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Chapter 3 The Dielectric Constant Detector
Chapter 3 The Dielectrib Constant Detector Theory
Under the influence of small fields, electrons movequite freely through conductors, whereas in insulators or dielectrics these fields displace the electrons only slightly from their equilibrium positions.
As an electric
field acting on a dielectric causes a separation of positive and negative charges, the field is said to polarize the
dielectric.
The polarization
can occur as a result of two effects: the induction effect and the orientation effect.
An electric field always induces dipoles in molecules
on which it is acting, whether or not they contain dipoles to begin with.
If
the dielectric does contain molecules that are permanent dipoles, the field tends to align these dipoles along its own direction.
As a result of the
induction or orientation it is found experimentally that when a dielectric is introduced between the plates of a capacitor the capacitance is increased by a factor E
,
called the dielectric constant.
Thus if Co is the
capacitance with a vacuum between its plates, the capacitance with a dielectric is C = ECO. can be defined;
In this way the dielectric constant of a substance
Due to the electro magnetic nature of light, it is also
a'ffected by the dielectric constant of the medium it passes through.
It
follows that the refractive index of a substance is a similar property to dielectric constant and in some circumstances is a direct function. of it. For example for non polar substances or mixtures of nonpolar substances the relationship between the dielectric constant€ and the refractive index of the substance or mixture, n, is given by
For semi polar substances or miytures or semi polar substances and non polar substances the above quation bas to be modif'nd to the following form
70
Liquid Chromatography Detectors
For polar substances or mixtures of polar substances and semi polar substances, however, the relationship breaks down and there is no simple function that describes refractive index in terms of dielectric constant. In general the more polar the substance the larger is its dielectric constant.
This is always true for substances having monofunctional groups
and generally true for substances having more than one functional group but there are exceptions.
For example, dioxane with two ether groups has a
fairly low dielectric constant although it is a very polar solvent. The low value for the dielectric constant results from the fact that the two dipoles are electrically in opposition and thus partially neutralize the effect of each others charge.
This effect is worth considering when choosing the
mobile phase for use with the dielectric constant detector. In chromatography the mobile phase is usually less polar than the solutes being eluted as they need to be retained on the column to effect a separation.
Thus the presence of a solute in the mobile phase will, in
general, change the dielectric constant of the mobile phase. If a device is situated at the end of the column that responds to changes in dielectric constant such a device can act as a chromatographic detector. In practice the sensory element usually takes the form of a cylindrical
or parallel plate condenser.
To maintain column efficiency the volume of
the condenser has to be very small and, as the sensitivity of the device is directly related to capacity of the condenser, the plates have to be very close together. The capacity (C) of a parallel plate condenser is given by
c = 0.0885 (N-1)AE d
where
E
is the dielectric constant
N is the total number of plates A
is the area of the plates in system in cm2
and d is the distance between the plates in cm The capacity of a cylindrical condenser is given by
Dielectric Constant Detectors
where 1 is the length of the cylinder in cm
r1 is the radius of the outer cylinder in cm r2 is the radius of the inner cylinder in cm. The impedance (i), of a condenser, which is in effect its resistance to an alternating electrical supply is given by i =
l/mfC
where f is the frequency of the applied AC potential. A simple circuit for use with a dielectric constant detector is shown in figure 1.
An AC potential resulting from the current passing through the
detector capacitor C develops a voltage across R1 which is rectified by the diode and the resulting DC potential across R2 is fed to an amplifier or
Figure 1 Simple Dielectric Constant Detector Circuit
Detector Cell C I
I
L
I I
1
1 recorder.
C
Diode
R
1
is solely a smoothing capacitor.
Recorder
The circuit merely illus-
trates the principal involved and is of little value in practice because it is not compensated for changes in the electrical supply and, furthermore,
71
12
Liquid Chromatography Detectors provides a standing current across R2 irrespective of the presence of a solute.
This standing current will give noise from fluctuation in supply
voltage or frequency even if backed off by a suitable DC potentiometric system. A more appropriate circuit to use is an AC bridge, the detector condenser being situated in one arm of the bridge; however the type of bridge that is appropriate depends on the design of the detector cell. If the capacity of the cell is reasonably large (100 pF or more) a Wein Bridge can be used, if small (1-10 pF) then it is more appropriate to use the Schering Bridge; both these bridge systems will be described but before this is done some discussion on the balancing of an AC bridge is appropriate.
No
capacitor is ideal insomuch that there is always some resistance component associated with it.
If the plates of the detector cell are not insulated
from the mobile phase and the mobile phase is conducting then the resistance component can obviously be very large. Now the voltage developed across the resistive component of the condenser is out of phase with the voltage developed across the capacity component.
It follows that to balance the
bridge the two components have to be balanced separately or no null balance point will be found.
It should also be noted that if the eluted solute
changes both the dielectric constant and the resistance of the mobile phase, as in the case of ionized solutes, then both the resistance and the capacity of the detecting cell will be changed and thus could provide a greater response than the effect of either alone.
Thus a dielectric constant
detector that responds to both dielectric constant and conductivity of the mobile phase would be very sensitive to ionic solutes and this could be achieved by using uninsulated plates in the detector capacitor. The theory of the combined effects of electrical conductivity and dielectric constant
on detector output has been discussed in detail by Haderka (1) and workers interested in this aspect of dielectric constant detection are recommended to read his original paper. A diagram of the Wein Bridge used for detectors having capacities of 100 pF or more is shown in figure 2 . ABEF is the bridqe with an AC potential applied across A and E. The out of balance signal is sensed across B and F by D which can be an AC amplifier and rectifier feeding a potentiometric recorder.
C and r represent the capacity and resistance of the detector
C0 is a standard reference capacitor or can be the capacity of the reference cell if one is employed; R is a fixed resistor and R and r are
cell.
0
variable resistances for obtaining balance.
Balancing is achieved by
Bridge Circuits
73
Figure 2 The Wein Bridge F
(Cell)
R
E
I
B
iterating adjustments of Ro and ro for zero output across FB. The conditions of balance are.
or
C cO
= - RO
R
14
Liquid Chromatography Detectors Any change in C or r due to the presence of solute in the detecting cell will result in an off balance signal across FB. For small capacity cells the Schering Bridge can be used which was originally designed for testing cables. A diagram of the Schering Bridge is
Figure 3 The Shering Bridge F
?
E
B
shown in figure 3 . The alternating supply is applied across AE and the out of balance signal taken across FB in a similar manner to the Wein Bridge, C and r represent the capacity and resistance of the detecting cell, R and Co are the reference resistance and capacitor and if a reference cell is employed Co can be the capacity of the reference cell. Ro and C' are a variable resistance and capacity respectively for obtaining balance.
Bridge Circuits
75
Balancing is achieved by the iterative adjustment of R
0
and C' and, when
balanced, any subsequent change in C or r resulting from solute in the detector cell will produce an off balance signal across FB.
The conditions
for balance are as follows
C' and 2 = R cO It should be emphasized that the resistance component of the cell across the detector capacity reduces the bridge sensitivity or makes the initial balancing procedure tedious.
To reduce this effect, the plates of the
detecting condenser are often well insulated from the mobile phase thus eliminating the resistive component of current. Another method of measuring changes in dielectric constant is to make the condenser containing the dielectric part of an oscillator circuit. For example, if the capacity is connected in parallel with an inductance and made the frequency source of an oscillator, the frequency will depend, among other things, on the capacity of the condenser.
If the output is hetero-
dyned, with the output of a stable reference oscillator and balanced, then the difference frequency resulting from a change in capacity due to the presence of a solute can be passed to a discriminator, rectified and the DC output fed to a recorder.
This alternative method of measuring changes in
dielectric constant can be extremely sensitive.
However, it is not the
electrical measuring system that determines the overall detector sensitivity, but the limitations inherent in bulk property detectors that have already been discussed. One of the early dielectric constant detectors to be described was that by Grant ( 2 ) , the cell consisted of a flattened glass bulb containing two thin platinum electrodes, 1 sq. cm in area and 4 mm apart.
The plates were
immersed in, and in contact with, the mobile phase and were fused to the wall of the bulb to prevent vibration giving rise to detector noise.
The
cell holder was made of 2 . 5 cm diameter brass tube and was connected to one plate of the condenser and to earth to provide electrical stability.
The
capacity measuring unit and detector cell derived its power from a stabilized power supply unit.
The volume of the cell, was fairly large (2-3 ml)
and this would obviously impair the resolution obtained from modern micro-
76
Liquid Chromatography Detectors particulate columns of high efficiency. Johansson and Karrman ( 3 ) described a dielectric constant system that used a different type of cell in which the plates were kept out of contact with the mobile phase.
As
well as improving the performance of the
measuring unit, the authors claimed that the isolation of the detector plates prevents the eluted solutes from being decomposed or adsorbed on exposed metal surfaces in the cell. The cell consisted of a straight glass tube that could be connected to the column by means of a ground glass spherical joint. The plates were semi-cylindrical in shape, 3 mm radius and 70 nun long.
To reduce wall effects the glass tube was chosen to have walls
as thin as possible (0.3 mm thick).
The glass tube and semi-cylindrical
plates were enclosed in a brass tube which was connected to one of the plates and earthed to improve stability.
Again, however, the cell volume
Figure 4 Schematic Section of Detector Cell
81
-7
1 = Detector body serving as earthed plate of the capacitor; 2 = core serving as second capacitor plate; 3 = Teflon sealing; 4 = washer; 5 , 6 = nuts; 7 = space for the dielectric; 8 = hole for tightening screw. All parts are made of brass. Eluate passage is marked with arrow.
Dielectric Constant Detectors was large,
-3.
microparticulate
77
160 ~1 and this could not be used with present day columns.
More
recently
Vespalec
and
Hina ( 4 , s )
described a detector suitable for detecting substances having no electrical conductivity and a diagram of their cell is shown in figure 4 .
The cell
consisted of two brass cylinders (between which the mobile phase passed) having radii of 9.85 and 10 nun respectively and were 4.96 mm long which gave a detector volume of about 12 p l . g/ml for acetone 4
be about 10
(E
The detector had a sensitivity of about
= 2 0 . 7 ) in hexane: the linear range was stated to
and so would be very suitable for preparative liquid chroma-
tography. Poppe and Kunysten (6) designed a dielectric constant detector which included a reference cell for temperature compensation. The cell consisted of two stainless steel plates 2 cm x 1 cm x 1 mm separated by a gasket
-
50
micron thick, the two cells, the reference cell and the detecting cell were identical and clamped back to back thus sharing a common electrode. The -6 g/ml for chloroform ( E = 4.81) in isoctane, the stated sensitivity was 10 cell system, however, was found to be very sensitive to pressure changes even when constant flow pumps were employed.
Fluctuations in the outlet
pressure of the column were thought to deform the plates and thus produce sporadic noise. Another detector described by Ooguri employed a capacitance cell, cylindrical in form with a central concentric electrode. The cell was used as the capacity of a tuned circuit that was heterodyned with 9 MHz oscillator, the difference frequency being rectified and fed to a suitable recorder.
The volume of the cell was stated to be 10 pl and 10 pg of
material was detectable. However, the sensitivity in terms of concentration was not given. Generally the same comments apply to dielectric constant detectors as to refractive index detectors.
They have relatively low sensitivity and are
best employed where chromatographic conditions are kept constant. They are not suitable for use with gradient elution, or where temperature programming or flow programming is used.
If carefully calibrated, they can be used for
quantitative analysis but they do not have a linear response over a significant concentration range. The main areas of application for dielectric constant detectors are the same as for refractive index detectors and if a suitable commercial dielectric content detector was available it could be used as an alternative to the refractive index detector.
At present, to
the best of the author's knowledge, there is no dielectric detector commercially available. The dielectric constant detector is one of the detectors
Liquid Chromatography Detectors
78
that could be designed to have a very small dead volume if, in the future, such a detector was required for use with microbore columns. REFERENCES Haderka, J. Chromatogr., 91 (1974) 167.
1.
S.
2.
R. A. Grant, J. Appl. Chem., 8 (1959) 136.
3.
G. Johansson and K. J. Karrman, Anal. Chem., 8 (1958) 1397. R. Vespalec and K. Ha’na, J. Chromatogr., 65 (1972) 53.
4. 5.
R. Vespalec, J. Chromatogr., 108 (1975) 243.
6.
M. Poppe and J. Kunysten, J. Chromatogr. Sci.,
7.
F. W. Karasek, Res./Develop.,
26 (1975) 34.
10 (1972) 16A.
Under the influence of small fields, electrons movequite freely through conductors, whereas in insulators or dielectrics these fields displace the electrons only slightly from their equilibrium positions.
As an electric
field acting on a dielectric causes a separation of positive and negative charges, the field is said to polarize the
dielectric.
The polarization
can occur as a result of two effects: the induction effect and the orientation effect.
An electric field always induces dipoles in molecules
on which it is acting, whether or not they contain dipoles to begin with.
If
the dielectric does contain molecules that are permanent dipoles, the field tends to align these dipoles along its own direction.
As a result of the
induction or orientation it is found experimentally that when a dielectric is introduced between the plates of a capacitor the capacitance is increased by a factor E
,
called the dielectric constant.
Thus if Co is the
capacitance with a vacuum between its plates, the capacitance with a dielectric is C = ECO. can be defined;
In this way the dielectric constant of a substance
Due to the electro magnetic nature of light, it is also
a'ffected by the dielectric constant of the medium it passes through.
It
follows that the refractive index of a substance is a similar property to dielectric constant and in some circumstances is a direct function. of it. For example for non polar substances or mixtures of nonpolar substances the relationship between the dielectric constant€ and the refractive index of the substance or mixture, n, is given by
For semi polar substances or miytures or semi polar substances and non polar substances the above quation bas to be modif'nd to the following form
70
Liquid Chromatography Detectors
For polar substances or mixtures of polar substances and semi polar substances, however, the relationship breaks down and there is no simple function that describes refractive index in terms of dielectric constant. In general the more polar the substance the larger is its dielectric constant.
This is always true for substances having monofunctional groups
and generally true for substances having more than one functional group but there are exceptions.
For example, dioxane with two ether groups has a
fairly low dielectric constant although it is a very polar solvent. The low value for the dielectric constant results from the fact that the two dipoles are electrically in opposition and thus partially neutralize the effect of each others charge.
This effect is worth considering when choosing the
mobile phase for use with the dielectric constant detector. In chromatography the mobile phase is usually less polar than the solutes being eluted as they need to be retained on the column to effect a separation.
Thus the presence of a solute in the mobile phase will, in
general, change the dielectric constant of the mobile phase. If a device is situated at the end of the column that responds to changes in dielectric constant such a device can act as a chromatographic detector. In practice the sensory element usually takes the form of a cylindrical
or parallel plate condenser.
To maintain column efficiency the volume of
the condenser has to be very small and, as the sensitivity of the device is directly related to capacity of the condenser, the plates have to be very close together. The capacity (C) of a parallel plate condenser is given by
c = 0.0885 (N-1)AE d
where
E
is the dielectric constant
N is the total number of plates A
is the area of the plates in system in cm2
and d is the distance between the plates in cm The capacity of a cylindrical condenser is given by
Dielectric Constant Detectors
where 1 is the length of the cylinder in cm
r1 is the radius of the outer cylinder in cm r2 is the radius of the inner cylinder in cm. The impedance (i), of a condenser, which is in effect its resistance to an alternating electrical supply is given by i =
l/mfC
where f is the frequency of the applied AC potential. A simple circuit for use with a dielectric constant detector is shown in figure 1.
An AC potential resulting from the current passing through the
detector capacitor C develops a voltage across R1 which is rectified by the diode and the resulting DC potential across R2 is fed to an amplifier or
Figure 1 Simple Dielectric Constant Detector Circuit
Detector Cell C I
I
L
I I
1
1 recorder.
C
Diode
R
1
is solely a smoothing capacitor.
Recorder
The circuit merely illus-
trates the principal involved and is of little value in practice because it is not compensated for changes in the electrical supply and, furthermore,
71
12
Liquid Chromatography Detectors provides a standing current across R2 irrespective of the presence of a solute.
This standing current will give noise from fluctuation in supply
voltage or frequency even if backed off by a suitable DC potentiometric system. A more appropriate circuit to use is an AC bridge, the detector condenser being situated in one arm of the bridge; however the type of bridge that is appropriate depends on the design of the detector cell. If the capacity of the cell is reasonably large (100 pF or more) a Wein Bridge can be used, if small (1-10 pF) then it is more appropriate to use the Schering Bridge; both these bridge systems will be described but before this is done some discussion on the balancing of an AC bridge is appropriate.
No
capacitor is ideal insomuch that there is always some resistance component associated with it.
If the plates of the detector cell are not insulated
from the mobile phase and the mobile phase is conducting then the resistance component can obviously be very large. Now the voltage developed across the resistive component of the condenser is out of phase with the voltage developed across the capacity component.
It follows that to balance the
bridge the two components have to be balanced separately or no null balance point will be found.
It should also be noted that if the eluted solute
changes both the dielectric constant and the resistance of the mobile phase, as in the case of ionized solutes, then both the resistance and the capacity of the detecting cell will be changed and thus could provide a greater response than the effect of either alone.
Thus a dielectric constant
detector that responds to both dielectric constant and conductivity of the mobile phase would be very sensitive to ionic solutes and this could be achieved by using uninsulated plates in the detector capacitor. The theory of the combined effects of electrical conductivity and dielectric constant
on detector output has been discussed in detail by Haderka (1) and workers interested in this aspect of dielectric constant detection are recommended to read his original paper. A diagram of the Wein Bridge used for detectors having capacities of 100 pF or more is shown in figure 2 . ABEF is the bridqe with an AC potential applied across A and E. The out of balance signal is sensed across B and F by D which can be an AC amplifier and rectifier feeding a potentiometric recorder.
C and r represent the capacity and resistance of the detector
C0 is a standard reference capacitor or can be the capacity of the reference cell if one is employed; R is a fixed resistor and R and r are
cell.
0
variable resistances for obtaining balance.
Balancing is achieved by
Bridge Circuits
73
Figure 2 The Wein Bridge F
(Cell)
R
E
I
B
iterating adjustments of Ro and ro for zero output across FB. The conditions of balance are.
or
C cO
= - RO
R
14
Liquid Chromatography Detectors Any change in C or r due to the presence of solute in the detecting cell will result in an off balance signal across FB. For small capacity cells the Schering Bridge can be used which was originally designed for testing cables. A diagram of the Schering Bridge is
Figure 3 The Shering Bridge F
?
E
B
shown in figure 3 . The alternating supply is applied across AE and the out of balance signal taken across FB in a similar manner to the Wein Bridge, C and r represent the capacity and resistance of the detecting cell, R and Co are the reference resistance and capacitor and if a reference cell is employed Co can be the capacity of the reference cell. Ro and C' are a variable resistance and capacity respectively for obtaining balance.
Bridge Circuits
75
Balancing is achieved by the iterative adjustment of R
0
and C' and, when
balanced, any subsequent change in C or r resulting from solute in the detector cell will produce an off balance signal across FB.
The conditions
for balance are as follows
C' and 2 = R cO It should be emphasized that the resistance component of the cell across the detector capacity reduces the bridge sensitivity or makes the initial balancing procedure tedious.
To reduce this effect, the plates of the
detecting condenser are often well insulated from the mobile phase thus eliminating the resistive component of current. Another method of measuring changes in dielectric constant is to make the condenser containing the dielectric part of an oscillator circuit. For example, if the capacity is connected in parallel with an inductance and made the frequency source of an oscillator, the frequency will depend, among other things, on the capacity of the condenser.
If the output is hetero-
dyned, with the output of a stable reference oscillator and balanced, then the difference frequency resulting from a change in capacity due to the presence of a solute can be passed to a discriminator, rectified and the DC output fed to a recorder.
This alternative method of measuring changes in
dielectric constant can be extremely sensitive.
However, it is not the
electrical measuring system that determines the overall detector sensitivity, but the limitations inherent in bulk property detectors that have already been discussed. One of the early dielectric constant detectors to be described was that by Grant ( 2 ) , the cell consisted of a flattened glass bulb containing two thin platinum electrodes, 1 sq. cm in area and 4 mm apart.
The plates were
immersed in, and in contact with, the mobile phase and were fused to the wall of the bulb to prevent vibration giving rise to detector noise.
The
cell holder was made of 2 . 5 cm diameter brass tube and was connected to one plate of the condenser and to earth to provide electrical stability.
The
capacity measuring unit and detector cell derived its power from a stabilized power supply unit.
The volume of the cell, was fairly large (2-3 ml)
and this would obviously impair the resolution obtained from modern micro-
76
Liquid Chromatography Detectors particulate columns of high efficiency. Johansson and Karrman ( 3 ) described a dielectric constant system that used a different type of cell in which the plates were kept out of contact with the mobile phase.
As
well as improving the performance of the
measuring unit, the authors claimed that the isolation of the detector plates prevents the eluted solutes from being decomposed or adsorbed on exposed metal surfaces in the cell. The cell consisted of a straight glass tube that could be connected to the column by means of a ground glass spherical joint. The plates were semi-cylindrical in shape, 3 mm radius and 70 nun long.
To reduce wall effects the glass tube was chosen to have walls
as thin as possible (0.3 mm thick).
The glass tube and semi-cylindrical
plates were enclosed in a brass tube which was connected to one of the plates and earthed to improve stability.
Again, however, the cell volume
Figure 4 Schematic Section of Detector Cell
81
-7
1 = Detector body serving as earthed plate of the capacitor; 2 = core serving as second capacitor plate; 3 = Teflon sealing; 4 = washer; 5 , 6 = nuts; 7 = space for the dielectric; 8 = hole for tightening screw. All parts are made of brass. Eluate passage is marked with arrow.
Dielectric Constant Detectors was large,
-3.
microparticulate
77
160 ~1 and this could not be used with present day columns.
More
recently
Vespalec
and
Hina ( 4 , s )
described a detector suitable for detecting substances having no electrical conductivity and a diagram of their cell is shown in figure 4 .
The cell
consisted of two brass cylinders (between which the mobile phase passed) having radii of 9.85 and 10 nun respectively and were 4.96 mm long which gave a detector volume of about 12 p l . g/ml for acetone 4
be about 10
(E
The detector had a sensitivity of about
= 2 0 . 7 ) in hexane: the linear range was stated to
and so would be very suitable for preparative liquid chroma-
tography. Poppe and Kunysten (6) designed a dielectric constant detector which included a reference cell for temperature compensation. The cell consisted of two stainless steel plates 2 cm x 1 cm x 1 mm separated by a gasket
-
50
micron thick, the two cells, the reference cell and the detecting cell were identical and clamped back to back thus sharing a common electrode. The -6 g/ml for chloroform ( E = 4.81) in isoctane, the stated sensitivity was 10 cell system, however, was found to be very sensitive to pressure changes even when constant flow pumps were employed.
Fluctuations in the outlet
pressure of the column were thought to deform the plates and thus produce sporadic noise. Another detector described by Ooguri employed a capacitance cell, cylindrical in form with a central concentric electrode. The cell was used as the capacity of a tuned circuit that was heterodyned with 9 MHz oscillator, the difference frequency being rectified and fed to a suitable recorder.
The volume of the cell was stated to be 10 pl and 10 pg of
material was detectable. However, the sensitivity in terms of concentration was not given. Generally the same comments apply to dielectric constant detectors as to refractive index detectors.
They have relatively low sensitivity and are
best employed where chromatographic conditions are kept constant. They are not suitable for use with gradient elution, or where temperature programming or flow programming is used.
If carefully calibrated, they can be used for
quantitative analysis but they do not have a linear response over a significant concentration range. The main areas of application for dielectric constant detectors are the same as for refractive index detectors and if a suitable commercial dielectric content detector was available it could be used as an alternative to the refractive index detector.
At present, to
the best of the author's knowledge, there is no dielectric detector commercially available. The dielectric constant detector is one of the detectors
Liquid Chromatography Detectors
78
that could be designed to have a very small dead volume if, in the future, such a detector was required for use with microbore columns. REFERENCES Haderka, J. Chromatogr., 91 (1974) 167.
1.
S.
2.
R. A. Grant, J. Appl. Chem., 8 (1959) 136.
3.
G. Johansson and K. J. Karrman, Anal. Chem., 8 (1958) 1397. R. Vespalec and K. Ha’na, J. Chromatogr., 65 (1972) 53.
4. 5.
R. Vespalec, J. Chromatogr., 108 (1975) 243.
6.
M. Poppe and J. Kunysten, J. Chromatogr. Sci.,
7.
F. W. Karasek, Res./Develop.,
26 (1975) 34.
10 (1972) 16A.