Note: Descriptions are shown in the official language in which they were submitted.
~1~~1~~
Method of Using a Computer to Collect Chemical Signals Directly
Field of the Invention
The present invention is related to a method of using a computer to collect
chemical signals directly.
Background of the Invention
There are three types of chemical sensors: chemical sensors used in
conductometry, chemical sensors used in amperometry and chemical sensors used
in potentiometry. For examples: pH electrodes, ion-selective electrodes, ISFET
(ion-selective field effect transistors), enzyme electrodes, biosensors, etc.
are
widely used in chemical, biochemical, biotechnological, environmental
protection
and medical analyzers, such as: pH-meter, ion analyzer, polarography, chemical
analyzer, bioanalyzer, bioreactor, ion chromatography, flow-injection
analyzer,
etc. Moreover, Chemical sensors are used in quality control analysis, on-line
analysis and monitor-control apparatus for chemical manufacturing processes.
U.S. patent No. 4,897,128 discloses a method of controlling the ionic
concentrations of reactants in a zinc phosphate coating sink by using pH-
electrode and fluorine-ion selective electrode.
A chemical sensor can convert a specific chemical signal (i.e.
concentration of a certain component of a sample) or the sum of many chemical
signals into an electronic signal such as electric potential, resistance, or
current.
However, in order for the users to understand the physical meanings of a
chemical signal, this electronic signal still needs to be further processed,
stored,
and/or displayed by an signal processing equipment. For example, a pI-1-
electrode
has to be incorporated with a pH meter to determine the pH value of a
solution.
CA 02173186 2002-05-02
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Similar requirement applies to the usage of a chemical analyzer, and pH
monitor-
control equipment. A chemical sensor for amperometry can determine the
reaction current in the potential static condition by relying on a
potentiostat, and
then indirectly obtain the concentration of a specific specie. Similar
requirement
applies to the usage of a chemical analyzer and a biochemical analyzer. A
chemical sensor for conductometry can determine the conductivity by relying on
a
conductometer, and the determined conductivity can then be used to indicate
the
ending of a conductometric titration, or used as the standards of ionic
concentrations in ion chromatography. Each kind of these signal processing
equipment has its specific usage, and it cannot be exchanged to be used in
another chemical sensor. For example, a p1-1-meter can not be a conductometer
or
a coulotneter, and it also can not be extended to another use. without a
special
design, a potentiometer cannot be extended to be used in potentiostatic
coulometry.
Generally speaking, conventional signal processing equipment can be
divided into 4 categories. The first category includes the simple instruments
which cannot be connected to a computer or a recorder. For example, pH-meters
(types 704, 620, 588) of Metrohm*Switzerland, do not have very powerful
functions, and do not have the ability to execute data communication with
other
instruments like chemical analyzers.
The second type of signal processing equipment, although cannot be
connected with a computer externally, is able to communicate with an external
recorder through its analog signal output node, and, therefore, enhance its
function. Examples are pH-meter (PI-IM82) of Radiometer*Denmark,
Potentio/Galvanostat and Coulomb/Arnperohour Meter of Nichia*Japan. The
functions of these signal processing equipment are still limited. Although an
* Trademarks
CA 02173186 2002-05-02
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analog signal output node is available, it is still physically difficult to
execute
data communication with other instruments:
The Third type of signal processing equipment, although cannot be
connected with a computer or a recorder externally, has its own build-in
display
and printer. Examples are modular biological fluid analyzer disclosed in U.S.
Design patent No. D330,770, and a clinic chemistry analyzer disclosed in U.S.
Design patent No. D332,314. Tliese build-in functions clearly can not be
compared with those of a computer. For example, the resolution of a computer
monitor is better than a build-in display of a signal processing equipment. A
computer also has a more strong function in data processing/storing and
various
accessories which can be mounted into the computer easily. Moreover, the
analyses and data processing functions of this type of signal processing
instruments cannot be extended or enhanced.
The fourth type of signal processing equipment can be connected with a
computer externally in order to enhance its data processing /storing/display
ability. For example, voltammetry Model 693 VA Processor from Metrohm,
Switzerland; PI-IM 85 pH-meter from Radiometer, Denmark; Potentiostat/
Galvanostat Model 273A from EG&G*U.S.A.; chemical analyzer disclosed in
U.S. patent No. 4,935,875; and On-line biological inhibition/toxicity detector
disclosed in U.S. patent No. 5,106,511. This type of signal processing
equipment
contains a central processing unit. For example, line 17, column 5 of U.S.
patent
No. 5,106,511 and line 45, column 6 of U.S. patent No. 4,935,875 state that
these
signal processing equipment use Model 6809 microprocessor (Motorola; U.S.A.),
ROM, RAM, timer, display or monitor, keyboard or I/O port, Analog-to-Digital
converter (ADC), etc. (For further details, please refer to Fig. 1 of U.S,
patent No.
4,935,875 and its explanation.) In addition, when these signal processing
* trademarks
~~.'~~1~~
-4-
equipment are to be connected externally with computers, RS-232 or GPIB card
has to be used as the medium for data communication.
In order to extend the analysis and data processing functions, the inventors
have focused their research on the structure of the fourth type of signal
processing equipment. The result is that except some minor components such as
ADC, the primary components such as CPU, ROM, RAM, timer, monitor,
keyboard, I/O port, printer and disk drive, are all included in a computer.
However, the primary components of a computer are generally more powerful
and more compatible to external accessories than the build-in components in
the
fourth type of signal processing equipment. Therefore, the fourth type of
signal
processing equipment may be replaced by a computer. In addition, ADC can be
easily purchased in the market. Accordingly, it is possible to use an ADC
bought
from the market to directly convert the analog signals from a chemical sensor
into
digital signals, and transfer the digital signals to a computer where they are
processed. If this can be accomplished, the signal processing equipment used
at
the present time can be entirely replaced by a computer with modifications.
Nowadays, part of mechanic-sensors or thermal sensors are using the same idea
of replacing signal processing equipment with computers and ADCs. However,
this idea has not been used in chemical sensors.
Based on the above analyses, the inventors used a market purchased ADC
to connect with a chemical sensor which is used in potentiometry (e.g. a pH
electrode) and a computer. In other words, the output signals from a chemical
sensor were received in a series as follows: "chemical sensor ~ ADC -~
computer". However, the results showed that although a large number of data
were collected, the average value of these data could not represent the actual
value accurately because the average values were not consistent for several
runs
~17~~.~~
-s-
repeated by the same procedures. The deviations were large and no pattern
could
be found.
After more intensive research, the inventors found out that the addition of
a voltage follower could solve the existing problem. That is to say, if the
connection is in a series of "chemical sensor --~ voltage follower -~ ADC -~
computer", the output signals of a chemical sensor whicli is used in
potentiometry
can be easily and accurately obtained.
Furthermore, current ADCs in the market often have an additional function
of Digital-to-Analog Conversion (DAC) at the same time. Therefore, it is
theoretically possible to use a DAC to~convert the digital signals sent by a
computer into analog signals, then through a chemical sensor to execute
voltammetry method; or under potentiostatic condition, execute amperometry to
obtain a concentration of a certain component of a sample. The actual
experimental results showed that although the voltage output of the DAC was
stationary, the electric potential of the working electrode was fluctuating.
However, this problem can be solved by the addition of a potentiostat circuit.
Similarly, a Galvanostat circuit can be used to solve the same problem in
potentiometry under Galvanostatic condition.
In the conventional signal processing equipment for the chemical sensor
used in conductometry, a transducer has to be added to reduce the voltage of
an
alternating current source for a conductance cell. However, the inventors
found
out that by executing a control program in the computer, the DAC can be used
as
an alternating current source.
Summary of the Invention
CA 02173186 2002-05-02
6
According to the present invention, there is
provided a system for collecting chemical signals,
comprising:
a computer for executing a control computer
program;
chemical sensors for providing output signals,
including a chemical sensor used in potentiometry and a
chemical sensor used in amperometry or conductometry;
transforming circuits for transforming said
output signals received from said chemical sensors into
desired electronic signals, said transforming circuits
having a first end connected with said chemical sensors,
and a second end, said transforming circuits including a
voltage follower and a current-potential converter; and
at least one analog-to-digital converter
interface card for converting said desired electronic
signals into digital signals and transferring said digital
signals to said computer, said at least one analog-to
digital converter interface card connecting the second end
of the transforming circuits with the computer;
wherein said voltage follower has an end
connected with said chemical sensor used in potentiometry;
and
the current-potential converter has an end
connected with said chemical sensor used in amperometry or
conductometry;
whereby said output signals from said chemical
sensors are converted into the digital signals using said
transforming circuits and said analog-to-digital converter
interface card in cooperation with said control computer
program executed in said computer, and said digital signals
i
CA 02173186 2002-05-02
7
are processed in said computer in accordance with types of
said chemical sensors;
and wherein:
said computer is further provided with a digital-
to-analog converter connected to said chemical sensor used
in potentiometry with a Galvanostat circuit so that a
Galvanostatic current is receivable by said chemical sensor
used in potentiometry from said Galvanostat circuit in
cooperation with said digital-to-analog converter and said
control computer program executed in said computer, for
carrying out a potentiometry under Galvanostatic condition;
and
said digital-to-analog converter is further
connected to said chemical sensor used in amperometry with
a potentiostat circuit so that a current having a desired
electric potential wave form or a potentiostatic current is
receivable by said chemical sensor used in amperometry from
said potentiostat circuit in cooperation with said digital-
to-analog converter and said control computer program
executed in said computer, for carrying out a voltammetry
or an amperometry under potentiostatic condition, or said
digital-to-analog converter is further connected to said
chemical sensor used in conductometry so that an
alternating current is receivable by said chemical sensor
used in conductometry from said digital-to-analog converter
in cooperation with said control computer program executed
in said computer, for carrying out a conductometry.
The following provides a non-restrictive summary
of certain features of the invention which are more fully
described hereinafter.
CA 02173186 2002-05-02
7a
Based on the above discoveries, the present inventors disclose a system for
carrying out amperometry, potentiometry, conductotnetry, and voltammetry for
chemical sensors of different types, which comprises a computer, an ADC/DAC,
a voltage follower, a current-potential converter, a potentiostat circuit, a
Galvanostat circuit and a proper computer program which can be executed in
said
computer. In other words, we can have the functions of a pH meter, an
amperometer, a conductometer, a potentiostat/Galvanostat, and a voltammetric
processor; substantially cover all the equipment which use chemical sensors or
any extension uses of these equipment, e.g. conductometer used in ion-
chromatography. On the contrary, the conventional signal processing equipment
for chemical sensors have their own specific usage, and they cannot be
exchanged.
For example, a pH meter can be used only as a pH meter, not a potentiostat,
and a
voltammetric processor can not be a conductometer at the same time.
In addition, ADC/DAC cards in the market usually have DIO (digital
input/output) function, hence they can also be used as the control of a pump
or a
valve. Generally, the system described above can be connected with other
accessories (if necessary) to be used as a chemical analyzer, bio-chemical
analyzer, clinic analyzer, pH/electric potential/conductance automatic
titration
meter, ion chromatography, polarography, and a quality control, on-line
analysis
and monitor-control equipment of a chemical manufacturing process.
An objective of this invention is to provide a method of converting
output signals of a chemical sensor into digital signals and processing said
digital
signals by using a computer.
Another objective of this invention is to provide a system for collecting
chemical signals from a chemical sensor, which comprises a computer, an ADC, a
CA 02173186 2002-05-02
transforming circuit and a proper computer program which can be executed in
said computer.
A further objective of this invention is to provide a system for collecting
chemical signals from a chemical sensor, which comprises a computer,
ADC/DAC/ DIO interface cards, a transforming circuit and a proper computer
program which can be executed in said computer.
Brief Description of the Drawings
The foregoing and other objects, aspects and advantages will be better
1p understood from the following detailed description of the preferred
embodiments
of the invention with reference to the accompanying drawings wherein like
numerals represent like elements and in which:
Figure 1 is a block diagram which shows a system for collecting chemical
signals from a chemical sensor according to a first preferred embodiment of
the
present invention;
Figure 2 is an algorithm of a control computer program to be executed in
the computer in Fig. 1 when the chemical sensor thereof is a pH meter;
Figure 3 is a block diagram which shows a system for collecting chemical
signals from a chemical sensor according to a second preferred embodiment of
20 the present invention;
Figure 4 is a block diagram which shows a system for collecting chemical
signals from a chemical sensor according to a third preferred embodiment of
the
present invention;
Figure 5 is a plot which shows a pH value distribution of acetic
acid/sodium acetate buffer solution measured by using the system in Fig. 1 and
the algorithm in Fig. 2; and
_g_
Fig. 6 is an electric circuit of an voltage follower, wherein an IC U 1 is
soled by Fujitsu Co., Japan under a code of OP41, FJ9201.
Detailed Description of the Invention
The present invention is related to a method of using a computer to collect
chemical signals directly from a chemical sensor, in which said computer is
provided with an Analog-to-Digital converter (ADC) and said chemical sensor is
connected to said ADC with a transforming circuit. The present method
comprises the followings steps:
converting output signals received from said chemical sensor into digital
signals by using said transforming circuit and said ADC in cooperation with a
control computer program executed in said computer;
transferring said digital signals from said ADC to said computer; and
processing said digital signals in said computer in accordance with the
type of said chemical sensor.
When the chemical sensor used in the present method is for potentiometry,
said transforming circuit is a voltage follower. In addition, said computer
may be
further provided with a Digital-to-Analog converter (DAC), and said DAC is
connected to said chemical sensor with a Galvanostat circuit, wherein a
Galvanostatic current is received by said chemical sensor from said
Galvanostat
circuit in cooperation with said DAC and said control computer program
executed said computer so that a potentiometry under Galvanostatic condition
is
carried out.
When the chemical sensor used in the present invention is for
amperometry, said transforming circuit is a current-potential converter. In
addition, said computer may be further provided with a Digital-to-Analog
r ~ ,f a
_.
-9-
converter (DAC), and said DAC is connected to said chemical sensor with a
potentiostat circuit, wherein a current having a desired electric potential
wave
form or a potentiostatic current is received by said chemical sensor from said
potentiostat circuit in cooperation with said DAC and said control computer
program executed said computer so that a voltammetry or an amperometry under
potentiostatic condition are carried out.
When the chemical sensor used in the present invention is for
conductometry, said transforming circuit is a current-potential converter, and
said
computer is further provided with a Digital-to-Analog converter (DAC) which is
connected to said chemical sensor, wherein an alternating current is received
by
said chemical sensor from said DAC in cooperation with said control computer
program executed said computer so that a conductometry is carried out.
Said chemical sensor can also a sensor array. In Chapter 6 entitled "Multi-
Component analysis in Chemical Sensing", Vol. 2 entitled "Chemical and
Biochemical Sensors", of ens rs (edited by W. Gopel, I. Hesse and J. N. Zemel,
and published by VCH company, Germany), a signal sensor, a sensor array, and
the combination of both are demonstrated. The chemical sensors described here
are the general chemical sensors, including the common biosensors, biochemical
sensors, enzyme electrodes, gas sensors, etc. The form of these chemical
sensors
can be a probe, an electrochemical sensor, a liquid electrolyte sensor, a
solid state
electrochemical sensor, a field effect chemical sensor, a calorimetric
chemical
sensor, an optochemical sensor, a piezoelectrically chemical sensor, etc.
These
sensors are described in Chapters 1, 5, 7, 8, 9, 10, 11, 12, 13, 14 and 16,
Vols. 2
and 3 of ~ens~ (edited by W. Gopel, I. Hesse and J. N. Zemel, and published by
VCI-I company, Germany), which can convert chemical signals into electronic
signals.
v. - ~ ~~'~1
-10-
The voltage follower described above is a known circuit. Please refer to
Microelectronics, Jacob Millman and Arvin Garbel, second edition, p. 445. This
voltage follower is used in this invention to convert the high impedance
electronic signals of the chemical sensors described above to medium or low
impedance signals. Generally, the output electronic signals of a chemical
sensor
are high impedance electronic signals of about 105 - 10~ Ohms. If these
signals
are connected with an ADC directly, the ADC cannot convert the analog signals
into digital signals accurately. However, if a voltage follower is inserted
between
a chemical sensor and an ADC, the problem will be solved.
l0 Said Galvanostat circuit is a known circuit and is described in Principles
of Instrumental Analysis, Dougls A. Skoog, third edition, p. 49. ,
Said current-potential converter is a known circuit. Please refer to
Microelectronics, Jacob Millman and Arvin Garbel, second edition, pp. 449-450.
'Chis current-potential converter can convert the electric current signals of
a
chemical sensor used in amperometry into voltage signals, in order for the ADC
to convert this analog voltage signals into digital signals.
Said potentiostat circuit a known circuit. Please refer to Principles of
Instrumental Analysis, Douglas A. Skoog, p. 49. This potentiostat circuit can
equalize the electric potential output of a DAC and the voltage of the working
20 electrode of the chemical sensor. In other words, the voltage of the
working
electrode is constant. If DAC is connected to a chemical sensor, the voltage
output of the DAC, V, and the voltage of the working electrode of the chemical
sensor, Vl, has the following relationship:
V=Vl+V2+IR+V3+V4
- z~.~~~~~
-Il-
V 1 stands for the voltage of the counter electrode, IR stands for the IR ,
drop caused by current - resistance, V3 and V4 are the overvoltage of the
working
electrode and counter electrode, respectively. Because V3, V4 are related to
the
complex kinetic polarization and concentration polarization, the voltage of
the
working electrode is not stable even though the DAC output voltage (V) is
constant. During an electro-chemical analysis, it is required that the voltage
of
the working electrode remains constant. Therefore, a potentiostat circuit has
to
be inserted between the DAC and the chemical sensor to solve the problem.
Each of these voltage follower, current - potential converter, potentiostat
circuit and/or Galvanostat circuit described above is a simple circuit. When
necessary, they can be combined to be in one circuit board, or even made into
a
computer serial port card, or be included in an ADC interface card. The ADC
described above is a known circuit. Some ADC interface cards on the market, in
addition to ADC, have DAC and DIO functions in one interface card. For
example, the PCL-718, PCL-818, PCL-812, PCL-812PG interface cards
manufactured by Advantech Co. Ltd.; Taiwan all have 16 channels ADC, 16 D1
(digital inputs), 16 DO (digital outputs) and 1-2 channels DAC. In each of
these
ADC interface cards described above, its DAC and/or DIO channels can also be
formed in a separate interface card. Moreover, remote sensor-to-computer
interface modules such as ADAM 4000 series manufactured by Advantech Co.
Ltd., Taiwan may be used as the ADC of the present invention so that said
output
sil;nals of said chemical sensor can be collected by a remote computer.
The computer describe above can be a desktop computer (a PC or a
minicomputer), or a portable computer (notebook or laptop computer),
preferably
a desktop PC or a notebook computer.
~~'~31~ j
_12_
Said control computer program can be stored as a firm-ware or a soft-ware
which can be read and executed by the computer, preferably as a soft-ware due
to
its flexibility of editing and change.
A system for collecting chemical signals disclosed by the present invention
comprises:
a computer for executing a control computer program;
one or more chemical sensors for providing output signals;
one or more transforming circuits for transforming said output signals
received from said one or more chemical sensors into desired electronic
signals,
l0 one end of said one or more transforming circuits being connected with said
one
or more chemical sensors;
one or more Analog-to-Digital Converter (ADC) interface cards for
converting said desired electronic signals into digital signals and
transferring said
digital signal to said computer, which connects the other end of said one or
more
transforming circuit with the computer;
in which said one or more transforming circuits are a voltage follower
provided that said one or more chemical sensors are the chemical sensor used
in
potentiometry; or
said one or more transforming circuits are a current-potential converter
20 provided that said one or more chemical sensors are the chemical sensor
used in
amperometry or eonductometry,
whereby said output signals from said chemical sensor are converted into
digital signals by using said transforming circuit and said ADC in cooperation
with said control computer program executed in said computer, and said digital
signals are processed in said computer in accordance with the type of said
chemical sensor.
-13-
When said one or more chemical sensors are the chemical sensor used in
potentiometry, said computer is further provided with a Digital-to-Analog
converter (DAC), and said DAC is connected to said one or more chemical
sensors with a Galvanostat circuit so that a Galvanostatic current can be
received
by said one or more chemical sensors from said Galvanostat circuit in
cooperation with said DAC and said control computer program executed in said
computer, and thus a potentiometry under Galvanostatic condition can be
carried
out.
When said one or more chemical sensors are the chemical sensor used in
amperometry, said computer is further provided with a Digital-to-Analog
converter (DAC), and said DAC is connected to said one or more chemical
sensors with a potentiostat circuit so that a current having a desired
electric
potential wave form or a potentiostatic current can be received by said one or
more chemical sensors from said potentiostat circuit in cooperation with said
DAC and said control computer program executed in said computer, and thus a
voltammetry or an amperometry under potentiostatic condition can be carried
out.
When said one or more chemical sensors are the chemical sensor used in
conductometry, said computer is further provided with a Digital-to-Analog
converter (DAC) which is connected to said one or more chemical sensors so
that
an alternating current can be received by said one or more chemical sensors
from
said DAC in cooperation with said control computer program executed in said
computer, and thus a conductometry can be carried out.
'Che function of this system entirely depends on the control computer
program executed by the computer.
Said computer, said ADC interface card, said chemical sensor, said voltage
follower, said current-potential converter, said potentiostat circuit and said
~~~J~~~
-14-
Galvanostat circuit contained in said system are the same as those described
in
the method of using a computer to collect chemical signals from a chemical
sensor directly.
Said one or more ADC interface cards can be connected with the computer
by inserting gold fingers provided on said one or more ADC interface cards
into
one or more slots provided by the computer or expanded therefrom.
Preferably, said one or more ADC interface cards further have digital-to-
analog converter (DAC) and digital input/output (DIO) functions.
Generally, the system described above can be connect with other
IO accessories (if necessary) to be used as a chemical analyzer, bio-chemical
analyzer, clinic analyzer, pH/electric potential/conductance automatic
titration
meter, ion chromatography, polarography, and a quality control, on-line
analysis
and monitor-control equipment of a chemical manufacturing process.
To further explain this invention, several preferred embodiments will be
described in the following text by referring to the figures accompanied.
Figure 1 is a block diagram which shows a system for collecting chemical
signals from a chemical sensor according to a first preferred embodiment of
the
present invention, wherein the chemical sensor 10 are connected to an ADC 30
with a voltage follower 20, and said ADC 30 is connected to a computer 40.
20 Figure 2 is an algorithm of a control computer program to be executed in
the computer in Fig. 1 when the chemical sensor thereof is a pH meter, in
which
the ADC/DAC is manufactured by Advantech Co. Ltd., Taiwan (model PCL-714).
The experiment data collected are shown in the following Example 1.
I~igure 3 is a block diagram which shows a system for collecting chemical
sibnals from a chemical sensor according to a second preferred embodiment of
the present invention, in which 10 stands for the chemical sensor used in
-IS-
amperometry, 21 stands for a potentiostat circuit, 22 stands for a current-
potential
converter, 30 stands for an interface card, 31 stands for DAC in the interface
card,
32 stands for ADC in the interface card, and 40 stands for a computer. DAC 31
gives a specific electric potential to the potentiostat circuit 21 to executes
potentiostatic electrolysis, cyclic voltammetry or square wave voltammetry.
The
current formed in the chemical sensor 10 is converted into voltage signals by
current-potential converter 22, and the voltage signals are converted to
digital
signals by ADC 32, which are then processed by the computer 40. This system
can be used in amperometry under potentiostatic condition or voltammetry like
polarography.
Figure 4 is a block diagram which shows a system for collecting chemical
signals from a chemical sensor according to a third preferred embodiment of
the
present invention, in which the numeral numbers of 22, 30, 31, 32 and 40
represent the same elements represented by the like numeral numbers in Fig. 3,
and 10 represents a chemical sensor for conductometry. DAC 31 gives an
electric
potential of sine wave to the chemical sensor 10. The resultant current,
through
the current-potential converter 22 is converted to resistance signals, which
are
then measured by ADC 32. This system can be used in conductometry.
Cxample 1: .
The system shown in Fig. 1 was used to measure pH value of an aqueous
buffer solution prepared by mixing 1:1 (v/v) of 0.1 M acetic acid solution and
0.1 M sodium acetate solution. A pH electrode Model PHM82 purchased from
Radiometer, Denmark, was used as the chemical sensor 10; a circuit shown in
Fig.
6 was used as the voltage follower 20; an IBM compatible AT computer was used
as the computer 40; and PCL-714 ADC/DAC interface card purchased from
T '
- 16-
Advantech Co. Ltd., Taiwan was used as the ADC 30 in Fig. 1. 174 average pH
values were obtained, each of which was obtained by recording about 30
thousand measurements ( 1-2 seconds measuring time) and calculating the
average
value of the about 30 thousand measurements. The results are shown as follows:
Average Appearing Accumulation of
~I-i times appearing times
4.6287 2 2
4.6288 17 19 (2+7)
l 0 4.6289 22 ~ 41 ( 19+22)
4.6290 54 95 (41 +54)
4.6291 41 136 (95+41 )
4.6292 23 159 (136+23)
4.6293 12 171 (159+12)
4.6294 . 1 172 (171+1)
4.6295 2 174 ( 172+2)
Two curves (normal distribution and accumulation distribution) were made
according to the above data and shown in Fig. 5. In Fig. 5, horizontal axis
stands
for the average pH values. The vertical line at each average pH value
represents
the appearing times of said each average pI-I value; the * at each average pH
value represents the accumulation of the appearing times of the average pH
values less and equal to said each average pH value. It can be seen from Fig.
5
that the distribution of experimental data fits the theoretical distribution.
The
standard deviation is 0.0002.
