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Dielectric properties of 1-cyanoadamantane C10H15CN, in its plastic phase
J.P. Amoureux, M. Castelain, M. D. Benadda, M. Bee, J.L. Sauvajol
To cite this version:
J.P. Amoureux, M. Castelain, M. D. Benadda, M. Bee, J.L. Sauvajol. Dielectric properties of 1- cyanoadamantane C10H15CN, in its plastic phase. Journal de Physique, 1983, 44 (4), pp.513-520.
�10.1051/jphys:01983004404051300�. �jpa-00209625�
Dielectric properties of 1-cyanoadamantane C10H15CN, in its plastic phase
J. P. Amoureux (*), M. Castelain (*), M. D. Benadda (**), M. Bee (+) and J. L. Sauvajol (*)
(*) Laboratoire de Physique des Solides. Equipe de dynamique des cristaux moléculaires (++). Université de Lille I, Villeneuve-d’Ascq Cedex, France
(**) Equipe « nouveau matériau », centre hyperfréquences et semi-conducteurs (+++), bât. P3, Université Lille I,
Villeneuve-d’Ascq Cedex, France
(Reçu le 24 mai 1982, révisé le I S novembre, accepté le 20 décembre 1982)
Résumé. 2014Les propriétés du 1-cyanoadamantane C10H1sCN sont analysées entre 200K et 400 K dans une
très large bande de fréquence (10-109 Hz). Les effets dynamiques de relaxation sont étudiés en relation avec la struc- ture de la phase plastique. Les variations avec la température du mouvement monomoléculaire et des molécules corrélées sont analysées. Le résultat que nous obtenons pour le mouvement monomoléculaire correspond exacte-
ment avec celui déduit en R.M.N. Avec le facteur de corrélation expérimental de Kirkwood g, un ordre local anti-
parallèle est mis en évidence dans toute la phase plastique du cyanoadamantane.
Abstract. 2014 Dielectric properties of 1-cyanoadamantane C10H15CN are analysed in a very wide frequency band (10-109 Hz) between 200 K and 400 K. Dynamical relaxation effects are studied in relation to the structure of the
plastic phase. The temperature variations of both single and correlated molecular motions are investigated. The
results we obtain for the single molecular motions agree exactly with the corresponding ones deduced from N.M.R.
The experimental Kirkwood correlation g factor indicates an anti-parallel local order in all the plastic phase of cyanoadamantane.
Classification Physics Abstracts
77.40
1. Introduction. - An extensive and comparative study of substituted adamantanes has been undertaken for some years in order to relate some macroscopic (heat capacity, phase transitions) or microscopic (crystallographic structure, molecular dynamics) phy-
sical properties to the intramolecular forces, Van der
Waals steric hindrance or dipole-dipole interactions.
This series of compounds are particularly interesting owing to their high symmetry, to the fact that most of them are in a cubic plastic phase at room temperature and to the wide range of substituents available, allowing a wide range of depart,ure from the quasi- spherical symmetry.
Two very important parts of this program concern
single and correlated molecular motions in these substituted adamantanes. 1 H-N.M.R. and Incoherent
Quasi-elastic Neutron Scattering (I.Q.N.S.) are sensi-
tive to single molecular motions only, while dielectric
relaxation, Raman and coherent neutron scatterings
are expected to give information about the static and
dynamic cooperative correlated molecular motions.
One of the most interesting substituted adamantanes is 1-cyanoadamantane : C10H1sCN. Its interest arises from its long cigar like shape substituent, from its
very large permanent dipole moment and from the fact that it forms a plastic phase at room temperature (melting point Tm = 458 K).
This compound, formally known as 1-cyano tri- cyclo [3, 3, 1, 1] decane is composed of globular
molecules. It can be obtained from adamantane
C 1 OH 16 by substituting (Fig. 1) a cyano group onto
a methine carbon. Microwave spectra [24] and 13C
chemical shifts [25] have shown that this substitution does not change the rest of the molecule whose sym- metry is then C3v.
X-ray scattering has enabled vs to obtain the
crystallographic structure of the room temperature plastic phase. It was resolved in two different ways.
The first was based on a Frenkel model [1] whilst the
second used cubic harmonic analysis [2]. The lattice is f.c.c., space group Fm3m with four molecules in the unit cell and with parameter a = 9.81 A at room
temperature. The determination of the molecular
equilibrium positions [1] together with the maxima of the orientational probability density [2], unambi- (+) Present address : Institut Laue-Langevin, 156X,
Centre de tri, 38042 Grenoble Cedex, France.
(++) Associee au CNRS, No 465.
(+ + +) LA associe au CNRS no 287.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01983004404051300
514
Fig. 1. - The molecule of cyanoadamantane. Carbons
are in white, hydrogens in black and nitrogen is dashed. A cube has been drawn to indicate the directions of atoms with respect to each other, it does not correspond to the direc-
tions of the unit cell.
guously shows that each cyano group C-C ---N
can take 6 distinguishable equilibrium orientations
along the ( 001 ) directions. For each of the six
dipolar orientations, the molecule can occupy four distinct equilibrium positions derived from each other by 300 rotations around its three-fold symmetry axis. However for this 12-fold uniaxial rotation the
equilibrium positions are not very well defined and this motion can be approximated by a free uniaxial rotation.
The dynamical nature of the disorder has been
clearly shown by I.Q.N.S. [3] and by 1 H-N. M. R. [4].
Two very different motions exist in the cubic plastic phase at the same temperature : a fast quasi-free
uniaxial rotation around the C-C --_ N group and a
slow tumbling reorientation of the dipole moment
between the 001) axes of the cubic lattice. The
frequencies corresponding to these two molecular
motions are very different, and at room temperature their respective values are approximately 1011 Hz
and 105 Hz.
Dielectric relaxation is sensitive only to the slow tumbling reorientations of the dipoles and not to the
fast molecular uniaxial rotation. In order to complete
the I.Q.N.S. and N.M.R. results and then to obtain
an accurate description of the dipole reorientations,
we have analysed the dielectric properties of 1-cyano- adamantane in its plastic phase (200-400 K) in a very wide frequency band (10-109 Hz).
2. Complex dielectric permittivity and dynamical
behaviour. - 2 .1 DISTRIBUTIONS OF RELAXATION TIMES.
- The complex dielectric permittivity 8*(m) is a frequency dependent function which can be written :
9*((o) = g’(cv) - 18"(m). We call Fc the « critical >>
frequency which corresponds to the maximum value
EM for the loss factor s"(co). Following Debye [26] we
say that the macroscopic dielectric behaviour of a
system is characterized by a single (no distribution) macroscopic relaxation time r, when one can write :
es stands for the static dielectric constant and eoo is the permittivity contribution due to induced pola-
rizations.
The Cole-Cole plot (E" versus g’) corresponding to
a single macroscopic relaxation time is a « Debye »
semi-circle centred on the s’ axis at (es + eoo)/2 and
with a radius (s. - s.)12. When the experimental
Cole-Cole plot does not correspond to a semi-circle,
and if there exists only one type of dipolar motion,
the data can be formally described by a normalized macroscopic distribution of the relaxation times
H(ln i) defined by :
with I
When the experimental Cole-Cole plot is a circular
arc with its centre below the s’ axis, one then uses the
Cole-Cole [21] relation :
This relation corresponds to a macroscopic distri-
bution [22] symmetrical with respect to In z (z = :
The half width at half maximum (thwhm) of this macro- scopic distribution function can be obtained from an
expansion of equation (4). The corresponding relative macroscopic width W(a) = Th,,h./T,,,, is given by :
From linear response theory, the dielectric relaxation is determined from the following correlation function :
y(t ) is the microscopic correlation function which takes
into account the correlated dipolar motions. The
susbcript 0 stands for the absence of an external electric field and the sum of the permanent molecular
moments Y pi is taken in a sphere of macroscopic
i
dimension around molecule 1 embedded in an infinite medium of the same composition (superscript oo ).
If there exists only one type of dipolar motion and if y(t) is not characterized by a single relaxation time :
y( t) #= exp(- t/i), one says that there exists a nor-
malized microscopic distribution h(ln i) defined by :
with
2.2 RELATION BETWEEN 8*(W) AND THE DIPOLAR MOTIONS. - * Glarum and Cole [6-7] have investi-
gated the relation between the microscopic time dependent correlation function y(t) and the macro- scopic frequency dependent complex dielectric per-
mittivity 8*(m). Their results correspond to :
Ciw stands for the Laplace transform for argument ico.
When 7(t) is characterized by a single relaxation
time i, equation (8) leads to a macroscopic dielectric
Fig. 2. - Example of suitable packing in the (001) plane.
behaviour also characterized by a single relaxation
time Tc with :
When the experimental Cole-Cole plot is a circular
arc with a depressed centre (Eq. (3)), then the micro-
scopic distribution function h(ln i) is equal to the
Fig. 3. - Cole-Cole plot corresponding to 222 K. The experimental values versus the frequency in kHz are repre- sented by points. The continuous line corresponds to the
semi-circle (Eq. ( 1 )), the dotted dashed curve to the Cole- Cole relation (Eq. (3)) and the dashed line to the Fatuzzo and Mason equation (10) for y(t) = exp(- t/i).
macroscopic one (Eq. (4)) shifted along the In i axis (Eq. (9)).
* Fatuzzo and Mason [15] have demonstrated that Glarum’s derivation was disputable and that for
isotropic systems, in the frequency range corresponding
to the dipolar reorientations, equation (8) must be replaced by :
In many cases (Gs > GcxJ this relation (10) can be simplified :
If y(t) is characterized by a single relaxation time T,
equation (10) leads to a Cole-Cole plot lying slightly
outside a semi-circle (Fig. 3), except when E. > Boo, where a single macroscopic relaxation time (11) is
observed : ’tc = i.
When the experimental Cole-Cole plot is a symme- trical depressed circular arc (Eq. (3)), then the norma-
lized microscopic distribution h(ln i) is slightly asym-
metrical [14] with respect to In z (z = tc/1) :
where K is equal to f,s/f,oo and H(z) is given by equa- tion (4).
Whatever K may be, if a 0.2, the corresponding
relative microscopic width : w(a), is nearly equal to W(Lx) in (5).
3. Dynamical behaviour of cyanoadamantane. -
3.1 DIELECTRIC RELAXATION AND SINGLE MOLECULAR MOTIONS. - The microscopic correlation function
y(t) is very difficult to evaluate and to our knowledge
it has been obtained only once for hexasubstituted
516
benzenes [13]. On the other hand the dipole correlation
function C(t) which corresponds to the uncorrelated motions for the permanent dipoles can be easily calculated :
This dipole correlation function C(t) equals the microscopic correlation function y(t) in systems where short-range interactions between neighbouring mole-
cules are absent.
As we deal with molecular reorientations, inertial
effects are completely neglected : ë(O) = 0. From
fundamental statistical mechanics all cross-correlation
terms are zero for t = 0 and then all the correlations have a negligible contribution to 8*(m) at high fre- quencies.
Therefore if the experimental complex permittivity e (m ) can be described by the macroscopic distribution
H(ln i), then [23] the initial decrease of the single
molecule dipole correlation function is given by :
It follows from the above that from the dielectric relaxation alone it is not possible to obtain the single
molecule dipole correlation function, but only its
initial decay. This initial decay can give direct informa- tion about the reorientation process.
3.2 THE DIPOLE CORRELATION FUNCTION OF CYANO- ADAMANTANE. - For cyanoadamantane, an impor-
tant problem concerns the bending motion of the C--C --_ N group. A very recent Raman scattering study [8] has shown that the frequency corresponding
to this deformation (4.5 THz) is much too high to be
accounted for in our dielectric analysis. Therefore we
have assumed that the molecule is rigid and we have
calculated C(t) with the method using group theory
described by Williams and Cook [9].
In most plastic crystals free isotropic rotation is
impossible on account of the intermolecular distances.
This is the case in cyanoadamantane where there is steric hindrance between first and even second
neighbouring molecules (Fig. 2).
In this compound the most reasonable model for the dipolar motions allows for reorientations bet-
ween the six ( 001 > directions, for which we have used a « jump Frenkel model ». In this model the
« jump time » from one equilibrium position to
another is equal to zero, which corresponds to the
very small amplitude [1] at room temperature for the dipolar librations : 2.80.
We assume that the dipole can jump only from one equilibrium position to its four next nearest ( 001 )
directions. Then the dipolar reorientations are well described by 3-fold rotations about the ( 111 axes only. The mean time a cyanogroup stays in an equi-
librium position (the residence time) is called tC3.
For example, the time density probability that the dipole moment jumps from [001] to [100] equals (4 ’t’C3)-1. Then if we neglect inertial effects :
Obviously ’tC3 is an averaged value and this residence time for a particular molecule depends of the exact surrounding (local order).
4. Experiments. - - 4.1 DETERMINATION OF THE PERMANENT DIPOLE MOMENT pv, - The most accurate method for determining permanent dipole moments
is based on measurements on the dilute gas. However, in the case of cyanoadamantane it is impossible to
obtain sufficient concentrations in the gaseous state without raising the temperature so much that des- truction of the molecules occurs. So the best method is to measure the static dielectric constant of dilute solutions of CloHisCN in a non polar solvent.
The dipole moment deduced by this method in solution (ps) deviates slightly from the exact value
measured on the isolated molecule in vapour (p,).
This « solvent effect » can be due to specific inter-
actions between the solute and the solvent molecules and also to the bulk properties of the solvent espe-
cially the dielectric constant.
In this case, for globular molecules one has [22]
the following relation :
Where 8so1v corresponds to the solvent and 800
to the solute : ClOH15CN. We have used CCl4 as
solvent and measured ,us = (3.93 ± 0.04) D. Then
03BCv = (3.83 ± 0.05) D.
4.2 EXPERIMENTAL CONDITIONS. - As we deal with cubic symmetry, the complex permittivity of the single crystal is isotropic [22] and can be directly
measured on a powder sample. Therefore the experi-
ments were performed on very homogeneous mixtures
of powdered cyanoadamantane (concentration
0 = 0.95) with air. For the whole study the experimen-
tal results were always reproducible within 2 % error, which justifies the filling method (i.e. : no concentration
gradient). Even at high temperatures, the sample has
never presented conductivity or sublimation pheno-
mena : cyanoadamantane has a very low vapour pressure.
In a recent paper [5] it was shown that the dyna-
mical dielectric properties of a highly concentrated mixture are well described by B6ttcher’s formula [10] :
Where e* and E Xp are respectively the complex permit- tivity of the single crystal and of the homogeneous
Fig. 4. - The loss factor s" versus the frequency F, for
the nine characteristic temperatures corresponding to table I.
mixture. The concentration 0 is the volume fraction taken up by cyanoadamantane (0 = 0.95 in our experiments).
The experimental accuracy being 3 %, (17) shows
that the complex permittivity for the single crystal
is known with 4 % relative precision.
The powder sample was put in an electrically open coaxial cell [19]. Its active capacitance was that of a cylindrical capacitor located at the extremity of the
coaxial line (see Fig. 4 of Ref. [19]). The capacitor is a
line 3 cm long with inner and outer conductor diame- ters respectively of 6.20 and 14.28 mm. For the whole structure, the characteristic impedance was equal
to 50 Q.
To make our measurements, we used successively :
* two impedance bridges up to 200 kHz;
* a resonant device commonly called resonator (see Fig. 4 of Ref. [19]) in the 0.1-300 MHz frequency
range;
* a standing wave ratio (S.W.R.) meter and reflec-
tometer devices for frequencies above 100 MHz.
The S.W.R. meter is a slotted coaxial transmission line
having a known characteristic impedance of 50 Q.
The measurement principle is as follows : the incident and reflected waves produce a stationary
interference pattern on the line which is called a
standing wave. We measure the S.W.R. (ratio between
the amplitudes of reflected and incident waves)
which gives dielectric information.
In our calculation, we have always taken into account the edge effects.
The relaxation of the cyanogroup has been observed down to 180 K, but due to the experimental frequency apparatus, the whole Cole-Cole plot has only been
obtained at temperatures higher than 200 K. We
have carried out the experiments only up to 400 K in order to avoid deformation of the cell. The complex
dielectric permittivity E*(w) has been measured at 25 temperatures and in table I we give the experimen-
tal results corrected for a single crystal only for nine
characteristic temperatures. We remark that 800 is
nearly constant and that its averaged value : Boo = 2.5 corresponds to a quite possible refractive index :
The 1.05 constant is an averaged value obtained
by Bottcher et al. ([10], page 180) on non-polar liquids
in order to take into account the atomic polarization.
Therefore we are sure that the observed relaxation domain was the only one.
Table I. - The experimental results of cyanoadamantane for nine characteristic temperatures.
518
5. Results. - 5.1 LOCAL ORDER. - The Kirk- wood-Frohlich theory for polar dielectric liquids
connects the molecular electrostatic parameters and the static dielectric constant ~s. One then uses [16-17]
the following relation :
N is the number of permanent dipoles contained in the
sample with volume V and p, is the dipole moment
for the isolated molecule in vapour phase. The dielec- tric static Kirkwood g factor :
takes only into account the short-range correlations between molecules. If locally the dipole moments are (anti) parallel, then g > 1 (g 1). If there are no
correlations or if the correlations arrange the perma- nent dipoles in a perpendicular way, then g = 1.
Fig. 5. - The correlation times versus 103/T (K). The two parallel lines correspond to the microscopic relaxation
time for correlated motions im according to equations (22)
and (23). The dashed and the dotted dashed lines correspond respectively to our present results (Eq. (24)) and to the N.M.R.
analysis [11] for the single molecular correlation time ’tC3.
Bordewijk [20] has shown that the relation of Kirkwood-Frohlich established only for liquids can
be generalized to solids. When the molecules (cha-
racterized by a scalar polarizability) are situated on
a cubic lattice, equation (19) is exact. The calculation of the Kirkwood correlation g factor has been per- formed by taking/Boo = 2.5, it, = 3.83 Debye and by assuming a constant density (1.13) equal to that of
the solid at room temperature because the experiments
were performed with a constant amount of material in the cell.
The experimental g Kirkwood factor is always quite a bit less than 1 (Fig. 5), and its extrapolated
value at the melting point (Tm = 458 K) is g = 0.55.
These small g values show that an anti-parallel
local order exists in all the plastic phase of cyano- adamantane.
5.2 DYNAMICAL RELAXATION. - The temperature variation of the « critical » frequency Fc follows an
Arrhenius law
The experimental Cole-Cole plots (Fig. 3) are always quasi-symmetrical (except below 220 K) and
inside the semi-circle corresponding to equation (1).
We have then used the Cole-Cole macroscopic des- cription (3) and we have calculated the corresponding
relative width (W(a) rr w(a)) for the distributions of relaxation times : table I.
At room temperature the dipolar librations (2.80)
are very small for a plastic crystal. The more the tem- perature is lowered, the more the cyano group is localized along the ( 001 > axes, the more the Frenkel model can a priori be applied and consequently the
more C(t ) can be described with a single relaxation
time TC3 (Eq. [15]). However, conversely one observes
a microscopic distribution function whose relative width increases with decreasing temperature (Table I).
Then one can say that the relative width w(a) (Table I)
describes qualitatively well the importance of the
correlations. Thus, as was easily foreseeable, we have pointed out the fact that in cyanoadamantane the
difference between single and correlated molecular motions increases with decreasing temperature.
We call im the correlation time corresponding to the maximum value of the microscopic distribution function h(In i). This microscopic correlation time which takes the correlations explicitly into account can be easily deduced from the « critical » frequency :
The single molecular correlation time ’tC3 can be deduced from equations (14) and (15) :
