) and Circularly Polarized Luminescence (CPL), respectively. While the ECD allows
to confirm the enantiopurity of a compound and confirms the stabilization (or not) of a
complex in the solid state and in solution, the presence of polarized emission (CPL) can be
useful for applications in materials and bioscience fields using the compounds as
biomarkers and biosensors.[16-20]
Following this reasoning, for this work we have synthesized a new family of mononuclear
compounds derived from the chiral Schiff base ligand N, N’-bis((1,2-diphenyl-(pyridine-2-
yl)methylene)-(R,R/S,S)-ethane-1,2-diamine ( Scheme 1) obtained from the condensation of
two equivalents of 2-pyridinecarboxaldehyde with one equivalent of (1R, 2R/1S, 2S)-
diphenylethylendiamine in methanolic solution with general formula formula [LnIII(L)Cl3]
(LnIII = Eu (1), Tb (2), Dy (3), Er (4), Yb (5)). All of these compounds present slow
relaxation of the magnetization under an applied external bias field with the exception of
TbIII and EuIII derivative. For complex 4, we also measured the diluted compound which
was also prepared, exploiting as dilution media the isostructural EuIII based complex (4b),
which has a non-magnetic ground state. This dilution allowed us to observe the hyperfine
coupling in the Electronic Paramagnetic Resonance (EPR) spectrum of the ErIII and to draw
some conclusions about the different processes influencing the relaxation dynamics.

Scheme 1. Chart of L ligand used for the synthesis of 1-5 complexes. Asterisk denotes the
chiral C-atoms.
2. Experimental
2.1 Physical measurements.
Ac susceptibility measurements were carried out on polycrystalline samples in a Quantum
Design PPMS on microcrystalline powdered samples pressed in a pellet to avoid field-
induced orientations. Diamagnetic corrections were calculated using Pascal’s constants.
Infrared spectra (4000-400 cm–1) were recorded from KBr pellets on a Bruker IFS-125 FT-
IR spectrophotometer. ECD spectra were measured on a Jasco-815 spectropolarimeter by
preparing a methanolic solution which was poured into 1 cm path length quartz cuvettes
and diluted until obtaining an adequate concentration. X-band (ν ~ 9.45 GHz) EPR
spectrum of complex 4b was recorded in a commercial Bruker E500 spectrometer equipped
with a continuous 4He flow ESR900(Oxford Instruments) for low temperature
measurements.
2. Syntheses.
Synthesis of L. The ligand solution of the Schiff base L was employed directly to
synthesize the corresponding complexes 1-5 without isolation of the solid ligand. The
syntheses of the ligands were common for the (RR) and for the (SS) enantiomers: 0.053 g
(0.5 mmol) of 2-pyridinecarboxaldehyde and 0.053 g (0.25 mmol) of (1R, 2R/1S, 2S)-
diphenylethylendiamine were dissolved in 20 mL of methanol and stirred at room
temperature for three hours.
[Ln(RR-L)2Cl6] and [Ln(SS-L)2Cl6] for all the lanthanide cations and were synthesized
following the same procedure and just changing the corresponding enantiopure ligand and
the corresponding lanthanide chloride. 20 mL (0.25 mmol) of the previously prepared
solution of the ligand (L) were added to an equimolar quantity of a LnCl3·nH2O methanolic
solution (10 mL). The resulting solution was stirred for one hour at room temperature.
Crystals suitable for monocrystal X-Ray diffraction in the shape of white needles were
obtained a few days later by slow diffusion with diethyl ether. Anal. calc./found for 2RR
(C26H22Cl3N4Tb): C, 47.62/47.2, N, 8.54/8.7; H, 3.38/3.5. IR spectra for 2RR and 2SS
compounds (cm-1) as an example for the 1-5 series (Figure S1).

3. Crystallographic measurements
White needles specimens of (2RR) and (2SS) were used for the monocrystal X-ray
crystallographic analysis. The X-ray intensity data were measured on a D8 Venture system
equipped with a multilayer monochromator and a Mo microfocus (λ = 0.71073 Å).
The frames were integrated with the Bruker SAINT software package using a narrow-frame
algorithm. The structures were solved and refined using the Bruker SHELXTL Software
Package. Crystal data and refinement details are summarized in Table 1. Powder X-Ray
diffractions were performed in a PANalytical X’Pert PRO MPD θ/θ powder diffractometer
of 240 mm of radius, in a configuration of convergent beam with a focalizing mirror and a
transmission geometry with flat samples sandwiched between low absorbing films and Cu
Kα radiation (λ=1.5418 nm).
4. Results and discussion
4.1 Structural description
Only complexes 2RR and 2SS were solved by single crystal X-Ray diffraction (the TbIII
derivatives) whereas the other complexes were characterized by Powder-X Ray diffraction.
The structures of complexes 2RR and 2SS show a mononuclear neutral complex of TbIII
whose crystalline system is triclinic (Figure 1). In the unit cell there are four non-
equivalent molecules (labelled A to D) with similar bond parameters. These four molecules
differ only slightly in the bond distances and angles. The further data reported in Table 2
refer to molecules A.
In complex 2, the terbium cation is heptacoordinated and its coordination sphere is a
pentagonal bipyramid. First, TbIII is coordinated to the tetradentate ligand L, which
occupies the equatorial positions of the complex. The linkage of the metal with the ligand is
via the four N-donors of the ligand, that form Npy-Tb-Nimine angles much lower than 90º due
to the small bite of the ligand, ranging from 64.4 to 64.8º in the case of complex 2SS, while
in the case of 2RR they range from 64.2 to 65.5º (see Table 2). In both cases, the
coordination of L leaves enough free space around the ion to coordinate the chloride ligand
as fifth donor in the same plane.

Figure 1. Top, labeled plot of the molecular structure of 2RR (left) and 2SS (right),
showing the H-atoms linked to the chiral carbons. Bottom, coordination environment
around the terbium cations. The ideal pentagonal bipyramidal polyhedron is depicted in red.
The coordination sphere is completed by two additional chloride ligands occupying the
axial positions, forming a Cl1-Tb1-Cl2 bond angle close to 180º. In compound 2SS, the
stated angle is 172.0º and for compound 2RR, 167.8º. CShM value calculate with SHAPE
[21,22] is 1.36 indicating an almost perfect BPP environment.
There are no relevant intermolecular hydrogen bonds as a consequence of the lack of
crystallization solvents, O-donors or accessible N atoms. The only intermolecular
interactions are promoted by weak CH···Cl contacts between the coordinated chloro
ligands and the nearest H-atoms from pyridinic fragments of the nearby molecule with
C···Cl distances around 3.5 Å which optimizes the maximum possible packing.
The powder X-Ray diffraction spectra for the complete series of mononuclear Ln
complexes 1-5 (Figure 2), show a complete agreement of the experimental diffraction
patterns with the spectrum calculated from the single crystal structure of compounds 2,
evidencing that compounds 1-5 are isostructural. The lack of crystallization solvents results
in stable crystals at ambient conditions. [23]

Figure 2. Powder X-Ray diffraction pattern obtained for compounds 1-5 (above) and the
calculated spectrum of compound 2 (bottom).
4.2 UV-visible spectrum and Electronic Circular Dichroism spectroscopies.
The UV-Visible spectra (Figure 3) were collected using samples from the ligand L and
compound 2 in methanolic solutions. UV-Vis spectra are dominated by the transitions
related to the ligand in the 200-325 nm range with one absorption at 206 nm due to the π-π*
transition of the aromatic ring and another band at 215 nm (265 nm shoulder) related to the
iminic group. For complex 4, the transition at 205 nm is maintained while the other one is
shifted to 300 nm.; however, bands corresponding to the LnIII atoms transitions were not
observed.
Figure 3. Representative UV-Vis spectrum for complex 2 and for the ligand L.

ECD spectra of the enantiomeric pair of pure 2RR and 2SS complexes were measured in
methanolic solutions and are mirror images of one another as should be expected for a pair
of enantiomers, Figure 4. The two CD spectra are similar since the bands that are observed
are due to the π-π* transitions of the ligand L. The chirality around the metal cation is not
observed in this case due to the low chirality transfer from ligand to metal.
Figure 4. Representative ECD spectra for both enantiomers of 2.
4.3. Dynamic magnetic properties
A few families of pentagonal bipyramidal complexes have been reported in recent years to
show very high barrier to the relaxation of the magnetization. [24,25] We then investigated
the dynamic magnetic properties of complexes 2-5 by ac susceptometry. No maxima appear
in the ’’ vs. T measurements above 1.8 K at zero field for any of the compounds; and no
maxima appear under any dc applied field for complex 2 probably due its non-Kramers
nature, which makes Quantum Tunneling of the magnetization extremely efficient.
For the DyIII derivative, 3, a dc field of 1000 G was selected to perform the measurements
after a preliminary study of the out-of-phase signal under different fields. Its out-of-phase
susceptibility dependence in function of the frequency between 10 and 1488 Hz is reported
in Figure 5, left. The corresponding relaxation times as a function of temperature were
extracted by fitting the Cole-Cole plots to an extended Debye relaxation model [26] (see
supplementary material, Figure S2) in the range 1.8-5.0 K, using the CCfit software. [27]
This also yielded a quite narrow distribution of the relaxation times, with α decreasing from
0.1 at 1.8 K to 0.05 at 5 K.
It is immediately evident from that large deviation from linearity is observed in the
Arrhenius plot (Figure 5, right), indicating the onset of relaxation mechanisms that are
different from the simple Orbach one involving a magnetic anisotropy barrier. In such cases

it is now customary to include in the modeling of the relaxation other terms, such as
Raman, direct, and quantum tunneling ones, according to:
1
푛
휏 = 휏 ‒ 1푒푥푝 ‒ ∆/푘퐵푇 + 퐴푅푎푚푇 + 퐵푑푖푟푇 + 퐶푄푇푀
(
)
(1)
0
Where the first term represents the over barrier Orbach relaxation, the second one is the
Raman relaxation rate, the third is the direct term and the fourth is the quantum tunneling
one. Since measurements were taken in applied field to minimize the effect of Quantum
tunneling processes we attempted the fit by keeping the fourth term to zero. Interestingly,
we could not find any combination that was able to reproduce the observed behaviour by
including an Orbach term. Best fit was then obtained by a combination of Raman and direct
relaxation processes, with ARam= 1.6 ± 0.2 s-1 K-n, n = 5.7 ± 0.1, Bdir = 275 ± 7 s-1 K-1. The
value of the Raman exponent, despite being smaller than that predicted by the original
Orbach theory, falls well within range reported values for molecular based Lanthanide
systems. [11, 28] (Table 3).
Figure 5. Left, representation of the out-of-phase susceptibility for complex 3 in the
frequency range 10-1488 Hz. Continuous lines are guides to the eye. Right, Arrhenius plot
of complex 3 and best fit obtained using model reported in the text.
The same procedure was applied for ErIII complex. 4 shows the dependency of the out of
phase susceptibility as a function of the frequency under different applied dc fields: in this
case the application of different magnetic fields results in a much faster relaxation at fields
larger than 1000 G, the maximum in ’’ shifting above 10 KHz even at 2 K (see
supplementary Figure S3). This is a clear proof of the relevance of the direct process in
determining the relaxation, since the corresponding rate is expected to scale as H2 and thus
to be extremely efficient at high field. A second relaxation process, much slower than the
first one and essentially temperature independent, also appears at high field (Figure
S3,3000G). Such behavior is not uncommon in lanthanide-based complexes and is usually
related to a collective process due to dipolar intermolecular interaction. [29] To reduce
them, we prepared a solid solution of the ErIII complex in one of its diamagnetic

isostructural analogues. The first choice for the magnetic dilution was to prepare the Er@Y
derivative with a 5% of ErIII in the sample. However, the synthesis was not successful
(further trials demonstrated that the YIII complex was not formed) and we decided to use
EuIII as a magnetic dilutor (complex 4b), taking into account that this cation has a non-
7
magnetic F0 ground state. [30] Figure S4 shows the susceptibility dependency vs.
frequency under applied fields of 500 and 1000 G for the Er@Eu system. The
corresponding relaxation times as a function of temperature extracted from fits of the ac
susceptibility data for both pure and doped samples in different fields are reported in
Figure 6: two aspects are immediately evident: (i) as expected, the doped sample relaxes
slower in the whole temperature range. (ii) even in the small temperature range in which
slow relaxation is observed the temperature dependences deviate from linearity of the
Arrhenius plot indicating that Orbach process is not the only one also in this case. Here, the
use of equation (1) by neglecting QT terms provides as best fit the following parameters:
Bdir = 89 ± 13 s-1 K-1, 0 = 3 ± 2 x 10-8 s-1,  = 40.6 ± 1.2 K for Er@Eu. We note that a fit
of similar quality could be obtained by excluding Orbach process and assuming
contributions from Raman and direct ones, but the best fit value for the n exponent of
Raman term is outside of the usually accepted range for this type of systems (n = 13.6 ±
0.1). Furthermore, no fit of the dynamic behaviour of the pure sample could be obtained by
including Raman and direct process, while Orbach and direct provided a reasonable fit for
these data (best fit parameters: Bdir = 2331 ± 17
31.7 ± 0.2 K) (Table 3).
s-1 K-1, 0 = 7.3 ± 0.3 x 10-10 s-1,  =
The magnetic dilution of the complex was also instrumental in obtaining a well-defined
Electron Paramagnetic Resonance (EPR) spectrum, compared to the broad one obtained for
the pure complex (Figure S5). The EPR spectrum of 4b is reported in Figure 7 showing a
parallel feature at low field (with signals from I=0 Er isotopes and from 167Er, I=7/2, nat.
ab.=22.9%) and an intense, partially split, perpendicular feature at high field also showing
sign of hyperfine coupling.
The spectrum was simulated [31] assuming only the ground doublet to be populated, and an
effective spin Hamiltonian:
퐻푒퐸푓푟푓 = 휇퐵푩 ∙ 품푒푓푓 ∙ 푺푒푓푓 + ℎ 푰 ∙ 푨푒푓푓 ∙ 푺푒푓푓
(2)
Where the second term represents the hyperfine coupling and has been included only to
take into account the contribution of 167Er. Best simulation was obtained with parameters
gxeff 1.72  0.03
,
geyff  2.12  0.02
,
gzeff 14.23 0.01 and Axeff  400  50MHz
,
Ayeff  500  50MHz
,
Azeff  2100  200MHz . Even if the deviation from axiality is far
from being negligible we stress here that, to the best of our knowledge, the value for gzeff is
the highest up to now experimentally measured by EPR in an Er(III) based molecular

system. [32-34] This is somehow in agreement with the suggestions of the ac
measurements of relaxation occurring predominantly via Orbach process.
Figure 6 Arrhenius plot of the temperature dependence of the magnetization relaxation rate
for 4 and 4b in 500G and 1000 G, respectively. Continuous lines are best fits to the models
described in the text.
Figure 7. EPR spectrum of the Er@Eu complex at 5 K and best simulation obtained with
parameters reported in the text.

For complex 5, the YbIII derivative, the ’’ vs. frequency dependence between 10 and
10000 Hz at different applied magnetic fields are shown in Figure 8. It is evident that in
this case there is essentially no dependence on the applied field of the magnetization
dynamics. At the same time, the non-linearity of the corresponding Arrhenius plot, obtained
by the fitting of the Argand plots (Figure S6), indicated also in this case the coexistence of
more than one process. The corresponding fit using eq.1 and neglecting QTM term
provided best fit when using a combination of Raman and direct processes, with the
following parameters: ARam = 11.4 ± 0.2 s-1 K-n, n = 5.38 ± 0.01, Bdir =1009 ± 6 s-1 K-1. It is
interesting to note that the overall behavior, and the corresponding best fit parameters are
close to those obtained for Dy derivative, suggesting that the vibration responsible for this
relaxation process are similar in the two cases (Figure 9, Table 3).
Figure 8. ’’ vs. frequency plots of YbIII complex 5 at different applied dc fields.

Figure 9. Arrhenius plot of the relaxation time of 5 measured in different applied fields ad
corresponding best fit curve using parameters reported in the text. Continuous line
represents the fitting of the 1000 G curve.
Concluding remarks
By using enantiomerically pure Schiff bases we obtained a new family of mononuclear
lanthanide complexes, in which the lanthanide cation is heptacoordinated with a
coordination sphere which is a pentagonal bipyramid.
Their dynamic magnetic characterization demonstrates the presence of slow relaxation of
the magnetization for complexes 3, 4 and 5 only under the application of an external
magnetic field, probably because of the drawback of relaxation through quantum tunneling
due to the largely distorted environments around the cations. This is also in agreement with
the fast relaxation of TbIII derivative, which is the only one with an integer spin ground
state. Analysis of the temperature dependence of the relaxation points to relaxation
occurring via Orbach process with relatively small barrier only for Er derivative, while Dy
and Yb are dominated by Raman and direct processes. These are increasingly recognized of
major relevance in degrading the performances of lanthanide based SMMs at low
temperatures, and their control is actively sought for.
The absence of dominant overbarrier (i.e. Orbach type) relaxation processes is not
surprising in this family, since Rinehart-Long model [12] suggests that the type of the
anisotropy for the different system has to be different. Indeed, if the coordination geometry
around the ion is the same, one would expect that the anisotropy of Yb(III) and of Dy(III),
characterized in their highest mJ values by oblate and prolate charge distribution,
respectively, should be opposite. In this respect, if one of these were to relax via overbarrier
process, the other should not. At the same time the EPR spectrum of Er derivative diluted

in Eu evidenced that these systems are characterized by a relevant deviation from axiality,
which hampers slow relaxation occurring by overcoming an anisotropy barrier in zero field.
6. Acknowledgements
Support from Ministerio de Economía y Competitividad, Project CTQ2015-63614-P are
acknowledged.
Appendix A. Supplementary data
CCDC 1826260-1826261contains the supplementary crystallographic data for compounds
2RR
and
2SS
These data can be obtained free of charge via
http://www.ccdc.cam.ac.uk/conts/retrieving.html, or from the Cambridge Crystallographic
Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44) 1223-336-033; or e-
mail: deposit@ccdc.cam.ac.uk.
Table 1. Crystal data and structure refinement for coordination compounds 1RR and 1SS.
1RR
C26H22Cl3N4Tb
655.74
1SS
C26H22Cl3N4Tb
655.74
Formula
FW
System
Space group
a/Å
Triclinic
P1
Triclinic
P1
8.7672(3)
10.9544(5)
27.502(1)
87.262(2)
82.056(2)
88.241(2)
2612.2(2)
4
8.7720(3)
10.9600(4)
27.4997(1)
87.025(2)
81.982(2)
88.059(2)
2613.5(2)
4
b/Å
c/Å
/deg.
ß/deg.
/deg.
V/ Å3
Z
T, K
100(2)
100(2)
(MoK), Å
0.71073
1.667
0.71073
1.667

calc, g·cm-3
µ(MoK), mm-1
Variables
3.036
1226
3.034
1063
Max/min peaks, e-Å-3
Flack parameter
R
2.210/-1.518
0.006(5)
0.0236
1.200/-1.057
0.003(5)
0.0345
R2
0.0319
0.0539

Table 2. Selected bond parameters for the A-molecule of the complexes 1RR and 1SS.
1RR -A
2.578(5)
2.520(5)
2.521(4)
2.583(6)
2.647(2)
2.609(2)
2.613(2)
63.2(2)
1SS -A
2.556(5)
2.513(5)
2.522(5)
2.576(5)
2.632(2)
2.604(2)
2.610(2)
64.4(2)
Tb1-N1
Tb1-N2
Tb1-N3
Tb1-N4
Tb1-C11
Tb1-C12
Tb1-C13
N1-Tb1-N2
N2-Tb1-N3
N3-Tb1-N4
N1-Tb1-C13
N4-Tb1-C13
C11-Tb1-C12
65.5(2)
64.8(2)
65.1(2)
64.7(2)
83.2(1)
83.5(1)
83.4(1)
83.7(1)
167.8(4)
172.0(6)
Table 3. Best fit parameters for the temperature dependencies of the relaxation rates of the
investigated family.
ARam (s-1 K-n)
n
Bdir (s-1 K-n) τ0 (s)
Δ(K)
3
1.6 ± 0.2
5.7 ± 0.1
275 ± 7
-
-
4
-
-
-
2331 ± 17
89 ± 13 s-1
(7.3 ± 0.3)x10-10 31.7 ± 0.2
4b
5
-
(3 ± 2) x 10-8
-
40.6 ± 1.2
-
11.4 ± 0.2
5.38 ± 0.01 1009 ± 6
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