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Magnetic susceptibilities and the order parameters of some 4,4’ -disubstituted biphenyl cyclohexanes
H.J. Müller, W. Haase
To cite this version:
H.J. Müller, W. Haase. Magnetic susceptibilities and the order parameters of some 4,4’
-disubstituted biphenyl cyclohexanes. Journal de Physique, 1983, 44 (10), pp.1209-1213.
�10.1051/jphys:0198300440100120900�. �jpa-00209705�
Magnetic susceptibilities and the order parameters of some 4,4’ -disubstituted biphenyl cyclohexanes
H. J. Müller and W. Haase
Institut für Physikalische Chemie, Technische Hochschule Darmstadt, Petersenstra03B2e 20, D-6100 Darmstadt, F.R.G.
(Reçu le 18 avril 1983, revise le 27 juin, accepté le 27 juin 1983)
Resume. 2014 Les susceptibilités diamagnétiques de quelques biphenyl cyclohexanes substitués 4,4’ sont données
en fonction de la température. Les paramètres d’ordre des phases uniaxial nématique, smectique A et smectique B
sont calculés. Les influences des substituants terminaux et des groupements centraux sur l’anisotropie magnétique
et sur le paramètre d’ordre sont discutées.
Abstract. 2014 The diamagnetic susceptibilities of some 4,4’-disubstituted biphenyl cyclohexanes are reported as a
function of temperature. The order parameters of the uniaxial nematic, smectic A and smectic B phases are cal-
culated. The effect of the terminal substituents and the central groups on the magnetic anisotropy and the order parameter is discussed.
Classification
Physics Abstracts
61. 30G
1. Introduction..
The synthesis and the transition temperatures of some of the biphenyl-cyclohexanes have been reported [l, 2].
The transition enthalpies have been measured [3-6].
The characterization of the phases by optical micros-
copy [3-6] and X-ray investigation [3-5, 7] showed
that some of these compounds have smectic B and smectic A phases. The refractive indices and densities of the same compounds were reported elsewhere [3-5, 8]. In this work we report measurements on the
diamagnetic susceptibility of eight compounds of 4,4’-disubstituted biphenyl cyclohexanes
The liquid crystalline phases are characterized by long-range orientational ordering, which is defined as
where 0 is the angle between the long molecular axis and the optical axis (director). They have macroscopic anisotropies in magnetic or in electric fields. Therefore,
information about the degree of orientational order
can be obtained from diamagnetic susceptibility,
electric permittivity and refractive index measure- ments. The various methods which can be used to determine the degree of orientational order (order parameter S) have been described [9].
It can be shown that [9]
where X’ and xt are the molar susceptibilities parallel
and perpendicular to the director, and xM and xt
are the longitudinal and transverse molar suscepti-
bilities.
In general (2) is applied for the uniaxial nematic
phase. We will apply this equation also for the uniaxial smectic phases, in our case the smectic B (SB) and
the smectic A (S,,) phases.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198300440100120900
1210
2. ExperimentaL
The diamagnetic susceptibility was measured by the Faraday-Curie method. The sample was put in a cylindrical quartz container (- 0.1 cm’ volume)
and suspended by a quartz fibre between the poles of
an electromagnet (Bruker B-E 20 va) with a magnetic
field of about 10 kOe. The force and the mass were
measured with an electrobalance (Cahn RG-2000).
This balance has an accuracy of 2 J.lg. The cali- bration of H F was carried out by a measurement on
z
HgCo(SCN)4, which has a mass susceptibility of
16.44 x 10 - 6 cm’/g at 20°C [10]. The sample con-
tainer was held in a double cylinder of glass in which temperatures were attained with a thermostated liquid.
The temperature of the sample was determined with
a chromel-alumel thermocouple, put near the sample,
and maintained at ± 0.2 OC. To avoid any parama-
gnetic impurities in the sample (dissolved oxygen),
the measurements were carried out in vacuum. The
mass susceptibilities, xg, either Xg in an isotropic phase or Xf, in an oriented uniaxial phase are measured
as a function of temperature.
At the beginning we measured the temperature dependence of the mass susceptibility of PAA as a
test of our experimental arrangement. The results were
in good agreement with the literature data [I I].
3. Results.
The diamagnetic mass susceptibility (xg) of the com- pounds studied are reported in table I as functions of temperature. Figure 1 shows some examples for the
molar susceptibility XM and the diamagnetic suscep-
tibility anisotropy (AX’ = X’ - X’ = 2-(X’ - 7m)), in
the smectic, nematic and isotropic phases, as functions
of a reduced temperature (t = TI TN I; T is in K). The
values of Xm and AXm in the smectic phases (Fig. 1)
were determined by cooling the samples.
Table I. - Mass susceptibilities [10-’ cm3 g-l] as a function of temperature.
+ Measured-by cooling.
Table I (continued.
By heating the crystalline phase, the alignment was
less perfect in the smectic phase. Only at the smectic- nematic phase transition did it improve due to the
effect of the magnetic field.
However, by cooling the isotropic phase in the magnetic field, we obtained a perfectly aligned and transparent smectic phase which was strongly super- cooled. The increase of OxM at the nematic-smectic B
phase transition indicates a good orienta.tiIDLQf- the
smectic B phase, in contrast to the difficulty in align-
ment with heating.
Comparison of the diamagnetic anisotropy AXm
for BCH52 with that for BCH54, and for BCH5CN with that for BCH7CN shows that AXM in the same homologous series decreases with increasing the
chain length. AXm increases discontinously at the
nematic-smectic B transition (N-SB). On the other hand OxM increases continously at the nematic-smectic A transition (N-S,,).
> Comparison of the molar susceptibility anisotropies
of BCH7CN, 4-n-heptyl-4’-cyanobiphenyl (CB-7),
trans - 4 - n - heptyl - (4’ - cyanophenyl) - cyclohexane (PCH-7) and trans, trans-4-n-heptyl-4’-cyanobicyclo-
hexane (CCH-7) (see Fig. 2) shows that a replacement of a phenyl group decreases åXM markedly. For CB-7,
PCH-7 and CCH-7 we used the volume susceptibility
data of Schad et al. [12] and the density data of Ibrahim
et ale [13].
Fig. 1. - Molar susceptibilities xM, scale on left, (·) and dxM, scale on right, (0) vs. a reduced temperature; upper part : BCH7CN, lower part : BCH52.
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Fig. 2. - Molar susceptibility anisotropies vs. a reduced temperature.
Assuming that the contributions of the cyclohexyl
and alkyl groups to the molar susceptibility anisotropy
are negligible, the contribution of the phenyl group
(17.7 ± 0.5 x 10 - 6 cm3/mol) is deduced by comparing xM of CB-7, PCH-7 and CCH-7 in the nematic phase
at r = 0.976 0. Also we can conclude that
where M is the molecular weight
4. Determination of the molecular diamagnetic sus- ceptibility anisotropy.
The diamagnetic susceptibility anisotropy (xl’ - xt)
of a perfectly ordered uniaxial liquid crystalline phase
must be known to determine the order parameter.
Because there is no single crystal magnetic data
for the studied compounds, we shall discuss in the
following some possibilities to determine xt- xt : a) The diamagnetic susceptibility anisotropy can
be calculated by an additive scheme as the sum of the anisotropy contributions of the different atoms or
groups with known molecular geometry.
The configuration of the molecule is shown in figure 3. The long molecular axis is considered to be
along the line joining the outer paracarbon atoms
of the benzene-benzene rings. This model is based on
the single crystal X-ray data [7]. The crystal structures
show torsion angles of 20 and 240 between the phenyl
groups of BCH5CN and BCH30, respectively. The
torsion angles between the neighbouring phenyl- cyclohexyl groups of BCH5CN and BCH30 are 820 and 760, respectively. By applying the additive scheme,
these torsion angles have no influence on the deter-
mination of xr - Xt.
In our calculations, the contributions of the different groups of atoms or bonds are obtained from the literature data [14-16]. The accuracy of the xt - xt
values calculated from the additive scheme was
estimated to be about 5 % [17].
Fig. 3. - Molecular model for the compounds studied.
b) The plot of log (S(Xr - Xm)) vs. log (T - T)
shows a linear relation in the nematic phase. But
there is a deviation from linearity near the clearing point. Therefore the extrapolation method was pro-
posed for the determination of Xm - Xm [18]. The
estimated uncertainty in xt - xt values calculated
by using the extrapolation method is of the order of
,20 % [17].
The Xr - Xm values, calculated by using a) and b) methods, are reported in table II. Comparison of
these values shows a discrepancy up to - 12 %.
Table II. - Molecular susceptibility anisotropies
x M - I Vtm [10-’ cm’ mol-’].
5. Order parameters.
According to equation 2, the order parameters are calculated using the additive scheme values for the molecular susceptibility anisotropies (Table II). These
values for S, in the nematic and smectic phases, are
shown in figure 4 as a function of a reduced tempera-
ture (i = TITNI). The broken lines in figure 4 are the theoretical order parameters obtained from Maier-
Saupe (MS) theory [19]. The differences between order parameters of the compounds studied which have
the same chemical framework are attributed to the influence of the terminal substituents.
The order parameter increases discontinuously
at the N-SB phase transition for the compounds BCH50, BCH52 and BCH54 which have small per- manent dipole moments (see Fig. 4). This indicates a
first order phase transition.
Figure 4 shows that the order parameter increases continuously at the N-SA phase transition. This is in agreement with the McMillan [20] prediction that
the N-SA transition is a second order phase transition
for TSAN/TNI 0.88 ; T SAN/TNI = 0.61 for BCH7CN.
Fig. 4. - Order parameter vs. reduced temperature for the compounds studied. The broken line is from the MS theory.
Comparison of the S-curves in the nematic phase
for compounds RCH52 and BCH54 and compounds
BCH5CN and BCH7CN, respectively, shows that the order parameter in the same homologous series
decreases with increasing the chain length. These
curves show also that the temperature dependence
of the order parameter, in the same homologous series,
becomes greater with increasing the chain length.
This confirms the results of Ibrahim [17]. The order parameters of the smectic phases show smaller tem- perature dependence than those of the nematic phases.
By comparing the order parameters of BCH5CN, BCH7CN, CB-5 [21] and CB-7 [21] we conclude that the adding of cyclohexyl group decreases the order parameter. On the other hand, the adding of a phenyl
group increases the order parameter. This is concluded from comparing the order parameters of BCH7CN and PCH-7 [13]. It was mentioned that a replacement
of a phenyl group by a cyclohexyl group decreases the order parameter markedly [13]. For the halogen compounds, the order parameter increases in the sequence F, Cl, Br as the packing density increases
in the same sequence [3-5, 8].
Acknowledgments.
We are grateful to the Deutsche Forschungsgemein-
schaft (DFG) for financial support and to E. Merck, Darmstadt, for supplying the samples. One of us (H.J.M.) thanks the Brasilian government (CAPES)
for scholarship. We thank Dr. I. H. Ibrahim for useful discussions.
References
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