Electric properties of material I.
Association
Electric dipole moment of a molecule is a measure of the charge asymmetry. Vibrating chemical bonds may produce dipole moment change which effect can be observed in a photometer as a peak in IR spectrum.
Determination of dipole moment, polarization, polarizability from capacitance measurements
A capacitor is applicable for determination capacitances e.g. of different non-ionic liquids. From capacitance data using Debye equation dipole moment and polarizability values can be calculated.
Parallel plate capacitor
Consider two metallic plates of equal area A separated by a distance d. The top plate carries a charge +q while the bottom plate carries a charge –q. The magnitude of charges +q and –q are the same (electroneutrality).
The charging of the plates can be accomplished by means of a battery which produces a potential difference.
Fig.1 Parallel plate capacitor
A dc voltage is switched on plates located parallel, as you can see in Fig. 1, a homogeneous field is generated. The electrostatic field can be described in terms of electric field strength.
Electric field strength, E
a vector quantity, is directly proportional to the potential difference, applied between points in the space at a distance d.
unit: Vm-1 1.
The magnitude and direction of E is visualized by drawing force field lines.
The density of lines is proportional to the magnitude of E. If the lines run parallel the field is uniform. Uniform field frequently forms in the inside of a capacitor having parallel metal plates (see Figure 2).
Fig. 2.The force field lines in a capacitor (homogeneous field)
Fig. 3. Parallel plate capacitor showing force field lines with material inside.
Vector E points toward the negative pole in the figure. At the edges of capacitor lines are bent (see Fig. 4.). A tangent fit to a particular point of a force field line shows the direction of the field at that point.
Fig.4. A capacitor showing force field lines bent at the edges of the plates. (inhomogeneous field)
Electric field can also be given by charge density σ = q/A, as
2.
where ε0 is the dielectric permittivity.
Capacitance, C
Experiments show that the amount of charge q stored in a capacitor is linearly proportional to the electric potential difference, Δφ between the plates. Thus, we may write
3.
where C is a positive proportionality constant called capacitance. Physically, capacitance of a device is a measure of how much charge the device can store per a 1 voltage potential difference, Δφ. The SI unit of capacitance is the farad (F).
A typical capacitance is in the picofarad to millifarad range, 10-12F = 1 pF, 10-9 F = 1nF, 10-6 F = 1µF, 10-3F = 1 mF.
From Equations 1, 2, 3 a formula is given containing geometric parameters of capacitor
4.
where ε0 = 8,85419 10-12 F/m is the permittivity of space in vacuum. The relative permittivity, k = ε/ε0 is the ratio of filled and emty capacitance of capacitor. The greater the area of plate (A) and smaller the separation of plates (d) the greater the capacitance of capacitor. The capacitor can be loaded with material of low electric conductivity. So, there is no electric current flowing between the plates.
A more polar material will store more charge, and thus has a higher capacitance than a less polar one . Thus easily polarized materials have a high permittivity .
Dipole moment, permanent dipole moment
A molecule has permanent electric dipole moment if possess a charge separation without the influence of an outer electric field. This property originates its molecular structure (CO2 ↔ H2O)
Fig. 5. The direction of dipole moment.
Permanent dipole moment stems from the partial charges on the atoms. Partial charges arise from differences in electronegativities of atoms in a molecule.
Molecules having no permanent dipole moment may have, through interaction with the field, an induced electric dipole moment that exists only when the molecule is in electrostatic or electromagnetic field. In other words:
molecules without charge separation are placed in external field going to acquire induced charges and induced dipole moment.
To obtain their geometry, permanent dipoles are generally fixed relative to molecular axes. An electric dipole is simply modeled as a two charge object, -q and +q, of equal magnitude and opposite sign, separated by distance r.
5.
When more than two charges belong to an object (molecule) the resultant is a vector quantity. The vector r points from the negative to the positive charge (on the contrary to electric field), and the dipole moment is given,
5.a
Note: the magnitude of q is always smaller than unit charge, the electron charge. The units are usually given in Debye (1 D= 3.336 x 10-30 C m).
The total dipole moment is the sum of permanent and induced moments
μtotal = μp + μi 6.
Example
Dipole moment of 3 charges.
A 2 nC (nano Coulomb) charge is at the origin of coordinate system (0,0,0). Two -1nC are at (1cm,0,0) and at(1cm,1cm,0).
Calculate the dipole moment vector.
By definition the dipole moment vector is:
The vector starts from origin and ends in point 0,
Polarization
A set of N molecule having permanent dipole moment exposed to electric field, tends to orient along the field.
The quantitative measure of the extent of dipole moment is called electric polarization, P.
SI unit P: Cm-2 7.
where is the sum of dipole moment vectors which is divided by the volume, V of the system. The same result we get when the average dipole moment, is multiplied by the number density (N) of system.
Fig.6. The aligning effect of switching on a potential difference.
At E=0 polar molecules orient randomly, at E≠0 the molecules tend to align parallel to the force field lines. In liquid phase thermal agitation (kT) counteracts the aligning effect of the field. With no field present in a liquid is zero, the most probable state for the system.
Fig.7. Polarization of neutral molecule
The position of positive centre of a molecule exposed to external electric field is hardly shifted referred to the electron distribution that moves lightly toward the more positive domain of the space. (Atomic framework)
Polarizability
At low field strength is linearly dependent on E,
unit α: C2m2J-1 7.
with a proportionality coefficient, α the polarizability characteristic to the molecule, referred as the deformability of electron cloud. Polarizability change with frequency of electromagnetic radiation is used in Raman spectroscopy.
Otherwise polarizability is a measure of the degree to which the electrons in the molecule can be displaced relative to the nuclei.
Bond moments, net moment
The identical chemical bond in different molecules (e.g. C=O bond in ketones or carboxylic acids) has almost the same moment (bond moment). This fact is used in the assignment of a spectral band in the IR and Raman spectroscopy (group vibrations).
Net dipole moment calculations by using simple geometry in Chlorobenzene derivatives.
Fig8. The dipole moment of Chlorobenzene and 1,4-dichlorobenzene.
Fig.9. The dipole moment of 1,2- and 1,3- dichlorobenzene.
Figures 8. and 9. show the component and resultant vectors of C-Cl bonds in the benzene ring underlying the effect of substitution. The application of parallelogram method for calculating dipole moments from this simple geometry proved to be good. The calculated results are very similar to that of experimentally observed.
Fig. 10. µ1 and µ2 are the components of resultant µ.
For two component moments (μ1, μ2) that make an angle θ the magnitude of net moment is given by,
8.
Charge and distance dependence of moments:
Fig.11. A: The reference dipole, B: more charges added, C: distance among charges are decreased.
Determination of relative permittivity, εr of materials in a capacitor
Dielectrics are insulators, containing no mobile, charged particle, e.g. alcohols, ethers, halogenated hydrocarbons and so on.
For a given configuration of electrodes, i.e. area and distance of metal plates, the capacitance depends only on the permittivity of the material between the plates.
Let C0 and C are the measured capacitances in the empty (vacuum) and filled capacitor respectively the relative permittivity, εr can easily be determined,
9.
therefore relative permittivity of a dielectric is measured in a capacitor. From relative permittivity data dipole moment and polarizability can be calculated.
Table Dielectric Constants of Some Pure Organic Liquids at 20C
Substance / εr / Substance / εrCCl4 / 2.238 / CHCl3 / 4.806
C6H14 / 1.890 / C6H12 (Cyclohexane) / 2.023
C4H10O (Diethyleteher) / 4.335 / C6H7N / 6.89
Source: R. C. Weast and M. J. Astle (eds.), CRC Handbook of Chemistry and Physics, 63rd Edition, CRC Press, Inc., Boca Raton, FL, 1982.
Calculation of polarizability and dipole moment
From εr measurements (see Eq. 9.) molar polarization, Pm, a permanent dipole moment and polarizability dependent quantity can be calculated. Pm is determined from measurable parameters
10.
where M/ρ is the molar volume, Vm and NA is the Avogadro number. Eq 10. is valid for cases of molecules without permanent dipole moment. The α and µ parameters for molecules with permanent dipole moment can be calculated from Debye equation
11.
where k is the Boltzmann constant and T is the temperature in Kelvins. Molar volume is temperature dependent. Data εr are determined from measured capacitances at different temperatures.
At higher temperatures the net permanent dipole moment component becomes zero, owing to the thermal agitation and purely α can be determined from Eq. 10. The induced moment remains the same in the temperature interval of measurement.
In smaller temperature ranges
Eq. 11. can be given in a linearized form. Identify variables and constants by using the general form of linear equations
(dependent variable)
(slope)
(independent variable)
(intercept at 1/T = 0 )
ε and Vm are coming from measurement at different temperatures.
Plot the data of Pm vs. 1/T function and fit a straight line.
Fig. 10. molar polarizability vs. T-1 function for camphor
Determination of α and μ for camphor. From fitting parameters slope and intercept can be determined.
10
El.prop.01.