Electricity: measuring and testing – Impedance – admittance or other quantities representative of... – Lumped type parameters
Reexamination Certificate
1997-03-01
2001-07-24
Metjahic, Safet (Department: 2858)
Electricity: measuring and testing
Impedance, admittance or other quantities representative of...
Lumped type parameters
Reexamination Certificate
active
06265883
ABSTRACT:
BACKGROUND—FIELD OF INVENTION
This invention relates to the measurement of physical and electronic properties, particularly to the measurement of electrical conductivity, dielectric constant, and depth of substances, namely fluids, fluid mixtures containing solid particles, and solids.
BACKGROUND—PRIOR-ART—FIGS.
1
TO
8
—MEASUREMENT OF ELECTRICAL
CONDUCTIVITY AND DIELECTRIC CONSTANT OF FLUIDS
Measurement of the electrical properties of fluids is frequently required in order to predict their performance in various situations. For example, the electrical conductivity of liquid toner is one of the determining factors of print quality in electrostatic printers. If the conductivity of the toner is higher or lower than an optimum value, the resultant optical density of prints will be low. In another example, the dielectric constant (permittivity or ability to concentrate flux in response to an applied electric field) of certain insulating oils determines their value as self-healing insulators in electrical transformers and capacitors.
Prior-art electrical conductivity and dielectric constant measurement methods and apparatus generally involve the use of “probes,” such as that shown in
FIG. 1. A
typical probe is manufactured and sold by Scientifica, 340 Wall Street, Princeton, N.J. U.S.A. Such a probe comprises first and second electrodes: two tubes or cylinders. The length and outer diameter of outer tube
100
are typically 65 mm and 19 mm, respectively. The length and outer diameter of inner tube
110
are typically 45 mm and 15 mm, respectively. The wall thickness of the tubes is typically 1 mm. This leaves a gap between tubes of 1.0 mm. The tubes are held in place with respect to each another by insulating screws
120
, typically made of a plastic material. Tubes
100
and
110
are connected to an external measuring apparatus (not shown) by wires
130
and
140
, respectively.
Measurement of the conductivity and dielectric constant of a liquid toner solution will be used as an example to describe the use of this prior-art probe. Liquid toner is used to develop latent (non-visible) electrostatic images in electrostatic printers and copiers in well-known fashion. Liquid toner generally comprises a colloidal suspension of charged particles in a buffered solvent liquid. The charged particles are typically smaller than one micron in diameter. A net charge is imparted to each of the particles at the time of their manufacture. This process is well known to those skilled in the art of manufacture of liquid toners and will not be discussed further here.
The conductivity of the liquid toner solution depends upon at least two components: the ionic contribution due to the mobile particles, and the bulk, electronic conductivity of the solvent. The total conductivity is expressed as &sgr;
T
=&sgr;
i
+&sgr;
e
, where &sgr;
i
is the ionic contribution and &sgr;
e
is the electronic contribution. The mobile toner particles are also called the mobile ionic species to physically distinguish them from the electrons, or electronic species, which also conduct charge through the solution.
FIGS. 2 and 3
are simplified diagrams showing a planar adaptation of the prior-art conductivity probe of FIG.
1
. The planar version of
FIGS. 2 and 3
is used to more clearly show the motion of mobile particles in the space between the electrodes. Outer and inner cylinders
100
and
110
are replaced by first and second planar conductors
200
and
210
(
200
′ and
210
′ in FIG.
3
), respectively. For purposes of the present discussion the cylindrical and planar configurations are equivalent. The mobile ionic species comprising toner particles
240
(
240
′) is assumed to have negative charge.
FIG. 2
shows the distribution of charged, mobile particles immediately after the application of an externally-applied, electrical field E. Field E is identified as a vector to show the relative direction of motion of the mobile particles while the field is applied.
FIG. 3
shows the distribution of charged, mobile particles after electrical field E has been applied for a very long time. The negatively charged, mobile particles are collected at the positively charged electrode. A source
220
(
220
′) of electrical potential energy which can vary as a function of time, V
0
, typically 5 volts, is connected between the electrodes to provide field E. An electrical current measuring meter
230
(
230
′) is connected in series with source
220
and the electrodes.
Under the action of field vector E, negatively charged mobile particles
240
(
240
′) move toward the positively charged electrode.
FIG. 2
shows the motion of particles
240
shortly after potential V is applied to the probe. As the particles come into contact with first probe electrode
200
(
200
′), they attract a “mirror” charge of opposite sign (not shown) within the metal of the electrode. The movement of this mirror charge registers as the passage of current in current meter
230
(
230
′). If the direction of applied field E remains constant, negatively charged particles
240
′ will eventually congregate on positively charged electrode
200
(
200
′). When this happens, their contribution to the electrical current measured by meter
230
(
230
′) becomes zero. Any remaining indication of current is due to the motion of electronic charge or other ionic species through the bulk of the solvent liquid. Other ionic species are not considered here.
A plot of a step function of voltage with value V
0
and the resultant current I vs. time are shown in FIG.
4
. When voltage V is first applied, mobile ionic particles
240
move toward first electrode
200
, resulting in a nominally steady current, I
0
. After a time, fewer mobile particles are available, and the measured current decreases as fewer particles impinge on first electrode
200
. In some cases a smaller, residual current, I
R
, will be measured. This residual current is due to electronic, or other ionic, processes, mentioned supra. The time required for the majority of mobile ionic particles to reach the first electrode is approximately 0.1 sec.
The contribution of the mobile species to conductivity is most easily measured using an alternating current (AC). If this is not the case and a direct current (DC) is applied to the probe, mobile species
240
(
240
′) will all move to one electrode and remain there, as indicated in FIG.
3
. In this case, they exhibit only a transient contribution to the total conductivity as they move. This transient current is shown in FIG.
4
. Such a measurement is possible, but is more cumbersome and prone to error than an AC measurement.
In an AC measurement of conductivity, two frequency ranges are important: “low”frequencies, and “high” frequencies. Low frequencies are determined by the mobility of the ionic species, the applied electric potential, V, and the distance between the first and second electrodes. In the case of liquid toner and the above-mentioned cylindrical probe geometry, “low” frequencies are typically in the range of 10 to 30 Hz. The ionic conductivity of the toner is measured at a frequency which keeps all the mobile species in motion. The current and voltage waveforms typical at this frequency are shown in FIG.
5
. In this case, the ionic population in the region between the first and second electrodes is never depleted and ionic current flow is limited by the mobile species' diffusion rate in the liquid. Hence the observed current does not decay during any half cycle of the AC. The quotient of the observed current, I, and the applied voltage, V, at any instant equals the electrical conductance between the two electrodes. Electrical conductance is a property which is measured by applying a potential to an electrical circuit and measuring the current through that circuit. Electrical conductivity is a physical property of a substance. This conductance can be directly related to the conductivity of the fluid in well-known ways, discussed infra. Measurement of
LeRoux Etienne
Metjahic Safet
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