J . S o p o u š e k ú l o h a
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2.a-b
2. Optical and electrical properties of molecules
2.b. Permittivity measurement of liquid substances
Permittivity as well as refractive index are important macroscopic constants
that characterize the properties of the investigated substances in terms of their
behaviour in the external electric field.
Experimentally, we usually measure relative permittivity.
ε𝑟𝑟 =
ε
ε0
(2.1.)
where εo is permittivity of the vacuum 8,854.10-12
C.m
-1
V
-1
. ε is absolute permittivity
(formerly dielectric constant), which is a measure of substance polarity.
The relative permittivity can also be determined as the ratio of the capacitance C of
the capacitor whose dielectric is the substance under investigation and the
capacitance of the same capacitor Co
whose dielectric is the vacuum:
ε𝑟𝑟 =
𝐶𝐶
𝐶𝐶0
≅
𝐶𝐶
𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎
(2.2.)
Here the capacity Co
can be replaced by the air capacity 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎, because relative
permittivity of dry air is approximately equal to one (exactly 1,000536 at 25°C and
101,33 kPa).
The capacity measurement, which is realized by a two-shell capacitance vessel, is
used for the determination of the relative permittivity. The capacitance plates are two
concentric cylinders from non-corrosive metal, which are insulated with a quartz or
teflon ring. The measured liquid is poured into the space between the two cylinders.
The capacitance vessel is connected to the dielectric resonance circuit of the
dielectrometer, which works on the electro-compensation principle. Without
connecting the capacitance vessel to device, the resonant circuit can be tuned to the
auxiliary capacitance so that the external capacity is "zero". When the capacitance
vessel is connected to device, the resonance is broken and the deflection appears on
the device indicator. We repeat the compensation of the circuit and measure the
external capacity Cm
.
The external capacitance is composed of the container's own capacity, which is
equal to εrel
.Co
and of the capacity of the connectors Cp
:
C C Cm rel p= +e 0 (2.3.)
To determine the relative permittivity of the liquid εrel
, it is therefore necessary to
know the parameters Co
and Cp
from the measurement of at least two liquids with
known εrel
values.
An increase in the capacity of the capacitor by inserting a measured dielectric
between its plates is due to the polarization of this dielectric. Polarization also occurs
in nonpolar molecules. We therefore recognize induced polarization for nonpolar
molecules and orientation polarization for polar molecules. In the electric field 𝐸𝐸�⃗, both
types of molecules are oriented in the opposite direction to the electric line forces and
weaken the intensity of the electric field by theirs own polarization effect 𝑃𝑃⃖�:
𝑃𝑃⃖� = (ε𝑟𝑟 − 1)ε0 𝐸𝐸�⃗ (2.4.)
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2.a-b
By multiplying the polarization P by the molar mass M of the monitored substance we
obtain the value of the molar polarization PM. Each polar molecule contributes to the
total molar polarization with its molar induced polarization Pin and with the molar
orientation polarization of Por . The relationship between relative permittivity rele and
PM polarization is given by Debye's equation:
P P P
M
M in or
rel
rel
= + =
−
+
e
e r
1
2
. (2.5.)
where r is specific mass of the substance under view.
The eqn (2.5.) was derived assuming the molecules of the polar substance are
sufficiently distant from each other, so they do not interact with each other. However,
this assumption is not fully met when polar substances are measured in the
condensed state. Therefore, the molar polarization value of the polar liquids is
obtained from the experimental data of their solutions in nonpolar solvents depending
on the concentration. The subsequent extrapolation to infinite dilution is used for an
obtaining of the molar polarization.
In the case of a non-polar substance (Por
= 0), the molar induced polarization Pin
consist of electron polarization Pe
and atomic polarization Pa
. At the same time, the
atomic molar polarization Pa
is equal to the difference between the molar polarization
PM and the molar refraction MR (also called optical polarization):
P P P P Ra in e M M= − = − (2.6.)
Refraction of RM
is obtained by measuring refractive index n using refractometer (see
relationship
∑ ⋅=
+
−
= i
AiM R
M
n
n
R n
ρ
.
2
1
2
2
(2.7.)
Molar polarization of PM is obtained by measuring relative permittivity (see relation
(2.5.)).
TASK: Measure relative permittivity of homological series of aliphatic alcohols.
Measure the relative permittivity and refractive index of two non-polar liquids
and calculate the difference between molar refraction and molecular polarization
values. Estimate the ratio of the molar atom polarization to the molar polarization.
LABORATORY AIDS AND CHEMICALS: Dielectrometer equipped by capacity vessel,
refractometer, pycnometer, automatic pipette, syringes; benzene, cyclohexane,
trichloromethane, carbon tetrachloride, methanol, ethanol, propanol, butanol,
pentanol, hexanol.
Certain substances used in this task are harmful to health. Therefore, we work
in the fume hood and use the automatic pipettes or syringes.
Instructions:
1. Calibration of the capacitance vessel. At laboratory temperature, we measure
the capacity Cm of the three selected dielectrics with a known εrel value (see TABLE
I). When selecting air as a dielectric, it is sufficient to measure the capacity of an
empty dry capacitance vessel. Then, continue with benzene and trichloromethane
for example.
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2.a-b
2. Measurement of relative permittivity. First, measure a homological series of
aliphatic alcohols. Begin with the lowest homologue and move towards higher
homologues. Do not wash the capacitance vessel, but let it dry out. Continue by
measuring capacity Cm for non-polar substances (carbon tetrachloride and
cyclohexane).
3. Measurement of refractive index and density for non-polar substances.
Measure the refractive index nD
of tetrachloromethane and cyclohexane using
refractometer with sodium lamp. The values should not differ noticeably from the
nD
values given in TABLE I. Subsequently, measure the density of the substances.
Use the glass pycnometer for example. Return the content of the pycnometer back
to the original bottle with the liquid being examined only if you are sure about the
substance.
DATA ANALYSIS: To calculate the relative permittivity of the examined alcohols
from experimental Cm
according to eqn (2.3.), the parameters Co and Cp must
be known. We evaluate the parameters from calibration of the capacitance vessel.
Plot linear function Cm
vs. rele (2.3.) and find the slope (i.e. Co) and intercept (i. e.
Cp). The calibration has to be repeated if the coefficient of determination 𝑅𝑅2
>
0.95.
REPORT: Table 1: the measured calibration values of the capacity Cm
and their
tabulated relative permittivity rele .(TABLE I). Graph 1: calibration plot Cm
vs. rele
. Parameters Co and Cp . Table 2: for homological series of aliphatic alcohols:
experimental capacity Cm, and relative permittivity εrεl , tabulated permittivity from
TABLE II. Graph 2: experimental dependence of relative permittivity on the number of
carbons in the alcohol molecule. Table 3: the table according to the task for density
determination using pycnometer. Tabule 4: for tetrachloromethane and cyclohexane:
experimental and tabulated refractive index n and specific mass r, experimental
values Cm and εrel , molar mass Mr, calculated value of molar polarization Pm using
eqn (2.5.), molar refraction Rm ((2.7.), atomic polarization Pa and ratio Pa /Pm (in %).


TABLE I: Specific mass, relative permittivity and refraction index of some liquids. The
refractive index is valid for 20°C and a wavelength of 589.3 nm (yellow sodium doublet).
substance 20ρ / kg m-3
εrεl
20 20
Dn
water 998.2 80.360 1.3330
trichloromethane 1498.5 4.810 1.4467
benzene 879.0 2.282 1.5015
tetrachloromethane 1595.0 2.236 1.4607
cyclohexane 779.0 2.020 1.4266
TABLE II: Hodnoty relativních permitivit vybraných alkoholů.
látka methanol ethanol n-propanol n-butanol n-pentanol n-hexanol
εrεl
20 33,5 25,1 21,0 17,9 15,0 13,1