Note: Descriptions are shown in the official language in which they were submitted.
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ENDPOINT DRIFT CORREC`~ION FOR AUTOMATIC TITRATIONS
This invention resides in a method and an
apparatus for coulometric titration. More parkicularly,
the invention resides in a method and an apparatus
for accurate and precise determination of the results
of a coulometric titration and compensation or drift.
In a particularly preferred embodiment,
the invention resides in an improved method and an
apparatus for the coulometric titration of water
by the Karl Fischer reaction. The amount of elec-
tric charge required by the electrolysis electrodes
(in order to reach the endpoint state~ is measured
to give a measurement of water titrated. By using
a constant electrolysis current, the coulometric
measurement can utilize conventional timers.
In such an apparatus, the signal from
the detector is inherently a rather noisy signal.
With conventional iltering methods the signal-to-
-noise ratio is improved by using a long time-
-constant RC ~ilter system, but the titration con-
trol is delayed, which can allow the titration to
27,741-F
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progress beyond the endpoint. Back titration must then
be employed. In addition baseline drift frequently
occurs after titration of sample water is complete,
necessitating both positive and negative stabilization.
As described in U.S. Patent No. 3,726,778,
titrations are subject to positive and negative base-
line drift, that is, drift away from the endpoint con-
dition not resulting from sample addition. Such drift
can be caused by a variety of factors, including side
reactions in the titration mixture which either generate
or consume the substance being titrated. In coulometric
titration of water, aldehydes or ketones in samples will
react to produce water. While U.S. Patent No. 3,726,778
provides one approach to compensation for drift, it would
be desirable to provide an apparatus and method for deter-
mining accurately the actual amount of drift in each
titration and for automatically correcting the titration
results.
The invention resides in an automatic coulometric
titrator comprising titration means for introducing a
titrant into a titration mixture, detection means for
detecting the endpoint of the titration, means responsive
to the endpoint detection means for controlling the titra-
tion means to introduce titrant when the titration mixture
is not at the endpoint, and titrant measuring means for
measuring the amount of titrant introduced, characterized
by
(a) timer means for measuring the titration
time until the titration mixture first
reaches an initial endpoint;
(b) means responsive to one of the endpoint
detection means and the titration means
27,741-F
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for detecting the introduction of titrant
during a predetermined post-titration time
period after the initial endpoint;
(c) means for measuring the amount of titrant
introduced during a second post-titration
time period after the initial endpoint,
said second time period beginning with
the detection of titrant introduction by
means (b), and ending with a predetermined
subsequent introduction of titrant;
(d) means including a timer for measuring the
duration of said second post-titration
period and the amount of titrant introduced
during said period, said time and amount
measurements by means (c) being indicative
of the drift rate during the titration,
and the drift rate and titration time
measured by means (a) being indicative of
the amount of drift.
The invention further resides in a coulometric
titrator having electrolysis electrodes for electrolytically
generating titrant in a titration mixture, a constant
current source for providing electrolysis current to said
electrodes, and an endpoint detector for providing an end-
point signal indicative of the status of the titration
mixture relative to the endpoint or the titration, char-
acterized by
a clock for generating a time signal T during
and after a titration;
a titration counter for generating a char~e
signal Q corresponding to the charge passed through the
titration mixture by the electrodes and constant current
source;
27,741-F
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a comparator connected to the endpoint
detector and adapted to provide a signal Sl having an
Sl=ON state when the endpoint signal is above a pre-
determined endpoint level and an Sl=OFF state ~hen the
endpoint signal is at or below the endpoint level;
means including a switch responsive to the
comparator signal Sl for activating the current source
and the titration counter when Sl=ON and inactivating
said source and counter when Sl=OFF;
first gate means responsive to the time sig~
nal T and comparator signal Sl for detecting a recurrence
of the Sl=ON state during a predetermined tim~ period
after Sl first attains the Sl=OFF state at the end of
a titration;
memory means responsive to ~ignals Sl, T and
Q including a titration time memory and a titration
charge memory for storing T and Q signals, Ttitr and
Qtitr~ when Sl first attains the Sl=OFF state at the
end of a titration;
display means for displaying the signal Q as
a titration result Qtitr in response to the first gate
means signal corresponding to the lapse of the first
gate time interval without a recurrence f ~1 attaining
the Sl=ON state;
first drift correction memory means responsive
to signals T and Q and the first gate means, for storing
the T and Q signals as Qco and TCo in response to the
first gate signal indicative of occurrence of the Sl=O~
state during the first gate time interval;
drift correction means including second and
third gates, the second gate being responsive to the
first gate and the time signal T to activ te the third
gate at a predetermined time after the first gate
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signal indicative of the occurrence of the Sl=ON state
during the first gate time interval, and the third gate
being responsive to the Sl signal and the second gate;
second drift correction memor~ means respon-
sive to the Q and T signals and to the third gate means
for storing the Q and T signals as QC and TC at the
time the third gate indicates occurrence of the Sl=ON
state of signal Sl.
The invention also resides in a method for
correcting positive drift in an automatic coulometric
titrator, characterized by the steps of
generating a signal Q corresponding to the
amount of titrant introduced into the titration mi~ture;
generating a time signal T corresponding to
time elapsed from beginning of the titration;
introducing titrant continuously until a pre-
determined endpoint condition is detected, and thereafter
reintroducing titrant periodically as needed to maintain
the reaction mixture àt the endpoint condition;
storing the Q and T signals as Qtitr and Ttitr
at the time the endpoint is first reached;
determining the titration result from (Qtitr)
when no additional titrant is introduced during a pre-
determined time interval after the endpoint is irst
reached; and
generating a drift rate signal DR when addi-
tional titrant is introduced during said interval, said
drift signal DR corresponding to the difference between
(i) the Q signal at the time (TCo) of an additional
titrant introduction (Qco~ and the Q signal at the time
(TC ) of a predetermined later additional titrant
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introduction (QC ) divided by (ii) the difference in time
(TC -TCo) between said introductions;
generating a correction signal (Qcorr) corres-
ponding to the product of the drift rate signal DR and
the stored (Ttitr) signal, said correction signal thus
corresponding to the amount of titrant consumed by drift
during the initial titration; and
determining the;titration result from the
difference between the stored (Ttitr) signal and the
(TCorr) signal. c
As with coulometric titrations generally, the
method and apparatus of the invention includes a titra-
tion compartment, with means for introducing a titration
reagent and sample, an electrolysis anode and cathode
in the compartment to pass current through the titration
mixture and generate a titrant from the reagent; a
detector for determining the state of the titration mix-
ture relative to a predetermined endpoint;. and a source of
electrolysis current for the electrolysis electrodes,
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and means for measuring the amount of electric
charge passed through the -titration mixture.
The appara-tus can also include additional com-
ponents, such as an auxiliary electrolysis current
source of opposite polarity to the main source
for back titration, appropriate filters, buffers,
amplifiers and control circuitry to allow the
detector to control the titration, and display
elements for displaying the results in various
convenient forms, such as coulombs, titration
time, or concentration units~
In coulometric titrations, and particu-
larly in coulometric titration of water by the
Karl Fischer reaction, the endpoint can be subject
to drift, due to a variety of factors such as side
reactions, or leakage of atmospheric contaminants
into the titration compartment. Depending on the
chemistry of different samples, drift due to side
reactions can vary in both direction and amount,
adversely affecting the results of the titration.
The invention provides a method and
apparatus for compensating for the actual drift
occurring during the titration, so that the effects
of drift elements in each titration can be accounted
for.
In describing the invention, it is con-
venient to refer to various states of the titration
mixture in terms of a graphical plot of the state
of the mixture (on the vertical axis) against time
(on the hori~ontal axis). It will also be convenient
to refer to state of the titration mixture as starting
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"above the endpoint", proceeding "downward" to the
endpoint during the titration, and possibly going
"below the endpoint" in cases of over titration
beyond the endpoint or negative drift. In this
frame of reference, positive drift is "upward"
drift, and negative dri~t is "downward" drift.
It is understood that the terminology of upward
and downward movement is merely a convention
adopted to simplify the description. Depending
on the parameters used in various embodiments to
monitor the state of the titration mixture relative
to the endpoint, the titration may result in either
a decrease in the selected parameter or an increase.
In the process of the invention, an elec-
trolysis current is passed through a titration
mixture of reagent and sample to generate titrant
therein. ~hen the titration mixture first reaches
a predetermined endpoint, as indicated by an end-
point signal provided by a detector, the elec-
trolysis current is turned off. After the endpointis reached, electrolysis current is again passed
through the mixture (whenever the detector signal
exceeds or rises above the endpoint level), until
the mixture is titrated back to the endpoint. The
amount of electric charge (Q) used for electrolysis
is measured, and the titration time (T) is also
measured. After the endpoint condition is reached
for the first time, the condition of the mixture
is monitored and the mixture titrated back to the
endpoint as needed, but the mixture is otherwise
held without measurements of charge being taken
for a first predetermined short time period to
allow the mixture to stabilize. Monitoring of the
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condition of the mixture is then continued for a second,
longer time period immediately following the first
time period, without interruption. If -the detector
signal does not depart from the endpoin-t level
during the second time period, the amount of the
sample is determined from the amount of electrolysis
current passed through the mixture until the initial
endpoint was reached. If, during the second time
period, the titration mixture departs from the end-
point, monitoring is continued over a third timeinterval (during which drift is measured), beginning
with a return to the endpoint continuing for a pre-
det~rmined time period and ending with another departure
from and subsequent retitration of the endpoint. Mixing
of the titration mixture is continued throughout the
process so that any heterogeneity due to localized dif-
fering conditions at the titration electrodes or detector
electrodes will be eliminated.
The first post-titration time interval
is relatively short, e.g. 5-10 seconds, being only
long enough to ensure that localized differences
in the titration mixture are eliminated. The second
post-titration time interval is generally longer;
e.g., 30-60 seconds, when there is no forward or
back titration of drift. The pxedetermined time
duration of ~he second time interval is selected
in relation to system time response of the titration
and titration rate to correspond to, or to exceed
the ordinary duration of the initial titration so
that the absence of forward or back titration during
this period will indicate that drift was also
absent during the initial titra-tion. The first
time period and the predetermined duration of the
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second time period can be preselected and con-trolled
by a timer. When titratable drift occurs, the end
of the second time period, and the beginning and
end of the third time period are determined in
response to the sta-te of the titration mixture.
The third time period must begin and end with
departures from, or retitrations returning to, -the
predeterminded endpoint in order to obtain an
accurate determination of the drift rate.
Since the first time period is provided
to allow stabilization of the titration mixture,
the second and third time periods are the two time
intervals during which drift observation measure-
ments and corrections are conducted. The first
time period can be referred to as a "stabilization
period". The second time period can be referred
to as a "drift monitoring period" during which the
titration mixture is monitored for drift away from
the endpoint. The third time period can be referred
to as a "drift measuring period" during which measure-
ments of drift rate are made (when drift has occurred
during the drift monitoring period). In titrations
for which no post-endpoint stabilization is required,
for example, with rapid mixing and a slow titration
rate, the stabilization period can be eliminated.
Electrolysis current is passed through
the mixture during the third time period, and the
total duration of the third time period are measured.
The average drift rate is determined from the amount
of electric charge used during the third drift
measurement period and the duration of the third
time period. The amount of sample titrated is
27,741-F
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determined from the amount of charge introduced
by the electrolysis current until the end o~ the
titration procedure, adjusted by the drift rate
and measured titration time.
AS mentioned above, coulometric titrations
can be subject to either positive or negative drift.
Preferably the detector signal is monitored and
reverse polarity back titration current is passed
through the mixture when the signal reaches a pre-
determined level below th~ endpoint, and the reverse
current is also measured as stated above, and used
to measure the negative drift rate and adjust the
titration results for negative drift.
The apparatus of the invention includes
conventional elements of a coulometric titrator in-
cluding electrolysis electrodes, current source,
titration compartment, and a detector ~or detecting
the condition of the titration mixture relative
to a predetermined endpoint. The detector output
signal is connected through a variable low pass
filter to a comparator for comparing -the detector
output to the predetermined endpoint level. The
filter is adapted to vary in response to the out-
put signal from the comparator between a short
time constant condition above the endpoint and a
long time constant, high damping condition at or
below the endpoint. The comparator is also con-
nected to means for controlling the titration cur-
rent.
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The apparatus also includes means for
measuring the titration electric charge, and clock
means for measuring titra-tion time and for generating
a time signal, first gate means responsive to the
time signal and to the comparator for controlling the
first post-titration period; a second gate means responsive
to the first gate means, the time signal and the
comparator for transmitting the titration charge measure-
ment to an output means such as a display when
the second post-titration time period (the drift
observation period) has elapsed without a depar-
ture from the endpoint, and for transmitting signals
indicative of the measurements of titration time
(Ttitr) and titration charge (Qtitr) at the end of
the initial titration and signals indicative of the
time and charge measurements ~Tco and Qco) at the
beginning of the third post-titration time period (the
drift measuring period) to first and second memory
means; a third gate means responsive to the second
gate means, the time signal and the comparator for
transmitting signals indicative of the measurements
of titration electric charge (Qcl) and time ~TCl)
from the charge measuring means and the clock means
when the selected retitration occurs; at the end of
the third time period. Subtractor/divide.r means
is provided which is responsive to the third gate
means and which is connected to the second memory
means for generating a signal corresponding to
Qcl ~ Qco which thus corresponds to the average
_
T 1 ~ T
drift rate (D.R.) during the third time interval;
a multiplier means connected to the subtractor/-
divider means and the first memory means for
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generating a signal corresponding to the amount
of drift taking place during the titration, (D. R.
X Ttitr = Qcorr)i and adder and subtractor means
connected to the first memory means and the multi-
plier means for correcting the titration result
Qtitr by subtracting or adding the amount of
electric charge Qcorr attributable to titration
of positive or negative drift.
The titration time, Ttitr measured in
lG the process and apparatus of the invention is the
total of (a) a relatively short term sample intro-
duction period (during which the sample to be
titrated is introduced into the titration reagent),
(b) the time between the end of the sample intro-
duction period and the beginning of titrant intro-
duction by switching on the main electrolysis current
source; and (c) the time during which titration
current is passed through the mixture until the
endpoint condition is first reached. Period (a)
is a relatively short period, e.g. 5-lO seconds
to allow time for the introduction of the sample.
Although, period (b) can be eliminated, it is
preferred in the case of certain samples to allow
a delay of 10 seconds to as long as one hour, to
permit complete mixing, or extraction of materials
from solid samples into the titration mixture.
This can be provided by including a conventional
timer to delay operation of the current source for
a preselected time period. Since drift due to
side reactions or atmospheric contamination, for
example, can occur during periods (a) and (b), it
is necessary to include such periods in the ti-
tration time, Ttitr, in addition to period ~c~
during which the titration itself actually occurs.
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Figure 1 illustrates a filtered detector
output signal in a titration exhibiting relatively
slow positive drift;
Figure 2 is a block diagram illustrating
the operating and control circuits of a titrator
of the invention;
~ igure 3 illustrates details of the
measurement and drift correction circuits of a
titrator of the invention in an embodiment adapted
for coulometric Karl Fischer titrations.
As illustrated in Figures 2 and 3, the
apparatus comprises a pair of electrolysis elec-
trodes 34, 36 connected to a main electrolysis cur-
rent source 35; an endpoint detector 39, which
includes a pair of electrometric sensing elec-
trodes 40, 41, and an indicator current source 42.
A negative drift auxiliary current source 56 is
connected to electrodes 34, 36 but with opposi~e
polarity to that of the main current source 35.
These basic elements are conventional and described,
for example, in U.S. Patent 3,726,778~
Endpoint detector 39 is connected through
a conventional buffer/amplifier and voltage limiter
43 to a variable low pass filter circuit 10. The
output of filter 10 (the filtered detector signal)
is connected to an endpoint comparator 24 and a
negative drift comparator 52. A voltage source 28
is connected to endpoint comparator 24 to provide a
pre-set reference voltage corresponding to the ti-
tration endpoint. The output signal of comparator 24(indicated as Sl in Fig. 3) is connected to a light
27,741-F
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actuated switch, LAS 33, which controls the operation
of the main current source 35 while electrically iso-
lating the comparator 24 from current source 35, a
titration counter 64, clocks 60, 62, and drift correction
and readout circuits 65. In a coulometric Karl Fischer
titrator embodiment with an amperometric sensing
electrode as th~ endpoint detector 39, the detector
signal is a voltage signal which decreases during the
titration as water is consumed to an endpoint value
lQ of, for example, about 70 millivolts. Comparator
24 and LAS 33 are connected to activate electrolysis
current source 35 when the signal from endpoint
detector 39 indicates the presence of any untitrated
sample (by a detector signal above the endpoint reference
level) and to switch off current source 35 when the
detector signal reaches the endpoint reference level
provided by reference voltage source 28. The current
source 35 remains switched off by LAS 33 until the
detector signal at comparator 24 rises above the end-
point level (due to drift, untitrated sample, or newsample addition,). The elect.rolysis current source 35
will be activated periodically after the endpoint is
first reached.
An unfiltered output signal from detector 39
is an extremely noisy signal, whereas a filtered output
signal is more ameanable to measurements in typical
titrations. As best shown in Figure 1, a titration
continues for an initial titration time Ttitr, beginning
with the start of a sample introduction period, con-
tinuing through a period during which the constantcurrent source operates, and ending when the titration
reaches it initial endpoint at T-Ttitr=O in Figure 1.
(The signal illustrated is a voltage limited to a maxi-
mum shown at (a)). Although the electrolysis current
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is swi-tched off at the endpoin-t, a-t T-Ttitr=0, the
detector signal drops below the endpoint to (f) and
then begins to rise during a five-second initial
post-titration stabilization period from T-Ttitr=0
to T-Ttitr=5. The second, drift observation time
period begins at T-Ttitr=5 seconds. The second
post-titration period ends and the third period
begins at T-Ttitr=10 seconds, when the titration
current is switched on (and later off), giving
rise to a retitration l'spike'l ~b).
In the vicinity of the endpoint, ~he
voltage signal from the endpoint detector 39 is
extremely sensitive to very small amounts of water
in the titration mixture which results in very large
changes in the output signal. During a spike (b),
(c), (d) or (e), the titration current is switGhed
on; titrant is generated at the electrodes 3~, 36;
titrant is mixed with the titration mixture, ti-
trating the water; the detector 39 detects the
return to the endpoint; and the titration current is
switched off again, all substantially instantaneously.
The sensitivity effects, as well as the response time
of the recorder pen, contribute to the height and shape
o~ the spikes. It is apparent from the spikes of
Figure 1 that it would be difficult, if not impossible,
to measure drift direc-tly from the spikes in the de-
tector output signal.
In the spike at (b), the signal again
returns substantially instantaneously, down to the
endpoint and below, then gradually drifts upward
at (g) during the third time period. The upward
drift ts followed by another retitration spike (c),
an "overshoot" (below the endpoint) and a gradual
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upward drift (h) to another retitration spike (d).
With the third time period having a minimum time
duration of, for example, 30 to 50 seconds, the
third time period would be 55 seconds long, from
the beginning of spike (b) at T-Ttitr=10 seconds
to the beginning of spike (c) at T=65 seconds.
With a minimum third period duration of 60 seconds,
th~ third time period would continue until the
beginning of spike (d) at T-Ttitr=102 seconds,
making the third period 92 seconds long (from
T-l'titr=10 to T Ttitr
As best shown in Figure 1, the drift
cycles, (f), (g), (h), and ~i~ are not uniform
in duration. It i5 necessary for the third time
period to begin and end with post-titration spikes,
preferably with the beginnings of spikes. The third
time period in different titrations will not neces-
sarily be of the same duration.
To provide a quick shut-off of titration
current at the endpoint, together with adequate
filtering o~ the detector si~nal so that return
to the endpoint can be reliably detected, the
filter circuit 10 is connected between the buffer/-
amplifier/voltage limiter circuit 43 and the com-
parators 24, 52. The ~ilter circuit 10 comprisesa capacitor 12, connected in series through resistors
15 and 17 to the buffer/amplifier and voltage limiter
43 to receive the detector input. Capacitor 12 is also
connected to an amplifier 22. Two additional resi~tors
14 and 16 are connected in series with each other and
each resistor is also connected in parallel with one
of the res~stors 15 and 17, respectively, via switches
18 and 20. Switches 18 and 20 ~both shown in the
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open position in Figure ~) are controlled by swltch
actuator 26 (connected to the output of comparator 24) so
that both the switches 18 and 20 are closed or bokh
switches are opened substantially simultaneously.
Resistors 14 and 16 are selected to provide different
resistances in the RC filter circuit and thus
pro~ide different cut off frequencies and time
constants depending on whether resistors 14 and
16 are switched into or out of the filter circuit.
Switch actuator 26 is connected to comparator 24
to provide short-time-constant/high-pass filtering
during th titration and long-time-constant/low-
-pass filter characteristics when the endpoint is
met or exceeded.
The input signal, e.g. the detector elec-
trode signal from the titrator, is connected through
the buffer/amplifier and voltage limiter 43 to the
filter 10 which can be connected as an RC filter circuit.
In one mode the RC filter circuit includes capacitor 12
and resistors 15, 17 or, in another mode, when switches
18 and 20 are closed, resistor 14 in parallel with
resistor 15 and resistor 16 in parallel with resistor
17. The filter signal is supplied to the input
amplifer 22.
The junction of resistors 15 and 17 is
connected through a capacitor 19 to the negative
input terminal and the output terminal of amplifier 22.
The filter circuit 10, including amplifier 22, can be
characterized as a second order VCVS (voltage-con-
trolled-voltage-source) low pass active filter
with variable frequency characteristics, depending
on whether switches 18 and 20 are open or closed.
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The output amplifier 22 is connected to
the input of the endpoint comparator-ampli~ier 24,
the other input of which is connected to the ref-
erence voltage source 28. The output of comparator-
-amplifier 24 is connected to the switch actuator 26.
The output of the comparator-amplifier 24 is also con-
nected, through a resistor 30, to the light activated
switch LAS 33, preferably using a light emitting
diode (not sho~n) which is connected to the com-
parator-amplifier 24 output and to ground, and
a phototransistor (not shown~.
In a coulometric titrator, the input
signal supplied to filter 10 is the output from
the endpoint detector (39), typically the amplified
signal from a potentiometric s~nsing electrode.
The reference voltage supplied by voltage source 28
is a predetermined voltage corresponding to the
titration endpoint conditions. The LAS 33 is con-
nected to the electrolysis circuit, so that the
electrolysis current can be switched on or off by
the LAS 33 in response to the output ~rom the
comparator-amplifier 24.
A representative endpoint voltage is 70
millivolts and the voltage-limited input signal
is preferabLy amplified by the amplifier/Yoltage
limiter 43 so that a reference voltage of 7.0 volts
can be used at the comparator-amplifier 24 to
identify the endpoint with amplifier 22 having a
gain of unity. In a typical coulometric titrator,
the input signal can be the detector electrode
signal amplified by a gain of 10, limited by
amplifier~voltage limiter 43, and amplified again
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by a gain of 10 by -the amplifier/voltage limiter
43. The amplifier/voltage limiter 43 preferably
limits the maximum signal voltage to, for example,
0.9 or 1.0 volt, to limi-~ the voltage range at the
filter 10. The maximum limited voltage is selected
to be sufficiently above the endpoint voltage so
as not to interfere with detection.
During the titration, switches 18 and 20
are closed, so that resistors 14 and 16 are in ~he
filter circuit. In this mode, the filter 10 has
as fast time response, with a time constant of
about 0.1 second and a cut-off frequency of about
10 Hertz. As the detector voltage approaches the
endpoint level, the filtered signal supplied to
comparator 24 approaches the reference voltage.
~hen the endpoint condition is reached, the short
time constant of the filter provides a fast re-
sponse at the comparator 24. The resulting end-
point output from the comparator 24 shuts off the
electrolysis current via LAS 33; and, through
switch actuator 26, switches 18 and 20 are both
opened. With the values given, the resulting
state of filter 10 now has a slow time response,
with a time constant of about lQ seconds and the
input signal is heavily filtered, with a cut-off
frequency of about 0.1 Hertz.
At this time the input signal continues
to drop below the predetermined endpoint level,
thus "overshooting" the endpoint for a brief period.
Some "overshooting" is an inherent result of locally
different conditions which may exist in the ~iquid
titration mixture at the titration electrodes and
at the detector electrodes. The input si~nal then
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gradually increases, as the ti-tration mixture be-
comes more uniform with continued mixing, and the
reaction conditions at the endpoint detector approach
a uniform condition of the entire titration mixture.
During this "catch-up" period, the input signal
increases slowly back to the endpoint level.
During the "catch-up" cycles, the input
signal is not only changing at a slower rate than
during the titration, but the input signal is much
closer to the endpoint than in the early titration
phase. The increased filtering provided by filter
10 during this phase allows an accurate and reliable
detection of the return to the endpoint at the end
of a "catch-up" phase.
When the input signal rises to the end-
point level, the filtered input to the comparator
24 indicates the presence of untitrated sample.
In response to the comparator 24 the electrol~sis
current is again switched on via LAS 33, to ti-
trate the residual untitrated sample. Simul-
taneously, actuator 26 opens switches 18 and 20
returning the filter 10 to its short-time-constant
state.
As shown in Figure 2, the filtered de-
tector signal is also fed to the negative driftcomparator 52, which is connected to a reference
voltage source 55. The reference voltage from the
source 55 is maintained at a predetermined level
corresponding to the negative dri~t of the detector
signal below the endpoint level. For example, in
a Karl Fischer titrator with an endpoint reference
27,741-F
. .
- ` 13 2;~
voltage of 70 millivolts, a suitable negative drift
reference voltage level can be 55 millivolts. Com-
parator 52 is connected to a LAS 54 which switches
the negative drift auxiliary current source 56 on or
off, in response to an output signal S2 (Fig. 3
of comparator 52.
The outputs of comparators 24 and 52 are
connected through the respective LAS 33 and 54 to
the resettable titration counter 64 which measures
the electric charge used to titrate or to correct
drift, and to the drift correction/readout circuit 65.
When both current sources 35 and 56 are constant current
sources, for example, the main electrolysis current
source 35 preferably provides ~100.35 milliamperes
when switched on, and the negative drift auxiliary
current source 56 provides -25.09 milliamperes. With
constant current electrolysis, the titration counter
64 is preferably a clock or timer which records the
time during which the current sources operate. Clock
60 is connected to both titration counter 64 and real
time clock 62 to provide uniform timing measurement.
As shown in Figure 3, endpoint comparator 24
through LAS 33 provides a signal Sl, which corresponds
to the endpoint status of the detector signal and the
main electrolysis current from main current source 35.
Similarly, a signal S2 from comparator 52 and its LAS 54
indicates the negative drift status of the detector
signal and negative drift auxiliary current source 56.
Titration counter 64 provides a signal Q which
corresponds to the electric charge used in the
titration, the signal Q being a measurement of the
time that either current source 35 or 56 has been
switched on. Real time clock 62 provides a signal T,
27,741-F
~
~%~;04
--19--
which corresponds to the actual duration of the ti-
tration procedure independently of switching on and
off of sources 35 and 56 before and after the endpoi~t
is first reached.
For simplicity, signals Sl, S2, T and Q
are shown repeatedly as inputs or connections to
various elements in Figure 3. It is understood
that the apparatus includes appropriate connections
bet~7een the comparators 24 and 52, LAS 33 and LAS 54;
counter 6~, and clock 62 to supply these signals.
The drift correction and readout circuits
65 include a series of gate circuits (gates 70 to 74);
reader/memory elements 75 to 78 for signals T and Q,
which are at various times controlled by real time
clock 62 and comparators 24 and 52 through the gates
70, 71, 72 and 73; and signal function manipulators
80, 81, 82, 83A, 83B and 84 some of which are con-
nected to certain of the reader/memory elements 75 to
78 and gate 74; and a readout circuit. The readout
~0 circuit includes conventional display counter 85A and
display 85B for displaying the results. A conven-
tional converter/multiplier 94 and unit factor
memory 98 is provided ~or converting the results
into desired numerical units, such as coulombs,
~5 moles, millimoles, or micrograms and into desired
numerical base, such as binary, octal, or decimal
units.
A reset element 86 is connected to real
time clock 62 and counter 64 to reset the real time
clock 62 and counter 64 and clear the memories
75-78 when a start signal from a start switch 90
27,741-F
':
,
.
Q~
-20-
is produced. A conventional clear display circuit
~37 is connected to start switch 90 to clear display
counter 85A and display 85B.
The gates 70-74, reader/memory elements
75-78, and signal function manipulators 80-84,
follow the titration and any post-titration drift,
correct the result for drift (if any) and transmit
the final result to the display circuits 85A and 85B.
When the display circuits receive the final result,
reset element 86 resets the titration counter 64
and real time clock 62. In a further embodiment,
the device can include additional circuits to
monitor drift periodically in the apparatus between
titrations, and -to apply the most recent drift
correction to the readout during subseguent -ti-
trations until the first endpoint.
The apparatus is controlled at several
points by signals S1 and S2 from comparators 24 and
52. Each comparator signal corresponds to one of
two states of the detector signal and current
sources 35 and 56. For brevity, the two signal states
are hereinafter referred to as OFF and ON, corres-
ponding to the following:
S1 = OFF, detector signal belo~ endpoint,
main titration current source 35
off;
S = ON, detector signal at or above end-
1 point, main titration current
source on;
S2 = OFF, detector signal above predeter-
mined negative drift limit
(which is below the endpoint
level); auxiliary current source
off; and
27,741-F
.
-21-
S2 = ON, detector signal below negative
drift limit; au~iliary current
source on.
Operation
A titration is started, e.g., by actuating
the "start" switch 90 just prior to adding a sample
to the titration reagent, clearing the display cir-
cuits 85A and 85B and actuating reset element 86.
Reset element 86 resets and starts the real time
clock 62, and resets counter 64 to zero and briefly
inhibits operation of the current source 35 for a
predetermined sample introduction period. If the
sample contains water detected by endpoint detector
39, Sl goes to the ON state, and starts counter 64.
When the titration first reaches the endpoint, the
signal Sl from the comparator 24 goes to OFF,
stopping the titration counter 64 but not the clock
62; and T and Q are transferred to memory elements
75 and 76. These signals are Ttit~ (titration time~
and Qtitr (titration charge). A 5-second stabili-
zation period, and a 3Q-second maximum drift obser-
vation period are suitable for use. The irst stabili-
zation period "5-second" gate 7Q follows the signal
T from real time clock 62 for 5 seconds after Sl
irst goes to OFF, then activates the drift obser-
vation period gate, "3Q-second" gate 71. The 3Q
second gate 71 monitors the clock signal T, and
Sl and S2. If both S1 and S2 remain OFF for the
entire 3Q-second observation period~ gate 71 directs
3Q the transmission of the signal Qtitr from memor~ 75
through subtractor 82 and converter/multiplier 94
to the display 85A. S1 and S2 both remain OFF only
if there is no detectable drift during this period,
therefore Qcorr in subtractor 82 is zero. Gate 70
27,741-F
, .
-22-
controls the post-titration stabilization period
and gate 71 controls the drift observation period
(the second post-titration time period).
In the usual case, some drift will occur
and either Sl or S2 will switch ON during the period
controlled by gate 71, as the device either titrates
positive drift back to the endpoint or back titrates
negative drift back to the pre-set limit. When
either Sl or S2 goes to ON during this period, the
30-second gate 71 directs the txansmission of the
signals T and Q from real time clock 62 and counter
64 to the memory element 77. T and Q at this time
can be designated as TCo and Qco the subscript
"Co" denoting the beginning of the drift correction
measurements. Gate 71 also activates gate 72 in
response to which comparator signal (Sl or S2)
is ON. Gate 71 also activates correction selector
gate 74 to connect function elements 81, 82 for
Sl = ON or function elements 83, 84 for S2 = ON.
A useful minimum duration or the drift
measurement period is 45 seconds. Once activated
by Sl or S2 going to ON, the gate 72 monitors the
time signal T from real time clock 62 and then activates
the Gate 73 after 45 seconds. The subscript "Cl"
for gate 73 denotes the end of the correction measure-
ment period. The activated Gate 73 monitors T, Sl and
S2 and when either Sl or S2 goes to ON again, or if
neither Sl or S2 goes ON for 30 seconds gate 73 trans-
fers Q and T at that time to QC ~ TC reader/memory
element 78.
27,741-F
2~ 4
-23-
The apparatus has thus de-termined the
titration char~e Qtitr and time Ttitr un
first reached OFF; delayed 5 seconds; then moni-tored
Sl and S2 during a second time interval, and de-
termined T and Q at the beginning (Tco, Qco) andend (TC ~ QC ) of a third time interval which started
with S1 or S2 switching ON after the 5 second delay
and ended with the next ON state of Sl or S2 which
occurxed after the expiration of 45 seconds from
the start of the third time interval or, if there
is no subsequent ON state within the 30 seconds of
~ate 73, which time period ended after the 45 seconds
of gate 72 plus the 30 seconds of gate 73.
Gate 73 also activates the drift rate
calculator function element 80, which uses Qco
and T from memorY 77 and QC1 and Tc1
memory element 78 to generate a drift rate signal
corresponding to:
QC ~ QC
D.R. =
TC1 Tco
Element 80 thus comprises subtractors and a
divider circuit element.
I~ S1 was ON durin~ the post-titration
period, correction selector gate 74 transmits the
drift rate signal from calculator 80 to correction
multiplier 81 which multiplies the drift rate sig-
nal D-R- by Ttitr stored in memory element 76 to
produce a drift correction value signal Qcorr
27,741~F
o~
-24-
corresponding to the amount of titration charge
Qcorr which was consumed during -the titration by
drift compensation ra-ther than by titrating sample
water. Qcorr is transmitted from multiplier 81
to sub~ractor 82, which receives Qtitr from memory
75. Subtractor 82 subtracts Qcorr from Qtitr
and transmits the resulting signal, now corres-
ponding to the titration result corrected for
t (~titr Qcorr) to display 85A via converter/-
multiplier 94.
If negative drift occurred, S2 was ONduring the post-titration period. Gate 74 trans-
mits the drift rate ~.R. from drift rate cal-
culator 80 to correction multipliers 83A and 83B,
which divides the drift rate D.R. (in 83A) by a
factor Kl corresponding to the ratio of main ti-
tration current to negative drift auxiliary current
to provide a drift rate signal DR' in units equivalent
to the main titration measurement Qtitr- Correction
multiplier 83B multiplies the thus adjusted drift
rate signal D~' by Ttitr. For example, when the main
current is 100.35ma and the auxiliary current is -25.Q9ma,
the drift rate from calculator 80 must be reduced by a
factor of 4~ since QCl ~ Qco is actually only a meaSurement
of time, not current. The resulting correction
value Qcorr from 83B corresponds to the amount of
additional charge which would have been used in
the titration if negative drift had not occurred.
Multiplier 83B transmits Qcorr to adder 84 which
dds Qcorr to Qtitr (transfered from memory 75)
and transmits the resulting signal to the display
circuit 85A through converter/multiplier 94.
27,741-F
s~
-25-
It will be apparent from the foregoin~
that the correc-ted result signal from either sub~
tractor 82 or adder 84 (or from counter 64 as
directed by gate 71 when there is no drift) is a
measurement of titration charge in terms of ti-
tration time at constant titration current. The
display circuits 85A and 85B preferably include
a conventional converter/multiplier 94 and unit
factor memory 98 to convert the corrected Q signal
to coulombs, or to moles, or micrograms of water
or some other desired units.
In an alternative embodiment of the inven-
tion the display elements 85A and 85B can be supplied
with a partially corrected Q signal during the titration
and before the drift correction process is com-
pleted. This allows the operator to observe approx-
imate results as the titration progresses so that
unusual conditions such as sample addition errors
can be signalled early. This can be done, for
example, by providing an additional memory element
(not shown) to store the most recently determined
drift rate DR (or DR/Kl in case of negative drift)
and correcting the Q display using the most recent
drift rate correction.
The interaction of the drift correction
circuits, drift monitor circuits and display cir-
cuits 85A and 85B is illustrated in Figure 3.
The display circuit comprises a digital
display panel 85B controlled by a display counter 85A.
The result signals Qtitr + Qcorr from the adder 84r
or Qtitr ~ Qcorr from the subtractor 82 are, as noted
27,741-F
,
-26-
above, in units corresponding to time a-t constant
current. The converter/multiplier 9~ is provided
to multiply the Q signals by the appropriate con-
version factor (from the unit factor memory 98~ so
that the display 85B is in desired units such as
micrograms of water. In construction and operation
the titration counter may be counting time at a much
higher rate than is desired for the display counter.
(e.g., if clocks 60 and 62 and titration counter 64
are counting at 600 Hertz, it may be desirable to
have the display counter operate at 1 Hertz or less,
partic~larly when it is desired to display a Q signal
during the titration.) Converter/multiplier 94 thus
can use two conversion factors, a display factor to
convert titration counter time units to display
counter time units, and a second conversion factor
proportional to the main electrolysis current
(coulombs/time~ to provide a display in units such
as coulombs, moles, or micrograms of water.
When it is desired to display a corrected
Q value continuously during the titration, the
apparatus can be modified to provide an additional
memory element (not shown) to store the drift rate
(DR, or DR' for negati~e drift) from the most re-
cent titration, and multiplier elements to continuously
apply that drift rate factor to the Q signal to be
displayed. If desired, a drift correction factor
used for continuous Q displays can be revised
periodically between titrations by resetting clock
62 and counter 64, and clearing memory elements
75-78 at the end of a titration correction se~uence,
and using the gates 70-74, memories 77 and 78 and
element 80 to monitor drift conditions between titrations.
27,741-F
-27-
Elements 70-84, 94 and 98 can be assembled
using separate integrated circuit chips, such as,
gates, memories, adders, subtractors, or multi-
pliers, or preferably using a conventional arith-
metic logic unit for the arithmetic operations.
Preferably, these elements as well as clocks 60,
62 and counter 64 are memory locations in a micro-
processor. Com~lercially available units such as
an Intel microprocessor No. 8085, with two program-
mable read-only memory units (Intel No. 2716) and a
random access memory ~Intel No. 8156), Intel Corp.,
Santa Clara, California are used in a preferred
apparatus. It will be apparent, also that the
memory elements 75 to 78 can be constructed using
separate display elements, or an appropriate printer,
to provide the necessary values of Qtitr Ttitr, Qco
Tco, QC and TC I so that the correct computations can
be carried out separatel~, either manually or on
a separate, appropriately programmed digital com-
puter, for example. Also the time periods applied
by the various gates 70, 71, 72 and 73 can be
varied.
The invention has been described with
2S respect to coulometric Karl Fischer titration of
water, with an endpoint condition sensed as volt-
age and approached during the titration from a
higher endpoint detector voltage so that positive
drift corresponds to increasing voltage and nega-
tive drift corresponds to negative voltage. Itwill be apparent, however, that the method and
apparatus can be readily adapted to other titrations
and other endpoint detection systems, such as,
27,741-F
~ . .
~2~ 4
-28-
for example, the system described in U.S. Patent
No. 3,723,062.
An apparatus of the type described was
constructed using a 100.35 milliampere titration
current a -25.09 ma negative drift titration cur-
rent, and 70 millivolt endpoint, with the above-
-mentioned Intel microprocessor and memory compo-
nents using a 5 second stabilization period at
gate 70, a 3~ second period for gate 71, a 45 second
period at gate 72 and a 30 second period for gate
73. In representative titrations of a sample con-
taining 450 micrograms of water, with no drift, the
mean result was 450 micrograms with a standard
deviation of ~5. With a 450 microgram sample and
positive drift (due to acetone in the sample) of
about 300 micrograms/minute, the mean result cor-
rected by the invention was ~68 micrograms with
a standard deviation of +13 micrograms. The un-
corrected mean result was 745 micrograms ~18 micro-
grams. In a similar operation with moderate drift,the uncorrected mean Qtitr of replicate samples
containing 608 micrograms i8.9 micrograms water was
2200 micrograms, while the apparatus and method of
the invention gave a mean corrected result of 575
micrograms with a standard deviation of ~25.6 micro-
grams. It will be apparent that the invention not
only provides improved results in coulometric titrations,
but allows coulometric titrations under drift conditions
in which coulometric titration was previously impractical.
27,741-F
